princeton-nlp/QuRatedPajama-1B_tokens_for_analysis

text stringlengths 310 8.3k	writing_style_average float64 -3.5 3.37	facts_and_trivia_average float64 -3.77 3.96	educational_value_average float64 -3.86 3.99	required_expertise_average float64 -3.75 4.36	writing_style_chunks sequencelengths 2 2	facts_and_trivia_chunks sequencelengths 2 2	educational_value_chunks sequencelengths 2 2	required_expertise_chunks sequencelengths 2 2	length int64 1.02k 1.02k	chunk_lengths sequencelengths 2 2	input_ids sequencelengths 1.02k 1.02k	document_index int64 75 1.18M	document_position int64 0 1.47M	source_domain stringclasses 7 values	cluster_id int64 -1 24	cluster_no int64 -1 25
Polyacrylonitrile (PAN) fibers were pre-oxidized in a temperature range of 180-275℃. The effects of positive and negative stretching on the structure and morphology of PAN fiber in the pre-oxidation process were studied by FTIR spectroscopy, XRD, and SEM. Mechanical property changes were also investigated. No changes in the movement and intensity of functional groups of PAN fibers were caused by positive stretching of up to 10% and negative stretching down to -8%. The crystal structure can be affected by the positive stretching and negative stretching. The maximum strength is 479.81 MPa when the stretching is positive,and the maximum strength is 420.55 MPa when the stretching is negative. It has been well established that polyacrylonitrile (PAN) fibers are one of the most suitable and widely used precursors for making high-performance carbon fiber, and PAN-based carbon fiber is stronger than other types precursor-based carbon fibers . Developing carbon fiber from PAN based fiber generally involves three processes, namely stabilization, carbonization, and graphitization under controlled conditions. Among those processes, pre-oxidation is a very important step because it largely governs the final structure and mechanical properties of the carbon fiber. During this process in a temperature range of 180-280℃, PAN precursors are converted into infusible and nonflammable fibers with a ladder structure suitable for further carbonization . Important factors such as temperature, time, and stretching have been studied previously [3 - 9] ; however, systematic investigations of the effects of positive and negative stretching have never been reported relating to the structure and properties of PAN fibers in the pre-oxidation process. In this work, the effects of positive and negative stretching on the structure and properties of PAN fibers in the pre-oxidation process were systematically investigated by using FTIR spectroscopy, XRD, and SEM observations. The PAN fiber used in this experiment was supplied by Zhongfu Shenying Carbon Fiber Co., Ltd. (Lianyungang, People's Republic of China) in tows of 1,000 fibers with an average density of 1.19 g/cm 3 and a mean diameter of 12.4 ㎛. Pre-oxidation was carried out in a furnace divided into nine temperature zones in a range of 180-300℃. Temperature gradually increased so as to control pre-oxidation temperature gradient. The stretching ratio was achieved by controlling the speed difference between the feed (v 1 ) and take-up rollers (v 2 ). The stretching ratio is determined by the follow equation: τ = [(v 2 -v 1 )/v 1 ] × 100%, where if τ = 0, it means no stretching, if τ > 0, it means positive stretching,and if τ < 0, it means negative stretching. Table 1 shows various stretching ratios during the increase of the pre-oxidation temperature. τ 1 means stretching ratio was 2% at 180℃, and it was increased 2% at 200℃ and then constantly sustained until 275℃. Therefore, the total positive stretching ratio was 4%. On the other hand, in the case of τ 5 , the fiber was relaxed 2% by supplying negative stretching at 270℃. Therefore, the total stretching ratio was also 4%; however, τ 5 contained negative stretching. where I C=N is the measured intensity of the conjugated band at 1630 cm -1 associated with the developing structure and I C≡N is the measured intensity of the nitrile band at 2240 cm -1 belonging to the unmodified PAN molecule. where λ is the wavelength of the X-rays. where I a is the intensity of diffraction at 2θ = 25.5°, which is given by the ladder structure and I p is the intensity of diffraction at 2θ = 17°. The mechanical properties of the PAN pre-oxidized fibers were measured with a single fiber strength machine (YG004E	-0.102295	1.312242	0.866501	1.461055	[ 0.3976363758701262, -0.602226687298969 ]	[ 1.8064554246926194, 0.8180284478096547 ]	[ 1.3483870385977887, 0.3846154489517664 ]	[ 1.7524081803535039, 1.1697012402648579 ]	1,024	[ 512, 512 ]	[ 21755, 562, 719, 12957, 277, 13816, 313, 29925, 2190, 29897, 18755, 414, 892, 758, 29899, 2251, 333, 1891, 297, 263, 10430, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29906, 29955, 29945, 229, 135, 134, 29889, 450, 9545, 310, 6374, 322, 8178, 16116, 292, 373, 278, 3829, 322, 18131, 3002, 310, 349, 2190, 5713, 495, 297, 278, 758, 29899, 2251, 333, 362, 1889, 892, 12399, 491, 383, 29911, 8193, 6683, 307, 1557, 2270, 29892, 1060, 29934, 29928, 29892, 322, 3725, 29924, 29889, 27439, 936, 2875, 3620, 892, 884, 7405, 630, 29889, 1939, 3620, 297, 278, 10298, 322, 26171, 310, 13303, 6471, 310, 349, 2190, 18755, 414, 892, 8581, 491, 6374, 16116, 292, 310, 701, 304, 29871, 29896, 29900, 29995, 322, 8178, 16116, 292, 1623, 304, 448, 29947, 15543, 450, 10901, 11195, 3829, 508, 367, 15201, 491, 278, 6374, 16116, 292, 322, 8178, 16116, 292, 29889, 450, 7472, 9324, 338, 29871, 29946, 29955, 29929, 29889, 29947, 29896, 341, 11868, 746, 278, 16116, 292, 338, 6374, 29892, 392, 278, 7472, 9324, 338, 29871, 29946, 29906, 29900, 29889, 29945, 29945, 341, 11868, 746, 278, 16116, 292, 338, 8178, 29889, 13, 3112, 756, 1063, 1532, 7841, 393, 15680, 562, 719, 12957, 277, 13816, 313, 29925, 2190, 29897, 18755, 414, 526, 697, 310, 278, 1556, 13907, 322, 17644, 1304, 8303, 1295, 943, 363, 3907, 1880, 29899, 546, 13390, 22004, 5713, 495, 29892, 322, 349, 2190, 29899, 6707, 22004, 5713, 495, 338, 23505, 1135, 916, 4072, 8303, 5966, 29899, 6707, 22004, 18755, 414, 29871, 869, 10682, 292, 22004, 5713, 495, 515, 349, 2190, 2729, 5713, 495, 6892, 20789, 2211, 10174, 29892, 18451, 16160, 2133, 29892, 22004, 2133, 29892, 322, 3983, 277, 2133, 1090, 20704, 5855, 29889, 17302, 1906, 10174, 29892, 758, 29899, 2251, 333, 362, 338, 263, 1407, 4100, 4331, 1363, 372, 18425, 14765, 1983, 278, 2186, 3829, 322, 28310, 4426, 310, 278, 22004, 5713, 495, 29889, 7133, 445, 1889, 297, 263, 10430, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29906, 29947, 29900, 229, 135, 134, 29892, 349, 2190, 8303, 1295, 943, 526, 11543, 964, 3041, 375, 1821, 322, 1661, 1579, 4850, 519, 18755, 414, 411, 263, 11979, 672, 3829, 13907, 363, 4340, 22004, 2133, 29871, 869, 16032, 424, 13879, 1316, 408, 10430, 29892, 931, 29892, 322, 16116, 292, 505, 1063, 12399, 9251, 518, 29941, 448, 29871, 29929, 29962, 2056, 3138, 29892, 1788, 2454, 7405, 800, 310, 278, 9545, 310, 6374, 322, 8178, 16116, 292, 505, 2360, 1063, 8967, 1104, 1218, 304, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 297, 278, 758, 29899, 2251, 333, 362, 1889, 29889, 13, 797, 445, 664, 29892, 278, 9545, 310, 6374, 322, 8178, 16116, 292, 373, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 297, 278, 758, 29899, 2251, 333, 362, 1889, 892, 1788, 19574, 7405, 630, 491, 773, 383, 29911, 8193, 6683, 307, 1557, 2270, 29892, 1060, 29934, 29928, 29892, 322, 3725, 29924, 13917, 29889, 13, 1576, 349, 2190, 5713, 495, 1304, 297, 445, 7639, 471, 19056, 491, 27134, 549, 21154, 1383, 264, 5414, 1704, 6718, 383, 12347, 3189, 1696, 19806, 29889, 313, 29931, 713, 29891, 686, 574, 29892, 11647, 29915, 29879, 8063, 310, 7551, 29897, 297, 304, 5652, 310, 29871, 29896, 29892, 29900, 29900, 29900, 18755, 414, 411, 385, 6588, 9027, 310, 29871, 29896, 29889, 29896, 29929, 330, 29914, 4912, 29871, 29941, 322, 263, 2099, 24235, 310, 29871, 29896, 29906, 29889, 29946, 29871, 230, 145, 158, 29889, 13, 6572, 29899, 2251, 333, 362, 471, 8988, 714, 297, 263, 15252, 815, 13931, 964, 14183, 10430, 20542, 297, 263, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29941, 29900, 29900, 229, 135, 134, 29889, 6789, 546, 1535, 22020, 11664, 577, 408, 304, 2761, 758, 29899, 2251, 333, 362, 10430, 16030, 29889, 450, 16116, 292, 11959, 471, 14363, 491, 640, 22155, 278, 6210, 4328, 1546, 278, 8343, 313, 29894, 29871, 29896, 1723, 322, 2125, 29899, 786, 9679, 414, 313, 29894, 29871, 29906, 13742, 450, 16116, 292, 11959, 338, 10087, 491, 278, 1101, 6306, 29901, 29871, 30137, 353, 17288, 29894, 29871, 29906, 448, 29894, 29871, 29896, 1723, 29914, 29894, 29871, 29896, 4514, 13105, 29871, 29896, 29900, 29900, 13667, 988, 565, 29871, 30137, 353, 29871, 29900, 29892, 372, 2794, 694, 16116, 292, 29892, 565, 29871, 30137, 1405, 29871, 29900, 29892, 372, 2794, 6374, 16116, 292, 29892, 392, 565, 29871, 30137, 529, 29871, 29900, 29892, 372, 2794, 8178, 16116, 292, 29889, 13, 3562, 29871, 29896, 3697, 5164, 16116, 292, 364, 2219, 359, 2645, 278, 7910, 310, 278, 758, 29899, 2251, 333, 362, 10430, 29889, 29871, 30137, 29871, 29896, 2794, 16116, 292, 11959, 471, 29871, 29906, 29995, 472, 29871, 29896, 29947, 29900, 229, 135, 134, 29892, 322, 372, 471, 11664, 29871, 29906, 29995, 472, 29871, 29906, 29900, 29900, 229, 135, 134, 322, 769, 21003, 15075, 7114, 2745, 29871, 29906, 29955, 29945, 229, 135, 134, 29889, 7857, 29892, 278, 3001, 6374, 16116, 292, 11959, 471, 29871, 29946, 15543, 1551, 278, 916, 1361, 29892, 297, 278, 1206, 310, 29871, 30137, 29871, 29945, 1919, 278, 5713, 495, 471, 26681, 287, 29871, 29906, 29995, 491, 1462, 5890, 8178, 16116, 292, 472, 29871, 29906, 29955, 29900, 229, 135, 134, 29889, 7857, 29892, 278, 3001, 16116, 292, 11959, 471, 884, 29871, 29946, 8874, 3138, 29892, 29871, 30137, 29871, 29945, 11122, 8178, 16116, 292, 29889, 13, 3062, 306, 315, 29922, 29940, 338, 278, 17005, 26171, 310, 278, 25482, 630, 3719, 472, 29871, 29896, 29953, 29941, 29900, 7477, 448, 29896, 6942, 411, 278, 14338, 3829, 322, 306, 315, 30616, 29940, 338, 278, 17005, 26171, 310, 278, 21767, 13816, 3719, 472, 29871, 29906, 29906, 29946, 29900, 7477, 448, 29896, 23329, 304, 278, 443, 1545, 2164, 349, 2190, 13206, 29883, 1297, 29889, 13, 3062, 29871, 30142, 338, 278, 281, 6447, 1477, 310, 278, 1060, 29899, 764, 29879, 29889, 13, 3062, 306, 263, 338, 278, 26171, 310, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29906, 29945, 29889, 29945, 30073, 29892, 607, 338, 2183, 491, 278, 11979, 672, 3829, 322, 306, 282, 338, 278, 26171, 310, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29896, 29955, 30073, 29889, 13, 1576, 28310, 4426, 310, 278, 349, 2190, 758, 29899, 2251, 333, 1891, 18755, 414, 892, 17005, 411, 263, 2323, 5713, 495, 9324, 4933, 313, 29979, 29954, 29900, 29900, 29946, 29923 ]	1,332,813	0	C4	7	9
, Ningbo Textile Machinery Co., China). In each case, at least 40 samples were tested. Discarding the top 5 and bottom 5, the average value of the remaining 30 can be automatically obtained. The diameter of each fiber was measured with a (Olympus) microscope before the tensile test. The fractured surface of PAN pre-oxidized fibers were observed by using a field emission-SEM (Hitachi S-4700, Japan) with a revolution of 15 kV. Before observation, the samples were embedded in an epoxy resin and sputter-coated using Pt (JEOL JFC-1200, USA). Fig. 1 shows the FTIR spectroscopy of the pre-oxidized PAN fibers at different positive stretching ratios. The positive stretching ratio did not show any influence on the movement and intensity of the functional groups until 10%. There were weak absorption bands at 2243 cm -1 assigned to the nitrile group and, at 1581 cm -1 , were assigned to the vibration of carboxyl groups, which indicated that oxidation has occurred. The cyclization rate was calculated according to Eq. (1) based on Fig. 1 and is listed in Table 2 . Fig. 1 shows there is no obvious influence on the movement and intensity of functional groups of FTIR, and the cyclization rate is also affected less, which indicates that positive stretching cannot affect the chemical structure. Fourier transform infrared spectroscopy of pre-oxidized polyacrylonitrile fibers at different positive stretching ratios. X-ray diffraction patterns of the pre-oxidized polyacrylonitrile fibers at different positive stretching ratios. values increased with an increase in the stretching ratio, indicating that stretching promoted the reactions. In fact, stretching affected the readjustment of the molecular chains (involving the rotation of nitrile groups around the C-C single bond) not only in the ordered domains but also and especially in the disordered domains. This might have brought more nitrile groups into a suitable position for cyclization. So, one can conclude that stretching offers molecular chains additional energy to readjust and pack into an ordered phase, which is accordant to the results of Wu et al . It was also found that stretching had a significant influence on the physical structure of PAN fibers . Structural parameters at different positive stretching ratiosAI: aromatization index. Structural parameters at different positive stretching ratios AI: aromatization index. Mechanical properties of pre-oxidized PAN fibers at different positive stretching ratiosPAN: polyacrylonitrile. Mechanical properties of pre-oxidized PAN fibers at different positive stretching ratios PAN: polyacrylonitrile. PAN fibers for the 4% stretching ratio were higher than those of the other three samples and had a decreasing trend. However, there was no obvious difference among the elongation to break. Tensile power stands for the work involved in breaking the fibers and could be defined in terms of the product of strength and tensile power. Fig. 3 shows the SEM images of pre-oxidized PAN fibers at different positive stretching ratios. When the stretching ratio is at 4% ( Fig. 3 a), the fractured surface radiates from the center to the surrounding is and distributes equally, indicating that the internal binding force of fibers are large and the tensile strength and tensile power are larger. When the stretching ratio was at 6% ( Fig. 3 b), the toughness decreased and the fractured surface became smooth, resulting in a dramatically drop in tensile strength and tensile power. When the stretching ratio was at 8% ( Fig. 3 c), the fractured surface of pre-oxidized PAN fibers became rough, and the tensile strength increased a little. When the stretching ratio was at 10%, it prevented penetration into the PAN molecule and broke the molecular order and orientation so that the pre-oxidation was insufficient with large radial differences, resulting in uneven molecular structure and decreased tensile strength. As shown in Fig. 3 d, the fractured surface is quite rough, implying that the internal stress was not equal and bonding force decreased, and then the tensile strength	-0.386503	0.785797	0.430268	1.159296	[ -0.4899133021210706, -0.2830923123422578 ]	[ 0.9612787343144322, 0.6103155323777273 ]	[ 0.44041275151022036, 0.4201228233071462 ]	[ 1.2217286456299155, 1.096862872753777 ]	1,024	[ 512, 512 ]	[ 29892, 405, 292, 833, 3992, 488, 17197, 262, 708, 3189, 1696, 7551, 467, 512, 1269, 1206, 29892, 472, 3203, 29871, 29946, 29900, 11916, 892, 9528, 29889, 3295, 7543, 292, 278, 2246, 29871, 29945, 322, 5970, 29871, 29945, 29892, 278, 6588, 995, 310, 278, 9886, 29871, 29941, 29900, 508, 367, 6336, 7625, 29889, 450, 24235, 310, 1269, 5713, 495, 471, 17005, 411, 263, 313, 29949, 4960, 375, 29897, 20710, 1883, 4338, 1434, 278, 25187, 488, 1243, 29889, 13, 1576, 285, 1461, 2955, 7101, 310, 349, 2190, 758, 29899, 2251, 333, 1891, 18755, 414, 892, 8900, 491, 773, 263, 1746, 25477, 29899, 1660, 29924, 313, 29950, 277, 26213, 317, 29899, 29946, 29955, 29900, 29900, 29892, 5546, 29897, 411, 263, 19479, 310, 29871, 29896, 29945, 413, 29963, 29889, 10949, 15500, 29892, 278, 11916, 892, 15685, 297, 385, 21502, 3594, 620, 262, 322, 269, 649, 357, 29899, 1111, 630, 773, 349, 29873, 313, 29967, 29923, 5607, 435, 8610, 29899, 29896, 29906, 29900, 29900, 29892, 8278, 467, 13, 13080, 29889, 29871, 29896, 3697, 278, 383, 29911, 8193, 6683, 307, 1557, 2270, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 450, 6374, 16116, 292, 11959, 1258, 451, 1510, 738, 9949, 373, 278, 10298, 322, 26171, 310, 278, 13303, 6471, 2745, 29871, 29896, 29900, 15543, 1670, 892, 8062, 17977, 683, 22706, 472, 29871, 29906, 29906, 29946, 29941, 7477, 448, 29896, 9859, 304, 278, 21767, 13816, 2318, 322, 29892, 472, 29871, 29896, 29945, 29947, 29896, 7477, 448, 29896, 1919, 892, 9859, 304, 278, 325, 26218, 310, 1559, 1884, 2904, 6471, 29892, 607, 18694, 393, 19100, 333, 362, 756, 10761, 29889, 450, 24502, 2133, 6554, 471, 12833, 5034, 304, 12345, 29889, 313, 29896, 29897, 2729, 373, 5104, 29889, 29871, 29896, 322, 338, 9904, 297, 6137, 29871, 29906, 869, 13, 13080, 29889, 29871, 29896, 3697, 727, 338, 694, 6924, 9949, 373, 278, 10298, 322, 26171, 310, 13303, 6471, 310, 383, 29911, 8193, 29892, 322, 278, 24502, 2133, 6554, 338, 884, 15201, 3109, 29892, 607, 14088, 393, 6374, 16116, 292, 2609, 6602, 278, 22233, 3829, 29889, 13, 29943, 283, 4336, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 13, 29990, 29899, 764, 2923, 13857, 15038, 310, 278, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 13, 5975, 11664, 411, 385, 7910, 297, 278, 16116, 292, 11959, 29892, 23941, 393, 16116, 292, 21201, 278, 337, 7387, 29889, 512, 2114, 29892, 16116, 292, 15201, 278, 1303, 5143, 358, 310, 278, 13206, 16637, 521, 2708, 313, 262, 1555, 1747, 278, 13733, 310, 21767, 13816, 6471, 2820, 278, 315, 29899, 29907, 2323, 21224, 29897, 451, 871, 297, 278, 10372, 21904, 541, 884, 322, 7148, 297, 278, 766, 21693, 21904, 29889, 910, 1795, 505, 6296, 901, 21767, 13816, 6471, 964, 263, 13907, 2602, 363, 24502, 2133, 29889, 1105, 29892, 697, 508, 17668, 393, 16116, 292, 16688, 13206, 16637, 521, 2708, 5684, 5864, 304, 1303, 5143, 322, 4870, 964, 385, 10372, 8576, 29892, 607, 338, 15017, 424, 304, 278, 2582, 310, 29624, 634, 394, 29871, 869, 739, 471, 884, 1476, 393, 16116, 292, 750, 263, 7282, 9949, 373, 278, 9128, 3829, 310, 349, 2190, 18755, 414, 29871, 869, 13, 19560, 3631, 4128, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 12, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 12, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 29925, 2190, 18755, 414, 363, 278, 29871, 29946, 29995, 16116, 292, 11959, 892, 6133, 1135, 1906, 310, 278, 916, 2211, 11916, 322, 750, 263, 9263, 5832, 534, 355, 29889, 2398, 29892, 727, 471, 694, 6924, 4328, 4249, 278, 560, 549, 362, 304, 2867, 29889, 323, 575, 488, 3081, 15028, 363, 278, 664, 9701, 297, 16679, 278, 18755, 414, 322, 1033, 367, 3342, 297, 4958, 310, 278, 3234, 310, 9324, 322, 25187, 488, 3081, 29889, 5104, 29889, 29871, 29941, 3697, 278, 3725, 29924, 4558, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 1932, 278, 16116, 292, 11959, 338, 472, 29871, 29946, 29995, 313, 5104, 29889, 29871, 29941, 263, 511, 278, 285, 1461, 2955, 7101, 17937, 1078, 515, 278, 4818, 304, 278, 18830, 338, 322, 1320, 5026, 18018, 29892, 23941, 393, 278, 7463, 9956, 4889, 310, 18755, 414, 526, 2919, 322, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 526, 7200, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29953, 29995, 313, 5104, 29889, 29871, 29941, 289, 511, 278, 260, 820, 2264, 9263, 1463, 322, 278, 285, 1461, 2955, 7101, 3897, 10597, 29892, 9819, 297, 263, 8541, 19574, 5768, 297, 25187, 488, 9324, 322, 25187, 488, 3081, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29947, 29995, 313, 5104, 29889, 29871, 29941, 274, 511, 278, 285, 1461, 2955, 7101, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 3897, 12164, 29892, 322, 278, 25187, 488, 9324, 11664, 263, 2217, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29896, 29900, 13667, 372, 5557, 287, 6584, 18184, 362, 964, 278, 349, 2190, 13206, 29883, 1297, 322, 14455, 278, 13206, 16637, 1797, 322, 19843, 577, 393, 278, 758, 29899, 2251, 333, 362, 471, 1663, 29884, 4543, 411, 2919, 28373, 12651, 29892, 9819, 297, 1597, 854, 13206, 16637, 3829, 322, 9263, 1463, 25187, 488, 9324, 29889, 1094, 4318, 297, 5104, 29889, 29871, 29941, 270, 29892, 278, 285, 1461, 2955, 7101, 338, 3755, 12164, 29892, 2411, 5890, 393, 278, 7463, 22884, 471, 451, 5186, 322, 21224, 292, 4889, 9263, 1463, 29892, 322, 769, 278, 25187, 488, 9324 ]	1,332,813	1,024	C4	12	5
and tensile power decreased. In a word, the tensile strength and tensile power have the same performance. It is necessary to consider the tensile strength and tensile power to obtain both the elongation and strength so that it performs well when it is used; meanwhile, the stretching ratio should not be too large so as to avoid performance degradation . Except for the results above, the evolution of structure and the changes of properties during the pre-oxidation on other important aspects have been studied by Zhang et al . Scanning electron microscope images of pre-oxidized polyacrylonitrile fibers at different positive stretching ratios: (a) 4 (b) 6 (c) 8 and (d) 10%. Fourier transform infrared spectroscopy of pre-oxidative polyacrylonitrile fibers at different negative stretching ratios. Wang et al has investigated the structure and properties of PAN fibers from the negative stretching in the high temperature zone. Fig. 4 shows the FTIR spectroscopy of the pre-oxidized PAN fibers at different negative stretching ratios. As with positive stretching, the FTIR spectra showed that negative stretching still has no influence on the movement and intensity of functional groups. The cyclization rate has been calculated according to Eq. (1) based on Fig. 4 and is listed in Table 5 . The effect of the cyclization rate by negative stretching is not obvious, just as with positive stretching. Fig. 5 shows WAXRD patterns of pre-oxidized PAN fibers at different negative stretching ratios. In general, the spectra of pre-oxidized PAN fibers showed weak diffraction at 2θ = 17° and a broad diffraction around 2θ = 25.5°. There are no obvious differences the ratios decrease. Relative cyclization rate based on FTIR spectroscopy inFig. 4FTIR: Fourier transform infrared spectroscopy. Relative cyclization rate based on FTIR spectroscopy in Fig. 4 FTIR: Fourier transform infrared spectroscopy. Wide-angle X-ray diffraction patterns of pre-oxidized polyacrylonitrile fibers at different negative stretching ratios. Structural parameters at different negative stretching ratiosAI: aromatization index. Structural parameters at different negative stretching ratios AI: aromatization index. Structural parameters were calculated according to Eqs. (2) and (3) and were listed in Table 6 . When the stretching ratio was -4%, the d-spacing diffraction at 17° and around 25.5° were the higher and lower than the other three samples, respectively; however, the AI values increased with an increase in the negative stretching ratio. Mechanical properties of pre-oxidized PAN d fibers at different negative stretching ratiosPAN: polyacrylonitrile. Mechanical properties of pre-oxidized PAN d fibers at different negative stretching ratios PAN: polyacrylonitrile. Scanning electron microscope images of pre-oxidized polyacrylonitrile fibers at different negative stretching ratios: (e) -2 (f ) -4 (g) -6 and (h) -8%. oxidation, it was difficult for oxygen to enter the PAN molecule, and this resistance caused the oxidation to not occur easily, resulting in the uneven structure of the pre-oxidized PAN fibers. Fig. 6 shows SEM images of pre-oxidized PAN fibers at different negative stretching ratios. When the stretching ratio was -2% ( Fig. 6 e), the fractured surface showed an uneven stress of internal molecules and could not spread after the tensile force; therefore, the tensile strength was not very high. When the stretching ratio was -4%, this was helpful for oxygen to penetrate into PAN molecular chains to oxidize and form an equal structure of pre-oxidized PAN fibers. The SEM image ( Fig. 6 f) also showed a better fractured surface than the other three groups of samples. As the stretching ratio was increased to -6%, oxygen molecules could penetrate into PAN molecular chains to peroxide and result in a decrease in tensile strength, but the	-0.743303	0.204738	0.188057	1.138485	[ -0.613184090730959, -0.8734224222407236 ]	[ 0.1644490156316074, 0.24502730179054474 ]	[ 0.36939800279946083, 0.00671553616951033 ]	[ 1.0240245052426962, 1.2529450888489502 ]	1,024	[ 512, 512 ]	[ 322, 25187, 488, 3081, 9263, 1463, 29889, 512, 263, 1734, 29892, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 505, 278, 1021, 4180, 29889, 739, 338, 5181, 304, 2050, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 304, 4017, 1716, 278, 560, 549, 362, 322, 9324, 577, 393, 372, 23233, 1532, 746, 372, 338, 1304, 29936, 2099, 8000, 29892, 278, 16116, 292, 11959, 881, 451, 367, 2086, 2919, 577, 408, 304, 4772, 4180, 316, 5105, 362, 29871, 869, 1222, 1547, 363, 278, 2582, 2038, 29892, 278, 14675, 310, 3829, 322, 278, 3620, 310, 4426, 2645, 278, 758, 29899, 2251, 333, 362, 373, 916, 4100, 21420, 505, 1063, 12399, 491, 796, 11895, 634, 394, 29871, 869, 13, 4421, 9450, 11966, 20710, 1883, 4338, 4558, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29901, 313, 29874, 29897, 29871, 29946, 313, 29890, 29897, 29871, 29953, 313, 29883, 29897, 29871, 29947, 322, 313, 29881, 29897, 29871, 29896, 29900, 15543, 13, 29943, 283, 4336, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 310, 758, 29899, 2251, 333, 1230, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 13, 29956, 574, 634, 394, 29871, 756, 7405, 630, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 515, 278, 8178, 16116, 292, 297, 278, 1880, 10430, 10640, 29889, 5104, 29889, 29871, 29946, 3697, 278, 383, 29911, 8193, 6683, 307, 1557, 2270, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 1094, 411, 6374, 16116, 292, 29892, 278, 383, 29911, 8193, 6683, 336, 10018, 393, 8178, 16116, 292, 1603, 756, 694, 9949, 373, 278, 10298, 322, 26171, 310, 13303, 6471, 29889, 450, 24502, 2133, 6554, 756, 1063, 12833, 5034, 304, 12345, 29889, 313, 29896, 29897, 2729, 373, 5104, 29889, 29871, 29946, 322, 338, 9904, 297, 6137, 29871, 29945, 869, 450, 2779, 310, 278, 24502, 2133, 6554, 491, 8178, 16116, 292, 338, 451, 6924, 29892, 925, 408, 411, 6374, 16116, 292, 29889, 13, 13080, 29889, 29871, 29945, 3697, 399, 6604, 29934, 29928, 15038, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 512, 2498, 29892, 278, 6683, 336, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 10018, 8062, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29896, 29955, 30073, 322, 263, 7300, 2923, 13857, 2820, 29871, 29906, 30209, 353, 29871, 29906, 29945, 29889, 29945, 30073, 29889, 1670, 526, 694, 6924, 12651, 278, 364, 2219, 359, 23806, 29889, 13, 18278, 24502, 2133, 6554, 2729, 373, 383, 29911, 8193, 6683, 307, 1557, 2270, 297, 13080, 29889, 29871, 29946, 7818, 8193, 29901, 27506, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 29889, 13, 18278, 24502, 2133, 6554, 2729, 373, 383, 29911, 8193, 6683, 307, 1557, 2270, 297, 5104, 29889, 29871, 29946, 12, 7818, 8193, 29901, 27506, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 29889, 13, 29956, 680, 29899, 2521, 1060, 29899, 764, 2923, 13857, 15038, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 13, 19560, 3631, 4128, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 12, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 892, 12833, 5034, 304, 12345, 29879, 29889, 313, 29906, 29897, 322, 313, 29941, 29897, 322, 892, 9904, 297, 6137, 29871, 29953, 869, 1932, 278, 16116, 292, 11959, 471, 448, 29946, 13667, 278, 270, 29899, 1028, 9390, 2923, 13857, 472, 29871, 29896, 29955, 30073, 322, 2820, 29871, 29906, 29945, 29889, 29945, 30073, 892, 278, 6133, 322, 5224, 1135, 278, 916, 2211, 11916, 29892, 8307, 29936, 3138, 29892, 278, 319, 29902, 1819, 11664, 411, 385, 7910, 297, 278, 8178, 16116, 292, 11959, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 270, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 270, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 12, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 4421, 9450, 11966, 20710, 1883, 4338, 4558, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29901, 313, 29872, 29897, 448, 29906, 313, 29888, 1723, 448, 29946, 313, 29887, 29897, 448, 29953, 322, 313, 29882, 29897, 448, 29947, 15543, 13, 2251, 333, 362, 29892, 372, 471, 5189, 363, 288, 28596, 304, 3896, 278, 349, 2190, 13206, 29883, 1297, 29892, 322, 445, 17711, 8581, 278, 19100, 333, 362, 304, 451, 6403, 5948, 29892, 9819, 297, 278, 1597, 854, 3829, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 29889, 5104, 29889, 29871, 29953, 3697, 3725, 29924, 4558, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 1932, 278, 16116, 292, 11959, 471, 448, 29906, 29995, 313, 5104, 29889, 29871, 29953, 321, 511, 278, 285, 1461, 2955, 7101, 10018, 385, 1597, 854, 22884, 310, 7463, 13206, 21337, 322, 1033, 451, 9677, 1156, 278, 25187, 488, 4889, 29936, 5480, 29892, 278, 25187, 488, 9324, 471, 451, 1407, 1880, 29889, 1932, 278, 16116, 292, 11959, 471, 448, 29946, 13667, 445, 471, 8444, 363, 288, 28596, 304, 6584, 300, 10492, 964, 349, 2190, 13206, 16637, 521, 2708, 304, 19100, 333, 675, 322, 883, 385, 5186, 3829, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 29889, 450, 3725, 29924, 1967, 313, 5104, 29889, 29871, 29953, 285, 29897, 884, 10018, 263, 2253, 285, 1461, 2955, 7101, 1135, 278, 916, 2211, 6471, 310, 11916, 29889, 1094, 278, 16116, 292, 11959, 471, 11664, 304, 448, 29953, 13667, 288, 28596, 13206, 21337, 1033, 6584, 300, 10492, 964, 349, 2190, 13206, 16637, 521, 2708, 304, 639, 2251, 680, 322, 1121, 297, 263, 23806, 297, 25187, 488, 9324, 29892, 541, 278 ]	1,332,813	2,048	C4	22	21
Everyday we hear about Artificial Intelligence (AI) and Machine learning in different contexts. Entrepreneurs like Elon Musk fear that it will doom the human race. Notably, the Russian President Mr Vladimir Putin was recently quoted telling students that whoever masters AI will rule the world. When ordinary people hear about A.I their thoughts immediately venture towards machine based programs encountered in movies like Star Trek and Star Wars. This is not the only form of AI that exists. We have previously covered Indian start-ups working in AI. In this post we will feature some start-ups in Europe who have incorporated artificial intelligence into their products and services. In computer science, AI refers to the study and demonstration of intelligent behaviour by machines. For a long time it was believed that machines will find it difficult to demonstrate human like intelligence. This has now been proven wrong because with each passing decade, technology has shown that machines can not only perform intelligent tasks but can also outperform humans in many areas. While humans still regain mastery over facial recognition, creativity and some aspects of visualisation, computers are catching up fast by learning to replicate human neural circuits digitally. You should check out Google's AI Experiments to know more. While the use of A.I will no doubt have disastrous consequences in military applications. It offers an edge to organisations when they use it for behavioural analytics and decision making. Given below are seven AI focused companies that are reshaping how corporations do business around the globe. Virtual Reality Worlds are powered by Artificial Intelligence. As these worlds become more complex, the AI's role will expand exponentially. This firm harness the power of cognitive computing to ensure computers understand data better and deliver accurate predictions. The company has built a suite of software that can learn and further build itself based on their environmental needs. Software that can learn in this manner is also called machine learning software and it is being used in a wide variety of sectors. By harnessing the power of cognitive computing, Digital Reasoning helps organisations and people make better decisions. The companies products are being used by government agencies, healthcare professionals and financial sector workers. Some of the users have reported enhanced productivity and large cost savings. These outcomes were a result of the timely decisions taken and insight garnered through their technology. Setting up a healthcare system for US Army Veterans. Members of the 40,000 strong Belgian Police force relies on systems built by Inter Systems for coordinating their policing activities. One of South Africa's largest NGO's fighting HIV/ AIDs has deployed their solution to support 4,400 clinics and hospitals. Money Hub provides financial solutions for employers, insurance companies and businesses. The company aims to drive customer and employee loyalty by harnessing personal analytics to offer financial solutions. The well being of employees is core concern of organisations and Money Hub can help your staff cope with financial issues facing them. With the Money Hub app users can see all their finances listed in one single platform. They can choose to get alerts when their balance dips below limits set by them. The company can also provide incentives which reduces financial worries and increases productivity. Studies have shown that regular usage of it's app can drive up productivity in the organisation and reduces employee abstentions. Cash rich companies have a niggling worry. How to generate optimum risk free returns on their cash holdings so that shareholder wealth is maximised. Interest rates offered by different banks on cash holdings is always changing and it is difficult for managers to get the best rate. Akoni helps such companies in cash management by re-balancing accounts automatically to ensure the maximum amount earns the highest interest rate. It's AI platform is integrated with multiple banks and you can personalise your saving options. The company was recently judged among the top ten fin-tech companies in Europe by the Spanish Wealth Management agency BBVA. A startup exhibiting it's AI products at a convention. Fixed income advisory is going digital with Bond It, which helps automate fixed income portfolio creation for its clients. By defining your yields and client constraints across 12 different variables, all it takes is 15 minutes to setup your client portfolio. Winner of several portfolio analytics awards, the company's products are being used by Private Wealth Managers and Institutional Banks. Their cloud based SaaS solution is today being used by investment managers to harness it'	0.608566	1.358798	1.17085	0.278732	[ 0.9509852491856253, 0.26614753468624514 ]	[ 1.5915799949354532, 1.1260165637949262 ]	[ 1.7338956744561975, 0.6078046591855821 ]	[ 0.534966894811154, 0.022496951965335868 ]	1,024	[ 512, 512 ]	[ 7569, 3250, 591, 8293, 1048, 3012, 928, 616, 3159, 28286, 313, 23869, 29897, 322, 6189, 6509, 297, 1422, 3030, 29879, 29889, 14447, 558, 1600, 1295, 763, 1260, 265, 3077, 29895, 8866, 393, 372, 674, 437, 290, 278, 5199, 8175, 29889, 2216, 2197, 29892, 278, 10637, 7178, 3237, 27880, 12065, 262, 471, 10325, 23153, 14509, 8041, 393, 1058, 1310, 5835, 29879, 319, 29902, 674, 5751, 278, 3186, 29889, 13, 10401, 15311, 2305, 8293, 1048, 319, 29889, 29902, 1009, 13133, 7389, 9712, 545, 7113, 4933, 2729, 11104, 18169, 297, 2351, 583, 763, 7828, 6479, 29895, 322, 7828, 9149, 29889, 910, 338, 451, 278, 871, 883, 310, 319, 29902, 393, 4864, 29889, 1334, 505, 9251, 10664, 7560, 1369, 29899, 14340, 1985, 297, 319, 29902, 29889, 512, 445, 1400, 591, 674, 4682, 777, 1369, 29899, 14340, 297, 4092, 1058, 505, 11039, 630, 23116, 21082, 964, 1009, 9316, 322, 5786, 29889, 13, 797, 6601, 10466, 29892, 319, 29902, 14637, 304, 278, 6559, 322, 9004, 362, 310, 13052, 296, 10468, 491, 14884, 29889, 1152, 263, 1472, 931, 372, 471, 13112, 393, 14884, 674, 1284, 372, 5189, 304, 22222, 5199, 763, 21082, 29889, 13, 4013, 756, 1286, 1063, 16413, 2743, 1363, 411, 1269, 6819, 316, 6332, 29892, 15483, 756, 4318, 393, 14884, 508, 451, 871, 2189, 13052, 296, 9595, 541, 508, 884, 714, 19826, 25618, 297, 1784, 10161, 29889, 5806, 25618, 1603, 1072, 475, 5835, 29891, 975, 2258, 1455, 19679, 29892, 907, 28157, 322, 777, 21420, 310, 7604, 4371, 29892, 23226, 526, 4380, 292, 701, 5172, 491, 6509, 304, 1634, 5926, 5199, 19677, 3449, 19544, 13615, 635, 29889, 887, 881, 1423, 714, 5087, 29915, 29879, 319, 29902, 28224, 7862, 304, 1073, 901, 29889, 13, 8809, 488, 278, 671, 310, 319, 29889, 29902, 674, 694, 7404, 505, 766, 7614, 681, 27721, 297, 9121, 8324, 29889, 739, 16688, 385, 7636, 304, 17459, 800, 746, 896, 671, 372, 363, 10468, 284, 16114, 1199, 322, 10608, 3907, 29889, 11221, 2400, 526, 9881, 319, 29902, 21309, 14582, 393, 526, 620, 29882, 21430, 920, 17266, 800, 437, 5381, 2820, 278, 15482, 915, 29889, 13, 21287, 830, 2877, 2787, 29879, 526, 3081, 287, 491, 3012, 928, 616, 3159, 28286, 29889, 1094, 1438, 3186, 29879, 4953, 901, 4280, 29892, 278, 319, 29902, 29915, 29879, 6297, 674, 7985, 18709, 9247, 29889, 13, 4013, 9226, 4023, 2264, 278, 3081, 310, 25323, 3321, 20602, 304, 9801, 23226, 2274, 848, 2253, 322, 12021, 16232, 27303, 29889, 450, 5001, 756, 4240, 263, 9460, 310, 7047, 393, 508, 5110, 322, 4340, 2048, 3528, 2729, 373, 1009, 29380, 4225, 29889, 18540, 393, 508, 5110, 297, 445, 8214, 338, 884, 2000, 4933, 6509, 7047, 322, 372, 338, 1641, 1304, 297, 263, 9377, 12875, 310, 409, 14359, 29889, 2648, 4023, 2264, 292, 278, 3081, 310, 25323, 3321, 20602, 29892, 15918, 830, 1658, 292, 6911, 17459, 800, 322, 2305, 1207, 2253, 1602, 12112, 29889, 13, 1576, 14582, 9316, 526, 1641, 1304, 491, 5874, 946, 15942, 29892, 9045, 18020, 6351, 1338, 322, 18161, 17535, 17162, 29889, 3834, 310, 278, 4160, 505, 8967, 427, 29308, 3234, 2068, 322, 2919, 3438, 4048, 886, 29889, 4525, 714, 26807, 892, 263, 1121, 310, 278, 5335, 873, 1602, 12112, 4586, 322, 25483, 7171, 1089, 287, 1549, 1009, 15483, 29889, 13, 29020, 701, 263, 9045, 18020, 1788, 363, 3148, 8811, 478, 1308, 550, 29889, 13, 29924, 13415, 310, 278, 29871, 29946, 29900, 29892, 29900, 29900, 29900, 4549, 9923, 713, 18923, 4889, 337, 3687, 373, 6757, 4240, 491, 4124, 23985, 363, 6615, 1218, 1009, 13665, 292, 14188, 29889, 13, 6716, 310, 4275, 10557, 29915, 29879, 10150, 405, 17080, 29915, 29879, 17770, 379, 5667, 29914, 319, 1367, 29879, 756, 21168, 1009, 1650, 304, 2304, 29871, 29946, 29892, 29946, 29900, 29900, 24899, 1199, 322, 29418, 277, 1338, 29889, 13, 29924, 4992, 14533, 8128, 18161, 6851, 363, 5703, 414, 29892, 1663, 18541, 14582, 322, 5381, 267, 29889, 450, 5001, 263, 9893, 304, 7899, 11962, 322, 19001, 28108, 1017, 491, 4023, 2264, 292, 7333, 16114, 1199, 304, 5957, 18161, 6851, 29889, 450, 1532, 1641, 310, 22873, 338, 7136, 5932, 310, 17459, 800, 322, 341, 4992, 14533, 508, 1371, 596, 13925, 1302, 412, 411, 18161, 5626, 14870, 963, 29889, 13, 3047, 278, 341, 4992, 14533, 623, 4160, 508, 1074, 599, 1009, 1436, 2925, 9904, 297, 697, 2323, 7481, 29889, 2688, 508, 6755, 304, 679, 6655, 29879, 746, 1009, 17346, 652, 567, 2400, 13071, 731, 491, 963, 29889, 450, 5001, 508, 884, 3867, 297, 1760, 3145, 607, 26830, 18161, 6365, 2722, 322, 16415, 3234, 2068, 29889, 16972, 505, 4318, 393, 4943, 8744, 310, 372, 29915, 29879, 623, 508, 7899, 701, 3234, 2068, 297, 278, 24788, 322, 26830, 19001, 633, 303, 296, 1080, 29889, 13, 29907, 1161, 8261, 14582, 505, 263, 302, 22817, 1847, 15982, 29889, 1128, 304, 5706, 5994, 398, 12045, 3889, 3639, 373, 1009, 274, 1161, 4808, 886, 577, 393, 6232, 7694, 17173, 338, 5256, 3368, 29889, 23829, 19257, 12520, 491, 1422, 24388, 373, 274, 1161, 4808, 886, 338, 2337, 6480, 322, 372, 338, 5189, 363, 767, 18150, 304, 679, 278, 1900, 6554, 29889, 10813, 5271, 6911, 1316, 14582, 297, 274, 1161, 10643, 491, 337, 29899, 5521, 19985, 15303, 6336, 304, 9801, 278, 7472, 5253, 2326, 1983, 278, 9939, 4066, 6554, 29889, 13, 3112, 29915, 29879, 319, 29902, 7481, 338, 23387, 411, 2999, 24388, 322, 366, 508, 7333, 895, 596, 14238, 3987, 29889, 450, 5001, 471, 10325, 6577, 3192, 4249, 278, 2246, 3006, 1436, 29899, 11345, 14582, 297, 4092, 491, 278, 10432, 1334, 4298, 15057, 946, 3819, 29449, 20449, 29889, 13, 29909, 20234, 10371, 11407, 372, 29915, 29879, 319, 29902, 9316, 472, 263, 15687, 29889, 13, 26262, 17869, 25228, 706, 338, 2675, 13436, 411, 26370, 739, 29892, 607, 6911, 3345, 403, 4343, 17869, 2011, 25648, 11265, 363, 967, 13154, 29889, 2648, 16184, 596, 17498, 322, 3132, 11938, 4822, 29871, 29896, 29906, 1422, 3651, 29892, 599, 372, 4893, 338, 29871, 29896, 29945, 6233, 304, 6230, 596, 3132, 2011, 25648, 29889, 399, 3993, 310, 3196, 2011, 25648, 16114, 1199, 24441, 29892, 278, 5001, 29915, 29879, 9316, 526, 1641, 1304, 491, 12230, 1334, 4298, 2315, 18150, 322, 28218, 284, 350, 1331, 29889, 13, 1576, 381, 9570, 2729, 5701, 29874, 29903, 1650, 338, 9826, 1641, 1304, 491, 13258, 358, 767, 18150, 304, 4023, 2264, 372, 29915 ]	1,332,815	0	C4	15	4
The IP legal regime in Hong Kong is well established and very similar to those of other modern and highly sophisticated economies such as the United Kingdom, Singapore and Australia. The IP laws of Hong Kong continue to be based on English legislation despite the change of sovereignty resulting from the handover of Hong Kong back to the People's Republic of China on July 1 1997; the common law will continue to be applicable until at least 2047 on the basis of the 'one country, two systems' policy. Hong Kong is a member of the World Intellectual Property Organization and a signatory to most of the important IP treaties, including the Paris Convention for the Protection of Industrial Property and the Agreement on Trade Related Aspects of Intellectual Property Rights. The two main statutes that govern the protection and enforcement of trademark rights in Hong Kong are the Trademarks Ordinance and the Trade Descriptions Ordinance. The latter protects consumers against false trade descriptions (which are defined as including trademarks under the ordinance) and false applications of trademarks registered in Hong Kong. as a result of such misrepresentation, it has suffered or is likely to suffer damage. litigation before the courts (in respect of civil disputes). We deal with these in turn in the paragraphs below, insofar as they relate to trademark and brand owners' rights. One of the key roles of Customs is the protection of the interests of IP rights owners in Hong Kong. Customs is made up of five branches, one of which is the Intellectual Property Investigation Bureau, which, as its name suggests, is focused on IP enforcement matters. Generally speaking, before Customs will take on an enforcement case, it is necessary for the relevant brand owner to register its rights and then file a complaint in respect of each particular case of infringement. (In Hong Kong, unlike in China, only trademark rights and copyrights may be registered with Customs. a letter of authorization issued by the trademark owner vesting the said examiner with the authority to act on its behalf in future cases led by Customs. Customs has wide powers of search and seizure, powers of arrest and discretion on whether to prosecute an infringer. Hence, the powers of Customs in Hong Kong exceed those of customs departments in other regions/countries, as Customs carries out all of the above procedures without encountering bureaucratic conflict with other government departments. It can seize counterfeit goods from anywhere in Hong Kong and not just in harbour or border areas. The Organized and Serious Crimes Ordinance confers extensive powers in certain appropriate circumstances on law enforcement officers (police and customs officers) for search and investigation in IP enforcement, including trademark infringement matters. The Trade Descriptions Ordinance contains criminal sanctions in respect of offences relating to false trade descriptions, trademark forgery and false application of trademarks registered in Hong Kong. Under the ordinance, any person who forges any trademark or falsely applies to any goods any trademark or any mark so nearly resembling a trademark as to be calculated to deceive commits an offence unless he or she proves that he or she acted without an intention to defraud. It is also an offence to sell or expose, or have in one's possession for sale or for any purpose of trade or manufacture, goods to which any forged trademark is applied, or to which any trademark or mark so nearly resembling a trademark as to be calculated to deceive is falsely applied. undertake personally, or through an authorized representative (who has good knowledge of the trademark), to assist Customs in the identification of infringing goods seized and testify in court as a prosecution witness if necessary. on summary conviction to a fine of HK$100,000 and to imprisonment for two years. there is a likelihood of irreparable damage to the plaintiff if the defendant's infringing activities are not stopped immediately. The timing of the application for an injunction is important, because any delay may prejudice the application. The plaintiff is also usually required to give a crossundertaking on damages in such cases. there is a real possibility that the defendant may destroy the evidence of infringement. Civil proceedings are instituted by filing a writ of summons with a general endorsement of claims or a detailed statement of claim,	0.484611	1.437586	0.886791	1.278959	[ 0.9400278457536352, 0.02919368546945958 ]	[ 1.6202300522364086, 1.254941821649226 ]	[ 1.257082361683955, 0.5164999822717484 ]	[ 1.367405380652077, 1.190512202410881 ]	1,024	[ 512, 512 ]	[ 450, 5641, 11706, 22384, 297, 12798, 12026, 338, 1532, 7841, 322, 1407, 2788, 304, 1906, 310, 916, 5400, 322, 10712, 269, 3021, 4695, 630, 7766, 583, 1316, 408, 278, 3303, 12626, 29892, 25960, 322, 8314, 29889, 450, 5641, 14243, 310, 12798, 12026, 6773, 304, 367, 2729, 373, 4223, 13332, 362, 15020, 278, 1735, 310, 577, 9359, 335, 593, 29891, 9819, 515, 278, 1361, 957, 310, 12798, 12026, 1250, 304, 278, 11647, 29915, 29879, 8063, 310, 7551, 373, 5468, 29871, 29896, 29871, 29896, 29929, 29929, 29955, 29936, 278, 3619, 4307, 674, 6773, 304, 367, 22903, 2745, 472, 3203, 29871, 29906, 29900, 29946, 29955, 373, 278, 8405, 310, 278, 525, 650, 4234, 29892, 1023, 6757, 29915, 8898, 29889, 13, 29950, 549, 12026, 338, 263, 4509, 310, 278, 2787, 18555, 781, 950, 9079, 9205, 2133, 322, 263, 1804, 7606, 304, 1556, 310, 278, 4100, 5641, 7539, 583, 29892, 3704, 278, 3681, 26774, 363, 278, 14409, 428, 310, 12157, 9315, 9079, 322, 278, 4059, 276, 882, 373, 27226, 6376, 630, 1094, 1103, 29879, 310, 18555, 781, 950, 9079, 26863, 29889, 13, 1576, 1023, 1667, 1002, 2667, 393, 4095, 278, 13047, 322, 24555, 13561, 310, 1020, 2310, 935, 10462, 297, 12798, 12026, 526, 278, 3201, 2310, 17862, 16557, 262, 749, 322, 278, 27226, 20355, 1980, 16557, 262, 749, 29889, 450, 7480, 12566, 29879, 11233, 414, 2750, 2089, 11302, 2342, 1980, 313, 4716, 526, 3342, 408, 3704, 1020, 2310, 17862, 1090, 278, 22420, 749, 29897, 322, 2089, 8324, 310, 1020, 2310, 17862, 15443, 297, 12798, 12026, 29889, 13, 294, 263, 1121, 310, 1316, 3984, 276, 26081, 29892, 372, 756, 17654, 470, 338, 5517, 304, 8812, 18658, 29889, 13, 19411, 335, 362, 1434, 278, 28033, 313, 262, 3390, 310, 7631, 8937, 267, 467, 13, 4806, 5376, 411, 1438, 297, 2507, 297, 278, 14880, 29879, 2400, 29892, 297, 578, 15641, 408, 896, 29279, 304, 1020, 2310, 935, 322, 14982, 1914, 414, 29915, 10462, 29889, 13, 6716, 310, 278, 1820, 16178, 310, 8701, 29879, 338, 278, 13047, 310, 278, 20017, 310, 5641, 10462, 1914, 414, 297, 12798, 12026, 29889, 8701, 29879, 338, 1754, 701, 310, 5320, 14202, 29892, 697, 310, 607, 338, 278, 18555, 781, 950, 9079, 28246, 362, 18903, 29892, 607, 29892, 408, 967, 1024, 14661, 29892, 338, 21309, 373, 5641, 24555, 13561, 13750, 29889, 13, 5631, 635, 13590, 29892, 1434, 8701, 29879, 674, 2125, 373, 385, 24555, 13561, 1206, 29892, 372, 338, 5181, 363, 278, 8018, 14982, 12271, 304, 6036, 967, 10462, 322, 769, 934, 263, 15313, 524, 297, 3390, 310, 1269, 3153, 1206, 310, 297, 1341, 292, 882, 29889, 313, 797, 12798, 12026, 29892, 25531, 297, 7551, 29892, 871, 1020, 2310, 935, 10462, 322, 3509, 1266, 29879, 1122, 367, 15443, 411, 8701, 29879, 29889, 13, 29874, 5497, 310, 28733, 16610, 491, 278, 1020, 2310, 935, 12271, 16779, 292, 278, 1497, 4392, 4983, 411, 278, 14329, 304, 1044, 373, 967, 2306, 3131, 297, 5434, 4251, 5331, 491, 8701, 29879, 29889, 13, 7281, 29879, 756, 9377, 10801, 310, 2740, 322, 409, 466, 545, 29892, 10801, 310, 22564, 322, 766, 4838, 291, 373, 3692, 304, 410, 3471, 1082, 385, 297, 1341, 5621, 29889, 10133, 29892, 278, 10801, 310, 8701, 29879, 297, 12798, 12026, 13461, 1906, 310, 2888, 29879, 5840, 1860, 297, 916, 12786, 29914, 2798, 2722, 29892, 408, 8701, 29879, 1559, 2722, 714, 599, 310, 278, 2038, 28648, 1728, 11735, 292, 289, 13411, 7283, 2454, 14529, 411, 916, 5874, 5840, 1860, 29889, 739, 508, 409, 675, 6795, 1725, 277, 22535, 515, 12214, 297, 12798, 12026, 322, 451, 925, 297, 4023, 6526, 470, 5139, 10161, 29889, 13, 1576, 9205, 1891, 322, 1816, 2738, 6781, 1355, 16557, 262, 749, 1970, 414, 20607, 10801, 297, 3058, 8210, 14209, 373, 4307, 24555, 13561, 13049, 313, 3733, 625, 322, 2888, 29879, 13049, 29897, 363, 2740, 322, 22522, 297, 5641, 24555, 13561, 29892, 3704, 1020, 2310, 935, 297, 1341, 292, 882, 13750, 29889, 13, 1576, 27226, 20355, 1980, 16557, 262, 749, 3743, 22161, 9753, 1953, 297, 3390, 310, 1283, 2063, 1104, 1218, 304, 2089, 11302, 2342, 1980, 29892, 1020, 2310, 935, 18879, 708, 322, 2089, 2280, 310, 1020, 2310, 17862, 15443, 297, 12798, 12026, 29889, 7634, 278, 22420, 749, 29892, 738, 2022, 1058, 363, 2710, 738, 1020, 2310, 935, 470, 285, 1338, 873, 16058, 304, 738, 22535, 738, 1020, 2310, 935, 470, 738, 2791, 577, 8886, 620, 1590, 1847, 263, 1020, 2310, 935, 408, 304, 367, 12833, 304, 23332, 573, 25741, 385, 1283, 663, 6521, 540, 470, 1183, 28281, 393, 540, 470, 1183, 27320, 1728, 385, 16392, 304, 822, 336, 566, 29889, 739, 338, 884, 385, 1283, 663, 304, 19417, 470, 24396, 29892, 470, 505, 297, 697, 29915, 29879, 17715, 363, 14686, 470, 363, 738, 6437, 310, 11302, 470, 12012, 545, 29892, 22535, 304, 607, 738, 363, 3192, 1020, 2310, 935, 338, 7436, 29892, 470, 304, 607, 738, 1020, 2310, 935, 470, 2791, 577, 8886, 620, 1590, 1847, 263, 1020, 2310, 935, 408, 304, 367, 12833, 304, 23332, 573, 338, 285, 1338, 873, 7436, 29889, 13, 7635, 1296, 22345, 29892, 470, 1549, 385, 4148, 1891, 21097, 313, 15970, 756, 1781, 7134, 310, 278, 1020, 2310, 935, 511, 304, 6985, 8701, 29879, 297, 278, 29769, 310, 297, 1341, 292, 292, 22535, 25291, 322, 1243, 1598, 297, 8973, 408, 263, 410, 3471, 918, 16277, 565, 5181, 29889, 13, 265, 15837, 7602, 2463, 304, 263, 2691, 310, 379, 29968, 29938, 29896, 29900, 29900, 29892, 29900, 29900, 29900, 322, 304, 29535, 358, 363, 1023, 2440, 29889, 13, 12711, 338, 263, 4188, 22342, 310, 19950, 862, 519, 18658, 304, 278, 2174, 524, 2593, 565, 278, 822, 5818, 29915, 29879, 297, 1341, 292, 292, 14188, 526, 451, 11084, 7389, 29889, 13, 1576, 28750, 310, 278, 2280, 363, 385, 10899, 651, 338, 4100, 29892, 1363, 738, 9055, 1122, 758, 17675, 625, 278, 2280, 29889, 450, 2174, 524, 2593, 338, 884, 5491, 3734, 304, 2367, 263, 4891, 7635, 5086, 373, 5625, 1179, 297, 1316, 4251, 29889, 13, 12711, 338, 263, 1855, 13331, 393, 278, 822, 5818, 1122, 8174, 278, 10757, 310, 297, 1341, 292, 882, 29889, 13, 29907, 5341, 8469, 886, 526, 25444, 3860, 491, 977, 292, 263, 2044, 310, 22792, 787, 411, 263, 2498, 1095, 943, 882, 310, 16726, 470, 263, 13173, 3229, 310, 5995, 29892 ]	1,332,817	0	C4	11	19
followed by the filing of pleadings according to certain statutorily prescribed time limits. Discovery follows the pleadings stage. Discovery is a process whereby the parties exchange and inspect documents and witness statements. Once this procedure is completed, matters are then set down for trial. It is possible to proceed by way of expedited procedures. In uncontested cases, default judgment may be applied for; on the other hand, in cases where the applicant can show that there are real prospects of success on a claim or part of a claim (or the defendant has no arguable case), it may seek Bird & Bird Anti-counterfeiting 2008 – A summary judgment of either the whole or that part of the claim without having to proceed to a full trial. Decisions handed down by the first instance court may be appealed. However, such appeals to the High Court must be filed by serving a notice of appeal on all the affected parties within 28 days of the date on which the judgment or order is sealed. This is subject to any application for leave to appeal out of time. A dissatisfied party can, with leave, appeal against a decision of the High Court to the Court of Appeal, whose decision shall be final. In Hong Kong, as in many jurisdictions worldwide, the sale of counterfeit goods through online channels poses a real threat to brand owners. Typically, online auction sites or trading platforms serve as a channel for individual sellers to sell their counterfeit goods. It is often difficult to track down such sellers as they provide limited identification information and are contactable only by email. However, there are practical measures that can be taken by trademark owners to counter the online sale of counterfeit products. If counterfeit goods are found to be offered for sale on auction websites, warning letters and demands for removal should be sent to the auction websites themselves, requiring that the offending offers for sale be removed from the websites and ceased forthwith. Further, as most of the goods sold on the online trading platforms are delivered to the purchasers by mail or courier, it is important for trademark owners to record their rights with Customs so that the counterfeit goods may be intercepted. In serious cases of infringement, trademark owners may consider applying to the courts for Norwich Pharmacal orders against internet service providers to disclose the IP address and the residential address (if the IP address originates from a residence) of the individuals behind the alleged acts of infringement. This then enables the trademark owner to take further action based on the information obtained. In addressing the threat of trademark infringements and trademark-related offences, brand owners may wish to adopt the measures and strategies outlined below. Clearly, there are numerous advantages in securing trademark registration rights, which are the strongest rights to rely upon in an enforcement scenario. As discussed above, one obvious advantage is the ability to record such registration rights with Customs to counter any possible infringement. To protect trademarks on the Internet, brand owners may wish to consider registering their key trademarks, trade names and company names as domain names, where appropriate. It is important to have a system to monitor trademarks that are being filed and/or used by third parties (on the Internet), in case these have an adverse impact on the brand owner's trademark rights. Brand owners may either subscribe to trademark watch services or conduct their own regular searches. The Intellectual Property Department of Hong Kong provides a free online search service at http://ipsearch.ipd.gov.hk. Trademark owners should also take care to look out for the illegitimate use of their trademarks by third parties and to retain the relevant evidence in support of any legal action that may be initiated as a result thereof. It is advisable for brand owners to work with local IP legal experts on trademark enforcement matters and in cases of infringement it is often helpful to hire local investigators who are sufficiently knowledgeable to be able to work closely with the legal team to help strategize on the gathering of relevant evidence in support of an enforcement action. If the trademark in question is used by parties other than the trademark owner through licensing or distributorship arrangements, the relevant arrangements should be devised bearing in mind the potential pitfalls that may result in potential trademark disputes – or worse still, inadvertently encouraging and permitting counterfeiting activity within the brand owner's authorized distribution network. Hence, the	0.429139	0.560178	0.983168	1.044835	[ 0.27436558726023774, 0.5839122342139575 ]	[ 0.542271646287958, 0.5780842179141524 ]	[ 0.9020086181301573, 1.0643280437547507 ]	[ 0.9511861377316155, 1.1384847970458232 ]	1,024	[ 512, 512 ]	[ 5643, 491, 278, 977, 292, 310, 5644, 328, 886, 5034, 304, 3058, 1002, 3406, 2354, 2225, 23059, 931, 13071, 29889, 8565, 22205, 4477, 278, 5644, 328, 886, 7408, 29889, 8565, 22205, 338, 263, 1889, 988, 1609, 278, 13973, 14523, 322, 16096, 10701, 322, 16277, 9506, 29889, 9038, 445, 8792, 338, 8676, 29892, 13750, 526, 769, 731, 1623, 363, 14260, 29889, 13, 3112, 338, 1950, 304, 8469, 491, 982, 310, 15310, 1573, 28648, 29889, 512, 443, 1285, 2868, 4251, 29892, 2322, 24284, 1122, 367, 7436, 363, 29936, 373, 278, 916, 1361, 29892, 297, 4251, 988, 278, 15576, 424, 508, 1510, 393, 727, 526, 1855, 27289, 29879, 310, 2551, 373, 263, 5995, 470, 760, 310, 263, 5995, 313, 272, 278, 822, 5818, 756, 694, 1852, 29884, 519, 1206, 511, 372, 1122, 16508, 17777, 669, 17777, 18473, 29899, 11808, 1725, 11407, 29871, 29906, 29900, 29900, 29947, 785, 319, 15837, 24284, 310, 2845, 278, 3353, 470, 393, 760, 310, 278, 5995, 1728, 2534, 304, 8469, 304, 263, 2989, 14260, 29889, 13, 6185, 12112, 29692, 1623, 491, 278, 937, 2777, 8973, 1122, 367, 5929, 7943, 29889, 2398, 29892, 1316, 5929, 1338, 304, 278, 5057, 9245, 1818, 367, 934, 29881, 491, 16330, 263, 8369, 310, 25530, 373, 599, 278, 15201, 13973, 2629, 29871, 29906, 29947, 3841, 310, 278, 2635, 373, 607, 278, 24284, 470, 1797, 338, 409, 7943, 29889, 910, 338, 4967, 304, 738, 2280, 363, 5967, 304, 25530, 714, 310, 931, 29889, 319, 16317, 27685, 1000, 6263, 508, 29892, 411, 5967, 29892, 25530, 2750, 263, 10608, 310, 278, 5057, 9245, 304, 278, 9245, 310, 2401, 29872, 284, 29892, 5069, 10608, 4091, 367, 2186, 29889, 13, 797, 12798, 12026, 29892, 408, 297, 1784, 24894, 8977, 1080, 3186, 8157, 29892, 278, 14686, 310, 6795, 1725, 277, 22535, 1549, 7395, 18196, 926, 267, 263, 1855, 28469, 304, 14982, 1914, 414, 29889, 14213, 1711, 29892, 7395, 782, 428, 11840, 470, 3534, 292, 21796, 9080, 408, 263, 8242, 363, 5375, 19417, 414, 304, 19417, 1009, 6795, 1725, 277, 22535, 29889, 739, 338, 4049, 5189, 304, 5702, 1623, 1316, 19417, 414, 408, 896, 3867, 9078, 29769, 2472, 322, 526, 6958, 519, 871, 491, 4876, 29889, 13, 17245, 29892, 727, 526, 15031, 15366, 393, 508, 367, 4586, 491, 1020, 2310, 935, 1914, 414, 304, 6795, 278, 7395, 14686, 310, 6795, 1725, 277, 9316, 29889, 960, 6795, 1725, 277, 22535, 526, 1476, 304, 367, 12520, 363, 14686, 373, 782, 428, 28007, 29892, 9177, 8721, 322, 1261, 4167, 363, 28744, 881, 367, 2665, 304, 278, 782, 428, 28007, 6053, 29892, 26795, 393, 278, 1283, 2548, 16688, 363, 14686, 367, 6206, 515, 278, 28007, 322, 24886, 11483, 2541, 29889, 8725, 29892, 408, 1556, 310, 278, 22535, 5239, 373, 278, 7395, 3534, 292, 21796, 526, 20115, 304, 278, 10596, 294, 414, 491, 10524, 470, 3581, 4336, 29892, 372, 338, 4100, 363, 1020, 2310, 935, 1914, 414, 304, 2407, 1009, 10462, 411, 8701, 29879, 577, 393, 278, 6795, 1725, 277, 22535, 1122, 367, 23404, 287, 29889, 13, 797, 10676, 4251, 310, 297, 1341, 292, 882, 29892, 1020, 2310, 935, 1914, 414, 1122, 2050, 15399, 304, 278, 28033, 363, 4186, 16416, 1963, 2817, 562, 284, 11299, 2750, 8986, 2669, 1326, 11376, 304, 2313, 2226, 278, 5641, 3211, 322, 278, 20201, 616, 3211, 313, 361, 278, 5641, 3211, 3978, 1078, 515, 263, 25488, 29897, 310, 278, 15724, 5742, 278, 16831, 287, 14741, 310, 297, 1341, 292, 882, 29889, 910, 769, 28936, 278, 1020, 2310, 935, 12271, 304, 2125, 4340, 3158, 2729, 373, 278, 2472, 7625, 29889, 13, 797, 3211, 292, 278, 28469, 310, 1020, 2310, 935, 297, 1341, 292, 4110, 322, 1020, 2310, 935, 29899, 12817, 1283, 2063, 29892, 14982, 1914, 414, 1122, 6398, 304, 9332, 278, 15366, 322, 16650, 583, 714, 21354, 2400, 29889, 13, 18759, 368, 29892, 727, 526, 12727, 25486, 297, 409, 2764, 292, 1020, 2310, 935, 22583, 10462, 29892, 607, 526, 278, 4549, 342, 10462, 304, 19104, 2501, 297, 385, 24555, 13561, 10483, 29889, 1094, 15648, 2038, 29892, 697, 6924, 10631, 338, 278, 11509, 304, 2407, 1316, 22583, 10462, 411, 8701, 29879, 304, 6795, 738, 1950, 297, 1341, 292, 882, 29889, 13, 1762, 12566, 1020, 2310, 17862, 373, 278, 4685, 29892, 14982, 1914, 414, 1122, 6398, 304, 2050, 6036, 292, 1009, 1820, 1020, 2310, 17862, 29892, 11302, 2983, 322, 5001, 2983, 408, 5354, 2983, 29892, 988, 8210, 29889, 13, 3112, 338, 4100, 304, 505, 263, 1788, 304, 11819, 1020, 2310, 17862, 393, 526, 1641, 934, 29881, 322, 29914, 272, 1304, 491, 4654, 13973, 313, 265, 278, 4685, 511, 297, 1206, 1438, 505, 385, 594, 3901, 10879, 373, 278, 14982, 12271, 29915, 29879, 1020, 2310, 935, 10462, 29889, 18007, 1914, 414, 1122, 2845, 1014, 13086, 304, 1020, 2310, 935, 6505, 5786, 470, 7512, 1009, 1914, 4943, 29645, 29889, 450, 18555, 781, 950, 9079, 10317, 310, 12798, 12026, 8128, 263, 3889, 7395, 2740, 2669, 472, 1732, 597, 666, 4478, 29889, 666, 29881, 29889, 13513, 29889, 29882, 29895, 29889, 3201, 2310, 935, 1914, 414, 881, 884, 2125, 2562, 304, 1106, 714, 363, 278, 980, 1397, 277, 6490, 671, 310, 1009, 1020, 2310, 17862, 491, 4654, 13973, 322, 304, 11551, 278, 8018, 10757, 297, 2304, 310, 738, 11706, 3158, 393, 1122, 367, 14511, 630, 408, 263, 1121, 727, 974, 29889, 13, 3112, 338, 25228, 519, 363, 14982, 1914, 414, 304, 664, 411, 1887, 5641, 11706, 2902, 1372, 373, 1020, 2310, 935, 24555, 13561, 13750, 322, 297, 4251, 310, 297, 1341, 292, 882, 372, 338, 4049, 8444, 304, 298, 533, 1887, 7405, 4097, 1058, 526, 18430, 7134, 519, 304, 367, 2221, 304, 664, 16467, 411, 278, 11706, 3815, 304, 1371, 16650, 675, 373, 278, 11705, 292, 310, 8018, 10757, 297, 2304, 310, 385, 24555, 13561, 3158, 29889, 13, 3644, 278, 1020, 2310, 935, 297, 1139, 338, 1304, 491, 13973, 916, 1135, 278, 1020, 2310, 935, 12271, 1549, 7794, 575, 292, 470, 22965, 3406, 3527, 15196, 4110, 29892, 278, 8018, 15196, 4110, 881, 367, 316, 11292, 24638, 297, 3458, 278, 7037, 22754, 12559, 393, 1122, 1121, 297, 7037, 1020, 2310, 935, 8937, 267, 785, 470, 15029, 1603, 29892, 297, 328, 1765, 2705, 18443, 292, 322, 3635, 5367, 6795, 1725, 11407, 6354, 2629, 278, 14982, 12271, 29915, 29879, 4148, 1891, 4978, 3564, 29889, 10133, 29892, 278 ]	1,332,817	1,024	C4	11	19
If men are good, you don't need government; if men are evil or ambivalent, you don't dare have one. ~ Robert LeFevre * Rethinking Hitler & National Socialism Author Topic: * Rethinking Hitler & National Socialism (Read 5054 times) Rethinking Hitler & National Socialism picture link I suppose it would eventually come to this: all the reading, investigating, and research I've done since discovering the truth about 9/11 would lead to a re-examination and re-learning of much of history, especially the mainstream version of WWI and WWII history. Since I began looking into 9/11, I've explored all sorts of "conspiracy theories", but lately, largely as a result of following the work of Deanna Spingola, ZionCrimeFactory, Carolyn Yeager, Veronica Clark, and others, I've began to delve deeper and deeper into revisionist history and what Adolf Hitler and the National Socialist German Workers' Party (NSDAP) really stood for. And today I'd like to share some of my thoughts with you about this subject. I've mentioned before that I once bought into Jim Condit, Jr.'s thesis about Adolf Hitler and the NSDAP, namely, that Hitler and many of the top Nazi leaders were either Jews themselves, or puppets of the international bankers and Jewish crime network, operating as part of the bankers controlled opposition in order to facilitate the establishment of the illegitimate, terrorist state of Israel as a safe haven and central headquarters for the global Jewish mafia, in the process fulfilling messianic Jewish prophecy in order to advance what is commonly known as "The New World Order", whose foundations are laid out in detail in the supremacist Jewish Talmud. However, I've always kept an open mind about this and many other subjects, and only recently (i.e., the past six months or so) began to really explore it in greater detail. And I'm now firmly convinced that Condit and others that promote this ridiculous theory about the NSDAP being puppets of the Rothschilds are 100% wrong in their assessment. I've concluded that all the other ridiculous theories and outright slanders against Adolf Hitler and National Socialist Germany are merely attempts to divert people's attention away from what Hitler and his movement actually stood for, what they represented, what they actually said, and what they actually did. By the way, Deanna Spingola and Veronica Clark refute many of these outlandish theories in a recent interview for those interested. One thing I want to make clear here: Hitler and the National Socialist movement were most definitely "anti-Semites", and used "anti-Semitism" in their political propaganda and messaging. After all, even critics of Hitler and the NSDAP recognize that their propaganda was based on truth, and in our ass-backwards, Jew-run world, the truth is fundamentally "anti-Semitic". So let's not get caught up in this childish meme of "Hitler and the Nazis were evil, racist anti-Semites'" nonsense, and simply refuse to investigate objectively what they stood for. Look at what they said, did, wrote about, and represented, and you will come to the obvious conclusion that I have: that this movement was the greatest threat the world has ever known to the parasitic, subversive, and destructive nature of the international Jewish criminal cabal largely controlling the West, pushing for their "New World Order" on every front imaginable. This is why Hitler and National Socialist Germany had to be destroyed. This is why Hitler and the NSDAP are constantly demonized, slandered, and blamed for every evil in the world. This is why the mass media, Hollywood and our educational system projects the crimes that the Jew-run Allies (the U.K., U.S. and Soviet Union) actually committed on to Hitler and National Socialist Germany. The Jews have completely flipped the script, blaming Hitler and the NSDAP for a fake "Holocaust" of European Jews and countless other alleged atrocities when in fact the Allies were responsible for the real holocausts and other crimes against humanity during WWII. Organized international Jewry, the primary network behind the push for a "New World Order", understand and recognize how dangerous Adolf Hitler and National Socialist ideology was – and potentially remains – to their totalitarian plan for world domination and subjugation. As	-0.114494	0.054102	-0.484681	0.649427	[ -0.1462103741566942, -0.08277728085118909 ]	[ -0.35886218725615787, 0.46706524587294984 ]	[ -0.3293363996939053, -0.6400259253034783 ]	[ 0.2644243869128541, 1.0344299863157078 ]	1,024	[ 512, 512 ]	[ 960, 1757, 526, 1781, 29892, 366, 1016, 29915, 29873, 817, 5874, 29936, 565, 1757, 526, 16126, 470, 3181, 27445, 29892, 366, 1016, 29915, 29873, 23222, 505, 697, 29889, 3695, 4755, 951, 29943, 5750, 276, 13, 29930, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 13720, 7488, 293, 29901, 334, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 313, 6359, 29871, 29945, 29900, 29945, 29946, 3064, 29897, 13, 29934, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 12095, 1544, 13, 29902, 7755, 372, 723, 10201, 2041, 304, 445, 29901, 599, 278, 5183, 29892, 7405, 1218, 29892, 322, 5925, 306, 29915, 345, 2309, 1951, 6523, 292, 278, 8760, 1048, 29871, 29929, 29914, 29896, 29896, 723, 3275, 304, 263, 337, 29899, 735, 314, 3381, 322, 337, 29899, 21891, 310, 1568, 310, 4955, 29892, 7148, 278, 1667, 5461, 1873, 310, 399, 22119, 322, 399, 29956, 2687, 4955, 29889, 4001, 306, 4689, 3063, 964, 29871, 29929, 29914, 29896, 29896, 29892, 306, 29915, 345, 3902, 4395, 599, 23551, 310, 376, 535, 1028, 29875, 10068, 25841, 613, 541, 301, 2486, 29892, 18425, 408, 263, 1121, 310, 1494, 278, 664, 310, 897, 9713, 1706, 292, 2963, 29892, 796, 291, 20647, 603, 5126, 29892, 8562, 948, 10134, 1875, 29892, 1798, 26082, 17129, 29892, 322, 4045, 29892, 306, 29915, 345, 4689, 304, 628, 345, 25871, 322, 25871, 964, 26554, 391, 4955, 322, 825, 21834, 23151, 322, 278, 3086, 10307, 391, 5332, 5244, 414, 29915, 9173, 313, 3059, 29928, 3301, 29897, 2289, 8389, 363, 29889, 1126, 9826, 306, 29915, 29881, 763, 304, 6232, 777, 310, 590, 13133, 411, 366, 1048, 445, 4967, 29889, 13, 29902, 29915, 345, 5276, 1434, 393, 306, 2748, 18093, 964, 8507, 11790, 277, 29892, 13843, 6169, 29879, 266, 6656, 1048, 21834, 23151, 322, 278, 3865, 29928, 3301, 29892, 18451, 29892, 393, 23151, 322, 1784, 310, 278, 2246, 11409, 29875, 20251, 892, 2845, 22057, 6053, 29892, 470, 2653, 27421, 310, 278, 6121, 9124, 414, 322, 16728, 17268, 3564, 29892, 13598, 408, 760, 310, 278, 9124, 414, 20704, 19626, 297, 1797, 304, 16089, 10388, 278, 25012, 310, 278, 980, 1397, 277, 6490, 29892, 15115, 391, 2106, 310, 11996, 408, 263, 9109, 7359, 322, 6555, 26463, 363, 278, 5534, 16728, 611, 29888, 423, 29892, 297, 278, 1889, 6095, 5589, 292, 4473, 713, 293, 16728, 3107, 354, 1270, 297, 1797, 304, 6564, 825, 338, 15574, 2998, 408, 376, 1576, 1570, 2787, 8170, 613, 5069, 1476, 800, 526, 12341, 714, 297, 9493, 297, 278, 22747, 8628, 391, 16728, 10288, 29885, 566, 29889, 2398, 29892, 306, 29915, 345, 2337, 8126, 385, 1722, 3458, 1048, 445, 322, 1784, 916, 17800, 29892, 322, 871, 10325, 313, 29875, 29889, 29872, 1696, 278, 4940, 4832, 7378, 470, 577, 29897, 4689, 304, 2289, 26987, 372, 297, 7621, 9493, 29889, 1126, 306, 29915, 29885, 1286, 9226, 368, 25617, 393, 11790, 277, 322, 4045, 393, 27391, 445, 8177, 12906, 681, 6368, 1048, 278, 3865, 29928, 3301, 1641, 2653, 27421, 310, 278, 21790, 816, 789, 29879, 526, 29871, 29896, 29900, 29900, 29995, 2743, 297, 1009, 24809, 358, 29889, 306, 29915, 345, 22834, 393, 599, 278, 916, 8177, 12906, 681, 25841, 322, 714, 1266, 269, 1049, 414, 2750, 21834, 23151, 322, 3086, 10307, 391, 9556, 526, 13586, 14734, 304, 652, 1765, 2305, 29915, 29879, 8570, 3448, 515, 825, 23151, 322, 670, 10298, 2869, 8389, 363, 29892, 825, 896, 9875, 29892, 825, 896, 2869, 1497, 29892, 322, 825, 896, 2869, 1258, 29889, 2648, 278, 982, 29892, 897, 9713, 1706, 292, 2963, 322, 1798, 26082, 17129, 2143, 1082, 1784, 310, 1438, 714, 1049, 728, 25841, 297, 263, 7786, 15593, 363, 1906, 8852, 29889, 13, 6716, 2655, 306, 864, 304, 1207, 2821, 1244, 29901, 23151, 322, 278, 3086, 10307, 391, 10298, 892, 1556, 11630, 376, 3656, 29899, 28516, 3246, 613, 322, 1304, 376, 3656, 29899, 29903, 21976, 1608, 29908, 297, 1009, 8604, 13089, 5863, 322, 4473, 6751, 29889, 2860, 599, 29892, 1584, 28431, 310, 23151, 322, 278, 3865, 29928, 3301, 18720, 393, 1009, 13089, 5863, 471, 2729, 373, 8760, 29892, 322, 297, 1749, 1223, 29899, 1627, 2935, 29892, 9576, 29899, 3389, 3186, 29892, 278, 8760, 338, 5220, 1166, 635, 376, 3656, 29899, 29903, 21976, 293, 1642, 1105, 1235, 29915, 29879, 451, 679, 12624, 701, 297, 445, 2278, 728, 286, 2004, 310, 376, 29950, 277, 1358, 322, 278, 11409, 275, 892, 16126, 29892, 11021, 391, 9418, 29899, 28516, 3246, 11838, 302, 787, 1947, 29892, 322, 3763, 26506, 304, 23033, 1203, 3598, 825, 896, 8389, 363, 29889, 7419, 472, 825, 896, 1497, 29892, 1258, 29892, 5456, 1048, 29892, 322, 9875, 29892, 322, 366, 674, 2041, 304, 278, 6924, 15997, 393, 306, 505, 29901, 393, 445, 10298, 471, 278, 14176, 28469, 278, 3186, 756, 3926, 2998, 304, 278, 610, 294, 277, 293, 29892, 1014, 874, 573, 29892, 322, 17912, 573, 5469, 310, 278, 6121, 16728, 22161, 7776, 284, 18425, 640, 22155, 278, 3122, 29892, 27556, 363, 1009, 376, 4373, 2787, 8170, 29908, 373, 1432, 4565, 6382, 262, 519, 29889, 13, 4013, 338, 2020, 23151, 322, 3086, 10307, 391, 9556, 750, 304, 367, 14416, 29889, 910, 338, 2020, 23151, 322, 278, 3865, 29928, 3301, 526, 21003, 8033, 1891, 29892, 269, 1049, 14561, 29892, 322, 1999, 2795, 363, 1432, 16126, 297, 278, 3186, 29889, 910, 338, 2020, 278, 4158, 5745, 29892, 19180, 322, 1749, 28976, 1788, 9279, 278, 2181, 1355, 393, 278, 9576, 29899, 3389, 838, 3687, 313, 1552, 501, 29889, 29968, 1696, 501, 29889, 29903, 29889, 322, 15308, 7761, 29897, 2869, 19355, 373, 304, 23151, 322, 3086, 10307, 391, 9556, 29889, 450, 22057, 505, 6446, 285, 492, 2986, 278, 2471, 29892, 1999, 11500, 23151, 322, 278, 3865, 29928, 3301, 363, 263, 25713, 376, 19984, 6400, 504, 29908, 310, 7824, 22057, 322, 2302, 2222, 916, 16831, 287, 472, 10198, 1907, 746, 297, 2114, 278, 838, 3687, 892, 14040, 363, 278, 1855, 8753, 6400, 504, 29879, 322, 916, 2181, 1355, 2750, 5199, 537, 2645, 399, 29956, 2687, 29889, 9205, 1891, 6121, 9576, 719, 29892, 278, 7601, 3564, 5742, 278, 5503, 363, 263, 376, 4373, 2787, 8170, 613, 2274, 322, 18720, 920, 18215, 21834, 23151, 322, 3086, 10307, 391, 1957, 3002, 471, 785, 322, 19998, 9242, 785, 304, 1009, 3001, 3673, 713, 3814, 363, 3186, 2432, 3381, 322, 1014, 29926, 688, 362, 29889, 13, 2887 ]	1,332,826	0	CommonCrawl	8	11
Veronica Clark explains in her must read article titled, Demystification of the Birth and Funding of the NSDAP, Hitler sought to overcome the class antagonism prevalent throughout Germany (and much of Europe) by establishing a political and social order based on merit, rather than class or wealth, and sought to unify German society around their common German heritage and Nordic race. Consider the following quote from Hitler, which underscores how he felt about the capitalist system that prevailed in Europe, Britain, and the United States: We are socialists, we are enemies of today's capitalistic economic system for the exploitation of the economically weak, with its unfair salaries, with its unseemly evaluation of a human being according to wealth and property instead of responsibility and performance, and we are all determined to destroy this system under all conditions. How true does that statement ring to you, especially in light of the criminal bailout of Wall Street and the absurd bonuses all the big shots were doling out for themselves and their crooked henchman following the (still on-going) financial collapse initiated in 2008? National Socialist ideology did have opinions about and openly discussed race and the "Jewish Problem", but it's far more nuanced than the mainstream version of history. For starters, National Socialism was more pro-German, pro-Aryan than anti-other races - except the Jewish "race". They cherished and sought to preserve their German race and identity, recognizing the destructive and subversive nature of Jewry, and their innate ability to corrupt society. They said and wrote some "extreme" things by today's Orwellian standards - but truthful things. The National Socialists were just being honest about the nature of organized Jewry, and their threat to Gentile societies. For instance, consider this excerpt from a 1935 bulletin published by the Reichspropagandaleitung, the Nazi Party's Central Propaganda office: Some believe that we are using methods in this battle that are too harsh. We reply that our attacks and methods in this battle cannot be determined by our way of thinking, by whether we find them ugly or harsh, but rather we must use methods in our attacks that are appropriate for the opponent that we are attacking. One cannot battle the Jews with the politeness of the noble Aryan soul, for which he as no understanding. We need only think back on the methods that the Jew used against our movement during the period of struggle. No lie or slander was too crude to be used, to be seized and passed on by the Jews and their Jewish lackeys with eagerness, enthusiasm, and Satanic joy. We would have had little success replying then with refined arguments. It is just as impossible today to combat this creeping, subterranean danger with methods that the Jew would only laugh at. The Führer's contribution has been to make the Jewish Question a matter for the entire people. The efforts völkisch groups, organizations, etc., made in the past to spread knowledge about the world enemy were never of great significance, since only a very limited circle was reached. With his movement, Adolf Hitler created an instrument that went far beyond these groups and made the nation see that the solution to this question was a prerequisite to changing Germany's fate. In answer to his brave act, all the powers at the command of the Jewish world were called on, including the mobilization of parties, of the press, of the radio, of finance, and of bloody terror. [...] I also recommend reading Those Damned Nazis, written by Joseph Goebbles in 1932, which explains National Socialist ideology in greater detail. Here are some excerpts that stand out to me: Why Are We Socialists? We are socialists because we see in socialism, that is the union of all citizens, the only chance to maintain our racial inheritance and to regain our political freedom and renew our German state. Socialism is the doctrine of liberation for the working class. It promotes the rise of the fourth class and its incorporation in the political organism of our Fatherland, and is inextricably bound to breaking the present slavery and regaining German freedom. Socialism, therefore, is not merely a matter of the oppressed class, but a matter for everyone, for freeing the German people from slavery is the goal of contemporary policy. [...] Why a Workers' Party? Work is not mankind's curse, but his blessing. A man becomes a man through labor. It elevates him, makes	0.904416	0.934419	0.437877	1.362203	[ 0.9016769337416699, 0.907155635457665 ]	[ 1.5700924519597366, 0.29874615922983633 ]	[ 0.5266449463732855, 0.34910807459638665 ]	[ 1.4714601913821923, 1.2529450888489502 ]	1,024	[ 512, 512 ]	[ 1798, 26082, 17129, 18568, 297, 902, 1818, 1303, 4274, 25278, 29892, 4432, 858, 2450, 310, 278, 350, 7515, 322, 13249, 292, 310, 278, 3865, 29928, 3301, 29892, 23151, 18365, 304, 25688, 278, 770, 3677, 12841, 1608, 758, 791, 296, 10106, 9556, 313, 392, 1568, 310, 4092, 29897, 491, 10127, 292, 263, 8604, 322, 5264, 1797, 2729, 373, 2778, 277, 29892, 3265, 1135, 770, 470, 17173, 29892, 322, 18365, 304, 443, 1598, 5332, 12459, 2820, 1009, 3619, 5332, 902, 16639, 322, 5245, 293, 8175, 29889, 10056, 278, 1494, 14978, 515, 23151, 29892, 607, 23400, 29883, 2361, 920, 540, 7091, 1048, 278, 7483, 391, 1788, 393, 758, 1564, 2356, 297, 4092, 29892, 14933, 29892, 322, 278, 3303, 3900, 29901, 13, 4806, 526, 5264, 2879, 29892, 591, 526, 22595, 310, 9826, 29915, 29879, 7483, 4695, 17407, 1788, 363, 278, 16035, 7018, 310, 278, 7766, 1711, 8062, 29892, 411, 967, 29395, 1466, 4497, 4314, 29892, 411, 967, 443, 344, 331, 368, 17983, 310, 263, 5199, 1641, 5034, 304, 17173, 322, 2875, 2012, 310, 23134, 322, 4180, 29892, 322, 591, 526, 599, 10087, 304, 8174, 445, 1788, 1090, 599, 5855, 29889, 13, 5328, 1565, 947, 393, 3229, 9228, 304, 366, 29892, 7148, 297, 3578, 310, 278, 22161, 289, 737, 449, 310, 14406, 7103, 322, 278, 6425, 18245, 10814, 6394, 599, 278, 4802, 528, 1862, 892, 8828, 292, 714, 363, 6053, 322, 1009, 8182, 12504, 19061, 305, 1171, 1494, 278, 313, 303, 453, 373, 29899, 17696, 29897, 18161, 24382, 14511, 630, 297, 29871, 29906, 29900, 29900, 29947, 29973, 13, 27325, 10307, 391, 1957, 3002, 1258, 505, 26971, 1048, 322, 1722, 368, 15648, 8175, 322, 278, 376, 29967, 809, 728, 11583, 613, 541, 372, 29915, 29879, 2215, 901, 4948, 8362, 1135, 278, 1667, 5461, 1873, 310, 4955, 29889, 1152, 5810, 2153, 29892, 3086, 10307, 1608, 471, 901, 410, 29899, 29954, 3504, 29892, 410, 29899, 29909, 719, 273, 1135, 9418, 29899, 1228, 19830, 448, 5174, 278, 16728, 376, 25525, 1642, 2688, 14954, 3276, 322, 18365, 304, 19905, 1009, 5332, 8175, 322, 10110, 29892, 5936, 5281, 278, 17912, 573, 322, 1014, 874, 573, 5469, 310, 9576, 719, 29892, 322, 1009, 7622, 403, 11509, 304, 1034, 6685, 12459, 29889, 2688, 1497, 322, 5456, 777, 376, 1062, 10291, 29908, 2712, 491, 9826, 29915, 29879, 1394, 29893, 5481, 273, 20801, 448, 541, 8760, 1319, 2712, 29889, 450, 3086, 10307, 2879, 892, 925, 1641, 15993, 1048, 278, 5469, 310, 19098, 9576, 719, 29892, 322, 1009, 28469, 304, 20655, 488, 5374, 20850, 29889, 13, 2831, 2777, 29892, 2050, 445, 429, 2265, 415, 515, 263, 29871, 29896, 29929, 29941, 29945, 24334, 262, 6369, 491, 278, 26981, 7728, 351, 392, 744, 10125, 29892, 278, 11409, 29875, 9173, 29915, 29879, 8068, 1019, 13573, 5863, 8034, 29901, 13, 9526, 4658, 393, 591, 526, 773, 3519, 297, 445, 10555, 393, 526, 2086, 4023, 845, 29889, 1334, 8908, 393, 1749, 16661, 322, 3519, 297, 445, 10555, 2609, 367, 10087, 491, 1749, 982, 310, 7291, 29892, 491, 3692, 591, 1284, 963, 22769, 470, 4023, 845, 29892, 541, 3265, 591, 1818, 671, 3519, 297, 1749, 16661, 393, 526, 8210, 363, 278, 23995, 296, 393, 591, 526, 5337, 292, 29889, 3118, 2609, 10555, 278, 22057, 411, 278, 2832, 18543, 310, 278, 15996, 319, 719, 273, 10752, 29892, 363, 607, 540, 408, 694, 8004, 29889, 1334, 817, 871, 1348, 1250, 373, 278, 3519, 393, 278, 9576, 1304, 2750, 1749, 10298, 2645, 278, 3785, 310, 21117, 29889, 1939, 3804, 470, 269, 1049, 261, 471, 2086, 7618, 311, 304, 367, 1304, 29892, 304, 367, 25291, 322, 4502, 373, 491, 278, 22057, 322, 1009, 16728, 425, 10055, 952, 411, 321, 351, 824, 404, 29892, 23644, 3173, 29885, 29892, 322, 12178, 273, 293, 15331, 29889, 1334, 723, 505, 750, 2217, 2551, 1634, 5890, 769, 411, 2143, 1312, 6273, 29889, 739, 338, 925, 408, 9301, 9826, 304, 15499, 445, 907, 26819, 29892, 1014, 357, 10800, 273, 9703, 411, 3519, 393, 278, 9576, 723, 871, 10569, 472, 29889, 13, 1576, 383, 4000, 261, 29915, 29879, 11896, 756, 1063, 304, 1207, 278, 16728, 894, 263, 4383, 363, 278, 4152, 2305, 29889, 450, 14231, 325, 5873, 29895, 783, 6471, 29892, 25700, 29892, 2992, 1696, 1754, 297, 278, 4940, 304, 9677, 7134, 1048, 278, 3186, 11103, 892, 2360, 310, 2107, 26002, 29892, 1951, 871, 263, 1407, 9078, 8607, 471, 7450, 29889, 2973, 670, 10298, 29892, 21834, 23151, 2825, 385, 11395, 393, 3512, 2215, 8724, 1438, 6471, 322, 1754, 278, 5233, 1074, 393, 278, 1650, 304, 445, 1139, 471, 263, 544, 406, 7680, 568, 304, 6480, 9556, 29915, 29879, 23779, 29889, 512, 1234, 304, 670, 26565, 1044, 29892, 599, 278, 10801, 472, 278, 1899, 310, 278, 16728, 3186, 892, 2000, 373, 29892, 3704, 278, 27227, 2133, 310, 13973, 29892, 310, 278, 3965, 29892, 310, 278, 7155, 29892, 310, 1436, 749, 29892, 322, 310, 6668, 1486, 15115, 29889, 21945, 13, 29902, 884, 6907, 5183, 16025, 9865, 9571, 11409, 275, 29892, 3971, 491, 6936, 2921, 774, 7586, 297, 29871, 29896, 29929, 29941, 29906, 29892, 607, 18568, 3086, 10307, 391, 1957, 3002, 297, 7621, 9493, 29889, 2266, 526, 777, 429, 2265, 16485, 393, 2317, 714, 304, 592, 29901, 3750, 4683, 1334, 10307, 2879, 29973, 13, 4806, 526, 5264, 2879, 1363, 591, 1074, 297, 5264, 1608, 29892, 393, 338, 278, 9833, 310, 599, 18363, 29892, 278, 871, 8825, 304, 7344, 1749, 1153, 1455, 20328, 322, 304, 1072, 475, 1749, 8604, 16082, 322, 23011, 1749, 5332, 2106, 29889, 13, 6295, 1455, 1608, 338, 278, 22542, 310, 7866, 362, 363, 278, 1985, 770, 29889, 739, 2504, 4769, 278, 14451, 310, 278, 11582, 770, 322, 967, 11039, 362, 297, 278, 8604, 2894, 1608, 310, 1749, 17852, 1049, 29892, 322, 338, 297, 1062, 2200, 2197, 3216, 304, 16679, 278, 2198, 8370, 1201, 322, 1072, 17225, 5332, 16082, 29889, 10307, 1608, 29892, 5480, 29892, 338, 451, 13586, 263, 4383, 310, 278, 4575, 1253, 287, 770, 29892, 541, 263, 4383, 363, 14332, 29892, 363, 3889, 292, 278, 5332, 2305, 515, 8370, 1201, 338, 278, 7306, 310, 24952, 8898, 29889, 21945, 13, 11008, 263, 5244, 414, 29915, 9173, 29973, 13, 5531, 338, 451, 767, 14380, 29915, 29879, 3151, 344, 29892, 541, 670, 17065, 292, 29889, 319, 767, 7415, 263, 767, 1549, 10212, 29889, 739, 11858, 1078, 1075, 29892, 3732 ]	1,332,826	1,024	CommonCrawl	6	2
him great and aware, raises him above all other creatures. It is in the deepest sense creative, productive, and culture-producing. Without labor, no food. Without food, no life. The idea that the dirtier one's hands get, the more degrading the work, is a Jewish, not a German, idea. [...] We call ourselves a workers' party because we want to rescue the word work from its current definition and give it back its original meaning. Anyone who creates value is a creator, that is, a worker. We refuse to distinguish kinds of work. Our only standard is whether the work serves the whole, or at least does not harm it, or if it is harmful. Work is service. If it works against the general welfare, then it is treason against the fatherland. [...] Why Do We Oppose the Jews? We oppose the Jews because we are defending the freedom of the German people. The Jew is the cause and beneficiary of our slavery. He has misused the social misery of the broad masses to deepen the dreadful split between the right and left of our people, to divide Germany into two halves thereby concealing the true reason for the loss of the Great War and falsifying the nature of the revolution. The Jew has no interest in solving the German question. He cannot have such an interest. He depends on it remaining unsolved. If the German people formed a united community and won back its freedom, there would be no place any longer for the Jew. His hand is strongest when a people lives in domestic and international slavery, not when it is free, industrious, self-aware and determined. The Jew caused our problems, and lives from them. That is why we oppose the Jew as nationalists and as socialists. He has ruined our race, corrupted our morals, hollowed out our customs and broken our strength. We owe it to him that we today are the Pariah of the world. He was the leper among as long as we were German. When we forgot our German nature, he triumphed over us and our future. The Jew is the plastic demon of decomposition. Where he finds filth and decay, he surfaces and begins his butcher's work among the nations. He hides behind a mask and presents himself as a friend to his victims, and before they know it he has broken their neck. The Jew is uncreative. He produces nothing, he only haggles with products. With rags, clothing, pictures, jewels, grain, stocks, cures, peoples and states. He has somehow stolen everything he deals in. When he attacks a state he is a revolutionary. As soon as he holds power, he preaches peace and order so that he can devour his conquests in comfort. What does anti-Semitism have to do with socialism? I would put the question this way: What does the Jew have to do with socialism? Socialism has to do with labor. When did one ever see him working instead of plundering, stealing and living from the sweat of others? As socialists we are opponents of the Jews because we see in the Hebrews the incarnation of capitalism, of the misuse of the nation's goods. What does anti-Semitism have to do with nationalism? I would put the question this way: What does the Jew have to do with nationalism? Nationalism has to do with blood and race. The Jew is the enemy and destroyer of the purity of blood, the conscious destroyer of our race. As nationalists we oppose the Jews because we see the Hebrews as the eternal enemy of our national honor and of our national freedom. But the Jew, after all, is also a human being. Certainly, none of us doubts that. We only doubt that he is a decent human being. He does not get along with us. He lives by other laws than we do. The fact that he is a human being is not sufficient reason for us to allow him to subject us in inhumane ways. He may be a human being — but what kind of a human being is he! If someone slaps your mother in the face, do you say: "Thank you! He is after all a human being!" That is not a human being, it is a monster. Yet how much worse has the Jew done to our mother Germany, and is still doing today! [...] Finally, consider Adolf Hitler's political testament he dictated shortly before he committed suicide: More than thirty years have passed since 1914 when I made my modest contribution as a volunteer in the	0.898938	0.261143	0.082803	1.008416	[ 1.1975268264054022, 0.6003483393619427 ]	[ 0.25577107327840304, 0.26651484476626136 ]	[ 0.323745664342544, -0.15814013048046716 ]	[ 1.0136190241696847, 1.003213543096673 ]	1,024	[ 512, 512 ]	[ 1075, 2107, 322, 9543, 29892, 1153, 4637, 1075, 2038, 599, 916, 907, 3698, 29889, 739, 338, 297, 278, 6483, 342, 4060, 907, 1230, 29892, 3234, 573, 29892, 322, 9257, 29899, 5498, 3277, 29889, 13932, 10212, 29892, 694, 9687, 29889, 13932, 9687, 29892, 694, 2834, 29889, 13, 1576, 2969, 393, 278, 270, 2728, 631, 697, 29915, 29879, 6567, 679, 29892, 278, 901, 316, 5105, 292, 278, 664, 29892, 338, 263, 16728, 29892, 451, 263, 5332, 29892, 2969, 29889, 21945, 13, 4806, 1246, 20278, 263, 17162, 29915, 6263, 1363, 591, 864, 304, 26429, 278, 1734, 664, 515, 967, 1857, 5023, 322, 2367, 372, 1250, 967, 2441, 6593, 29889, 26407, 1058, 10017, 995, 338, 263, 907, 1061, 29892, 393, 338, 29892, 263, 15645, 29889, 1334, 26506, 304, 20820, 17690, 310, 664, 29889, 8680, 871, 3918, 338, 3692, 278, 664, 19700, 278, 3353, 29892, 470, 472, 3203, 947, 451, 10311, 372, 29892, 470, 565, 372, 338, 10311, 1319, 29889, 5244, 338, 2669, 29889, 960, 372, 1736, 2750, 278, 2498, 281, 761, 598, 29892, 769, 372, 338, 2578, 1658, 2750, 278, 4783, 1049, 29889, 21945, 13, 11008, 1938, 1334, 438, 407, 852, 278, 22057, 29973, 13, 4806, 4575, 852, 278, 22057, 1363, 591, 526, 822, 2548, 278, 16082, 310, 278, 5332, 2305, 29889, 450, 9576, 338, 278, 4556, 322, 7795, 1654, 653, 310, 1749, 8370, 1201, 29889, 940, 756, 3984, 3880, 278, 5264, 3984, 708, 310, 278, 7300, 23063, 304, 6483, 264, 278, 21005, 1319, 6219, 1546, 278, 1492, 322, 2175, 310, 1749, 2305, 29892, 304, 16429, 9556, 964, 1023, 8870, 1960, 27999, 10628, 12818, 278, 1565, 2769, 363, 278, 6410, 310, 278, 7027, 3362, 322, 285, 1338, 9215, 278, 5469, 310, 278, 19479, 29889, 13, 1576, 9576, 756, 694, 4066, 297, 17069, 278, 5332, 1139, 29889, 940, 2609, 505, 1316, 385, 4066, 29889, 940, 7111, 373, 372, 9886, 443, 2929, 1490, 29889, 960, 278, 5332, 2305, 8429, 263, 443, 1573, 7881, 322, 2113, 1250, 967, 16082, 29892, 727, 723, 367, 694, 2058, 738, 5520, 363, 278, 9576, 29889, 3600, 1361, 338, 4549, 342, 746, 263, 2305, 12080, 297, 21849, 322, 6121, 8370, 1201, 29892, 451, 746, 372, 338, 3889, 29892, 21136, 681, 29892, 1583, 29899, 28327, 322, 10087, 29889, 450, 9576, 8581, 1749, 4828, 29892, 322, 12080, 515, 963, 29889, 13, 7058, 338, 2020, 591, 4575, 852, 278, 9576, 408, 4797, 2879, 322, 408, 5264, 2879, 29889, 940, 756, 5796, 1312, 1749, 8175, 29892, 1034, 14214, 1749, 3036, 1338, 29892, 298, 2952, 287, 714, 1749, 2888, 29879, 322, 9391, 1749, 9324, 29889, 1334, 288, 705, 372, 304, 1075, 393, 591, 9826, 526, 278, 1459, 21071, 310, 278, 3186, 29889, 940, 471, 278, 454, 546, 4249, 408, 1472, 408, 591, 892, 5332, 29889, 1932, 591, 9640, 1749, 5332, 5469, 29892, 540, 24124, 287, 975, 502, 322, 1749, 5434, 29889, 13, 1576, 9576, 338, 278, 715, 6288, 8033, 310, 26227, 29889, 6804, 540, 14061, 977, 386, 322, 20228, 29892, 540, 28001, 322, 16410, 670, 541, 4630, 29915, 29879, 664, 4249, 278, 19079, 29889, 940, 298, 2247, 5742, 263, 11105, 322, 22981, 3654, 408, 263, 5121, 304, 670, 6879, 9893, 29892, 322, 1434, 896, 1073, 372, 540, 756, 9391, 1009, 18873, 29889, 13, 1576, 9576, 338, 443, 1037, 1230, 29889, 940, 13880, 3078, 29892, 540, 871, 298, 16170, 793, 411, 9316, 29889, 2973, 1153, 3174, 29892, 1067, 6046, 29892, 14956, 29892, 432, 809, 1379, 29892, 2646, 262, 29892, 10961, 29879, 29892, 274, 1973, 29892, 1236, 459, 793, 322, 5922, 29889, 940, 756, 10431, 380, 18975, 4129, 540, 316, 1338, 297, 29889, 1932, 540, 16661, 263, 2106, 540, 338, 263, 19479, 653, 29889, 1094, 4720, 408, 540, 8640, 3081, 29892, 540, 758, 14520, 10776, 322, 1797, 577, 393, 540, 508, 2906, 473, 670, 378, 1119, 29879, 297, 13016, 29889, 13, 5618, 947, 9418, 29899, 29903, 21976, 1608, 505, 304, 437, 411, 5264, 1608, 29973, 306, 723, 1925, 278, 1139, 445, 982, 29901, 1724, 947, 278, 9576, 505, 304, 437, 411, 5264, 1608, 29973, 10307, 1608, 756, 304, 437, 411, 10212, 29889, 1932, 1258, 697, 3926, 1074, 1075, 1985, 2012, 310, 715, 870, 3241, 29892, 1886, 12818, 322, 8471, 515, 278, 7901, 271, 310, 4045, 29973, 1094, 5264, 2879, 591, 526, 23995, 1237, 310, 278, 22057, 1363, 591, 1074, 297, 278, 18472, 3973, 29879, 278, 5528, 2753, 362, 310, 7483, 1608, 29892, 310, 278, 3984, 1509, 310, 278, 5233, 29915, 29879, 22535, 29889, 13, 5618, 947, 9418, 29899, 29903, 21976, 1608, 505, 304, 437, 411, 4797, 1608, 29973, 306, 723, 1925, 278, 1139, 445, 982, 29901, 1724, 947, 278, 9576, 505, 304, 437, 411, 4797, 1608, 29973, 3086, 1608, 756, 304, 437, 411, 10416, 322, 8175, 29889, 450, 9576, 338, 278, 11103, 322, 8174, 261, 310, 278, 3708, 537, 310, 10416, 29892, 278, 19861, 8174, 261, 310, 1749, 8175, 29889, 1094, 4797, 2879, 591, 4575, 852, 278, 22057, 1363, 591, 1074, 278, 18472, 3973, 29879, 408, 278, 634, 17196, 11103, 310, 1749, 4797, 10657, 322, 310, 1749, 4797, 16082, 29889, 13, 6246, 278, 9576, 29892, 1156, 599, 29892, 338, 884, 263, 5199, 1641, 29889, 315, 13946, 368, 29892, 5642, 310, 502, 27455, 1372, 393, 29889, 1334, 871, 7404, 393, 540, 338, 263, 27189, 5199, 1641, 29889, 940, 947, 451, 679, 3412, 411, 502, 29889, 940, 12080, 491, 916, 14243, 1135, 591, 437, 29889, 450, 2114, 393, 540, 338, 263, 5199, 1641, 338, 451, 8002, 2769, 363, 502, 304, 2758, 1075, 304, 4967, 502, 297, 297, 16063, 1662, 5837, 29889, 940, 1122, 367, 263, 5199, 1641, 813, 541, 825, 2924, 310, 263, 5199, 1641, 338, 540, 29991, 960, 4856, 8370, 567, 596, 5637, 297, 278, 3700, 29892, 437, 366, 1827, 29901, 376, 25271, 366, 29991, 940, 338, 1156, 599, 263, 5199, 1641, 3850, 2193, 338, 451, 263, 5199, 1641, 29892, 372, 338, 263, 1601, 2475, 29889, 15175, 920, 1568, 15029, 756, 278, 9576, 2309, 304, 1749, 5637, 9556, 29892, 322, 338, 1603, 2599, 9826, 29991, 21945, 13, 12881, 635, 29892, 2050, 21834, 23151, 29915, 29879, 8604, 1243, 1166, 540, 9657, 630, 21734, 1434, 540, 19355, 23921, 680, 29901, 13, 20761, 1135, 17058, 2440, 505, 4502, 1951, 29871, 29896, 29929, 29896, 29946, 746, 306, 1754, 590, 878, 342, 11896, 408, 263, 27886, 261, 297, 278 ]	1,332,826	2,048	CommonCrawl	6	2
First World War, which was forced upon the Reich. In these three decades love and loyalty to my people have guided all my thoughts, actions and my life. They gave me the strength to make the most difficult decisions ever to confront mortal man. In these three decades I have spent my strength and my health. It is untrue that I or anyone else in Germany wanted war in 1939. It was wanted and provoked solely by international statesmen either of Jewish origin or working for Jewish interests. I have made too many offers for the limitation and control of armaments, which posterity will not be cowardly enough always to disregard, for responsibility for the outbreak of this war to be placed on me. Nor have I ever wished that, after the appalling First World War, there would ever be a second against either England or America. Centuries will go by, but from the ruins of our towns and monuments the hatred of those ultimately responsible will always grow anew against the people whom we have to thank for all this: international Jewry and its henchmen. [...] Hitler and the National Socialist movement in Germany, from what I can tell after honestly assessing the situation, were leaders and statesmen in the truest sense. They were true patriots that cared deeply about their country and their people, unlike the puppets, sell-outs and traitors in the West today that do nothing but lie to the people they allegedly represent, all the while serving a foreign criminal cabal. The National Socialists were honest with their fellow Germans, and treated them with respect by and large, certainly compared to governments in the West today. Is it any wonder then that Hitler specifically, and National Socialist Germany generally, are so demonized, slandered, and hated by the Jews, and thus much of Western society due to their control over the mass media and educational system? Hitler and the National Socialists not only spoke openly and honestly about important subjects, clearly identifying the enemy of all humanity – international Jewry – they made serious moves against this destructive, parasitic network of criminals that had wrecked their country and sought to destroy their people. Hitler and National Socialism were the anti-thesis to Jewish Communism and Jewish plutocratic capitalism, and it's time we recognize this fact. « Last Edit: August 17, 2012, 09:08:24 PM by sushigirl » "At any given moment there is an orthodoxy, a body of ideas which it is assumed all right-thinking people will accept without question. It is not exactly forbidden to state this or that or the other, but it is "not done". ...Anyone who challenges the prevailing orthodoxy finds himself silenced with. - * Rethinking Hitler & National Socialism I don't know if this is the appropriate place to post this, but concerning Hitler, my favorite quote from him about the jews is this one, concerning their method of argument (I used to post this a few times back in the Nolajbs days): The more I argued with them, the better I came to know their dialectic. First they counted on the stupidity of their adversary, and then, when there was no other way out, they themselves simply played stupid. If all this didn't help, they pretended not to understand, or, if challenged, they changed the subject in a hurry, quoted platitudes which, if you accepted them, they immediately related to entirely different matters, and then, if again attacked, gave ground and pretended not to know exactly what you were talking about. Whenever you tried to attack one of these apostles, your hand closed on a jelly-like slime which divided up and poured through your fingers, but in the next moment collected again. But if you really struck one of these fellows so telling a blow that, observed by the audience, he couldn't help but agree, and if you believed that this had taken you at least one step forward, your amazement was great the next day. The Jew had not the slightest recollection of the day before, he rattled off his same old nonsense as though nothing at all had happened, and, if indignantly challenged, affected amazement; he couldn't remember a thing, except that he had proved the correctness of his assertions the previous day. Sometimes I stood there thunderstruck. I didn't know what to be more amazed at: the agility of their tongues or their virtuosity at lying. Gradually I began to hate them. http://www.hitler.org/writings/Mein_	0.504129	-0.033415	-0.45488	0.428311	[ 1.0057722663455757, 0.002485014603983752 ]	[ 0.3846963311327028, -0.4515272163389358 ]	[ -0.1784300586835413, -0.7313306022173119 ]	[ 0.8991587323665579, -0.042537304740986236 ]	1,024	[ 512, 512 ]	[ 3824, 2787, 3362, 29892, 607, 471, 11826, 2501, 278, 9320, 29889, 13, 797, 1438, 2211, 1602, 3076, 5360, 322, 28108, 1017, 304, 590, 2305, 505, 1410, 2618, 599, 590, 13133, 29892, 8820, 322, 590, 2834, 29889, 2688, 4846, 592, 278, 9324, 304, 1207, 278, 1556, 5189, 1602, 12112, 3926, 304, 21751, 5758, 284, 767, 29889, 512, 1438, 2211, 1602, 3076, 306, 505, 10398, 590, 9324, 322, 590, 9045, 29889, 13, 3112, 338, 443, 3009, 393, 306, 470, 5019, 1683, 297, 9556, 5131, 1370, 297, 29871, 29896, 29929, 29941, 29929, 29889, 739, 471, 5131, 322, 1326, 12504, 14419, 368, 491, 6121, 5922, 1527, 2845, 310, 16728, 3978, 470, 1985, 363, 16728, 20017, 29889, 306, 505, 1754, 2086, 1784, 16688, 363, 278, 29485, 322, 2761, 310, 5075, 20060, 29892, 607, 10368, 537, 674, 451, 367, 21282, 538, 368, 3307, 2337, 304, 766, 1727, 538, 29892, 363, 23134, 363, 278, 714, 8690, 310, 445, 1370, 304, 367, 7180, 373, 592, 29889, 4186, 505, 306, 3926, 20024, 393, 29892, 1156, 278, 623, 27855, 3824, 2787, 3362, 29892, 727, 723, 3926, 367, 263, 1473, 2750, 2845, 5408, 470, 6813, 29889, 2895, 14886, 674, 748, 491, 29892, 541, 515, 278, 5796, 1144, 310, 1749, 20248, 322, 22586, 278, 3056, 1127, 310, 1906, 18973, 14040, 674, 2337, 6548, 385, 809, 2750, 278, 2305, 6029, 591, 505, 304, 6452, 363, 599, 445, 29901, 6121, 9576, 719, 322, 967, 19061, 305, 1527, 29889, 21945, 13, 29950, 277, 1358, 322, 278, 3086, 10307, 391, 10298, 297, 9556, 29892, 515, 825, 306, 508, 2649, 1156, 15993, 368, 24809, 292, 278, 6434, 29892, 892, 20251, 322, 5922, 1527, 297, 278, 534, 16139, 4060, 29889, 2688, 892, 1565, 16967, 1862, 393, 274, 1965, 24344, 1048, 1009, 4234, 322, 1009, 2305, 29892, 25531, 278, 2653, 27421, 29892, 19417, 29899, 17718, 322, 1020, 17259, 297, 278, 3122, 9826, 393, 437, 3078, 541, 3804, 304, 278, 2305, 896, 16831, 23244, 2755, 29892, 599, 278, 1550, 16330, 263, 9117, 22161, 7776, 284, 29889, 450, 3086, 10307, 2879, 892, 15993, 411, 1009, 10404, 7287, 550, 29892, 322, 14914, 963, 411, 3390, 491, 322, 2919, 29892, 8959, 9401, 304, 4095, 1860, 297, 278, 3122, 9826, 29889, 13, 3624, 372, 738, 4997, 769, 393, 23151, 10816, 29892, 322, 3086, 10307, 391, 9556, 6892, 29892, 526, 577, 8033, 1891, 29892, 269, 1049, 14561, 29892, 322, 298, 630, 491, 278, 22057, 29892, 322, 4550, 1568, 310, 10504, 12459, 2861, 304, 1009, 2761, 975, 278, 4158, 5745, 322, 28976, 1788, 29973, 23151, 322, 278, 3086, 10307, 2879, 451, 871, 12707, 1722, 368, 322, 15993, 368, 1048, 4100, 17800, 29892, 9436, 2893, 9215, 278, 11103, 310, 599, 5199, 537, 785, 6121, 9576, 719, 785, 896, 1754, 10676, 16229, 2750, 445, 17912, 573, 29892, 610, 294, 277, 293, 3564, 310, 15116, 19016, 393, 750, 281, 18217, 287, 1009, 4234, 322, 18365, 304, 8174, 1009, 2305, 29889, 23151, 322, 3086, 10307, 1608, 892, 278, 9418, 29899, 26533, 304, 16728, 20473, 1608, 322, 16728, 28185, 8415, 2454, 7483, 1608, 29892, 322, 372, 29915, 29879, 931, 591, 18720, 445, 2114, 29889, 13, 30009, 9208, 7641, 29901, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29929, 29901, 29900, 29947, 29901, 29906, 29946, 11278, 491, 269, 1878, 335, 5168, 2047, 13, 29908, 4178, 738, 2183, 3256, 727, 338, 385, 14219, 17324, 29891, 29892, 263, 3573, 310, 7014, 607, 372, 338, 12023, 599, 1492, 29899, 386, 18159, 2305, 674, 3544, 1728, 1139, 29889, 739, 338, 451, 3721, 19752, 4215, 304, 2106, 445, 470, 393, 470, 278, 916, 29892, 541, 372, 338, 376, 1333, 2309, 1642, 13, 856, 10773, 650, 1058, 18066, 267, 278, 12379, 737, 292, 14219, 17324, 29891, 14061, 3654, 4047, 9223, 411, 29889, 13, 29899, 334, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 29902, 1016, 29915, 29873, 1073, 565, 445, 338, 278, 8210, 2058, 304, 1400, 445, 29892, 541, 19813, 23151, 29892, 590, 25448, 14978, 515, 1075, 1048, 278, 432, 809, 29879, 338, 445, 697, 29892, 19813, 1009, 1158, 310, 2980, 313, 29902, 1304, 304, 1400, 445, 263, 2846, 3064, 1250, 297, 278, 405, 324, 1175, 5824, 3841, 1125, 13, 1576, 901, 306, 28705, 411, 963, 29892, 278, 2253, 306, 2996, 304, 1073, 1009, 23725, 293, 29889, 3824, 896, 29115, 373, 278, 20239, 537, 310, 1009, 19901, 653, 29892, 322, 769, 29892, 746, 727, 471, 694, 916, 982, 714, 29892, 896, 6053, 3763, 5318, 20239, 29889, 960, 599, 445, 3282, 29915, 29873, 1371, 29892, 896, 14794, 2760, 451, 304, 2274, 29892, 470, 29892, 565, 18066, 287, 29892, 896, 3939, 278, 4967, 297, 263, 12166, 719, 29892, 23153, 18870, 20816, 607, 29892, 565, 366, 9259, 963, 29892, 896, 7389, 4475, 304, 9186, 1422, 13750, 29892, 322, 769, 29892, 565, 1449, 22630, 29892, 4846, 5962, 322, 14794, 2760, 451, 304, 1073, 3721, 825, 366, 892, 9963, 1048, 29889, 1932, 1310, 366, 1898, 304, 5337, 697, 310, 1438, 18115, 793, 29892, 596, 1361, 5764, 373, 263, 12736, 368, 29899, 4561, 2243, 603, 607, 13931, 701, 322, 7446, 1127, 1549, 596, 23915, 29892, 541, 297, 278, 2446, 3256, 16531, 1449, 29889, 1205, 565, 366, 2289, 15469, 697, 310, 1438, 8379, 1242, 577, 14509, 263, 13031, 393, 29892, 8900, 491, 278, 20026, 29892, 540, 8496, 29915, 29873, 1371, 541, 8661, 29892, 322, 565, 366, 13112, 393, 445, 750, 4586, 366, 472, 3203, 697, 4331, 6375, 29892, 596, 21863, 882, 471, 2107, 278, 2446, 2462, 29889, 450, 9576, 750, 451, 278, 7248, 342, 337, 10855, 310, 278, 2462, 1434, 29892, 540, 364, 1131, 839, 1283, 670, 1021, 2030, 302, 787, 1947, 408, 2466, 3078, 472, 599, 750, 9559, 29892, 322, 29892, 565, 1399, 647, 10835, 18066, 287, 29892, 15201, 21863, 882, 29936, 540, 8496, 29915, 29873, 6456, 263, 2655, 29892, 5174, 393, 540, 750, 11827, 278, 1959, 2264, 310, 670, 4974, 1080, 278, 3517, 2462, 29889, 13, 29903, 14618, 306, 8389, 727, 266, 5062, 10582, 384, 29889, 13, 29902, 3282, 29915, 29873, 1073, 825, 304, 367, 901, 21863, 287, 472, 29901, 278, 946, 1793, 310, 1009, 21861, 1041, 470, 1009, 4610, 29884, 359, 537, 472, 19214, 29889, 13, 25584, 1474, 306, 4689, 304, 26277, 963, 29889, 13, 1124, 597, 1636, 29889, 27342, 1358, 29889, 990, 29914, 8231, 886, 29914, 6816, 262, 29918 ]	1,332,826	3,072	CommonCrawl	8	11
Kampf/mkv1ch02.html All that said, Hitler really started to lose it mentally some time after America got involved in WWII. I don't know if it was the speed, the juice (steroids) he was shooting, and/or some ingrained mental illness. Not to say he wasn't brilliant, just crazy in his later life. "Divert, distort, denigrate, disrupt or destroy any discussion of the corruption of American liberty by the organized lobby of a foreign power." ~ WindRiverShoshoni Quote from: dominique on August 17, 2012, 08:20:28 PM Just to be fair, the realization that the USA had decided to enter the war against Germany had to be extremely unsettling. Insane - absolutely NOT - just deeply unsettled. Their war machinery was just too much, too overwhelming. More thoughts about Adolf Hitler and National Socialism I'd like to express a few more thoughts to follow up the post I wrote a couple weeks ago, Rethinking Adolf Hitler and National Socialism. First, Hitler and the NSDAP were not, I repeat, were not funded by Jews. They were not "Rothschild agents" or "puppets of the bankers" or "stooges for the Jews". They were diametrically opposed to the Jewish supremacist goal of a "New World Order", which is essentially Jewish domination and subjugation of the entire globe, a Jewish Utopia so to speak. I linked this article by Veronica Clark in the last post, which explains in great detail the rise of the NSDAP in Germany, dispelling all of these myths about Hitler being funded by Jews, or the Rothschilds, or the Illuminati, or the bankers, ect. Sit down and read it if you haven't yet. I'm also currently reading Heiki B. Gortemaker's Eva Braun: Life with Hitler, which succinctly summarizes the rise of the NSDAP in just a few pages. She discusses the central importance of the Munich beer halls as gathering places and recruitment centers (beer halls have a long history as political gathering places in Germany) of the NSDAP, the increase in popularity of the NSDAP following the economic crash of 1929, and Hitler's efforts to unite all segments of German society - industrialists, aristocrats, soldiers, civil servants, farmers, workers, teachers, students, mothers, fathers, children - under the banner of National Socialism. Just to further discredit this idea that Hitler and the NSDAP were funded by "the Jews", consider the following excerpt of Michael Collins Piper's must read book, The New Babylon: Those Who Reign Supreme - A Panoramic Overview of the Historical, Religious and Economic Origins of the New World Order: There is also the legend that "The Jewish bankers" or "The Zionist bankers" (used often interchangeably) financed Hitler. Not true. James Pool, in his authortative work, Who Financed Hitler?, demonstrates quite to the contrary. In one instance, a Jewish financier in Germany did give money to the Nazi Party–prior to the rise of Adolf Hitler–but those funds were designed to help Hitler's intra-party opposition to stop Hitler. But despite this fact, some "patriots" still say that "The Jews Backed Hitler." Many of those who worship at the altar of this nonsense cite a flagrantly-fraudulent document of shadowy origins entitled Hitler's Secret Bankers, ostensibly written by one "Sidney Warburg," one of those "Jewish bankers." But this document, as we've said, is a fraud. The late Dr. Anthony Sutton's Wall Street and the Rise of Hitler has promoted this theory, based in part on the Warburg travesty and has given further institutionalization to this mythology–truth be damned. American banks and corporations did work with the Hitler regime, usually a continuation of previous financial arrangements going back decades, but this was not part of any grand conspiracy to bring Hitler to power. The claim that the Bush family was integral to the rise of Hitler is another myth. Kevin Phillips–no admirer of the Bush dynasty–examines the actual circumstances surrounding the Bush-Hitler scenario in his book, American Dynasty: Aristocracy,	-0.087229	0.752671	-0.418105	0.554477	[ -0.6159234415889565, 0.4414659895980865 ]	[ 0.09282387237921866, 1.4125171368044813 ]	[ -0.9316936432226692, 0.09548397205795975 ]	[ -0.2168291127139295, 1.3257834563600308 ]	1,024	[ 512, 512 ]	[ 29968, 16817, 29914, 11256, 29894, 29896, 305, 29900, 29906, 29889, 1420, 13, 3596, 393, 1497, 29892, 23151, 2289, 4687, 304, 14074, 372, 6042, 635, 777, 931, 1156, 6813, 2355, 9701, 297, 399, 29956, 2687, 29889, 306, 1016, 29915, 29873, 1073, 565, 372, 471, 278, 6210, 29892, 278, 3623, 625, 313, 303, 1489, 4841, 29897, 540, 471, 27904, 29892, 322, 29914, 272, 777, 2348, 22042, 19119, 4486, 2264, 29889, 2216, 304, 1827, 540, 9007, 29915, 29873, 27592, 29892, 925, 12220, 1537, 297, 670, 2678, 2834, 29889, 13, 29908, 12130, 1765, 29892, 1320, 441, 29892, 972, 4481, 403, 29892, 766, 6685, 470, 8174, 738, 10679, 310, 278, 1034, 18953, 310, 3082, 24169, 491, 278, 19098, 658, 1327, 29891, 310, 263, 9117, 3081, 1213, 3695, 17311, 29934, 2147, 2713, 10578, 5271, 13, 2182, 866, 515, 29901, 8022, 1387, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29947, 29901, 29906, 29900, 29901, 29906, 29947, 11278, 13, 14084, 304, 367, 6534, 29892, 278, 1855, 2133, 393, 278, 8278, 750, 8459, 304, 3896, 278, 1370, 2750, 9556, 750, 304, 367, 14154, 443, 9915, 1847, 29889, 13377, 1662, 448, 13312, 6058, 448, 925, 24344, 443, 9915, 839, 29889, 11275, 1370, 7672, 262, 708, 471, 925, 2086, 1568, 29892, 2086, 975, 1332, 295, 4056, 29889, 13, 20761, 13133, 1048, 21834, 23151, 322, 3086, 10307, 1608, 13, 29902, 29915, 29881, 763, 304, 4653, 263, 2846, 901, 13133, 304, 1101, 701, 278, 1400, 306, 5456, 263, 7303, 11405, 8020, 29892, 390, 621, 18159, 21834, 23151, 322, 3086, 10307, 1608, 29889, 13, 6730, 29892, 23151, 322, 278, 3865, 29928, 3301, 892, 451, 29892, 306, 12312, 29892, 892, 451, 5220, 287, 491, 22057, 29889, 2688, 892, 451, 376, 29934, 720, 816, 789, 19518, 29908, 470, 376, 3746, 27421, 310, 278, 9124, 414, 29908, 470, 376, 7864, 468, 267, 363, 278, 22057, 1642, 2688, 892, 11502, 18184, 1711, 15869, 304, 278, 16728, 22747, 8628, 391, 7306, 310, 263, 376, 4373, 2787, 8170, 613, 607, 338, 13674, 16728, 2432, 3381, 322, 1014, 29926, 688, 362, 310, 278, 4152, 15482, 915, 29892, 263, 16728, 501, 3332, 423, 577, 304, 7726, 29889, 13, 29902, 9024, 445, 4274, 491, 1798, 26082, 17129, 297, 278, 1833, 1400, 29892, 607, 18568, 297, 2107, 9493, 278, 14451, 310, 278, 3865, 29928, 3301, 297, 9556, 29892, 12272, 7807, 599, 310, 1438, 22082, 29879, 1048, 23151, 1641, 5220, 287, 491, 22057, 29892, 470, 278, 21790, 816, 789, 29879, 29892, 470, 278, 8408, 9735, 2219, 29892, 470, 278, 9124, 414, 29892, 321, 312, 29889, 21988, 1623, 322, 1303, 372, 565, 366, 7359, 29915, 29873, 3447, 29889, 306, 29915, 29885, 884, 5279, 5183, 940, 10058, 350, 29889, 402, 441, 331, 5790, 29915, 29879, 27040, 23514, 29901, 4634, 411, 23151, 29892, 607, 8348, 5562, 368, 19138, 7093, 278, 14451, 310, 278, 3865, 29928, 3301, 297, 925, 263, 2846, 6515, 29889, 2296, 5353, 267, 278, 6555, 13500, 310, 278, 13564, 436, 367, 261, 298, 4293, 408, 11705, 292, 7600, 322, 1162, 9216, 358, 1644, 414, 313, 915, 261, 298, 4293, 505, 263, 1472, 4955, 408, 8604, 11705, 292, 7600, 297, 9556, 29897, 310, 278, 3865, 29928, 3301, 29892, 278, 7910, 297, 5972, 537, 310, 278, 3865, 29928, 3301, 1494, 278, 17407, 8095, 310, 29871, 29896, 29929, 29906, 29929, 29892, 322, 23151, 29915, 29879, 14231, 304, 443, 568, 599, 24611, 310, 5332, 12459, 448, 18408, 2879, 29892, 28672, 8415, 1446, 29892, 13936, 29892, 7631, 26202, 29892, 2215, 13269, 29892, 17162, 29892, 27335, 29892, 8041, 29892, 25550, 414, 29892, 285, 19467, 29892, 4344, 448, 1090, 278, 289, 7310, 310, 3086, 10307, 1608, 29889, 13, 14084, 304, 4340, 766, 11944, 277, 445, 2969, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 5220, 287, 491, 376, 1552, 22057, 613, 2050, 278, 1494, 429, 2265, 415, 310, 5765, 26410, 7362, 546, 29915, 29879, 1818, 1303, 3143, 29892, 450, 1570, 14525, 2904, 265, 29901, 16025, 11644, 830, 647, 22569, 448, 319, 6518, 272, 314, 293, 6811, 1493, 310, 278, 20315, 29892, 16221, 2738, 322, 12884, 293, 29766, 1144, 310, 278, 1570, 2787, 8170, 29901, 13, 8439, 338, 884, 278, 15983, 393, 376, 1576, 16728, 9124, 414, 29908, 470, 376, 1576, 796, 291, 391, 9124, 414, 29908, 313, 3880, 4049, 1006, 3167, 2197, 29897, 1436, 8362, 23151, 29889, 2216, 1565, 29889, 5011, 28625, 29892, 297, 670, 4817, 441, 1230, 664, 29892, 11644, 4231, 8362, 23151, 14579, 9004, 1078, 3755, 304, 278, 21138, 29889, 13, 797, 697, 2777, 29892, 263, 16728, 22347, 261, 297, 9556, 1258, 2367, 6909, 304, 278, 11409, 29875, 9173, 29994, 29886, 13479, 304, 278, 14451, 310, 21834, 23151, 29994, 4187, 1906, 29199, 892, 8688, 304, 1371, 23151, 29915, 29879, 938, 336, 29899, 22633, 19626, 304, 5040, 23151, 29889, 1205, 15020, 445, 2114, 29892, 777, 376, 5031, 374, 1862, 29908, 1603, 1827, 393, 376, 1576, 22057, 7437, 287, 23151, 1213, 13, 14804, 310, 1906, 1058, 26320, 472, 278, 5272, 279, 310, 445, 302, 787, 1947, 274, 568, 263, 7353, 29878, 10835, 29899, 20910, 566, 352, 296, 1842, 310, 15504, 29891, 1677, 1144, 23437, 23151, 29915, 29879, 10213, 10253, 414, 29892, 14750, 575, 14981, 3971, 491, 697, 376, 29903, 333, 3801, 3362, 3074, 1699, 697, 310, 1906, 376, 29967, 809, 728, 9124, 414, 1213, 1205, 445, 1842, 29892, 408, 591, 29915, 345, 1497, 29892, 338, 263, 5227, 566, 29889, 13, 1576, 5683, 4942, 29889, 16477, 317, 1851, 29915, 29879, 14406, 7103, 322, 278, 390, 895, 310, 23151, 756, 21201, 445, 6368, 29892, 2729, 297, 760, 373, 278, 3362, 3074, 6427, 14596, 322, 756, 2183, 4340, 12666, 284, 2133, 304, 445, 22082, 3002, 29994, 509, 2806, 367, 5625, 9571, 29889, 13, 14689, 24388, 322, 17266, 800, 1258, 664, 411, 278, 23151, 22384, 29892, 5491, 263, 3133, 362, 310, 3517, 18161, 15196, 4110, 2675, 1250, 1602, 3076, 29892, 541, 445, 471, 451, 760, 310, 738, 4595, 21588, 29875, 10068, 304, 6963, 23151, 304, 3081, 29889, 450, 5995, 393, 278, 24715, 3942, 471, 10160, 304, 278, 14451, 310, 23151, 338, 1790, 22082, 29889, 19323, 21856, 4512, 29994, 1217, 7336, 381, 261, 310, 278, 24715, 22337, 29891, 29994, 735, 314, 1475, 278, 3935, 14209, 18830, 278, 24715, 29899, 29950, 277, 1358, 10483, 297, 670, 3143, 29892, 3082, 360, 15290, 29891, 29901, 25068, 25804, 29892 ]	1,332,826	4,096	CommonCrawl	8	11
Fortune and the Politics of Deceit in the House of Bush and puts the facts in proper perspective. If Hitler and the NSDAP were "Rothschild agents" or "Jewish puppets", why on earth did they do things like this or this or this? Why did they make movies like this or the one shown below if they were in the pocket of the Rothschilds and other Jewish bankers? Why did Hitler perfectly describe the Big Lie technique (Holohoax & 9/11) used by the Jews to advance their "New World Order", deceive and rob Gentiles, and subvert their governments, economy, and culture if he was secretly working for them? But it remained for the Jews, with their unqualified capacity for falsehood, and their fighting comrades, the Marxists, to impute responsibility for the downfall precisely to the man who alone had shown a superhuman will and energy in his effort to prevent the catastrophe which he had foreseen and to save the nation from that hour of complete overthrow and shame. By placing responsibility for the loss of the world war on the shoulders of Ludendorff they took away the weapon of moral right from the only adversary dangerous enough to be likely to succeed in bringing the betrayers of the Fatherland to Justice. All this was inspired by the principle - which is quite true in itself - that in the big lie there is always a certain force of credibility; because the broad masses of a nation are always more easily corrupted in the deeper strata of their emotional nature than consciously or voluntarily; and thus in the primitive simplicity of their minds they more readily fall victims to the big lie than the small lie, since they themselves often tell small lies in little matters but would be ashamed to resort to large-scale falsehoods. It would never come into their heads to fabricate colossal untruths, and they would not believe that others could have the impudence to distort the truth so infamously. Even though the facts which prove this to be so may be brought clearly to their minds, they will still doubt and waver and will continue to think that there may be some other explanation. For the grossly impudent lie always leaves traces behind it, even after it has been nailed down, a fact which is known to all expert liars in this world and to all who conspire together in the art of lying. These people know only too well how to use falsehood for the basest purposes. From time immemorial; however, the Jews have known better than any others how falsehood and calumny can be exploited. Is not their very existence founded on one great lie, namely, that they are a religious community, whereas in reality they are a race? And what a race! One of the greatest thinkers that mankind has produced has branded the Jews for all time with a statement which is profoundly and exactly true. He (Schopenhauer) called the Jew "The Great Master of Lies". Those who do not realize the truth of that statement, or do not wish to believe it, will never be able to lend a hand in helping Truth to prevail. - Adolf Hitler, quote from Mein Kampf (page 184-185) Why did Joseph Goebbels and other NSDAP leaders say things like this if they weren't for real about their convictions? The historic responsibility of world Jewry for the outbreak and widening of this war has been proven so clearly that it does not need to be talked about any further. The Jews wanted war, and now they have it. But the Führer's prophecy of 30 January 1939 to the German Reichstag is also being fulfilled: If international finance Jewry should succeed in plunging the world into war once again, the result will be not the Bolshevization of the world and thereby the victory of the Jews, but rather the destruction of the Jewish race in Europe. We are seeing the fulfillment of the prophecy. The Jews are receiving a penalty that is certainly hard, but more than deserved. World Jewry erred in adding up the forces available to it for this war, and now is gradually experiencing the destructon that it planned for us, and would have carried out without a second thought if it had possessed the ability. It is perishing according its own law: "An eye for an eye, a tooth for a tooth." Every Jew is our enemy in this historic struggle, regardless of whether he vegetates in a Polish ghetto or carries on his parasitic existence in Berlin or Hamburg or blows the trumpets of war in New York or Washington	0.415442	0.350674	-0.520664	1.070849	[ 0.20862116666829722, 0.6222631462259228 ]	[ 0.44557770289723325, 0.25577107327840304 ]	[ -0.43902882404177496, -0.6022993400508873 ]	[ 0.9824025809506501, 1.1592957591918462 ]	1,024	[ 512, 512 ]	[ 7236, 1540, 322, 278, 6934, 1199, 310, 897, 346, 277, 297, 278, 5619, 310, 24715, 322, 15223, 278, 17099, 297, 1571, 18520, 29889, 13, 3644, 23151, 322, 278, 3865, 29928, 3301, 892, 376, 29934, 720, 816, 789, 19518, 29908, 470, 376, 29967, 809, 728, 2653, 27421, 613, 2020, 373, 8437, 1258, 896, 437, 2712, 763, 445, 470, 445, 470, 445, 29973, 13, 11008, 1258, 896, 1207, 2351, 583, 763, 445, 470, 278, 697, 4318, 2400, 565, 896, 892, 297, 278, 24589, 310, 278, 21790, 816, 789, 29879, 322, 916, 16728, 9124, 414, 29973, 13, 11008, 1258, 23151, 7970, 8453, 278, 7997, 7326, 11043, 313, 19984, 1148, 29877, 1165, 669, 29871, 29929, 29914, 29896, 29896, 29897, 1304, 491, 278, 22057, 304, 6564, 1009, 376, 4373, 2787, 8170, 613, 23332, 573, 322, 10832, 20655, 5475, 29892, 322, 1014, 1765, 1009, 4095, 1860, 29892, 26504, 29892, 322, 9257, 565, 540, 471, 7035, 368, 1985, 363, 963, 29973, 13, 6246, 372, 9488, 363, 278, 22057, 29892, 411, 1009, 443, 15380, 2164, 13284, 363, 2089, 6614, 29892, 322, 1009, 17770, 419, 29878, 3076, 29892, 278, 28579, 2879, 29892, 304, 527, 649, 29872, 23134, 363, 278, 1623, 11950, 17503, 304, 278, 767, 1058, 7432, 750, 4318, 263, 2428, 26029, 674, 322, 5864, 297, 670, 7225, 304, 5557, 278, 6635, 579, 1336, 354, 607, 540, 750, 363, 968, 264, 322, 304, 4078, 278, 5233, 515, 393, 7234, 310, 4866, 975, 20539, 322, 28503, 29889, 2648, 24421, 23134, 363, 278, 6410, 310, 278, 3186, 1370, 373, 278, 26671, 310, 8591, 12184, 600, 896, 3614, 3448, 278, 28639, 310, 14731, 1492, 515, 278, 871, 19901, 653, 18215, 3307, 304, 367, 5517, 304, 9269, 297, 20794, 278, 1010, 764, 414, 310, 278, 17852, 1049, 304, 17181, 29889, 2178, 445, 471, 20603, 491, 278, 12502, 448, 607, 338, 3755, 1565, 297, 3528, 448, 393, 297, 278, 4802, 3804, 727, 338, 2337, 263, 3058, 4889, 310, 6625, 4127, 29936, 1363, 278, 7300, 23063, 310, 263, 5233, 526, 2337, 901, 5948, 1034, 14214, 297, 278, 25871, 851, 532, 310, 1009, 23023, 1848, 5469, 1135, 1136, 455, 5794, 470, 27081, 6275, 29936, 322, 4550, 297, 278, 19269, 23205, 310, 1009, 27656, 896, 901, 28520, 6416, 6879, 9893, 304, 278, 4802, 3804, 1135, 278, 2319, 3804, 29892, 1951, 896, 6053, 4049, 2649, 2319, 12185, 297, 2217, 13750, 541, 723, 367, 23723, 2795, 304, 25362, 304, 2919, 29899, 7052, 2089, 6614, 29879, 29889, 739, 723, 2360, 2041, 964, 1009, 15883, 304, 18187, 403, 784, 2209, 284, 443, 509, 2806, 29879, 29892, 322, 896, 723, 451, 4658, 393, 4045, 1033, 505, 278, 2411, 566, 663, 304, 1320, 441, 278, 8760, 577, 3041, 314, 5794, 29889, 7753, 2466, 278, 17099, 607, 6356, 445, 304, 367, 577, 1122, 367, 6296, 9436, 304, 1009, 27656, 29892, 896, 674, 1603, 7404, 322, 11324, 369, 322, 674, 6773, 304, 1348, 393, 727, 1122, 367, 777, 916, 8252, 29889, 1152, 278, 22683, 368, 2411, 10385, 3804, 2337, 11308, 26695, 5742, 372, 29892, 1584, 1156, 372, 756, 1063, 1055, 2356, 1623, 29892, 263, 2114, 607, 338, 2998, 304, 599, 17924, 619, 1503, 297, 445, 3186, 322, 304, 599, 1058, 21588, 533, 4208, 297, 278, 1616, 310, 19214, 29889, 4525, 2305, 1073, 871, 2086, 1532, 920, 304, 671, 2089, 6614, 363, 278, 2362, 342, 11976, 29889, 13, 4591, 931, 5198, 331, 9020, 29936, 3138, 29892, 278, 22057, 505, 2998, 2253, 1135, 738, 4045, 920, 2089, 6614, 322, 1208, 1227, 29891, 508, 367, 16035, 1573, 29889, 1317, 451, 1009, 1407, 10379, 11091, 373, 697, 2107, 3804, 29892, 18451, 29892, 393, 896, 526, 263, 12962, 7881, 29892, 13452, 297, 16832, 896, 526, 263, 8175, 29973, 1126, 825, 263, 8175, 29991, 3118, 310, 278, 14176, 1348, 414, 393, 767, 14380, 756, 7371, 756, 14982, 287, 278, 22057, 363, 599, 931, 411, 263, 3229, 607, 338, 2600, 618, 368, 322, 3721, 1565, 29889, 940, 313, 4504, 3150, 29882, 7547, 29897, 2000, 278, 9576, 376, 1576, 7027, 9082, 310, 365, 583, 1642, 16025, 1058, 437, 451, 16289, 278, 8760, 310, 393, 3229, 29892, 470, 437, 451, 6398, 304, 4658, 372, 29892, 674, 2360, 367, 2221, 304, 301, 355, 263, 1361, 297, 19912, 1605, 2806, 304, 12379, 737, 29889, 13, 29899, 21834, 23151, 29892, 14978, 515, 2191, 262, 476, 16817, 313, 3488, 29871, 29896, 29947, 29946, 29899, 29896, 29947, 29945, 29897, 13, 11008, 1258, 6936, 2921, 27885, 1379, 322, 916, 3865, 29928, 3301, 20251, 1827, 2712, 763, 445, 565, 896, 2949, 264, 29915, 29873, 363, 1855, 1048, 1009, 7602, 919, 1080, 29973, 13, 1576, 22879, 23134, 310, 3186, 9576, 719, 363, 278, 714, 8690, 322, 281, 3615, 292, 310, 445, 1370, 756, 1063, 16413, 577, 9436, 393, 372, 947, 451, 817, 304, 367, 24867, 1048, 738, 4340, 29889, 450, 22057, 5131, 1370, 29892, 322, 1286, 896, 505, 372, 29889, 1205, 278, 383, 4000, 261, 29915, 29879, 3107, 354, 1270, 310, 29871, 29941, 29900, 5490, 29871, 29896, 29929, 29941, 29929, 304, 278, 5332, 9320, 24403, 338, 884, 1641, 6095, 26940, 29901, 960, 6121, 1436, 749, 9576, 719, 881, 9269, 297, 715, 686, 292, 278, 3186, 964, 1370, 2748, 1449, 29892, 278, 1121, 674, 367, 451, 278, 350, 3775, 354, 29894, 2133, 310, 278, 3186, 322, 27999, 278, 15354, 310, 278, 22057, 29892, 541, 3265, 278, 22104, 310, 278, 16728, 8175, 297, 4092, 29889, 13, 4806, 526, 8790, 278, 6095, 5589, 358, 310, 278, 3107, 354, 1270, 29889, 450, 22057, 526, 13442, 263, 27368, 393, 338, 8959, 2898, 29892, 541, 901, 1135, 553, 9841, 29889, 2787, 9576, 719, 604, 1127, 297, 4417, 701, 278, 8249, 3625, 304, 372, 363, 445, 1370, 29892, 322, 1286, 338, 22020, 10623, 3277, 278, 17912, 265, 393, 372, 20458, 363, 502, 29892, 322, 723, 505, 8988, 714, 1728, 263, 1473, 2714, 565, 372, 750, 25622, 278, 11509, 29889, 739, 338, 639, 14424, 5034, 967, 1914, 4307, 29901, 376, 2744, 10977, 363, 385, 10977, 29892, 263, 304, 720, 363, 263, 304, 720, 1213, 13, 26526, 9576, 338, 1749, 11103, 297, 445, 22879, 21117, 29892, 17126, 310, 3692, 540, 18655, 1078, 297, 263, 19919, 24170, 8563, 470, 1559, 2722, 373, 670, 610, 294, 277, 293, 10379, 297, 5115, 470, 14847, 470, 13031, 29879, 278, 534, 3427, 1691, 310, 1370, 297, 1570, 3088, 470, 7660 ]	1,332,826	5,120	CommonCrawl	8	11
. All Jews by virtue of their birth and their race are part of an international conspiracy against National Socialist Germany. They want its defeat and annihilation, and do all in their power to bring it about. That they can do nothing inside the Reich is hardly a sign of their loyalty, but rather of the appropriate measures we took against them. [...] If Hitler and the NSDAP were indeed "puppets of the bankers" or "stooges of the Jews", why on earth were they speaking openly and honestly about the Jews, publicly naming the enemy and exposing his agenda? And Hitler and the NSDAP were not only being honest with their fellow countryman (and world, really) about the Jews and the disgraceful Versailles Treaty, they made serious moves to counteract and redress these problems. Second, Hitler was not "the founder of Israel". This is absurd, and I'll explain why. It was Britain, through the Balfour Declaration, addressed to none other than Lord Rothschild himself, that initially facilitated the establishment of the illegitimate terrorist state of Israel, not Germany. Germany never supported or wanted a Jewish state in Palestine. Hitler and NSDAP policy were primarily concerned with getting the Jews out of Germany (and eventually all of Europe), and did in fact collaborate with Zionist organizations and factions that promoted Jewish emigration to Palestine. They even entered into economic agreements with these organizations to not only facilitate the emigration of Jews from Germany, but also bolster Germans exports. Mark Weber of the Institute for Historical Review lays this out quite clearly in an article titled, Zionism and the Third Reich: [...] German support for Zionism was not unlimited. Government and Party officials were very mindful of the continuing campaign by powerful Jewish communities in the United States, Britain and other countries to mobilize "their" governments and fellow citizens against Germany. As long as world Jewry remained implacably hostile toward National Socialist Germany, and as long as the great majority of Jews around the world showed little eagerness to resettle in the Zionist "promised land," a sovereign Jewish state in Palestine would not really "solve" the international Jewish question. Instead, German officials reasoned, it would immeasurably strengthen this dangerous anti-German campaign. German backing for Zionism was therefore limited to support for a Jewish homeland in Palestine under British control, not a sovereign Jewish state. A Jewish state in Palestine, the Foreign Minister informed diplomats in June 1937, would not be in Germany's interest because it would not be able to absorb all Jews around the world, but would only serve as an additional power base for international Jewry, in much the same way as Moscow served as a base for international Communism. Reflecting something of a shift in official policy, the German press expressed much greater sympathy in 1937 for Palestinian Arab resistance to Zionist ambitions, at a time when tension and conflict between Jews and Arabs in Palestine was sharply increasing. A Foreign Office circular bulletin of June 22, 1937, cautioned that in spite of support for Jewish settlement in Palestine, "it would nevertheless be a mistake to assume that Germany supports the formation of a state structure in Palestine under some form of Jewish control. In view of the anti-German agitation of international Jewry, Germany cannot agree that the formation of a Palestine Jewish state would help the peaceful development of the nations of the world." "The proclamation of a Jewish state or a Jewish-administrated Palestine," warned an internal memorandum by the Jewish affairs section of the SS, "would create for Germany a new enemy, one that would have a deep influence on developments in the Near East." Another SS agency predicted that a Jewish state "would work to bring special minority protection to Jews in every country, therefore giving legal protection to the exploitation activity of world Jewry." In January 1939, Hitler's new Foreign Minister, Joachim von Ribbentrop, likewise warned in another circular bulletin that "Germany must regard the formation of a Jewish state as dangerous" because it "would bring an international increase in power to world Jewry." Hitler and the NSDAP did not advocate for or support a Jewish state in Palestine. In fact, in Mein Kampf Hitler accurately described what a Jewish state would look like should the Gentile world allow it to happen: The Jew's domination in the state seems so assured that now not only can he call himself a Jew again,	0.712662	1.383867	0.281898	1.575515	[ 0.5017317084740319, 0.9235917406056501 ]	[ 1.1188540494696875, 1.6488801095373642 ]	[ 0.06251283872796425, 0.5012825361194428 ]	[ 1.4714601913821923, 1.679569812842423 ]	1,024	[ 512, 512 ]	[ 29889, 2178, 22057, 491, 27935, 310, 1009, 12060, 322, 1009, 8175, 526, 760, 310, 385, 6121, 21588, 29875, 10068, 2750, 3086, 10307, 391, 9556, 29889, 2688, 864, 967, 20653, 322, 6957, 29882, 8634, 29892, 322, 437, 599, 297, 1009, 3081, 304, 6963, 372, 1048, 29889, 2193, 896, 508, 437, 3078, 2768, 278, 9320, 338, 15155, 263, 1804, 310, 1009, 28108, 1017, 29892, 541, 3265, 310, 278, 8210, 15366, 591, 3614, 2750, 963, 29889, 21945, 13, 3644, 23151, 322, 278, 3865, 29928, 3301, 892, 6200, 376, 3746, 27421, 310, 278, 9124, 414, 29908, 470, 376, 7864, 468, 267, 310, 278, 22057, 613, 2020, 373, 8437, 892, 896, 13590, 1722, 368, 322, 15993, 368, 1048, 278, 22057, 29892, 970, 368, 22006, 278, 11103, 322, 14060, 292, 670, 946, 8395, 29973, 1126, 23151, 322, 278, 3865, 29928, 3301, 892, 451, 871, 1641, 15993, 411, 1009, 10404, 2613, 509, 21909, 313, 392, 3186, 29892, 2289, 29897, 1048, 278, 22057, 322, 278, 766, 3874, 346, 1319, 10138, 29874, 7545, 6479, 11156, 29892, 896, 1754, 10676, 16229, 304, 6795, 627, 322, 2654, 1253, 1438, 4828, 29889, 13, 11863, 29892, 23151, 471, 451, 376, 1552, 25331, 310, 11996, 1642, 910, 338, 6425, 18245, 29892, 322, 306, 29915, 645, 5649, 2020, 29889, 13, 3112, 471, 14933, 29892, 1549, 278, 350, 3131, 473, 3826, 23838, 29892, 20976, 304, 5642, 916, 1135, 6171, 21790, 816, 789, 3654, 29892, 393, 12919, 16089, 22731, 278, 25012, 310, 278, 980, 1397, 277, 6490, 15115, 391, 2106, 310, 11996, 29892, 451, 9556, 29889, 9556, 2360, 6969, 470, 5131, 263, 16728, 2106, 297, 22053, 457, 29889, 23151, 322, 3865, 29928, 3301, 8898, 892, 19434, 15041, 411, 2805, 278, 22057, 714, 310, 9556, 313, 392, 10201, 599, 310, 4092, 511, 322, 1258, 297, 2114, 11465, 403, 411, 796, 291, 391, 25700, 322, 2258, 1953, 393, 21201, 16728, 953, 16783, 304, 22053, 457, 29889, 2688, 1584, 7802, 964, 17407, 8571, 4110, 411, 1438, 25700, 304, 451, 871, 16089, 10388, 278, 953, 16783, 310, 22057, 515, 9556, 29892, 541, 884, 15772, 2475, 7287, 550, 29586, 29889, 13, 9802, 1334, 495, 310, 278, 8907, 363, 20315, 13957, 301, 1036, 445, 714, 3755, 9436, 297, 385, 4274, 25278, 29892, 796, 291, 1608, 322, 278, 18008, 9320, 29901, 13, 29961, 17361, 5332, 2304, 363, 796, 291, 1608, 471, 451, 443, 29044, 29889, 10354, 322, 9173, 24921, 892, 1407, 3458, 1319, 310, 278, 3133, 292, 11531, 491, 13988, 16728, 23507, 297, 278, 3303, 3900, 29892, 14933, 322, 916, 10916, 304, 27227, 675, 376, 1552, 381, 29908, 4095, 1860, 322, 10404, 18363, 2750, 9556, 29889, 1094, 1472, 408, 3186, 9576, 719, 9488, 2411, 4620, 2197, 3495, 488, 11183, 3086, 10307, 391, 9556, 29892, 322, 408, 1472, 408, 278, 2107, 13638, 310, 22057, 2820, 278, 3186, 10018, 2217, 321, 351, 824, 404, 304, 620, 1803, 280, 297, 278, 796, 291, 391, 376, 14032, 3368, 2982, 1699, 263, 577, 369, 7577, 16728, 2106, 297, 22053, 457, 723, 451, 2289, 376, 2929, 345, 29908, 278, 6121, 16728, 1139, 29889, 8669, 29892, 5332, 24921, 2769, 287, 29892, 372, 723, 527, 1004, 294, 332, 2197, 9324, 264, 445, 18215, 9418, 29899, 29954, 3504, 11531, 29889, 5332, 27436, 363, 796, 291, 1608, 471, 5480, 9078, 304, 2304, 363, 263, 16728, 3632, 14045, 297, 22053, 457, 1090, 4908, 2761, 29892, 451, 263, 577, 369, 7577, 16728, 2106, 29889, 13, 29909, 16728, 2106, 297, 22053, 457, 29892, 278, 19358, 7668, 23388, 13487, 1446, 297, 5306, 29871, 29896, 29929, 29941, 29955, 29892, 723, 451, 367, 297, 9556, 29915, 29879, 4066, 1363, 372, 723, 451, 367, 2221, 304, 6425, 11831, 599, 22057, 2820, 278, 3186, 29892, 541, 723, 871, 9080, 408, 385, 5684, 3081, 2967, 363, 6121, 9576, 719, 29892, 297, 1568, 278, 1021, 982, 408, 25820, 6766, 408, 263, 2967, 363, 6121, 20473, 1608, 29889, 9897, 781, 292, 1554, 310, 263, 9500, 297, 6221, 8898, 29892, 278, 5332, 3965, 13384, 1568, 7621, 29738, 297, 29871, 29896, 29929, 29941, 29955, 363, 22053, 262, 713, 10387, 17711, 304, 796, 291, 391, 3181, 2187, 29892, 472, 263, 931, 746, 260, 2673, 322, 14529, 1546, 22057, 322, 10387, 29879, 297, 22053, 457, 471, 15301, 368, 10231, 29889, 13, 29909, 19358, 11367, 19308, 24334, 262, 310, 5306, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 29892, 5777, 918, 287, 393, 297, 21100, 310, 2304, 363, 16728, 16493, 297, 22053, 457, 29892, 376, 277, 723, 2360, 16561, 367, 263, 10171, 304, 5251, 393, 9556, 11286, 278, 12409, 310, 263, 2106, 3829, 297, 22053, 457, 1090, 777, 883, 310, 16728, 2761, 29889, 512, 1776, 310, 278, 9418, 29899, 29954, 3504, 946, 7018, 310, 6121, 9576, 719, 29892, 9556, 2609, 8661, 393, 278, 12409, 310, 263, 22053, 457, 16728, 2106, 723, 1371, 278, 10776, 1319, 5849, 310, 278, 19079, 310, 278, 3186, 1213, 376, 1576, 410, 15719, 362, 310, 263, 16728, 2106, 470, 263, 16728, 29899, 6406, 2132, 630, 22053, 457, 1699, 1370, 9571, 385, 7463, 26959, 392, 398, 491, 278, 16728, 19469, 4004, 310, 278, 5886, 29892, 376, 29893, 483, 1653, 363, 9556, 263, 716, 11103, 29892, 697, 393, 723, 505, 263, 6483, 9949, 373, 2693, 1860, 297, 278, 26206, 6932, 1213, 7280, 5886, 946, 3819, 25383, 393, 263, 16728, 2106, 376, 29893, 483, 664, 304, 6963, 4266, 9461, 537, 13047, 304, 22057, 297, 1432, 4234, 29892, 5480, 6820, 11706, 13047, 304, 278, 16035, 7018, 6354, 310, 3186, 9576, 719, 1213, 512, 5490, 29871, 29896, 29929, 29941, 29929, 29892, 23151, 29915, 29879, 716, 19358, 7668, 29892, 3650, 24039, 1005, 27461, 29890, 296, 1336, 29892, 763, 3538, 1370, 9571, 297, 1790, 19308, 24334, 262, 393, 376, 29954, 837, 1384, 1818, 4880, 278, 12409, 310, 263, 16728, 2106, 408, 18215, 29908, 1363, 372, 376, 29893, 483, 6963, 385, 6121, 7910, 297, 3081, 304, 3186, 9576, 719, 1213, 13, 29950, 277, 1358, 322, 278, 3865, 29928, 3301, 1258, 451, 22545, 403, 363, 470, 2304, 263, 16728, 2106, 297, 22053, 457, 29889, 512, 2114, 29892, 297, 2191, 262, 476, 16817, 23151, 7913, 2486, 5439, 825, 263, 16728, 2106, 723, 1106, 763, 881, 278, 20655, 488, 3186, 2758, 372, 304, 3799, 29901, 13, 1576, 9576, 29915, 29879, 2432, 3381, 297, 278, 2106, 2444, 577, 28715, 393, 1286, 451, 871, 508, 540, 1246, 3654, 263, 9576, 1449, 29892 ]	1,332,826	6,144	CommonCrawl	8	11
but he ruthlessly admits his ultimate national and political designs. A section of his race openly owns itself to be a foreign people, yet even here they lie. For while the Zionists try to make the rest of the world believe that the national consciousness of the Jew finds its satisfaction in the creation of a Palestinian state, the Jews again slyly dupe the dumb Goyim. It doesn't even enter their heads to build up a Jewish state in Palestine for the purpose of living there; all they want is a central organization for their international world swindle, endowed with its own sovereign rights and removed from the intervention of other states: a haven for convicted scoundrels and a university for budding crooks. Bottom line is, the Jews were dead set on establishing their criminal, usurping state in Palestine, not only to fulfill their twisted messianic prophecies, but also to gain a safe haven and central headquarters for their global crime syndicate, a fact Hitler recognized. He wanted the Jews out of Germany in order to rebuild German society after the devastation of WWI. The Jews in Palestine perfected their use of terrorism and underhandedness and declared "independence" shortly after Germany's defeat in WWII, using their fake "Holocaust" story and agents of influence across the globe to sell their false narrative of history to the rest of the world. And who were the first governments to recognize the illegitimate, terrorist state of Israel? Two of international Jewry's biggest puppets: the United States and the Soviet Union. On May 14, 1948, the leaders of the Jewish organizations in Palestine, headed byDavid Ben-Gurion,proclaimed the establishment of the State of Israel, to take effect at midnight that night. At that point, the State of Israel came into existence. The United States recognized the provisional Jewish government as de facto authority of the Jewish state within minutes. The Soviet Union granted de jure recognition almost immediately in 1948 along with seven other states within the next five days (Guatemala, Byelorussia, the Ukraine, Poland, Czechoslovakia, Uruguay, and Yugoslavia). [Source] Hitler and National Socialist Germany's ultimate aim was the removal of the Jews from Germany and Europe, and they collaborated with the Zionist movement to accomplish this goal. After the Jews and their puppet Allies brutally destroyed Germany in WWII, which represented the greatest threat in history to the global Jewish crime network behind "The New World Order", it was only a matter of time before "Israel" would be officially established. Hitler was not "the founder of Israel" as many continue to claim, and was not responsible for the establishment of that illegitimate, criminal hellhole brutally occupying Palestine. Hitler and National Socialist Germany were destroyed to pave the way for the establishment of Israel. Blaming Hitler and National Socialist Germany for something the Jews were determined to do on their own – with the assistance of their puppets in the West – is a gross distortion of history. Third, Hitler did not start WWII, and he was not a war-monger. Hitler wanted work and peace, as he outlined in numerous speeches after he was elected Chancellor in 1933. He wanted to rebuild the German economy, and help the German worker and farmer. Read all about it here. Further, we have to remember that international Jewry declared war on Germany in 1933, and some Jewish leaders, while projecting their own tribe's long established goals of world domination onto the Germans, actually called for the total annihilation of Germany: For it must be patent by now that while all the Germans may not approve of the means being employed by the Nazis in achieving German-world-dominion, they are practically unanimous in agreeing that that goal must, now or in the future, be definitely achieved by Germany. Were the German nations to win this war, not one German would hesitate laying claim to a share in the loot … Yet defeat will on no account erase their desire to conquer and rule the world. There is only one way to frustrate such a desire: the goal of world-dominion must be removed from the reach of the German and the only way to accomplish that is to remove the German from the world! -Theodore Kaufman, Germany Must Perish! Organized Jewry has been and remains the inciter of global war and genocide, including WWII. Consider what Jewish	-0.198172	0.617478	-1.03568	1.330986	[ 0.3455887095681733, -0.7419335810568426 ]	[ 0.861003533761088, 0.3739525596448445 ]	[ -0.741475566318849, -1.3298834842079996 ]	[ 1.4714601913821923, 1.190512202410881 ]	1,024	[ 512, 512 ]	[ 541, 540, 364, 2806, 23769, 7336, 1169, 670, 8494, 6490, 4797, 322, 8604, 25517, 29889, 319, 4004, 310, 670, 8175, 1722, 368, 1914, 29879, 3528, 304, 367, 263, 9117, 2305, 29892, 3447, 1584, 1244, 896, 3804, 29889, 1152, 1550, 278, 796, 291, 2879, 1018, 304, 1207, 278, 1791, 310, 278, 3186, 4658, 393, 278, 4797, 19861, 2264, 310, 278, 9576, 14061, 967, 26470, 297, 278, 11265, 310, 263, 22053, 262, 713, 2106, 29892, 278, 22057, 1449, 269, 368, 368, 868, 412, 278, 270, 3774, 2921, 29891, 326, 29889, 739, 1838, 29915, 29873, 1584, 3896, 1009, 15883, 304, 2048, 701, 263, 16728, 2106, 297, 22053, 457, 363, 278, 6437, 310, 8471, 727, 29936, 599, 896, 864, 338, 263, 6555, 13013, 363, 1009, 6121, 3186, 2381, 513, 280, 29892, 1095, 20937, 411, 967, 1914, 577, 369, 7577, 10462, 322, 6206, 515, 278, 1006, 7316, 310, 916, 5922, 29901, 263, 7359, 363, 7602, 18186, 885, 618, 2674, 29879, 322, 263, 16372, 363, 8619, 8497, 8182, 12117, 29889, 13, 15342, 1196, 338, 29892, 278, 22057, 892, 7123, 731, 373, 10127, 292, 1009, 22161, 29892, 502, 332, 15702, 2106, 297, 22053, 457, 29892, 451, 871, 304, 6095, 5589, 1009, 3252, 12652, 4473, 713, 293, 3107, 354, 2478, 29892, 541, 884, 304, 11581, 263, 9109, 7359, 322, 6555, 26463, 363, 1009, 5534, 17268, 22898, 9593, 29892, 263, 2114, 23151, 14831, 29889, 940, 5131, 278, 22057, 714, 310, 9556, 297, 1797, 304, 337, 4282, 5332, 12459, 1156, 278, 2906, 579, 362, 310, 399, 22119, 29889, 450, 22057, 297, 22053, 457, 4922, 287, 1009, 671, 310, 15115, 1608, 322, 1090, 3179, 287, 2264, 322, 8052, 376, 262, 2716, 355, 663, 29908, 21734, 1156, 9556, 29915, 29879, 20653, 297, 399, 29956, 2687, 29892, 773, 1009, 25713, 376, 19984, 6400, 504, 29908, 5828, 322, 19518, 310, 9949, 4822, 278, 15482, 915, 304, 19417, 1009, 2089, 15474, 1230, 310, 4955, 304, 278, 1791, 310, 278, 3186, 29889, 1126, 1058, 892, 278, 937, 4095, 1860, 304, 18720, 278, 980, 1397, 277, 6490, 29892, 15115, 391, 2106, 310, 11996, 29973, 7803, 310, 6121, 9576, 719, 29915, 29879, 24842, 2653, 27421, 29901, 278, 3303, 3900, 322, 278, 15308, 7761, 29889, 13, 2951, 2610, 29871, 29896, 29946, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 278, 20251, 310, 278, 16728, 25700, 297, 22053, 457, 29892, 2343, 287, 491, 19504, 4111, 29899, 29954, 332, 291, 29892, 15439, 13190, 278, 25012, 310, 278, 4306, 310, 11996, 29892, 304, 2125, 2779, 472, 7145, 11147, 393, 4646, 29889, 13, 4178, 393, 1298, 29892, 278, 4306, 310, 11996, 2996, 964, 10379, 29889, 450, 3303, 3900, 14831, 278, 1326, 275, 1848, 16728, 5874, 408, 316, 2114, 29877, 14329, 310, 278, 16728, 2106, 2629, 6233, 29889, 450, 15308, 7761, 16896, 316, 432, 545, 19679, 4359, 7389, 297, 29871, 29896, 29929, 29946, 29947, 3412, 411, 9881, 916, 5922, 2629, 278, 2446, 5320, 3841, 313, 9485, 17533, 2883, 29892, 2648, 12779, 1558, 423, 29892, 278, 23961, 29892, 18898, 29892, 21489, 24022, 557, 423, 29892, 29233, 29892, 322, 612, 688, 17464, 423, 467, 518, 4435, 29962, 13, 29950, 277, 1358, 322, 3086, 10307, 391, 9556, 29915, 29879, 8494, 6490, 12242, 471, 278, 28744, 310, 278, 22057, 515, 9556, 322, 4092, 29892, 322, 896, 11465, 630, 411, 278, 796, 291, 391, 10298, 304, 12709, 445, 7306, 29889, 2860, 278, 22057, 322, 1009, 2653, 7988, 838, 3687, 26644, 635, 14416, 9556, 297, 399, 29956, 2687, 29892, 607, 9875, 278, 14176, 28469, 297, 4955, 304, 278, 5534, 16728, 17268, 3564, 5742, 376, 1576, 1570, 2787, 8170, 613, 372, 471, 871, 263, 4383, 310, 931, 1434, 376, 3624, 9058, 29908, 723, 367, 22444, 7841, 29889, 13, 29950, 277, 1358, 471, 451, 376, 1552, 25331, 310, 11996, 29908, 408, 1784, 6773, 304, 5995, 29892, 322, 471, 451, 14040, 363, 278, 25012, 310, 393, 980, 1397, 277, 6490, 29892, 22161, 23927, 29716, 26644, 635, 6919, 5414, 22053, 457, 29889, 23151, 322, 3086, 10307, 391, 9556, 892, 14416, 304, 282, 1351, 278, 982, 363, 278, 25012, 310, 11996, 29889, 3164, 11500, 23151, 322, 3086, 10307, 391, 9556, 363, 1554, 278, 22057, 892, 10087, 304, 437, 373, 1009, 1914, 785, 411, 278, 18872, 310, 1009, 2653, 27421, 297, 278, 3122, 785, 338, 263, 22683, 1320, 441, 291, 310, 4955, 29889, 13, 1349, 1823, 29892, 23151, 1258, 451, 1369, 399, 29956, 2687, 29892, 322, 540, 471, 451, 263, 1370, 29899, 29885, 549, 261, 29889, 23151, 5131, 664, 322, 10776, 29892, 408, 540, 714, 21354, 297, 12727, 12032, 267, 1156, 540, 471, 11467, 22433, 3729, 272, 297, 29871, 29896, 29929, 29941, 29941, 29889, 940, 5131, 304, 337, 4282, 278, 5332, 26504, 29892, 322, 1371, 278, 5332, 15645, 322, 2215, 1050, 29889, 7523, 599, 1048, 372, 1244, 29889, 13, 29943, 332, 721, 29892, 591, 505, 304, 6456, 393, 6121, 9576, 719, 8052, 1370, 373, 9556, 297, 29871, 29896, 29929, 29941, 29941, 29892, 322, 777, 16728, 20251, 29892, 1550, 2060, 292, 1009, 1914, 29563, 29915, 29879, 1472, 7841, 14433, 310, 3186, 2432, 3381, 11480, 278, 7287, 550, 29892, 2869, 2000, 363, 278, 3001, 6957, 29882, 8634, 310, 9556, 29901, 13, 2831, 372, 1818, 367, 2373, 296, 491, 1286, 393, 1550, 599, 278, 7287, 550, 1122, 451, 2134, 345, 310, 278, 2794, 1641, 15723, 491, 278, 11409, 275, 297, 3657, 15387, 5332, 29899, 11526, 29899, 24130, 291, 29892, 896, 526, 4120, 1711, 443, 11576, 681, 297, 8661, 292, 393, 393, 7306, 1818, 29892, 1286, 470, 297, 278, 5434, 29892, 367, 11630, 14363, 491, 9556, 29889, 399, 406, 278, 5332, 19079, 304, 5401, 445, 1370, 29892, 451, 697, 5332, 723, 19066, 10388, 6568, 292, 5995, 304, 263, 6232, 297, 278, 658, 327, 16088, 15175, 20653, 674, 373, 694, 3633, 604, 559, 1009, 13521, 304, 26474, 322, 5751, 278, 3186, 29889, 1670, 338, 871, 697, 982, 304, 1424, 4627, 403, 1316, 263, 13521, 29901, 278, 7306, 310, 3186, 29899, 24130, 291, 1818, 367, 6206, 515, 278, 6159, 310, 278, 5332, 322, 278, 871, 982, 304, 12709, 393, 338, 304, 3349, 278, 5332, 515, 278, 3186, 29991, 448, 1576, 29221, 29462, 1171, 29892, 9556, 19928, 2431, 728, 29991, 13, 27356, 1891, 9576, 719, 756, 1063, 322, 9242, 278, 5528, 1524, 310, 5534, 1370, 322, 2531, 29877, 8204, 29892, 3704, 399, 29956, 2687, 29889, 10056, 825, 16728 ]	1,332,826	7,168	CommonCrawl	8	11
writer Marcus Eli Ravage said in the January 1928 issue of Century Magazine: We [Jews] have been at the bottom not merely of the latest great war but of nearly all your wars, not only of the Russian but of every other major revolution in your history. We have brought discord and confusion and frustration into your personal and public life. We are still doing it. No one can tell how long we shall go on doing it. Fourth, I haven't bothered to read all of this or this, which allege that Hitler and the NSDAP were homosexuals. I think it's pretty ridiculous on its face. The demonization and slanders against this man are never ending it seems. Hitler is a Jew, Hitler is a Rothschild, Hitler is a puppet of the bankers, he's a homosexual, the Nazis secretly run the world, the Nazis have underground bases in Antarctica, the Nazis are on the moon… all of these ridiculous claims about Hitler and the NSDAP can't all be true, can they? Let's assume that Hitler and the NSDAP were in fact homosexuals. Can someone who supports this theory explain to me why that would matter? Would that change anything that Hitler said, wrote about, and accomplished? Finally, National Socialist Germany demonstrated how to effectively deal with the international Jewish conspiracy for a "New World Order", their subversion and perversion of the German culture, economy, and government, and their control of the mass media, at least temporarily. What are the prospects of a movement of this type gaining a foothold in American society? America today, as opposed to Germany in the 1920s and 30s, is essentially a multinational empire, a true melting pot of all races, nationalities, cultures, and lifestyles. National Socialism sought to unite all elements of Germany society on their common German heritage and Nordic (or Aryan or white, whatever term you want to use) race, and wasn't afraid or intimidated by organized Jewry, which long ago declared war on the Gentile world. How is that going to happen in America? What is going to unite all Americans to overcome and defeat the forces of the "New World Order", especially when there is (increasingly) no common race, no common culture, or no common ideology? Making matters worse, most Americans are abysmally ignorant and totally brainwashed by Jewish propaganda, "entertainment", and false history. I'd venture to say that most Americans don't even know how to use their brains properly. Not to mention the rise of harmful vaccines, pharmaceutical drugs, alcohol and other narcotics, poisonous foods and the general degeneracy of American society… we have a lot to overcome, anyone know where to start? http://johnfriendsblog.blogspot.ca/2012/06/more-thoughts-about-adolf-hitler-and.html laconas So, what lessons can be learned by studying the failed revolt against Jewish banking power by the rise of the NSDAP? Nobody censors what they agree with Quote from: laconas on August 17, 2012, 10:05:26 PM I'm dead tired and off to bed, I need to do some errands out of town early tomorrow. Meanwhile laconas, please do feel free to post YOUR thoughts, I would love to read them when I get back. Good night. Judson Great article sushigirl .... good info. 'Even if you didn't do it, we don't want you to do it again' jacob gold Quote from: sushigirl on August 17, 2012, 10:40:21 PM That film is what happened to america Quote from: jacob gold on August 18, 2012, 03:52:23 PM Precisely! I would choose a good dictator over this so-called democracy [with umpteen 'choices'] B.S. anytime. Whoever coined these words was correct: Democracy is "two wolves and a sheep deciding what to have for dinner." Quote from: sushigirl on August 19, 2012, 07:53:	-0.773094	-0.406762	-0.999538	0.041682	[ -0.0646290814169555, -1.4815583127161733 ]	[ 0.517202846149622, -1.3307258497620076 ]	[ -0.3902061843031278, -1.6088699970002691 ]	[ 0.8575368080745117, -0.7741726926871099 ]	1,024	[ 512, 512 ]	[ 9227, 27390, 26864, 28093, 482, 1497, 297, 278, 5490, 29871, 29896, 29929, 29906, 29947, 2228, 310, 24027, 17880, 29901, 13, 4806, 518, 29967, 809, 29879, 29962, 505, 1063, 472, 278, 5970, 451, 13586, 310, 278, 9281, 2107, 1370, 541, 310, 8886, 599, 596, 29129, 29892, 451, 871, 310, 278, 10637, 541, 310, 1432, 916, 4655, 19479, 297, 596, 4955, 29889, 1334, 505, 6296, 2313, 536, 322, 14679, 322, 1424, 11036, 964, 596, 7333, 322, 970, 2834, 29889, 1334, 526, 1603, 2599, 372, 29889, 1939, 697, 508, 2649, 920, 1472, 591, 4091, 748, 373, 2599, 372, 29889, 13, 29943, 473, 386, 29892, 306, 7359, 29915, 29873, 24738, 287, 304, 1303, 599, 310, 445, 470, 445, 29892, 607, 394, 4424, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 3632, 29438, 27101, 29889, 306, 1348, 372, 29915, 29879, 5051, 8177, 12906, 681, 373, 967, 3700, 29889, 450, 8033, 2133, 322, 269, 1049, 414, 2750, 445, 767, 526, 2360, 17140, 372, 2444, 29889, 13, 29950, 277, 1358, 338, 263, 9576, 29892, 23151, 338, 263, 21790, 816, 789, 29892, 23151, 338, 263, 2653, 7988, 310, 278, 9124, 414, 29892, 540, 29915, 29879, 263, 3632, 29438, 950, 29892, 278, 11409, 275, 7035, 368, 1065, 278, 3186, 29892, 278, 11409, 275, 505, 1090, 2057, 22561, 297, 5459, 27014, 983, 29892, 278, 11409, 275, 526, 373, 278, 18786, 30098, 599, 310, 1438, 8177, 12906, 681, 16726, 1048, 23151, 322, 278, 3865, 29928, 3301, 508, 29915, 29873, 599, 367, 1565, 29892, 508, 896, 29973, 13, 12024, 29915, 29879, 5251, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 297, 2114, 3632, 29438, 27101, 29889, 1815, 4856, 1058, 11286, 445, 6368, 5649, 304, 592, 2020, 393, 723, 4383, 29973, 10878, 393, 1735, 3099, 393, 23151, 1497, 29892, 5456, 1048, 29892, 322, 24799, 29973, 13, 12881, 635, 29892, 3086, 10307, 391, 9556, 28585, 920, 304, 17583, 5376, 411, 278, 6121, 16728, 21588, 29875, 10068, 363, 263, 376, 4373, 2787, 8170, 613, 1009, 1014, 3259, 322, 639, 3259, 310, 278, 5332, 9257, 29892, 26504, 29892, 322, 5874, 29892, 322, 1009, 2761, 310, 278, 4158, 5745, 29892, 472, 3203, 5382, 6275, 29889, 1724, 526, 278, 27289, 29879, 310, 263, 10298, 310, 445, 1134, 11581, 292, 263, 1701, 720, 1025, 297, 3082, 12459, 29973, 13, 29048, 9826, 29892, 408, 15869, 304, 9556, 297, 278, 29871, 29896, 29929, 29906, 29900, 29879, 322, 29871, 29941, 29900, 29879, 29892, 338, 13674, 263, 1773, 262, 1288, 3710, 533, 29892, 263, 1565, 9232, 1259, 3104, 310, 599, 19830, 29892, 4797, 1907, 29892, 4185, 1973, 29892, 322, 301, 7004, 5577, 29889, 3086, 10307, 1608, 18365, 304, 443, 568, 599, 3161, 310, 9556, 12459, 373, 1009, 3619, 5332, 902, 16639, 322, 5245, 293, 313, 272, 319, 719, 273, 470, 4796, 29892, 6514, 1840, 366, 864, 304, 671, 29897, 8175, 29892, 322, 9007, 29915, 29873, 13421, 470, 938, 326, 333, 630, 491, 19098, 9576, 719, 29892, 607, 1472, 8020, 8052, 1370, 373, 278, 20655, 488, 3186, 29889, 13, 5328, 338, 393, 2675, 304, 3799, 297, 6813, 29973, 1724, 338, 2675, 304, 443, 568, 599, 23035, 304, 25688, 322, 20653, 278, 8249, 310, 278, 376, 4373, 2787, 8170, 613, 7148, 746, 727, 338, 313, 262, 1037, 5832, 368, 29897, 694, 3619, 8175, 29892, 694, 3619, 9257, 29892, 470, 694, 3619, 1957, 3002, 29973, 13, 29924, 5086, 13750, 15029, 29892, 1556, 23035, 526, 633, 952, 29885, 635, 16245, 424, 322, 14909, 17294, 29893, 25936, 491, 16728, 13089, 5863, 29892, 376, 296, 13946, 358, 613, 322, 2089, 4955, 29889, 306, 29915, 29881, 9712, 545, 304, 1827, 393, 1556, 23035, 1016, 29915, 29873, 1584, 1073, 920, 304, 671, 1009, 4105, 1144, 6284, 29889, 2216, 304, 3585, 278, 14451, 310, 10311, 1319, 325, 5753, 1475, 29892, 1374, 22824, 346, 329, 936, 5883, 3174, 29892, 27231, 5391, 322, 916, 302, 5666, 327, 1199, 29892, 27908, 681, 9687, 29879, 322, 278, 2498, 3587, 759, 4135, 310, 3082, 12459, 30098, 591, 505, 263, 3287, 304, 25688, 29892, 5019, 1073, 988, 304, 1369, 29973, 13, 1124, 597, 29926, 6547, 7932, 1975, 7312, 29889, 7312, 17500, 29889, 1113, 29914, 29906, 29900, 29896, 29906, 29914, 29900, 29953, 29914, 5514, 29899, 386, 1774, 29879, 29899, 12717, 29899, 328, 4369, 29899, 27342, 1358, 29899, 392, 29889, 1420, 13, 433, 535, 294, 13, 6295, 29892, 825, 3109, 787, 508, 367, 10972, 491, 23382, 278, 5229, 13819, 29873, 2750, 16728, 9124, 292, 3081, 491, 278, 14451, 310, 278, 3865, 29928, 3301, 29973, 13, 29940, 711, 1486, 19343, 943, 825, 896, 8661, 411, 13, 2182, 866, 515, 29901, 425, 535, 294, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29896, 29900, 29901, 29900, 29945, 29901, 29906, 29953, 11278, 13, 29902, 29915, 29885, 7123, 23407, 322, 1283, 304, 6592, 29892, 306, 817, 304, 437, 777, 4589, 4167, 714, 310, 4726, 4688, 6454, 22396, 29889, 25065, 425, 535, 294, 29892, 3113, 437, 4459, 3889, 304, 1400, 612, 22970, 13133, 29892, 306, 723, 5360, 304, 1303, 963, 746, 306, 679, 1250, 29889, 7197, 4646, 29889, 13, 29967, 566, 1100, 13, 25120, 271, 4274, 269, 1878, 335, 5168, 13035, 1781, 5235, 29889, 13, 29915, 29923, 854, 565, 366, 3282, 29915, 29873, 437, 372, 29892, 591, 1016, 29915, 29873, 864, 366, 304, 437, 372, 1449, 29915, 13, 29926, 562, 711, 7684, 13, 2182, 866, 515, 29901, 269, 1878, 335, 5168, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29896, 29900, 29901, 29946, 29900, 29901, 29906, 29896, 11278, 13, 7058, 2706, 338, 825, 9559, 304, 7902, 983, 13, 2182, 866, 515, 29901, 432, 562, 711, 7684, 373, 3111, 29871, 29896, 29947, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29941, 29901, 29945, 29906, 29901, 29906, 29941, 11278, 13, 6572, 3476, 873, 29991, 13, 29902, 723, 6755, 263, 1781, 9657, 1061, 975, 445, 577, 29899, 13998, 1261, 25804, 518, 2541, 318, 1526, 9404, 525, 1859, 1575, 2033, 350, 29889, 29903, 29889, 738, 2230, 29889, 11644, 1310, 1302, 1312, 1438, 3838, 471, 1959, 29901, 4432, 25804, 338, 376, 10184, 20040, 1960, 322, 263, 29735, 1602, 4821, 825, 304, 505, 363, 17803, 1213, 13, 2182, 866, 515, 29901, 269, 1878, 335, 5168, 373, 3111, 29871, 29896, 29929, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29955, 29901, 29945, 29941, 29901 ]	1,332,826	8,192	CommonCrawl	8	11
17 AM I would choose a good dictator over this so-called democracy [with umpteen 'choices'] B.S. anytime. "Umpteen" 'choices'? No, more like two, if you're lucky. In many offices (particularly local), sometimes there is only one. That's why we desperately need NOTA on the ballot. If NOTA wins, it's a do-over with a clean slate of candidates. Quote from: dominique on August 19, 2012, 08:06:41 AM Sorry, I meant numerous ''candidates'' serving the elite and not the people. Carlin said it best. "The politicians are put there to give you the idea that you have freedom of choice. YOU DON'T. You have no choice. You have OWNERS. They OWN YOU.... " Best monologue of all time.... "It's called the American Dream...because you have to be asleep to believe it." I have seen this one, Carlin is great!!! Nazi Expert: 'I Have Proof Hitler Died In 1960s' Painting depicting an aged Adolf Hitler in his 70s By Terrence Aym ~ Thursday, September 29, 2011 18:00 source: http://beforeitsnews.com/conspiracy-theories/2011/09/nazi-expert-i-have-proof-hitler-died-in-1960s-1163749.html "The biggest revelation is an authenticated secret German document which lists Hitler as one of the passengers evacuated by plane from Austria to Barcelona on April 26, 1945." Although official history contends Hitler committed suicide with his newlywed wife, Eva Braun, on April, 30 1945 and their corpses were burned by others in the Berlin bunker, Abel Basti claims proof the story is a fabrication. According to Basti's meticulous research, the leader of the Third Reich spent his last years as an art dealer and had facial plastic surgery to change his appearance. Those are just two of the astounding revelations that respected Argentine journalist and historian Abel Basti documents in his book, Hitler's Exile. TIME magazine announces Hitler's death in 1945 While the book was a runaway bestseller across South America, it's been suppressed in the United States and the Russian Federation. Those two countries still maintain that Germany's Führer committed suicide during the last days of World War Two. World newspapers report Hitler dead…were they wrong? The claim that Hitler and some high-ranking Schutzstaffel (SS) officers escaped Germany and fled to South America is not new. Nil Nikandrov observes (Strategic Culture Foundation, "All the Leaders of the Third Reich Fled to Latin America"): "In his well-documented, The Hitler Survival Myth (1981), Donald McKale identifies the earliest source of the myth of Hitler's escape to the southern hemisphere as the unexpected surrender of a German submarine in early July 1945 at Mar del Plata, Argentina. "Several Buenos Aires newspapers, in defiance of Argentine Navy statements, said that rubber boats had been seen landing from it, and other submarines spotted in the area. "On July 16, 1945, the Chicago Times carried a sensational article on the Hitlers having slipped off to Argentina." July 16, 1945: Chicago Times reports Hitler fled to South America The Hitler-in-Argentina tale first surfaced in a book back in 1947 "Ladislao Zsabó, a Hungarian advertiser, witnessed the arrival of the U-530 and saw its crew disembarking. He had heard that the destination was the German Antarctica and, mistakenly, made a supposition that Hitler had escaped to Antarctica, and published the book Hitler está Vivo (Hitler is Alive), where he speaks about the possible location of Hitler, in Queen's Maud properties, opposite the Weddel Sea, that was then renamed Neuschwabenland, when the area was explored in 1938/39	-0.278983	0.893235	-0.847998	-0.31438	[ -1.2185806303484112, 0.6606140582378881 ]	[ -0.8078623040195698, 2.5943320004688952 ]	[ -1.7965518328787051, 0.1005564541087283 ]	[ -1.2677827010880947, 0.6390217055412695 ]	1,024	[ 512, 512 ]	[ 29896, 29955, 13862, 13, 29902, 723, 6755, 263, 1781, 9657, 1061, 975, 445, 577, 29899, 13998, 1261, 25804, 518, 2541, 318, 1526, 9404, 525, 1859, 1575, 2033, 350, 29889, 29903, 29889, 738, 2230, 29889, 13, 29908, 29965, 1526, 9404, 29908, 525, 1859, 1575, 29915, 29973, 1939, 29892, 901, 763, 1023, 29892, 565, 366, 29915, 276, 9885, 29891, 29889, 512, 1784, 25222, 313, 1595, 16311, 368, 1887, 511, 6041, 727, 338, 871, 697, 29889, 13, 7058, 29915, 29879, 2020, 591, 553, 546, 2486, 817, 6058, 29909, 373, 278, 8287, 327, 29889, 960, 6058, 29909, 21614, 29892, 372, 29915, 29879, 263, 437, 29899, 957, 411, 263, 5941, 2243, 403, 310, 21669, 29889, 13, 2182, 866, 515, 29901, 8022, 1387, 373, 3111, 29871, 29896, 29929, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29947, 29901, 29900, 29953, 29901, 29946, 29896, 13862, 13, 29903, 3818, 29892, 306, 6839, 12727, 6629, 29883, 5380, 1078, 4907, 16330, 278, 560, 568, 322, 451, 278, 2305, 29889, 13, 8179, 1915, 1497, 372, 1900, 29889, 13, 29908, 1576, 2832, 14722, 526, 1925, 727, 304, 2367, 366, 278, 2969, 393, 366, 505, 16082, 310, 7348, 29889, 612, 27269, 360, 1164, 29915, 29911, 29889, 887, 505, 694, 7348, 29889, 887, 505, 438, 29956, 13865, 29903, 29889, 2688, 438, 16048, 612, 27269, 3045, 376, 13, 25353, 1601, 1189, 434, 310, 599, 931, 3045, 376, 3112, 29915, 29879, 2000, 278, 3082, 16814, 856, 18103, 366, 505, 304, 367, 408, 5436, 304, 4658, 372, 1213, 13, 29902, 505, 3595, 445, 697, 29892, 1704, 1915, 338, 2107, 21004, 13, 29940, 18861, 1222, 10700, 29901, 525, 29902, 6975, 18319, 23151, 360, 1000, 512, 29871, 29896, 29929, 29953, 29900, 29879, 29915, 13, 29925, 475, 1259, 1401, 919, 292, 385, 26552, 21834, 23151, 297, 670, 29871, 29955, 29900, 29879, 13, 2059, 23707, 663, 319, 962, 3695, 498, 1295, 3250, 29892, 3839, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29896, 29896, 29871, 29896, 29947, 29901, 29900, 29900, 13, 4993, 29901, 1732, 597, 11083, 1169, 15753, 29889, 510, 29914, 535, 1028, 29875, 10068, 29899, 1552, 3842, 29914, 29906, 29900, 29896, 29896, 29914, 29900, 29929, 29914, 29876, 18861, 29899, 735, 10700, 29899, 29875, 29899, 17532, 29899, 8017, 29899, 27342, 1358, 29899, 29881, 1000, 29899, 262, 29899, 29896, 29929, 29953, 29900, 29879, 29899, 29896, 29896, 29953, 29941, 29955, 29946, 29929, 29889, 1420, 13, 29908, 1576, 24842, 20474, 362, 338, 385, 15585, 630, 7035, 5332, 1842, 607, 8857, 23151, 408, 13, 650, 310, 278, 28134, 3415, 22061, 630, 491, 10694, 515, 17362, 304, 12408, 373, 3786, 29871, 29906, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 1213, 13, 2499, 3592, 6221, 4955, 640, 1975, 23151, 19355, 23921, 680, 411, 670, 15141, 8734, 6532, 29892, 27040, 23514, 29892, 373, 3786, 29892, 29871, 29941, 29900, 29871, 29896, 29929, 29946, 29945, 322, 1009, 14913, 267, 892, 12138, 287, 491, 4045, 297, 278, 5115, 289, 27560, 29892, 1976, 295, 25315, 29875, 16726, 5296, 278, 5828, 338, 263, 18187, 362, 29889, 13, 7504, 3278, 304, 25315, 29875, 29915, 29879, 1539, 12906, 681, 5925, 29892, 278, 11822, 310, 278, 18008, 9320, 10398, 670, 1833, 2440, 408, 385, 1616, 5376, 261, 322, 750, 2258, 1455, 715, 6288, 25300, 708, 304, 1735, 670, 10097, 29889, 13, 1349, 852, 526, 925, 1023, 310, 278, 8717, 12449, 20474, 800, 393, 3390, 287, 9385, 457, 24452, 322, 27629, 1976, 295, 25315, 29875, 10701, 297, 670, 3143, 29892, 23151, 29915, 29879, 1222, 488, 29889, 13, 15307, 14853, 7475, 778, 23151, 29915, 29879, 4892, 297, 29871, 29896, 29929, 29946, 29945, 13, 8809, 488, 278, 3143, 471, 263, 1065, 21694, 1900, 29879, 4539, 4822, 4275, 6813, 29892, 372, 29915, 29879, 1063, 21301, 287, 297, 278, 3303, 3900, 322, 278, 10637, 20438, 29889, 16025, 1023, 10916, 1603, 7344, 393, 9556, 29915, 29879, 383, 4000, 261, 19355, 23921, 680, 2645, 278, 1833, 3841, 310, 2787, 3362, 7803, 29889, 13, 14058, 14578, 21321, 3461, 23151, 7123, 30098, 29893, 406, 896, 2743, 29973, 13, 1576, 5995, 393, 23151, 322, 777, 1880, 29899, 661, 9292, 27651, 303, 3470, 295, 313, 1799, 29897, 13049, 19824, 9556, 322, 27481, 304, 4275, 6813, 338, 451, 716, 29889, 13, 27823, 11535, 392, 10139, 5366, 1960, 313, 5015, 1845, 293, 14062, 10606, 29892, 376, 3596, 278, 951, 24574, 310, 278, 18008, 9320, 383, 839, 304, 13548, 6813, 29908, 1125, 376, 797, 670, 1532, 29899, 3225, 287, 29892, 450, 23151, 6298, 29894, 2561, 341, 1541, 313, 29896, 29929, 29947, 29896, 511, 18935, 24053, 744, 2893, 11057, 278, 24577, 2752, 310, 278, 22082, 310, 23151, 29915, 29879, 10169, 304, 278, 14841, 9736, 275, 9085, 408, 278, 15668, 27503, 310, 263, 5332, 1014, 24556, 297, 4688, 5468, 29871, 29896, 29929, 29946, 29945, 472, 1085, 628, 1858, 532, 29892, 13798, 29889, 13, 29908, 29903, 1310, 284, 17882, 16981, 14578, 21321, 29892, 297, 822, 8837, 310, 9385, 457, 13166, 9506, 29892, 1497, 393, 14051, 495, 25462, 750, 1063, 3595, 25325, 515, 372, 29892, 322, 916, 1014, 3034, 1475, 805, 15048, 297, 278, 4038, 29889, 13, 29908, 2951, 5468, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 278, 10059, 10277, 8988, 263, 4771, 1288, 4274, 373, 278, 14309, 9306, 2534, 20662, 2986, 1283, 304, 13798, 1213, 13, 29967, 11850, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 29901, 10059, 10277, 13676, 23151, 27481, 304, 4275, 6813, 13, 1576, 23151, 29899, 262, 29899, 1433, 5362, 1099, 17694, 937, 1190, 17470, 287, 297, 263, 3143, 1250, 297, 29871, 29896, 29929, 29946, 29955, 13, 29908, 29931, 328, 275, 433, 29877, 796, 29879, 370, 29980, 29892, 263, 14198, 13956, 18811, 7608, 29892, 16277, 287, 278, 18517, 310, 278, 501, 29899, 29945, 29941, 29900, 322, 4446, 967, 17616, 766, 1590, 935, 292, 29889, 940, 750, 6091, 393, 278, 12551, 471, 278, 5332, 5459, 27014, 983, 322, 29892, 25257, 368, 29892, 1754, 263, 1462, 4490, 393, 23151, 750, 19824, 304, 5459, 27014, 983, 29892, 322, 6369, 278, 3143, 23151, 7919, 478, 4243, 313, 29950, 277, 1358, 338, 319, 9258, 511, 988, 540, 7726, 29879, 1048, 278, 1950, 4423, 310, 23151, 29892, 297, 10470, 29915, 29879, 3219, 566, 4426, 29892, 11564, 278, 15050, 6144, 14070, 29892, 393, 471, 769, 19533, 2448, 17974, 29893, 12792, 1049, 29892, 746, 278, 4038, 471, 3902, 4395, 297, 29871, 29896, 29929, 29941, 29947, 29914, 29941, 29929 ]	1,332,826	9,216	CommonCrawl	8	11
by the German expedition [led] by Captain Ritschter. Brick from wall of Nazi complex in Patagonia "Zsabó made the wrong assumption. "Had he read the book by Professor Hugo Fernandez Artucio published in 1940, Nazis en el Uruguay, (Nazis in Uruguay) he would had discovered that there actually was a plan referring to German Antarctica, but this was nothing but the term they used for the Patagonia and that this information had been made public in New York in 1939." [Nil Nikandrov] 'Eagle's Nest" stonework on wall of German complex, Argentina. Basti doggedly digs deeper When there's so much smoke there's usually a fire. Basti tracked down that fire during seven years of sometimes grueling investigations. Author-journalist Abel Basti holds copy of his bestselling book He personally visited German compounds surrounded by security and stern-faced guards, interviewed surviving witnesses in villages near the strongholds, and even obtained authenticated photographs of Hitler and Braun during their exile years. Alleged photo of Adolf and Eva with daughter Urich in Argentina "Basti wrote that A. Hitler, E. Braun, and Führer's closest aides flew from the burning Berlin to Spain…and then crossed the Atlantic Ocean by three submarines and reached Argentina. "In July-August, 1945 Hitler and his clique landed in the Rio Negro province near the Caleta de los Loros village and moved on further into Argentine. "Allegedly, the same secret route prepared by SS chief Himmler's staff was later used by Bormann, Mengele, and Eichmann. "Basti detailed the journey of A. Hitler and E. Braun across Argentina assisted by local Nazi sympathizers and described the couple's family life during which—despite the hardships of hiding—they even had children." Alleged photo of Hitler in disguise, Buenos Aires meeting, 1952 Stonewalling Soviets The Soviets weren't helpful on the matter of the German leader's death. "The Soviets continued to be difficult. They refused to allow Westerners into Berlin even after the surrender of Dönitz's government and the last armies in the field on May 7-9. On May 10, they announced the existence of the burned bodies in the Chancellory courtyard, but only allowed that one might be Hitler. The same report went on to say that his body might never be found. "On June 6, a spokesman for the Soviet army in Berlin announced unequivocally that Hitler had committed suicide and that his body had been identified. Three days later, Marshall Zhukov, the head of the Soviet army gave a press conference with Deputy Foreign Minister Andrei Vishinski looking over his shoulder. 'We did not identify the body of Hitler,' he said. 'I can say nothing definite about his fate. He could have flown away from Berlin at the very last moment.'" [Nil Nikandrov ] Interview with Basti In an interview on Deadline – Live, an Argentine news program, journalist Santiago Romero interviewed Abel Basti about Hitler's escape, life in Patagonia, and the events that followed World War Two. ["Hitler huyó a la Patagonia en un submarino que zarpó desde Vigo" Edited.] Romero: What is your opinion on Hitler's escape? Basti: "Hitler escaped via air from Austria to Barcelona. The last stage of his escape was in a submarine, from Vigo, heading straight to the coast of Patagonia. Finally, Hitler and Eva Braun, in a car with a chauffeur and bodyguard—a motorcade of at least three cars—drove to Bariloche (Argentina). "He took refuge in a place called San Ramon, about 15 miles east of that town. It is a property of about 250,000 acres with a lake-front view of Lake Nahuel Huapi, which had been German property since the early twentieth century, when it belonged to a German firm by the name of Schamburg-Lippe." An alleged Hitler family home: Hacienda San Ramon Romero: "On what basis do you claim that Hitler was in Spain after leaving his Berlin bunker?" Basti: "I was able to confirm the presence of Hitler in	0.394897	2.229044	0.062513	0.836726	[ 0.2771049381182352, 0.5126891119060221 ]	[ 2.4081066280126846, 2.049980911750741 ]	[ 0.14620879256564515, -0.02118311510971663 ]	[ 0.9719970998776386, 0.7014545919793387 ]	1,024	[ 512, 512 ]	[ 491, 278, 5332, 24431, 518, 839, 29962, 491, 10842, 390, 20641, 357, 29889, 13, 29933, 9131, 515, 10090, 310, 11409, 29875, 4280, 297, 4121, 351, 6405, 13, 29908, 29999, 29879, 370, 29980, 1754, 278, 2743, 11833, 29889, 13, 29908, 29950, 328, 540, 1303, 278, 3143, 491, 11386, 20650, 7139, 4182, 29920, 3012, 29884, 3934, 6369, 297, 29871, 29896, 29929, 29946, 29900, 29892, 11409, 275, 427, 560, 29233, 29892, 313, 29940, 834, 275, 297, 29233, 29897, 540, 723, 750, 10943, 393, 727, 2869, 471, 263, 3814, 16811, 304, 5332, 5459, 27014, 983, 29892, 541, 445, 471, 3078, 541, 278, 1840, 896, 1304, 363, 278, 4121, 351, 6405, 322, 393, 445, 2472, 750, 1063, 1754, 970, 297, 1570, 3088, 297, 29871, 29896, 29929, 29941, 29929, 1213, 518, 27823, 11535, 392, 10139, 29962, 13, 29915, 29923, 20860, 29915, 29879, 405, 342, 29908, 12565, 1287, 373, 10090, 310, 5332, 4280, 29892, 13798, 29889, 13, 29933, 579, 29875, 437, 1505, 23244, 4697, 29879, 25871, 13, 10401, 727, 29915, 29879, 577, 1568, 25158, 727, 29915, 29879, 5491, 263, 3974, 29889, 25315, 29875, 5702, 287, 1623, 393, 3974, 2645, 9881, 2440, 310, 6041, 4500, 14067, 7405, 800, 29889, 13, 13720, 29899, 29926, 4659, 391, 1976, 295, 25315, 29875, 8640, 3509, 310, 670, 1900, 29879, 7807, 3143, 13, 3868, 22345, 16669, 5332, 752, 3885, 22047, 491, 6993, 322, 27784, 29899, 17470, 287, 1410, 3163, 29892, 15593, 287, 10503, 4357, 16277, 267, 297, 18481, 2978, 278, 4549, 23177, 29892, 322, 1584, 7625, 15585, 630, 17739, 29879, 310, 23151, 322, 23514, 2645, 1009, 429, 488, 2440, 29889, 13, 2499, 1397, 287, 15373, 310, 21834, 322, 27040, 411, 8750, 501, 4018, 297, 13798, 13, 29908, 29933, 579, 29875, 5456, 393, 319, 29889, 23151, 29892, 382, 29889, 23514, 29892, 322, 383, 4000, 261, 29915, 29879, 21438, 263, 2247, 9115, 29893, 515, 278, 25535, 5115, 304, 13616, 30098, 392, 769, 21692, 278, 19948, 21091, 491, 2211, 1014, 3034, 1475, 322, 7450, 13798, 29889, 13, 29908, 797, 5468, 29899, 26197, 29892, 29871, 29896, 29929, 29946, 29945, 23151, 322, 670, 9335, 802, 2982, 287, 297, 278, 11611, 12610, 307, 12291, 2978, 278, 315, 744, 941, 316, 1232, 10980, 359, 5720, 322, 6153, 373, 4340, 964, 9385, 457, 29889, 13, 29908, 2499, 1397, 23244, 29892, 278, 1021, 7035, 5782, 13240, 491, 5886, 9087, 18136, 828, 261, 29915, 29879, 13925, 471, 2678, 1304, 491, 350, 555, 812, 29892, 7567, 28253, 29892, 322, 382, 436, 4403, 29889, 13, 29908, 29933, 579, 29875, 13173, 278, 16342, 310, 319, 29889, 23151, 322, 382, 29889, 23514, 4822, 13798, 6985, 287, 491, 1887, 11409, 29875, 17520, 19427, 322, 5439, 278, 7303, 29915, 29879, 3942, 2834, 2645, 607, 30003, 2783, 29886, 568, 278, 2898, 9981, 310, 25508, 30003, 19562, 1584, 750, 4344, 1213, 13, 2499, 1397, 287, 15373, 310, 23151, 297, 766, 2543, 895, 29892, 17882, 16981, 11781, 29892, 29871, 29896, 29929, 29945, 29906, 13, 855, 650, 11358, 292, 317, 6895, 1691, 13, 1576, 317, 6895, 1691, 2949, 264, 29915, 29873, 8444, 373, 278, 4383, 310, 278, 5332, 11822, 29915, 29879, 4892, 29889, 13, 29908, 1576, 317, 6895, 1691, 7572, 304, 367, 5189, 29889, 2688, 15964, 304, 2758, 10504, 414, 964, 5115, 1584, 1156, 278, 27503, 310, 360, 3042, 2784, 29915, 29879, 5874, 322, 278, 1833, 5075, 583, 297, 278, 1746, 373, 2610, 29871, 29955, 29899, 29929, 29889, 1551, 2610, 29871, 29896, 29900, 29892, 896, 9326, 278, 10379, 310, 278, 12138, 287, 17873, 297, 278, 22433, 3729, 706, 2085, 1017, 538, 29892, 541, 871, 6068, 393, 697, 1795, 367, 23151, 29889, 450, 1021, 3461, 3512, 373, 304, 1827, 393, 670, 3573, 1795, 2360, 367, 1476, 29889, 13, 29908, 2951, 5306, 29871, 29953, 29892, 263, 805, 23195, 1171, 363, 278, 15308, 9987, 297, 5115, 9326, 1597, 339, 440, 542, 635, 393, 23151, 750, 19355, 23921, 680, 322, 393, 670, 3573, 750, 1063, 15659, 29889, 12753, 3841, 2678, 29892, 23072, 27134, 2679, 586, 29892, 278, 2343, 310, 278, 15308, 9987, 4846, 263, 3965, 21362, 411, 26721, 29891, 19358, 7668, 1126, 5803, 478, 728, 262, 2574, 3063, 975, 670, 23468, 29889, 525, 4806, 1258, 451, 12439, 278, 3573, 310, 23151, 5501, 540, 1497, 29889, 525, 29902, 508, 1827, 3078, 24860, 1048, 670, 23779, 29889, 940, 1033, 505, 4972, 29876, 3448, 515, 5115, 472, 278, 1407, 1833, 3256, 6169, 29908, 518, 27823, 11535, 392, 10139, 4514, 13, 4074, 1493, 411, 25315, 29875, 13, 797, 385, 15593, 373, 16992, 1220, 785, 10782, 29892, 385, 9385, 457, 9763, 1824, 29892, 24452, 18135, 6033, 1489, 15593, 287, 1976, 295, 25315, 29875, 1048, 23151, 29915, 29879, 10169, 29892, 2834, 297, 4121, 351, 6405, 29892, 322, 278, 4959, 393, 5643, 2787, 3362, 7803, 29889, 6796, 29950, 277, 1358, 298, 8631, 29980, 263, 425, 4121, 351, 6405, 427, 443, 1014, 3034, 1789, 712, 503, 6834, 29980, 5125, 478, 5973, 29908, 2155, 1573, 5586, 13, 29934, 290, 1489, 29901, 1724, 338, 596, 9426, 373, 23151, 29915, 29879, 10169, 29973, 13, 29933, 579, 29875, 29901, 376, 29950, 277, 1358, 19824, 3025, 4799, 515, 17362, 304, 12408, 29889, 450, 1833, 7408, 310, 670, 10169, 471, 297, 263, 1014, 24556, 29892, 515, 478, 5973, 29892, 28435, 7812, 304, 278, 12180, 310, 4121, 351, 6405, 29889, 9788, 29892, 23151, 322, 27040, 23514, 29892, 297, 263, 1559, 411, 263, 521, 28411, 5411, 322, 3573, 17728, 30003, 29874, 10992, 6332, 310, 472, 3203, 2211, 18647, 30003, 26419, 345, 304, 2261, 7820, 1173, 313, 1433, 5362, 1099, 467, 13, 29908, 3868, 3614, 25447, 297, 263, 2058, 2000, 3087, 8292, 265, 29892, 1048, 29871, 29896, 29945, 7800, 9755, 310, 393, 4726, 29889, 739, 338, 263, 2875, 310, 1048, 29871, 29906, 29945, 29900, 29892, 29900, 29900, 29900, 23931, 411, 263, 19437, 29899, 8862, 1776, 310, 9459, 405, 801, 2491, 12895, 2754, 29892, 607, 750, 1063, 5332, 2875, 1951, 278, 4688, 3252, 7268, 621, 6462, 29892, 746, 372, 28911, 304, 263, 5332, 9226, 491, 278, 1024, 310, 1102, 1117, 2007, 29899, 23410, 4798, 1213, 13, 2744, 16831, 287, 23151, 3942, 3271, 29901, 5952, 455, 8395, 3087, 8292, 265, 13, 29934, 290, 1489, 29901, 376, 2951, 825, 8405, 437, 366, 5995, 393, 23151, 471, 297, 13616, 1156, 10124, 670, 5115, 289, 27560, 3026, 13, 29933, 579, 29875, 29901, 376, 29902, 471, 2221, 304, 9659, 278, 10122, 310, 23151, 297 ]	1,332,826	10,240	CommonCrawl	8	11
Spain thanks to a—now elderly—Jesuit priest, whose family members were friends of the Nazi leader. And I have witnesses that allude to meetings he had with his entourage at the place where they stayed in Cantabria. Mr. and Mrs Hitler in Spain before voyage to Patagonia "In addition, a document of the British secret services reveals that in those days, a Nazi submarine convoy left Spain, and after stopping in the Canary Islands, it continued its journey to the south of Argentina. "Hitler and Eva Braun traveled onboard one of these submarines, which later arrived in Patagonia between July and August of 1945, under the de facto President Edelmiro Farrell and later Juan Domingo Peron, then his Minister of War. There is also another important document mentioning that the FBI was looking for Hitler in Spain after World War II." Romero: "From where did he leave to Patagonia?" Basti: "All the evidence points to the Galician coast, which was a significant base of supplies for Nazi submarines during the Battle of the Atlantic, to the extent that Churchill considered the possibility of invading it—an action that was scrapped when they built the code-breaking "Enigma" machine and managed to decipher Nazi submarine fleet messages and the course of submarine warfare was reversed. "There is the possibility that he left from Vigo or Ferrol, but it is almost certain that he did from Vigo, according to Britain's MI6." Romero: "What was Hitler's life in Argentina like?" Basti: "Hitler lived as a fugitive with his wife and his bodyguard. His first years were in Patagonia, and then he lived in the more northern provinces [of Argentina]. "In the early years, he held meetings in different parts of Argentina, and with other Nazis in Paraguay, as well as with sympathizers from foreign countries. "He shaved his head and mustache, so he was not easily recognizable. He lived away from large urban areas, although he had a few meetings in Buenos Aires. He died in the sixties in Argentina. "I'm currently investigating where he was buried and how he lived his last days." Romero: "Did you have access to documents from the former Soviet Union?" Basti: "Until his death in 1953, Stalin always believed that Hitler had escaped. In 1945, Stalin told the Allies this same information. There are three different shorthand writings in which Stalin mentioned that the German leader had fled. "In Argentina, I have interviewed people who had seen and met with Hitler. In the Russian archives, there is abundant documentation that shows that Hitler had escaped." Romero: "How did your book impact the official story of Hitler's death?" Basti: "Despite the recent investigations that proved that Hitler's remains at the Kremlin in Russia did not belong to him, most Russians have always rejected the theory that he escaped. The same applies to the nations involved in the war. "The U.S. has just reclassified [under national security auspices] for 20 [more] years all official material related to this story, and when that deadline is met, it will probably be reclassified. "The British reclassified all related documentation for 60 more years. The researchers cannot access that information." Also read Before It's News': Irish Soldier: 'I Saved Hitler's Life In 1919' - In one of those odd quirks of history, World War II and the 70 million lives lost could have been averted if, on a fateful day during 1919, a young Irishman had let Adolf Hitler die … Instead he unwittingly saved the life of Germany's future Führer. Hitler and Eva with child One can only dream It is truly amazing how much stuff is actually out there in net-land. Facts, fictions, outright lies, you name it... Adolf Hitler's Secret FBI files Timothy W Maier For almost 30 years, J. Edgar Hoover and the FBI maintained a detailed dossier on Adolf Hitler and closely investigated any report that indicated he still was alive. ADOLF HITLER LIVES -- in cyberspace, that is, where 734 pages of Hitler's raw FBI file can be downloaded from the Internet	0.334631	2.408107	0.029542	0.930375	[ 0.5784335324979625, 0.0908290797744038 ]	[ 2.5370318858669845, 2.2791813701583847 ]	[ -0.02118311510971663, 0.08026652590565414 ]	[ 1.2737560509949732, 0.5869943001762118 ]	1,024	[ 512, 512 ]	[ 13616, 3969, 304, 263, 30003, 3707, 27008, 368, 30003, 29967, 267, 3121, 18781, 29892, 5069, 3942, 5144, 892, 7875, 310, 278, 11409, 29875, 11822, 29889, 1126, 306, 505, 16277, 267, 393, 599, 1151, 304, 5870, 886, 540, 750, 411, 670, 875, 283, 6617, 472, 278, 2058, 988, 896, 27661, 297, 15498, 370, 2849, 29889, 13, 20335, 29889, 322, 6285, 23151, 297, 13616, 1434, 17775, 304, 4121, 351, 6405, 13, 29908, 797, 6124, 29892, 263, 1842, 310, 278, 4908, 7035, 5786, 10320, 1338, 393, 297, 1906, 3841, 29892, 263, 11409, 29875, 1014, 24556, 378, 18644, 2175, 13616, 29892, 322, 1156, 25480, 297, 278, 1815, 653, 17839, 29892, 372, 7572, 967, 16342, 304, 278, 7062, 310, 13798, 29889, 13, 29908, 29950, 277, 1358, 322, 27040, 23514, 1020, 345, 839, 373, 3377, 697, 310, 1438, 1014, 3034, 1475, 29892, 607, 2678, 11977, 297, 4121, 351, 6405, 1546, 5468, 322, 3111, 310, 29871, 29896, 29929, 29946, 29945, 29892, 1090, 278, 316, 2114, 29877, 7178, 2155, 295, 2460, 307, 8413, 15044, 322, 2678, 8699, 7809, 20191, 2431, 265, 29892, 769, 670, 7668, 310, 3362, 29889, 1670, 338, 884, 1790, 4100, 1842, 3585, 292, 393, 278, 383, 12809, 471, 3063, 363, 23151, 297, 13616, 1156, 2787, 3362, 1944, 1213, 13, 29934, 290, 1489, 29901, 376, 4591, 988, 1258, 540, 5967, 304, 4121, 351, 6405, 3026, 13, 29933, 579, 29875, 29901, 376, 3596, 278, 10757, 3291, 304, 278, 5208, 8910, 12180, 29892, 607, 471, 263, 7282, 2967, 310, 28075, 363, 11409, 29875, 1014, 3034, 1475, 2645, 278, 12788, 310, 278, 19948, 29892, 304, 278, 15834, 393, 6291, 453, 5545, 278, 13331, 310, 2437, 9382, 372, 30003, 273, 3158, 393, 471, 24559, 2986, 746, 896, 4240, 278, 775, 29899, 1030, 5086, 376, 2369, 2934, 29908, 4933, 322, 8745, 304, 316, 455, 8096, 11409, 29875, 1014, 24556, 22338, 7191, 322, 278, 3236, 310, 1014, 24556, 1370, 24658, 471, 18764, 287, 29889, 13, 29908, 8439, 338, 278, 13331, 393, 540, 2175, 515, 478, 5973, 470, 7756, 1467, 29892, 541, 372, 338, 4359, 3058, 393, 540, 1258, 515, 478, 5973, 29892, 5034, 304, 14933, 29915, 29879, 341, 29902, 29953, 1213, 13, 29934, 290, 1489, 29901, 376, 5618, 471, 23151, 29915, 29879, 2834, 297, 13798, 763, 3026, 13, 29933, 579, 29875, 29901, 376, 29950, 277, 1358, 10600, 408, 263, 20924, 3321, 411, 670, 6532, 322, 670, 3573, 17728, 29889, 3600, 937, 2440, 892, 297, 4121, 351, 6405, 29892, 322, 769, 540, 10600, 297, 278, 901, 14622, 28058, 518, 974, 13798, 1822, 13, 29908, 797, 278, 4688, 2440, 29892, 540, 4934, 5870, 886, 297, 1422, 5633, 310, 13798, 29892, 322, 411, 916, 11409, 275, 297, 1459, 10617, 388, 29892, 408, 1532, 408, 411, 17520, 19427, 515, 9117, 10916, 29889, 13, 29908, 3868, 528, 10511, 670, 2343, 322, 1818, 1829, 29892, 577, 540, 471, 451, 5948, 5936, 13902, 29889, 940, 10600, 3448, 515, 2919, 17164, 10161, 29892, 5998, 540, 750, 263, 2846, 5870, 886, 297, 17882, 16981, 29889, 940, 6423, 297, 278, 1354, 486, 583, 297, 13798, 29889, 13, 29908, 29902, 29915, 29885, 5279, 7405, 1218, 988, 540, 471, 18550, 322, 920, 540, 10600, 670, 1833, 3841, 1213, 13, 29934, 290, 1489, 29901, 376, 9260, 366, 505, 2130, 304, 10701, 515, 278, 4642, 15308, 7761, 3026, 13, 29933, 579, 29875, 29901, 376, 29965, 20233, 670, 4892, 297, 29871, 29896, 29929, 29945, 29941, 29892, 624, 25977, 2337, 13112, 393, 23151, 750, 19824, 29889, 512, 29871, 29896, 29929, 29946, 29945, 29892, 624, 25977, 5429, 278, 838, 3687, 445, 1021, 2472, 29889, 1670, 526, 2211, 1422, 528, 2072, 392, 2044, 886, 297, 607, 624, 25977, 5276, 393, 278, 5332, 11822, 750, 27481, 29889, 13, 29908, 797, 13798, 29892, 306, 505, 15593, 287, 2305, 1058, 750, 3595, 322, 1539, 411, 23151, 29889, 512, 278, 10637, 3190, 3145, 29892, 727, 338, 18666, 424, 5106, 393, 3697, 393, 23151, 750, 19824, 1213, 13, 29934, 290, 1489, 29901, 376, 5328, 1258, 596, 3143, 10879, 278, 6221, 5828, 310, 23151, 29915, 29879, 4892, 3026, 13, 29933, 579, 29875, 29901, 376, 4002, 29886, 568, 278, 7786, 7405, 800, 393, 11827, 393, 23151, 29915, 29879, 9242, 472, 278, 7706, 828, 262, 297, 12710, 1258, 451, 6852, 304, 1075, 29892, 1556, 11688, 1039, 550, 505, 2337, 22225, 278, 6368, 393, 540, 19824, 29889, 450, 1021, 16058, 304, 278, 19079, 9701, 297, 278, 1370, 29889, 13, 29908, 1576, 501, 29889, 29903, 29889, 756, 925, 1162, 605, 2164, 518, 5062, 4797, 6993, 1770, 29886, 1575, 29962, 363, 29871, 29906, 29900, 518, 5514, 29962, 2440, 599, 6221, 5518, 4475, 304, 445, 5828, 29892, 322, 746, 393, 7123, 1220, 338, 1539, 29892, 372, 674, 3117, 367, 1162, 605, 2164, 29889, 13, 29908, 1576, 4908, 1162, 605, 2164, 599, 4475, 5106, 363, 29871, 29953, 29900, 901, 2440, 29889, 450, 5925, 414, 2609, 2130, 393, 2472, 1213, 13, 17351, 1303, 10949, 739, 29915, 29879, 10130, 2396, 12601, 19019, 631, 29901, 525, 29902, 9583, 287, 23151, 29915, 29879, 4634, 512, 29871, 29896, 29929, 29896, 29929, 29915, 448, 512, 697, 310, 1906, 7736, 439, 27064, 310, 4955, 29892, 2787, 3362, 1944, 322, 278, 29871, 29955, 29900, 7284, 12080, 5714, 1033, 505, 1063, 263, 1765, 287, 565, 29892, 373, 263, 285, 22279, 2462, 2645, 29871, 29896, 29929, 29896, 29929, 29892, 263, 4123, 12601, 1171, 750, 1235, 21834, 23151, 762, 16088, 8669, 540, 18500, 5367, 368, 7160, 278, 2834, 310, 9556, 29915, 29879, 5434, 383, 4000, 261, 29889, 13, 29950, 277, 1358, 322, 27040, 411, 2278, 13, 6716, 508, 871, 12561, 13, 3112, 338, 19781, 21863, 292, 920, 1568, 6433, 338, 2869, 714, 727, 297, 7787, 29899, 1049, 29889, 26748, 29879, 29892, 26797, 1080, 29892, 714, 1266, 12185, 29892, 366, 1024, 372, 856, 13, 3253, 4369, 23151, 29915, 29879, 10213, 383, 12809, 2066, 13, 13711, 20336, 399, 3219, 631, 13, 2831, 4359, 29871, 29941, 29900, 2440, 29892, 435, 29889, 2155, 5397, 8335, 957, 322, 278, 383, 12809, 19949, 263, 13173, 270, 2209, 631, 373, 21834, 23151, 322, 16467, 7405, 630, 738, 3461, 393, 18694, 540, 1603, 471, 18758, 29889, 13, 3035, 5607, 29943, 379, 1806, 29931, 1001, 365, 5667, 2890, 1192, 297, 5094, 2596, 3535, 29892, 393, 338, 29892, 988, 29871, 29955, 29941, 29946, 6515, 310, 23151, 29915, 29879, 10650, 383, 12809, 934, 508, 367, 16532, 515, 278, 4685 ]	1,332,826	11,264	CommonCrawl	8	11
. The files contain speeches, rare photographs, old newspaper clippings, details about discovery of the Führer's personal notes and chinaware and assassination plots -- as well as an extensive 11-year probe into the possibility that Hitler faked his own death with a bogus suicide in 1945. At times these files read like a supermarket tabloid, with outrageous conspiracy theories that remind readers that FBI Director J. Edgar Hoover was a suspicious man. At other times, the files reveal how serious the FBI considered allegations that one of this century's most evil despots may have escaped his Berlin Bunker. The records begin with President Franklin Roosevelt becoming enraged upon learning of a 1933 New York conspiracy to kill Hitler and continue into the fifties with a Western Union telegram declaring: I have positive proof that Hitler is living. There are seven volumes of these records. A photographic exhibit of Hitler in uniform dominates the final volume. Scattered throughout are clippings from newspapers. The last story is a 1956 article about the plans of Hitler's sister, Paula Wolf, to write a book about her brother to "set some facts straight" as soon as a Munich court declares her brother dead. "The readers will forgive me," she says, "if I abstain from depicting my brother at all costs as a wicked character just for the sake of profit." An accompanying Associated Press article noted boldly: He Is Officially Alive 'Til Court Issues Certificate. As for that Western Union tipster, the FBI never tracked down the sender nor did it ever identify the members of the 1933 conspiracy plot to kill Hitler. But that plot sure kept Hoover's G-men busy. The file reveals that the plot began when the German Embassy asked the State Department to initiate an investigation based upon a letter signed by a "Daniel Stern," which said that unless FDR rebuked Hitler for his outrages against Jews, then "I notify you that I shall go to Germany and assassinate Hitler." The State Department handed off the probe to the FBI, which never found Stern. But the probe opened the door for Hoover to look at pro-Nazi organizations. Don Whitehead, one of the few authors to research the plot, wrote about it in his book, The FBI Story, A Report to the People. He calls it a "diplomatic fumble" by the German ambassador in Washington, who probably wished he never had called the State Department. That's because Hoover's investigation ultimately became "a valuable reference when the Department of Justice requested additional investigations. And Hoover passed the information to the president," Whitehead observes. All of this is in Hitler's FBI file -- even Whitehead's observations. Between the poor copies -- some nearly impossible to read because, says FBI Freedom of Information Officer Linda Gloss, the copies were not made from originals -- and the heavy black ink blocking out what today still is considered classified, there rests a fascinating tale of the FBI's role during the World War II era. For example, deep in the files are a series of memos written by Hoover on Oct. 5, 1939, reviewing intelligence from a confidential informant. The Hoover memos to various U.S. military-intelligence agencies and the president's chief of staff warned of future Japanese aggression and Germany's attack on France. "The Japanese will attack British Indochina and other colonies without warning, simultaneously with the German advance on France," Hoover wrote. For the last nine years of his life Adolf Hitler, a lifelong hypochondriac had as his physician Dr Theodor Morell. Hitler's mood swings, Parkinson's disease, gastro-intestinal symptoms, skin problems and steady decline until his suicide in 1945 are documented by reliable observers and historians, and in Morell's diaries. The bizarre and unorthodox medications given to Hitler, often for undisclosed reasons, include topical cocaine, injected amphetamines, glucose, testosterone, estradiol, and corticosteroids. In addition, he was given a preparation made from a gun cleaner, a compound of strychnine and atropine, an extract of seminal vesicles, and numerous vitamins and 'tonics'. It seems possible	0.775667	2.837857	0.442949	1.14889	[ 0.9893361611975906, 0.5619974273499774 ]	[ 3.195983203788961, 2.4797317712650733 ]	[ 0.5266449463732855, 0.35925303869792374 ]	[ 1.2425396077759385, 1.0552409484617309 ]	1,024	[ 512, 512 ]	[ 29889, 450, 2066, 1712, 12032, 267, 29892, 10812, 17739, 29879, 29892, 2030, 19656, 9335, 27775, 29892, 4902, 1048, 20699, 310, 278, 383, 4000, 261, 29915, 29879, 7333, 11486, 322, 521, 1099, 2519, 322, 20105, 3381, 24580, 1192, 408, 1532, 408, 385, 20607, 29871, 29896, 29896, 29899, 6360, 410, 915, 964, 278, 13331, 393, 23151, 285, 12535, 670, 1914, 4892, 411, 263, 26652, 375, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 4178, 3064, 1438, 2066, 1303, 763, 263, 2428, 28549, 4434, 417, 333, 29892, 411, 714, 6617, 681, 21588, 29875, 10068, 25841, 393, 1083, 513, 22176, 393, 383, 12809, 15944, 435, 29889, 2155, 5397, 8335, 957, 471, 263, 8872, 14803, 767, 29889, 2180, 916, 3064, 29892, 278, 2066, 10320, 284, 920, 10676, 278, 383, 12809, 5545, 16831, 800, 393, 697, 310, 445, 6462, 29915, 29879, 1556, 16126, 8913, 1862, 1122, 505, 19824, 670, 5115, 350, 27560, 29889, 13, 1576, 6475, 3380, 411, 7178, 21504, 1528, 852, 955, 29873, 14171, 427, 1431, 287, 2501, 6509, 310, 263, 29871, 29896, 29929, 29941, 29941, 1570, 3088, 21588, 29875, 10068, 304, 12088, 23151, 322, 6773, 964, 278, 285, 2027, 583, 411, 263, 10504, 7761, 4382, 1393, 25136, 29901, 13, 29902, 505, 6374, 5296, 393, 23151, 338, 8471, 29889, 13, 8439, 526, 9881, 18167, 310, 1438, 6475, 29889, 319, 6731, 12122, 10371, 277, 310, 23151, 297, 9090, 8022, 1078, 278, 2186, 7977, 29889, 2522, 2620, 287, 10106, 526, 9335, 27775, 515, 14578, 21321, 29889, 450, 1833, 5828, 338, 263, 29871, 29896, 29929, 29945, 29953, 4274, 1048, 278, 13900, 310, 23151, 29915, 29879, 9883, 29892, 2621, 2497, 10441, 29892, 304, 2436, 263, 3143, 1048, 902, 8099, 304, 376, 842, 777, 17099, 7812, 29908, 408, 4720, 408, 263, 13564, 436, 8973, 4845, 5114, 902, 8099, 7123, 29889, 376, 1576, 22176, 674, 18879, 573, 592, 1699, 1183, 4083, 29892, 376, 361, 306, 633, 303, 475, 515, 1401, 919, 292, 590, 8099, 472, 599, 21544, 408, 263, 281, 17840, 2931, 925, 363, 278, 16563, 310, 21665, 1213, 530, 10259, 1384, 292, 6853, 630, 5254, 4274, 11682, 14288, 368, 29901, 13, 3868, 1317, 10564, 368, 319, 9258, 525, 29911, 309, 9245, 16982, 1041, 18410, 8021, 29889, 13, 2887, 363, 393, 10504, 7761, 6872, 2475, 29892, 278, 383, 12809, 2360, 5702, 287, 1623, 278, 10004, 3643, 1258, 372, 3926, 12439, 278, 5144, 310, 278, 29871, 29896, 29929, 29941, 29941, 21588, 29875, 10068, 6492, 304, 12088, 23151, 29889, 1205, 393, 6492, 1854, 8126, 8335, 957, 29915, 29879, 402, 29899, 1527, 19587, 29889, 450, 934, 10320, 1338, 393, 278, 6492, 4689, 746, 278, 5332, 28735, 465, 29891, 4433, 278, 4306, 10317, 304, 14511, 403, 385, 22522, 2729, 2501, 263, 5497, 8794, 491, 263, 376, 29866, 23413, 1699, 607, 1497, 393, 6521, 383, 8353, 337, 2423, 17713, 23151, 363, 670, 714, 22428, 2750, 22057, 29892, 769, 376, 29902, 26051, 366, 393, 306, 4091, 748, 304, 9556, 322, 20105, 16976, 23151, 1213, 13, 1576, 4306, 10317, 29692, 1283, 278, 410, 915, 304, 278, 383, 12809, 29892, 607, 2360, 1476, 23413, 29889, 1205, 278, 410, 915, 6496, 278, 3050, 363, 8335, 957, 304, 1106, 472, 410, 29899, 29940, 18861, 25700, 29889, 3872, 8037, 2813, 29892, 697, 310, 278, 2846, 15717, 304, 5925, 278, 6492, 29892, 5456, 1048, 372, 297, 670, 3143, 29892, 450, 383, 12809, 13740, 29892, 319, 13969, 304, 278, 11647, 29889, 940, 5717, 372, 263, 376, 6051, 8840, 2454, 285, 15563, 29908, 491, 278, 5332, 3181, 28760, 297, 7660, 29892, 1058, 3117, 20024, 540, 2360, 750, 2000, 278, 4306, 10317, 29889, 2193, 29915, 29879, 1363, 8335, 957, 29915, 29879, 22522, 18973, 3897, 376, 29874, 21114, 3407, 746, 278, 10317, 310, 17181, 13877, 5684, 7405, 800, 29889, 1126, 8335, 957, 4502, 278, 2472, 304, 278, 6673, 1699, 8037, 2813, 5366, 1960, 29889, 13, 3596, 310, 445, 338, 297, 23151, 29915, 29879, 383, 12809, 934, 1192, 1584, 8037, 2813, 29915, 29879, 13917, 29889, 13, 29933, 300, 1452, 278, 6460, 14591, 1192, 777, 8886, 9301, 304, 1303, 1363, 29892, 4083, 383, 12809, 3878, 11607, 310, 10343, 28288, 365, 11054, 402, 6758, 29892, 278, 14591, 892, 451, 1754, 515, 2441, 29879, 1192, 322, 278, 9416, 4628, 297, 29895, 23473, 714, 825, 9826, 1603, 338, 5545, 770, 2164, 29892, 727, 1791, 29879, 263, 21028, 262, 1218, 17694, 310, 278, 383, 12809, 29915, 29879, 6297, 2645, 278, 2787, 3362, 1944, 3152, 29889, 13, 2831, 1342, 29892, 6483, 297, 278, 2066, 526, 263, 3652, 310, 2626, 359, 3971, 491, 8335, 957, 373, 4756, 29889, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29929, 29892, 9076, 292, 21082, 515, 263, 24332, 616, 1871, 424, 29889, 450, 8335, 957, 2626, 359, 304, 5164, 501, 29889, 29903, 29889, 9121, 29899, 524, 28286, 946, 15942, 322, 278, 6673, 29915, 29879, 9087, 310, 13925, 1370, 9571, 310, 5434, 10369, 946, 11476, 322, 9556, 29915, 29879, 5337, 373, 3444, 29889, 376, 1576, 10369, 674, 5337, 4908, 1894, 2878, 1099, 322, 916, 8104, 583, 1728, 9177, 29892, 21699, 411, 278, 5332, 6564, 373, 3444, 1699, 8335, 957, 5456, 29889, 13, 2831, 278, 1833, 14183, 2440, 310, 670, 2834, 21834, 23151, 29892, 263, 11747, 295, 549, 7498, 1129, 305, 898, 374, 562, 750, 408, 670, 4824, 8910, 4942, 450, 17606, 3879, 514, 29889, 13, 29950, 277, 1358, 29915, 29879, 286, 2092, 2381, 886, 29892, 4815, 26803, 29915, 29879, 17135, 29892, 330, 23364, 29899, 524, 342, 979, 25828, 4835, 29892, 19309, 4828, 322, 27357, 4845, 457, 2745, 670, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 526, 23531, 491, 23279, 5366, 874, 322, 3603, 5834, 29892, 322, 297, 3879, 514, 29915, 29879, 652, 4314, 29889, 13, 1576, 289, 15356, 276, 322, 443, 2072, 17324, 13589, 800, 2183, 304, 23151, 29892, 4049, 363, 563, 275, 15603, 9590, 29892, 3160, 2246, 936, 274, 6400, 457, 29892, 11658, 287, 626, 561, 300, 314, 1475, 29892, 3144, 1682, 852, 29892, 1243, 15664, 650, 29892, 707, 3665, 29875, 324, 29892, 322, 13979, 293, 520, 1489, 4841, 29889, 13, 797, 6124, 29892, 540, 471, 2183, 263, 10223, 362, 1754, 515, 263, 13736, 27372, 29892, 263, 752, 618, 310, 380, 719, 3049, 457, 322, 472, 1336, 457, 29892, 385, 6597, 310, 3031, 979, 28999, 4027, 29892, 322, 12727, 13901, 314, 1144, 322, 525, 880, 1199, 4286, 13, 3112, 2444, 1950 ]	1,332,826	12,288	CommonCrawl	8	11
that some of Hitler's behaviour, illnesses and suffering can be attributed to his medical care. Whether he blindly accepted such unorthodox medications or demanded them is unclear. And there is ample evidence in the files to undermine rumors that Hitler's personal physician tried to poison him or "administer narcotics that might have contributed to the impairment of Hitler's health" or that "Hitler inherited certain [psychophysical] traits in his childhood and later on, and that these might account for his crimes and other actions," according to an FBI investigation into the matter. The FBI's Hitler files have been available for some time to anyone who cared to schedule an appointment at FBI headquarters in Washington, but few have done so. Two recent critically acclaimed books, Hitler: Diagnosis of a Destructive Prophet by Fritz Redlich and Explaining Hitler by Ron Rosenbaum, fail to mention the FBI files -- although some of the records used to support these authors' opinions, such as Hitler's medical records, are duplicated in the files from other sources. Redlich and Rosenbaum may have avoided Hitler's FBI file because some of the information there concerns allegations that border on the absurd -- for instance, that Hitler survived the war. Historians generally accept that Hitler committed suicide April 30, 1945, in a Berlin bunker as Allied troops closed in on him. The Soviets recently made available forensic proof of this in their possession since the war's end. But there was no such certainty in the West 50 years ago when opinion polls showed that two of every three Americans believed Hitler indeed was alive. Hoover didn't rule it out but never concluded that the Nazi dictator was dead. Besieged with letters from witnesses swearing they had spotted the defeated Nazi dictator, the files show, the Hitler hunt began. Some tips were considered credible. One of these came from a doctor who claimed to have treated Hitler for an intestinal disorder in St. Louis -- an alarming story because the FBI obtained Hitler's classified medical records and verified that Hitler suffered from a similar condition. That information was not publicly known at the time. Other reports simply were bizarre. A 77-year-old man claimed to have found a letter written by Hitler in 1947. "Call it a Hitler hoax, if you will," the man wrote Hoover, "and believe its delivery in German over a USA radio would be the most startling sensation since Orson Welles' attack of the Martians." During an FBI interview with the elderly man, he admitted to "perpetrating this hoax to create a sensation," according to the interrogating agent's notes. "He seemed to be a psychopathic case," the agent wrote. And that was far from the only nut to roll out of the barrel. Others told tales of Hitler dining in a Washington restaurant in 1946; jumping out of a New Orleans train in 1948; purchasing 8,960 acres of land near Kit Carson, Colo.; and finding work as a butler in London in 1946. Most of the letters had one thing in common: suspicions and allegations but no proof -- such as this Oct. 15, 1945, letter from a New York man who wrote: I'll bet a dollar to a doughnut that Hitler is located right in New York City. There's no other city in the world where he could so easily be absorbed. No doubt you have considered this possibility, but I mention it for what it is worth anyway. As incredible as all of this sounds now, the FBI treated such matters very seriously. If the G-men couldn't chase down the tip, they made every effort to find the tipster and either expose a mistake or identify a prankster or mental case. For instance, on Oct. 10, 1948, a Washington woman who operated a boardinghouse wrote to the FBI, claiming one of her borders was Hitler. She mostly was worried about whether she might be prosecuted for harboring him and wanted to know if any "action could possibly be taken against her." The FBI dismissed the complaint with the note: "She is obviously demented." But while some sightings were dismissed without an intense investigation, others weren't. The files show that Hoover's G-men conducted a massive manhunt for Hitler on a scale not seen since	0.740055	2.465407	0.480993	0.906963	[ 0.8523686182977145, 0.6277418479419179 ]	[ 2.3651315420612513, 2.56568194316794 ]	[ 0.8208489053178607, 0.1411363105148766 ]	[ 1.2841615320679847, 0.5297641542746483 ]	1,024	[ 512, 512 ]	[ 393, 777, 310, 23151, 29915, 29879, 10468, 29892, 4486, 2264, 267, 322, 23164, 508, 367, 29393, 304, 670, 16083, 2562, 29889, 26460, 540, 16842, 368, 9259, 1316, 443, 2072, 17324, 13589, 800, 470, 24432, 963, 338, 20871, 29889, 13, 2855, 727, 338, 626, 552, 10757, 297, 278, 2066, 304, 563, 837, 457, 16558, 943, 393, 23151, 29915, 29879, 7333, 4824, 8910, 1898, 304, 27908, 1075, 470, 376, 6406, 1531, 302, 5666, 327, 1199, 393, 1795, 505, 26869, 304, 278, 2411, 1466, 358, 310, 23151, 29915, 29879, 9045, 29908, 470, 393, 376, 29950, 277, 1358, 23878, 3058, 518, 567, 3376, 3021, 952, 936, 29962, 1020, 1169, 297, 670, 2278, 6614, 322, 2678, 373, 29892, 322, 393, 1438, 1795, 3633, 363, 670, 2181, 1355, 322, 916, 8820, 1699, 5034, 304, 385, 383, 12809, 22522, 964, 278, 4383, 29889, 13, 1576, 383, 12809, 29915, 29879, 23151, 2066, 505, 1063, 3625, 363, 777, 931, 304, 5019, 1058, 274, 1965, 304, 20410, 385, 28573, 472, 383, 12809, 26463, 297, 7660, 29892, 541, 2846, 505, 2309, 577, 29889, 7803, 7786, 3994, 1711, 1035, 13190, 8277, 29892, 23151, 29901, 4671, 4211, 19263, 310, 263, 15435, 1247, 573, 1019, 561, 300, 491, 22839, 4367, 1470, 322, 12027, 433, 2827, 23151, 491, 11546, 28929, 29602, 29892, 4418, 304, 3585, 278, 383, 12809, 2066, 1192, 5998, 777, 310, 278, 6475, 1304, 304, 2304, 1438, 15717, 29915, 26971, 29892, 1316, 408, 23151, 29915, 29879, 16083, 6475, 29892, 526, 5141, 9169, 297, 278, 2066, 515, 916, 8974, 29889, 13, 9039, 1470, 322, 28929, 29602, 1122, 505, 28305, 23151, 29915, 29879, 383, 12809, 934, 1363, 777, 310, 278, 2472, 727, 21838, 16831, 800, 393, 5139, 373, 278, 6425, 18245, 1192, 363, 2777, 29892, 393, 23151, 10503, 2347, 278, 1370, 29889, 4731, 5834, 6892, 3544, 393, 23151, 19355, 23921, 680, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 297, 263, 5115, 289, 27560, 408, 838, 2957, 13230, 5764, 297, 373, 1075, 29889, 450, 317, 6895, 1691, 10325, 1754, 3625, 363, 575, 293, 5296, 310, 445, 297, 1009, 17715, 1951, 278, 1370, 29915, 29879, 1095, 29889, 1205, 727, 471, 694, 1316, 3058, 1017, 297, 278, 3122, 29871, 29945, 29900, 2440, 8020, 746, 9426, 1248, 3137, 10018, 393, 1023, 310, 1432, 2211, 23035, 13112, 23151, 6200, 471, 18758, 29889, 8335, 957, 3282, 29915, 29873, 5751, 372, 714, 541, 2360, 22834, 393, 278, 11409, 29875, 9657, 1061, 471, 7123, 29889, 6952, 347, 3192, 411, 8721, 515, 16277, 267, 7901, 4362, 896, 750, 805, 15048, 278, 16235, 11409, 29875, 9657, 1061, 29892, 278, 2066, 1510, 29892, 278, 23151, 298, 1657, 4689, 29889, 13, 9526, 25562, 892, 5545, 6625, 1821, 29889, 3118, 310, 1438, 2996, 515, 263, 11619, 1058, 17049, 304, 505, 14914, 23151, 363, 385, 938, 342, 979, 766, 2098, 297, 624, 29889, 5899, 1192, 385, 21200, 292, 5828, 1363, 278, 383, 12809, 7625, 23151, 29915, 29879, 770, 2164, 16083, 6475, 322, 26834, 393, 23151, 17654, 515, 263, 2788, 4195, 29889, 2193, 2472, 471, 451, 970, 368, 2998, 472, 278, 931, 29889, 13, 16107, 13676, 3763, 892, 289, 15356, 276, 29889, 319, 29871, 29955, 29955, 29899, 6360, 29899, 1025, 767, 17049, 304, 505, 1476, 263, 5497, 3971, 491, 23151, 297, 29871, 29896, 29929, 29946, 29955, 29889, 376, 5594, 372, 263, 23151, 5089, 1165, 29892, 565, 366, 674, 1699, 278, 767, 5456, 8335, 957, 29892, 376, 392, 4658, 967, 28289, 297, 5332, 975, 263, 8278, 7155, 723, 367, 278, 1556, 1369, 1847, 4771, 362, 1951, 1394, 1100, 399, 4999, 29915, 5337, 310, 278, 3760, 5834, 1213, 13, 29928, 3864, 385, 383, 12809, 15593, 411, 278, 27008, 368, 767, 29892, 540, 20186, 304, 376, 546, 10963, 29741, 445, 5089, 1165, 304, 1653, 263, 4771, 362, 1699, 5034, 304, 278, 1006, 9102, 1218, 10823, 29915, 29879, 11486, 29889, 376, 3868, 6140, 304, 367, 263, 11643, 459, 493, 293, 1206, 1699, 278, 10823, 5456, 29889, 1126, 393, 471, 2215, 515, 278, 871, 18254, 304, 9679, 714, 310, 278, 2594, 2674, 29889, 438, 3341, 5429, 29763, 310, 23151, 270, 2827, 297, 263, 7660, 27144, 297, 29871, 29896, 29929, 29946, 29953, 29936, 12500, 292, 714, 310, 263, 1570, 26884, 7945, 297, 29871, 29896, 29929, 29946, 29947, 29936, 10596, 5832, 29871, 29947, 29892, 29929, 29953, 29900, 23931, 310, 2982, 2978, 26240, 1704, 1100, 29892, 1530, 29877, 8670, 322, 9138, 664, 408, 263, 541, 1358, 297, 4517, 297, 29871, 29896, 29929, 29946, 29953, 29889, 13, 29924, 520, 310, 278, 8721, 750, 697, 2655, 297, 3619, 29901, 8872, 293, 1080, 322, 16831, 800, 541, 694, 5296, 1192, 1316, 408, 445, 4756, 29889, 29871, 29896, 29945, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 5497, 515, 263, 1570, 3088, 767, 1058, 5456, 29901, 13, 29902, 29915, 645, 1010, 263, 11232, 279, 304, 263, 270, 820, 21305, 393, 23151, 338, 5982, 1492, 297, 1570, 3088, 4412, 29889, 1670, 29915, 29879, 694, 916, 4272, 297, 278, 3186, 988, 540, 1033, 577, 5948, 367, 17977, 2580, 29889, 1939, 7404, 366, 505, 5545, 445, 13331, 29892, 541, 306, 3585, 372, 363, 825, 372, 338, 7088, 8763, 29889, 13, 2887, 29811, 1821, 408, 599, 310, 445, 10083, 1286, 29892, 278, 383, 12809, 14914, 1316, 13750, 1407, 25798, 29889, 960, 278, 402, 29899, 1527, 8496, 29915, 29873, 521, 559, 1623, 278, 6872, 29892, 896, 1754, 1432, 7225, 304, 1284, 278, 6872, 2475, 322, 2845, 24396, 263, 10171, 470, 12439, 263, 544, 804, 2475, 470, 19119, 1206, 29889, 1152, 2777, 29892, 373, 4756, 29889, 29871, 29896, 29900, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 263, 7660, 6114, 1058, 19623, 263, 7613, 292, 8697, 5456, 304, 278, 383, 12809, 29892, 5995, 292, 697, 310, 902, 28199, 471, 23151, 29889, 2296, 11149, 471, 6365, 1255, 1048, 3692, 1183, 1795, 367, 410, 3471, 3860, 363, 4023, 4089, 292, 1075, 322, 5131, 304, 1073, 565, 738, 376, 2467, 1033, 10075, 367, 4586, 2750, 902, 1213, 450, 383, 12809, 18918, 287, 278, 15313, 524, 411, 278, 4443, 29901, 376, 13468, 338, 12879, 316, 358, 287, 1213, 13, 6246, 1550, 777, 11126, 886, 892, 18918, 287, 1728, 385, 17818, 344, 22522, 29892, 4045, 2949, 264, 29915, 29873, 29889, 450, 2066, 1510, 393, 8335, 957, 29915, 29879, 402, 29899, 1527, 18043, 263, 20364, 767, 29882, 1657, 363, 23151, 373, 263, 6287, 451, 3595, 1951 ]	1,332,826	13,312	CommonCrawl	8	11
Charles Lindbergh's baby was kidnapped and murdered, with agents trekking to the four corners of the globe in search of the Nazi leader. The most frequent sighting was in South America -- a notoriously safe haven for Nazi war criminals, according to the FBI files. And so the FBI dispatched a team of G-men to investigate reports from newspaper articles (many contained in the FBI file) and independent witnesses apparently claiming Hitler was in Argentina. The Argentina stories intrigued Hoover. In 1944, a year before Hitler's reported death, Hoover received a tip that Hitler would receive refuge in Argentina, according to a Sept. 4, 1944, memo written by an FBI agent. The memo noted that Argentine political leaders had plans to conduct clandestine meetings with Hitler "for the arranging of importing arms and technicians into Argentina." The memo notes that bicycle factories there had been converted to plants for manufacturing munitions and that a "large wealthy German colony in Argentina affords tremendous possibilities" as a refuge for Hitler and his henchmen. "One of the members [of the postwar German planners], Count Luxburg, has been mentioned as operating a ranch which would serve in providing a haven." Within a year witnesses began flooding the FBI with Hitler sightings in Argentina. Some of these, the FBI rationalized, resulted from tabloid press reports claiming Hitler had escaped and was waiting for war to break out between the Soviet Union and the United States before emerging as a leader in the new world. And there were outspoken Nazi sympathizers such as Otto Abetz, Germany's wartime ambassador to France, boasting that Hitler "is certainly not dead" and was "not a coward -- I believe one day he will return." The most sensational story appeared June 20, 1948, in El Tiempo, a Spanish newspaper published in Colombia, claiming Hitler had escaped via submarine to Bogotà. The paper provided a detailed account of Hitler's supposedly cowardly flight and fueled dozens of similar stories around the world. Many of those appeared in the FBI files as clippings ranging from obscure magazines to the Associated Press. One such story claimed that the Swedes observed a mysterious yacht moving in and out of inlets on the North Sea or a Brazilian ship reportedly sunk by an unidentified submarine transporting a woman some claimed to be Eva Braun, Hitler's wife. Braun landed from that submarine off the coast of Argentina, one article claimed. The same article suggested a Japanese navy staff officer had volunteered details of a plan to evacuate Hitler and Braun to Japan after the fall of Germany. Closer to home a mysterious submarine reportedly was seen about 1,300 miles north of Catalina, Calif., in a location where Theodore Donay, a wealthy Detroit importer, disappeared. According to wire reports, Donay was convicted in 1943 as a traitor for aiding Hans Peter Krug, an escaped Nazi, and never was found. But none of these reports apparently could be directly linked to Hitler and the FBI repeatedly concluded they were baseless rumors. One agent expressed shock in the files that the Chicago Times carried such rumor and innuendo and chastised an unnamed writer. His reputation is extremely poor and he is generally considered to be a journalist of the most sensational and unreliable nature. One reason that Hitler's death was not believed for so long was that the Russians deliberately withheld information, writes Redlich. In fact, it wasn't until Russian journalist Lev Bezymenski wrote a book translated into English in 1968 that the West learned that the Russians performed autopsies on corpses recovered May 2, 1945, in shallow graves in a garden near the Berlin bunker. The bodies were believed to be Hitler, his wife and their two dogs. The United States was angered by the slow Russian revelations -- but the Russian government defended its actions, saying 30 years was customary for declassification of secrets. Meanwhile, at the Yalta conference in 1945, Stalin declared that Hitler had escaped. Further adding to continuing suspicions are the autopsy reports concerning a missing testicle and superficial accounts of main body organs. Indeed, Bezymenski since has acknowledged that the autopsy reports were false, casting more mystery on Hitler's	0.737316	2.945295	0.234977	0.935578	[ 1.038644476641546, 0.43598728788209146 ]	[ 3.238958289740394, 2.6516321150708064 ]	[ 0.5367899104748226, -0.06683545356663348 ]	[ 1.1592957591918462, 0.7118600730523502 ]	1,024	[ 512, 512 ]	[ 5322, 17277, 2552, 29882, 29915, 29879, 24354, 471, 26397, 29876, 17280, 322, 13406, 287, 29892, 411, 19518, 2578, 6859, 292, 304, 278, 3023, 26995, 310, 278, 15482, 915, 297, 2740, 310, 278, 11409, 29875, 11822, 29889, 13, 1576, 1556, 17091, 11126, 292, 471, 297, 4275, 6813, 1192, 263, 451, 272, 17365, 9109, 7359, 363, 11409, 29875, 1370, 15116, 19016, 29892, 5034, 304, 278, 383, 12809, 2066, 29889, 1126, 577, 278, 383, 12809, 13916, 287, 263, 3815, 310, 402, 29899, 1527, 304, 23033, 13676, 515, 19656, 7456, 313, 13011, 11122, 297, 278, 383, 12809, 934, 29897, 322, 7417, 16277, 267, 13229, 5995, 292, 23151, 471, 297, 13798, 29889, 13, 1576, 13798, 15874, 11158, 5526, 287, 8335, 957, 29889, 512, 29871, 29896, 29929, 29946, 29946, 29892, 263, 1629, 1434, 23151, 29915, 29879, 8967, 4892, 29892, 8335, 957, 4520, 263, 6872, 393, 23151, 723, 7150, 25447, 297, 13798, 29892, 5034, 304, 263, 28742, 29889, 29871, 29946, 29892, 29871, 29896, 29929, 29946, 29946, 29892, 2626, 29877, 3971, 491, 385, 383, 12809, 10823, 29889, 450, 2626, 29877, 11682, 393, 9385, 457, 8604, 20251, 750, 13900, 304, 7512, 274, 1049, 342, 457, 5870, 886, 411, 23151, 376, 1454, 278, 3948, 9776, 310, 28348, 10188, 322, 5722, 14722, 964, 13798, 1213, 450, 2626, 29877, 11486, 393, 289, 4245, 2841, 2114, 3842, 727, 750, 1063, 11543, 304, 18577, 363, 12012, 3864, 286, 348, 2187, 322, 393, 263, 376, 16961, 17173, 29891, 5332, 784, 2592, 297, 13798, 2756, 4339, 14586, 355, 681, 24496, 29908, 408, 263, 25447, 363, 23151, 322, 670, 19061, 305, 1527, 29889, 376, 6716, 310, 278, 5144, 518, 974, 278, 1400, 4495, 5332, 715, 812, 414, 1402, 3917, 18624, 3074, 29892, 756, 1063, 5276, 408, 13598, 263, 6350, 305, 607, 723, 9080, 297, 13138, 263, 7359, 1213, 13, 3047, 262, 263, 1629, 16277, 267, 4689, 5685, 3689, 278, 383, 12809, 411, 23151, 11126, 886, 297, 13798, 29889, 3834, 310, 1438, 29892, 278, 383, 12809, 17903, 1891, 29892, 20601, 515, 4434, 417, 333, 3965, 13676, 5995, 292, 23151, 750, 19824, 322, 471, 10534, 363, 1370, 304, 2867, 714, 1546, 278, 15308, 7761, 322, 278, 3303, 3900, 1434, 11176, 3460, 408, 263, 11822, 297, 278, 716, 3186, 29889, 1126, 727, 892, 714, 1028, 4476, 11409, 29875, 17520, 19427, 1316, 408, 13832, 1976, 6618, 29892, 9556, 29915, 29879, 281, 442, 603, 3181, 28760, 304, 3444, 29892, 1045, 579, 292, 393, 23151, 376, 275, 8959, 451, 7123, 29908, 322, 471, 376, 1333, 263, 21282, 538, 1192, 306, 4658, 697, 2462, 540, 674, 736, 1213, 13, 1576, 1556, 4771, 1288, 5828, 7470, 5306, 29871, 29906, 29900, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 297, 1260, 323, 3768, 1129, 29892, 263, 10432, 19656, 6369, 297, 21078, 29892, 5995, 292, 23151, 750, 19824, 3025, 1014, 24556, 304, 15872, 327, 30001, 29889, 450, 5650, 4944, 263, 13173, 3633, 310, 23151, 29915, 29879, 7424, 368, 21282, 538, 368, 16286, 322, 3576, 839, 437, 29920, 575, 310, 2788, 15874, 2820, 278, 3186, 29889, 9267, 310, 1906, 7470, 297, 278, 383, 12809, 2066, 408, 9335, 27775, 364, 9776, 515, 19726, 545, 2320, 834, 1475, 304, 278, 6853, 630, 5254, 29889, 13, 6716, 1316, 5828, 17049, 393, 278, 3925, 11696, 8900, 263, 22277, 2738, 343, 5860, 8401, 297, 322, 714, 310, 297, 10376, 373, 278, 4644, 14070, 470, 263, 16078, 713, 7751, 8967, 368, 269, 2960, 491, 385, 443, 1693, 2164, 1014, 24556, 8608, 292, 263, 6114, 777, 17049, 304, 367, 27040, 23514, 29892, 23151, 29915, 29879, 6532, 29889, 23514, 2982, 287, 515, 393, 1014, 24556, 1283, 278, 12180, 310, 13798, 29892, 697, 4274, 17049, 29889, 450, 1021, 4274, 7829, 263, 10369, 302, 5301, 13925, 12139, 750, 27886, 14561, 4902, 310, 263, 3814, 304, 3415, 22061, 403, 23151, 322, 23514, 304, 5546, 1156, 278, 6416, 310, 9556, 29889, 13, 29907, 5409, 261, 304, 3271, 263, 22277, 2738, 1014, 24556, 8967, 368, 471, 3595, 1048, 29871, 29896, 29892, 29941, 29900, 29900, 7800, 6641, 310, 11732, 1099, 29892, 3037, 361, 1696, 297, 263, 4423, 988, 450, 29221, 3872, 388, 29892, 263, 17173, 29891, 25749, 527, 18505, 29892, 24273, 29889, 7579, 304, 8014, 13676, 29892, 3872, 388, 471, 7602, 18186, 297, 29871, 29896, 29929, 29946, 29941, 408, 263, 1020, 2105, 363, 263, 4821, 6971, 5310, 476, 11124, 29892, 385, 19824, 11409, 29875, 29892, 322, 2360, 471, 1476, 29889, 13, 6246, 5642, 310, 1438, 13676, 13229, 1033, 367, 4153, 9024, 304, 23151, 322, 278, 383, 12809, 28424, 22834, 896, 892, 2362, 6393, 16558, 943, 29889, 3118, 10823, 13384, 19253, 297, 278, 2066, 393, 278, 10059, 10277, 8988, 1316, 16558, 272, 322, 297, 3433, 2765, 322, 521, 579, 3368, 385, 443, 17514, 9227, 29889, 13, 29950, 275, 19821, 338, 14154, 6460, 322, 540, 338, 6892, 5545, 304, 367, 263, 24452, 310, 278, 1556, 4771, 1288, 322, 443, 276, 492, 519, 5469, 29889, 13, 6716, 2769, 393, 23151, 29915, 29879, 4892, 471, 451, 13112, 363, 577, 1472, 471, 393, 278, 11688, 1039, 550, 23663, 2486, 411, 29882, 2495, 2472, 29892, 15873, 4367, 1470, 29889, 512, 2114, 29892, 372, 9007, 29915, 29873, 2745, 10637, 24452, 20708, 1522, 14022, 575, 1984, 5456, 263, 3143, 20512, 964, 4223, 297, 29871, 29896, 29929, 29953, 29947, 393, 278, 3122, 10972, 393, 278, 11688, 1039, 550, 8560, 1120, 3554, 583, 373, 14913, 267, 24776, 2610, 29871, 29906, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 297, 4091, 340, 2646, 1960, 297, 263, 16423, 2978, 278, 5115, 289, 27560, 29889, 450, 17873, 892, 13112, 304, 367, 23151, 29892, 670, 6532, 322, 1009, 1023, 26361, 29889, 13, 1576, 3303, 3900, 471, 27343, 287, 491, 278, 5232, 10637, 20474, 800, 1192, 541, 278, 10637, 5874, 822, 2760, 967, 8820, 29892, 5934, 29871, 29941, 29900, 2440, 471, 2888, 653, 363, 1602, 605, 2450, 310, 22183, 1372, 29889, 25065, 29892, 472, 278, 612, 284, 941, 21362, 297, 29871, 29896, 29929, 29946, 29945, 29892, 624, 25977, 8052, 393, 23151, 750, 19824, 29889, 13, 29943, 332, 721, 4417, 304, 3133, 292, 8872, 293, 1080, 526, 278, 1120, 3554, 29891, 13676, 19813, 263, 4567, 1243, 2512, 322, 2428, 29888, 5611, 15303, 310, 1667, 3573, 1638, 550, 29889, 14598, 29892, 1522, 14022, 575, 1984, 1951, 756, 24084, 3192, 393, 278, 1120, 3554, 29891, 13676, 892, 2089, 29892, 23013, 901, 29236, 373, 23151, 29915, 29879 ]	1,332,826	14,336	CommonCrawl	8	11
death. Redlich says: This only confirms what Western historians and forensic experts suspected: that the Soviet investigation was fraught with deceit, secrecy and incompetence. Compounding the mystery was how Hitler died. It generally was believed by historians that Hitler bit down on a glass ampoule containing potassium cyanide while shooting himself in the head on April 30, 1945. But Redlich observes: The question can be raised as to whether Hitler's Parkinson's tremor would have allowed him to follow this procedure. Proving that theory ended after it was learned that Hitler's remains had been transferred nine times from one burial site to another and, finally, to the Lefortove prison in Moscow where they were cremated. It wasn't until 1973 when two Western experts in forensic dentistry compared Russian medical reports and X-rays of Hitler's teeth that it became evident that the corpse found outside the bunker indeed was the Führer. For Redlich and others that is enough proof. It is certain that Hitler, who at present would be over 100 years old, is dead and that he died by suicide. No serious student of history maintains that he escaped with the help of his paladins. Meanwhile, the definitive proof that the X-rays of the corpse provided by the Russians to that forensic dentistry team are legitimate, rests in a Russian classified vault. What's inside that archive? Hitler's lower jawbone. At least that's what the Russians claim. Such details no doubt are being added to Hitler's FBI file even now. The FBI believed that Nazi dictator Adolf Hitler faked his suicide in 1945, and tried to track him down for nearly 30 years after his death, according to de-classified files. On 29 April 1945, Hitler and his lover Eva Braun killed themselves in the Berlin bunker. Now, 66 years on, the FBI files reveal that the US agency had maintained a detailed dossier on the Fuhrer and closely investigated any report that indicated he still was alive. The files reveal how FBI agents ranch in Argentina, living in a hotel in Denmark and in New York City. He was bearded, clean-shaven, suffered from asthma and stomach ulcers, according to informants who wrote their sightings in to the then FBI director, J Edgar Hoover. The FBI office in Los Angeles noted on 21 Sept, 1945: "Hitler and 50 of his closest family landed approximately 10 days after the fall of Berlin in two submarines in southern Argentina. Hitler has grown a beard and is hiding on a ranch." One theory Hoover ordered his agents to pursue was an extensive 11-year probe into the possibility that Hitler faked his own death with a bogus suicide in 1945. One sighting came from a doctor in 1954 who claimed to have treated Hitler for an intestinal disorder in St Louis. Others told tales of Hitler dining in a Washington restaurant in 1946, The Scotsman reported. ~The Indian Express There always have been doubts as to Hitler's alleged suicide in his bunker in Berlin on April 30, 1945. The most authoritarian doubter was the Russian Dictator Josef Stalin who was convinced that Hitler escaped to Spain in April of 1945. Even if one takes the submitted Russian report on Hitler's autopsy at face value, there still remains the fact that there was no trace of the corpse of Eva Braun, Hitler's mistress and later wife. This alone disproves the double-suicide theory now part of German history. There never was an identifiable corpse of Adolf Hitler nor of Eva Braun. The whole suicide story of Hitler rests solely on the concocted testimony of four fanatical Nazis. The Russians found the buried (and un-burned) corpse of the double of Adolf Hitler near the bunker. An Argentinean researcher has now claimed that Adolf Hitler did not commit suicide in the bunker in Berlin, but in fact fled to Spain in 1945. Journalist Abel Basti is basing his claim on an FBI document published in 1947 saying the United States was looking for him in Spain, and says	0.354492	2.307831	0.049198	0.854935	[ 0.6058270410779377, 0.10315615863539264 ]	[ 2.451081713964118, 2.1645811409545628 ]	[ 0.43026778740868327, -0.3318726407192896 ]	[ 1.0448354673887195, 0.6650354082237983 ]	1,024	[ 512, 512 ]	[ 4892, 29889, 13, 9039, 1470, 4083, 29901, 13, 4013, 871, 12388, 1516, 825, 10504, 3603, 5834, 322, 363, 575, 293, 2902, 1372, 2858, 6021, 29901, 393, 278, 15308, 22522, 471, 5227, 688, 400, 411, 23332, 277, 29892, 22183, 1270, 322, 297, 2388, 300, 663, 29889, 13, 6843, 12449, 278, 29236, 471, 920, 23151, 6423, 29889, 739, 6892, 471, 13112, 491, 3603, 5834, 393, 23151, 2586, 1623, 373, 263, 12917, 21332, 283, 280, 6943, 3104, 465, 1974, 5094, 273, 680, 1550, 27904, 3654, 297, 278, 2343, 373, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29889, 1205, 4367, 1470, 5366, 1960, 29901, 13, 1576, 1139, 508, 367, 10425, 408, 304, 3692, 23151, 29915, 29879, 4815, 26803, 29915, 29879, 14586, 272, 723, 505, 6068, 1075, 304, 1101, 445, 8792, 29889, 13, 1184, 1747, 393, 6368, 9698, 1156, 372, 471, 10972, 393, 23151, 29915, 29879, 9242, 750, 1063, 18440, 14183, 3064, 515, 697, 6866, 616, 3268, 304, 1790, 322, 29892, 7146, 29892, 304, 278, 951, 3921, 994, 8475, 297, 25820, 988, 896, 892, 907, 29885, 630, 29889, 13, 3112, 9007, 29915, 29873, 2745, 29871, 29896, 29929, 29955, 29941, 746, 1023, 10504, 2902, 1372, 297, 363, 575, 293, 12042, 6020, 9401, 10637, 16083, 13676, 322, 1060, 29899, 764, 29879, 310, 23151, 29915, 29879, 25287, 393, 372, 3897, 13602, 393, 278, 1034, 27358, 1476, 5377, 278, 289, 27560, 6200, 471, 278, 383, 4000, 261, 29889, 1152, 4367, 1470, 322, 4045, 393, 338, 3307, 5296, 29889, 13, 3112, 338, 3058, 393, 23151, 29892, 1058, 472, 2198, 723, 367, 975, 29871, 29896, 29900, 29900, 2440, 2030, 29892, 338, 7123, 322, 393, 540, 6423, 491, 23921, 680, 29889, 1939, 10676, 8368, 310, 4955, 7344, 29879, 393, 540, 19824, 411, 278, 1371, 310, 670, 5112, 328, 1144, 29889, 13, 6816, 273, 8000, 29892, 278, 8422, 573, 5296, 393, 278, 1060, 29899, 764, 29879, 310, 278, 1034, 27358, 4944, 491, 278, 11688, 1039, 550, 304, 393, 363, 575, 293, 12042, 6020, 3815, 526, 25204, 6490, 29892, 1791, 29879, 297, 263, 10637, 770, 2164, 325, 1292, 29889, 1724, 29915, 29879, 2768, 393, 18871, 29973, 23151, 29915, 29879, 5224, 432, 1450, 15933, 29889, 2180, 3203, 393, 29915, 29879, 825, 278, 11688, 1039, 550, 5995, 29889, 10506, 4902, 694, 7404, 526, 1641, 2715, 304, 23151, 29915, 29879, 383, 12809, 934, 1584, 1286, 29889, 13, 1576, 383, 12809, 13112, 393, 11409, 29875, 9657, 1061, 21834, 23151, 285, 12535, 670, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29892, 322, 1898, 304, 5702, 1075, 1623, 363, 8886, 29871, 29941, 29900, 2440, 1156, 670, 4892, 29892, 5034, 304, 316, 29899, 1990, 2164, 2066, 29889, 13, 2951, 29871, 29906, 29929, 3786, 29871, 29896, 29929, 29946, 29945, 29892, 23151, 322, 670, 658, 369, 27040, 23514, 9445, 6053, 297, 278, 5115, 289, 27560, 29889, 2567, 29892, 29871, 29953, 29953, 2440, 373, 29892, 278, 383, 12809, 2066, 10320, 284, 393, 278, 3148, 946, 3819, 750, 19949, 263, 13173, 270, 2209, 631, 373, 278, 11871, 26768, 322, 16467, 7405, 630, 738, 3461, 393, 18694, 540, 1603, 471, 18758, 29889, 13, 1576, 2066, 10320, 284, 920, 383, 12809, 19518, 6350, 305, 297, 13798, 29892, 8471, 297, 263, 16730, 297, 3384, 3502, 322, 297, 1570, 3088, 4412, 29889, 940, 471, 367, 25600, 29892, 5941, 29899, 845, 3496, 29892, 17654, 515, 8717, 29882, 655, 322, 380, 290, 496, 9238, 22543, 29892, 5034, 304, 1871, 1934, 1058, 5456, 1009, 11126, 886, 297, 304, 278, 769, 383, 12809, 8881, 29892, 435, 2155, 5397, 8335, 957, 29889, 13, 1576, 383, 12809, 8034, 297, 4602, 10722, 11682, 373, 29871, 29906, 29896, 28742, 29892, 29871, 29896, 29929, 29946, 29945, 29901, 376, 29950, 277, 1358, 322, 29871, 29945, 29900, 310, 670, 21438, 3942, 2982, 287, 14235, 29871, 29896, 29900, 3841, 1156, 278, 6416, 310, 5115, 297, 1023, 1014, 3034, 1475, 297, 14841, 13798, 29889, 23151, 756, 21633, 263, 367, 538, 322, 338, 25508, 373, 263, 6350, 305, 1213, 13, 6716, 6368, 8335, 957, 10372, 670, 19518, 304, 12359, 434, 471, 385, 20607, 29871, 29896, 29896, 29899, 6360, 410, 915, 964, 278, 13331, 393, 23151, 285, 12535, 670, 1914, 4892, 411, 263, 26652, 375, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 6716, 11126, 292, 2996, 515, 263, 11619, 297, 29871, 29896, 29929, 29945, 29946, 1058, 17049, 304, 505, 14914, 23151, 363, 385, 938, 342, 979, 766, 2098, 297, 624, 5899, 29889, 438, 3341, 5429, 29763, 310, 23151, 270, 2827, 297, 263, 7660, 27144, 297, 29871, 29896, 29929, 29946, 29953, 29892, 450, 2522, 1862, 1171, 8967, 29889, 13, 30022, 1576, 7560, 14657, 13, 8439, 2337, 505, 1063, 27455, 1372, 408, 304, 23151, 29915, 29879, 16831, 287, 23921, 680, 297, 670, 289, 27560, 297, 5115, 373, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29889, 450, 1556, 4148, 3673, 713, 27455, 357, 471, 278, 10637, 360, 919, 1061, 17374, 624, 25977, 1058, 471, 25617, 393, 23151, 19824, 304, 13616, 297, 3786, 310, 29871, 29896, 29929, 29946, 29945, 29889, 13, 29923, 854, 565, 697, 4893, 278, 18397, 10637, 3461, 373, 23151, 29915, 29879, 1120, 3554, 29891, 472, 3700, 995, 29892, 727, 1603, 9242, 278, 2114, 393, 727, 471, 694, 9637, 310, 278, 1034, 27358, 310, 27040, 23514, 29892, 23151, 29915, 29879, 5862, 1253, 322, 2678, 6532, 29889, 910, 7432, 766, 771, 1960, 278, 3765, 29899, 2146, 293, 680, 6368, 1286, 760, 310, 5332, 4955, 29889, 13, 8439, 2360, 471, 385, 2893, 28677, 1034, 27358, 310, 21834, 23151, 3643, 310, 27040, 23514, 29889, 450, 3353, 23921, 680, 5828, 310, 23151, 1791, 29879, 14419, 368, 373, 278, 378, 1111, 2954, 28523, 2592, 310, 3023, 13524, 271, 936, 11409, 275, 29889, 450, 11688, 1039, 550, 1476, 278, 18550, 313, 392, 443, 29899, 18712, 287, 29897, 1034, 27358, 310, 278, 3765, 310, 21834, 23151, 2978, 278, 289, 27560, 29889, 13, 2744, 9385, 457, 273, 5925, 261, 756, 1286, 17049, 393, 21834, 23151, 1258, 451, 9063, 23921, 680, 297, 278, 289, 27560, 297, 5115, 29892, 541, 297, 2114, 27481, 304, 13616, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 29967, 4659, 391, 1976, 295, 25315, 29875, 338, 2362, 292, 670, 5995, 373, 385, 383, 12809, 1842, 6369, 297, 29871, 29896, 29929, 29946, 29955, 5934, 278, 3303, 3900, 471, 3063, 363, 1075, 297, 13616, 29892, 322, 4083 ]	1,332,826	15,360	CommonCrawl	8	11
Flexibility of deployment: challenges and policy options for retaining health workers during crisis in Zimbabwe Wilson Mashange1, Tim Martineau ORCID: orcid.org/0000-0003-4833-31492, Pamela Chandiwana1, Yotamu Chirwa1, Vongai Mildred Pepukai1, Shungu Munyati1 & Alvaro Alonso-Garbayo ORCID: orcid.org/0000-0002-4120-15412 Zimbabwe experienced a socio-economic crisis from 1997 to 2008 which heavily impacted all sectors. In this context, human resource managers were confronted with the challenge of health worker shortage in rural areas and, at the same time, had to operate under a highly centralised, government-centred system which defined health worker deployment policies. This study examines the implementation of deployment policies in Zimbabwe before, during and after the crisis in order to analyse how the official policy environment evolved over time, present the actual practices used by managers to cope with the crisis and draw lessons. 'Deployment' here was considered to include all the human resource management functions for getting staff into posts and managing subsequent movements: recruitment, bonding, transfer and secondment. The study contributes to address the existing paucity of evidence on flexibility on implementation of policies in crisis/conflict settings. This retrospective study investigates deployment policies in government and faith-based organisation health facilities in Zimbabwe before, during and after the crisis. A document review was done to understand the policy environment. In-depth interviews with key informant including policy makers, managers and health workers in selected facilities in three mainly rural districts in the Midlands province were conducted. Data generated was analysed using a framework approach. Before the crisis, health workers were allowed to look for jobs on their own, while during the crisis, they were given three choices and after the crisis the preference choice was withdrawn. The government froze recruitment in all sectors during the crisis which severely affected health workers' deployment. In practice, the implementation of the deployment policies was relatively flexible. In some cases, health workers were transferred to retain them, the recruitment freeze was temporarily lifted to fill priority vacancies, the length of the bonding period was reduced including relaxation of withholding certificates, and managers used secondment to relocate workers to priority areas. Flexibility in the implementation of deployment policies during crises may increase the resilience of the system and contribute to the retention of health workers. This, in turn, may assist in ensuring coverage of health services in hard-to-reach areas. Scaling up the healthcare workforce as well as improving distribution, management, performance and quality were solutions proposed to address human resources for health (HRH) crisis in the last decade [1, 2]. The inequitable distribution of HRH, especially between urban and rural areas, and the problems related to filling posts in remote areas have been identified as barriers in the provision of healthcare and the achievement of the health-related Sustainable Development Goal [3]. This is particularly prevalent in post conflict and crisis-affected settings [4, 5]. Much research has already been devoted to understanding health worker (HW) behaviour in relation to taking up and remaining in posts in rural/remote locations [6, 7]. Additionally, research has shown that the problem of mal-distribution of HRH is often made worse by the mismanagement of deployment systems [8, 9]. The term 'deployment' is frequently used in relation to distribution of staff, but rarely defined. More specifically, deployment is defined as 'the movement of staff from one's current assignment to another, to meet operational needs' [10] or simply 'the transfer of a person from one position to another' [11]. In this study, however, we define deployment as a 'bundle' of human resource management functions for getting staff into posts and managing subsequent movements including recruitment, reappointment, bonding, secondment and transfer [12]. Within a country's healthcare system and regulations, each of these human resource management (HRM) functions is governed by a set of policies which are sometimes official and explicit, but in other cases, they remain unwritten rules. In this paper, we explore the official policies and the informal practices that rule deployment of HWs in Zimbabwe, with	0.44626	0.989929	1.673026	1.102066	[ 0.08398070262941, 0.8085390045697542 ]	[ 0.7535658188825048, 1.2262917643482705 ]	[ 1.3280971103947146, 2.0179546692992356 ]	[ 1.0136190241696847, 1.190512202410881 ]	1,024	[ 512, 512 ]	[ 383, 2506, 4127, 310, 18209, 29901, 18066, 267, 322, 8898, 3987, 363, 11551, 292, 9045, 17162, 2645, 24161, 297, 796, 19977, 370, 705, 13, 29594, 1100, 341, 1161, 927, 29896, 29892, 13, 13711, 3760, 457, 585, 6323, 29907, 1367, 29901, 470, 25232, 29889, 990, 29914, 29900, 29900, 29900, 29900, 29899, 29900, 29900, 29900, 29941, 29899, 29946, 29947, 29941, 29941, 29899, 29941, 29896, 29946, 29929, 29906, 29892, 13, 29925, 314, 3100, 678, 392, 9429, 1648, 29896, 29892, 13, 29979, 327, 314, 29884, 678, 381, 2766, 29896, 29892, 13, 29963, 549, 1794, 341, 789, 1127, 349, 1022, 22971, 29875, 29896, 29892, 13, 2713, 686, 29884, 13564, 29891, 2219, 29896, 669, 13, 2499, 1707, 29877, 838, 16911, 29899, 29954, 279, 27495, 29877, 6323, 29907, 1367, 29901, 470, 25232, 29889, 990, 29914, 29900, 29900, 29900, 29900, 29899, 29900, 29900, 29900, 29906, 29899, 29946, 29896, 29906, 29900, 29899, 29896, 29945, 29946, 29896, 29906, 13, 29999, 19977, 370, 705, 18860, 263, 577, 3934, 29899, 29872, 4599, 293, 24161, 515, 29871, 29896, 29929, 29929, 29955, 304, 29871, 29906, 29900, 29900, 29947, 607, 20365, 10879, 287, 599, 409, 14359, 29889, 512, 445, 3030, 29892, 5199, 6503, 767, 18150, 892, 21751, 287, 411, 278, 18766, 310, 9045, 15645, 3273, 482, 297, 17692, 10161, 322, 29892, 472, 278, 1021, 931, 29892, 750, 304, 21994, 1090, 263, 10712, 6555, 3368, 29892, 5874, 29899, 1760, 1127, 1788, 607, 3342, 9045, 15645, 18209, 24833, 29889, 910, 6559, 4392, 1475, 278, 5314, 310, 18209, 24833, 297, 796, 19977, 370, 705, 1434, 29892, 2645, 322, 1156, 278, 24161, 297, 1797, 304, 16455, 344, 920, 278, 6221, 8898, 5177, 15220, 1490, 975, 931, 29892, 2198, 278, 3935, 23274, 1304, 491, 767, 18150, 304, 1302, 412, 411, 278, 24161, 322, 4216, 3109, 787, 29889, 525, 8498, 22812, 29915, 1244, 471, 5545, 304, 3160, 599, 278, 5199, 6503, 10643, 3168, 363, 2805, 13925, 964, 11803, 322, 767, 6751, 15352, 24147, 29901, 1162, 9216, 358, 29892, 21224, 292, 29892, 6782, 322, 1473, 358, 29889, 450, 6559, 640, 5026, 304, 3211, 278, 5923, 24571, 12690, 310, 10757, 373, 8525, 4127, 373, 5314, 310, 24833, 297, 24161, 29914, 5527, 29176, 6055, 29889, 13, 4013, 3240, 1883, 12645, 6559, 7405, 1078, 18209, 24833, 297, 5874, 322, 10847, 29899, 6707, 24788, 9045, 23330, 297, 796, 19977, 370, 705, 1434, 29892, 2645, 322, 1156, 278, 24161, 29889, 319, 1842, 9076, 471, 2309, 304, 2274, 278, 8898, 5177, 29889, 512, 29899, 19488, 1006, 7406, 411, 1820, 1871, 424, 3704, 8898, 2136, 414, 29892, 767, 18150, 322, 9045, 17162, 297, 4629, 23330, 297, 2211, 14364, 17692, 24172, 297, 278, 13370, 5252, 12291, 892, 18043, 29889, 3630, 5759, 471, 3483, 952, 287, 773, 263, 6890, 2948, 29889, 13, 18743, 278, 24161, 29892, 9045, 17162, 892, 6068, 304, 1106, 363, 17643, 373, 1009, 1914, 29892, 1550, 2645, 278, 24161, 29892, 896, 892, 2183, 2211, 19995, 322, 1156, 278, 24161, 278, 24583, 7348, 471, 411, 19811, 1233, 29889, 450, 5874, 14671, 911, 1162, 9216, 358, 297, 599, 409, 14359, 2645, 278, 24161, 607, 2775, 873, 15201, 9045, 17162, 29915, 18209, 29889, 512, 6944, 29892, 278, 5314, 310, 278, 18209, 24833, 471, 13774, 25706, 29889, 512, 777, 4251, 29892, 9045, 17162, 892, 18440, 304, 11551, 963, 29892, 278, 1162, 9216, 358, 3889, 911, 471, 5382, 6275, 26239, 304, 5445, 20136, 11757, 273, 2478, 29892, 278, 3309, 310, 278, 21224, 292, 3785, 471, 12212, 3704, 26681, 362, 310, 411, 8948, 292, 23199, 1078, 29892, 322, 767, 18150, 1304, 1473, 358, 304, 337, 2029, 403, 17162, 304, 20136, 10161, 29889, 13, 29943, 2506, 4127, 297, 278, 5314, 310, 18209, 24833, 2645, 2181, 4637, 1122, 7910, 278, 620, 2638, 663, 310, 278, 1788, 322, 29126, 304, 278, 3240, 2509, 310, 9045, 17162, 29889, 910, 29892, 297, 2507, 29892, 1122, 6985, 297, 5662, 3864, 23746, 310, 9045, 5786, 297, 2898, 29899, 517, 29899, 276, 496, 10161, 29889, 13, 29636, 292, 701, 278, 9045, 18020, 664, 10118, 408, 1532, 408, 4857, 1747, 4978, 29892, 10643, 29892, 4180, 322, 11029, 892, 6851, 7972, 304, 3211, 5199, 7788, 363, 9045, 313, 20938, 29950, 29897, 24161, 297, 278, 1833, 316, 6332, 518, 29896, 29892, 29871, 29906, 1822, 450, 297, 1686, 8270, 4978, 310, 379, 29934, 29950, 29892, 7148, 1546, 17164, 322, 17692, 10161, 29892, 322, 278, 4828, 4475, 304, 27523, 11803, 297, 7592, 10161, 505, 1063, 15659, 408, 2594, 26536, 297, 278, 25161, 310, 9045, 18020, 322, 278, 27012, 882, 310, 278, 9045, 29899, 12817, 317, 504, 475, 519, 14650, 2921, 284, 518, 29941, 1822, 910, 338, 10734, 758, 791, 296, 297, 1400, 14529, 322, 24161, 29899, 3470, 26458, 6055, 518, 29946, 29892, 29871, 29945, 1822, 13, 29924, 987, 5925, 756, 2307, 1063, 24600, 304, 8004, 9045, 15645, 313, 29950, 29956, 29897, 10468, 297, 8220, 304, 5622, 701, 322, 9886, 297, 11803, 297, 17692, 29914, 16674, 14354, 518, 29953, 29892, 29871, 29955, 1822, 19814, 29892, 5925, 756, 4318, 393, 278, 1108, 310, 4439, 29899, 27691, 310, 379, 29934, 29950, 338, 4049, 1754, 15029, 491, 278, 3984, 21895, 310, 18209, 6757, 518, 29947, 29892, 29871, 29929, 1822, 450, 1840, 525, 16519, 358, 29915, 338, 13672, 1304, 297, 8220, 304, 4978, 310, 13925, 29892, 541, 23703, 3342, 29889, 5853, 10816, 29892, 18209, 338, 3342, 408, 525, 1552, 10298, 310, 13925, 515, 697, 29915, 29879, 1857, 12827, 304, 1790, 29892, 304, 5870, 1751, 1288, 4225, 29915, 518, 29896, 29900, 29962, 470, 3763, 525, 1552, 6782, 310, 263, 2022, 515, 697, 2602, 304, 1790, 29915, 518, 29896, 29896, 1822, 512, 445, 6559, 29892, 3138, 29892, 591, 4529, 18209, 408, 263, 525, 16718, 29915, 310, 5199, 6503, 10643, 3168, 363, 2805, 13925, 964, 11803, 322, 767, 6751, 15352, 24147, 3704, 1162, 9216, 358, 29892, 337, 932, 2461, 358, 29892, 21224, 292, 29892, 1473, 358, 322, 6782, 518, 29896, 29906, 1822, 23732, 263, 4234, 29915, 29879, 9045, 18020, 1788, 322, 1072, 8250, 29892, 1269, 310, 1438, 5199, 6503, 10643, 313, 20938, 29924, 29897, 3168, 338, 4095, 287, 491, 263, 731, 310, 24833, 607, 526, 6041, 6221, 322, 6261, 29892, 541, 297, 916, 4251, 29892, 896, 3933, 443, 17625, 6865, 29889, 512, 445, 5650, 29892, 591, 26987, 278, 6221, 24833, 322, 278, 1871, 284, 23274, 393, 5751, 18209, 310, 379, 29956, 29879, 297, 796, 19977, 370, 705, 29892, 411 ]	1,332,829	0	CommonCrawl	6	2
the aim of reviewing the changes in deployment policies and the implementation practices during the crisis and post-crisis periods. Zimbabwe experienced a decade of severe economic, social and political crisis between 1997 and 2008. The crisis led to a reversal of gains made in key health indicators including immunisation, maternal mortality or infant mortality [13,14,15,16] and had an important impact on the health workforce. While out-migration of HWs was reported before 1997 [17, 18], it increased substantially during the crisis leaving the staffing situation severely deteriorated with high vacancy rates which peaked between 2008 and 2009 reaching up to 43% [13, 15, 19]. Prior to 2005, the health services in Zimbabwe were delivered through facilities run separately by government, faith-based organisations (FBOs) or private sector. Government hospitals and primary healthcare facilities are managed either by the Ministry of Health and Child Care (MOHCC) or Ministry of Local and Urban Development [20]. The Zimbabwe Association of Church Related Hospitals manages church-related health providers in coordination with the MOHCC particularly for issues related to their workforce. The majority of FBO facilities operate in rural settings [21] while government run facilities cover both urban and rural areas. In 2005, Government of Zimbabwe decided to unify health services provided by both government and FBOs. The Health Services Board (HSB) was established through the Health Act of 2004 which resulted in both government and FBO health service providers being under one central authority. Due to the enactment of the Health Services Regulations (HSR) in 2006, the deployment of government HWs employed in government and FBO facilities should be managed by MOHCC through the HSB. However, implementation of the new policy was uneven. Service contracts between MOHCC and FBOs were not implemented in all provinces simultaneously [14] which resulted in the uneven adoption of the terms comprised in the new regulation [22] particularly in those related to staff recruitment and deployment by health services managed by FBOs. This retrospective study looks at changes in deployment policies and practices in Zimbabwe's health sector during the pre-crisis period (1980–1997), crisis period (1997–2008) and the post-crisis period (2009–2013). There is little evidence of flexibility of these policies and practices in time of conflict or crisis [23] with the exception of post-conflict Timor Leste [24, 25]. This study sought to contribute to this evidence. This retrospective qualitative study was undertaken in two healthcare providers (FBOs and Government) in three largely rural districts in Zimbabwe where implementation of deployment policies and practices was explored. Data was collected through interviews with key informants involved in policy development and with managers and HWs involved in their implementation. Narratives about the life of HWs were used to generate data about the impact that changes in HRH deployment systems and practices have on their professional trajectory and experiences [26]. A total of 76 documents were extracted from published and unpublished literature and analysed using content analysis to explore the evolution of deployment policies including the rationale for changes. The study focuses on four main HRM functions related to deployment: recruitment, bonding, transfer and secondment. We define recruitment as the process of attracting the right people and selecting and offering employment to the best candidates. We have also included here appointment, which in this study refers to the allocation of a position to a HW when entering the health workforce for the first time. We consider bonding as the formal agreement with the government comprising compulsory service that newly graduated HWs who were beneficiaries of public financial support for their studies agree to provide after graduation to compensate for the government's investment. Transfer in this study refers to the process of moving HWs from one post to another and secondment, which is often considered as a modality of transfer, refers in this study to the temporary transfer of workers to another post for a limited period for a specific reason. The study was undertaken in three largely rural districts of the Midlands province. The districts are referred to numerically in this paper as districts 1, 2	0.437357	1.552186	1.693316	1.247742	[ 0.40585442844411873, 0.4688594981780617 ]	[ 1.4698172514063923, 1.6345550808868863 ]	[ 1.5614312847300673, 1.8252003513700312 ]	[ 1.1488902781188348, 1.3465944185060539 ]	1,024	[ 512, 512 ]	[ 278, 12242, 310, 9076, 292, 278, 3620, 297, 18209, 24833, 322, 278, 5314, 23274, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 29889, 13, 29999, 19977, 370, 705, 18860, 263, 316, 6332, 310, 22261, 17407, 29892, 5264, 322, 8604, 24161, 1546, 29871, 29896, 29929, 29929, 29955, 322, 29871, 29906, 29900, 29900, 29947, 29889, 450, 24161, 5331, 304, 263, 18764, 284, 310, 330, 2708, 1754, 297, 1820, 9045, 4221, 4097, 3704, 5198, 348, 4371, 29892, 1775, 17196, 5758, 2877, 470, 28056, 5758, 2877, 518, 29896, 29941, 29892, 29896, 29946, 29892, 29896, 29945, 29892, 29896, 29953, 29962, 322, 750, 385, 4100, 10879, 373, 278, 9045, 664, 10118, 29889, 5806, 714, 29899, 29885, 16783, 310, 379, 29956, 29879, 471, 8967, 1434, 29871, 29896, 29929, 29929, 29955, 518, 29896, 29955, 29892, 29871, 29896, 29947, 1402, 372, 11664, 23228, 368, 2645, 278, 24161, 10124, 278, 13925, 292, 6434, 2775, 873, 270, 1308, 1611, 630, 411, 1880, 11757, 6906, 19257, 607, 1236, 12535, 1546, 29871, 29906, 29900, 29900, 29947, 322, 29871, 29906, 29900, 29900, 29929, 20888, 701, 304, 29871, 29946, 29941, 29995, 518, 29896, 29941, 29892, 29871, 29896, 29945, 29892, 29871, 29896, 29929, 1822, 13, 29925, 13479, 304, 29871, 29906, 29900, 29900, 29945, 29892, 278, 9045, 5786, 297, 796, 19977, 370, 705, 892, 20115, 1549, 23330, 1065, 16949, 491, 5874, 29892, 10847, 29899, 6707, 17459, 800, 313, 29943, 8456, 29879, 29897, 470, 2024, 17535, 29889, 10354, 29418, 277, 1338, 322, 7601, 9045, 18020, 23330, 526, 8745, 2845, 491, 278, 20886, 310, 15202, 322, 10517, 10057, 313, 6720, 29950, 4174, 29897, 470, 20886, 310, 9959, 322, 22589, 14650, 518, 29906, 29900, 1822, 450, 796, 19977, 370, 705, 7993, 310, 6291, 6376, 630, 379, 4705, 277, 1338, 767, 1179, 6586, 29899, 12817, 9045, 1326, 11376, 297, 29311, 3381, 411, 278, 16999, 29950, 4174, 10734, 363, 5626, 4475, 304, 1009, 664, 10118, 29889, 450, 13638, 310, 383, 8456, 23330, 21994, 297, 17692, 6055, 518, 29906, 29896, 29962, 1550, 5874, 1065, 23330, 4612, 1716, 17164, 322, 17692, 10161, 29889, 13, 797, 29871, 29906, 29900, 29900, 29945, 29892, 10354, 310, 796, 19977, 370, 705, 8459, 304, 443, 1598, 9045, 5786, 4944, 491, 1716, 5874, 322, 383, 8456, 29879, 29889, 450, 15202, 15538, 12590, 313, 29950, 1744, 29897, 471, 7841, 1549, 278, 15202, 3185, 310, 29871, 29906, 29900, 29900, 29946, 607, 20601, 297, 1716, 5874, 322, 383, 8456, 9045, 2669, 1326, 11376, 1641, 1090, 697, 6555, 14329, 29889, 16809, 304, 278, 427, 627, 358, 310, 278, 15202, 15538, 2169, 8250, 313, 29950, 14098, 29897, 297, 29871, 29906, 29900, 29900, 29953, 29892, 278, 18209, 310, 5874, 379, 29956, 29879, 15723, 297, 5874, 322, 383, 8456, 23330, 881, 367, 8745, 491, 16999, 29950, 4174, 1549, 278, 379, 1744, 29889, 2398, 29892, 5314, 310, 278, 716, 8898, 471, 1597, 854, 29889, 6692, 8078, 29879, 1546, 16999, 29950, 4174, 322, 383, 8456, 29879, 892, 451, 8762, 297, 599, 28058, 21699, 518, 29896, 29946, 29962, 607, 20601, 297, 278, 1597, 854, 594, 3385, 310, 278, 4958, 7199, 3368, 297, 278, 716, 1072, 2785, 518, 29906, 29906, 29962, 10734, 297, 1906, 4475, 304, 13925, 1162, 9216, 358, 322, 18209, 491, 9045, 5786, 8745, 491, 383, 8456, 29879, 29889, 910, 3240, 1883, 12645, 6559, 3430, 472, 3620, 297, 18209, 24833, 322, 23274, 297, 796, 19977, 370, 705, 29915, 29879, 9045, 17535, 2645, 278, 758, 29899, 29883, 3780, 275, 3785, 313, 29896, 29929, 29947, 29900, 29994, 29896, 29929, 29929, 29955, 511, 24161, 3785, 313, 29896, 29929, 29929, 29955, 29994, 29906, 29900, 29900, 29947, 29897, 322, 278, 1400, 29899, 29883, 3780, 275, 3785, 313, 29906, 29900, 29900, 29929, 29994, 29906, 29900, 29896, 29941, 467, 13, 8439, 338, 2217, 10757, 310, 8525, 4127, 310, 1438, 24833, 322, 23274, 297, 931, 310, 14529, 470, 24161, 518, 29906, 29941, 29962, 411, 278, 3682, 310, 1400, 29899, 5527, 29176, 7870, 272, 365, 4196, 518, 29906, 29946, 29892, 29871, 29906, 29945, 1822, 910, 6559, 18365, 304, 29126, 304, 445, 10757, 29889, 13, 4013, 3240, 1883, 12645, 4021, 23378, 6559, 471, 22332, 9424, 297, 1023, 9045, 18020, 1326, 11376, 313, 29943, 8456, 29879, 322, 10354, 29897, 297, 2211, 18425, 17692, 24172, 297, 796, 19977, 370, 705, 988, 5314, 310, 18209, 24833, 322, 23274, 471, 3902, 4395, 29889, 3630, 471, 16531, 1549, 1006, 7406, 411, 1820, 1871, 1934, 9701, 297, 8898, 5849, 322, 411, 767, 18150, 322, 379, 29956, 29879, 9701, 297, 1009, 5314, 29889, 405, 2749, 5056, 1048, 278, 2834, 310, 379, 29956, 29879, 892, 1304, 304, 5706, 848, 1048, 278, 10879, 393, 3620, 297, 379, 29934, 29950, 18209, 6757, 322, 23274, 505, 373, 1009, 10257, 23324, 706, 322, 27482, 518, 29906, 29953, 1822, 13, 29909, 3001, 310, 29871, 29955, 29953, 10701, 892, 23892, 515, 6369, 322, 443, 5467, 3726, 12845, 322, 3483, 952, 287, 773, 2793, 7418, 304, 26987, 278, 14675, 310, 18209, 24833, 3704, 278, 364, 11464, 363, 3620, 29889, 13, 1576, 6559, 8569, 267, 373, 3023, 1667, 379, 29934, 29924, 3168, 4475, 304, 18209, 29901, 1162, 9216, 358, 29892, 21224, 292, 29892, 6782, 322, 1473, 358, 29889, 1334, 4529, 1162, 9216, 358, 408, 278, 1889, 310, 13978, 292, 278, 1492, 2305, 322, 18851, 322, 27032, 5703, 358, 304, 278, 1900, 21669, 29889, 1334, 505, 884, 5134, 1244, 28573, 29892, 607, 297, 445, 6559, 14637, 304, 278, 24082, 310, 263, 2602, 304, 263, 379, 29956, 746, 18055, 278, 9045, 664, 10118, 363, 278, 937, 931, 29889, 1334, 2050, 21224, 292, 408, 278, 11595, 17327, 411, 278, 5874, 7199, 5921, 752, 7273, 706, 2669, 393, 15141, 23588, 379, 29956, 29879, 1058, 892, 7795, 1654, 4314, 310, 970, 18161, 2304, 363, 1009, 11898, 8661, 304, 3867, 1156, 10591, 362, 304, 22874, 403, 363, 278, 5874, 29915, 29879, 13258, 358, 29889, 17934, 297, 445, 6559, 14637, 304, 278, 1889, 310, 8401, 379, 29956, 29879, 515, 697, 1400, 304, 1790, 322, 1473, 358, 29892, 607, 338, 4049, 5545, 408, 263, 878, 2877, 310, 6782, 29892, 14637, 297, 445, 6559, 304, 278, 13201, 6782, 310, 17162, 304, 1790, 1400, 363, 263, 9078, 3785, 363, 263, 2702, 2769, 29889, 13, 1576, 6559, 471, 22332, 9424, 297, 2211, 18425, 17692, 24172, 310, 278, 13370, 5252, 12291, 29889, 450, 24172, 526, 12992, 304, 4825, 1711, 297, 445, 5650, 408, 24172, 29871, 29896, 29892, 29871, 29906 ]	1,332,829	1,024	CommonCrawl	6	2
and 3. The major providers of healthcare in the selected districts are government and a large FBO which owns 52% of the faith-based hospitals in the country (Table 1). Government-run facilities in this study are comprised of those managed by HSB and rural district councils (RDC). Table 1 Population and numbers of facilities by ownership in study districts A total of 17 key informant interviews (KIIs) from national and local levels for both government and FBOs were purposively selected according to their knowledge and experience of policy development relating to deployment (Table 2). Table 2 Number of key informant interviews The overall manager and the officer responsible for HRM including deployment at facilities were selected in each study district for interviews and asked questions mainly about deployment practices. A total of 11 in-depth interviews (IDI) were carried out at both government and FBO institutions (Table 3). Table 3 Distribution of IDIs with facility managers by sector and gender A total of 67 interviews with midwives, nurses and environmental health practitioners (42 females and 25 males) working in the three different sectors with different lengths of service (11 < 5 years; 56 ≥ 5 years) were conducted (Table 4) using the 'life history' technique to elicit their views and perspectives [26]. Table 4 Distribution of IDIs with HWs by sector and gender Separate topic guides for semi-structured interviews for each group were developed and used flexibly as a guide for the interviewer allowing for new emerging thematic areas introduced by interviewees. The interviews for the KIIs lasted an average of 25 min while those for managers and health workers interviews with life histories lasted between 30 and 45 min. During data collection, researchers met on daily basis to discuss the emerging themes assessing whether research questions were being answered. Saturation was achieved with the initially planned interview schedule with no need for further additional interviews [27]. All interviews were transcribed verbatim and checked for accuracy by a second transcriber. Transcriptions of the combined set on interviews were analysed using a framework approach [28]. A coding framework was initially developed based on the document review, key research questions and new themes emerging during the analysis were added. All transcriptions were coded using the developed coding framework. The data was managed using NVIVO qualitative analysis software version 10. Recruitment and appointment Initial policies and further adaptations Recruitment in Zimbabwe is regulated through the Public Service Regulations (PSR), 2000 sections 2 and 3/1a-d [29]. These policies envisage that recruitment should be merit-based on the applicant's knowledge about their tasks and their ability to perform them. Appointments can be either under 'indefinite pensionable conditions' or 'temporary' to fill casual vacancies or supernumerary posts. All appointments should follow principles of equality of fair competition among candidates and need to be included in the Estimates of Expenditure approved by the Ministry of Finance each fiscal year. To confirm the suitability of new workers, they need to go through a probation period which initially was not less than 1 year after which and, if satisfactory, appointment was confirmed. With the introduction of HSR 2006, recruitment responsibility for the health sector was shifted to the HSB [22]. Besides merit, HSR 2006 introduced criteria of professional and moral standing and considered apprenticeship for individuals less than 18 years (previously not allowed under PSR 2000) as legal to allow health professional students to undertake their required internships to complete their studies. In order to address the high attrition from the public to the private sector observed after Independence, the new regulation provided greater flexibility for dual practice allowing HSB to authorise specific workers to devote part of their time to private practice and reducing the minimum probation period from 1 year to 6 months. Implementation practices During the pre-crisis period, HWs would search for jobs on their own after training. From 1992 to 1995 I did my nursing training as an RGN at Harare central hospital […] we were not being deployed. Each person would look for his/her own place (HW Gvt District 3).	-0.394721	0.889654	1.287517	0.971997	[ -0.5474396701390185, -0.24200204947229498 ]	[ 1.1689916497463595, 0.6103155323777273 ]	[ 1.388966895003937, 1.1860676129731955 ]	[ 1.096862872753777, 0.8471313270015002 ]	1,024	[ 512, 512 ]	[ 322, 29871, 29941, 29889, 450, 4655, 1326, 11376, 310, 9045, 18020, 297, 278, 4629, 24172, 526, 5874, 322, 263, 2919, 383, 8456, 607, 1914, 29879, 29871, 29945, 29906, 29995, 310, 278, 10847, 29899, 6707, 29418, 277, 1338, 297, 278, 4234, 313, 3562, 29871, 29896, 467, 10354, 29899, 3389, 23330, 297, 445, 6559, 526, 7199, 3368, 310, 1906, 8745, 491, 379, 1744, 322, 17692, 6474, 2613, 29883, 2719, 313, 29934, 12696, 467, 13, 3562, 29871, 29896, 24810, 322, 3694, 310, 23330, 491, 27428, 297, 6559, 24172, 13, 29909, 3001, 310, 29871, 29896, 29955, 1820, 1871, 424, 1006, 7406, 313, 29968, 2687, 29879, 29897, 515, 4797, 322, 1887, 11174, 363, 1716, 5874, 322, 383, 8456, 29879, 892, 3708, 1066, 3598, 4629, 5034, 304, 1009, 7134, 322, 7271, 310, 8898, 5849, 1104, 1218, 304, 18209, 313, 3562, 29871, 29906, 467, 13, 3562, 29871, 29906, 9681, 310, 1820, 1871, 424, 1006, 7406, 13, 1576, 12463, 8455, 322, 278, 12139, 14040, 363, 379, 29934, 29924, 3704, 18209, 472, 23330, 892, 4629, 297, 1269, 6559, 6474, 363, 1006, 7406, 322, 4433, 5155, 14364, 1048, 18209, 23274, 29889, 319, 3001, 310, 29871, 29896, 29896, 297, 29899, 19488, 1006, 7406, 313, 1367, 29902, 29897, 892, 8988, 714, 472, 1716, 5874, 322, 383, 8456, 21561, 313, 3562, 29871, 29941, 467, 13, 3562, 29871, 29941, 17740, 310, 3553, 3624, 411, 24454, 767, 18150, 491, 17535, 322, 23346, 13, 29909, 3001, 310, 29871, 29953, 29955, 1006, 7406, 411, 7145, 29893, 3145, 29892, 302, 1295, 267, 322, 29380, 9045, 4120, 654, 414, 313, 29946, 29906, 24473, 322, 29871, 29906, 29945, 25269, 29897, 1985, 297, 278, 2211, 1422, 409, 14359, 411, 1422, 27497, 310, 2669, 313, 29896, 29896, 529, 30080, 29945, 30080, 6360, 29879, 29936, 29871, 29945, 29953, 29871, 30386, 30080, 29945, 30080, 6360, 29879, 29897, 892, 18043, 313, 3562, 29871, 29946, 29897, 773, 278, 525, 19264, 4955, 29915, 11043, 304, 560, 293, 277, 1009, 8386, 322, 3736, 1103, 3145, 518, 29906, 29953, 1822, 13, 3562, 29871, 29946, 17740, 310, 3553, 3624, 411, 379, 29956, 29879, 491, 17535, 322, 23346, 13, 2008, 862, 403, 11261, 1410, 2247, 363, 12647, 29899, 4984, 2955, 1006, 7406, 363, 1269, 2318, 892, 8906, 322, 1304, 8525, 14981, 408, 263, 10754, 363, 278, 1006, 29894, 15580, 14372, 363, 716, 11176, 3460, 963, 2454, 10161, 9129, 491, 15593, 12712, 29889, 450, 1006, 7406, 363, 278, 476, 2687, 29879, 1833, 287, 385, 6588, 310, 29871, 29906, 29945, 30080, 1195, 1550, 1906, 363, 767, 18150, 322, 9045, 17162, 1006, 7406, 411, 2834, 3603, 583, 1833, 287, 1546, 29871, 29941, 29900, 322, 29871, 29946, 29945, 30080, 1195, 29889, 7133, 848, 4333, 29892, 5925, 414, 1539, 373, 14218, 8405, 304, 5353, 278, 11176, 3460, 963, 267, 24809, 292, 3692, 5925, 5155, 892, 1641, 7699, 29889, 317, 1337, 362, 471, 14363, 411, 278, 12919, 20458, 15593, 20410, 411, 694, 817, 363, 4340, 5684, 1006, 7406, 518, 29906, 29955, 1822, 2178, 1006, 7406, 892, 1301, 23059, 9750, 271, 326, 322, 7120, 363, 13600, 491, 263, 1473, 1301, 699, 495, 29889, 4103, 699, 1980, 310, 278, 12420, 731, 373, 1006, 7406, 892, 3483, 952, 287, 773, 263, 6890, 2948, 518, 29906, 29947, 1822, 319, 14137, 6890, 471, 12919, 8906, 2729, 373, 278, 1842, 9076, 29892, 1820, 5925, 5155, 322, 716, 963, 267, 11176, 3460, 2645, 278, 7418, 892, 2715, 29889, 2178, 1301, 699, 1980, 892, 274, 6797, 773, 278, 8906, 14137, 6890, 29889, 450, 848, 471, 8745, 773, 405, 29963, 5667, 29949, 4021, 23378, 7418, 7047, 1873, 29871, 29896, 29900, 29889, 13, 4789, 9216, 358, 322, 28573, 13, 15514, 24833, 322, 4340, 7744, 800, 13, 4789, 9216, 358, 297, 796, 19977, 370, 705, 338, 1072, 7964, 1549, 278, 5236, 6692, 2169, 8250, 313, 7024, 29934, 511, 29871, 29906, 29900, 29900, 29900, 13926, 29871, 29906, 322, 29871, 29941, 29914, 29896, 29874, 29899, 29881, 518, 29906, 29929, 1822, 4525, 24833, 427, 1730, 482, 393, 1162, 9216, 358, 881, 367, 2778, 277, 29899, 6707, 373, 278, 15576, 424, 29915, 29879, 7134, 1048, 1009, 9595, 322, 1009, 11509, 304, 2189, 963, 29889, 2401, 2461, 1860, 508, 367, 2845, 1090, 525, 262, 25476, 568, 282, 2673, 519, 5855, 29915, 470, 525, 1356, 1971, 653, 29915, 304, 5445, 3209, 950, 11757, 273, 2478, 470, 2428, 8058, 653, 11803, 29889, 2178, 8167, 1860, 881, 1101, 18671, 310, 17193, 310, 6534, 13888, 4249, 21669, 322, 817, 304, 367, 5134, 297, 278, 2661, 326, 1078, 310, 12027, 355, 17252, 23454, 491, 278, 20886, 310, 4231, 749, 1269, 16436, 1052, 1629, 29889, 1763, 9659, 278, 14726, 3097, 310, 716, 17162, 29892, 896, 817, 304, 748, 1549, 263, 2070, 362, 3785, 607, 12919, 471, 451, 3109, 1135, 29871, 29896, 1629, 1156, 607, 322, 29892, 565, 5119, 3832, 29892, 28573, 471, 16725, 29889, 13, 3047, 278, 18707, 310, 379, 14098, 29871, 29906, 29900, 29900, 29953, 29892, 1162, 9216, 358, 23134, 363, 278, 9045, 17535, 471, 9500, 287, 304, 278, 379, 1744, 518, 29906, 29906, 1822, 19065, 2778, 277, 29892, 379, 14098, 29871, 29906, 29900, 29900, 29953, 9129, 16614, 310, 10257, 322, 14731, 13407, 322, 5545, 623, 7771, 1575, 4034, 363, 15724, 3109, 1135, 29871, 29896, 29947, 30080, 6360, 29879, 313, 1457, 16604, 451, 6068, 1090, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29897, 408, 11706, 304, 2758, 9045, 10257, 8041, 304, 22332, 1296, 1009, 3734, 2836, 9981, 304, 4866, 1009, 11898, 29889, 512, 1797, 304, 3211, 278, 1880, 12421, 654, 515, 278, 970, 304, 278, 2024, 17535, 8900, 1156, 28052, 663, 29892, 278, 716, 1072, 2785, 4944, 7621, 8525, 4127, 363, 14581, 6944, 14372, 379, 1744, 304, 4148, 895, 2702, 17162, 304, 2906, 866, 760, 310, 1009, 931, 304, 2024, 6944, 322, 27668, 278, 9212, 2070, 362, 3785, 515, 29871, 29896, 1629, 304, 29871, 29953, 7378, 29889, 13, 1888, 14607, 23274, 13, 29928, 3864, 278, 758, 29899, 29883, 3780, 275, 3785, 29892, 379, 29956, 29879, 723, 2740, 363, 17643, 373, 1009, 1914, 1156, 6694, 29889, 13, 4591, 29871, 29896, 29929, 29929, 29906, 304, 29871, 29896, 29929, 29929, 29945, 306, 1258, 590, 302, 1295, 292, 6694, 408, 385, 390, 20728, 472, 3536, 598, 6555, 13457, 518, 30098, 29962, 591, 892, 451, 1641, 21168, 29889, 7806, 2022, 723, 1106, 363, 670, 29914, 2276, 1914, 2058, 313, 29950, 29956, 402, 21908, 7457, 29871, 29941, 467 ]	1,332,829	2,048	CommonCrawl	6	2
Before the crisis, recruitment of students was done by the relevant health service providers (government or FBO), drawing from their own training schools, but it was carried out in accordance to the MOHCC/HSB standards and criteria. Despite being regulated by the same framework, church-run nursing schools had the opportunity to retain the nurses they like at their facilities after completion of training: …the DNO [District Nursing Officer] will deploy them to us but [the nurse training school] can just say we need three here [at FBO facility] and they can even mention names preferably so and so […] (Manager FBO District 1) However, during the crisis period (1997–2008), they had the option to choose three priority provinces, both for students who had trained in government and in FBO-run training schools. Preference listing was withdrawn during the crisis period for nurses and paramedical staff mainly to address the shortage of HWs particularly in rural areas. On the other hand, doctors were still allowed to choose, although the human resources (HR) department at MOHCC head office would intervene to ensure even deployment in areas where majority of newly qualified doctors would have chosen one hospital. Most people (80%) would choose Harare and only 20% would choose Bulawayo but it was supposed to be 50-50. This meant that 30% of those who chose Harare were then forced to go and work in Bulawayo. To solve the issue there was a list that would come from the head office Human Resources Directorate of who would go where. (Manager Gvt District 1) Despite the establishment of the HSB which, in the views of the government, aimed at the unification of all health services, there were some differences in the implementation of HSR 2006 between government and FBO service providers. Some managers reported having two different and parallel processes for recruiting new workers: one triggered by the HSB and another one by the specific FBO: When we are recruiting [under the FBO process] we advertise the posts, and then people apply. When they are sent by the DNO [official HSB process] we just accept them. We sit down with them and do a bit of an interview but not as we do with those we recruit on our own because there is no option to say we want you or we don't because the person would have been already sent to us. We then ask them to fill the assumption of duty forms and other forms which are needed. (Manager FBO District 3) These overlapping recruitment systems with different degrees of thoroughness in terms of merit-based selection may have resulted in different recruitment outputs with a fairer system applied to these recruited through the FBO system (e.g. using interviews) as compared with these recruited through the HSB which may be more prone to patronage and weaker accountability. However, this was not substantiated by the study. Another factor that contributed to the poor staffing situation during the crisis was the recruitment freeze introduced as a response to an over-inflated civil service [30]. However, given its key role and its already precarious staffing situation, the freeze in the health sector was temporarily relaxed to allow for limited recruitment on a periodical basis to cover urgent needs [20]. This affected equally government and FBO-run facilities. When we have people, who qualify we wait for the unfreezing of posts. The HR [department] will allocate the posts to the provinces and provinces allocate to the districts. (National Manager Gvt) During the crisis, the number of absconders (i.e. workers leaving the workforce without prior notice or authorisation) increased substantially. While before the crisis the process of re-appointment of absconders was long and often unsuccessful, this was adjusted after the crisis to allow for fast-tracked re-appointment to mitigate the increasing vacancy rate. A new cadre, a primary care nurse (PCN), was introduced during the crisis to resolve staff shortages in rural areas and this cadre was meant to work at rural health centres/clinics only. In hospital [District Hospital] it [introduction of PCNs] did not help in any way, but it helped in the rural areas, that cadre was meant to work in the rural areas. They are not supposed to work at district hospitals or other upper hospitals. (Manager Gvt District 2) Bond	-0.463119	0.638966	0.605268	0.482939	[ -0.1706077177357346, -0.7556303353468302 ]	[ 0.9039786197125211, 0.3739525596448445 ]	[ 0.8715737258255462, 0.33896311049484956 ]	[ 0.7014545919793387, 0.2644243869128541 ]	1,024	[ 512, 512 ]	[ 13, 18743, 278, 24161, 29892, 1162, 9216, 358, 310, 8041, 471, 2309, 491, 278, 8018, 9045, 2669, 1326, 11376, 313, 29887, 6170, 358, 470, 383, 8456, 511, 11580, 515, 1009, 1914, 6694, 12462, 29892, 541, 372, 471, 8988, 714, 297, 15017, 749, 304, 278, 16999, 29950, 4174, 29914, 29950, 1744, 20801, 322, 16614, 29889, 19454, 1641, 1072, 7964, 491, 278, 1021, 6890, 29892, 6586, 29899, 3389, 302, 1295, 292, 12462, 750, 278, 15130, 304, 11551, 278, 302, 1295, 267, 896, 763, 472, 1009, 23330, 1156, 13285, 310, 6694, 29901, 13, 30098, 1552, 360, 6632, 518, 29928, 6801, 405, 1295, 292, 28288, 29962, 674, 7246, 963, 304, 502, 541, 518, 1552, 5595, 344, 6694, 3762, 29962, 508, 925, 1827, 591, 817, 2211, 1244, 518, 271, 383, 8456, 24454, 29962, 322, 896, 508, 1584, 3585, 2983, 5821, 2197, 577, 322, 577, 518, 30098, 29962, 313, 3260, 383, 8456, 7457, 29871, 29896, 29897, 13, 17245, 29892, 2645, 278, 24161, 3785, 313, 29896, 29929, 29929, 29955, 29994, 29906, 29900, 29900, 29947, 511, 896, 750, 278, 2984, 304, 6755, 2211, 20136, 28058, 29892, 1716, 363, 8041, 1058, 750, 16370, 297, 5874, 322, 297, 383, 8456, 29899, 3389, 6694, 12462, 29889, 4721, 1659, 18028, 471, 411, 19811, 1233, 2645, 278, 24161, 3785, 363, 302, 1295, 267, 322, 1828, 287, 936, 13925, 14364, 304, 3211, 278, 3273, 482, 310, 379, 29956, 29879, 10734, 297, 17692, 10161, 29889, 1551, 278, 916, 1361, 29892, 437, 14359, 892, 1603, 6068, 304, 6755, 29892, 5998, 278, 5199, 7788, 313, 20938, 29897, 14311, 472, 16999, 29950, 4174, 2343, 8034, 723, 26314, 29872, 304, 9801, 1584, 18209, 297, 10161, 988, 13638, 310, 15141, 18698, 437, 14359, 723, 505, 10434, 697, 13457, 29889, 13, 29924, 520, 2305, 313, 29947, 29900, 10997, 723, 6755, 3536, 598, 322, 871, 29871, 29906, 29900, 29995, 723, 6755, 8313, 21694, 29877, 541, 372, 471, 7424, 304, 367, 29871, 29945, 29900, 29899, 29945, 29900, 29889, 910, 6839, 393, 29871, 29941, 29900, 29995, 310, 1906, 1058, 12784, 3536, 598, 892, 769, 11826, 304, 748, 322, 664, 297, 8313, 21694, 29877, 29889, 1763, 4505, 278, 2228, 727, 471, 263, 1051, 393, 723, 2041, 515, 278, 2343, 8034, 12968, 27562, 15944, 403, 310, 1058, 723, 748, 988, 29889, 313, 3260, 402, 21908, 7457, 29871, 29896, 29897, 13, 4002, 29886, 568, 278, 25012, 310, 278, 379, 1744, 607, 29892, 297, 278, 8386, 310, 278, 5874, 29892, 12242, 287, 472, 278, 443, 2450, 310, 599, 9045, 5786, 29892, 727, 892, 777, 12651, 297, 278, 5314, 310, 379, 14098, 29871, 29906, 29900, 29900, 29953, 1546, 5874, 322, 383, 8456, 2669, 1326, 11376, 29889, 3834, 767, 18150, 8967, 2534, 1023, 1422, 322, 8943, 10174, 363, 1162, 9216, 292, 716, 17162, 29901, 697, 19799, 491, 278, 379, 1744, 322, 1790, 697, 491, 278, 2702, 383, 8456, 29901, 13, 10401, 591, 526, 1162, 9216, 292, 518, 5062, 278, 383, 8456, 1889, 29962, 591, 18811, 895, 278, 11803, 29892, 322, 769, 2305, 3394, 29889, 1932, 896, 526, 2665, 491, 278, 360, 6632, 518, 29877, 7880, 379, 1744, 1889, 29962, 591, 925, 3544, 963, 29889, 1334, 7845, 1623, 411, 963, 322, 437, 263, 2586, 310, 385, 15593, 541, 451, 408, 591, 437, 411, 1906, 591, 1162, 9216, 373, 1749, 1914, 1363, 727, 338, 694, 2984, 304, 1827, 591, 864, 366, 470, 591, 1016, 29915, 29873, 1363, 278, 2022, 723, 505, 1063, 2307, 2665, 304, 502, 29889, 1334, 769, 2244, 963, 304, 5445, 278, 11833, 310, 13360, 7190, 322, 916, 7190, 607, 526, 4312, 29889, 313, 3260, 383, 8456, 7457, 29871, 29941, 29897, 13, 1349, 968, 975, 433, 3262, 1162, 9216, 358, 6757, 411, 1422, 14496, 310, 17826, 2264, 297, 4958, 310, 2778, 277, 29899, 6707, 9262, 1122, 505, 20601, 297, 1422, 1162, 9216, 358, 14391, 411, 263, 6534, 261, 1788, 7436, 304, 1438, 1162, 582, 1573, 1549, 278, 383, 8456, 1788, 313, 29872, 29889, 29887, 29889, 773, 1006, 7406, 29897, 408, 9401, 411, 1438, 1162, 582, 1573, 1549, 278, 379, 1744, 607, 1122, 367, 901, 544, 650, 304, 18259, 482, 322, 591, 5790, 3633, 3097, 29889, 2398, 29892, 445, 471, 451, 5960, 3656, 630, 491, 278, 6559, 29889, 13, 2744, 1228, 7329, 393, 26869, 304, 278, 6460, 13925, 292, 6434, 2645, 278, 24161, 471, 278, 1162, 9216, 358, 3889, 911, 9129, 408, 263, 2933, 304, 385, 975, 29899, 13453, 630, 7631, 2669, 518, 29941, 29900, 1822, 2398, 29892, 2183, 967, 1820, 6297, 322, 967, 2307, 8303, 1306, 681, 13925, 292, 6434, 29892, 278, 3889, 911, 297, 278, 9045, 17535, 471, 5382, 6275, 26681, 287, 304, 2758, 363, 9078, 1162, 9216, 358, 373, 263, 3785, 936, 8405, 304, 4612, 5065, 5362, 4225, 518, 29906, 29900, 1822, 910, 15201, 18018, 5874, 322, 383, 8456, 29899, 3389, 23330, 29889, 13, 10401, 591, 505, 2305, 29892, 1058, 4021, 1598, 591, 4480, 363, 278, 443, 9021, 19583, 310, 11803, 29889, 450, 379, 29934, 518, 311, 8076, 29962, 674, 23632, 278, 11803, 304, 278, 28058, 322, 28058, 23632, 304, 278, 24172, 29889, 313, 27325, 15629, 402, 21908, 29897, 13, 29928, 3864, 278, 24161, 29892, 278, 1353, 310, 6425, 1116, 414, 313, 29875, 29889, 29872, 29889, 17162, 10124, 278, 664, 10118, 1728, 7536, 8369, 470, 4148, 4371, 29897, 11664, 23228, 368, 29889, 5806, 1434, 278, 24161, 278, 1889, 310, 337, 29899, 932, 2461, 358, 310, 6425, 1116, 414, 471, 1472, 322, 4049, 443, 8698, 1319, 29892, 445, 471, 10365, 287, 1156, 278, 24161, 304, 2758, 363, 5172, 29899, 11294, 287, 337, 29899, 932, 2461, 358, 304, 1380, 335, 403, 278, 10231, 11757, 6906, 6554, 29889, 13, 29909, 716, 25915, 29892, 263, 7601, 2562, 5595, 344, 313, 9026, 29940, 511, 471, 9129, 2645, 278, 24161, 304, 8814, 13925, 3273, 1179, 297, 17692, 10161, 322, 445, 25915, 471, 6839, 304, 664, 472, 17692, 9045, 1644, 690, 29914, 695, 262, 1199, 871, 29889, 13, 797, 13457, 518, 29928, 6801, 15967, 29962, 372, 518, 524, 13210, 310, 9609, 29940, 29879, 29962, 1258, 451, 1371, 297, 738, 982, 29892, 541, 372, 9213, 297, 278, 17692, 10161, 29892, 393, 25915, 471, 6839, 304, 664, 297, 278, 17692, 10161, 29889, 2688, 526, 451, 7424, 304, 664, 472, 6474, 29418, 277, 1338, 470, 916, 7568, 29418, 277, 1338, 29889, 313, 3260, 402, 21908, 7457, 29871, 29906, 29897, 13, 29933, 898 ]	1,332,829	3,072	CommonCrawl	6	2
ing policies were first adopted in Zimbabwe through the "Health for All Action Plan" in 1986. Initially bonding arrangements were between MOHCW and professional associations [13, 17, 31] by which all new HWs were to serve generally in the public sector for a period equivalent to the period of their training. However, bonding was not mentioned in the PSR 2000 or in the HSR 2006. This policy gap may be the cause behind recent research showing inconsistent implementation of this specific policy element [20]. New regulation was introduced in 2007 by which all newly graduated nurses had their certificates withheld until they completed their bonding obligations. However, after the introduction of the recruitment freeze and the subsequent difficulties for new professionals in finding a job in the public sector, the regulation was not enforced from 2010. Before the crisis, bonding regulations were well enforced with bonding playing a dual role: improving retention and providing a supervised induction after the training. Long back it [bonding] was there to retain nurses as the nurses were trained using public funds. It was also used to make sure that the nurse will be moulded through the supervision by the senior [staff] during the bonding period. (Provincial Manager Gvt). There was change in bonding policy in 2007 when it included withholding of certificates to mitigate the increasing attrition from the public to the private sector and through out-migration. Bonding rules were the same for staff working in both government and FBO sectors especially after the creation of the HSB. The nurses were bonded for a period equivalent to the training period and you would not get certificates for the three years you are bonded. (Provincial Manager Gvt) There were some exceptions in the application of bonding rules within the FBO sector for ordained staff who are directly managed by the church authorities through internal church policies Like after the training we used to know that a person will be bonded for a year before he/she can say I no longer want to be here, but for us, sisters [ordained staff], that rule doesn't apply, we stay at a place until we are told to move. (HW Gvt District 2) The introduction of the recruitment freeze led to discontinuation of withholding of certificates as the government could no longer guarantee employment to new graduates. At the moment because of the shortage of vacancies and the freezing of posts, the nurses are now being given their certificates immediately after qualifying. (Provincial Manager Gvt) Bonding for in-service training, particularly after the crisis, was perceived as fairer than for pre-service training, as it was reported by many HWs as a way of giving back to the system what the system invested in their education: It is good in the sense that you would have been sent by the facility, so you have to render back the service, if you think of going somewhere it would not be fair that after training you will just go without rendering the service. (HW Gvt District 3) Before 2006, transfer of civil servants was regulated through section 13 of PSR 2000. The policy reflects a compulsory top-down approach to transfer, for example stating, 'a member may at any time without his consent be transferred by the Commission or a delegated authority from the post which he occupies to any other post in the Public Service whether the post is inside or outside Zimbabwe' (page 16). Refusal to obey an instruction of transfer is treated as an act of misconduct. However, the regulations say that transfer should be planned to minimise discomfort to the member concerned and their family and that the member should be provided with all necessary information relating to the transfer and notified in time. Transfers cannot be used as a punitive measure except in cases of disciplinary procedures. The PSR 2000 was replaced by HSR 2006 and in the new regulation the length of a temporary posting was left to be determined by the HSB as opposed to the initial transfer for a limited period of maximum 3 years. During the pre-crisis period, managers were more in control of the processes of transferring workers, but during the crisis, due to substantial problems with attrition, they were less eager to allow transfers of staff. …as an HOD [Head of Department] I just realize	-0.374005	0.318443	0.655993	0.433513	[ -0.21426612203507006, -0.5337429158490309 ]	[ 0.5673404464262941, 0.06954570082219232 ]	[ 0.8309938694193978, 0.48099260791636866 ]	[ 0.7742929594904194, 0.09273394920816375 ]	1,024	[ 512, 512 ]	[ 292, 24833, 892, 937, 16356, 297, 796, 19977, 370, 705, 1549, 278, 376, 3868, 4298, 363, 2178, 9123, 8402, 29908, 297, 29871, 29896, 29929, 29947, 29953, 29889, 17250, 368, 21224, 292, 15196, 4110, 892, 1546, 16999, 19127, 29956, 322, 10257, 27733, 518, 29896, 29941, 29892, 29871, 29896, 29955, 29892, 29871, 29941, 29896, 29962, 491, 607, 599, 716, 379, 29956, 29879, 892, 304, 9080, 6892, 297, 278, 970, 17535, 363, 263, 3785, 7126, 304, 278, 3785, 310, 1009, 6694, 29889, 2398, 29892, 21224, 292, 471, 451, 5276, 297, 278, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 470, 297, 278, 379, 14098, 29871, 29906, 29900, 29900, 29953, 29889, 910, 8898, 17261, 1122, 367, 278, 4556, 5742, 7786, 5925, 6445, 22435, 9696, 5314, 310, 445, 2702, 8898, 1543, 518, 29906, 29900, 1822, 1570, 1072, 2785, 471, 9129, 297, 29871, 29906, 29900, 29900, 29955, 491, 607, 599, 15141, 23588, 302, 1295, 267, 750, 1009, 23199, 1078, 411, 29882, 2495, 2745, 896, 8676, 1009, 21224, 292, 10788, 800, 29889, 2398, 29892, 1156, 278, 18707, 310, 278, 1162, 9216, 358, 3889, 911, 322, 278, 15352, 23553, 363, 716, 6351, 1338, 297, 9138, 263, 4982, 297, 278, 970, 17535, 29892, 278, 1072, 2785, 471, 451, 24555, 1133, 515, 29871, 29906, 29900, 29896, 29900, 29889, 13, 18743, 278, 24161, 29892, 21224, 292, 1072, 8250, 892, 1532, 24555, 1133, 411, 21224, 292, 8743, 263, 14581, 6297, 29901, 4857, 1747, 3240, 2509, 322, 13138, 263, 2428, 11292, 21445, 1156, 278, 6694, 29889, 13, 8208, 1250, 372, 518, 29890, 898, 292, 29962, 471, 727, 304, 11551, 302, 1295, 267, 408, 278, 302, 1295, 267, 892, 16370, 773, 970, 29199, 29889, 739, 471, 884, 1304, 304, 1207, 1854, 393, 278, 5595, 344, 674, 367, 286, 483, 287, 1549, 278, 2428, 4924, 491, 278, 16336, 518, 303, 3470, 29962, 2645, 278, 21224, 292, 3785, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 467, 13, 8439, 471, 1735, 297, 21224, 292, 8898, 297, 29871, 29906, 29900, 29900, 29955, 746, 372, 5134, 411, 8948, 292, 310, 23199, 1078, 304, 1380, 335, 403, 278, 10231, 12421, 654, 515, 278, 970, 304, 278, 2024, 17535, 322, 1549, 714, 29899, 29885, 16783, 29889, 26370, 292, 6865, 892, 278, 1021, 363, 13925, 1985, 297, 1716, 5874, 322, 383, 8456, 409, 14359, 7148, 1156, 278, 11265, 310, 278, 379, 1744, 29889, 13, 1576, 302, 1295, 267, 892, 21224, 287, 363, 263, 3785, 7126, 304, 278, 6694, 3785, 322, 366, 723, 451, 679, 23199, 1078, 363, 278, 2211, 2440, 366, 526, 21224, 287, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 29897, 13, 8439, 892, 777, 15283, 297, 278, 2280, 310, 21224, 292, 6865, 2629, 278, 383, 8456, 17535, 363, 4356, 7114, 13925, 1058, 526, 4153, 8745, 491, 278, 6586, 21142, 1549, 7463, 6586, 24833, 13, 27552, 1156, 278, 6694, 591, 1304, 304, 1073, 393, 263, 2022, 674, 367, 21224, 287, 363, 263, 1629, 1434, 540, 29914, 11360, 508, 1827, 306, 694, 5520, 864, 304, 367, 1244, 29892, 541, 363, 502, 29892, 9883, 29879, 518, 536, 7114, 13925, 1402, 393, 5751, 1838, 29915, 29873, 3394, 29892, 591, 7952, 472, 263, 2058, 2745, 591, 526, 5429, 304, 4337, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29906, 29897, 13, 1576, 18707, 310, 278, 1162, 9216, 358, 3889, 911, 5331, 304, 766, 20621, 362, 310, 411, 8948, 292, 310, 23199, 1078, 408, 278, 5874, 1033, 694, 5520, 18818, 5703, 358, 304, 716, 10591, 1078, 29889, 13, 4178, 278, 3256, 1363, 310, 278, 3273, 482, 310, 11757, 273, 2478, 322, 278, 3889, 19583, 310, 11803, 29892, 278, 302, 1295, 267, 526, 1286, 1641, 2183, 1009, 23199, 1078, 7389, 1156, 4021, 9215, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 29897, 13, 29933, 898, 292, 363, 297, 29899, 5509, 6694, 29892, 10734, 1156, 278, 24161, 29892, 471, 17189, 2347, 408, 6534, 261, 1135, 363, 758, 29899, 5509, 6694, 29892, 408, 372, 471, 8967, 491, 1784, 379, 29956, 29879, 408, 263, 982, 310, 6820, 1250, 304, 278, 1788, 825, 278, 1788, 2437, 2868, 297, 1009, 9793, 29901, 13, 3112, 338, 1781, 297, 278, 4060, 393, 366, 723, 505, 1063, 2665, 491, 278, 24454, 29892, 577, 366, 505, 304, 4050, 1250, 278, 2669, 29892, 565, 366, 1348, 310, 2675, 9051, 372, 723, 451, 367, 6534, 393, 1156, 6694, 366, 674, 925, 748, 1728, 15061, 278, 2669, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29941, 29897, 13, 18743, 29871, 29906, 29900, 29900, 29953, 29892, 6782, 310, 7631, 26202, 471, 1072, 7964, 1549, 4004, 29871, 29896, 29941, 310, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29889, 450, 8898, 9432, 29879, 263, 752, 7273, 706, 2246, 29899, 3204, 2948, 304, 6782, 29892, 363, 1342, 23659, 29892, 525, 29874, 4509, 1122, 472, 738, 931, 1728, 670, 20218, 367, 18440, 491, 278, 11444, 470, 263, 16000, 630, 14329, 515, 278, 1400, 607, 540, 6919, 583, 304, 738, 916, 1400, 297, 278, 5236, 6692, 3692, 278, 1400, 338, 2768, 470, 5377, 796, 19977, 370, 705, 29915, 313, 3488, 29871, 29896, 29953, 467, 9897, 375, 284, 304, 26449, 385, 15278, 310, 6782, 338, 14914, 408, 385, 1044, 310, 3984, 535, 2199, 29889, 2398, 29892, 278, 1072, 8250, 1827, 393, 6782, 881, 367, 20458, 304, 6260, 895, 766, 510, 3921, 304, 278, 4509, 15041, 322, 1009, 3942, 322, 393, 278, 4509, 881, 367, 4944, 411, 599, 5181, 2472, 1104, 1218, 304, 278, 6782, 322, 451, 2164, 297, 931, 29889, 4103, 25534, 2609, 367, 1304, 408, 263, 6035, 3321, 5645, 5174, 297, 4251, 310, 17119, 3821, 28648, 29889, 13, 1576, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 471, 8611, 491, 379, 14098, 29871, 29906, 29900, 29900, 29953, 322, 297, 278, 716, 1072, 2785, 278, 3309, 310, 263, 13201, 16742, 471, 2175, 304, 367, 10087, 491, 278, 379, 1744, 408, 15869, 304, 278, 2847, 6782, 363, 263, 9078, 3785, 310, 7472, 29871, 29941, 30080, 6360, 29879, 29889, 13, 29928, 3864, 278, 758, 29899, 29883, 3780, 275, 3785, 29892, 767, 18150, 892, 901, 297, 2761, 310, 278, 10174, 310, 6782, 5393, 17162, 29892, 541, 2645, 278, 24161, 29892, 2861, 304, 23228, 4828, 411, 12421, 654, 29892, 896, 892, 3109, 19888, 304, 2758, 1301, 25534, 310, 13925, 29889, 13, 30098, 294, 385, 379, 13668, 518, 5494, 310, 10317, 29962, 306, 925, 16289 ]	1,332,829	4,096	CommonCrawl	3	13
that if someone moves away there will be less [fewer] nurses here so I might refuse the person to move to another facility. (Manager Gvt District 3) These circumstances made it difficult for managers to deploy staff in a way that would improve geographical coverage. Managers also needed to balance carefully the requests from workers willing to be transferred as refusals may trigger greatly needed HRH to withdraw, abscond and go to private sector or leave the country. Transfers were easy during the crisis because there were more vacancies than HWs seeking those posts. One [a manager] had to be reasonable; it was either you let the cadre transfer to a preferred post or the system will lose the cadre altogether. (Manager Gvt District 1) In this regard, workers were allowed to transfer only when they found another worker in a similar position willing to exchange/swap positions. […] when I tried to talk to the DNO that I want to go to XXXX [Province] I was told that I should seek for a lateral transfer. I should convince somebody who is at a facility where I want to go so that he will come here, and I will go there. (HW Gvt District 1) The PSR 2000 states that a worker may at any time, with his/her consent and at the invitation of head of Ministry or the Commission, be seconded (a temporary form of transfer) by the Commission for a period not exceeding 3 years to a post in an approved service. Terms and conditions of services for seconded workers should be governed by the contract between the worker and the service concerned. The HSR 2006 revision points out that the period of secondment will be determined by the HSB without his/her consent while the rest of the terms and conditions are as stipulated by PSR 2000. During the crisis, because of the challenges of transferring staff explained above, managers used secondment to fill vacant posts, but it was unpopular among HWs as the legal terms for secondment were not appropriately applied. In some cases, HWs were seconded for a longer period of time than stipulated and sometimes communication about the secondment was not provided timely and it was not clear: I heard that the first group volunteered but as for our group we did not volunteer we were told to go. We were just told that you are going tomorrow, and we were not prepared to go. We could not even give excuses we were just told to go (HW FBO District 3) Some key positions within the FBO health services such as medical doctors were historically staffed through internal church-related networks and were never made explicit and included in the Public Service staffing norms when the HSB was introduced. During the crisis, when even FBO facilities faced problems with mobilisation of resources from external sources, many FBOs found themselves with shortage of this specific cadre. In these cases, secondment was used to allocate physicians to these facilities. My post is at XXX District Hospital [HSB]. When I came into the district, mission hospitals did not have posts for doctors from the government, so I was seconded here at XXX Hospital [FBO]. (Manager FBO District 1) This study was designed to review the changes and flexibility in deployment policies and the implementation practices during the crisis and post-crisis periods in Zimbabwe. Much of the response to the crisis and post-crisis situations relating to deployment was in the implementation of policies and in particular to transfer and secondment. The pragmatic response of the district-level managers was to be flexible in the use of the transfer rules aiming more at retaining HWs than to ensure equitable staffing of health facilities. Here, flexibility was used in a positive way, though elsewhere flexible interpretation of rules may be seen as negative [32]. However, secondment was used as an alternative and temporary way of filling vacancies. The aim of this, in the view of managers, was to at least retain staff. Interestingly, while we found that secondment (also known as deputation in some organisations) was driven by management in our study, elsewhere it is frequently used by employees as a means of changing their place of work through "side payments" to managers [33]. Several changes in the broader context that were highly relevant to understand the evolution of HRH deployment were identified. The first was the desire to improve equitable access to health services by bringing in and coordinating the then well-resourced FBO facilities in line with government plans and funding. The introduction of a blanket recruitment freeze	-0.266399	0.486762	0.5165	0.529764	[ -0.40636310095214623, -0.12643568515052458 ]	[ 0.37037130248222505, 0.6031530180524884 ]	[ 0.4454852335609889, 0.587514730982508 ]	[ 0.4673312678365791, 0.5921970407127175 ]	1,024	[ 512, 512 ]	[ 393, 565, 4856, 16229, 3448, 727, 674, 367, 3109, 518, 1725, 556, 29962, 302, 1295, 267, 1244, 577, 306, 1795, 26506, 278, 2022, 304, 4337, 304, 1790, 24454, 29889, 313, 3260, 402, 21908, 7457, 29871, 29941, 29897, 13, 1349, 968, 14209, 1754, 372, 5189, 363, 767, 18150, 304, 7246, 13925, 297, 263, 982, 393, 723, 11157, 1737, 19711, 23746, 29889, 2315, 18150, 884, 4312, 304, 17346, 16112, 278, 7274, 515, 17162, 17762, 304, 367, 18440, 408, 2143, 375, 1338, 1122, 7135, 11180, 4312, 379, 29934, 29950, 304, 28679, 29892, 6425, 1116, 322, 748, 304, 2024, 17535, 470, 5967, 278, 4234, 29889, 13, 4300, 25534, 892, 4780, 2645, 278, 24161, 1363, 727, 892, 901, 11757, 273, 2478, 1135, 379, 29956, 29879, 25738, 1906, 11803, 29889, 3118, 518, 29874, 8455, 29962, 750, 304, 367, 15590, 29936, 372, 471, 2845, 366, 1235, 278, 25915, 6782, 304, 263, 16389, 1400, 470, 278, 1788, 674, 14074, 278, 25915, 19148, 29889, 313, 3260, 402, 21908, 7457, 29871, 29896, 29897, 13, 797, 445, 4880, 29892, 17162, 892, 6068, 304, 6782, 871, 746, 896, 1476, 1790, 15645, 297, 263, 2788, 2602, 17762, 304, 14523, 29914, 26276, 11909, 29889, 13, 29961, 30098, 29962, 746, 306, 1898, 304, 5193, 304, 278, 360, 6632, 393, 306, 864, 304, 748, 304, 6193, 6247, 518, 1184, 29894, 1239, 29962, 306, 471, 5429, 393, 306, 881, 16508, 363, 263, 2678, 284, 6782, 29889, 306, 881, 7602, 1239, 18462, 1058, 338, 472, 263, 24454, 988, 306, 864, 304, 748, 577, 393, 540, 674, 2041, 1244, 29892, 322, 306, 674, 748, 727, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29896, 29897, 13, 1576, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 5922, 393, 263, 15645, 1122, 472, 738, 931, 29892, 411, 670, 29914, 2276, 20218, 322, 472, 278, 2437, 7018, 310, 2343, 310, 20886, 470, 278, 11444, 29892, 367, 1473, 287, 313, 29874, 13201, 883, 310, 6782, 29897, 491, 278, 11444, 363, 263, 3785, 451, 13461, 292, 29871, 29941, 2440, 304, 263, 1400, 297, 385, 23454, 2669, 29889, 11814, 29879, 322, 5855, 310, 5786, 363, 1473, 287, 17162, 881, 367, 4095, 287, 491, 278, 8078, 1546, 278, 15645, 322, 278, 2669, 15041, 29889, 450, 379, 14098, 29871, 29906, 29900, 29900, 29953, 26554, 3291, 714, 393, 278, 3785, 310, 1473, 358, 674, 367, 10087, 491, 278, 379, 1744, 1728, 670, 29914, 2276, 20218, 1550, 278, 1791, 310, 278, 4958, 322, 5855, 526, 408, 380, 666, 7964, 491, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29889, 13, 29928, 3864, 278, 24161, 29892, 1363, 310, 278, 18066, 267, 310, 6782, 5393, 13925, 10824, 2038, 29892, 767, 18150, 1304, 1473, 358, 304, 5445, 11757, 424, 11803, 29892, 541, 372, 471, 443, 7323, 1070, 4249, 379, 29956, 29879, 408, 278, 11706, 4958, 363, 1473, 358, 892, 451, 7128, 2486, 7436, 29889, 512, 777, 4251, 29892, 379, 29956, 29879, 892, 1473, 287, 363, 263, 5520, 3785, 310, 931, 1135, 380, 666, 7964, 322, 6041, 12084, 1048, 278, 1473, 358, 471, 451, 4944, 5335, 873, 322, 372, 471, 451, 2821, 29901, 13, 29902, 6091, 393, 278, 937, 2318, 27886, 14561, 541, 408, 363, 1749, 2318, 591, 1258, 451, 27886, 261, 591, 892, 5429, 304, 748, 29889, 1334, 892, 925, 5429, 393, 366, 526, 2675, 6454, 22396, 29892, 322, 591, 892, 451, 13240, 304, 748, 29889, 1334, 1033, 451, 1584, 2367, 5566, 6394, 591, 892, 925, 5429, 304, 748, 313, 29950, 29956, 383, 8456, 7457, 29871, 29941, 29897, 13, 9526, 1820, 11909, 2629, 278, 383, 8456, 9045, 5786, 1316, 408, 16083, 437, 14359, 892, 3603, 1711, 13925, 287, 1549, 7463, 6586, 29899, 12817, 14379, 322, 892, 2360, 1754, 6261, 322, 5134, 297, 278, 5236, 6692, 13925, 292, 6056, 29879, 746, 278, 379, 1744, 471, 9129, 29889, 7133, 278, 24161, 29892, 746, 1584, 383, 8456, 23330, 20050, 4828, 411, 27227, 4371, 310, 7788, 515, 7029, 8974, 29892, 1784, 383, 8456, 29879, 1476, 6053, 411, 3273, 482, 310, 445, 2702, 25915, 29889, 512, 1438, 4251, 29892, 1473, 358, 471, 1304, 304, 23632, 4824, 14722, 304, 1438, 23330, 29889, 13, 3421, 1400, 338, 472, 22615, 7457, 15967, 518, 29950, 1744, 1822, 1932, 306, 2996, 964, 278, 6474, 29892, 10655, 29418, 277, 1338, 1258, 451, 505, 11803, 363, 437, 14359, 515, 278, 5874, 29892, 577, 306, 471, 1473, 287, 1244, 472, 22615, 15967, 518, 29943, 8456, 1822, 313, 3260, 383, 8456, 7457, 29871, 29896, 29897, 13, 4013, 6559, 471, 8688, 304, 9076, 278, 3620, 322, 8525, 4127, 297, 18209, 24833, 322, 278, 5314, 23274, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 297, 796, 19977, 370, 705, 29889, 18927, 310, 278, 2933, 304, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 18845, 1104, 1218, 304, 18209, 471, 297, 278, 5314, 310, 24833, 322, 297, 3153, 304, 6782, 322, 1473, 358, 29889, 450, 282, 1431, 29885, 2454, 2933, 310, 278, 6474, 29899, 5563, 767, 18150, 471, 304, 367, 25706, 297, 278, 671, 310, 278, 6782, 6865, 12242, 292, 901, 472, 11551, 292, 379, 29956, 29879, 1135, 304, 9801, 1592, 8270, 13925, 292, 310, 9045, 23330, 29889, 2266, 29892, 8525, 4127, 471, 1304, 297, 263, 6374, 982, 29892, 2466, 17551, 25706, 19854, 310, 6865, 1122, 367, 3595, 408, 8178, 518, 29941, 29906, 1822, 2398, 29892, 1473, 358, 471, 1304, 408, 385, 8671, 322, 13201, 982, 310, 27523, 11757, 273, 2478, 29889, 450, 12242, 310, 445, 29892, 297, 278, 1776, 310, 767, 18150, 29892, 471, 304, 472, 3203, 11551, 13925, 29889, 23829, 11687, 29892, 1550, 591, 1476, 393, 1473, 358, 313, 15189, 2998, 408, 316, 14584, 297, 777, 17459, 800, 29897, 471, 18225, 491, 10643, 297, 1749, 6559, 29892, 17551, 372, 338, 13672, 1304, 491, 22873, 408, 263, 2794, 310, 6480, 1009, 2058, 310, 664, 1549, 376, 2975, 5146, 1860, 29908, 304, 767, 18150, 518, 29941, 29941, 1822, 13, 29903, 1310, 284, 3620, 297, 278, 2545, 1664, 3030, 393, 892, 10712, 8018, 304, 2274, 278, 14675, 310, 379, 29934, 29950, 18209, 892, 15659, 29889, 450, 937, 471, 278, 13521, 304, 11157, 1592, 8270, 2130, 304, 9045, 5786, 491, 20794, 297, 322, 6615, 1218, 278, 769, 1532, 29899, 690, 473, 1133, 383, 8456, 23330, 297, 1196, 411, 5874, 13900, 322, 5220, 292, 29889, 450, 18707, 310, 263, 9654, 300, 1162, 9216, 358, 3889, 911 ]	1,332,829	5,120	CommonCrawl	6	2
for the Civil Service represented a major challenge for district- and facility-level health service managers, particularly in rural areas. However, the system managed to mitigate some of the constraints by allowing flexibility on its implementation like temporarily lifting the freeze to allow recruitment and appointment for critical positions. Such exemptions for doctors and nurses were used during a lengthy recruitment freeze in Zambia in 2002 and 2004 [9]. Similarly, the policy on bonding was changed during the crisis and post-crisis periods, with for example the bonding period for nurses going from 3 to 2 years. With such a big staff shortage and a fluid labour market, the government could not afford to drive people away from the sector, so understandably they became more lenient. When even the reduced period of bonding was not being accepted by workers, the government initially used the common strategy of withholding graduation certificates during the bonding period [34] but following the recruitment freeze when jobs could no longer be guaranteed both the bonding policy and the policy of withholding of certificates were relaxed which also shows the flexibility of the system. On the other hand, the actions—or to some extent the lack of action—of policy makers in a crisis such as that experienced in Zimbabwe can be (at least partially) explained by the fact that it was difficult or impossible for them to predict how long the crisis would last, and, based on that, it was difficult to decide what changes to make to deployment policy even when the health workforce was clearly haemorrhaging. While the changes in response to the crisis in deployment-related policy might have been limited, adjustments and adaptations at the practice level, in particular in relation to transfer and secondment, were more prominent. In particular, the relaxation of transfer rules at the height of the crisis and the tactical use of secondment demonstrated the ability of managers' flexibility in implementing policy—what Bossert [35] refers to as 'decision space'—and to carry out actions to achieve their objectives, which in this case were to retain staff and to fill vacancies. Nevertheless, the bonding policies were clearly adapted at various stages of the crisis and post-crisis periods in response to the changing labour market situation. The shift on the policy of reappointment was clearly triggered by the window of opportunity as HWs who had left the sector were beginning to return in view of the apparent improvements in the overall situation. The timing of this window was fortunate, as such opportunities may be quite delayed as found by our research colleagues in Sierra Leone [36].The introduction of the PCN was also timely as it made sure posts were filled in rural areas. However, no official changes in the transfer and secondment policies were made specifically in response to the crisis and post-crisis situation. Though the deployment objectives might have been achieved reasonably successfully in the short term, the actions of FBO managers of preventing HWs from transferring and of government managers to force staff into short-term secondments meant that in the longer term staff in both cases may have left at the first opportunity. Hence, the longer-term objective of retention would not have been achieved, illustrating the challenge of developing coherent HR strategies [37, 38]. In these situations, managers should be supported to take the initiative to solve problems but should also be supported in understanding both the short- and longer-term implications of HRM actions. An ironic finding of this study is that although the reforms enacted through the Health Services Act of 2004 created a centralised system, in the context of crisis, district-level managers were able to push their degree of 'decision space' [39]—or 'room for manoeuvre'—more than in some stable but supposedly decentralised contexts [40, 41] with regard to staff deployment. In the absence of a central response to deployment policy, this must be seen as positive behaviour. However, without support on effective HRM, some decisions made run the risk of having negative longer-term consequences. This finding is an essential lesson for Zimbabwe as it deals with the aftermath of the peak of the economic crisis, as well as potentially for other countries facing similar situations. The policy should acknowledge that decision space must be increased for deployment managers in underserved rural areas. There were some limitations to this study. Documentation on policies and interviews with high-ranking key informants was difficult to obtain. Also, different accounts of the implementation of the policies were given between managers and between health	0.748273	0.660453	1.216503	1.138485	[ 0.8140177062857492, 0.6825288651018683 ]	[ 0.796540904833938, 0.5243653604748608 ]	[ 1.3078071821916404, 1.125197828363973 ]	[ 1.076051910607754, 1.2009176834838924 ]	1,024	[ 512, 512 ]	[ 363, 278, 12886, 6692, 9875, 263, 4655, 18766, 363, 6474, 29899, 322, 24454, 29899, 5563, 9045, 2669, 767, 18150, 29892, 10734, 297, 17692, 10161, 29889, 2398, 29892, 278, 1788, 8745, 304, 1380, 335, 403, 777, 310, 278, 11938, 491, 14372, 8525, 4127, 373, 967, 5314, 763, 5382, 6275, 11747, 1259, 278, 3889, 911, 304, 2758, 1162, 9216, 358, 322, 28573, 363, 12187, 11909, 29889, 10506, 11875, 1980, 363, 437, 14359, 322, 302, 1295, 267, 892, 1304, 2645, 263, 3309, 29891, 1162, 9216, 358, 3889, 911, 297, 796, 1117, 423, 297, 29871, 29906, 29900, 29900, 29906, 322, 29871, 29906, 29900, 29900, 29946, 518, 29929, 1822, 20175, 29892, 278, 8898, 373, 21224, 292, 471, 3939, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 29892, 411, 363, 1342, 278, 21224, 292, 3785, 363, 302, 1295, 267, 2675, 515, 29871, 29941, 304, 29871, 29906, 2440, 29889, 2973, 1316, 263, 4802, 13925, 3273, 482, 322, 263, 22576, 23390, 9999, 29892, 278, 5874, 1033, 451, 21750, 304, 7899, 2305, 3448, 515, 278, 17535, 29892, 577, 2274, 2197, 896, 3897, 901, 7431, 993, 29889, 1932, 1584, 278, 12212, 3785, 310, 21224, 292, 471, 451, 1641, 9259, 491, 17162, 29892, 278, 5874, 12919, 1304, 278, 3619, 13705, 310, 411, 8948, 292, 10591, 362, 23199, 1078, 2645, 278, 21224, 292, 3785, 518, 29941, 29946, 29962, 541, 1494, 278, 1162, 9216, 358, 3889, 911, 746, 17643, 1033, 694, 5520, 367, 22688, 1716, 278, 21224, 292, 8898, 322, 278, 8898, 310, 411, 8948, 292, 310, 23199, 1078, 892, 26681, 287, 607, 884, 3697, 278, 8525, 4127, 310, 278, 1788, 29889, 13, 2951, 278, 916, 1361, 29892, 278, 8820, 30003, 272, 304, 777, 15834, 278, 10225, 310, 3158, 30003, 974, 8898, 2136, 414, 297, 263, 24161, 1316, 408, 393, 18860, 297, 796, 19977, 370, 705, 508, 367, 313, 271, 3203, 22039, 29897, 10824, 491, 278, 2114, 393, 372, 471, 5189, 470, 9301, 363, 963, 304, 8500, 920, 1472, 278, 24161, 723, 1833, 29892, 322, 29892, 2729, 373, 393, 29892, 372, 471, 5189, 304, 11097, 825, 3620, 304, 1207, 304, 18209, 8898, 1584, 746, 278, 9045, 664, 10118, 471, 9436, 447, 28927, 19046, 6751, 29889, 13, 8809, 488, 278, 3620, 297, 2933, 304, 278, 24161, 297, 18209, 29899, 12817, 8898, 1795, 505, 1063, 9078, 29892, 10365, 1860, 322, 7744, 800, 472, 278, 6944, 3233, 29892, 297, 3153, 297, 8220, 304, 6782, 322, 1473, 358, 29892, 892, 901, 19555, 29889, 512, 3153, 29892, 278, 26681, 362, 310, 6782, 6865, 472, 278, 3171, 310, 278, 24161, 322, 278, 28476, 936, 671, 310, 1473, 358, 28585, 278, 11509, 310, 767, 18150, 29915, 8525, 4127, 297, 16049, 8898, 30003, 5816, 10211, 1940, 518, 29941, 29945, 29962, 14637, 304, 408, 525, 7099, 2459, 2913, 29915, 30003, 392, 304, 8677, 714, 8820, 304, 6176, 1009, 1203, 3145, 29892, 607, 297, 445, 1206, 892, 304, 11551, 13925, 322, 304, 5445, 11757, 273, 2478, 29889, 25678, 29892, 278, 21224, 292, 24833, 892, 9436, 23430, 472, 5164, 22950, 310, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 297, 2933, 304, 278, 6480, 23390, 9999, 6434, 29889, 450, 9500, 373, 278, 8898, 310, 337, 932, 2461, 358, 471, 9436, 19799, 491, 278, 3474, 310, 15130, 408, 379, 29956, 29879, 1058, 750, 2175, 278, 17535, 892, 6763, 304, 736, 297, 1776, 310, 278, 20295, 28473, 297, 278, 12463, 6434, 29889, 450, 28750, 310, 445, 3474, 471, 5162, 348, 403, 29892, 408, 1316, 28602, 1907, 1122, 367, 3755, 29801, 408, 1476, 491, 1749, 5925, 23056, 21628, 297, 24790, 951, 650, 518, 29941, 29953, 1822, 1576, 18707, 310, 278, 9609, 29940, 471, 884, 5335, 873, 408, 372, 1754, 1854, 11803, 892, 10423, 297, 17692, 10161, 29889, 2398, 29892, 694, 6221, 3620, 297, 278, 6782, 322, 1473, 358, 24833, 892, 1754, 10816, 297, 2933, 304, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 6434, 29889, 13, 1349, 820, 278, 18209, 1203, 3145, 1795, 505, 1063, 14363, 2769, 2197, 8472, 297, 278, 3273, 1840, 29892, 278, 8820, 310, 383, 8456, 767, 18150, 310, 5557, 292, 379, 29956, 29879, 515, 6782, 5393, 322, 310, 5874, 767, 18150, 304, 4889, 13925, 964, 3273, 29899, 8489, 1473, 1860, 6839, 393, 297, 278, 5520, 1840, 13925, 297, 1716, 4251, 1122, 505, 2175, 472, 278, 937, 15130, 29889, 10133, 29892, 278, 5520, 29899, 8489, 12091, 310, 3240, 2509, 723, 451, 505, 1063, 14363, 29892, 8632, 1218, 278, 18766, 310, 14338, 16165, 261, 296, 379, 29934, 16650, 583, 518, 29941, 29955, 29892, 29871, 29941, 29947, 1822, 512, 1438, 18845, 29892, 767, 18150, 881, 367, 6969, 304, 2125, 278, 14511, 1230, 304, 4505, 4828, 541, 881, 884, 367, 6969, 297, 8004, 1716, 278, 3273, 29899, 322, 5520, 29899, 8489, 2411, 5795, 310, 379, 29934, 29924, 8820, 29889, 13, 2744, 3805, 8927, 9138, 310, 445, 6559, 338, 393, 5998, 278, 337, 9514, 427, 627, 287, 1549, 278, 15202, 15538, 3185, 310, 29871, 29906, 29900, 29900, 29946, 2825, 263, 6555, 3368, 1788, 29892, 297, 278, 3030, 310, 24161, 29892, 6474, 29899, 5563, 767, 18150, 892, 2221, 304, 5503, 1009, 7426, 310, 525, 7099, 2459, 2913, 29915, 518, 29941, 29929, 29962, 30003, 272, 525, 8345, 363, 767, 7297, 4090, 276, 29915, 30003, 5514, 1135, 297, 777, 13714, 541, 7424, 368, 27189, 1705, 3368, 3030, 29879, 518, 29946, 29900, 29892, 29871, 29946, 29896, 29962, 411, 4880, 304, 13925, 18209, 29889, 512, 278, 18070, 310, 263, 6555, 2933, 304, 18209, 8898, 29892, 445, 1818, 367, 3595, 408, 6374, 10468, 29889, 2398, 29892, 1728, 2304, 373, 11828, 379, 29934, 29924, 29892, 777, 1602, 12112, 1754, 1065, 278, 12045, 310, 2534, 8178, 5520, 29899, 8489, 27721, 29889, 910, 9138, 338, 385, 18853, 3109, 265, 363, 796, 19977, 370, 705, 408, 372, 316, 1338, 411, 278, 1156, 755, 310, 278, 19224, 310, 278, 17407, 24161, 29892, 408, 1532, 408, 19998, 363, 916, 10916, 14870, 2788, 18845, 29889, 450, 8898, 881, 18145, 5485, 393, 10608, 2913, 1818, 367, 11664, 363, 18209, 767, 18150, 297, 23400, 9841, 17692, 10161, 29889, 1670, 892, 777, 27028, 304, 445, 6559, 29889, 10854, 362, 373, 24833, 322, 1006, 7406, 411, 1880, 29899, 661, 9292, 1820, 1871, 1934, 471, 5189, 304, 4017, 29889, 3115, 29892, 1422, 15303, 310, 278, 5314, 310, 278, 24833, 892, 2183, 1546, 767, 18150, 322, 1546, 9045 ]	1,332,829	6,144	CommonCrawl	6	2
workers. However, triangulation of data types and sources was used to ensure the credibility of the findings. We had initially planned to measure the impact of changing policies using routine staffing data. However, this was not finally possible as data was not available at the national level and insufficiently complete in the study districts to provide a representative sample across the categories of HWs. Nevertheless, the multi-method approach of this study allowed for qualitative data gathered through interviews with key informants, managers and staff—in particular the life histories [26]—to provide insights on the changing staffing situation. The 'uniqueness' of the situation in Zimbabwe makes these results very specific and therefore not directly transferable, but they add to the knowledge about how deployment policy and practice is or is not responsive to particular crises. How the crisis affected other HR policy and practice may be different and could be the subject of further study. Flexibility in implementing deployment policies is vital especially during changing conditions created by crisis in order to improve system responsiveness, retain HWs and manage their inequitable distribution in urban and rural areas. Managers at facilities and in provinces must be given mandate and support to be able to implement the policies for the interest of the HWs and facility at large. BRTI: Biomedical Research and Training Institute DFID: Department for International Development (UK Aid) DNO: District nursing officer FBO: Faith-based organisation Gvt: HOD: HRM: HSB: Health service board HSR: Health Services Regulations HW: IDI: Key informant interview MOHCC: Ministry of Health and Child Care MOHCW: Ministry of Health and Child Welfare PCN: Primary care nurse PSR: Public Service Regulation RDC: RGN: Chen L, Evans T, Anand S, Ivey Boufford J, Brown H, Chowdhury M, et al. Human resources for health: overcoming the crisis. Lancet. 2004;364(9449):1984–90. Scaling up, saving lives. Task force for scaling up education and training for health workers. Geneva: WHO/Global Health Workforce Alliance. 2008. Campbell J, Buchan J, Cometto G, David B, Dussault G, Fogstad H, et al. Human resources for health and universal health coverage : fostering equity and effective coverage. Policy Pract. 2013;(August:853–63. Varpilah ST, Safer M, Frenkel E, Baba D, Massaquoi M, Barrow G. Rebuilding human resources for health: a case study from Liberia. Hum Resour Health [Internet]. 2011;9(1):11. Available from: http://www.human-resources-health.com/content/9/1/11. Newbrander W, Yoder R, Debevoise AB. Rebuilding health systems in post-conflict countries: estimating the costs of basic services. Int J Heal Plan Manag. 2007;22(4):319–36. Lehmann U, Dieleman M, Martineau T. Staffing remote rural areas in middle- and low-income countries: a literature review of attraction and retention. BMC Health Serv Res [Internet]. 2008;8(1):19 Available from: http://bmchealthservres.biomedcentral.com/articles/10.1186/1472-6963-8-19. Dussault G, Franceschini MC. Not enough there, too many here: understanding geographical imbalances in the distribution of the health workforce. Hum Resour Health. 2006;4:12. Schaaf M, Freedman LP. Unmasking the open secret of posting and transfer practices in the health sector. Health Policy Plan. 2015;30(1):121–30. Vujicic M, Ohiri K, Sparkes S. Working in health. In: Financing and managing the public sector health workforce. Washington, DC: World Bank; 2009. Mponda JM, Biwot GK. The effects of deployment practices on employee performance among	-0.044769	0.918304	1.546214	0.951186	[ 0.42229053359210383, -0.5118281089850508 ]	[ 1.0902039921687319, 0.746403304557266 ]	[ 1.652735961643901, 1.4396917155116224 ]	[ 1.096862872753777, 0.805509402709454 ]	1,024	[ 512, 512 ]	[ 17162, 29889, 2398, 29892, 3367, 574, 2785, 310, 848, 4072, 322, 8974, 471, 1304, 304, 9801, 278, 6625, 4127, 310, 278, 1284, 886, 29889, 1334, 750, 12919, 20458, 304, 5645, 278, 10879, 310, 6480, 24833, 773, 26529, 13925, 292, 848, 29889, 2398, 29892, 445, 471, 451, 7146, 1950, 408, 848, 471, 451, 3625, 472, 278, 4797, 3233, 322, 1663, 29884, 4543, 368, 4866, 297, 278, 6559, 24172, 304, 3867, 263, 21097, 4559, 4822, 278, 13997, 310, 379, 29956, 29879, 29889, 25678, 29892, 278, 2473, 29899, 5696, 2948, 310, 445, 6559, 6068, 363, 4021, 23378, 848, 22229, 1549, 1006, 7406, 411, 1820, 1871, 1934, 29892, 767, 18150, 322, 13925, 30003, 262, 3153, 278, 2834, 3603, 583, 518, 29906, 29953, 29962, 30003, 517, 3867, 1663, 5861, 373, 278, 6480, 13925, 292, 6434, 29889, 450, 525, 3909, 339, 18543, 29915, 310, 278, 6434, 297, 796, 19977, 370, 705, 3732, 1438, 2582, 1407, 2702, 322, 5480, 451, 4153, 6782, 519, 29892, 541, 896, 788, 304, 278, 7134, 1048, 920, 18209, 8898, 322, 6944, 338, 470, 338, 451, 5544, 573, 304, 3153, 2181, 4637, 29889, 1128, 278, 24161, 15201, 916, 379, 29934, 8898, 322, 6944, 1122, 367, 1422, 322, 1033, 367, 278, 4967, 310, 4340, 6559, 29889, 13, 29943, 2506, 4127, 297, 16049, 18209, 24833, 338, 27131, 7148, 2645, 6480, 5855, 2825, 491, 24161, 297, 1797, 304, 11157, 1788, 5544, 20193, 29892, 11551, 379, 29956, 29879, 322, 10933, 1009, 297, 1686, 8270, 4978, 297, 17164, 322, 17692, 10161, 29889, 2315, 18150, 472, 23330, 322, 297, 28058, 1818, 367, 2183, 9619, 403, 322, 2304, 304, 367, 2221, 304, 2334, 278, 24833, 363, 278, 4066, 310, 278, 379, 29956, 29879, 322, 24454, 472, 2919, 29889, 13, 29933, 13079, 29902, 29901, 13, 29933, 14910, 287, 936, 10550, 322, 26101, 8907, 13, 4037, 1367, 29901, 13, 8498, 442, 358, 363, 4623, 14650, 313, 19960, 319, 333, 29897, 13, 29928, 6632, 29901, 13, 29928, 6801, 302, 1295, 292, 12139, 13, 29943, 8456, 29901, 13, 14206, 389, 29899, 6707, 24788, 13, 29954, 21908, 29901, 13, 8187, 29928, 29901, 13, 20938, 29924, 29901, 13, 29950, 1744, 29901, 13, 3868, 4298, 2669, 7613, 13, 29950, 14098, 29901, 13, 3868, 4298, 15538, 2169, 8250, 13, 29950, 29956, 29901, 13, 1367, 29902, 29901, 13, 2558, 1871, 424, 15593, 13, 6720, 29950, 4174, 29901, 13, 8140, 6020, 310, 15202, 322, 10517, 10057, 13, 6720, 19127, 29956, 29901, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 13, 9026, 29940, 29901, 13, 26666, 2562, 5595, 344, 13, 7024, 29934, 29901, 13, 19858, 6692, 2169, 2785, 13, 29934, 12696, 29901, 13, 29934, 20728, 29901, 13, 1451, 264, 365, 29892, 24056, 323, 29892, 530, 392, 317, 29892, 306, 6950, 12476, 600, 536, 435, 29892, 9817, 379, 29892, 678, 340, 12744, 2857, 341, 29892, 634, 394, 29889, 12968, 7788, 363, 9045, 29901, 975, 11506, 278, 24161, 29889, 24994, 300, 29889, 29871, 29906, 29900, 29900, 29946, 29936, 29941, 29953, 29946, 29898, 29929, 29946, 29946, 29929, 1125, 29896, 29929, 29947, 29946, 29994, 29929, 29900, 29889, 13, 29636, 292, 701, 29892, 14238, 12080, 29889, 9330, 4889, 363, 21640, 701, 9793, 322, 6694, 363, 9045, 17162, 29889, 15350, 1564, 29901, 399, 8187, 29914, 12756, 15202, 5244, 10118, 29855, 29889, 29871, 29906, 29900, 29900, 29947, 29889, 13, 29907, 1160, 12562, 435, 29892, 10586, 273, 435, 29892, 422, 8563, 402, 29892, 4699, 350, 29892, 360, 1558, 1292, 402, 29892, 383, 468, 17569, 379, 29892, 634, 394, 29889, 12968, 7788, 363, 9045, 322, 15968, 9045, 23746, 584, 9926, 3241, 1592, 537, 322, 11828, 23746, 29889, 25219, 29124, 29889, 29871, 29906, 29900, 29896, 29941, 29936, 29898, 26197, 29901, 29947, 29945, 29941, 29994, 29953, 29941, 29889, 13, 29963, 6834, 309, 801, 6850, 29892, 5701, 571, 341, 29892, 383, 1267, 10265, 382, 29892, 350, 5363, 360, 29892, 7360, 18463, 7768, 341, 29892, 2261, 798, 402, 29889, 12936, 29884, 789, 292, 5199, 7788, 363, 9045, 29901, 263, 1206, 6559, 515, 10895, 423, 29889, 13863, 2538, 473, 15202, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29896, 29936, 29929, 29898, 29896, 1125, 29896, 29896, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 26029, 29899, 13237, 29899, 354, 4298, 29889, 510, 29914, 3051, 29914, 29929, 29914, 29896, 29914, 29896, 29896, 29889, 13, 4373, 1182, 3825, 399, 29892, 612, 6119, 390, 29892, 7089, 29872, 1365, 895, 17571, 29889, 12936, 29884, 789, 292, 9045, 6757, 297, 1400, 29899, 5527, 29176, 10916, 29901, 4844, 1218, 278, 21544, 310, 6996, 5786, 29889, 3159, 435, 940, 284, 8402, 2315, 351, 29889, 29871, 29906, 29900, 29900, 29955, 29936, 29906, 29906, 29898, 29946, 1125, 29941, 29896, 29929, 29994, 29941, 29953, 29889, 13, 3226, 29882, 4403, 501, 29892, 1640, 280, 1171, 341, 29892, 3760, 457, 585, 323, 29889, 15351, 292, 7592, 17692, 10161, 297, 7256, 29899, 322, 4482, 29899, 262, 2763, 10916, 29901, 263, 12845, 9076, 310, 1098, 13857, 322, 3240, 2509, 29889, 350, 12513, 15202, 9635, 2538, 518, 26341, 1822, 29871, 29906, 29900, 29900, 29947, 29936, 29947, 29898, 29896, 1125, 29896, 29929, 7740, 3106, 515, 29901, 1732, 597, 5838, 1173, 4298, 2140, 690, 29889, 5365, 27067, 25171, 29889, 510, 29914, 18569, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29896, 29946, 29955, 29906, 29899, 29953, 29929, 29953, 29941, 29899, 29947, 29899, 29896, 29929, 29889, 13, 29928, 1558, 1292, 402, 29892, 10986, 305, 2172, 21271, 29889, 2216, 3307, 727, 29892, 2086, 1784, 1244, 29901, 8004, 1737, 19711, 527, 5521, 2925, 297, 278, 4978, 310, 278, 9045, 664, 10118, 29889, 13863, 2538, 473, 15202, 29889, 29871, 29906, 29900, 29900, 29953, 29936, 29946, 29901, 29896, 29906, 29889, 13, 4504, 29874, 2142, 341, 29892, 3878, 287, 1171, 23671, 29889, 853, 13168, 292, 278, 1722, 7035, 310, 16742, 322, 6782, 23274, 297, 278, 9045, 17535, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29896, 29945, 29936, 29941, 29900, 29898, 29896, 1125, 29896, 29906, 29896, 29994, 29941, 29900, 29889, 13, 29963, 8016, 293, 293, 341, 29892, 438, 2918, 374, 476, 29892, 20814, 267, 317, 29889, 24176, 297, 9045, 29889, 512, 29901, 4231, 19985, 322, 767, 6751, 278, 970, 17535, 9045, 664, 10118, 29889, 7660, 29892, 13681, 29901, 2787, 10253, 29936, 29871, 29906, 29900, 29900, 29929, 29889, 13, 29924, 2818, 29874, 435, 29924, 29892, 3457, 29893, 327, 402, 29968, 29889, 450, 9545, 310, 18209, 23274, 373, 19001, 4180, 4249 ]	1,332,829	7,168	CommonCrawl	14	10
the public banking institutions in Kenya a survey of post Bank coast. Region. 2015;5(9):1–13. Government of Canada. Public Service Employment Act; 2016. p. 5–8. Chirwa Y, Chandiwana P, Pepukai M, Mashange W, Buzuzi S, Munyati S, et al. Deployment of human resources for health in Zimbabwe : synthesis report. 2016. Ministry of Health and Child Welfare. Human resources for health policy. 2006; Ministry of Health and Child Welfare. National Health Strategy Zimbabwe 2009-2013. 2013; Osika J, Altman D, Ekbladh L, Katz I, Nguyen H, Rosenfeld J. Zimbabwe health system assessment, vol. 2011; 2010. ZIMSTATS. Zimbabwe population census 2012 [internet]. 2012. Available from: http://www.zimstat.co.zw/dmdocuments/Census/CensusResults2012/National_Report.pdf Chikanda A. Nurse migration from Zimbabwe: analysis of recent trends and impacts. Nurs Inq. 2005;12(3):162–74. Sikhosana PLN 2nd edition VT publishing. Challenges in reforming the health sector in Africa. 2nd editio. Victoria: Trafford publishing; 2005. Ministry of Health and Child Welfare. Human Resources for Health Strategic Plan 2010–2014; 2007. p. 83. Dieleman M, Watson M, Sisimayi C. Impact assessment of the Zimbabwe health worker retention scheme. Final Report. 2012. Mudyarabikwa O, Mbengwa A. Distribution of public sector health workers in Zimbabwe : a challenge for equity in health [Internet]. 2006. Available from: http://www.equinetafrica.org/bibl/docs/Diss34hresZim.pdf Government of Zimbabwe. Health service regulation 2006. Zimbabwe; 2006. Roome E, Raven J, Martineau T. Human resource management in post-conflict health systems: review of research and knowledge gaps. Confl Health [Internet]. 2014;8(1):18 Available from: http://conflictandhealth.biomedcentral.com/articles/10.1186/1752-1505-8-18. Alonso A, Brugha R. Rehabilitating the health system after conflict in East Timor : a shift from NGO to government leadership; September 1999. p. 2006. Bertone MP, Martins JS, Pereira SM, Martineau T, Alonso-Garbayo A. Understanding HRH recruitment in post- conflict settings : an analysis of central-level policies and processes in Timor-Leste ( 1999–2018 ), vol. 5; 2018. p. 1–12. Witter S, Namakula J, Alonso-Garbayo A, Wurie H, Theobald S, Mashange W, et al. Experiences of using life histories with health workers in post-conflict and crisis settings: methodological reflections. Health Policy Plan [Internet. 2017:czw166 Available from: https://academic.oup.com/heapol/article-lookup/doi/10.1093/heapol/czw166. Saunders B, Sim J, Kingstone T, Baker S, Waterfield J, Bartlam B, et al. Saturation in qualitative research : exploring its conceptualization and operationalization. Qual Quant. 2018;52(4):1893–907. Richie J, Spencer L. In: Burgess R, Bryman A, editors. Analyzing Qualitative Data. Rout	-1.00902	0.696266	0.803095	0.576589	[ -1.2514528406443814, -0.7665877387788202 ]	[ 0.8538410194358491, 0.5386903891253386 ]	[ 0.6331670694394248, 0.9730233668409168 ]	[ 0.41010112193501563, 0.7430765162713848 ]	1,024	[ 512, 512 ]	[ 278, 970, 9124, 292, 21561, 297, 10015, 3761, 263, 18994, 310, 1400, 10253, 12180, 29889, 11069, 29889, 29871, 29906, 29900, 29896, 29945, 29936, 29945, 29898, 29929, 1125, 29896, 29994, 29896, 29941, 29889, 13, 29954, 6170, 358, 310, 7400, 29889, 5236, 6692, 7361, 22812, 3185, 29936, 29871, 29906, 29900, 29896, 29953, 29889, 282, 29889, 29871, 29945, 29994, 29947, 29889, 13, 1451, 381, 2766, 612, 29892, 678, 392, 9429, 1648, 349, 29892, 349, 1022, 22971, 29875, 341, 29892, 341, 1161, 927, 399, 29892, 350, 3365, 29884, 2526, 317, 29892, 13564, 29891, 2219, 317, 29892, 634, 394, 29889, 10034, 22812, 310, 5199, 7788, 363, 9045, 297, 796, 19977, 370, 705, 584, 14710, 6656, 3461, 29889, 29871, 29906, 29900, 29896, 29953, 29889, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 12968, 7788, 363, 9045, 8898, 29889, 29871, 29906, 29900, 29900, 29953, 29936, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 3086, 15202, 3767, 8963, 796, 19977, 370, 705, 29871, 29906, 29900, 29900, 29929, 29899, 29906, 29900, 29896, 29941, 29889, 29871, 29906, 29900, 29896, 29941, 29936, 13, 24768, 4106, 435, 29892, 10790, 1171, 360, 29892, 16462, 2204, 328, 29882, 365, 29892, 476, 4101, 306, 29892, 405, 2543, 11771, 379, 29892, 28929, 10612, 435, 29889, 796, 19977, 370, 705, 9045, 1788, 24809, 358, 29892, 1700, 29889, 29871, 29906, 29900, 29896, 29896, 29936, 29871, 29906, 29900, 29896, 29900, 29889, 13, 29999, 7833, 17816, 29903, 29889, 796, 19977, 370, 705, 4665, 16411, 29871, 29906, 29900, 29896, 29906, 518, 14168, 300, 1822, 29871, 29906, 29900, 29896, 29906, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 29920, 326, 6112, 29889, 1111, 29889, 7659, 29914, 18933, 3225, 29879, 29914, 29907, 8841, 29914, 29907, 8841, 12191, 29906, 29900, 29896, 29906, 29914, 27325, 29918, 13020, 29889, 5140, 13, 1451, 638, 5863, 319, 29889, 25651, 344, 20332, 515, 796, 19977, 370, 705, 29901, 7418, 310, 7786, 534, 1975, 322, 10879, 29879, 29889, 405, 1295, 512, 29939, 29889, 29871, 29906, 29900, 29900, 29945, 29936, 29896, 29906, 29898, 29941, 1125, 29896, 29953, 29906, 29994, 29955, 29946, 29889, 13, 29903, 638, 15656, 1648, 16507, 29940, 29871, 29906, 299, 12203, 478, 29911, 27256, 29889, 678, 16047, 267, 297, 11736, 292, 278, 9045, 17535, 297, 10557, 29889, 29871, 29906, 299, 3863, 601, 29889, 14212, 29901, 3201, 600, 536, 27256, 29936, 29871, 29906, 29900, 29900, 29945, 29889, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 12968, 27562, 363, 15202, 3767, 1845, 293, 8402, 29871, 29906, 29900, 29896, 29900, 29994, 29906, 29900, 29896, 29946, 29936, 29871, 29906, 29900, 29900, 29955, 29889, 282, 29889, 29871, 29947, 29941, 29889, 13, 29928, 9152, 1171, 341, 29892, 28284, 341, 29892, 317, 275, 326, 388, 29875, 315, 29889, 14305, 627, 24809, 358, 310, 278, 796, 19977, 370, 705, 9045, 15645, 3240, 2509, 11380, 29889, 9550, 13969, 29889, 29871, 29906, 29900, 29896, 29906, 29889, 13, 29924, 566, 8553, 370, 638, 2766, 438, 29892, 341, 29890, 996, 2766, 319, 29889, 17740, 310, 970, 17535, 9045, 17162, 297, 796, 19977, 370, 705, 584, 263, 18766, 363, 1592, 537, 297, 9045, 518, 26341, 1822, 29871, 29906, 29900, 29900, 29953, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 1686, 262, 1187, 18961, 29889, 990, 29914, 18508, 29880, 29914, 2640, 29914, 29928, 790, 29941, 29946, 29882, 690, 29999, 326, 29889, 5140, 13, 29954, 6170, 358, 310, 796, 19977, 370, 705, 29889, 15202, 2669, 1072, 2785, 29871, 29906, 29900, 29900, 29953, 29889, 796, 19977, 370, 705, 29936, 29871, 29906, 29900, 29900, 29953, 29889, 13, 9588, 608, 382, 29892, 390, 3496, 435, 29892, 3760, 457, 585, 323, 29889, 12968, 6503, 10643, 297, 1400, 29899, 5527, 29176, 9045, 6757, 29901, 9076, 310, 5925, 322, 7134, 330, 2547, 29889, 1281, 1579, 15202, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29946, 29936, 29947, 29898, 29896, 1125, 29896, 29947, 7740, 3106, 515, 29901, 1732, 597, 5527, 29176, 392, 354, 4298, 29889, 5365, 27067, 25171, 29889, 510, 29914, 18569, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29896, 29955, 29945, 29906, 29899, 29896, 29945, 29900, 29945, 29899, 29947, 29899, 29896, 29947, 29889, 13, 2499, 16911, 319, 29892, 8135, 29887, 2350, 390, 29889, 830, 29882, 4427, 277, 1218, 278, 9045, 1788, 1156, 14529, 297, 6932, 7870, 272, 584, 263, 9500, 515, 405, 17080, 304, 5874, 26001, 29936, 3839, 29871, 29896, 29929, 29929, 29929, 29889, 282, 29889, 29871, 29906, 29900, 29900, 29953, 29889, 13, 29933, 814, 650, 16379, 29892, 3760, 1144, 7649, 29892, 23133, 3055, 13766, 29892, 3760, 457, 585, 323, 29892, 838, 16911, 29899, 29954, 279, 27495, 29877, 319, 29889, 7634, 11235, 379, 29934, 29950, 1162, 9216, 358, 297, 1400, 29899, 14529, 6055, 584, 385, 7418, 310, 6555, 29899, 5563, 24833, 322, 10174, 297, 7870, 272, 29899, 29931, 4196, 313, 29871, 29896, 29929, 29929, 29929, 29994, 29906, 29900, 29896, 29947, 10353, 1700, 29889, 29871, 29945, 29936, 29871, 29906, 29900, 29896, 29947, 29889, 282, 29889, 29871, 29896, 29994, 29896, 29906, 29889, 13, 29956, 5171, 317, 29892, 13041, 557, 2497, 435, 29892, 838, 16911, 29899, 29954, 279, 27495, 29877, 319, 29892, 399, 332, 347, 379, 29892, 450, 711, 2741, 317, 29892, 341, 1161, 927, 399, 29892, 634, 394, 29889, 28224, 819, 778, 310, 773, 2834, 3603, 583, 411, 9045, 17162, 297, 1400, 29899, 5527, 29176, 322, 24161, 6055, 29901, 1158, 5996, 2143, 5942, 29889, 15202, 25219, 8402, 518, 26341, 29889, 29871, 29906, 29900, 29896, 29955, 29901, 2067, 29893, 29896, 29953, 29953, 7740, 3106, 515, 29901, 2045, 597, 562, 1943, 13076, 29889, 1132, 29889, 510, 29914, 354, 481, 324, 29914, 7914, 29899, 20401, 29914, 1867, 29875, 29914, 29896, 29900, 29889, 29896, 29900, 29929, 29941, 29914, 354, 481, 324, 29914, 2067, 29893, 29896, 29953, 29953, 29889, 13, 29903, 585, 299, 414, 350, 29892, 3439, 435, 29892, 4088, 12734, 323, 29892, 22652, 317, 29892, 13062, 2671, 435, 29892, 12245, 5288, 350, 29892, 634, 394, 29889, 317, 1337, 362, 297, 4021, 23378, 5925, 584, 3902, 8253, 967, 6964, 950, 2133, 322, 1751, 1288, 2133, 29889, 15146, 22746, 29889, 29871, 29906, 29900, 29896, 29947, 29936, 29945, 29906, 29898, 29946, 1125, 29896, 29947, 29929, 29941, 29994, 29929, 29900, 29955, 29889, 13, 25627, 347, 435, 29892, 1706, 22687, 365, 29889, 512, 29901, 11202, 404, 390, 29892, 13307, 1171, 319, 29892, 3863, 943, 29889, 11597, 12339, 292, 15146, 23378, 3630, 29889, 20829 ]	1,332,829	8,192	CommonCrawl	9	22
ledge Qualitative data analysis for applied policy research; 1994. p. 173–94. Government of Zimbabwe. Public Service Regulation, 2000. 2000. International Monetary Fund. IMF. Zimbabwe 2012 article IV consultation. IMF country report no. 12/279. Washington, DC: International Monetary Fund; 2012. 2012. Mutizwa-Manziga D. The impact of health sector reform on public sector health worker motivation in Zimbabwe. Major applied research 5 working paper no. 4. Bethesda, MD: partnerships for health reform project: Abt Associates Inc; 1998. Purohit B, Martineau T, Sheikh K. Opening the black box of transfer systems in public sector health services in a Western state in India. BMC Health Serv Res. 2016;16(1):1–12. Available from. https://doi.org/10.1186/s12913-016-1675-0. Forgia G La, Raha S, Shaik S, Maheshwari S, Ali R. Parallel Systems and Human Resource Management in India's Public Health Services A View from the Front Lines. 2014;(June). Frehywot S, Mullan F, Payne W, Ross H. Compulsory service programmes for recruiting health workers in remote and rural areas : do they work ? Bull World Heal Organ. 2010:364–70. Bossert TJ. Analyzing the decentralization of health systems in developing countries: decision space, innovation and performance. Soc Sci Med. 1998;47:1513–27. Bertone MP, Samai M, Edem-hotah J, Witter S. A window of opportunity for reform in post-conflict settings ? The case of human resources for health policies in Sierra Leone , 2002 – 2012. Conflcit Heal. 2014;8(1):1–12. McCourt W, Eldridge D. Global human resource management: managing people in developing and transitional countries. Cheltenham: Edward Elgar; 2003. Fujita N, Zwi A, Nagai M, Akashi H. A comprehensive framework for human resources for health system development in fragile and post-conflict states. PLoS Med. 2011;8(12). Bossert TJ, Beauvais J. Decentralization of health systems in Ghana, Zambia, Uganda and the Philippines: a comparative analysis of decision space. Health Policy Plan. 2002;17(1):14–31 Available from: https://academic.oup.com/heapol/article-lookup/doi/10.1093/heapol/17.1.14. Bonenberger M, Aikins M, Akweongo P, Wyss K. Factors influencing the work efficiency of district health managers in low-resource settings : a qualitative study in Ghana. BMC Health Serv Res [Internet]. 2016;1–10. Available from: https://doi.org/10.1186/s12913-016-1271-3. Alonso-Garbayo A, Raven J, Theobald S, Ssengooba F, Nattimba M, Martineau T. Decision space for health workforce management in decentralized settings : a case study in Uganda. Health Policy Plan. 2017;32(suppl_3(August):iii59–66. This study is part of the ReBUILD consortium's work on health worker in crisis and conflicted-affected session and has a particular focus on deployment policies and practice during and post conflict or crisis. It contributes to the consortium's work on developing recommendations for strengthening health systems in such contexts. The ReBUILD consortium is funded by the UK Department for International Development (DFID). The authors are grateful to Dr. Maria Bertone for comments on a draft of this paper. This	-0.535455	1.05081	1.160705	0.998011	[ -0.8186354050807731, -0.25227461518978567 ]	[ 1.1403415924454041, 0.9612787343144322 ]	[ 0.8411388335209349, 1.4802715719177708 ]	[ 0.8471313270015002, 1.1488902781188348 ]	1,024	[ 512, 512 ]	[ 5485, 15146, 23378, 848, 7418, 363, 7436, 8898, 5925, 29936, 29871, 29896, 29929, 29929, 29946, 29889, 282, 29889, 29871, 29896, 29955, 29941, 29994, 29929, 29946, 29889, 13, 29954, 6170, 358, 310, 796, 19977, 370, 705, 29889, 5236, 6692, 2169, 2785, 29892, 29871, 29906, 29900, 29900, 29900, 29889, 29871, 29906, 29900, 29900, 29900, 29889, 13, 17579, 1288, 2598, 300, 653, 13249, 29889, 22313, 29943, 29889, 796, 19977, 370, 705, 29871, 29906, 29900, 29896, 29906, 4274, 6599, 8799, 362, 29889, 22313, 29943, 4234, 3461, 694, 29889, 29871, 29896, 29906, 29914, 29906, 29955, 29929, 29889, 7660, 29892, 13681, 29901, 4623, 2598, 300, 653, 13249, 29936, 29871, 29906, 29900, 29896, 29906, 29889, 29871, 29906, 29900, 29896, 29906, 29889, 13, 29924, 329, 466, 2766, 29899, 2517, 29920, 4324, 360, 29889, 450, 10879, 310, 9045, 17535, 11736, 373, 970, 17535, 9045, 15645, 17385, 362, 297, 796, 19977, 370, 705, 29889, 11019, 7436, 5925, 29871, 29945, 1985, 5650, 694, 29889, 29871, 29946, 29889, 23408, 267, 1388, 29892, 20672, 29901, 22056, 14587, 363, 9045, 11736, 2060, 29901, 1976, 29873, 6853, 1078, 9266, 29936, 29871, 29896, 29929, 29929, 29947, 29889, 13, 29925, 2192, 27342, 350, 29892, 3760, 457, 585, 323, 29892, 2296, 28464, 476, 29889, 4673, 292, 278, 4628, 3800, 310, 6782, 6757, 297, 970, 17535, 9045, 5786, 297, 263, 10504, 2106, 297, 7513, 29889, 350, 12513, 15202, 9635, 2538, 29889, 29871, 29906, 29900, 29896, 29953, 29936, 29896, 29953, 29898, 29896, 1125, 29896, 29994, 29896, 29906, 29889, 7740, 3106, 515, 29889, 2045, 597, 1867, 29875, 29889, 990, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29879, 29896, 29906, 29929, 29896, 29941, 29899, 29900, 29896, 29953, 29899, 29896, 29953, 29955, 29945, 29899, 29900, 29889, 13, 29943, 990, 423, 402, 997, 29892, 16790, 29874, 317, 29892, 1383, 29874, 638, 317, 29892, 10082, 12094, 29893, 1306, 317, 29892, 10785, 390, 29889, 1459, 6553, 23985, 322, 12968, 18981, 15057, 297, 7513, 29915, 29879, 5236, 15202, 15538, 319, 4533, 515, 278, 13960, 365, 1475, 29889, 29871, 29906, 29900, 29896, 29946, 29936, 29898, 29967, 1540, 467, 13, 29943, 9003, 5693, 327, 317, 29892, 341, 913, 273, 383, 29892, 14617, 484, 399, 29892, 13693, 379, 29889, 3831, 7273, 706, 2669, 1824, 4467, 363, 1162, 9216, 292, 9045, 17162, 297, 7592, 322, 17692, 10161, 584, 437, 896, 664, 1577, 20293, 2787, 940, 284, 9205, 29889, 29871, 29906, 29900, 29896, 29900, 29901, 29941, 29953, 29946, 29994, 29955, 29900, 29889, 13, 29933, 359, 1940, 323, 29967, 29889, 11597, 12339, 292, 278, 27189, 1705, 2133, 310, 9045, 6757, 297, 14338, 10916, 29901, 10608, 2913, 29892, 24233, 362, 322, 4180, 29889, 28239, 5636, 3436, 29889, 29871, 29896, 29929, 29929, 29947, 29936, 29946, 29955, 29901, 29896, 29945, 29896, 29941, 29994, 29906, 29955, 29889, 13, 29933, 814, 650, 16379, 29892, 3685, 1794, 341, 29892, 382, 2310, 29899, 8711, 801, 435, 29892, 399, 5171, 317, 29889, 319, 3474, 310, 15130, 363, 11736, 297, 1400, 29899, 5527, 29176, 6055, 1577, 450, 1206, 310, 5199, 7788, 363, 9045, 24833, 297, 24790, 951, 650, 1919, 29871, 29906, 29900, 29900, 29906, 785, 29871, 29906, 29900, 29896, 29906, 29889, 1281, 1579, 20752, 940, 284, 29889, 29871, 29906, 29900, 29896, 29946, 29936, 29947, 29898, 29896, 1125, 29896, 29994, 29896, 29906, 29889, 13, 27297, 29907, 14316, 399, 29892, 382, 430, 8605, 360, 29889, 12002, 5199, 6503, 10643, 29901, 767, 6751, 2305, 297, 14338, 322, 1301, 3245, 10916, 29889, 678, 295, 841, 3391, 29901, 9300, 1260, 5397, 29936, 29871, 29906, 29900, 29900, 29941, 29889, 13, 29943, 8016, 2028, 405, 29892, 796, 4353, 319, 29892, 14461, 1794, 341, 29892, 10813, 18321, 379, 29889, 319, 15171, 6270, 6890, 363, 5199, 7788, 363, 9045, 1788, 5849, 297, 13855, 488, 322, 1400, 29899, 5527, 29176, 5922, 29889, 349, 3410, 29903, 3436, 29889, 29871, 29906, 29900, 29896, 29896, 29936, 29947, 29898, 29896, 29906, 467, 13, 29933, 359, 1940, 323, 29967, 29892, 23826, 1564, 275, 435, 29889, 3826, 296, 1705, 2133, 310, 9045, 6757, 297, 13491, 1648, 29892, 796, 1117, 423, 29892, 501, 29887, 5863, 322, 278, 26260, 29901, 263, 5734, 1230, 7418, 310, 10608, 2913, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29900, 29906, 29936, 29896, 29955, 29898, 29896, 1125, 29896, 29946, 29994, 29941, 29896, 7740, 3106, 515, 29901, 2045, 597, 562, 1943, 13076, 29889, 1132, 29889, 510, 29914, 354, 481, 324, 29914, 7914, 29899, 20401, 29914, 1867, 29875, 29914, 29896, 29900, 29889, 29896, 29900, 29929, 29941, 29914, 354, 481, 324, 29914, 29896, 29955, 29889, 29896, 29889, 29896, 29946, 29889, 13, 29933, 19131, 15734, 341, 29892, 319, 638, 1144, 341, 29892, 10813, 705, 7443, 349, 29892, 10167, 893, 476, 29889, 26748, 943, 13787, 3277, 278, 664, 19201, 310, 6474, 9045, 767, 18150, 297, 4482, 29899, 10314, 6055, 584, 263, 4021, 23378, 6559, 297, 13491, 1648, 29889, 350, 12513, 15202, 9635, 2538, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29953, 29936, 29896, 29994, 29896, 29900, 29889, 7740, 3106, 515, 29901, 2045, 597, 1867, 29875, 29889, 990, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29879, 29896, 29906, 29929, 29896, 29941, 29899, 29900, 29896, 29953, 29899, 29896, 29906, 29955, 29896, 29899, 29941, 29889, 13, 2499, 16911, 29899, 29954, 279, 27495, 29877, 319, 29892, 390, 3496, 435, 29892, 450, 711, 2741, 317, 29892, 317, 29879, 22260, 15330, 383, 29892, 405, 1131, 326, 2291, 341, 29892, 3760, 457, 585, 323, 29889, 3826, 2459, 2913, 363, 9045, 664, 10118, 10643, 297, 27189, 1705, 1891, 6055, 584, 263, 1206, 6559, 297, 501, 29887, 5863, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29896, 29955, 29936, 29941, 29906, 29898, 19303, 29880, 29918, 29941, 29898, 26197, 1125, 25609, 29945, 29929, 29994, 29953, 29953, 29889, 13, 4013, 6559, 338, 760, 310, 278, 830, 29933, 25282, 1136, 441, 1974, 29915, 29879, 664, 373, 9045, 15645, 297, 24161, 322, 9476, 9446, 29899, 3470, 26458, 4867, 322, 756, 263, 3153, 8569, 373, 18209, 24833, 322, 6944, 2645, 322, 1400, 14529, 470, 24161, 29889, 739, 640, 5026, 304, 278, 1136, 441, 1974, 29915, 29879, 664, 373, 14338, 6907, 800, 363, 9324, 8333, 9045, 6757, 297, 1316, 3030, 29879, 29889, 450, 830, 29933, 25282, 1136, 441, 1974, 338, 5220, 287, 491, 278, 10261, 10317, 363, 4623, 14650, 313, 4037, 1367, 467, 450, 15717, 526, 28656, 304, 4942, 29889, 6217, 16662, 650, 363, 6589, 373, 263, 18195, 310, 445, 5650, 29889, 13, 4013 ]	1,332,829	9,216	CommonCrawl	17	12
Understanding effects of nose-cone bluntness on hypersonic boundary layer transition using input-output analysis Cook, D. A., Thome, J. S., Brock, J. M., Nichols, J. W. & Candler, G. V., 2018, AIAA Aerospace Sciences Meeting. 210059 ed. American Institute of Aeronautics and Astronautics Inc, AIAA, (AIAA Aerospace Sciences Meeting, 2018; no. 210059). Understanding effects of personalized vs. aggregate ratings on user preferences Adomavicius, G., Bockstedt, J., Curley, S. & Zhang, J., Jan 1 2016, In: CEUR Workshop Proceedings. 1679, p. 14-21 8 p. Understanding elementary landscapes Whitley, L. D., Sutton, A. M. & Howe, A. E., 2008, GECCO'08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation 2008. Association for Computing Machinery, p. 585-592 8 p. (GECCO'08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation 2008). Understanding emoji ambiguity in context: The role of text in emoji-related miscommunication Miller, H., Kluver, D., Thebault-Spieker, J., Terveen, L. & Hecht, B., 2017, Proceedings of the 11th International Conference on Web and Social Media, ICWSM 2017. AAAI press, p. 152-161 10 p. (Proceedings of the 11th International Conference on Web and Social Media, ICWSM 2017). Understanding employee awareness of health care quality information: How can employers benefit? Abraham, J., Feldman, R. & Carlin, C., Dec 2004, In: Health services research. 39, 6 I, p. 1799-1816 18 p. Understanding Environmental Public Opinion by Dimension: How Heuristic Processing Mitigates High Information Costs on Complex Issues Rugeley, C. R. & Gerlach, J. D., Jun 1 2012, In: Politics and Policy. 40, 3, p. 444-470 27 p. Understanding ethical concerns surrounding big data and learning analytics in higher education Duin, A. H. & Swenson, J., 2018, The Wiley Handbook of Education Policy. Papa, R. & Armfield, S. (eds.). Blackwell Publishing, p. 479-511 Understanding evolution in technology ecosystems Adomavicius, G., Bockstedt, J., Gupta, A. & Kauffman, R. J., Oct 1 2008, In: Communications of the ACM. 51, 10, p. 117-122 6 p. Understanding external and cascading benefits for HIV/AIDS control in a subsistence marketplace: Insights from Indonesia Arli, D. & Cadeaux, J., Mar 1 2017, In: Journal of Public Policy and Marketing. 36, 1, p. 117-136 20 p. Understanding factors affecting participation in online formative quizzes: An interview study Abney, A. J., Amin, S. & Kibble, J. D., Jan 1 2017, In: Advances in Physiology Education. 41, 3, p. 457-463 7 p. Understanding factors that trigger entrepreneurial behavior in established companies Morris, M. H., Zahra, S. A. & Schindehutte, M., 2000, Entrepreneurship and economic growth in the American economy. JAI Press, p. 133-159 27 p.	-1.01039	-0.619846	0.321209	0.264424	[ -0.9610816496966442, -1.059698280584555 ]	[ -0.4533178449202455, -0.7863747610438532 ]	[ 0.23751346947947882, 0.4049053771548406 ]	[ 0.3580737165699579, 0.17077505725575026 ]	1,024	[ 512, 512 ]	[ 7634, 11235, 9545, 310, 26414, 29899, 535, 29872, 1999, 1657, 2264, 373, 10163, 1330, 293, 10452, 7546, 9558, 773, 1881, 29899, 4905, 7418, 13, 19159, 29892, 360, 29889, 319, 1696, 498, 608, 29892, 435, 29889, 317, 1696, 4358, 384, 29892, 435, 29889, 341, 1696, 16371, 3775, 29892, 435, 29889, 399, 29889, 669, 28433, 1358, 29892, 402, 29889, 478, 1696, 29871, 29906, 29900, 29896, 29947, 29892, 319, 29902, 6344, 319, 9672, 3535, 17253, 2191, 15133, 29889, 29871, 29906, 29896, 29900, 29900, 29945, 29929, 1226, 29889, 3082, 8907, 310, 18682, 20546, 1199, 322, 319, 710, 20546, 1199, 9266, 29892, 319, 29902, 6344, 29892, 313, 23869, 6344, 319, 9672, 3535, 17253, 2191, 15133, 29892, 29871, 29906, 29900, 29896, 29947, 29936, 694, 29889, 29871, 29906, 29896, 29900, 29900, 29945, 29929, 467, 13, 29177, 11235, 9545, 310, 7333, 1891, 7186, 29889, 20431, 26838, 373, 1404, 5821, 2063, 13, 29909, 3129, 485, 1654, 375, 29892, 402, 1696, 350, 1698, 16470, 29873, 29892, 435, 1696, 10837, 2330, 29892, 317, 29889, 669, 796, 11895, 29892, 435, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 14645, 4574, 5244, 19032, 1019, 3947, 886, 29889, 29871, 29896, 29953, 29955, 29929, 29892, 282, 29889, 29871, 29896, 29946, 29899, 29906, 29896, 29871, 29947, 282, 29889, 13, 29177, 11235, 22470, 2982, 1557, 11603, 13, 8809, 1740, 29891, 29892, 365, 29889, 360, 1696, 317, 1851, 29892, 319, 29889, 341, 29889, 669, 1128, 29872, 29892, 319, 29889, 382, 1696, 29871, 29906, 29900, 29900, 29947, 29892, 402, 11206, 3217, 29915, 29900, 29947, 29901, 1019, 3947, 886, 310, 278, 29871, 29896, 29900, 386, 8081, 950, 16377, 373, 5739, 7492, 322, 382, 4068, 653, 11796, 362, 29871, 29906, 29900, 29900, 29947, 29889, 7993, 363, 11796, 292, 17197, 262, 708, 29892, 282, 29889, 29871, 29945, 29947, 29945, 29899, 29945, 29929, 29906, 29871, 29947, 282, 29889, 313, 1692, 29907, 3217, 29915, 29900, 29947, 29901, 1019, 3947, 886, 310, 278, 29871, 29896, 29900, 386, 8081, 950, 16377, 373, 5739, 7492, 322, 382, 4068, 653, 11796, 362, 29871, 29906, 29900, 29900, 29947, 467, 13, 29177, 11235, 953, 29877, 2397, 22363, 537, 297, 3030, 29901, 450, 6297, 310, 1426, 297, 953, 29877, 2397, 29899, 12817, 3984, 27820, 362, 13, 29924, 5495, 29892, 379, 1696, 476, 6092, 369, 29892, 360, 1696, 450, 29890, 1292, 29899, 5592, 347, 3946, 29892, 435, 1696, 5061, 345, 264, 29892, 365, 29889, 669, 940, 2570, 29892, 350, 1696, 29871, 29906, 29900, 29896, 29955, 29892, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 4623, 16377, 373, 2563, 322, 10307, 8213, 29892, 18340, 7811, 29924, 29871, 29906, 29900, 29896, 29955, 29889, 319, 6344, 29902, 3965, 29892, 282, 29889, 29871, 29896, 29945, 29906, 29899, 29896, 29953, 29896, 29871, 29896, 29900, 282, 29889, 313, 1184, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 4623, 16377, 373, 2563, 322, 10307, 8213, 29892, 18340, 7811, 29924, 29871, 29906, 29900, 29896, 29955, 467, 13, 29177, 11235, 19001, 3773, 8326, 404, 310, 9045, 2562, 11029, 2472, 29901, 1128, 508, 5703, 414, 14169, 29973, 13, 29909, 2634, 3391, 29892, 435, 1696, 21113, 1171, 29892, 390, 29889, 669, 1704, 1915, 29892, 315, 1696, 3826, 29871, 29906, 29900, 29900, 29946, 29892, 512, 29901, 15202, 5786, 5925, 29889, 29871, 29941, 29929, 29892, 29871, 29953, 306, 29892, 282, 29889, 29871, 29896, 29955, 29929, 29929, 29899, 29896, 29947, 29896, 29953, 29871, 29896, 29947, 282, 29889, 13, 29177, 11235, 16738, 284, 5236, 6461, 262, 291, 491, 4792, 2673, 29901, 1128, 940, 332, 4695, 10554, 292, 4573, 335, 1078, 5057, 10343, 9839, 29879, 373, 26596, 16982, 1041, 13, 29934, 5710, 2330, 29892, 315, 29889, 390, 29889, 669, 5681, 22617, 29892, 435, 29889, 360, 1696, 8378, 29871, 29896, 29871, 29906, 29900, 29896, 29906, 29892, 512, 29901, 6934, 1199, 322, 25219, 29889, 29871, 29946, 29900, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29946, 29946, 29946, 29899, 29946, 29955, 29900, 29871, 29906, 29955, 282, 29889, 13, 29177, 11235, 11314, 936, 21838, 18830, 4802, 848, 322, 6509, 16114, 1199, 297, 6133, 9793, 13, 29928, 29884, 262, 29892, 319, 29889, 379, 29889, 669, 3925, 25151, 29892, 435, 1696, 29871, 29906, 29900, 29896, 29947, 29892, 450, 399, 15168, 5166, 2909, 310, 13151, 25219, 29889, 27412, 29892, 390, 29889, 669, 8481, 2671, 29892, 317, 29889, 313, 5779, 6250, 6054, 5872, 19088, 29892, 282, 29889, 29871, 29946, 29955, 29929, 29899, 29945, 29896, 29896, 13, 29177, 11235, 14675, 297, 15483, 321, 3944, 973, 29879, 13, 29909, 3129, 485, 1654, 375, 29892, 402, 1696, 350, 1698, 16470, 29873, 29892, 435, 1696, 2088, 28363, 29892, 319, 29889, 669, 476, 28411, 1171, 29892, 390, 29889, 435, 1696, 4756, 29871, 29896, 29871, 29906, 29900, 29900, 29947, 29892, 512, 29901, 22365, 800, 310, 278, 14614, 29924, 29889, 29871, 29945, 29896, 29892, 29871, 29896, 29900, 29892, 282, 29889, 29871, 29896, 29896, 29955, 29899, 29896, 29906, 29906, 29871, 29953, 282, 29889, 13, 29177, 11235, 7029, 322, 3209, 29883, 9382, 23633, 363, 379, 5667, 29914, 29909, 1367, 29903, 2761, 297, 263, 11684, 11416, 9999, 6689, 29901, 13377, 5861, 515, 16704, 423, 13, 1433, 492, 29892, 360, 29889, 669, 315, 1943, 2993, 29892, 435, 1696, 1085, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 8237, 310, 5236, 25219, 322, 4485, 15133, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29896, 29896, 29955, 29899, 29896, 29941, 29953, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 13879, 6602, 292, 27577, 297, 7395, 883, 1230, 439, 4981, 267, 29901, 530, 15593, 6559, 13, 4920, 3801, 29892, 319, 29889, 435, 1696, 319, 1195, 29892, 317, 29889, 669, 476, 747, 569, 29892, 435, 29889, 360, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 25215, 2925, 297, 11661, 29875, 3002, 13151, 29889, 29871, 29946, 29896, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29946, 29945, 29955, 29899, 29946, 29953, 29941, 29871, 29955, 282, 29889, 13, 29177, 11235, 13879, 393, 7135, 23440, 1600, 332, 616, 6030, 297, 7841, 14582, 13, 28581, 3780, 29892, 341, 29889, 379, 1696, 796, 801, 336, 29892, 317, 29889, 319, 29889, 669, 1102, 25201, 29882, 329, 371, 29892, 341, 1696, 29871, 29906, 29900, 29900, 29900, 29892, 14447, 558, 1600, 332, 3527, 322, 17407, 14321, 297, 278, 3082, 26504, 29889, 435, 23869, 5254, 29892, 282, 29889, 29871, 29896, 29941, 29941, 29899, 29896, 29945, 29929, 29871, 29906, 29955, 282, 29889 ]	1,332,834	0	CommonCrawl	17	12
(Advances in the Study of Entrepreneurship, Innovation, and Economic Growth; vol. 12). Understanding family communication patterns and family functioning: The roles of conversation orientation and conformity orientation Koerner, A. F., Fitzpatrick, M. A. & Koerner, A. F., 2002, In: Communication Yearbook. p. 37-69 Understanding family interaction patterns in families with Alzheimer's disease Schaber, P., Blair, K., Jost, E., Schaffer, M. & Thurner, E., Jan 2016, In: OTJR Occupation, Participation and Health. 36, 1, p. 25-33 9 p. Understanding farmers' decision making processes and improving managerial assistance Öhlmér, B., Olson, K. & Brehmer, B., May 29 1998, In: Agricultural Economics. 18, 3, p. 273-290 18 p. Understanding farmscapes and their potential for improving IPM programs Rogers, M. A., Aug 4 2014, In: Journal of Integrated Pest Management. 5, 3 Understanding firewomen's fit problems with their coats and pants and its impact on mobility and safety Mckinney, E., Morris, K., Wu, Y., Griffin, L., Sokolowski, S., Carufel, R. & Park, J., Jun 24 2021, In: Work. 69, 2, p. 449-464 16 p. Understanding forced convective drying of apple tissue: Combining neutron radiography and numerical modelling Aregawi, W., Defraeye, T., Saneinejad, S., Vontobel, P., Lehmann, E., Carmeliet, J., Verboven, P., Derome, D. & Nicolai, B., Aug 2014, In: Innovative Food Science and Emerging Technologies. 24, p. 97-105 9 p. Understanding Galectin Structure-Function Relationships to Design Effective Antagonists Nesmelova, I. V., Dings, R. P. M. & Mayo, K. H., Jan 29 2008, Galectins. John Wiley & Sons, Inc., p. 33-69 37 p. Understanding gardening and dietary habits among youth garden program participants using the Theory of Planned Behavior Lautenschlager, L. & Smith, C., Jul 2007, In: Appetite. 49, 1, p. 122-130 9 p. Understanding gender roles in teen pregnancy prevention among American Indian youth Hanson, J. D., McMahon, T. R., Griese, E. R. & Kenyon, D. Y. B., Nov 1 2014, In: American journal of health behavior. 38, 6, p. 807-815 9 p. Understanding general and specific connections between psychopathology and marital distress: A model based approach South, S. C., Krueger, R. F. & Iacono, W. G., Nov 2011, In: Journal of abnormal psychology. 120, 4, p. 935-947 13 p. Understanding generational differences in financial literacy in Hmong immigrant families Solheim, C. A. & Yang, P. N. D., Jun 1 2010, In: Family and Consumer Sciences Research Journal. 38, 4, p. 435-454 20 p. Understanding genre through the lens of advocacy: The rhetorical work of the victim impact statement Propen, A. D. & Schuster, M. L., Jan 2010, In: Written Communication. 27, 1, p. 3-35 33 p. Understanding globalization Pesut, D. J. &	-0.996693	-0.550907	0.534254	0.062818	[ -0.9336881411166691, -1.059698280584555 ]	[ -0.49629293087167875, -0.6055212743315715 ]	[ 0.5114275002209799, 0.5570798386778968 ]	[ 0.03810517357485317, 0.08753120867165798 ]	1,024	[ 512, 512 ]	[ 313, 3253, 29894, 2925, 297, 278, 29301, 310, 14447, 558, 1600, 332, 3527, 29892, 512, 13715, 362, 29892, 322, 12884, 293, 402, 798, 386, 29936, 1700, 29889, 29871, 29896, 29906, 467, 13, 29177, 11235, 3942, 12084, 15038, 322, 3942, 740, 292, 29901, 450, 16178, 310, 14983, 19843, 322, 14670, 537, 19843, 13, 29968, 29877, 15479, 29892, 319, 29889, 383, 1696, 22963, 5031, 9131, 29892, 341, 29889, 319, 29889, 669, 8224, 15479, 29892, 319, 29889, 383, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 512, 29901, 22365, 362, 8905, 2909, 29889, 282, 29889, 29871, 29941, 29955, 29899, 29953, 29929, 13, 29177, 11235, 3942, 14881, 15038, 297, 13175, 411, 838, 29920, 27400, 29915, 29879, 17135, 13, 4504, 370, 261, 29892, 349, 1696, 10465, 381, 29892, 476, 1696, 435, 520, 29892, 382, 1696, 1102, 2142, 571, 29892, 341, 29889, 669, 498, 595, 261, 29892, 382, 1696, 2627, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 438, 29911, 29967, 29934, 16117, 786, 362, 29892, 3455, 12654, 362, 322, 15202, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29906, 29945, 29899, 29941, 29941, 29871, 29929, 282, 29889, 13, 29177, 11235, 2215, 13269, 29915, 10608, 3907, 10174, 322, 4857, 1747, 8455, 616, 18872, 13, 30094, 4415, 29885, 1064, 29892, 350, 1696, 7137, 1100, 29892, 476, 29889, 669, 5826, 29882, 1050, 29892, 350, 1696, 2610, 29871, 29906, 29929, 29871, 29896, 29929, 29929, 29947, 29892, 512, 29901, 27051, 3631, 12884, 1199, 29889, 29871, 29896, 29947, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29906, 29955, 29941, 29899, 29906, 29929, 29900, 29871, 29896, 29947, 282, 29889, 13, 29177, 11235, 2215, 1516, 5030, 267, 322, 1009, 7037, 363, 4857, 1747, 5641, 29924, 11104, 13, 29934, 468, 414, 29892, 341, 29889, 319, 1696, 22333, 29871, 29946, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 8237, 310, 17100, 630, 349, 342, 15057, 29889, 29871, 29945, 29892, 29871, 29941, 13, 29177, 11235, 3974, 29893, 2770, 29915, 29879, 6216, 4828, 411, 1009, 1302, 1446, 322, 282, 1934, 322, 967, 10879, 373, 22458, 1793, 322, 15332, 13, 29924, 384, 262, 3801, 29892, 382, 1696, 23112, 29892, 476, 1696, 29624, 29892, 612, 1696, 22990, 262, 29892, 365, 1696, 317, 554, 324, 11716, 29892, 317, 1696, 1704, 1137, 295, 29892, 390, 29889, 669, 4815, 29892, 435, 1696, 8378, 29871, 29906, 29946, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 5244, 29889, 29871, 29953, 29929, 29892, 29871, 29906, 29892, 282, 29889, 29871, 29946, 29946, 29929, 29899, 29946, 29953, 29946, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 11826, 378, 345, 312, 573, 15589, 292, 310, 26163, 260, 15118, 29901, 422, 2109, 292, 11553, 1617, 17937, 5275, 322, 16259, 878, 7807, 13, 29909, 1727, 1450, 29875, 29892, 399, 1696, 5282, 336, 1032, 29872, 29892, 323, 1696, 317, 1662, 457, 29926, 328, 29892, 317, 1696, 9299, 517, 6596, 29892, 349, 1696, 951, 29882, 4403, 29892, 382, 1696, 1704, 12873, 2035, 29892, 435, 1696, 26646, 9813, 29892, 349, 1696, 2452, 608, 29892, 360, 29889, 669, 13488, 1794, 29892, 350, 1696, 22333, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 512, 13715, 1230, 25453, 9327, 322, 27718, 3460, 8364, 11763, 29889, 29871, 29906, 29946, 29892, 282, 29889, 29871, 29929, 29955, 29899, 29896, 29900, 29945, 29871, 29929, 282, 29889, 13, 29177, 11235, 402, 744, 312, 262, 3767, 12425, 29899, 6678, 6376, 800, 14587, 304, 12037, 26475, 573, 530, 14103, 2879, 13, 29940, 267, 12873, 4273, 29892, 306, 29889, 478, 1696, 360, 886, 29892, 390, 29889, 349, 29889, 341, 29889, 669, 2610, 29877, 29892, 476, 29889, 379, 1696, 2627, 29871, 29906, 29929, 29871, 29906, 29900, 29900, 29947, 29892, 402, 744, 312, 1144, 29889, 2259, 399, 15168, 669, 317, 787, 29892, 9266, 1696, 282, 29889, 29871, 29941, 29941, 29899, 29953, 29929, 29871, 29941, 29955, 282, 29889, 13, 29177, 11235, 16423, 292, 322, 652, 300, 653, 2299, 1169, 4249, 12397, 16423, 1824, 27138, 773, 278, 24134, 310, 1858, 11310, 1522, 16300, 13, 29931, 1300, 3586, 29880, 1875, 29892, 365, 29889, 669, 7075, 29892, 315, 1696, 2739, 29871, 29906, 29900, 29900, 29955, 29892, 512, 29901, 2401, 300, 568, 29889, 29871, 29946, 29929, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29896, 29906, 29906, 29899, 29896, 29941, 29900, 29871, 29929, 282, 29889, 13, 29177, 11235, 23346, 16178, 297, 734, 264, 758, 5138, 6906, 5557, 291, 4249, 3082, 7560, 12397, 13, 29950, 16307, 29892, 435, 29889, 360, 1696, 4052, 29924, 801, 265, 29892, 323, 29889, 390, 1696, 402, 374, 968, 29892, 382, 29889, 390, 29889, 669, 10015, 29891, 265, 29892, 360, 29889, 612, 29889, 350, 1696, 2864, 29871, 29896, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 3082, 8955, 310, 9045, 6030, 29889, 29871, 29941, 29947, 29892, 29871, 29953, 29892, 282, 29889, 29871, 29947, 29900, 29955, 29899, 29947, 29896, 29945, 29871, 29929, 282, 29889, 13, 29177, 11235, 2498, 322, 2702, 12368, 1546, 11643, 459, 493, 3002, 322, 1766, 2410, 1320, 1253, 29901, 319, 1904, 2729, 2948, 13, 29903, 2438, 29892, 317, 29889, 315, 1696, 28499, 387, 261, 29892, 390, 29889, 383, 29889, 669, 306, 29874, 21441, 29892, 399, 29889, 402, 1696, 2864, 29871, 29906, 29900, 29896, 29896, 29892, 512, 29901, 8237, 310, 633, 8945, 11643, 3002, 29889, 29871, 29896, 29906, 29900, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29929, 29941, 29945, 29899, 29929, 29946, 29955, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 1176, 1288, 12651, 297, 18161, 4631, 4135, 297, 379, 29885, 549, 5198, 4481, 424, 13175, 13, 13296, 6391, 29892, 315, 29889, 319, 29889, 669, 27583, 29892, 349, 29889, 405, 29889, 360, 1696, 8378, 29871, 29896, 29871, 29906, 29900, 29896, 29900, 29892, 512, 29901, 14662, 322, 2138, 4680, 17253, 10550, 8237, 29889, 29871, 29941, 29947, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29946, 29941, 29945, 29899, 29946, 29945, 29946, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 16151, 1549, 278, 301, 575, 310, 22545, 4135, 29901, 450, 364, 9188, 272, 936, 664, 310, 278, 28985, 10879, 3229, 13, 1184, 2238, 29892, 319, 29889, 360, 29889, 669, 1102, 5402, 29892, 341, 29889, 365, 1696, 2627, 29871, 29906, 29900, 29896, 29900, 29892, 512, 29901, 16849, 841, 22365, 362, 29889, 29871, 29906, 29955, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29941, 29899, 29941, 29945, 29871, 29941, 29941, 282, 29889, 13, 29177, 11235, 5534, 2133, 13, 29925, 267, 329, 29892, 360, 29889, 435, 29889, 669 ]	1,332,834	1,024	CommonCrawl	17	12
Horton-Deutsch, S., 2002, In: Nursing outlook. 50, 3, p. 87-88 2 p. Understanding global teleconnections of climate to regional model estimates of Amazon ecosystem carbon fluxes Potter, C., Klooster, S., Steinbach, M., Tan, P. N., Kumar, V., Shekhar, S. & Reis de Carvalho, C., May 2004, In: Global change biology. 10, 5, p. 693-703 11 p. Understanding gradient clipping in private SGD: A geometric perspective Chen, X., Wu, S. & Hong, M., 2020, In: Advances in Neural Information Processing Systems. 2020-December Understanding horizontal Bridgman shelf growth of cadmium telluride and cadmium zinc telluride I. Heat and momentum transfer Edwards, K. & Derby, J. J., Aug 1997, In: Journal of Crystal Growth. 179, 1-2, p. 120-132 13 p. Understanding horizontal Bridgman shelf growth of cadmium telluride and cadmium zinc telluride II. Thermoelastic stresses Understanding How Acoustic Vibrations Modulate the Optical Response of Plasmonic Metal Nanoparticles Ahmed, A., Pelton, M. & Guest, J. R., Sep 26 2017, In: ACS nano. 11, 9, p. 9360-9369 10 p. Understanding 'How computing has changed the world' Misa, T. J., Oct 2007, In: IEEE Annals of the History of Computing. 29, 4, p. 52-63 12 p. Understanding how gay, bisexual, and other men who have sex with men in China cope with hiv care-related stressors Li, C., Giovenco, D., Dong, W., Smith, M. K., Golin, C. E., Fisher, E. B., Lei, G., Jiang, H., Tang, P. Y. & Muessig, K. E., Feb 1 2021, In: AIDS Education and Prevention. 33, 1, p. 46-61 16 p. Understanding how language matters Yang, K. K., Mar 15 2015, In: Index on Censorship. 44, 1, p. 64-66 3 p. Understanding How Language of Instruction Impacts Early Literacy Growth for Spanish-Speaking Children Wackerle-Hollman, A., Durán, L., Miranda, A., Chávez, C., Rodriguez, M. & Medina Morales, N., Jun 2 2021, In: School Psychology Review. Understanding how microbiomes influence the systems they inhabit Hall, E. K., Bernhardt, E. S., Bier, R. L., Bradford, M. A., Boot, C. M., Cotner, J. B., del Giorgio, P. A., Evans, S. E., Graham, E. B., Jones, S. E., Lennon, J. T., Locey, K. J., Nemergut, D., Osborne, B. B., Rocca, J. D., Schimel, J. P., Waldrop, M. P. & Wallenstein, M. D., Sep 1 2018, In: Nature Microbiology. 3, 9, p. 977-982 6 p. Understanding how people use natural language to ask for recommendations Kang, J., Condiff, K., Chang, S., Konstan, J. A., Terveen, L. & Harper, F. M., Aug 27 2017, RecSys 2017 - Proceedings of the 11th ACM Conference on Recommender Systems. Association for Computing Machinery, Inc, p. 229-237 9 p. (RecSys 2	-0.821375	-0.410063	0.437877	0.164272	[ -0.9665603514126393, -0.6761891604649021 ]	[ -0.2486266152192783, -0.571499331286687 ]	[ 0.0041792951441260605, 0.8715737258255462 ]	[ 0.37368193817947526, -0.04513867500923912 ]	1,024	[ 512, 512 ]	[ 379, 26342, 29899, 2772, 2434, 29892, 317, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 512, 29901, 405, 1295, 292, 714, 6914, 29889, 29871, 29945, 29900, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29947, 29955, 29899, 29947, 29947, 29871, 29906, 282, 29889, 13, 29177, 11235, 5534, 4382, 11958, 1953, 310, 23622, 304, 14014, 1904, 21875, 310, 16631, 321, 3944, 973, 22004, 19389, 267, 13, 29925, 327, 357, 29892, 315, 1696, 476, 417, 15664, 29892, 317, 1696, 14808, 6740, 29892, 341, 1696, 15066, 29892, 349, 29889, 405, 1696, 476, 24540, 29892, 478, 1696, 2296, 29895, 8222, 29892, 317, 29889, 669, 830, 275, 316, 1704, 791, 1251, 29892, 315, 1696, 2610, 29871, 29906, 29900, 29900, 29946, 29892, 512, 29901, 12002, 1735, 4768, 3002, 29889, 29871, 29896, 29900, 29892, 29871, 29945, 29892, 282, 29889, 29871, 29953, 29929, 29941, 29899, 29955, 29900, 29941, 29871, 29896, 29896, 282, 29889, 13, 29177, 11235, 16030, 9335, 3262, 297, 2024, 317, 29954, 29928, 29901, 319, 26224, 18520, 13, 1451, 264, 29892, 1060, 1696, 29624, 29892, 317, 29889, 669, 12798, 29892, 341, 1696, 29871, 29906, 29900, 29906, 29900, 29892, 512, 29901, 25215, 2925, 297, 2448, 3631, 10343, 10554, 292, 23985, 29889, 29871, 29906, 29900, 29906, 29900, 29899, 6185, 1096, 13, 29177, 11235, 14698, 1771, 333, 29887, 1171, 528, 761, 14321, 310, 13840, 29885, 1974, 2649, 332, 680, 322, 13840, 29885, 1974, 503, 3742, 2649, 332, 680, 306, 29889, 940, 271, 322, 19399, 6782, 13, 3853, 2935, 29892, 476, 29889, 669, 29520, 29892, 435, 29889, 435, 1696, 22333, 29871, 29896, 29929, 29929, 29955, 29892, 512, 29901, 8237, 310, 22121, 11195, 402, 798, 386, 29889, 29871, 29896, 29955, 29929, 29892, 29871, 29896, 29899, 29906, 29892, 282, 29889, 29871, 29896, 29906, 29900, 29899, 29896, 29941, 29906, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 14698, 1771, 333, 29887, 1171, 528, 761, 14321, 310, 13840, 29885, 1974, 2649, 332, 680, 322, 13840, 29885, 1974, 503, 3742, 2649, 332, 680, 1944, 29889, 498, 20772, 295, 6288, 851, 15322, 13, 29177, 11235, 1128, 7255, 18291, 293, 478, 4626, 800, 3382, 5987, 278, 20693, 936, 13291, 310, 1858, 294, 3712, 293, 24992, 25701, 459, 18569, 13, 17565, 2168, 29892, 319, 1696, 15549, 880, 29892, 341, 29889, 669, 2088, 342, 29892, 435, 29889, 390, 1696, 29639, 29871, 29906, 29953, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 319, 9295, 302, 1562, 29889, 29871, 29896, 29896, 29892, 29871, 29929, 29892, 282, 29889, 29871, 29929, 29941, 29953, 29900, 29899, 29929, 29941, 29953, 29929, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 525, 5328, 20602, 756, 3939, 278, 3186, 29915, 13, 29924, 8069, 29892, 323, 29889, 435, 1696, 4756, 29871, 29906, 29900, 29900, 29955, 29892, 512, 29901, 7159, 17896, 8081, 1338, 310, 278, 5298, 310, 11796, 292, 29889, 29871, 29906, 29929, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29945, 29906, 29899, 29953, 29941, 29871, 29896, 29906, 282, 29889, 13, 29177, 11235, 920, 23852, 29892, 2652, 735, 950, 29892, 322, 916, 1757, 1058, 505, 7916, 411, 1757, 297, 7551, 1302, 412, 411, 298, 440, 2562, 29899, 12817, 22884, 943, 13, 23410, 29892, 315, 1696, 4406, 9813, 1111, 29892, 360, 1696, 360, 549, 29892, 399, 1696, 7075, 29892, 341, 29889, 476, 1696, 20268, 262, 29892, 315, 29889, 382, 1696, 12030, 261, 29892, 382, 29889, 350, 1696, 951, 29875, 29892, 402, 1696, 18122, 574, 29892, 379, 1696, 27378, 29892, 349, 29889, 612, 29889, 669, 8229, 404, 335, 29892, 476, 29889, 382, 1696, 26319, 29871, 29896, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 319, 1367, 29903, 13151, 322, 4721, 7316, 29889, 29871, 29941, 29941, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29946, 29953, 29899, 29953, 29896, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 920, 4086, 13750, 13, 29979, 574, 29892, 476, 29889, 476, 1696, 1085, 29871, 29896, 29945, 29871, 29906, 29900, 29896, 29945, 29892, 512, 29901, 11374, 373, 315, 6073, 3527, 29889, 29871, 29946, 29946, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29953, 29946, 29899, 29953, 29953, 29871, 29941, 282, 29889, 13, 29177, 11235, 1128, 17088, 310, 2799, 4080, 14305, 627, 29879, 11095, 5449, 4135, 402, 798, 386, 363, 10432, 29899, 10649, 5086, 20986, 13, 29956, 28940, 280, 29899, 29950, 3028, 1171, 29892, 319, 1696, 7073, 1715, 29892, 365, 1696, 11612, 5863, 29892, 319, 1696, 678, 29976, 13325, 29892, 315, 1696, 7733, 8966, 24448, 29892, 341, 29889, 669, 3436, 1099, 3879, 2122, 29892, 405, 1696, 8378, 29871, 29906, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 4523, 16777, 3002, 13957, 29889, 13, 29177, 11235, 920, 9200, 5365, 290, 267, 9949, 278, 6757, 896, 14117, 277, 13, 29950, 497, 29892, 382, 29889, 476, 1696, 6209, 25603, 29892, 382, 29889, 317, 1696, 350, 631, 29892, 390, 29889, 365, 1696, 15862, 4006, 29892, 341, 29889, 319, 1696, 13760, 29892, 315, 29889, 341, 1696, 26783, 1089, 29892, 435, 29889, 350, 1696, 628, 25906, 601, 29892, 349, 29889, 319, 1696, 24056, 29892, 317, 29889, 382, 1696, 22196, 29892, 382, 29889, 350, 1696, 10920, 29892, 317, 29889, 382, 1696, 365, 2108, 265, 29892, 435, 29889, 323, 1696, 4309, 346, 29891, 29892, 476, 29889, 435, 1696, 18268, 15064, 329, 29892, 360, 1696, 6657, 4089, 484, 29892, 350, 29889, 350, 1696, 25111, 1113, 29892, 435, 29889, 360, 1696, 1102, 326, 295, 29892, 435, 29889, 349, 1696, 17721, 1336, 29892, 341, 29889, 349, 29889, 669, 399, 5442, 5465, 29892, 341, 29889, 360, 1696, 29639, 29871, 29896, 29871, 29906, 29900, 29896, 29947, 29892, 512, 29901, 17677, 20140, 5365, 3002, 29889, 29871, 29941, 29892, 29871, 29929, 29892, 282, 29889, 29871, 29929, 29955, 29955, 29899, 29929, 29947, 29906, 29871, 29953, 282, 29889, 13, 29177, 11235, 920, 2305, 671, 5613, 4086, 304, 2244, 363, 6907, 800, 13, 29968, 574, 29892, 435, 1696, 11790, 2593, 29892, 476, 1696, 678, 574, 29892, 317, 1696, 5250, 14411, 29892, 435, 29889, 319, 1696, 5061, 345, 264, 29892, 365, 29889, 669, 3536, 546, 29892, 383, 29889, 341, 1696, 22333, 29871, 29906, 29955, 29871, 29906, 29900, 29896, 29955, 29892, 3599, 29903, 952, 29871, 29906, 29900, 29896, 29955, 448, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 14614, 29924, 16377, 373, 830, 2055, 1581, 23985, 29889, 7993, 363, 11796, 292, 17197, 262, 708, 29892, 9266, 29892, 282, 29889, 29871, 29906, 29906, 29929, 29899, 29906, 29941, 29955, 29871, 29929, 282, 29889, 313, 4789, 29903, 952, 29871, 29906 ]	1,332,834	2,048	CommonCrawl	17	12
017 - Proceedings of the 11th ACM Conference on Recommender Systems). Understanding how product attributes influence product categorization: Development and validation of fuzzy set-based measures of gradedness in product categories Viswanathan, M. & Childers, T. L., Feb 1999, In: Journal of Marketing Research. 36, 1, p. 75-94 20 p. Understanding How Sustainability Initiatives Fail: A Framework to Aid Design of Effective Interventions Brough, A. R., Donnelly, G. E., Griskevicius, V., Markowitz, E. M., Raimi, K. T., Reeck, C., Trudel, R., Waldman, K. B., Winterich, K. P. & Wolske, K. S., Dec 2020, In: Social Marketing Quarterly. 26, 4, p. 309-324 16 p. Understanding how we talk about space: An examination of the meaning of English spatial prepositions: Cognitive and Computational Perspectives Manning, C., Sera, M. & Pick, H., 2002, Spatial Language: Cognitive and Computational Perspectives. Coventry, K. R. & Oliver, P. (eds.). Dordrecht, NL: Kluwer Academic Publishers, p. 147-164 Understanding human-landscape interactions in the "anthropocene" Harden, C. P., Chin, A., English, M. R., Fu, R., Galvin, K. A., Gerlak, A. K., McDowell, P. F., McNamara, D. E., Peterson, J. M., Poff, N. L., Rosa, E. A., Solecki, W. D. & Wohl, E. E., Jan 2014, In: Environmental management. 53, 1, p. 4-13 10 p. Understanding human motion and gestures for underwater human–robot collaboration Islam, M. J., Ho, M. & Sattar, J., Aug 2019, In: Journal of Field Robotics. 36, 5, p. 851-873 23 p. Understanding Humility and Its Role in Relational Therapy Rowden, T. J., Harris, S. M. & Wickel, K., Sep 2014, In: Contemporary Family Therapy. 36, 3, p. 380-391 12 p. Understanding identity integration: Theoretical, methodological, and applied issues Syed, M. & McLean, K. C., Feb 1 2016, In: Journal of Adolescence. 47, p. 109-118 10 p. Understanding immigrant college students: Applying a developmental ecology framework to the practice of academic advising Stebleton, M. J., 2011, In: NACADA Journal. 31, p. 42-54 Understanding implementation fidelity in a pragmatic randomized clinical trial in the nursing home setting:a mixed-methods examination Palmer, J. A., Parker, V. A., Barre, L. R., Mor, V., Volandes, A. E., Belanger, E., Loomer, L., McCreedy, E. & Mitchell, S. L., Nov 28 2019, In: Trials. 20, 1, 656. Understanding improved lifetime in mixed emissive layer organic light-emitting devices (OLEDs) Bangsund, J. S. & Holmes, R. J., Jan 1 2017, Solid-State Lighting, SSL 2017. OSA - The Optical Society, Vol. Part F72-SSL 2017. Understanding India's forest bureaucracy: a review Fleischman, F., Aug 1 2016, In: Regional Environmental Change. 16, p. 153-165 13 p. Understanding Infidelity Forgiveness	-0.60976	-0.420639	0.625558	0.303445	[ -0.4173205043841363, -0.802199299932788 ]	[ -0.10862184301812468, -0.7326559036045616 ]	[ 0.8715737258255462, 0.37954296690099787 ]	[ 0.4517230462270618, 0.15516683564623296 ]	1,024	[ 512, 512 ]	[ 29900, 29896, 29955, 448, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 14614, 29924, 16377, 373, 830, 2055, 1581, 23985, 467, 13, 29177, 11235, 920, 3234, 8393, 9949, 3234, 11608, 2133, 29901, 14650, 322, 8845, 310, 285, 3365, 1537, 731, 29899, 6707, 15366, 310, 4656, 287, 2264, 297, 3234, 13997, 13, 6116, 11440, 11385, 29892, 341, 29889, 669, 10517, 414, 29892, 323, 29889, 365, 1696, 26319, 29871, 29896, 29929, 29929, 29929, 29892, 512, 29901, 8237, 310, 4485, 15133, 10550, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29955, 29945, 29899, 29929, 29946, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 1128, 317, 504, 475, 3097, 512, 4812, 5056, 29098, 29901, 319, 16657, 304, 319, 333, 12037, 310, 26475, 573, 4124, 794, 1080, 13, 29933, 10573, 29892, 319, 29889, 390, 1696, 360, 3409, 14112, 29892, 402, 29889, 382, 1696, 1632, 19456, 29894, 1654, 375, 29892, 478, 1696, 4485, 340, 2784, 29892, 382, 29889, 341, 1696, 6981, 10233, 29892, 476, 29889, 323, 1696, 830, 29872, 384, 29892, 315, 1696, 1605, 566, 295, 29892, 390, 1696, 17721, 1171, 29892, 476, 29889, 350, 1696, 12267, 436, 29892, 476, 29889, 349, 29889, 669, 399, 3775, 446, 29892, 476, 29889, 317, 1696, 3826, 29871, 29906, 29900, 29906, 29900, 29892, 512, 29901, 10307, 4485, 15133, 751, 4254, 368, 29889, 29871, 29906, 29953, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29941, 29900, 29929, 29899, 29941, 29906, 29946, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 920, 591, 5193, 1048, 2913, 29901, 530, 4392, 3381, 310, 278, 6593, 310, 4223, 18652, 758, 1066, 2187, 29901, 315, 3811, 3321, 322, 11796, 1288, 9034, 1103, 3145, 13, 29924, 9450, 29892, 315, 1696, 317, 1572, 29892, 341, 29889, 669, 23868, 29892, 379, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 1706, 15238, 17088, 29901, 315, 3811, 3321, 322, 11796, 1288, 9034, 1103, 3145, 29889, 25669, 8269, 29892, 476, 29889, 390, 29889, 669, 19731, 29892, 349, 29889, 313, 5779, 6250, 360, 536, 15320, 29892, 405, 29931, 29901, 476, 6092, 556, 16146, 293, 12904, 414, 29892, 282, 29889, 29871, 29896, 29946, 29955, 29899, 29896, 29953, 29946, 13, 29177, 11235, 5199, 29899, 5252, 5738, 22060, 297, 278, 376, 9716, 1336, 542, 1600, 29908, 13, 29950, 7879, 29892, 315, 29889, 349, 1696, 678, 262, 29892, 319, 1696, 4223, 29892, 341, 29889, 390, 1696, 11871, 29892, 390, 1696, 5208, 3845, 29892, 476, 29889, 319, 1696, 5681, 18170, 29892, 319, 29889, 476, 1696, 4052, 29928, 340, 514, 29892, 349, 29889, 383, 1696, 4052, 29940, 314, 2518, 29892, 360, 29889, 382, 1696, 5879, 1330, 29892, 435, 29889, 341, 1696, 349, 2696, 29892, 405, 29889, 365, 1696, 21974, 29892, 382, 29889, 319, 1696, 1105, 280, 22736, 29892, 399, 29889, 360, 29889, 669, 399, 10330, 29892, 382, 29889, 382, 1696, 2627, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 16738, 284, 10643, 29889, 29871, 29945, 29941, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29946, 29899, 29896, 29941, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 5199, 10884, 322, 7737, 1973, 363, 1090, 13405, 5199, 29994, 307, 7451, 24771, 13, 29902, 2536, 314, 29892, 341, 29889, 435, 1696, 8335, 29892, 341, 29889, 669, 317, 1131, 279, 29892, 435, 1696, 22333, 29871, 29906, 29900, 29896, 29929, 29892, 512, 29901, 8237, 310, 8989, 6417, 327, 1199, 29889, 29871, 29941, 29953, 29892, 29871, 29945, 29892, 282, 29889, 29871, 29947, 29945, 29896, 29899, 29947, 29955, 29941, 29871, 29906, 29941, 282, 29889, 13, 29177, 11235, 13863, 1793, 322, 8011, 1528, 280, 297, 6376, 1288, 25451, 27580, 13, 4301, 1145, 29892, 323, 29889, 435, 1696, 20349, 29892, 317, 29889, 341, 29889, 669, 399, 860, 295, 29892, 476, 1696, 29639, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 27183, 653, 14662, 25451, 27580, 29889, 29871, 29941, 29953, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29941, 29947, 29900, 29899, 29941, 29929, 29896, 29871, 29896, 29906, 282, 29889, 13, 29177, 11235, 10110, 13465, 29901, 450, 12116, 936, 29892, 1158, 5996, 29892, 322, 7436, 5626, 13, 29903, 28133, 29892, 341, 29889, 669, 4052, 3226, 273, 29892, 476, 29889, 315, 1696, 26319, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 8237, 310, 2087, 6544, 29883, 663, 29889, 29871, 29946, 29955, 29892, 282, 29889, 29871, 29896, 29900, 29929, 29899, 29896, 29896, 29947, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 5198, 4481, 424, 12755, 8041, 29901, 2401, 5890, 263, 5849, 284, 321, 1054, 6933, 6890, 304, 278, 6944, 310, 21567, 25228, 292, 13, 7789, 569, 880, 29892, 341, 29889, 435, 1696, 29871, 29906, 29900, 29896, 29896, 29892, 512, 29901, 405, 2477, 3035, 29909, 8237, 29889, 29871, 29941, 29896, 29892, 282, 29889, 29871, 29946, 29906, 29899, 29945, 29946, 13, 29177, 11235, 5314, 285, 10652, 537, 297, 263, 282, 1431, 29885, 2454, 4036, 1891, 24899, 936, 14260, 297, 278, 302, 1295, 292, 3271, 4444, 29901, 29874, 12849, 29899, 23515, 4392, 3381, 13, 18210, 1050, 29892, 435, 29889, 319, 1696, 24239, 29892, 478, 29889, 319, 1696, 2261, 276, 29892, 365, 29889, 390, 1696, 3879, 29892, 478, 1696, 3684, 392, 267, 29892, 319, 29889, 382, 1696, 3741, 4600, 29892, 382, 1696, 4309, 12392, 29892, 365, 1696, 4052, 9832, 7584, 29892, 382, 29889, 669, 26676, 29892, 317, 29889, 365, 1696, 2864, 29871, 29906, 29947, 29871, 29906, 29900, 29896, 29929, 29892, 512, 29901, 8602, 1338, 29889, 29871, 29906, 29900, 29892, 29871, 29896, 29892, 29871, 29953, 29945, 29953, 29889, 13, 29177, 11235, 16710, 25423, 297, 12849, 953, 790, 573, 7546, 2894, 293, 3578, 29899, 331, 5367, 9224, 313, 29949, 20566, 29879, 29897, 13, 29933, 25128, 870, 29892, 435, 29889, 317, 29889, 669, 4168, 4467, 29892, 390, 29889, 435, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 4956, 333, 29899, 2792, 12790, 292, 29892, 17122, 29871, 29906, 29900, 29896, 29955, 29889, 6570, 29909, 448, 450, 20693, 936, 7765, 29892, 3684, 29889, 3455, 383, 29955, 29906, 29899, 18641, 29871, 29906, 29900, 29896, 29955, 29889, 13, 29177, 11235, 7513, 29915, 29879, 13569, 289, 13411, 29883, 10068, 29901, 263, 9076, 13, 29943, 280, 783, 1171, 29892, 383, 1696, 22333, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 16208, 16738, 284, 10726, 29889, 29871, 29896, 29953, 29892, 282, 29889, 29871, 29896, 29945, 29941, 29899, 29896, 29953, 29945, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 9969, 10652, 537, 383, 990, 20193 ]	1,332,834	3,072	CommonCrawl	17	12
Hidden Away – Part 2 Posted: February 21, 2016 in Book I Terror in Texas They drove deserted vehicles and abandoned stores. They passed a cluster of buildings in the distance but no one seemed to want to explore it. When Zack pointed toward the ranch, Steve frowned. "Too close to the road. Too many abandoned vehicles. There could be infected around." The pickup weaved around yet another abandoned vehicle while the light quickly began to fade as the sun dipped below the rim of a distant tree-covered ridge. A glimmer of light flashed against glass in the distance and they saw a small cabin on a high ridge. They neared a gravel road that turned to the right and disappeared into the trees. Zack stopped the truck. "Well, what do you think?" "It would be off the beaten path, for sure." Steve answered. "Let's try it." They turned onto the gravel road heading up trees. The path climbed the side of a hill. The further they drove, the steeper the slope at the side of the road and the narrower the path grew. Della sat up in the seat and whispered to Steve. "Are you sure about this?" "No but there's no place to turn around right, now." Steve answered. "Keep going, Zack." They drove another mile over deep ruts and washes then the path widened at a cattle pen and shed. Zack eased the truck to a stop. "What now? It looks like the wrong road." "No. I see the cabin through those trees. I think the road loops around the shed. Wait here." He stepped out of the truck and followed the path to the back of the shed. He disappeared for a few moments then came back to announce. "We're still going in the right direction. I can see a cabin. It looks pretty narrow ahead, but if we get beyond there the cabin is right ahead. Let me check it out." Steve retraced the narrow path to the back of the shed and then around a stand of trees. Ahead he could see the hunting cabin. It was a narrow trail that looked to be used by four wheeled ATVs in the past, but nothing recently. He limped farther down the track and saw an open yard in front of the cabin. He made his way back to the truck and climbed inside. On the way back he rolled half a dozen large rocks to the side of the trail. Steve limped back to the truck and announced. "It's doable." He climbed in the truck. "Around the back of the shed, head up the trail." Zack did as directed. When he pulled around the shed, he slammed on the breaks. "That's not wide enough!" He stared at the narrow trail with the rough drop off to the left and the steep rise of dirt and brush o the right. "I can't do this. We'll go over." Steve placed his hand on Zack's shoulder. "You can do this. Just keep your left tire on the trail. The slope on the inside is gentle enough that you can drive on it. It'll tilt the truck, but the tires are big enough to climb over a few rocks at the side of the road. The trail is wider around just beyond there." "You can do this Zack." Della echoed. Zack chuckled nervously. "Okay, at least ya'll get out, just in case." "Good idea. Della, you four get out. I'll ride with Zack." Stave answered. "We'll pick you up on the other side." The three women and child stepped out of the truck and waited as the vehicle pulled ahead. They watched as the massive vehicle rolled toward the narrowing of the trail. Zack shifted into low gear and the sound of the engine growled. The tires rolled forward with Steve urging Zack to guide the truck toward the upper slope. Zack turned the steering wheel to the right. The front tire climbed up the incline while the left tires rolled along-side the drop-off at the side of the trek. Zack's brow glistened with perspiration. "Am I good?" He asked. "I can't see the road." "You're doing fine." Steve leaned out the window judging the distance. "To the right. More to the right. The tire can roll up the rocks at the side. Slow and	0.290802	-0.3038	-0.096002	-0.795715	[ 0.24971142953826003, 0.33189195527818566 ]	[ 0.06954570082219232, -0.6771464175839603 ]	[ -0.18603878175969413, -0.005965668957411016 ]	[ -0.6019944980571221, -0.9894360823850361 ]	1,024	[ 512, 512 ]	[ 379, 4215, 319, 1582, 785, 3455, 29871, 29906, 13, 6747, 287, 29901, 6339, 29871, 29906, 29896, 29892, 29871, 29906, 29900, 29896, 29953, 297, 6726, 306, 323, 2704, 297, 10319, 13, 15597, 26603, 18197, 287, 24413, 322, 23181, 14422, 29889, 2688, 4502, 263, 9867, 310, 13814, 297, 278, 5418, 541, 694, 697, 6140, 304, 864, 304, 26987, 372, 29889, 1932, 796, 547, 11520, 11183, 278, 6350, 305, 29892, 13981, 285, 4708, 287, 29889, 376, 1762, 29877, 3802, 304, 278, 6520, 29889, 1763, 29877, 1784, 23181, 24413, 29889, 1670, 1033, 367, 3041, 26458, 2820, 1213, 13, 1576, 5839, 786, 591, 10511, 2820, 3447, 1790, 23181, 19716, 1550, 278, 3578, 9098, 4689, 304, 28747, 408, 278, 6575, 652, 2986, 2400, 278, 12726, 310, 263, 21188, 5447, 29899, 11911, 287, 364, 5525, 29889, 319, 330, 2576, 1050, 310, 3578, 11013, 287, 2750, 12917, 297, 278, 5418, 322, 896, 4446, 263, 2319, 28830, 373, 263, 1880, 364, 5525, 29889, 2688, 452, 1965, 263, 2646, 955, 6520, 393, 6077, 304, 278, 1492, 322, 24273, 964, 278, 10697, 29889, 13, 29999, 547, 11084, 278, 534, 2707, 29889, 376, 11284, 29892, 825, 437, 366, 1348, 3026, 13, 29908, 3112, 723, 367, 1283, 278, 367, 2579, 2224, 29892, 363, 1854, 1213, 13981, 7699, 29889, 376, 12024, 29915, 29879, 1018, 372, 1213, 13, 15597, 6077, 11480, 278, 2646, 955, 6520, 28435, 701, 10697, 29889, 450, 2224, 10784, 2580, 278, 2625, 310, 263, 17306, 29889, 450, 4340, 896, 26603, 29892, 278, 1886, 11356, 278, 24968, 472, 278, 2625, 310, 278, 6520, 322, 278, 17655, 307, 556, 278, 2224, 13631, 29889, 13, 29928, 3547, 3290, 701, 297, 278, 12949, 322, 21039, 287, 304, 13981, 29889, 376, 17506, 366, 1854, 1048, 445, 3026, 13, 29908, 3782, 541, 727, 29915, 29879, 694, 2058, 304, 2507, 2820, 1492, 29892, 1286, 1213, 13981, 7699, 29889, 376, 9598, 1022, 2675, 29892, 796, 547, 1213, 13, 15597, 26603, 1790, 17967, 975, 6483, 364, 8842, 322, 471, 13244, 769, 278, 2224, 281, 3615, 287, 472, 263, 27498, 6584, 322, 28453, 29889, 13, 29999, 547, 321, 1463, 278, 534, 2707, 304, 263, 5040, 29889, 376, 5618, 1286, 29973, 739, 3430, 763, 278, 2743, 6520, 1213, 13, 29908, 3782, 29889, 306, 1074, 278, 28830, 1549, 1906, 10697, 29889, 306, 1348, 278, 6520, 12104, 2820, 278, 28453, 29889, 20340, 1244, 1213, 940, 28996, 714, 310, 278, 534, 2707, 322, 5643, 278, 2224, 304, 278, 1250, 310, 278, 28453, 29889, 940, 24273, 363, 263, 2846, 19462, 769, 2996, 1250, 304, 7475, 346, 29889, 376, 4806, 29915, 276, 1603, 2675, 297, 278, 1492, 5305, 29889, 306, 508, 1074, 263, 28830, 29889, 739, 3430, 5051, 12474, 14432, 29892, 541, 565, 591, 679, 8724, 727, 278, 28830, 338, 1492, 14432, 29889, 2803, 592, 1423, 372, 714, 1213, 13, 7789, 345, 3240, 945, 287, 278, 12474, 2224, 304, 278, 1250, 310, 278, 28453, 322, 769, 2820, 263, 2317, 310, 10697, 29889, 319, 2813, 540, 1033, 1074, 278, 29826, 28830, 29889, 739, 471, 263, 12474, 26203, 393, 5148, 304, 367, 1304, 491, 3023, 21266, 29872, 839, 319, 8050, 29879, 297, 278, 4940, 29892, 541, 3078, 10325, 29889, 940, 2485, 9795, 26645, 1623, 278, 5702, 322, 4446, 385, 1722, 29413, 297, 4565, 310, 278, 28830, 29889, 940, 1754, 670, 982, 1250, 304, 278, 534, 2707, 322, 10784, 2580, 2768, 29889, 1551, 278, 982, 1250, 540, 29081, 4203, 263, 24231, 2919, 23150, 304, 278, 2625, 310, 278, 26203, 29889, 13, 7789, 345, 2485, 9795, 1250, 304, 278, 534, 2707, 322, 9326, 29889, 376, 3112, 29915, 29879, 437, 519, 1213, 940, 10784, 2580, 297, 278, 534, 2707, 29889, 376, 1433, 618, 278, 1250, 310, 278, 28453, 29892, 2343, 701, 278, 26203, 1213, 13, 29999, 547, 1258, 408, 10624, 29889, 1932, 540, 20043, 2820, 278, 28453, 29892, 540, 2243, 28913, 373, 278, 16706, 29889, 376, 7058, 29915, 29879, 451, 9377, 3307, 3850, 940, 380, 1965, 472, 278, 12474, 26203, 411, 278, 12164, 5768, 1283, 304, 278, 2175, 322, 278, 1886, 1022, 14451, 310, 270, 2728, 322, 1506, 1878, 288, 278, 1492, 29889, 376, 29902, 508, 29915, 29873, 437, 445, 29889, 1334, 29915, 645, 748, 975, 1213, 13, 7789, 345, 7180, 670, 1361, 373, 796, 547, 29915, 29879, 23468, 29889, 376, 3492, 508, 437, 445, 29889, 3387, 3013, 596, 2175, 260, 533, 373, 278, 26203, 29889, 450, 24968, 373, 278, 2768, 338, 9914, 3307, 393, 366, 508, 7899, 373, 372, 29889, 739, 29915, 645, 260, 2782, 278, 534, 2707, 29892, 541, 278, 260, 2658, 526, 4802, 3307, 304, 10784, 29890, 975, 263, 2846, 23150, 472, 278, 2625, 310, 278, 6520, 29889, 450, 26203, 338, 25734, 2820, 925, 8724, 727, 1213, 13, 29908, 3492, 508, 437, 445, 796, 547, 1213, 360, 3547, 2916, 287, 29889, 13, 29999, 547, 521, 2707, 839, 23547, 5794, 29889, 376, 20434, 388, 29892, 472, 3203, 9343, 29915, 645, 679, 714, 29892, 925, 297, 1206, 1213, 13, 29908, 18420, 2969, 29889, 360, 3547, 29892, 366, 3023, 679, 714, 29889, 306, 29915, 645, 22203, 411, 796, 547, 1213, 624, 1351, 7699, 29889, 376, 4806, 29915, 645, 5839, 366, 701, 373, 278, 916, 2625, 1213, 13, 1576, 2211, 5866, 322, 2278, 28996, 714, 310, 278, 534, 2707, 322, 25993, 408, 278, 19716, 20043, 14432, 29889, 2688, 20654, 408, 278, 20364, 19716, 29081, 11183, 278, 12474, 292, 310, 278, 26203, 29889, 796, 547, 9500, 287, 964, 4482, 330, 799, 322, 278, 6047, 310, 278, 6012, 6548, 839, 29889, 13, 1576, 260, 2658, 29081, 6375, 411, 13981, 5065, 3460, 796, 547, 304, 10754, 278, 534, 2707, 11183, 278, 7568, 24968, 29889, 796, 547, 6077, 278, 1886, 3241, 18875, 304, 278, 1492, 29889, 450, 4565, 260, 533, 10784, 2580, 701, 278, 1343, 457, 1550, 278, 2175, 260, 2658, 29081, 3412, 29899, 2975, 278, 5768, 29899, 2696, 472, 278, 2625, 310, 278, 2578, 29895, 29889, 796, 547, 29915, 29879, 3347, 330, 1761, 6419, 411, 3736, 29886, 12232, 29889, 13, 29908, 6833, 306, 1781, 3026, 940, 4433, 29889, 376, 29902, 508, 29915, 29873, 1074, 278, 6520, 1213, 13, 29908, 3492, 29915, 276, 2599, 2691, 1213, 13981, 20793, 287, 714, 278, 3474, 6577, 3460, 278, 5418, 29889, 376, 1762, 278, 1492, 29889, 5853, 304, 278, 1492, 29889, 450, 260, 533, 508, 9679, 701, 278, 23150, 472, 278, 2625, 29889, 317, 677, 322 ]	1,332,837	0	CommonCrawl	10	8
What is Fiscal Sponsorship? Fiscal Agency allows an organization without tax-exempt status to receive funds via an established nonprofit with 501[3] tax-exempt status. This is a great first step in fundraising. The historic water tower was originally consigned by the City of Brainerd's Water and Light Commission. It was constructed between 1919 & 1920; it is said to be the first ever poured in place concrete for municipal water storage in the United States. Over the past 100 years the tower has had its share of wear and tear. Efforts to maintain it have come to a pivotal point which is where the City of Brainerd's Citizens Historic Water Tower Committee began.The committee has spearheaded this enormous effort with the simple goal of preserving the heart of our community. To be a success we ask for any and all help from people just like you to save part of our rich collective history in the great state of Minnesota. You can follow the journey through their Facebook page and website at BrainerdWaterTower.com Have you ever wanted a fun, affordable and safe water experience for the whole family, without the added stress of watching multiple children at the lake or water park? The Brainerd Splash Pad project is all about family fun, in a safe environment with no risk of drowning. Together with Brainerd Community Action, Brainerd Splash Pad are gathering sponsorships representing Brainerd Lakes Area families and businesses. With YOUR help not only will they be providing an AWESOME addition to our green space, but you will also get to see your name on the pad for years to come! Please consider a donation today so we make a SPLASH in the BLA! 💦 Visit their website for more information www.brainerdsplashpad.com Crow Wing County Beyond the Yellow Ribbon Community (CWCBTYRC) is a volunteer organization that aims to continue Minnesota's proud history of supporting our nation's military. CWCBTYRC is a diverse group of citizens and community leaders uniting key areas within our communities to leverage existing support activities, build awareness and take action to recognize and support Service members, Veterans, military families and employers. For more information please email [email protected] Tummies is a collaboration between, The Baxter Cafe, The Raboin & Francis Law Firm, Pan-O-Gold Bakeries and Hubbard Radio. The program provides free kids' meals on weekends for hungry children in the Brainerd Lakes Area. The Brainerd Outreach Program also distributes family meal packets through this program. During the last two months, a number of other local businesses have volunteered to partner with Full Tummies to donate items families with children might find useful during these trying times. Brainerd Community Action has acted as their fiscal agent making donations to Full Tummies possible. Let's make sure no child goes hungry! Friends of the BLA Treatment Courts is made up of three Treatment Courts, Aitkin County Sobriety Court, Crow Wing County DWI Court, and Crow Wing County Drug Court, have been proud partners with Brainerd Community Action for the past 6 years. The Treatment Courts are grant funded, and work with high risk/high needs alcohol and drug offenders that are Aitkin and Crow Wing County residence. Their focus is to enhance public safety by increasing the supervision of the offenders, reducing recidivism rates and increasing the success of treatment. We work together to provide a safe and healthy community. Crow Wing Crow Wing Food Co-op is a cooperatively owned grocery store dedicated to sustaining a healthy and thriving community. Founded in 1979, Crow Wing Food Co-op is a trusted local source for natural, organic, local, and allergen-friendly foods. Crow Wing Food Co-op is owned and overseen by its member-owners; membership is open to everyone, and anyone can shop no matter if you're a member. Learn more at www.crowwingcoop.com. Since 2015, Brainerd Riverfront has been a city advisory committee advocating for equitable access to the Mississippi River through parks, overlooks, and trails. Over the past five years their 10 member community has worked with stakeholders including Central Lakes College, Brainerd YMCA and many others to	0.212045	0.384696	0.562152	-1.032359	[ 0.2853229906922278, 0.13876771978936042 ]	[ 0.3811150739700834, 0.3882775882953222 ]	[ 0.5773697668809709, 0.5469348745763597 ]	[ -1.0466662282865995, -1.0180511553358178 ]	1,024	[ 512, 512 ]	[ 1724, 338, 383, 275, 1052, 1706, 787, 272, 3527, 29973, 13, 29943, 275, 1052, 29353, 6511, 385, 13013, 1728, 8818, 29899, 735, 3456, 4660, 304, 7150, 29199, 3025, 385, 7841, 1661, 771, 9202, 411, 29871, 29945, 29900, 29896, 29961, 29941, 29962, 8818, 29899, 735, 3456, 4660, 29889, 910, 338, 263, 2107, 937, 4331, 297, 5220, 336, 5921, 29889, 13, 1576, 22879, 4094, 19372, 471, 10437, 1136, 12961, 491, 278, 4412, 310, 5032, 262, 2018, 29915, 29879, 13062, 322, 12790, 11444, 29889, 739, 471, 13319, 1546, 29871, 29896, 29929, 29896, 29929, 669, 29871, 29896, 29929, 29906, 29900, 29936, 372, 338, 1497, 304, 367, 278, 937, 3926, 7446, 1127, 297, 2058, 18387, 363, 11677, 4094, 8635, 297, 278, 3303, 3900, 29889, 6811, 278, 4940, 29871, 29896, 29900, 29900, 2440, 278, 19372, 756, 750, 967, 6232, 310, 19531, 322, 734, 279, 29889, 382, 600, 441, 29879, 304, 7344, 372, 505, 2041, 304, 263, 282, 440, 7288, 1298, 607, 338, 988, 278, 4412, 310, 5032, 262, 2018, 29915, 29879, 21353, 466, 575, 17939, 13062, 23615, 12930, 4689, 29889, 1576, 21118, 756, 961, 279, 2813, 287, 445, 18886, 681, 7225, 411, 278, 2560, 7306, 310, 2225, 29530, 278, 5192, 310, 1749, 7881, 29889, 1763, 367, 263, 2551, 591, 2244, 363, 738, 322, 599, 1371, 515, 2305, 925, 763, 366, 304, 4078, 760, 310, 1749, 8261, 6314, 573, 4955, 297, 278, 2107, 2106, 310, 20994, 29889, 887, 508, 1101, 278, 16342, 1549, 1009, 13327, 1813, 322, 4700, 472, 5032, 262, 2018, 29956, 1008, 29911, 1680, 29889, 510, 13, 25559, 366, 3926, 5131, 263, 2090, 29892, 21750, 519, 322, 9109, 4094, 7271, 363, 278, 3353, 3942, 29892, 1728, 278, 2715, 22884, 310, 21217, 2999, 4344, 472, 278, 19437, 470, 4094, 14089, 29973, 450, 5032, 262, 2018, 317, 572, 1161, 18011, 2060, 338, 599, 1048, 3942, 2090, 29892, 297, 263, 9109, 5177, 411, 694, 12045, 310, 270, 798, 1076, 29889, 323, 12966, 411, 5032, 262, 2018, 19184, 9123, 29892, 5032, 262, 2018, 317, 572, 1161, 18011, 526, 11705, 292, 21955, 272, 9981, 15783, 5032, 262, 2018, 365, 6926, 18320, 13175, 322, 5381, 267, 29889, 2973, 612, 22970, 1371, 451, 871, 674, 896, 367, 13138, 385, 319, 29956, 2890, 29949, 2303, 6124, 304, 1749, 7933, 2913, 29892, 541, 366, 674, 884, 679, 304, 1074, 596, 1024, 373, 278, 17132, 363, 2440, 304, 2041, 29991, 3529, 2050, 263, 1016, 362, 9826, 577, 591, 1207, 263, 317, 7390, 24943, 297, 278, 350, 4375, 29991, 29871, 243, 162, 149, 169, 5741, 277, 1009, 4700, 363, 901, 2472, 7821, 29889, 2634, 262, 2018, 23579, 1161, 8305, 29889, 510, 13, 29907, 798, 27792, 5127, 18502, 898, 278, 612, 4743, 27461, 6718, 19184, 313, 29907, 29956, 21685, 15631, 10363, 29897, 338, 263, 27886, 261, 13013, 393, 263, 9893, 304, 6773, 20994, 29915, 29879, 22314, 4955, 310, 20382, 1749, 5233, 29915, 29879, 9121, 29889, 315, 29956, 21685, 15631, 10363, 338, 263, 16984, 2318, 310, 18363, 322, 7881, 20251, 5190, 292, 1820, 10161, 2629, 1749, 23507, 304, 454, 19698, 5923, 2304, 14188, 29892, 2048, 3773, 8326, 404, 322, 2125, 3158, 304, 18720, 322, 2304, 6692, 5144, 29892, 478, 1308, 550, 29892, 9121, 13175, 322, 5703, 414, 29889, 1152, 901, 2472, 3113, 4876, 518, 5269, 6364, 29962, 13, 29911, 23824, 583, 338, 263, 24771, 1546, 29892, 450, 350, 1165, 357, 9243, 1725, 29892, 450, 16155, 28230, 669, 5845, 7927, 383, 3568, 29892, 6518, 29899, 29949, 29899, 29954, 1025, 22652, 583, 322, 14533, 29890, 538, 9204, 29889, 450, 1824, 8128, 3889, 413, 4841, 29915, 592, 1338, 373, 4723, 1975, 363, 9074, 14793, 4344, 297, 278, 5032, 262, 2018, 365, 6926, 18320, 29889, 450, 5032, 262, 2018, 4451, 276, 496, 7835, 884, 1320, 5026, 3942, 592, 284, 23912, 1549, 445, 1824, 29889, 7133, 278, 1833, 1023, 7378, 29892, 263, 1353, 310, 916, 1887, 5381, 267, 505, 27886, 14561, 304, 18096, 411, 14846, 323, 23824, 583, 304, 1016, 403, 4452, 13175, 411, 4344, 1795, 1284, 5407, 2645, 1438, 1811, 3064, 29889, 5032, 262, 2018, 19184, 9123, 756, 27320, 408, 1009, 16436, 1052, 10823, 3907, 1016, 800, 304, 14846, 323, 23824, 583, 1950, 29889, 2803, 29915, 29879, 1207, 1854, 694, 2278, 5771, 9074, 14793, 29991, 13, 27034, 1975, 310, 278, 350, 4375, 6479, 271, 358, 6325, 1372, 338, 1754, 701, 310, 2211, 6479, 271, 358, 6325, 1372, 29892, 319, 277, 9089, 5127, 25147, 374, 3305, 9245, 29892, 29445, 27792, 5127, 360, 22119, 9245, 29892, 322, 29445, 27792, 5127, 360, 11124, 9245, 29892, 505, 1063, 22314, 22056, 411, 5032, 262, 2018, 19184, 9123, 363, 278, 4940, 29871, 29953, 2440, 29889, 450, 6479, 271, 358, 6325, 1372, 526, 16690, 5220, 287, 29892, 322, 664, 411, 1880, 12045, 29914, 9812, 4225, 27231, 5391, 322, 15721, 1283, 21043, 393, 526, 319, 277, 9089, 322, 29445, 27792, 5127, 25488, 29889, 11275, 8569, 338, 304, 26371, 749, 970, 15332, 491, 10231, 278, 2428, 4924, 310, 278, 1283, 21043, 29892, 27668, 1162, 333, 440, 1608, 19257, 322, 10231, 278, 2551, 310, 14502, 29889, 1334, 664, 4208, 304, 3867, 263, 9109, 322, 9045, 29891, 7881, 29889, 13, 29907, 798, 27792, 29445, 27792, 25453, 3189, 29899, 459, 338, 263, 1302, 3372, 6703, 15205, 4071, 29883, 708, 3787, 16955, 304, 15075, 17225, 263, 9045, 29891, 322, 266, 1150, 292, 7881, 29889, 383, 7261, 297, 29871, 29896, 29929, 29955, 29929, 29892, 29445, 27792, 25453, 3189, 29899, 459, 338, 263, 9311, 287, 1887, 2752, 363, 5613, 29892, 2894, 293, 29892, 1887, 29892, 322, 16454, 1885, 29899, 18326, 368, 9687, 29879, 29889, 29445, 27792, 25453, 3189, 29899, 459, 338, 15205, 322, 975, 28026, 491, 967, 4509, 29899, 776, 414, 29936, 28512, 338, 1722, 304, 14332, 29892, 322, 5019, 508, 18296, 694, 4383, 565, 366, 29915, 276, 263, 4509, 29889, 19530, 29876, 901, 472, 7821, 29889, 29883, 798, 16958, 1111, 459, 29889, 510, 29889, 13, 23036, 29871, 29906, 29900, 29896, 29945, 29892, 5032, 262, 2018, 6163, 8862, 756, 1063, 263, 4272, 25228, 706, 21118, 22545, 1218, 363, 1592, 8270, 2130, 304, 278, 24743, 6163, 1549, 610, 2039, 29892, 975, 6914, 29879, 29892, 322, 1020, 2719, 29889, 6811, 278, 4940, 5320, 2440, 1009, 29871, 29896, 29900, 4509, 7881, 756, 3796, 411, 380, 1296, 8948, 414, 3704, 8068, 365, 6926, 6346, 29892, 5032, 262, 2018, 612, 29924, 5454, 322, 1784, 4045, 304 ]	1,332,838	0	CommonCrawl	1	6
DeMar: "It's Not Who Homosexuals Are … It's What They Do that Matters" Apr 16, 2019 American Vision, Gary DeMar, Hate groups Beyond all of that, the ultra-religious treat LGBTQ people as those who have made very bad choices. We are not just evil. We are presumed to have terrible judgment. Gary DeMar – American Vision via Southern Poverty Law Center Hate group leader Gary DeMar (American Vision) stopped targeting LGBT people for some time. Perhaps he was trying to get off the list compiled by the Southern Poverty Law Center which he admitted negatively affected institutional donations. Perhaps he no longer cares because he has reverted to form. Predictable certainty: There's a great deal of sloppy thinking going on about human sexuality. Many Christians have capitulated on the topic of same-sex sexuality. They've given into the premise that God's Word does not disapprove of such relationships. Students at some Christian colleges are the worst offenders. Students and alumni at Taylor University, a Christian College in Upland, Indiana, are denouncing the decision to have Vice President Mike Pence deliver this year's Commencement because of his opposition to same-sex sexuality. For the record, Taylor University is on Campus Pride's Shame List because of its Title IX exemption which permits the school to discriminate without losing federal student aid. Pence will be the commencement speaker. Some anti-Darwin rhetoric while he is at it: Sex is a good thing. It was created by God. It didn't evolve, and if it did, then any type of sex is OK, even rape. According to evolutionists, human beings, homo sapiens (wise man) to use the scientific vernacular, are evolved animals. Animals passed on their genes via rape and stopped genetic inferiors through "murder." Human primacy developed because of religious devotion. After all, they argued, only a human being has an immortal soul. Darwin and modern science changed all of that with the evolution continuum. Human beings have primacy because they are the most intelligent of animals. We also possess a level of emotional intelligence that does not exist in animals. I agree with DeMar that sex is, indeed, a good thing. Not only does it produce offspring but it feels great. Sex defines morality: People who engage in same-sex behavior must decide what side of the moral wall they are on. If they decide to abandon God, then homosexuality is just something evolved bags of meat and bones with an evolved monkey brain do. We do not have to make that decision. Gary DeMar has saved us the trouble of doing so. Note the absence of the phrase "gay people." They do not exist in DeMar's world. They are substituted with people who have gay sex. Otherwise, Mr. DeMar is in the uncomfortable position of having to explain why some people have a different sexual orientation than most people. If you believe in an omnipotent god then the continuum -of sexual orientation is god-given. It follows that we are sexual beings with sexual desires that we are compelled to act on. Why would the deity make people only to frustrate their sexual longings? Therefore, DeMar and others of similar mind are obligated to dispense with the entire concept of sexual orientation. Our sexuality is not defined by intersecting points of gender and orientation continua. Oh no. Out of convenience our sexuality is defined by the kind of sex that we engage in which, in turn, defines us. The entire narrative is intellectually dishonest at the outset because it seeks to redefine reality to suit the dogma of a belief system. Most assuredly morality is not defined by the kind of sex that we engage in. DeMar continues with the idea that if gay sex is acceptable then there are no guardrails: There is no right or wrong about anything. No hate crimes. No murder. No theft. No rape. No adultery. No prohibition against sex with children of any age. The above is ludicrous. Sex (gay and straight), for example, is only acceptable when the participants are consenting adults. DeMar is manufacturing a condition that does not exist. Our civil society can accept homosexuality while, at the same time, condem	-0.306783	-0.467195	-0.491656	0.155167	[ -0.47621654783108297, -0.13735028622535844 ]	[ -0.11936561450598299, -0.8150248183448087 ]	[ -0.4637571740392716, -0.5195544765977255 ]	[ 0.11874765189069258, 0.19158601940177333 ]	1,024	[ 512, 512 ]	[ 897, 7083, 29901, 376, 3112, 29915, 29879, 2216, 11644, 15089, 29438, 27101, 4683, 16088, 739, 29915, 29879, 1724, 2688, 1938, 393, 5345, 2153, 29908, 13, 29909, 558, 29871, 29896, 29953, 29892, 29871, 29906, 29900, 29896, 29929, 3082, 478, 2459, 29892, 23529, 897, 7083, 29892, 379, 403, 6471, 13, 29933, 1032, 898, 599, 310, 393, 29892, 278, 8494, 336, 29899, 2674, 335, 2738, 7539, 365, 7210, 29911, 29984, 2305, 408, 1906, 1058, 505, 1754, 1407, 4319, 19995, 29889, 1334, 526, 451, 925, 16126, 29889, 1334, 526, 2225, 21571, 304, 505, 16403, 24284, 29889, 13, 29954, 653, 897, 7083, 785, 3082, 478, 2459, 13, 6071, 14234, 349, 957, 1017, 7927, 7817, 13, 29950, 403, 2318, 11822, 23529, 897, 7083, 313, 14689, 478, 2459, 29897, 11084, 3646, 292, 365, 7210, 29911, 2305, 363, 777, 931, 29889, 11637, 540, 471, 1811, 304, 679, 1283, 278, 1051, 13126, 491, 278, 14234, 349, 957, 1017, 7927, 7817, 607, 540, 20186, 3480, 6703, 15201, 12666, 284, 1016, 800, 29889, 11637, 540, 694, 5520, 1559, 267, 1363, 540, 756, 29538, 287, 304, 883, 29889, 13, 23084, 919, 519, 3058, 1017, 29901, 13, 8439, 29915, 29879, 263, 2107, 5376, 310, 14216, 23717, 7291, 2675, 373, 1048, 5199, 18287, 537, 29889, 9267, 27353, 505, 11934, 7964, 373, 278, 11261, 310, 1021, 29899, 14167, 18287, 537, 29889, 2688, 29915, 345, 2183, 964, 278, 5188, 895, 393, 4177, 29915, 29879, 10803, 947, 451, 8796, 307, 345, 310, 1316, 21702, 29889, 5088, 1237, 472, 777, 6111, 18400, 267, 526, 278, 17322, 1283, 21043, 29889, 5088, 1237, 322, 394, 1227, 29875, 472, 12537, 3014, 29892, 263, 6111, 6346, 297, 501, 572, 392, 29892, 21817, 29892, 526, 972, 1309, 3277, 278, 10608, 304, 505, 21400, 7178, 12828, 349, 663, 12021, 445, 1629, 29915, 29879, 422, 1527, 13561, 1363, 310, 670, 19626, 304, 1021, 29899, 14167, 18287, 537, 29889, 13, 2831, 278, 2407, 29892, 12537, 3014, 338, 373, 7259, 375, 349, 2426, 29915, 29879, 1383, 420, 2391, 1363, 310, 967, 18527, 16841, 11875, 683, 607, 3635, 1169, 278, 3762, 304, 2313, 5632, 16976, 1728, 19035, 17097, 8368, 16226, 29889, 349, 663, 674, 367, 278, 844, 3977, 882, 25657, 29889, 13, 9526, 9418, 29899, 29928, 279, 5080, 364, 9188, 272, 293, 1550, 540, 338, 472, 372, 29901, 13, 29903, 735, 338, 263, 1781, 2655, 29889, 739, 471, 2825, 491, 4177, 29889, 739, 3282, 29915, 29873, 15220, 345, 29892, 322, 565, 372, 1258, 29892, 769, 738, 1134, 310, 7916, 338, 9280, 29892, 1584, 1153, 412, 29889, 7579, 304, 14675, 2879, 29892, 5199, 367, 886, 29892, 3632, 29877, 269, 2754, 575, 313, 3538, 767, 29897, 304, 671, 278, 16021, 24604, 562, 1070, 29892, 526, 15220, 1490, 15006, 29889, 24980, 1338, 4502, 373, 1009, 2531, 267, 3025, 1153, 412, 322, 11084, 2531, 7492, 10115, 18930, 1549, 376, 29885, 332, 672, 1213, 13, 29950, 7889, 1903, 4135, 8906, 1363, 310, 12962, 2906, 8194, 29889, 2860, 599, 29892, 896, 28705, 29892, 871, 263, 5199, 1641, 756, 385, 5198, 441, 284, 10752, 29889, 7335, 5080, 322, 5400, 10466, 3939, 599, 310, 393, 411, 278, 14675, 3133, 398, 29889, 12968, 367, 886, 505, 1903, 4135, 1363, 896, 526, 278, 1556, 13052, 296, 310, 15006, 29889, 1334, 884, 22592, 263, 3233, 310, 23023, 1848, 21082, 393, 947, 451, 1863, 297, 15006, 29889, 306, 8661, 411, 897, 7083, 393, 7916, 338, 29892, 6200, 29892, 263, 1781, 2655, 29889, 2216, 871, 947, 372, 7738, 1283, 4278, 541, 372, 23880, 2107, 29889, 13, 29903, 735, 17645, 3036, 2877, 29901, 13, 15666, 1991, 1058, 3033, 482, 297, 1021, 29899, 14167, 6030, 1818, 11097, 825, 2625, 310, 278, 14731, 10090, 896, 526, 373, 29889, 960, 896, 11097, 304, 11807, 4177, 29892, 769, 3632, 29438, 950, 537, 338, 925, 1554, 15220, 1490, 289, 810, 310, 27654, 322, 289, 2873, 411, 385, 15220, 1490, 1601, 1989, 17294, 437, 29889, 13, 4806, 437, 451, 505, 304, 1207, 393, 10608, 29889, 23529, 897, 7083, 756, 7160, 502, 278, 7458, 310, 2599, 577, 29889, 3940, 278, 18070, 310, 278, 16549, 376, 29887, 388, 2305, 1213, 2688, 437, 451, 1863, 297, 897, 7083, 29915, 29879, 3186, 29889, 2688, 526, 5960, 277, 3860, 411, 2305, 1058, 505, 23852, 7916, 29889, 13466, 29892, 3237, 29889, 897, 7083, 338, 297, 278, 443, 510, 3921, 519, 2602, 310, 2534, 304, 5649, 2020, 777, 2305, 505, 263, 1422, 18287, 19843, 1135, 1556, 2305, 29889, 960, 366, 4658, 297, 385, 2703, 29876, 666, 327, 296, 7339, 769, 278, 3133, 398, 448, 974, 18287, 19843, 338, 7339, 29899, 29887, 5428, 29889, 13, 3112, 4477, 393, 591, 526, 18287, 367, 886, 411, 18287, 553, 2658, 393, 591, 526, 752, 14356, 304, 1044, 373, 29889, 3750, 723, 278, 316, 537, 1207, 2305, 871, 304, 1424, 4627, 403, 1009, 18287, 1472, 886, 29973, 13, 8439, 1079, 29892, 897, 7083, 322, 4045, 310, 2788, 3458, 526, 10788, 630, 304, 12272, 1947, 411, 278, 4152, 6964, 310, 18287, 19843, 29889, 8680, 18287, 537, 338, 451, 3342, 491, 25869, 292, 3291, 310, 23346, 322, 19843, 3133, 29874, 29889, 6439, 694, 29889, 4451, 310, 29703, 1749, 18287, 537, 338, 3342, 491, 278, 2924, 310, 7916, 393, 591, 3033, 482, 297, 607, 29892, 297, 2507, 29892, 17645, 502, 29889, 450, 4152, 15474, 1230, 338, 18715, 1474, 270, 728, 265, 342, 472, 278, 714, 842, 1363, 372, 1074, 2039, 304, 337, 7922, 16832, 304, 14726, 278, 11203, 655, 310, 263, 17750, 1788, 29889, 13, 29924, 520, 28715, 368, 3036, 2877, 338, 451, 3342, 491, 278, 2924, 310, 7916, 393, 591, 3033, 482, 297, 29889, 13, 2772, 7083, 18172, 411, 278, 2969, 393, 565, 23852, 7916, 338, 22691, 769, 727, 526, 694, 8372, 9912, 29901, 13, 8439, 338, 694, 1492, 470, 2743, 1048, 3099, 29889, 1939, 26277, 2181, 1355, 29889, 1939, 13406, 29889, 1939, 278, 615, 29889, 1939, 1153, 412, 29889, 1939, 594, 352, 22005, 29889, 1939, 21460, 654, 2750, 7916, 411, 4344, 310, 738, 5046, 29889, 13, 1576, 2038, 338, 21615, 293, 29878, 681, 29889, 21703, 313, 29887, 388, 322, 7812, 511, 363, 1342, 29892, 338, 871, 22691, 746, 278, 27138, 526, 20218, 292, 16157, 29879, 29889, 897, 7083, 338, 12012, 3864, 263, 4195, 393, 947, 451, 1863, 29889, 8680, 7631, 12459, 508, 3544, 3632, 29438, 950, 537, 1550, 29892, 472, 278, 1021, 931, 29892, 24905 ]	1,332,839	0	CommonCrawl	19	18
ning murder, theft and rape. DeMar is actually providing us with examples of the limitations and constrictions of unquestioned obedience to religious dogma. In point of fact, some very moral people are gay or have had abortions. Some highly immoral people are — or at least claim to be — ultra-religious. As a society we have evolved past the point where religion defines morality. We are quite capable of differentiating between sin (my consumption of a lobster tail) and depravity (pedophiles). Lumping them together is dishonest. Rewriting the rules with a straw man: According to atheists, morality is a social construct foisted on humans based on religious myths. Atheistic materialism cannot account for any kind of morality since there is no ultimate lawgiver to pass judgment. "Foisted" means an unwelcome imposition. Morality is an important construct for society. Morality is not dependent upon religious belief nor is it related to materialism. The belief that morality is defined by an interpretation and presumption of a deity's judgment causes all sorts of problems. These include the ethnic cleansing of Native Americans, slavery and then segregation. They were all deemed to be moral on the premise that a god would approve. In a truly moral society the means are never justified by the end. In our society today we have a number of sanctimonious supposedly moral Christian leaders who are making excuses for Donald Trump's sociopathic behavior — past and present — to get some judges that they like appointed. As critical as I am of the Catholic Church, at least they condemned Trump for his cruel family separation policy. Evangelical Christians have not done so. Nor have they criticized the obvious greed and corruption in our government. None of that matters because they are obsessed with women's reproductive rights. In fact, evangelical Christians have enabled some of Trump's worst behavior towards Muslims and other minorities. Those good Christians do so without apology. None of it matters if they have a possibility of eroding abortion rights and if they can keep LGBTQ Americans in check. Our world is different. For example, we treat transgender people with dignity and kindness because it is the right thing to do. Conservative Christians treat them with inhumanity because their morality is defined — not by right and wrong — but, in this case, by a passage in Genesis. Where is the morality in treating children with savagery? Where is the morality in doing violence to people by the simple politeness of using appropriate pronouns in order to demonstrate their disapproval? Beyond all of that, the ultra-religious set treat LGBTQ people as those who have made very bad choices. We are not just evil. We are presumed to have terrible judgment. I am quite comfortable in my own skin. But LGBTQ children hear the same barbaric messages. Where is the morality in malice directed at vulnerable kids? In the end, opposition to Pete Buttigieg is not about him personally; it's about what he does. The same standard that's used against his sexual practices applies to everyone equally. It's the same moral law for everyone. No it is not the same moral law for everyone and who the hell appointed Mr. DeMar to be the arbiter of moral law? That passage in Leviticus that supposedly condemns gay sex is subject to the interpretations of people as scholarly as Mr. DeMar presumes to be. Many faithful Christians and Jews believe that the Hebrew Bible and Christian scripture reflect the times in which they were written. What was prohibited was the violation of young boy slaves by their owners. The slavery, however, was not a sin. Nor was it sinful to murder an insolent child or a bride who was not a virgin. At least not according to the same ancient screeds. In conclusion quoting a windbag: I happen to think that Everett Piper is an incoherent blowhard as evidenced by DeMar's quoted text regarding Pete Buttigieg: Your sexual appetites are your business. The thing about obedient and faithful Christians is this; we consider someone else's private life to be just that — Private. Please stop telling us what kind of sex you like. We don't want to know. If you want us to stay out of your bedroom, please shut the door. Stop opening it up and forcing us to applaud and celebrate. I think that	0.860587	-0.040578	0.217224	0.652029	[ 0.9838574594815955, 0.7373158822618187 ]	[ 0.2772586162541197, -0.3584145301108304 ]	[ 0.4962100540686743, -0.06176297151586494 ]	[ 0.7326710351983733, 0.5713860785666944 ]	1,024	[ 512, 512 ]	[ 1076, 13406, 29892, 278, 615, 322, 1153, 412, 29889, 897, 7083, 338, 2869, 13138, 502, 411, 6455, 310, 278, 27028, 322, 378, 710, 919, 1080, 310, 443, 12470, 287, 704, 287, 5597, 304, 12962, 11203, 655, 29889, 13, 797, 1298, 310, 2114, 29892, 777, 1407, 14731, 2305, 526, 23852, 470, 505, 750, 27450, 1080, 29889, 3834, 10712, 5198, 11251, 2305, 526, 813, 470, 472, 3203, 5995, 304, 367, 813, 8494, 336, 29899, 2674, 335, 2738, 29889, 1094, 263, 12459, 591, 505, 15220, 1490, 4940, 278, 1298, 988, 13433, 17645, 3036, 2877, 29889, 1334, 526, 3755, 15390, 310, 17473, 1218, 1546, 4457, 313, 1357, 27430, 310, 263, 658, 29890, 2475, 12464, 29897, 322, 1401, 5705, 537, 313, 9795, 3021, 5475, 467, 365, 3427, 292, 963, 4208, 338, 270, 728, 265, 342, 29889, 13, 29934, 809, 768, 292, 278, 6865, 411, 263, 380, 1610, 767, 29901, 13, 7504, 3278, 304, 472, 354, 2879, 29892, 3036, 2877, 338, 263, 5264, 3386, 1701, 12652, 373, 25618, 2729, 373, 12962, 22082, 29879, 29889, 319, 1552, 4695, 5518, 1608, 2609, 3633, 363, 738, 2924, 310, 3036, 2877, 1951, 727, 338, 694, 8494, 6490, 4307, 29887, 2147, 304, 1209, 24284, 29889, 13, 29908, 29943, 29877, 12652, 29908, 2794, 385, 18500, 295, 2763, 527, 3283, 29889, 3879, 2877, 338, 385, 4100, 3386, 363, 12459, 29889, 3879, 2877, 338, 451, 14278, 2501, 12962, 17750, 3643, 338, 372, 4475, 304, 5518, 1608, 29889, 450, 17750, 393, 3036, 2877, 338, 3342, 491, 385, 19854, 322, 2225, 28069, 310, 263, 316, 537, 29915, 29879, 24284, 9946, 599, 23551, 310, 4828, 29889, 4525, 3160, 278, 11314, 7823, 4531, 550, 292, 310, 19042, 23035, 29892, 8370, 1201, 322, 769, 2377, 1727, 362, 29889, 2688, 892, 599, 316, 22580, 304, 367, 14731, 373, 278, 5188, 895, 393, 263, 7339, 723, 2134, 345, 29889, 13, 797, 263, 19781, 14731, 12459, 278, 2794, 526, 2360, 925, 2164, 491, 278, 1095, 29889, 512, 1749, 12459, 9826, 591, 505, 263, 1353, 310, 9753, 312, 20170, 2738, 7424, 368, 14731, 6111, 20251, 1058, 526, 3907, 5566, 6394, 363, 18935, 27504, 29915, 29879, 5374, 459, 493, 293, 6030, 813, 4940, 322, 2198, 813, 304, 679, 777, 6577, 2710, 393, 896, 763, 10658, 29889, 1094, 12187, 408, 306, 626, 310, 278, 11865, 6291, 29892, 472, 3203, 896, 24905, 9571, 27504, 363, 670, 24116, 3942, 23683, 8898, 29889, 21827, 936, 27353, 505, 451, 2309, 577, 29889, 4186, 505, 896, 11164, 1891, 278, 6924, 1395, 287, 322, 1034, 18953, 297, 1749, 5874, 29889, 6213, 310, 393, 13750, 1363, 896, 526, 20881, 11517, 411, 5866, 29915, 29879, 337, 4704, 573, 10462, 29889, 13, 797, 2114, 29892, 23077, 936, 27353, 505, 9615, 777, 310, 27504, 29915, 29879, 17322, 6030, 7113, 23772, 29879, 322, 916, 9461, 1907, 29889, 16025, 1781, 27353, 437, 577, 1728, 3095, 3002, 29889, 6213, 310, 372, 13750, 565, 896, 505, 263, 13331, 310, 604, 3689, 27450, 291, 10462, 322, 565, 896, 508, 3013, 365, 7210, 29911, 29984, 23035, 297, 1423, 29889, 13, 29949, 332, 3186, 338, 1422, 29889, 1152, 1342, 29892, 591, 7539, 1301, 26098, 2305, 411, 18085, 537, 322, 2924, 2264, 1363, 372, 338, 278, 1492, 2655, 304, 437, 29889, 15312, 1230, 27353, 7539, 963, 411, 297, 26029, 537, 1363, 1009, 3036, 2877, 338, 3342, 813, 451, 491, 1492, 322, 2743, 813, 541, 29892, 297, 445, 1206, 29892, 491, 263, 13382, 297, 5739, 6656, 29889, 6804, 338, 278, 3036, 2877, 297, 2578, 1218, 4344, 411, 4048, 351, 708, 29973, 6804, 338, 278, 3036, 2877, 297, 2599, 21448, 304, 2305, 491, 278, 2560, 2832, 18543, 310, 773, 8210, 11504, 1309, 29879, 297, 1797, 304, 22222, 1009, 8796, 307, 791, 29973, 13, 29933, 1032, 898, 599, 310, 393, 29892, 278, 8494, 336, 29899, 2674, 335, 2738, 731, 7539, 365, 7210, 29911, 29984, 2305, 408, 1906, 1058, 505, 1754, 1407, 4319, 19995, 29889, 1334, 526, 451, 925, 16126, 29889, 1334, 526, 2225, 21571, 304, 505, 16403, 24284, 29889, 306, 626, 3755, 25561, 297, 590, 1914, 19309, 29889, 1205, 365, 7210, 29911, 29984, 4344, 8293, 278, 1021, 2594, 1646, 293, 7191, 29889, 6804, 338, 278, 3036, 2877, 297, 4439, 625, 10624, 472, 23180, 519, 413, 4841, 29973, 13, 797, 278, 1095, 29892, 19626, 304, 349, 2650, 1205, 29873, 335, 5876, 338, 451, 1048, 1075, 22345, 29936, 372, 29915, 29879, 1048, 825, 540, 947, 29889, 450, 1021, 3918, 393, 29915, 29879, 1304, 2750, 670, 18287, 23274, 16058, 304, 14332, 18018, 29889, 739, 29915, 29879, 278, 1021, 14731, 4307, 363, 14332, 29889, 13, 3782, 372, 338, 451, 278, 1021, 14731, 4307, 363, 14332, 322, 1058, 278, 23927, 10658, 3237, 29889, 897, 7083, 304, 367, 278, 564, 29890, 1524, 310, 14731, 4307, 29973, 2193, 13382, 297, 20708, 277, 12473, 393, 7424, 368, 24905, 1983, 23852, 7916, 338, 4967, 304, 278, 6613, 800, 310, 2305, 408, 21344, 368, 408, 3237, 29889, 897, 7083, 2225, 9351, 304, 367, 29889, 13, 14804, 27057, 27353, 322, 22057, 4658, 393, 278, 18472, 3973, 21958, 322, 6111, 2471, 545, 9432, 278, 3064, 297, 607, 896, 892, 3971, 29889, 1724, 471, 21460, 1573, 471, 278, 5537, 362, 310, 4123, 8023, 25569, 491, 1009, 1914, 414, 29889, 450, 8370, 1201, 29892, 3138, 29892, 471, 451, 263, 4457, 29889, 4186, 471, 372, 4457, 1319, 304, 13406, 385, 1663, 324, 296, 2278, 470, 263, 289, 2426, 1058, 471, 451, 263, 10636, 5359, 29889, 2180, 3203, 451, 5034, 304, 278, 1021, 12297, 885, 276, 5779, 29889, 13, 797, 15997, 439, 11427, 263, 8805, 23156, 29901, 13, 29902, 3799, 304, 1348, 393, 18274, 1803, 7362, 546, 338, 385, 297, 1111, 2276, 296, 13031, 6800, 408, 3415, 3615, 1133, 491, 897, 7083, 29915, 29879, 23153, 1426, 11211, 349, 2650, 1205, 29873, 335, 5876, 29901, 13, 10858, 18287, 623, 300, 3246, 526, 596, 5381, 29889, 450, 2655, 1048, 704, 287, 993, 322, 27057, 27353, 338, 445, 29936, 591, 2050, 4856, 1683, 29915, 29879, 2024, 2834, 304, 367, 925, 393, 813, 12230, 29889, 3529, 5040, 14509, 502, 825, 2924, 310, 7916, 366, 763, 29889, 1334, 1016, 29915, 29873, 864, 304, 1073, 29889, 960, 366, 864, 502, 304, 7952, 714, 310, 596, 6592, 8345, 29892, 3113, 12522, 278, 3050, 29889, 22303, 8718, 372, 701, 322, 28172, 502, 304, 623, 433, 566, 322, 10894, 403, 29889, 13, 29902, 1348, 393 ]	1,332,839	1,024	CommonCrawl	19	18
Over the course this year so far, you've seen my adoration for a certain button up sewing pattern (McCall's 6649 - now out of print) and then a couple of hacks of things I've made from it (here and here). I thought I would take a sec, stop down and say a little more about it. It's exciting. Well, at least I think so. Hopefully this post will help clear up some questions I've been getting and hopefully it will show you that you can take a pattern and hack it up and not have to re-invent the fitting wheel. This is a skill I've cultivated over several years and one that is well worth the time invested and when you get to the pattern drafting part, it's really quite fun to learn (in like a scrapbooking sort of way!). In my recent hack of my beloved McCall's 6649, I mentioned a Craftsy class I had taken. One Pattern, Many Looks with Sarah Holden. I enrolled in the class last year sometime and then it sat in my Craftsy cue for many months. One night, I was really tired and decided to watch this Craftsy class as I was sitting in bed. I watched all the episodes right there and then. I was riveted and I was so excited to get up and get started in the morning. Dreamt of pattern hacks all night! Yessssss! The class takes you through this pretty fascinating process. First you're supposed to fit the pattern. This process actually took a few weeks (the longest part of this whole business) because I wanted something that truly, was perfect and that usually means, for me, that I work out any and all kinks in a pattern by making it up at least 3 times. Seriously, 3 times is the charm. I have some more thoughts about the fitting process in my next post, but yeah, I made this shirt up a good 3 times (and then one more time, making that 4 times!!) before I moved on to the rest of the content of the class. Update: Just so you are aware, this Craftsy class does not cover anything about fitting! It's only about pattern drafting and manipulation. After a perfect fit, then it was time to reverse engineer the pattern back to sloper form. What is a sloper? In the most basic terms, a sloper is a base pattern, without seam allowances, from which other patterns can be created or hacked from. You can have different types of slopers. For example, you can have bodice, sleeve, dress, pants, etc. From there you can even have varying types of those basic patterns like a button-up shirt sloper or a raglan sleeve sloper. The idea is that you'll start forming an entire collection of base patterns that are closer in idea to what you want an end pattern to be. More colors in a crayon box if you will. Anyway, back to McCall's 6649. I created a sloper from this pattern and transferred all of the pertinent markings to posterboard. All of the seam allowances have been cut off here and there are holes and notches in specific places. Putting a pattern like this on posterboard is fantastic because then when I'm ready to create a new top from this pattern, I can just trace it off in a matter of seconds. The posterboard is stiff so you can just trace around it really easily. In the Craftsy class, Sarah shows you some really great hacks. And these are just starting points. I mean you really do have the entire world at your feet when you start creating your own patterns - from patterns that already fit you! Since you've already addressed the fit, that tends to not be a problem anymore. You might run into some issues here and there, but they are minimal by comparison. All in all, I'm very very pleased with how my hacks have turned out from this process. It took a lot of time, but was well worth the investment. Onward and upward from here. Have you gone through this process before? What kinds of slopers do you have? If you haven't, I can't recommend something like this enough. You learn a ton about fitting and about your body and what things you should be looking out for when you go to try a new sewing pattern. Plus then there's the creative gratification that comes from creating a pattern of your very own. Fun, fun! Thank you! I've had that class in my Crafty listing for ages and never "found"	0.619524	-0.726389	0.704182	-0.564762	[ 0.6496566548058981, 0.5893909359299526 ]	[ -0.9188812760607723, -0.5338961310791829 ]	[ 0.5063550181702113, 0.9020086181301573 ]	[ -0.8242490703509779, -0.30527570183452757 ]	1,024	[ 512, 512 ]	[ 6811, 278, 3236, 445, 1629, 577, 2215, 29892, 366, 29915, 345, 3595, 590, 594, 12418, 363, 263, 3058, 2826, 701, 409, 16958, 4766, 313, 27297, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 448, 1286, 714, 310, 1596, 29897, 322, 769, 263, 7303, 310, 447, 4684, 310, 2712, 306, 29915, 345, 1754, 515, 372, 313, 4150, 322, 1244, 467, 306, 2714, 306, 723, 2125, 263, 5226, 29892, 5040, 1623, 322, 1827, 263, 2217, 901, 1048, 372, 29889, 739, 29915, 29879, 5566, 11407, 29889, 5674, 29892, 472, 3203, 306, 1348, 577, 29889, 13, 29950, 2300, 3730, 445, 1400, 674, 1371, 2821, 701, 777, 5155, 306, 29915, 345, 1063, 2805, 322, 27581, 372, 674, 1510, 366, 393, 366, 508, 2125, 263, 4766, 322, 15833, 372, 701, 322, 451, 505, 304, 337, 29899, 262, 794, 278, 28221, 18875, 29889, 910, 338, 263, 19911, 306, 29915, 345, 18834, 630, 975, 3196, 2440, 322, 697, 393, 338, 1532, 7088, 278, 931, 2437, 2868, 322, 746, 366, 679, 304, 278, 4766, 18195, 292, 760, 29892, 372, 29915, 29879, 2289, 3755, 2090, 304, 5110, 313, 262, 763, 263, 885, 2390, 2909, 292, 2656, 310, 982, 29991, 467, 512, 590, 7786, 15833, 310, 590, 1339, 8238, 4052, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 29892, 306, 5276, 263, 315, 4154, 29879, 29891, 770, 306, 750, 4586, 29889, 3118, 25860, 29892, 9267, 19887, 411, 19235, 21771, 264, 29889, 306, 427, 24476, 297, 278, 770, 1833, 1629, 1047, 5410, 322, 769, 372, 3290, 297, 590, 315, 4154, 29879, 29891, 274, 434, 363, 1784, 7378, 29889, 3118, 4646, 29892, 306, 471, 2289, 23407, 322, 8459, 304, 6505, 445, 315, 4154, 29879, 29891, 770, 408, 306, 471, 16246, 297, 6592, 29889, 306, 20654, 599, 278, 23238, 1492, 727, 322, 769, 29889, 306, 471, 9050, 300, 287, 322, 306, 471, 577, 24173, 304, 679, 701, 322, 679, 4687, 297, 278, 7250, 29889, 16814, 29873, 310, 4766, 447, 4684, 599, 4646, 29991, 612, 404, 893, 893, 29991, 13, 1576, 770, 4893, 366, 1549, 445, 5051, 21028, 262, 1218, 1889, 29889, 3824, 366, 29915, 276, 7424, 304, 6216, 278, 4766, 29889, 910, 1889, 2869, 3614, 263, 2846, 11405, 313, 1552, 27217, 760, 310, 445, 3353, 5381, 29897, 1363, 306, 5131, 1554, 393, 19781, 29892, 471, 4922, 322, 393, 5491, 2794, 29892, 363, 592, 29892, 393, 306, 664, 714, 738, 322, 599, 413, 19363, 297, 263, 4766, 491, 3907, 372, 701, 472, 3203, 29871, 29941, 3064, 29889, 1816, 17365, 29892, 29871, 29941, 3064, 338, 278, 21192, 29889, 306, 505, 777, 901, 13133, 1048, 278, 28221, 1889, 297, 590, 2446, 1400, 29892, 541, 21915, 29892, 306, 1754, 445, 528, 2728, 701, 263, 1781, 29871, 29941, 3064, 313, 392, 769, 697, 901, 931, 29892, 3907, 393, 29871, 29946, 3064, 6824, 29897, 1434, 306, 6153, 373, 304, 278, 1791, 310, 278, 2793, 310, 278, 770, 29889, 10318, 29901, 3387, 577, 366, 526, 9543, 29892, 445, 315, 4154, 29879, 29891, 770, 947, 451, 4612, 3099, 1048, 28221, 29991, 739, 29915, 29879, 871, 1048, 4766, 18195, 292, 322, 11525, 2785, 29889, 13, 13555, 263, 4922, 6216, 29892, 769, 372, 471, 931, 304, 11837, 22055, 278, 4766, 1250, 304, 14216, 546, 883, 29889, 1724, 338, 263, 14216, 546, 29973, 512, 278, 1556, 6996, 4958, 29892, 263, 14216, 546, 338, 263, 2967, 4766, 29892, 1728, 409, 314, 2758, 2925, 29892, 515, 607, 916, 15038, 508, 367, 2825, 470, 15833, 287, 515, 29889, 887, 508, 505, 1422, 4072, 310, 269, 4757, 414, 29889, 1152, 1342, 29892, 366, 508, 505, 13004, 625, 29892, 12844, 29872, 345, 29892, 10714, 29892, 282, 1934, 29892, 2992, 29889, 3645, 727, 366, 508, 1584, 505, 24099, 4072, 310, 1906, 6996, 15038, 763, 263, 2826, 29899, 786, 528, 2728, 14216, 546, 470, 263, 1153, 3820, 273, 12844, 29872, 345, 14216, 546, 29889, 450, 2969, 338, 393, 366, 29915, 645, 1369, 25391, 385, 4152, 4333, 310, 2967, 15038, 393, 526, 17649, 297, 2969, 304, 825, 366, 864, 385, 1095, 4766, 304, 367, 29889, 5853, 11955, 297, 263, 274, 764, 265, 3800, 565, 366, 674, 29889, 13, 10773, 1582, 29892, 1250, 304, 4052, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 29889, 306, 2825, 263, 14216, 546, 515, 445, 4766, 322, 18440, 599, 310, 278, 13499, 8946, 2791, 886, 304, 10368, 3377, 29889, 2178, 310, 278, 409, 314, 2758, 2925, 505, 1063, 5700, 1283, 1244, 322, 727, 526, 26532, 322, 451, 6609, 297, 2702, 7600, 29889, 12065, 1259, 263, 4766, 763, 445, 373, 10368, 3377, 338, 13568, 6288, 1363, 769, 746, 306, 29915, 29885, 7960, 304, 1653, 263, 716, 2246, 515, 445, 4766, 29892, 306, 508, 925, 9637, 372, 1283, 297, 263, 4383, 310, 6923, 29889, 450, 10368, 3377, 338, 380, 2593, 577, 366, 508, 925, 9637, 2820, 372, 2289, 5948, 29889, 13, 797, 278, 315, 4154, 29879, 29891, 770, 29892, 19235, 3697, 366, 777, 2289, 2107, 447, 4684, 29889, 1126, 1438, 526, 925, 6257, 3291, 29889, 306, 2099, 366, 2289, 437, 505, 278, 4152, 3186, 472, 596, 6900, 746, 366, 1369, 4969, 596, 1914, 15038, 448, 515, 15038, 393, 2307, 6216, 366, 29991, 4001, 366, 29915, 345, 2307, 20976, 278, 6216, 29892, 393, 29867, 304, 451, 367, 263, 1108, 15128, 29889, 887, 1795, 1065, 964, 777, 5626, 1244, 322, 727, 29892, 541, 896, 526, 13114, 491, 10230, 29889, 13, 3596, 297, 599, 29892, 306, 29915, 29885, 1407, 1407, 22301, 411, 920, 590, 447, 4684, 505, 6077, 714, 515, 445, 1889, 29889, 739, 3614, 263, 3287, 310, 931, 29892, 541, 471, 1532, 7088, 278, 13258, 358, 29889, 1551, 1328, 322, 701, 1328, 515, 1244, 29889, 6975, 366, 7695, 1549, 445, 1889, 1434, 29973, 1724, 17690, 310, 269, 4757, 414, 437, 366, 505, 29973, 960, 366, 7359, 29915, 29873, 29892, 306, 508, 29915, 29873, 6907, 1554, 763, 445, 3307, 29889, 887, 5110, 263, 15243, 1048, 28221, 322, 1048, 596, 3573, 322, 825, 2712, 366, 881, 367, 3063, 714, 363, 746, 366, 748, 304, 1018, 263, 716, 409, 16958, 4766, 29889, 15113, 769, 727, 29915, 29879, 278, 907, 1230, 20715, 2450, 393, 5304, 515, 4969, 263, 4766, 310, 596, 1407, 1914, 29889, 13811, 29892, 2090, 29991, 13, 25271, 366, 29991, 306, 29915, 345, 750, 393, 770, 297, 590, 14279, 3312, 18028, 363, 24646, 322, 2360, 376, 11940, 29908 ]	1,332,841	0	C4	4	1
the time to watch it. I am watching one class each morning this week. This is exactly what I want to do!Thank you! I've been interested in learning the sloper approach to sewing/pattern making and have been looking at books on slopers I could buy, but reviews seems to often be mixed on their quality, so I've been eyeing the bodice sloper class on Craftsy and the one you've mentionned (amongst so many others, I want to get them all..). It's good to know I'll get my moneys worth for the Many Shirts class when I buy it. I made some shirts in the past, but I see much room for emprouvement and would love to get (or make) a TNT shirt pattern. I've taken the sloper class on Craftsy, but this one seemed really interesting as well. The theory behind it sounds pretty fascinating! I like the concept of a sloper, but I just don't wear too many shirts, so I overlooked this class. I will take another look. Thanks, Sunni! I have a pants and a skirt sloper. I have really worked on the ginger jeans and archer shirt patterns into my idea of perfect jeans and button up patterns. They aren't slopers but now I am curious about doing that. I really believe in taking the time to fine tune patterns , it has been totally worth it for me. I got really tired of reinventing the wheel each go around with mixed results. Perfect timing on this topic! I was just doing some fitting through a new craftsy class (not the one you've mentioned but I will be checking it out now) and wondering if I could apply my new form fitting pattern as a sloper of sorts. Thanks for the insight. Amen! I hear ya sister! Trying to fit new sewing patterns gets so old. Gosh, I got so sick of starting at square zero everytime I wanted to make something a little different and so, it really was finally time to get some slopers done. They are a lot of work, but in the end, I'm so much happier with how these work instead of trying to fit a new sewing pattern. I have to weigh in because I've purchased several patternmaking books over the course of several years. While they are all good and they have wonderful information, drafting a sloper from your measurements is well, just as hard as getting a pattern to fit you. It's about a ton easier if you have a teacher there to help and hold your hand a bit, but if you're doing it on your own, I definitely say, take the Craftsy classes. It's so much easier to be guided by someone than try to decipher how to do it on your own! You'll go through about 1000 iterations of just the drafting trying to get it right - at least I did. I tried many, many different methods and books and found the same for all of them. Almost easier to just fit a sewing pattern from scratch. I think you would be glad you did once you were done. I've been taking my sloper out a TON and playing around with different ideas for different blouses from it - even dresses! It's getting a ton of play and use from me. I think the sloper class would be well worth the time - also have that one in my cue. I found this class really approachable. I like that she used a regular sewing pattern and then took that pattern and created a bunch of different blouses from it. It's really creative and fun! So many possibilities. I think there's one for pants too if I'm not mistaken. A Craftsy class I mean. Same idea. You take a pair of pants and create all the different pants patterns that you want from a single pattern. Makes it so you don't have to deal with fitting a new pattern. It's quite liberating and fun! I'm sure you can. Fitting is the #1 reason people don't sew their own clothes. When you start taking the fit out of the equation, it makes you want to sew more and believe me, you do! You can start cranking out patterns and projects left and right. I truly miss wearing shirts with buttons. Or even a shirtdress as the retro look is coming back. But my bust has a fuller shape from the sides so all RTW blouses get the gappies on me. Honestly, why sew a shirt I have to keep	0.354492	-1.176732	0.554544	-1.055771	[ 0.14698577236335297, 0.5619974273499774 ]	[ -1.5026261935677405, -0.850837389971003 ]	[ 0.4049053771548406, 0.7041818181501843 ]	[ -1.2755868118928533, -0.8359552365581159 ]	1,024	[ 512, 512 ]	[ 278, 931, 304, 6505, 372, 29889, 306, 626, 21217, 697, 770, 1269, 7250, 445, 4723, 29889, 910, 338, 3721, 825, 306, 864, 304, 437, 29991, 25271, 366, 29991, 13, 29902, 29915, 345, 1063, 8852, 297, 6509, 278, 14216, 546, 2948, 304, 409, 16958, 29914, 11037, 3907, 322, 505, 1063, 3063, 472, 8277, 373, 269, 4757, 414, 306, 1033, 15649, 29892, 541, 21804, 2444, 304, 4049, 367, 12849, 373, 1009, 11029, 29892, 577, 306, 29915, 345, 1063, 10977, 292, 278, 13004, 625, 14216, 546, 770, 373, 315, 4154, 29879, 29891, 322, 278, 697, 366, 29915, 345, 3585, 9571, 313, 314, 549, 303, 577, 1784, 4045, 29892, 306, 864, 304, 679, 963, 599, 636, 467, 739, 29915, 29879, 1781, 304, 1073, 306, 29915, 645, 679, 590, 286, 650, 952, 7088, 363, 278, 9267, 1383, 381, 1372, 770, 746, 306, 15649, 372, 29889, 306, 1754, 777, 528, 381, 1372, 297, 278, 4940, 29892, 541, 306, 1074, 1568, 5716, 363, 953, 558, 5128, 882, 322, 723, 5360, 304, 679, 313, 272, 1207, 29897, 263, 323, 20321, 528, 2728, 4766, 29889, 13, 29902, 29915, 345, 4586, 278, 14216, 546, 770, 373, 315, 4154, 29879, 29891, 29892, 541, 445, 697, 6140, 2289, 8031, 408, 1532, 29889, 450, 6368, 5742, 372, 10083, 5051, 21028, 262, 1218, 29991, 13, 29902, 763, 278, 6964, 310, 263, 14216, 546, 29892, 541, 306, 925, 1016, 29915, 29873, 19531, 2086, 1784, 528, 381, 1372, 29892, 577, 306, 975, 6914, 287, 445, 770, 29889, 306, 674, 2125, 1790, 1106, 29889, 1834, 29892, 8991, 1240, 29991, 13, 29902, 505, 263, 282, 1934, 322, 263, 2071, 2728, 14216, 546, 29889, 306, 505, 2289, 3796, 373, 278, 330, 5621, 1444, 550, 322, 3190, 261, 528, 2728, 15038, 964, 590, 2969, 310, 4922, 1444, 550, 322, 2826, 701, 15038, 29889, 2688, 9455, 29915, 29873, 269, 4757, 414, 541, 1286, 306, 626, 12758, 1048, 2599, 393, 29889, 306, 2289, 4658, 297, 5622, 278, 931, 304, 2691, 260, 1540, 15038, 1919, 372, 756, 1063, 14909, 7088, 372, 363, 592, 29889, 306, 2355, 2289, 23407, 310, 15561, 794, 292, 278, 18875, 1269, 748, 2820, 411, 12849, 2582, 29889, 13, 5894, 3647, 28750, 373, 445, 11261, 29991, 306, 471, 925, 2599, 777, 28221, 1549, 263, 716, 25554, 29879, 29891, 770, 313, 1333, 278, 697, 366, 29915, 345, 5276, 541, 306, 674, 367, 8454, 372, 714, 1286, 29897, 322, 9873, 565, 306, 1033, 3394, 590, 716, 883, 28221, 4766, 408, 263, 14216, 546, 310, 23551, 29889, 1834, 363, 278, 25483, 29889, 13, 29909, 1527, 29991, 306, 8293, 9343, 9883, 29991, 24428, 304, 6216, 716, 409, 16958, 15038, 4947, 577, 2030, 29889, 402, 10578, 29892, 306, 2355, 577, 17319, 310, 6257, 472, 6862, 5225, 1432, 2230, 306, 5131, 304, 1207, 1554, 263, 2217, 1422, 322, 577, 29892, 372, 2289, 471, 7146, 931, 304, 679, 777, 269, 4757, 414, 2309, 29889, 2688, 526, 263, 3287, 310, 664, 29892, 541, 297, 278, 1095, 29892, 306, 29915, 29885, 577, 1568, 2250, 631, 411, 920, 1438, 664, 2012, 310, 1811, 304, 6216, 263, 716, 409, 16958, 4766, 29889, 13, 29902, 505, 304, 591, 1141, 297, 1363, 306, 29915, 345, 20848, 3196, 4766, 28990, 8277, 975, 278, 3236, 310, 3196, 2440, 29889, 5806, 896, 526, 599, 1781, 322, 896, 505, 20695, 2472, 29892, 18195, 292, 263, 14216, 546, 515, 596, 20398, 338, 1532, 29892, 925, 408, 2898, 408, 2805, 263, 4766, 304, 6216, 366, 29889, 739, 29915, 29879, 1048, 263, 15243, 6775, 565, 366, 505, 263, 15703, 727, 304, 1371, 322, 4808, 596, 1361, 263, 2586, 29892, 541, 565, 366, 29915, 276, 2599, 372, 373, 596, 1914, 29892, 306, 11630, 1827, 29892, 2125, 278, 315, 4154, 29879, 29891, 4413, 29889, 739, 29915, 29879, 577, 1568, 6775, 304, 367, 1410, 2618, 491, 4856, 1135, 1018, 304, 316, 455, 8096, 920, 304, 437, 372, 373, 596, 1914, 29991, 887, 29915, 645, 748, 1549, 1048, 29871, 29896, 29900, 29900, 29900, 24372, 310, 925, 278, 18195, 292, 1811, 304, 679, 372, 1492, 448, 472, 3203, 306, 1258, 29889, 306, 1898, 1784, 29892, 1784, 1422, 3519, 322, 8277, 322, 1476, 278, 1021, 363, 599, 310, 963, 29889, 838, 3242, 6775, 304, 925, 6216, 263, 409, 16958, 4766, 515, 22728, 29889, 13, 29902, 1348, 366, 723, 367, 10932, 366, 1258, 2748, 366, 892, 2309, 29889, 306, 29915, 345, 1063, 5622, 590, 14216, 546, 714, 263, 323, 1164, 322, 8743, 2820, 411, 1422, 7014, 363, 1422, 1999, 23676, 515, 372, 448, 1584, 10714, 267, 29991, 739, 29915, 29879, 2805, 263, 15243, 310, 1708, 322, 671, 515, 592, 29889, 13, 29902, 1348, 278, 14216, 546, 770, 723, 367, 1532, 7088, 278, 931, 448, 884, 505, 393, 697, 297, 590, 274, 434, 29889, 306, 1476, 445, 770, 2289, 2948, 519, 29889, 306, 763, 393, 1183, 1304, 263, 4943, 409, 16958, 4766, 322, 769, 3614, 393, 4766, 322, 2825, 263, 14928, 310, 1422, 1999, 23676, 515, 372, 29889, 739, 29915, 29879, 2289, 907, 1230, 322, 2090, 29991, 1105, 1784, 24496, 29889, 13, 29902, 1348, 727, 29915, 29879, 697, 363, 282, 1934, 2086, 565, 306, 29915, 29885, 451, 25257, 29889, 319, 315, 4154, 29879, 29891, 770, 306, 2099, 29889, 19491, 2969, 29889, 887, 2125, 263, 5101, 310, 282, 1934, 322, 1653, 599, 278, 1422, 282, 1934, 15038, 393, 366, 864, 515, 263, 2323, 4766, 29889, 341, 6926, 372, 577, 366, 1016, 29915, 29873, 505, 304, 5376, 411, 28221, 263, 716, 4766, 29889, 739, 29915, 29879, 3755, 7866, 1218, 322, 2090, 29991, 13, 29902, 29915, 29885, 1854, 366, 508, 29889, 383, 5367, 338, 278, 396, 29896, 2769, 2305, 1016, 29915, 29873, 409, 29893, 1009, 1914, 22095, 29889, 1932, 366, 1369, 5622, 278, 6216, 714, 310, 278, 6306, 29892, 372, 3732, 366, 864, 304, 409, 29893, 901, 322, 4658, 592, 29892, 366, 437, 29991, 887, 508, 1369, 274, 661, 9292, 714, 15038, 322, 9279, 2175, 322, 1492, 29889, 13, 29902, 19781, 3052, 591, 4362, 528, 381, 1372, 411, 9828, 29889, 1394, 1584, 263, 528, 381, 1594, 1253, 408, 278, 24877, 1106, 338, 6421, 1250, 29889, 1205, 590, 289, 504, 756, 263, 2989, 261, 8267, 515, 278, 11192, 577, 599, 390, 16240, 1999, 23676, 679, 278, 330, 932, 583, 373, 592, 29889, 7906, 342, 368, 29892, 2020, 409, 29893, 263, 528, 2728, 306, 505, 304, 3013 ]	1,332,841	1,024	C4	4	1
closed with safety pins? This class is in my Crafty wish list but haven't taken the plunge yet. You've convinced me now that I may find my answer here. The idea of perfecting a pattern sloper has been brewing so I think on their next sale I'll get it. On a side note, I mentioned you and your Crafty class on zippers in my latest blog post. I reference that class ALL the time. Can you do a post about a dress with a lining and an invisible zipper? One that has that nice machine finish? Since I drafted my bodice, skirt and pant sloper from the book European Cut by Elizabeth Allemong, they have been invaluable to achieving fit that is 95% right the first time. The other 5% is the vagaries of the pattern and fabric I'm using which can be dealt with, with a muslin and then I'm good to go to make multiples :) I also use RTW items in my wardrobe to compare then tweak the patterns. I'm sure I could come up with something! Give me a bit and I'll see if I can't put this together! As for the Craftsy class I'm talking about here, I do want to state that it's not a fitting class by any means. Sarah Holden only talks and goes into depth about pattern drafting. But I still think the class would be worth everyone's while. The pattern drafting alone is great and it really does get you to think outside the box. I know exactly what you mean about wearing button-up shirts. I never did for a long time either because they never fit across the back. Couldn't put my arms in front of me! Now I can that I make my own. It's marvelous! Yes, I'm completely on board with you here! I feel the same way about the fit and I usually tend to make a muslin, if only just to check things like the neckline and such. Otherwise, the fit is so much easier and all I have to worry about is the design. Fun! I don't remember her using a lot of measurements, but sadly they are in inches. So sorry! We definitely need to convert over to the metric system! ugh! Someday I'll get to only 3 tries before fitting! It took me 8 Sorbettos before I got one that fit. Three sounds like a lovely goal! I am honestly still a little scared of the idea of a blank slate. I'm not familiar enough with my body and how clothes fit it yet to be able to envision something. I do look forward to that time, though, because frankly, I also find it hard to envision something from a pattern fitting me. It helps to troll the internet for someone similar to my body shape who has made the pattern, but it's still a wee bit exhausting. I have just finished fitting and putting together a dress sloper. But I don't know what to do with it now. Take it apart and trace it? Keep the darts closed? I used Vogue dress sloper pattern and really all it does is tell you to keep fitting it, but how do I use it against other patterns so that I will know they fit? This thing was a lot of work and I don't know how to use it now. Let me know if you have information on where to go from here. Hi Haze! Some great questions here. Hopefully I can answer them and give you some insight. The concept of using your sloper up against another sewing pattern to diagnose the fit before you make it is, well, a hard one. Additionally, I personally feel - since this is a method that I have tried - that it is full of holes and you end up still have to make a muslin and work out some fitting issues. If you are hell-bent on this method, I recommend Lynda Maynard's book Demystifying Fit. I would say that if you do want to do this method then you do need to take your muslin apart and copy it onto paper. You'll need to do this if you want to create sewing patterns from it, so I recommend that you do that step. If you want to create your own sewing patterns - which I find to be a much superior method to trying to use it to fit other sewing patterns - then I would recommend the Craftsy class above to give you a taste of how this works. You could still use your bodice section for most of the designs in the class or take the ideas and apply them to your sloper.	0.483926	-1.359376	0.271753	-0.945863	[ 0.5236465153380121, 0.444205340456084 ]	[ -1.2949132781358133, -1.423838535990113 ]	[ -0.07444417664278628, 0.6179496232871192 ]	[ -1.1585251498214735, -0.733201110962127 ]	1,024	[ 512, 512 ]	[ 5764, 411, 15332, 282, 1144, 29973, 910, 770, 338, 297, 590, 14279, 3312, 6398, 1051, 541, 7359, 29915, 29873, 4586, 278, 715, 19440, 3447, 29889, 887, 29915, 345, 25617, 592, 1286, 393, 306, 1122, 1284, 590, 1234, 1244, 29889, 450, 2969, 310, 4922, 292, 263, 4766, 14216, 546, 756, 1063, 2078, 16958, 577, 306, 1348, 373, 1009, 2446, 14686, 306, 29915, 645, 679, 372, 29889, 13, 2951, 263, 2625, 4443, 29892, 306, 5276, 366, 322, 596, 14279, 3312, 770, 373, 503, 8377, 414, 297, 590, 9281, 12618, 1400, 29889, 306, 3407, 393, 770, 15149, 278, 931, 29889, 1815, 366, 437, 263, 1400, 1048, 263, 10714, 411, 263, 301, 2827, 322, 385, 27597, 503, 29875, 2496, 29973, 3118, 393, 756, 393, 7575, 4933, 8341, 29973, 13, 23036, 306, 18195, 287, 590, 13004, 625, 29892, 2071, 2728, 322, 282, 424, 14216, 546, 515, 278, 3143, 7824, 315, 329, 491, 13061, 838, 2409, 549, 29892, 896, 505, 1063, 297, 4387, 519, 304, 3657, 15387, 6216, 393, 338, 29871, 29929, 29945, 29995, 1492, 278, 937, 931, 29889, 450, 916, 29871, 29945, 29995, 338, 278, 325, 351, 4314, 310, 278, 4766, 322, 18187, 306, 29915, 29885, 773, 607, 508, 367, 316, 1997, 411, 29892, 411, 263, 2301, 1915, 322, 769, 306, 29915, 29885, 1781, 304, 748, 304, 1207, 2473, 2701, 4248, 306, 884, 671, 390, 16240, 4452, 297, 590, 281, 538, 307, 915, 304, 7252, 769, 7780, 557, 278, 15038, 29889, 13, 29902, 29915, 29885, 1854, 306, 1033, 2041, 701, 411, 1554, 29991, 25538, 592, 263, 2586, 322, 306, 29915, 645, 1074, 565, 306, 508, 29915, 29873, 1925, 445, 4208, 29991, 13, 2887, 363, 278, 315, 4154, 29879, 29891, 770, 306, 29915, 29885, 9963, 1048, 1244, 29892, 306, 437, 864, 304, 2106, 393, 372, 29915, 29879, 451, 263, 28221, 770, 491, 738, 2794, 29889, 19235, 21771, 264, 871, 5969, 2039, 322, 5771, 964, 10809, 1048, 4766, 18195, 292, 29889, 1205, 306, 1603, 1348, 278, 770, 723, 367, 7088, 14332, 29915, 29879, 1550, 29889, 450, 4766, 18195, 292, 7432, 338, 2107, 322, 372, 2289, 947, 679, 366, 304, 1348, 5377, 278, 3800, 29889, 306, 1073, 3721, 825, 366, 2099, 1048, 591, 4362, 2826, 29899, 786, 528, 381, 1372, 29889, 306, 2360, 1258, 363, 263, 1472, 931, 2845, 1363, 896, 2360, 6216, 4822, 278, 1250, 29889, 6527, 29876, 29915, 29873, 1925, 590, 10188, 297, 4565, 310, 592, 29991, 2567, 306, 508, 393, 306, 1207, 590, 1914, 29889, 739, 29915, 29879, 1766, 955, 681, 29991, 13, 8241, 29892, 306, 29915, 29885, 6446, 373, 7613, 411, 366, 1244, 29991, 306, 4459, 278, 1021, 982, 1048, 278, 6216, 322, 306, 5491, 10331, 304, 1207, 263, 2301, 1915, 29892, 565, 871, 925, 304, 1423, 2712, 763, 278, 18873, 1220, 322, 1316, 29889, 13466, 29892, 278, 6216, 338, 577, 1568, 6775, 322, 599, 306, 505, 304, 15982, 1048, 338, 278, 2874, 29889, 13811, 29991, 13, 29902, 1016, 29915, 29873, 6456, 902, 773, 263, 3287, 310, 20398, 29892, 541, 14610, 368, 896, 526, 297, 22831, 29889, 1105, 7423, 29991, 1334, 11630, 817, 304, 3588, 975, 304, 278, 12714, 1788, 29991, 318, 12443, 29991, 13, 29903, 27067, 388, 306, 29915, 645, 679, 304, 871, 29871, 29941, 14335, 1434, 28221, 29991, 739, 3614, 592, 29871, 29947, 317, 11831, 1803, 359, 1434, 306, 2355, 697, 393, 6216, 29889, 12753, 10083, 763, 263, 12355, 873, 7306, 29991, 13, 29902, 626, 15993, 368, 1603, 263, 2217, 885, 1965, 310, 278, 2969, 310, 263, 9654, 2243, 403, 29889, 306, 29915, 29885, 451, 9985, 3307, 411, 590, 3573, 322, 920, 22095, 6216, 372, 3447, 304, 367, 2221, 304, 427, 4924, 1554, 29889, 306, 437, 1106, 6375, 304, 393, 931, 29892, 2466, 29892, 1363, 2524, 29895, 368, 29892, 306, 884, 1284, 372, 2898, 304, 427, 4924, 1554, 515, 263, 4766, 28221, 592, 29889, 739, 6911, 304, 260, 1245, 278, 8986, 363, 4856, 2788, 304, 590, 3573, 8267, 1058, 756, 1754, 278, 4766, 29892, 541, 372, 29915, 29879, 1603, 263, 591, 29872, 2586, 27096, 292, 29889, 13, 29902, 505, 925, 7743, 28221, 322, 10594, 4208, 263, 10714, 14216, 546, 29889, 13, 6246, 306, 1016, 29915, 29873, 1073, 825, 304, 437, 411, 372, 1286, 29889, 11190, 372, 12435, 322, 9637, 372, 29973, 19152, 278, 270, 5708, 5764, 29973, 306, 1304, 20797, 434, 10714, 14216, 546, 4766, 322, 2289, 599, 372, 947, 338, 2649, 366, 304, 3013, 28221, 372, 29892, 541, 920, 437, 306, 671, 372, 2750, 916, 15038, 577, 393, 306, 674, 1073, 896, 6216, 29973, 910, 2655, 471, 263, 3287, 310, 664, 322, 306, 1016, 29915, 29873, 1073, 920, 304, 671, 372, 1286, 29889, 13, 12024, 592, 1073, 565, 366, 505, 2472, 373, 988, 304, 748, 515, 1244, 29889, 13, 18567, 25606, 29872, 29991, 3834, 2107, 5155, 1244, 29889, 7963, 3730, 306, 508, 1234, 963, 322, 2367, 366, 777, 25483, 29889, 450, 6964, 310, 773, 596, 14216, 546, 701, 2750, 1790, 409, 16958, 4766, 304, 24876, 852, 278, 6216, 1434, 366, 1207, 372, 338, 29892, 1532, 29892, 263, 2898, 697, 29889, 19814, 29892, 306, 22345, 4459, 448, 1951, 445, 338, 263, 1158, 393, 306, 505, 1898, 448, 393, 372, 338, 2989, 310, 26532, 322, 366, 1095, 701, 1603, 505, 304, 1207, 263, 2301, 1915, 322, 664, 714, 777, 28221, 5626, 29889, 960, 366, 526, 23927, 29899, 29890, 296, 373, 445, 1158, 29892, 306, 6907, 8626, 299, 29874, 2610, 29876, 538, 29915, 29879, 3143, 4432, 858, 9215, 383, 277, 29889, 306, 723, 1827, 393, 565, 366, 437, 864, 304, 437, 445, 1158, 769, 366, 437, 817, 304, 2125, 596, 2301, 1915, 12435, 322, 3509, 372, 11480, 5650, 29889, 887, 29915, 645, 817, 304, 437, 445, 565, 366, 864, 304, 1653, 409, 16958, 15038, 515, 372, 29892, 577, 306, 6907, 393, 366, 437, 393, 4331, 29889, 13, 3644, 366, 864, 304, 1653, 596, 1914, 409, 16958, 15038, 448, 607, 306, 1284, 304, 367, 263, 1568, 11558, 1158, 304, 1811, 304, 671, 372, 304, 6216, 916, 409, 16958, 15038, 448, 769, 306, 723, 6907, 278, 315, 4154, 29879, 29891, 770, 2038, 304, 2367, 366, 263, 21779, 310, 920, 445, 1736, 29889, 887, 1033, 1603, 671, 596, 13004, 625, 4004, 363, 1556, 310, 278, 25517, 297, 278, 770, 470, 2125, 278, 7014, 322, 3394, 963, 304, 596, 14216, 546, 29889 ]	1,332,841	2,048	C4	4	1
Q: Rails server panic: repeating GET requests I was doing something unrelated to coding (and in a different Safari windows), when out of nowhere i see the logs generating a bunch of GET requests. The beginning looks like this: Started GET "/" for ::1 at 2015-06-28 18:19:41 -0400 Processing by StaticPagesController#home as HTML Rendered static_pages/home.html.erb within layouts/application (0.3ms) Rendered layouts/_shim.html.erb (0.1ms) Rendered layouts/_header.html.erb (3.0ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 375ms (Views: 373.9ms \| ActiveRecord: 0.0ms) Started GET "/login" for ::1 at 2015-06-28 18:19:12 -0400 Processing by SessionsController#new as HTML Rendered sessions/new.html.erb within layouts/application (920.0ms) Rendered layouts/_shim.html.erb (0.1ms) Rendered layouts/_header.html.erb (101.4ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 1884ms (Views: 1883.2ms \| ActiveRecord: 0.0ms) [2015-06-28 18:19:14] ERROR Errno::ECONNRESET: Connection reset by peer /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/httpserver.rb:80:in `eof?' /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/httpserver.rb:80:in `run' /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/server.rb:295:in `block in start_thread' The first block then repeats again for n times until I stopped the server. The only anomaly is the following: Started GET "/" for ::1 at 2015-06-28 18:19:41 -0400 Processing by StaticPagesController#home as HTML Rendered static_pages/home.html.erb within layouts/application (0.3ms) Rendered layouts/_shim.html.erb (0.1ms) User Load (0.4ms) SELECT "users".* FROM "users" WHERE "users"."id" = ? LIMIT 1 [["id", 13]] Rendered layouts/_header.html.erb (4.5ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 237ms (Views: 235.3ms \| ActiveRecord: 0.4ms) ID:13 was the user_id i was working with. Any clue what might this be ? Looks suspicious. A: Does your app run any AJAX requests? Since this is on localhost, before assuming malice or hackery, I'd assume some rogue process related to your Rails server. In specific I'd make a checklist like the following: * Does my app have any Javascript that might be sending an AJAX request? Do the requests still occur when I disable all javascript? Do I have any gems installed which might be triggering an AJAX request? Do the requests occur when I don't have the site open in any browser? Do the requests occur regardless of which browser I have open? (perhaps some strange browser add-on is causing the requests) If I create a new empty / scaffolded Rails app, can I get the requests to occur on that one too? Do the requests occur when I don't have any browsers open? What other people / computers are on my network? Is	-1.613047	-1.167779	-1.139665	-0.524116	[ -1.7226211882199551, -1.5034731195801534 ]	[ -1.31640082111153, -1.0191564766141166 ]	[ -1.4516230534264445, -0.8277077611819142 ]	[ -0.7663685818823512, -0.2818633694202516 ]	1,024	[ 512, 512 ]	[ 660, 29901, 15144, 1923, 7243, 293, 29901, 28769, 12354, 7274, 306, 471, 2599, 1554, 443, 12817, 304, 14137, 313, 392, 297, 263, 1422, 24544, 5417, 511, 746, 714, 310, 1286, 4150, 474, 1074, 278, 10748, 14655, 263, 14928, 310, 12354, 7274, 29889, 450, 6763, 3430, 763, 445, 29901, 13, 4763, 287, 12354, 5591, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29946, 29896, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 624, 2454, 27514, 2956, 29937, 5184, 408, 4544, 13, 10716, 287, 2294, 29918, 12292, 29914, 5184, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29900, 29889, 29941, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29941, 29889, 29900, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29941, 29955, 29945, 1516, 313, 23825, 29901, 29871, 29941, 29955, 29941, 29889, 29929, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29900, 1516, 29897, 13, 13, 4763, 287, 12354, 5591, 7507, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29896, 29906, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 317, 10964, 2956, 29937, 1482, 408, 4544, 13, 26000, 287, 21396, 29914, 1482, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29929, 29906, 29900, 29889, 29900, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29896, 29900, 29896, 29889, 29946, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29896, 29947, 29947, 29946, 1516, 313, 23825, 29901, 29871, 29896, 29947, 29947, 29941, 29889, 29906, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29900, 1516, 29897, 13, 29961, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29896, 29946, 29962, 14431, 25361, 1217, 1057, 29923, 6007, 29940, 1525, 10490, 29901, 15160, 10092, 491, 23533, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 991, 261, 369, 29889, 6050, 29901, 29947, 29900, 29901, 262, 421, 29872, 974, 17901, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 991, 261, 369, 29889, 6050, 29901, 29947, 29900, 29901, 262, 421, 3389, 29915, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 2974, 29889, 6050, 29901, 29906, 29929, 29945, 29901, 262, 421, 1271, 297, 1369, 29918, 7097, 29915, 13, 13, 1576, 937, 2908, 769, 5565, 1446, 1449, 363, 302, 3064, 2745, 306, 11084, 278, 1923, 29889, 450, 871, 29342, 14997, 338, 278, 1494, 29901, 13, 4763, 287, 12354, 5591, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29946, 29896, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 624, 2454, 27514, 2956, 29937, 5184, 408, 4544, 13, 29871, 26000, 287, 2294, 29918, 12292, 29914, 5184, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29900, 29889, 29941, 1516, 29897, 13, 29871, 26000, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 29871, 4911, 16012, 313, 29900, 29889, 29946, 1516, 29897, 29871, 5097, 29871, 376, 7193, 1642, 29930, 3895, 376, 7193, 29908, 5754, 376, 7193, 29908, 1213, 333, 29908, 353, 1577, 27848, 29871, 29896, 29871, 518, 3366, 333, 613, 29871, 29896, 29941, 5262, 13, 29871, 26000, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29946, 29889, 29945, 1516, 29897, 13, 29871, 26000, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29906, 29941, 29955, 1516, 313, 23825, 29901, 29871, 29906, 29941, 29945, 29889, 29941, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29946, 1516, 29897, 13, 13, 1367, 29901, 29896, 29941, 471, 278, 1404, 29918, 333, 474, 471, 1985, 411, 29889, 13, 10773, 23960, 825, 1795, 445, 367, 1577, 19887, 8872, 14803, 29889, 13, 13, 29909, 29901, 5538, 596, 623, 1065, 738, 18891, 7274, 29973, 4001, 445, 338, 373, 15683, 29892, 1434, 10241, 4439, 625, 470, 15833, 708, 29892, 306, 29915, 29881, 5251, 777, 696, 13000, 1889, 4475, 304, 596, 15144, 1923, 29889, 512, 2702, 306, 29915, 29881, 1207, 263, 1423, 1761, 763, 278, 1494, 29901, 13, 13, 13, 29930, 13, 13, 29930, 25125, 590, 623, 505, 738, 12728, 393, 1795, 367, 9348, 385, 18891, 2009, 29973, 13, 13, 29930, 6132, 278, 7274, 1603, 6403, 746, 306, 11262, 599, 3513, 29973, 13, 13, 29930, 6132, 306, 505, 738, 330, 1567, 5130, 607, 1795, 367, 7135, 292, 385, 18891, 2009, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 746, 306, 1016, 29915, 29873, 505, 278, 3268, 1722, 297, 738, 4714, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 17126, 310, 607, 4714, 306, 505, 1722, 29973, 313, 546, 4252, 777, 8515, 4714, 788, 29899, 265, 338, 10805, 278, 7274, 29897, 13, 13, 29930, 3644, 306, 1653, 263, 716, 4069, 847, 885, 3470, 1025, 287, 15144, 623, 29892, 508, 306, 679, 278, 7274, 304, 6403, 373, 393, 697, 2086, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 746, 306, 1016, 29915, 29873, 505, 738, 14376, 1722, 29973, 13, 13, 29930, 5618, 916, 2305, 847, 23226, 526, 373, 590, 3564, 29973, 1317 ]	1,332,842	0	StackExchange	-1	-1
Need a Dumpster Rental in Rives Junction? We have the commercial and residential dumpster service you need in Rives Junction. At Royal Dumpster, we strive to bring you the best service at the best price available. We have a wide selection of dumpster sizes in stock in Rives Junction, MI, with flexible & timley pickup and delivery. Give us a call today for all your dumpster rental and roll off needs. Your roll-off dumpster in Rives Junction, MI is only a phone call away. Don't delay! Dumpsters are available* in Rives Junction. Most Rives Junction dumpster rental companies will take care of securing this permit for you if you rent from them. Make sure that if you're planning to put the dumpster on the street, the company has made the appropriate arrangements. You should also ensure that you get the permit in a timely manner and at the correct cost. If you thought the dumpster company was getting a permit and they did not, you will be the one who will have to pay the fine that is issued by the authorities. In the spring you may want to start school restorations that need to happen now. Increasingly more, schools are getting more and more jampacked. Additions are necessary as well as educational setting sizes created larger. In the course of spring break you possibly can have a contractor lined up to start your renovations. To acheive the restorations done swiftly you will need to find a person that the cost of rent next day dumpsters. Your contractors can readily do their work in addition to clean up subsequently with a dumpster right next to them. Make sure you cope with a company which includes dumpsters with wheels on the bottom. Your contractors can easily move the dumpster from one place to another whilst working. Dealing with these massive tons of junk on do it yourself would be a problem and requires lot of investment in terms of time and money. Your current painstaking research to find an inexpensive way of disposing the trash inside shortest moment possible could end up in 20 Yard Dumpster Rentals in Rives Junction, MI program. Dumpsters are usually easily obtainable in different your sizes in which range between 10 lawn and 45 yard. You need to be extra careful while picking out the size of dumpster simply because choosing the completely wrong sized dumpster aside from required will probably impose further charges as you have to go for multiple pickups to dispose your own trash when the dumpster is tiny in size. You'll be paying for the disposable space if you choose a dumpster that's large wide. A major cleanout might be stressful in addition to exhausting. Regardless of whether you're planning for an upcoming cross-country transfer to a smaller home, cleaning out a senior relative's home ahead of an real estate sale or perhaps foreclosure, or perhaps gut-renovating your office in addition to installing all-new fittings, all of the rubbish you pitch has to move somewhere. It is possible to divide the trash and rubbish up straight into small plenty and generate back and forth on the dump as well as the recycling center, wasting time, fuel, as well as. Or you can save the hassle by means of hiring a professional junk trucking team to perform the heavy lifting and discretion for you. Just what does a rubbish hauler do? All depends on the particular company, thus consider your requirements your budget before you make a hiring decision. Once you embark on an important cleaning, development, or remodelling project, not what you want to concern yourself with is getting rid of the producing debris. Executing it is hard plenty of. There's no reasons why you should be burdened with hand bags and lots of junk afterward. These may clutter your property, which regularly directly negates the intention of doing the work to begin with and can warrant special journeys to the remove or other discretion facility afterwards. Instead of dealing with your junk removal inside a piecemeal way, it could be worth your while to investigate renting a dumpster. While sporting a dumpster on your property may seem like a step backwards, this process simplifies your cleanup course of action. You can rent a new dumpster for as long as you'll need, you can put all your trash in addition to debris within it, and then you could get rid of all things in one fell swoop when you find yourself done. If you are doing a residence clean	-1.245974	-1.653039	-1.076893	-1.676198	[ -1.6459193641960246, -0.8460289136607484 ]	[ -1.653038994397757, -1.653038994397757 ]	[ -1.5074203559848984, -0.6463665278669389 ]	[ -1.9727540437846263, -1.3796416226229686 ]	1,024	[ 512, 512 ]	[ 20768, 263, 360, 3427, 2475, 390, 13703, 297, 390, 3145, 435, 651, 29973, 13, 4806, 505, 278, 12128, 322, 20201, 616, 16766, 2475, 2669, 366, 817, 297, 390, 3145, 435, 651, 29889, 13, 4178, 7021, 360, 3427, 2475, 29892, 591, 380, 4401, 304, 6963, 366, 278, 1900, 2669, 472, 278, 1900, 8666, 3625, 29889, 1334, 505, 263, 9377, 9262, 310, 16766, 2475, 15786, 297, 10961, 297, 390, 3145, 435, 651, 29892, 341, 29902, 29892, 411, 25706, 669, 5335, 2330, 5839, 786, 322, 28289, 29889, 25538, 502, 263, 1246, 9826, 363, 599, 596, 16766, 2475, 364, 13703, 322, 9679, 1283, 4225, 29889, 13, 10858, 9679, 29899, 2696, 16766, 2475, 297, 390, 3145, 435, 651, 29892, 341, 29902, 338, 871, 263, 9008, 1246, 3448, 29889, 3872, 29915, 29873, 9055, 29991, 13, 29928, 3427, 23080, 526, 3625, 29930, 297, 390, 3145, 435, 651, 29889, 13, 29924, 520, 390, 3145, 435, 651, 16766, 2475, 364, 13703, 14582, 674, 2125, 2562, 310, 409, 2764, 292, 445, 14257, 363, 366, 565, 366, 23990, 515, 963, 29889, 8561, 1854, 393, 565, 366, 29915, 276, 18987, 304, 1925, 278, 16766, 2475, 373, 278, 11952, 29892, 278, 5001, 756, 1754, 278, 8210, 15196, 4110, 29889, 887, 881, 884, 9801, 393, 366, 679, 278, 14257, 297, 263, 5335, 873, 8214, 322, 472, 278, 1959, 3438, 29889, 960, 366, 2714, 278, 16766, 2475, 5001, 471, 2805, 263, 14257, 322, 896, 1258, 451, 29892, 366, 674, 367, 278, 697, 1058, 674, 505, 304, 5146, 278, 2691, 393, 338, 16610, 491, 278, 21142, 29889, 13, 797, 278, 6709, 366, 1122, 864, 304, 1369, 3762, 1791, 272, 800, 393, 817, 304, 3799, 1286, 29889, 512, 1037, 5832, 368, 901, 29892, 12462, 526, 2805, 901, 322, 901, 432, 1160, 547, 287, 29889, 3462, 2187, 526, 5181, 408, 1532, 408, 28976, 4444, 15786, 2825, 7200, 29889, 512, 278, 3236, 310, 6709, 2867, 366, 10075, 508, 505, 263, 8078, 272, 301, 1312, 701, 304, 1369, 596, 25615, 800, 29889, 1763, 263, 1173, 573, 278, 1791, 272, 800, 2309, 12086, 368, 366, 674, 817, 304, 1284, 263, 2022, 393, 278, 3438, 310, 23990, 2446, 2462, 16766, 23080, 29889, 3575, 8078, 943, 508, 28520, 437, 1009, 664, 297, 6124, 304, 5941, 701, 17602, 411, 263, 16766, 2475, 1492, 2446, 304, 963, 29889, 8561, 1854, 366, 1302, 412, 411, 263, 5001, 607, 7805, 16766, 23080, 411, 21266, 1379, 373, 278, 5970, 29889, 3575, 8078, 943, 508, 5948, 4337, 278, 16766, 2475, 515, 697, 2058, 304, 1790, 21109, 1985, 29889, 13, 2772, 12818, 411, 1438, 20364, 23864, 310, 432, 2960, 373, 437, 372, 7535, 723, 367, 263, 1108, 322, 6858, 3287, 310, 13258, 358, 297, 4958, 310, 931, 322, 6909, 29889, 3575, 1857, 6788, 303, 5086, 5925, 304, 1284, 385, 297, 4548, 6270, 982, 310, 11549, 292, 278, 534, 1161, 2768, 3273, 342, 3256, 1950, 1033, 1095, 701, 297, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 29892, 341, 29902, 1824, 29889, 13, 29928, 3427, 23080, 526, 5491, 5948, 4017, 519, 297, 1422, 596, 15786, 297, 607, 3464, 1546, 29871, 29896, 29900, 425, 1233, 322, 29871, 29946, 29945, 29413, 29889, 887, 817, 304, 367, 4805, 16010, 1550, 5839, 292, 714, 278, 2159, 310, 16766, 2475, 3763, 1363, 23906, 278, 6446, 2743, 269, 1891, 16766, 2475, 17786, 515, 3734, 674, 3117, 2411, 852, 4340, 21090, 408, 366, 505, 304, 748, 363, 2999, 5839, 14340, 304, 27905, 596, 1914, 534, 1161, 746, 278, 16766, 2475, 338, 21577, 297, 2159, 29889, 887, 29915, 645, 367, 5146, 292, 363, 278, 11549, 519, 2913, 565, 366, 6755, 263, 16766, 2475, 393, 29915, 29879, 2919, 9377, 29889, 13, 29909, 4655, 5941, 449, 1795, 367, 22884, 1319, 297, 6124, 304, 27096, 292, 29889, 2169, 538, 2222, 310, 3692, 366, 29915, 276, 18987, 363, 385, 701, 11506, 4891, 29899, 13509, 6782, 304, 263, 7968, 3271, 29892, 5941, 292, 714, 263, 16336, 6198, 29915, 29879, 3271, 14432, 310, 385, 1855, 19989, 14686, 470, 6060, 29821, 5409, 545, 29892, 470, 6060, 22341, 29899, 1267, 586, 1218, 596, 8034, 297, 6124, 304, 15476, 599, 29899, 1482, 285, 986, 886, 29892, 599, 310, 278, 14051, 29890, 728, 366, 15905, 756, 304, 4337, 9051, 29889, 739, 338, 1950, 304, 16429, 278, 534, 1161, 322, 14051, 29890, 728, 701, 7812, 964, 2319, 20947, 322, 5706, 1250, 322, 11483, 373, 278, 16766, 408, 1532, 408, 278, 1162, 29891, 19914, 4818, 29892, 471, 1259, 931, 29892, 26413, 29892, 408, 1532, 408, 29889, 1394, 366, 508, 4078, 278, 298, 465, 280, 491, 2794, 310, 298, 8491, 263, 10257, 432, 2960, 534, 2707, 292, 3815, 304, 2189, 278, 9416, 11747, 1259, 322, 766, 4838, 291, 363, 366, 29889, 3387, 825, 947, 263, 14051, 29890, 728, 447, 8584, 437, 29973, 2178, 7111, 373, 278, 3153, 5001, 29892, 4550, 2050, 596, 11780, 596, 23562, 1434, 366, 1207, 263, 298, 8491, 10608, 29889, 13, 26222, 366, 7232, 935, 373, 385, 4100, 5941, 292, 29892, 5849, 29892, 470, 1083, 397, 7807, 2060, 29892, 451, 825, 366, 864, 304, 5932, 7535, 411, 338, 2805, 8177, 310, 278, 20811, 316, 1182, 275, 29889, 11080, 17068, 372, 338, 2898, 20947, 310, 29889, 1670, 29915, 29879, 694, 9590, 2020, 366, 881, 367, 6866, 1145, 287, 411, 1361, 289, 810, 322, 14568, 310, 432, 2960, 1156, 1328, 29889, 4525, 1122, 1067, 6463, 596, 2875, 29892, 607, 25704, 4153, 3480, 1078, 278, 16392, 310, 2599, 278, 664, 304, 3380, 411, 322, 508, 1370, 21867, 4266, 8694, 484, 952, 304, 278, 3349, 470, 916, 766, 4838, 291, 24454, 12335, 29889, 8669, 310, 16743, 411, 596, 432, 2960, 28744, 2768, 263, 5036, 29883, 2004, 284, 982, 29892, 372, 1033, 367, 7088, 596, 1550, 304, 23033, 23990, 292, 263, 16766, 2475, 29889, 5806, 7980, 292, 263, 16766, 2475, 373, 596, 2875, 1122, 2833, 763, 263, 4331, 28953, 29892, 445, 1889, 5466, 11057, 596, 5941, 786, 3236, 310, 3158, 29889, 887, 508, 23990, 263, 716, 16766, 2475, 363, 408, 1472, 408, 366, 29915, 645, 817, 29892, 366, 508, 1925, 599, 596, 534, 1161, 297, 6124, 304, 316, 1182, 275, 2629, 372, 29892, 322, 769, 366, 1033, 679, 8177, 310, 599, 2712, 297, 697, 8379, 16768, 459, 746, 366, 1284, 7535, 2309, 29889, 960, 366, 526, 2599, 263, 25488, 5941 ]	1,332,847	0	C4	0	3
-out, construction cleanup, or other redesigning or remodelling projects, renting a new dumpster can be a fantastic option. Dumpsters are workhorses in addition to aren't generally considered the celebs of the development or home renovation business. At the rear of every commercial business in the nation, there's normally a dumpster. These are generally under 15 yards, and the stars from the construction marketplace run 15, twenty, 30 or forty yards. How do you locate this sort of huge and incredibly heavy metal pack? By renting your own personal star dumpster from an online company - that's precisely how. Saving money in 20 Yard Dumpster Rentals in Rives Junctions is straightforward if you consider the above-mentioned tips. Simply by ensuring these pointers, you can easily obtain an affordable in addition to reliable services that can help you remove waste large quantities, without costing you a fortune. As soon as hiring a or maybe 20 Yard Dumpster Rentals in Rives Junction company to assistance with your property cleanout, look for someone who will address you having compassion in addition to care through what may be a difficult time. The speed and alleviate gained from professional property cleaning help will be made moot if the company's representatives tend to be pushy, rude or obnoxious, or disrespectful. Look at each company's Web site to see whether they listing estate cleaning as one of their particular specialties, or maybe call to speak to a customer services representative. The correct company can understand what you are heading through in addition to do whatever it takes to meet your needs. An alternative choice is to gather the bulk spend and carry it off with your car to any local disposal capability, one fill at a time. Many municipalities could accept this waste while others may not. Many may impose a fee for fingertips. Meanwhile, due to realize simply how much waste you've got until you try to fit all this in your auto. If you are a roofing contractor you know you will need to keep your roofer jobs moving. The time to top flies by with the moment you have thanks to the weather. Chances are you'll live in states that get passionate hot into the 90's in addition to 100's otherwise you may live in a state that possesses brutal winter months. With the times and thanks to time constraints, people are calling an individual left and right to acquire roof accomplished. Some of the consumer's roofs tend to be emergencies because they are leaking in addition to causing mould to form within the ceilings. You and your crew want to quickly give your customer an estimate. Once you increase the risk for time to evaluate the damage and exactly how much it will cost the customer to correct his or her top, you can warning the contract to practice it. When you start on a major cleaning, construction, or maybe renovation task, the last thing you need to worry about becomes rid of the particular resulting debris. Doing the work is challenging enough. There's no reason why you ought to be burdened having bags in addition to piles connected with trash later. These can clutter up your residence, which often right negates the purpose of working on the project in the first place and will necessitate specific trips to the particular dump or other disposal capability after the fact. Instead of tackling your own trash elimination in a piecemeal technique, it may be beneficial to look into hiring a dumpster. While wearing a dumpster on the property might appear to be a step back, it actually shortens the clean-up process. It is possible to rent a dumpster so long as you need, place all of your junk and debris in it, and you can get rid of everything in just one fell jump when you're accomplished. If you're carrying out a home clean-out, development cleaning, or other home improvement or maybe renovation tasks, renting a dumpster can be a great option. The idea of using a substantial bag to be able to load up and haul absent heavy junk items may seem like it could not work, but the Big Bag's layout is an clever fusion involving form and function that makes it a superb garbage removing choice. When you really need to get rid of plenty of trash, you can contact a crap remover that offers bag program, purchase a reusable Big Bag, and set this anywhere on your property. Then, you can get on with what ever work you should do. You can stock up the Big Bag with what you need to	-0.906295	-1.438164	-0.847998	-1.496703	[ -0.9172520359686839, -0.8953372291047038 ]	[ -1.2949132781358133, -1.5814138511453681 ]	[ -0.8124903150296086, -0.8835050637403682 ]	[ -1.5357238387181418, -1.4576827306705553 ]	1,024	[ 512, 512 ]	[ 29899, 449, 29892, 7632, 5941, 786, 29892, 470, 916, 2654, 267, 647, 292, 470, 1083, 397, 7807, 9279, 29892, 23990, 292, 263, 716, 16766, 2475, 508, 367, 263, 13568, 6288, 2984, 29889, 13, 29928, 3427, 23080, 526, 664, 29882, 943, 267, 297, 6124, 304, 9455, 29915, 29873, 6892, 5545, 278, 7793, 5824, 310, 278, 5849, 470, 3271, 25615, 362, 5381, 29889, 2180, 278, 18983, 310, 1432, 12128, 5381, 297, 278, 5233, 29892, 727, 29915, 29879, 12891, 263, 16766, 2475, 29889, 4525, 526, 6892, 1090, 29871, 29896, 29945, 17454, 29892, 322, 278, 10819, 515, 278, 7632, 9999, 6689, 1065, 29871, 29896, 29945, 29892, 10081, 29892, 29871, 29941, 29900, 470, 20949, 17454, 29889, 1128, 437, 366, 26694, 445, 2656, 310, 12176, 322, 29811, 14981, 9416, 11915, 4870, 29973, 2648, 23990, 292, 596, 1914, 7333, 5810, 16766, 2475, 515, 385, 7395, 5001, 448, 393, 29915, 29879, 17503, 920, 29889, 13, 29903, 5555, 6909, 297, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 29879, 338, 20837, 565, 366, 2050, 278, 2038, 29899, 358, 28487, 25562, 29889, 3439, 17632, 491, 5662, 3864, 1438, 12589, 29892, 366, 508, 5948, 4017, 385, 21750, 519, 297, 6124, 304, 23279, 5786, 393, 508, 1371, 366, 3349, 19863, 2919, 26855, 29892, 1728, 3438, 292, 366, 263, 19717, 29889, 13, 2887, 4720, 408, 298, 8491, 263, 470, 5505, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 5001, 304, 18872, 411, 596, 2875, 5941, 449, 29892, 1106, 363, 4856, 1058, 674, 3211, 366, 2534, 752, 465, 291, 297, 6124, 304, 2562, 1549, 825, 1122, 367, 263, 5189, 931, 29889, 450, 6210, 322, 4788, 1403, 403, 17515, 515, 10257, 2875, 5941, 292, 1371, 674, 367, 1754, 2730, 327, 565, 278, 5001, 29915, 29879, 2755, 5056, 10331, 304, 367, 5503, 29891, 29892, 364, 1151, 470, 704, 1217, 29916, 2738, 29892, 470, 766, 690, 1103, 1319, 29889, 7419, 472, 1269, 5001, 29915, 29879, 2563, 3268, 304, 1074, 3692, 896, 18028, 19989, 5941, 292, 408, 697, 310, 1009, 3153, 4266, 2938, 29892, 470, 5505, 1246, 304, 7726, 304, 263, 11962, 5786, 21097, 29889, 450, 1959, 5001, 508, 2274, 825, 366, 526, 28435, 1549, 297, 6124, 304, 437, 6514, 372, 4893, 304, 5870, 596, 4225, 29889, 13, 2744, 8671, 7348, 338, 304, 11705, 278, 21610, 18864, 322, 8677, 372, 1283, 411, 596, 1559, 304, 738, 1887, 11549, 284, 2117, 3097, 29892, 697, 5445, 472, 263, 931, 29889, 9267, 11677, 1907, 1033, 3544, 445, 19863, 1550, 4045, 1122, 451, 29889, 9267, 1122, 2411, 852, 263, 27684, 363, 285, 292, 814, 4512, 29889, 25065, 29892, 2861, 304, 16289, 3763, 920, 1568, 19863, 366, 29915, 345, 2355, 2745, 366, 1018, 304, 6216, 599, 445, 297, 596, 4469, 29889, 13, 3644, 366, 526, 263, 17526, 292, 8078, 272, 366, 1073, 366, 674, 817, 304, 3013, 596, 696, 29877, 571, 17643, 8401, 29889, 450, 931, 304, 2246, 285, 3687, 491, 411, 278, 3256, 366, 505, 3969, 304, 278, 14826, 29889, 678, 2925, 526, 366, 29915, 645, 5735, 297, 5922, 393, 679, 15935, 403, 7375, 964, 278, 29871, 29929, 29900, 29915, 29879, 297, 6124, 304, 29871, 29896, 29900, 29900, 29915, 29879, 6467, 366, 1122, 5735, 297, 263, 2106, 393, 3119, 15322, 26644, 284, 13851, 7378, 29889, 2973, 278, 3064, 322, 3969, 304, 931, 11938, 29892, 2305, 526, 5432, 385, 5375, 2175, 322, 1492, 304, 1274, 1548, 17526, 24799, 29889, 3834, 310, 278, 21691, 29915, 29879, 17526, 29879, 10331, 304, 367, 11176, 1885, 2478, 1363, 896, 526, 454, 5086, 297, 6124, 304, 10805, 286, 483, 304, 883, 2629, 278, 2257, 309, 886, 29889, 887, 322, 596, 17616, 864, 304, 9098, 2367, 596, 11962, 385, 12678, 29889, 9038, 366, 7910, 278, 12045, 363, 931, 304, 14707, 278, 18658, 322, 3721, 920, 1568, 372, 674, 3438, 278, 11962, 304, 1959, 670, 470, 902, 2246, 29892, 366, 508, 9177, 278, 8078, 304, 6944, 372, 29889, 13, 10401, 366, 1369, 373, 263, 4655, 5941, 292, 29892, 7632, 29892, 470, 5505, 25615, 362, 3414, 29892, 278, 1833, 2655, 366, 817, 304, 15982, 1048, 7415, 8177, 310, 278, 3153, 9819, 316, 1182, 275, 29889, 1938, 292, 278, 664, 338, 18066, 292, 3307, 29889, 1670, 29915, 29879, 694, 2769, 2020, 366, 12722, 304, 367, 6866, 1145, 287, 2534, 289, 810, 297, 6124, 304, 282, 5475, 6631, 411, 534, 1161, 2678, 29889, 4525, 508, 1067, 6463, 701, 596, 25488, 29892, 607, 4049, 1492, 3480, 1078, 278, 6437, 310, 1985, 373, 278, 2060, 297, 278, 937, 2058, 322, 674, 3520, 10388, 2702, 3367, 567, 304, 278, 3153, 16766, 470, 916, 11549, 284, 2117, 3097, 1156, 278, 2114, 29889, 8669, 310, 22002, 1847, 596, 1914, 534, 1161, 29007, 3381, 297, 263, 5036, 29883, 2004, 284, 11043, 29892, 372, 1122, 367, 7795, 5611, 304, 1106, 964, 298, 8491, 263, 16766, 2475, 29889, 5806, 591, 4362, 263, 16766, 2475, 373, 278, 2875, 1795, 2615, 304, 367, 263, 4331, 1250, 29892, 372, 2869, 3273, 575, 278, 5941, 29899, 786, 1889, 29889, 739, 338, 1950, 304, 23990, 263, 16766, 2475, 577, 1472, 408, 366, 817, 29892, 2058, 599, 310, 596, 432, 2960, 322, 316, 1182, 275, 297, 372, 29892, 322, 366, 508, 679, 8177, 310, 4129, 297, 925, 697, 8379, 12500, 746, 366, 29915, 276, 24799, 29889, 960, 366, 29915, 276, 19436, 714, 263, 3271, 5941, 29899, 449, 29892, 5849, 5941, 292, 29892, 470, 916, 3271, 20414, 470, 5505, 25615, 362, 9595, 29892, 23990, 292, 263, 16766, 2475, 508, 367, 263, 2107, 2984, 29889, 13, 1576, 2969, 310, 773, 263, 23228, 19548, 304, 367, 2221, 304, 2254, 701, 322, 447, 352, 29207, 9416, 432, 2960, 4452, 1122, 2833, 763, 372, 1033, 451, 664, 29892, 541, 278, 7997, 18341, 29915, 29879, 5912, 338, 385, 23455, 21736, 21677, 883, 322, 740, 393, 3732, 372, 263, 2428, 29890, 25861, 11077, 7348, 29889, 1932, 366, 2289, 817, 304, 679, 8177, 310, 20947, 310, 534, 1161, 29892, 366, 508, 6958, 263, 274, 2390, 1083, 957, 393, 16688, 19548, 1824, 29892, 20590, 263, 337, 27979, 7997, 18341, 29892, 322, 731, 445, 12214, 373, 596, 2875, 29889, 1987, 29892, 366, 508, 679, 373, 411, 825, 3926, 664, 366, 881, 437, 29889, 887, 508, 10961, 701, 278, 7997, 18341, 411, 825, 366, 817, 304 ]	1,332,847	1,024	C4	15	4
President Trump and Joe Biden Offer Study in Contrasts in Dueling Town Halls President Trump and Joe Biden offered starkly different visions for the country and a sharp contrast in leadership styles on Thursday as the presidential contenders took part in dueling town halls on NBC and ABC. NBC's hourlong event with Trump drew strong criticism from the entertainment industry and many others who saw it as a way of indulging Trump, who pulled out of a planned second presidential debate with his Democratic opponent. NBC was urged to move its event out of the 8 p.m. hour so as not to conflict with ABC's 90-minute session with Biden, which was announced first after Trump dropped out of the debate. "Today" anchor Savannah Guthrie sparred aggressively with Trump throughout the one-hour event. She set the tone early, asking him to disavow white supremacy and QAnon, the online conspiracy theory about a pedophile cult. Trump said he knew little about it, though he had heard they were "strongly against pedophilia." "I agree with that," he said. When she followed up, asking him to say there was no pedophile cult, he declined. "I don't know that," Trump said. "Neither do you know that. Why aren't you asking me about antifa?" Guthrie appeared ready for a fight. "You're not like someone's crazy uncle that can just retweet whatever," she said at one point. Guthrie also grilled Trump about his tax returns, asking if it was true — as the New York Times reported — that he paid only $750 a year. He said the figure was a "statutory number — a filing fee." "If they have my tax returns, they have to go to jail," Trump said. "It's illegal." Meanwhile on ABC, chief anchor George Stephanopoulos pressed Biden about whether Democrats will seek to add justices to the Supreme Court, assuming that conservatives take a 6-3 advantage with the confirmation of Judge Amy Coney Barrett. Biden declined to answer directly, but said he would offer "a clear position before Election Day pending on how they handle this." Biden said he wants to keep the focus on the inappropriate nature of Barrett's confirmation process, and that if he were to declare his position one way or another now, "that's the headline." He also advised viewers: "Presidents come and go. Justices stay and stay and stay." Speaking at Philadelphia's National Constitution Center, Biden fielded questions about racial justice, income inequality, infrastructure and police reform. His avuncular delivery and ease in discussing the nitty-gritty details of policy stood in sharp contrast to the more belligerent tone over on NBC. Biden offered some personal asides, such as his oft-repeated line that when he was a kid growing up in Clermont, Penn., most men "either became a cop, a firefighter or a priest. I wasn't qualified to do any of them." He made a point of asking each questioner whether he had sufficiently answered the query. He also castigated Trump's leadership during the pandemic. "The president has a responsibility to lead and he didn't do that," Biden said. "He didn't talk about what needed to be done. He kept worrying, in my view, about the (stock) market." On NBC, Trump bristled as Guthrie pressed hard on his administration's response to the virus. "I knew you'd be doing this," he said. "I know you very well." Biden made a strong statement about protecting LGBTQ rights, and he promised to end policies enacted by Trump that curb the rights of transgender people. He noted with dismay the recent rash of murders of transgender women of color. About 60 voters, all wearing masks, attended the event at the Pérez Art Museum in Miami. Several got to ask questions, many of which were quite pointed. One questioner complimented Trump on his smile, and then asked why he was trying to do away with DACA, the program that shields immigrant children from deportation. Trump responded that the pandemic had led to a clampdown on immigration. As for the third presidential debate, scheduled for Oct. 22, Biden said, "I expect to	0.445575	-0.320364	-0.071908	-0.339094	[ 0.27984428897623276, 0.6113057427939328 ]	[ -0.3396129300070784, -0.30111441550891943 ]	[ -0.1961837458612312, 0.052367874626427176 ]	[ -0.3481983112607001, -0.32998871938292995 ]	1,024	[ 512, 512 ]	[ 7178, 27504, 322, 11131, 350, 3615, 4587, 571, 29301, 297, 1281, 509, 19416, 297, 360, 2491, 292, 8421, 379, 4293, 13, 13504, 1693, 27504, 322, 11131, 350, 3615, 12520, 18561, 368, 1422, 1998, 1080, 363, 278, 4234, 322, 263, 15301, 12814, 297, 26001, 11949, 373, 498, 1295, 3250, 408, 278, 6673, 616, 640, 21043, 3614, 760, 297, 868, 14067, 4726, 298, 4293, 373, 405, 5371, 322, 16417, 29889, 13, 29940, 5371, 29915, 29879, 7234, 5426, 1741, 411, 27504, 15010, 4549, 29035, 515, 278, 22684, 358, 13661, 322, 1784, 4045, 1058, 4446, 372, 408, 263, 982, 310, 29156, 3460, 27504, 29892, 1058, 20043, 714, 310, 263, 20458, 1473, 6673, 616, 27836, 411, 670, 19083, 23995, 296, 29889, 405, 5371, 471, 5065, 3192, 304, 4337, 967, 1741, 714, 310, 278, 29871, 29947, 282, 29889, 29885, 29889, 7234, 577, 408, 451, 304, 14529, 411, 16417, 29915, 29879, 29871, 29929, 29900, 29899, 1195, 1082, 4867, 411, 350, 3615, 29892, 607, 471, 9326, 937, 1156, 27504, 13700, 714, 310, 278, 27836, 29889, 13, 29908, 29911, 397, 388, 29908, 17360, 9583, 812, 801, 24032, 1092, 347, 805, 279, 1127, 946, 3663, 3598, 411, 27504, 10106, 278, 697, 29899, 18721, 1741, 29889, 2296, 731, 278, 16225, 4688, 29892, 6721, 1075, 304, 766, 485, 340, 4796, 22747, 29885, 4135, 322, 660, 2744, 265, 29892, 278, 7395, 21588, 29875, 10068, 6368, 1048, 263, 8939, 3021, 488, 4185, 29889, 13, 2308, 3427, 1497, 540, 6363, 2217, 1048, 372, 29892, 2466, 540, 750, 6091, 896, 892, 376, 1110, 368, 2750, 8939, 3021, 11836, 1213, 13, 29908, 29902, 8661, 411, 393, 1699, 540, 1497, 29889, 13, 10401, 1183, 5643, 701, 29892, 6721, 1075, 304, 1827, 727, 471, 694, 8939, 3021, 488, 4185, 29892, 540, 4845, 1312, 29889, 13, 29908, 29902, 1016, 29915, 29873, 1073, 393, 1699, 27504, 1497, 29889, 376, 8139, 2121, 437, 366, 1073, 393, 29889, 3750, 9455, 29915, 29873, 366, 6721, 592, 1048, 3677, 26056, 3026, 13, 29954, 329, 1092, 347, 7470, 7960, 363, 263, 8589, 29889, 376, 3492, 29915, 276, 451, 763, 4856, 29915, 29879, 12220, 1537, 22169, 393, 508, 925, 3240, 16668, 6514, 1699, 1183, 1497, 472, 697, 1298, 29889, 13, 29954, 329, 1092, 347, 884, 867, 24455, 27504, 1048, 670, 8818, 3639, 29892, 6721, 565, 372, 471, 1565, 813, 408, 278, 1570, 3088, 10277, 8967, 813, 393, 540, 12530, 871, 395, 29955, 29945, 29900, 263, 1629, 29889, 940, 1497, 278, 4377, 471, 263, 376, 6112, 329, 706, 1353, 813, 263, 977, 292, 27684, 1213, 13, 29908, 3644, 896, 505, 590, 8818, 3639, 29892, 896, 505, 304, 748, 304, 432, 737, 1699, 27504, 1497, 29889, 376, 3112, 29915, 29879, 27302, 1213, 13, 6816, 273, 8000, 373, 16417, 29892, 9087, 17360, 5122, 2443, 16711, 459, 5059, 359, 15385, 350, 3615, 1048, 3692, 14189, 1446, 674, 16508, 304, 788, 925, 1575, 304, 278, 22569, 9245, 29892, 10241, 393, 8976, 5056, 2125, 263, 29871, 29953, 29899, 29941, 10631, 411, 278, 9659, 362, 310, 26817, 28533, 315, 4992, 2261, 13158, 29889, 13, 29933, 3615, 4845, 1312, 304, 1234, 4153, 29892, 541, 1497, 540, 723, 5957, 376, 29874, 2821, 2602, 1434, 382, 1464, 8373, 28235, 373, 920, 896, 4386, 445, 1213, 13, 29933, 3615, 1497, 540, 10753, 304, 3013, 278, 8569, 373, 278, 297, 932, 6649, 403, 5469, 310, 2261, 13158, 29915, 29879, 9659, 362, 1889, 29892, 322, 393, 565, 540, 892, 304, 9607, 670, 2602, 697, 982, 470, 1790, 1286, 29892, 376, 5747, 29915, 29879, 278, 2343, 1220, 1213, 13, 3868, 884, 594, 11292, 1776, 414, 29901, 376, 13504, 16719, 2041, 322, 748, 29889, 3387, 1575, 7952, 322, 7952, 322, 7952, 1213, 13, 10649, 5086, 472, 18292, 29915, 29879, 3086, 20063, 7817, 29892, 350, 3615, 1746, 287, 5155, 1048, 1153, 1455, 15426, 29892, 17869, 14585, 29892, 22035, 12425, 322, 10974, 11736, 29889, 3600, 1029, 4661, 1070, 28289, 322, 16326, 297, 5353, 292, 278, 302, 986, 29891, 29899, 629, 986, 29891, 4902, 310, 8898, 8389, 297, 15301, 12814, 304, 278, 901, 22623, 4087, 296, 16225, 975, 373, 405, 5371, 29889, 13, 29933, 3615, 12520, 777, 7333, 408, 2247, 29892, 1316, 408, 670, 18941, 29899, 276, 412, 630, 1196, 393, 746, 540, 471, 263, 26397, 15678, 701, 297, 2233, 837, 609, 29892, 349, 2108, 1696, 1556, 1757, 376, 29872, 2121, 3897, 263, 5614, 29892, 263, 3974, 1003, 29882, 357, 470, 263, 18781, 29889, 306, 9007, 29915, 29873, 18698, 304, 437, 738, 310, 963, 1213, 940, 1754, 263, 1298, 310, 6721, 1269, 1139, 261, 3692, 540, 750, 18430, 7699, 278, 2346, 29889, 13, 3868, 884, 4320, 335, 630, 27504, 29915, 29879, 26001, 2645, 278, 7243, 24552, 29889, 13, 29908, 1576, 6673, 756, 263, 23134, 304, 3275, 322, 540, 3282, 29915, 29873, 437, 393, 1699, 350, 3615, 1497, 29889, 376, 3868, 3282, 29915, 29873, 5193, 1048, 825, 4312, 304, 367, 2309, 29889, 940, 8126, 15982, 292, 29892, 297, 590, 1776, 29892, 1048, 278, 313, 17712, 29897, 9999, 1213, 13, 2951, 405, 5371, 29892, 27504, 1506, 391, 839, 408, 24032, 1092, 347, 15385, 2898, 373, 670, 17517, 29915, 29879, 2933, 304, 278, 24424, 29889, 13, 29908, 29902, 6363, 366, 29915, 29881, 367, 2599, 445, 1699, 540, 1497, 29889, 376, 29902, 1073, 366, 1407, 1532, 1213, 13, 29933, 3615, 1754, 263, 4549, 3229, 1048, 12566, 292, 365, 7210, 29911, 29984, 10462, 29892, 322, 540, 22399, 304, 1095, 24833, 427, 627, 287, 491, 27504, 393, 3151, 29890, 278, 10462, 310, 1301, 26098, 2305, 29889, 940, 11682, 411, 766, 13029, 278, 7786, 364, 1161, 310, 7167, 8623, 310, 1301, 26098, 5866, 310, 2927, 29889, 13, 28173, 29871, 29953, 29900, 9014, 414, 29892, 599, 591, 4362, 11105, 29879, 29892, 14283, 278, 1741, 472, 278, 28098, 3012, 6838, 297, 23740, 29889, 21882, 2355, 304, 2244, 5155, 29892, 1784, 310, 607, 892, 3755, 11520, 29889, 3118, 1139, 261, 13162, 2073, 287, 27504, 373, 670, 17819, 29892, 322, 769, 4433, 2020, 540, 471, 1811, 304, 437, 3448, 411, 360, 2477, 29909, 29892, 278, 1824, 393, 28761, 29879, 5198, 4481, 424, 4344, 515, 21455, 362, 29889, 27504, 10049, 287, 393, 278, 7243, 24552, 750, 5331, 304, 263, 1067, 1160, 3204, 373, 5198, 16783, 29889, 13, 2887, 363, 278, 4654, 6673, 616, 27836, 29892, 21467, 363, 4756, 29889, 29871, 29906, 29906, 29892, 350, 3615, 1497, 29892, 376, 29902, 2149, 304 ]	1,332,853	0	CommonCrawl	18	15
COLLECTION: Recent Obituaries in the Kenosha News (July 1-9, 2020) alert top story web only Here are the obituaries published online and in the print product of the Kenosha News between July 1 and July 9, 2020. Edmund F. Kretschmer Edmund F. Kretschmer, 92, of Wheatland, passed away Monday, July 6, 2020 at his home. Born in New Munster, Wisconsin on June 5, 1928, he was the son of John and Anna "Louise" (nee Epping) Kretschmer. His early life was spent in New Munster, where he attended St. Alphonsus Catholic School. He served in the U.S. Army during the Korean War. On June 30, 1956, he was united in marriage to Louise Gedemer. Following marriage, they made Burlington their home. Louise preceded him in death on April 12, 1994. Edmund worked for Lois Feedmill before working as a loader operator for and retiring from the Kenosha County Highway Department after over 30 years of service. He was a member of St. Alphonsus Catholic Church and treasurer for Catholic Order of Foresters for many years. He was a member of the VFW in Burlington and a volunteer firefighter for Wheatland. He was a hard worker who enjoyed gardening vegetables, lawn cutting and playing cards. Ed is survived by his children, Daniel (Elizabeth) Kretschmer, Ronald (Sandra) Kretschmer, Theresa (Dennis) Clapp, Kenneth (Johanna) Kretschmer, Susan (Tony) Pink and Judith (Kevin) Meyers; grandchildren, David Kretschmer, Matthew Kretschmer, Samantha Kretschmer, Ashley Kretschmer, Jessica (Chad) Birkholz, Kristina (Marc) Paprzyca, Gabrielle Clapp, Kristin (Daniel) Stroening, Brian Kretschmer, Adam Pink, Steven Pink, Lindsey Pink, Jordan Meyers, MacKenzie Meyers and Zachary Meyers; great-grandchildren, Emma Paprzyca, Audrey Paprzyca, Josephine Birkholz, Dylan Birkholz and Madison Stroening; sister, Armella Rossmiller; sister-in-laws, Eleanor Maller and Barbara Gedemer; along with many nieces, nephews, other relatives and friends. He was preceded in death by his parents; wife; infant son, Thomas; siblings, Joseph (Veronica) Kretschmer, Arthur Kretschmer, Father Albert Kretschmer, Henry Kretschmer, Agnes (Clem) Kerkman, Mary (Harold) Richter, Sister Martha Kretschmer and Rose Kretschmer; and brother-in-law, Harold Rossmiller. In lieu of flowers, memorial contributions may be made to St. Alphonsus Church or the Wheatland Fire Department. Visitation for Edmund will be held on Monday, July 13, 2020 from 4 until 7PM at Schuette-Daniels Funeral Home. Services will be held on Tuesday, July 14, 2020 at 11AM at St. Alphonsus Catholic Church with burial to follow at St. Alphonsus Cemetery. Schuette-Daniels Funeral Home & Crematory 625 S. Browns Lake Drive Burlington, WI 53105 www.danielsfamilyfuneral.com Renee Ann Galster Renee Ann Galster, 67, of Pleasant Prairie, passed away on Saturday, July 4, 2020, at Froedtert Hospital—Wauwatosa. Visitation will take place on Monday, July 13th, at Proko Funeral Home, from 5:00 p.m. until the time of service at 7:00 p.m. Interment will take place privately at St. George Cemetery at a later date. A full obituary will be published in Sunday's paper. Proko Funeral Home & Crematory 5111-60th Street Kenosha, WI 5	-0.466629	-1.059446	-1.494739	-1.840084	[ -0.45978044268309787, -0.4734771969730855 ]	[ -0.6449151031203854, -1.4739761362667851 ]	[ -1.1472741303803322, -1.8422041713356219 ]	[ -1.8843074546640282, -1.7958608655434303 ]	1,024	[ 512, 512 ]	[ 23958, 3281, 2725, 29901, 3599, 296, 4250, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 11850, 29871, 29896, 29899, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 12888, 2246, 5828, 1856, 871, 13, 10605, 526, 278, 704, 1981, 4314, 6369, 7395, 322, 297, 278, 1596, 3234, 310, 278, 10015, 359, 2350, 10130, 1546, 5468, 29871, 29896, 322, 5468, 29871, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 3853, 15282, 383, 29889, 476, 2267, 816, 1050, 13, 3853, 15282, 383, 29889, 476, 2267, 816, 1050, 29892, 29871, 29929, 29906, 29892, 310, 26286, 271, 1049, 29892, 4502, 3448, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 1570, 13564, 2475, 29892, 22581, 373, 5306, 29871, 29945, 29892, 29871, 29896, 29929, 29906, 29947, 29892, 540, 471, 278, 1487, 310, 2259, 322, 11230, 376, 20555, 895, 29908, 313, 484, 29872, 382, 3262, 29897, 476, 2267, 816, 1050, 29889, 3600, 4688, 2834, 471, 10398, 297, 1570, 13564, 2475, 29892, 988, 540, 14283, 624, 29889, 838, 561, 787, 375, 11865, 4523, 29889, 940, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 2645, 278, 22467, 3362, 29889, 1551, 5306, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29945, 29953, 29892, 540, 471, 443, 1573, 297, 13718, 304, 24417, 16836, 25154, 29889, 12206, 13718, 29892, 896, 1754, 6640, 1847, 880, 1009, 3271, 29889, 24417, 9399, 287, 1075, 297, 4892, 373, 3786, 29871, 29896, 29906, 29892, 29871, 29896, 29929, 29929, 29946, 29889, 13, 3853, 15282, 3796, 363, 4309, 275, 5169, 287, 19958, 1434, 1985, 408, 263, 23466, 5455, 363, 322, 3240, 8491, 515, 278, 10015, 359, 2350, 5127, 22080, 10317, 1156, 975, 29871, 29941, 29900, 2440, 310, 2669, 29889, 940, 471, 263, 4509, 310, 624, 29889, 838, 561, 787, 375, 11865, 6291, 322, 2578, 294, 9945, 363, 11865, 8170, 310, 17300, 414, 363, 1784, 2440, 29889, 940, 471, 263, 4509, 310, 278, 478, 29943, 29956, 297, 6640, 1847, 880, 322, 263, 27886, 261, 3974, 1003, 29882, 357, 363, 26286, 271, 1049, 29889, 940, 471, 263, 2898, 15645, 1058, 27849, 16423, 292, 18655, 1849, 29892, 425, 1233, 28967, 322, 8743, 15889, 29889, 13, 3853, 338, 10503, 2347, 491, 670, 4344, 29892, 8432, 313, 6489, 466, 9394, 29897, 476, 2267, 816, 1050, 29892, 11546, 2741, 313, 29903, 10738, 29897, 476, 2267, 816, 1050, 29892, 25451, 8625, 313, 29928, 9517, 29897, 6015, 407, 29892, 28576, 313, 29967, 1148, 9713, 29897, 476, 2267, 816, 1050, 29892, 25914, 313, 29911, 2592, 29897, 349, 682, 322, 8660, 389, 313, 9598, 3845, 29897, 18154, 414, 29936, 4595, 11991, 29892, 4699, 476, 2267, 816, 1050, 29892, 22292, 476, 2267, 816, 1050, 29892, 3685, 9716, 29874, 476, 2267, 816, 1050, 29892, 12835, 2330, 476, 2267, 816, 1050, 29892, 23010, 983, 313, 1451, 328, 29897, 350, 6793, 5391, 29920, 29892, 17773, 1099, 313, 29924, 5666, 29897, 8579, 29878, 1537, 1113, 29892, 9899, 374, 1808, 6015, 407, 29892, 17773, 262, 313, 29866, 29897, 624, 307, 8333, 29892, 15733, 476, 2267, 816, 1050, 29892, 11783, 349, 682, 29892, 24703, 349, 682, 29892, 17277, 7759, 349, 682, 29892, 18284, 18154, 414, 29892, 4326, 29968, 264, 3914, 18154, 414, 322, 29103, 653, 18154, 414, 29936, 2107, 29899, 27857, 11991, 29892, 26422, 8579, 29878, 1537, 1113, 29892, 8612, 8903, 8579, 29878, 1537, 1113, 29892, 6936, 457, 350, 6793, 5391, 29920, 29892, 360, 2904, 273, 350, 6793, 5391, 29920, 322, 4104, 2285, 624, 307, 8333, 29936, 9883, 29892, 8481, 3547, 13693, 29885, 5495, 29936, 9883, 29899, 262, 29899, 433, 5652, 29892, 8317, 273, 272, 341, 12572, 322, 18506, 16836, 25154, 29936, 3412, 411, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 916, 14576, 322, 7875, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29936, 6532, 29936, 28056, 1487, 29892, 5569, 29936, 27767, 18964, 29892, 6936, 313, 6565, 26082, 29897, 476, 2267, 816, 1050, 29892, 11498, 476, 2267, 816, 1050, 29892, 17852, 10537, 476, 2267, 816, 1050, 29892, 6498, 476, 2267, 816, 1050, 29892, 4059, 4515, 313, 29907, 2409, 29897, 476, 5968, 1171, 29892, 6182, 313, 21972, 1025, 29897, 4385, 357, 29892, 28088, 1085, 15457, 476, 2267, 816, 1050, 322, 14008, 476, 2267, 816, 1050, 29936, 322, 8099, 29899, 262, 29899, 10653, 29892, 25422, 13693, 29885, 5495, 29889, 13, 797, 13003, 310, 18281, 29892, 2626, 9020, 20706, 1122, 367, 1754, 304, 624, 29889, 838, 561, 787, 375, 6291, 470, 278, 26286, 271, 1049, 6438, 10317, 29889, 13, 6116, 7018, 363, 28925, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29896, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29946, 2745, 29871, 29955, 13427, 472, 1102, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 29889, 15538, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29896, 5194, 472, 624, 29889, 838, 561, 787, 375, 11865, 6291, 411, 6866, 616, 304, 1101, 472, 624, 29889, 838, 561, 787, 375, 315, 22875, 29889, 13, 4504, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 669, 315, 1745, 7606, 13, 29953, 29906, 29945, 317, 29889, 22415, 1983, 9459, 22850, 13, 29933, 332, 1847, 880, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29900, 29945, 13, 1636, 29889, 18386, 709, 4668, 1344, 29891, 7692, 13537, 29889, 510, 13, 29934, 1600, 29872, 8081, 5208, 2475, 13, 29934, 1600, 29872, 8081, 5208, 2475, 29892, 29871, 29953, 29955, 29892, 310, 19777, 13186, 9002, 24135, 29892, 4502, 3448, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 25022, 287, 357, 29873, 15967, 30003, 29956, 585, 29893, 271, 3628, 29889, 13, 6116, 7018, 674, 2125, 2058, 373, 27822, 29892, 5468, 29871, 29896, 29941, 386, 29892, 472, 1019, 2901, 13811, 13537, 8778, 29892, 515, 29871, 29945, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 278, 931, 310, 2669, 472, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 4124, 358, 674, 2125, 2058, 5999, 2486, 472, 624, 29889, 5122, 315, 22875, 472, 263, 2678, 2635, 29889, 319, 2989, 704, 1981, 653, 674, 367, 6369, 297, 16340, 29915, 29879, 5650, 29889, 13, 1184, 2901, 13811, 13537, 8778, 669, 315, 1745, 7606, 13, 29945, 29896, 29896, 29896, 29899, 29953, 29900, 386, 7103, 13, 29968, 264, 359, 2350, 29892, 399, 29902, 29871, 29945 ]	1,332,858	0	CommonCrawl	0	3
3144 Visit & Sign Renee's Online Memorial Book at: www.prokofuneralhome.com Robert R. Bonn Robert R. Bonn, 68, of Kenosha, passed away on Friday, June 26, 2020, at Froedtert South Pleasant Prairie. Born in Halifax Nova Scotia, on April 22, 1952, he was the son of the late Roy and Irene (Conrad) Bonn. On August 24, 1974, he married the love of his life, Michele Yung. Robert was an Athletic Director for 38 years. He enjoyed sports, golfing but most of all spending time with his family. Survivors include his wife, Michele Bonn; sons, Ryan (Christine) Bonn and Steven (Meaghan) Bonn; two grandchildren, Alec and Bradyn; siblings, Gary Bonn and Karen Bonn. He is further survived by other loving family and friends Due to the current health crisis, a private service was held. In lieu of flowers, memorials may be made to the Michele and Robert Bonn Athletic Endowment at Carthage College. Visit & Sign Robert's John Joseph Karnes September 22, 1937—July 03, 2020 John Joseph Karnes, age 82, of the Town of Three Lakes, died on July 3, 2020, at his home, with his family at his side. He was born on September 22, 1937 in Kenosha, Wisconsin to Ralph and Margaret (McQuestion) Karnes. He was raised in Kenosha and attended schools there graduating from the Kenosha High School in 1955. After his schooling he served his country as a member of the US Army. Upon his honorable discharge he returned to Kenosha where he was employed by AMC/Chrysler for 31 years as a die-setter in department 808. John retired in 1989 and moved to Three Lakes where he has lived since. In his retirement he drove for the Commission on Aging and also worked for 11 years at Trigs in Eagle River, or as he put it "a large corporation on Wall Street". He served his Lord and Savior as a member of St. Theresa Catholic Church in Three Lakes, Wisconsin. John is survived by his sister Margaret "Peggy" Bain, his nieces and nephews, Donnalee Bain, Jeanine Wolf, D Thomas Bain, Mike Bain, Patricia Johnson, Margaret "Maggie" Bain, Ralph Bain, Colleen "Kelly" Bain, Richard "Rick" Fanning, Leann Schuster, Maureen Modory, Erin Grimmer, Brian Fanning, Richelle "Shelly" Boslau, Lawrence "Larry" Fanning and his step son Michael Freeman and many great and great great nieces and nephews. He was preceded in death by his parents, his sister Alice Fanning and his brother Ralph Karnes. Graveside services and interment will be held at this time for John at the Three Lakes Cemetery. Due to the pandemic a Mass of Christian Burial will be held at a later date at the St. Theresa Catholic Church in Three Lakes. You may leave your private condolences for the Karnes family at www.carlsonfh.com. The Carlson Funeral Home (715-369-1414) is handling the arrangements for John's family. Michael D. Lamers MT. PLEASANT—Michael D. Lamers, 71, passed away at his beloved lake home in Lake Tomahawk on June 28, 2020. A memorial service celebrating his life will be held in the funeral home on Friday, July 10th at 6:00 p.m. Visitation will be in the funeral home on that Friday from 4:00 p.m. until the time of the service. Please see the funeral home website for the complete obituary. In accordance with Racine County mandate, only 50 people will be allowed to enter the funeral home at a time. You may be required to wait outside until others leave the building. For the safety and security of our guests we also require those	-0.434441	-1.090782	-1.553073	-1.782854	[ -0.5994873364409714, -0.26939555805227017 ]	[ -1.1086879056796026, -1.072875334053408 ]	[ -1.5429277303402782, -1.5632176585433524 ]	[ -1.9623485627116148, -1.6033594656927168 ]	1,024	[ 512, 512 ]	[ 29941, 29896, 29946, 29946, 13, 6116, 277, 669, 9954, 390, 1600, 29872, 29915, 29879, 13, 2951, 1220, 19722, 6726, 472, 29901, 13, 1636, 29889, 771, 29895, 974, 348, 13537, 5184, 29889, 510, 13, 9588, 2151, 390, 29889, 25056, 13, 9588, 2151, 390, 29889, 25056, 29892, 29871, 29953, 29947, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 25022, 287, 357, 29873, 4275, 19777, 13186, 9002, 24135, 29889, 13, 29933, 1398, 297, 8142, 361, 1165, 16216, 11032, 423, 29892, 373, 3786, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29945, 29906, 29892, 540, 471, 278, 1487, 310, 278, 5683, 15793, 322, 306, 28593, 313, 1168, 3665, 29897, 25056, 29889, 13, 2951, 3111, 29871, 29906, 29946, 29892, 29871, 29896, 29929, 29955, 29946, 29892, 540, 8300, 278, 5360, 310, 670, 2834, 29892, 341, 4070, 280, 612, 686, 29889, 13, 9588, 2151, 471, 385, 17183, 293, 15944, 363, 29871, 29941, 29947, 2440, 29889, 940, 27849, 14717, 29892, 29416, 292, 541, 1556, 310, 599, 805, 2548, 931, 411, 670, 3942, 29889, 13, 18498, 24759, 943, 3160, 670, 6532, 29892, 341, 4070, 280, 25056, 29936, 18025, 29892, 20916, 313, 18687, 457, 29897, 25056, 322, 24703, 313, 6816, 351, 5403, 29897, 25056, 29936, 1023, 4595, 11991, 29892, 7801, 29883, 322, 15862, 948, 29936, 27767, 18964, 29892, 23529, 25056, 322, 3467, 264, 25056, 29889, 940, 338, 4340, 10503, 2347, 491, 916, 12355, 292, 3942, 322, 7875, 13, 29928, 434, 304, 278, 1857, 9045, 24161, 29892, 263, 2024, 2669, 471, 4934, 29889, 512, 13003, 310, 18281, 29892, 2626, 9020, 29879, 1122, 367, 1754, 304, 278, 341, 4070, 280, 322, 4755, 25056, 17183, 293, 2796, 340, 358, 472, 13, 8179, 386, 482, 6346, 29889, 13, 6116, 277, 669, 9954, 4755, 29915, 29879, 13, 11639, 6936, 476, 2753, 267, 13, 2008, 3266, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 30003, 29967, 11850, 29871, 29900, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 13, 11639, 6936, 476, 2753, 267, 29892, 5046, 29871, 29947, 29906, 29892, 310, 278, 8421, 310, 12753, 365, 6926, 29892, 6423, 373, 5468, 29871, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 670, 3271, 29892, 411, 670, 3942, 472, 670, 2625, 29889, 940, 471, 6345, 373, 3839, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 297, 10015, 359, 2350, 29892, 22581, 304, 23438, 322, 18364, 313, 27297, 16492, 29897, 476, 2753, 267, 29889, 940, 471, 10425, 297, 10015, 359, 2350, 322, 14283, 12462, 727, 10591, 1218, 515, 278, 10015, 359, 2350, 5057, 4523, 297, 29871, 29896, 29929, 29945, 29945, 29889, 2860, 670, 3762, 292, 540, 6766, 670, 4234, 408, 263, 4509, 310, 278, 3148, 8811, 29889, 19956, 670, 10657, 519, 766, 23367, 540, 4133, 304, 10015, 359, 2350, 988, 540, 471, 15723, 491, 319, 12513, 29914, 1451, 18450, 1358, 363, 29871, 29941, 29896, 2440, 408, 263, 762, 29899, 842, 357, 297, 14311, 29871, 29947, 29900, 29947, 29889, 13, 11639, 16528, 297, 29871, 29896, 29929, 29947, 29929, 322, 6153, 304, 12753, 365, 6926, 988, 540, 756, 10600, 1951, 29889, 512, 670, 3240, 19211, 540, 26603, 363, 278, 11444, 373, 319, 3460, 322, 884, 3796, 363, 29871, 29896, 29896, 2440, 472, 1605, 23379, 297, 382, 20860, 6163, 29892, 470, 408, 540, 1925, 372, 376, 29874, 2919, 17266, 362, 373, 14406, 7103, 1642, 940, 6766, 670, 6171, 322, 9583, 1611, 408, 263, 4509, 310, 624, 29889, 25451, 8625, 11865, 6291, 297, 12753, 365, 6926, 29892, 22581, 29889, 13, 11639, 338, 10503, 2347, 491, 670, 9883, 18364, 376, 29925, 387, 1927, 29908, 350, 475, 29892, 670, 4930, 778, 322, 23446, 354, 5652, 29892, 360, 3409, 744, 29872, 350, 475, 29892, 4581, 457, 10441, 29892, 360, 5569, 350, 475, 29892, 12828, 350, 475, 29892, 4121, 2200, 423, 11717, 29892, 18364, 376, 19095, 12053, 29908, 350, 475, 29892, 23438, 350, 475, 29892, 1530, 280, 264, 376, 29968, 14112, 29908, 350, 475, 29892, 6123, 376, 29934, 860, 29908, 383, 9450, 29892, 951, 812, 1102, 5402, 29892, 3219, 545, 264, 3382, 706, 29892, 1425, 262, 1632, 19400, 29892, 15733, 383, 9450, 29892, 4385, 1808, 376, 2713, 14112, 29908, 10211, 25855, 29892, 19520, 376, 24105, 719, 29908, 383, 9450, 322, 670, 4331, 1487, 5765, 3878, 11422, 322, 1784, 2107, 322, 2107, 2107, 4930, 778, 322, 23446, 354, 5652, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29892, 670, 9883, 16308, 383, 9450, 322, 670, 8099, 23438, 476, 2753, 267, 29889, 13, 29954, 336, 1960, 680, 5786, 322, 1006, 358, 674, 367, 4934, 472, 445, 931, 363, 2259, 472, 278, 12753, 365, 6926, 315, 22875, 29889, 16809, 304, 278, 7243, 24552, 263, 7360, 310, 6111, 6640, 616, 674, 367, 4934, 472, 263, 2678, 2635, 472, 278, 624, 29889, 25451, 8625, 11865, 6291, 297, 12753, 365, 6926, 29889, 887, 1122, 5967, 596, 2024, 2148, 324, 2063, 363, 278, 476, 2753, 267, 3942, 472, 7821, 29889, 4287, 29880, 1100, 29888, 29882, 29889, 510, 29889, 450, 8965, 1100, 13811, 13537, 8778, 313, 29955, 29896, 29945, 29899, 29941, 29953, 29929, 29899, 29896, 29946, 29896, 29946, 29897, 338, 11415, 278, 15196, 4110, 363, 2259, 29915, 29879, 3942, 29889, 13, 24083, 360, 29889, 12718, 414, 13, 11490, 29889, 349, 1307, 3289, 13566, 30003, 24083, 360, 29889, 12718, 414, 29892, 29871, 29955, 29896, 29892, 4502, 3448, 472, 670, 1339, 8238, 19437, 3271, 297, 9459, 4335, 801, 20011, 373, 5306, 29871, 29906, 29947, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 319, 2626, 9020, 2669, 10894, 1218, 670, 2834, 674, 367, 4934, 297, 278, 2090, 13537, 3271, 373, 28728, 29892, 5468, 29871, 29896, 29900, 386, 472, 29871, 29953, 29901, 29900, 29900, 282, 29889, 29885, 29889, 5741, 7018, 674, 367, 297, 278, 2090, 13537, 3271, 373, 393, 28728, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 278, 931, 310, 278, 2669, 29889, 13, 12148, 1074, 278, 2090, 13537, 3271, 4700, 363, 278, 4866, 704, 1981, 653, 29889, 13, 797, 15017, 749, 411, 390, 562, 457, 5127, 9619, 403, 29892, 871, 29871, 29945, 29900, 2305, 674, 367, 6068, 304, 3896, 278, 2090, 13537, 3271, 472, 263, 931, 29889, 887, 1122, 367, 3734, 304, 4480, 5377, 2745, 4045, 5967, 278, 5214, 29889, 1152, 278, 15332, 322, 6993, 310, 1749, 28865, 591, 884, 1996, 1906 ]	1,332,858	1,024	CommonCrawl	0	3
in attendance to wear a face covering. We thank everyone for their understanding and cooperation during this difficult time. DRAEGER-LANGENDORF FUNERAL HOME AND CREMATORY 4600 County Line Rd. draeger-langendorf.com Lynne Cleereman Lynne Cleereman (nee Drajkowski) Found peace on Wednesday, March 25, 2020, age 79. Cherished and devoted wife of Douglas P. Cleereman for 58 years. Loving mother of Kelly (Dr. Michael) Mindiola and Shannon Doberstein. Treasured grandmother of Madison, Marissa, Maxwell and Mikayla Mindiola and Matthew and Daniel Doberstein. Special sister-in-law of Bonnie Jean Becker Fronek (late Jerry). Special aunt to the Becker boys: David (Donna Misurelli), Daniel (Lisa Serpe), Darren (Angie Castellano) and Jimmy (Autumn Meyer) and other cherished nieces and nephews. Also survived by special, life-long friends from Kenosha and many sewing and quilting friends and the Skylark Ladies group. Lynne is preceded in death by her mother Elinor Drajkowski (nee Zwolinski) and her in-laws Charlie and Jean Cleereman, her brother Gary Drajkowski (Sharon), sister-in-law Shirley (Gene) Clippard, and devoted cousin and friend Dorothy Zeier. Lynne and Doug met at Allen-Bradley Company and were married in 1962. Lynne had a strong, quiet faith in God and practiced her religion beyond the church doors, within her circle of friends and through her generosity to many charitable causes and her special family. She loved connecting with her bible study group. Her devotion was immense; her warm, gentle giving spirit lives on in all the quilts she made. Her goal was to create a quilt for everyone important in her life and she left instructions on a few that she didn't finish. Kelly is now the family quilter and the times they spent on projects will be forever cherished. Memorials suggested to the Sarah Mindiola Barse Sunflower Endowment Fund at WCTC. Memorial services on Wednesday, July 15 at Carl's Catering, 5110 W. Loomis Rd, Greendale, WI. Visitation begins at 10:30 with service and luncheon to follow all at Carl's Catering. Please wear a mask to the visitation and service, thank you! December 2, 1964 – June 29, 2020 Laura Gonzalez, age 55, passed away on Monday, June 29, 2020 from complications of Covid-19 at Froedtert South-Kenosha Medical Center. She was a stage 4 colon cancer survivor who had an immense love of God, her family, and friends. She enjoyed sewing and quilting, cooking, baking, dancing and reading the Bible. She left behind her husband of 29 years J. Angel Gonzalez, two daughters, Sabrina (Jesse) Gonzalez and Bianca Gonzalez, two brothers, Edmundo Bernal and Efrain Bernal, a niece Karina Bernal, and two granddaughters, Arianni Lopez and Nori Lopez. Funeral services honoring Laura's life will be held privately. Interment will take place in Sunset Ridge Memorial Park. A visitation for Laura will be held at the Piasecki Funeral Home on Monday, July 13, 2020 from 5:00 p.m. until 7:00 p.m. Piasecki Funeral Home & Cremation Services 3720 39th Avenue 262-658-4101 www.KenoshaFuneralHome.com Eve Vaughn Eve Vaughn, age 80, was born into eternal life and reunited with her loving husband Ron on Saturday, July 4, 2020 surrounded by her loving daughters. Those left to remember Eve are her children, Teresa Vaughn, Tracie (Mark) Vidas, Laurie (Darren)	-0.142358	-1.253729	-1.296912	-1.923328	[ 0.005909203176480653, -0.29062552720175094 ]	[ -1.3880259643639186, -1.1194316771674608 ]	[ -1.2588687354972399, -1.334955966258768 ]	[ -1.9051184168100512, -1.9415376005655918 ]	1,024	[ 512, 512 ]	[ 297, 14333, 749, 304, 19531, 263, 3700, 21653, 29889, 1334, 6452, 14332, 363, 1009, 8004, 322, 1302, 16453, 2645, 445, 5189, 931, 29889, 13, 29928, 4717, 11787, 1001, 29899, 29931, 19453, 11794, 1955, 29943, 383, 3904, 1001, 1964, 29832, 2303, 5300, 315, 1525, 29924, 1299, 18929, 13, 29946, 29953, 29900, 29900, 5127, 7407, 390, 29881, 29889, 13, 19811, 387, 261, 29899, 3893, 21466, 29889, 510, 13, 29931, 948, 484, 21386, 261, 11422, 13, 29931, 948, 484, 21386, 261, 11422, 313, 484, 29872, 360, 10665, 7000, 2574, 29897, 7460, 10776, 373, 15050, 4515, 3250, 29892, 4779, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 5046, 29871, 29955, 29929, 29889, 23816, 3276, 322, 24600, 6532, 310, 16721, 349, 29889, 21386, 261, 11422, 363, 29871, 29945, 29947, 2440, 29889, 365, 21081, 5637, 310, 21872, 313, 25639, 29889, 5765, 29897, 341, 14108, 2963, 322, 1383, 23453, 1938, 495, 5465, 29889, 6479, 294, 2955, 4595, 29885, 1228, 310, 4104, 2285, 29892, 1085, 16343, 29892, 5918, 5872, 322, 13803, 388, 433, 341, 14108, 2963, 322, 22292, 322, 8432, 1938, 495, 5465, 29889, 12630, 9883, 29899, 262, 29899, 10653, 310, 8396, 2786, 4581, 1522, 4937, 4693, 650, 29895, 313, 9632, 23052, 467, 12630, 263, 1657, 304, 278, 1522, 4937, 12544, 29901, 4699, 313, 10310, 1056, 20929, 545, 29880, 492, 511, 8432, 313, 29931, 8069, 1816, 412, 511, 7335, 1267, 313, 9928, 347, 4834, 514, 1562, 29897, 322, 20636, 313, 6147, 1227, 26581, 29897, 322, 916, 14954, 3276, 4930, 778, 322, 23446, 354, 5652, 29889, 3115, 10503, 2347, 491, 4266, 29892, 2834, 29899, 5426, 7875, 515, 10015, 359, 2350, 322, 1784, 409, 16958, 322, 439, 309, 1259, 7875, 322, 278, 4971, 2904, 935, 19955, 583, 2318, 29889, 18989, 484, 338, 9399, 287, 297, 4892, 491, 902, 5637, 1260, 262, 272, 360, 10665, 7000, 2574, 313, 484, 29872, 12017, 22878, 2574, 29897, 322, 902, 297, 29899, 433, 5652, 20283, 322, 4581, 21386, 261, 11422, 29892, 902, 8099, 23529, 360, 10665, 7000, 2574, 313, 2713, 5022, 511, 9883, 29899, 262, 29899, 10653, 1383, 381, 2330, 313, 29954, 1600, 29897, 315, 492, 407, 538, 29892, 322, 24600, 22618, 322, 5121, 9579, 20336, 3091, 631, 29889, 13, 29931, 948, 484, 322, 13215, 1539, 472, 16092, 29899, 29933, 3665, 2330, 6938, 322, 892, 8300, 297, 29871, 29896, 29929, 29953, 29906, 29889, 13, 29931, 948, 484, 750, 263, 4549, 29892, 11813, 10847, 297, 4177, 322, 4120, 7612, 902, 13433, 8724, 278, 6586, 24189, 29892, 2629, 902, 8607, 310, 7875, 322, 1549, 902, 1176, 359, 537, 304, 1784, 1373, 8270, 9946, 322, 902, 4266, 3942, 29889, 2296, 18012, 16791, 411, 902, 289, 1821, 6559, 2318, 29889, 2439, 2906, 8194, 471, 29403, 29936, 902, 14294, 29892, 9914, 6820, 8548, 12080, 373, 297, 599, 278, 439, 309, 1372, 1183, 1754, 29889, 2439, 7306, 471, 304, 1653, 263, 439, 2782, 363, 14332, 4100, 297, 902, 2834, 322, 1183, 2175, 11994, 373, 263, 2846, 393, 1183, 3282, 29915, 29873, 8341, 29889, 21872, 338, 1286, 278, 3942, 439, 309, 357, 322, 278, 3064, 896, 10398, 373, 9279, 674, 367, 22296, 14954, 3276, 29889, 13, 11442, 9020, 29879, 7829, 304, 278, 19235, 341, 14108, 2963, 2261, 344, 8991, 1731, 261, 2796, 340, 358, 13249, 472, 399, 1783, 29907, 29889, 13, 11442, 9020, 5786, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29945, 472, 8965, 29915, 29879, 315, 1008, 292, 29892, 29871, 29945, 29896, 29896, 29900, 399, 29889, 4309, 290, 275, 390, 29881, 29892, 4122, 355, 744, 29892, 399, 29902, 29889, 5741, 7018, 16410, 472, 29871, 29896, 29900, 29901, 29941, 29900, 411, 2669, 322, 25081, 1173, 265, 304, 1101, 599, 472, 8965, 29915, 29879, 315, 1008, 292, 29889, 3529, 19531, 263, 11105, 304, 278, 6493, 362, 322, 2669, 29892, 6452, 366, 29991, 13, 6185, 1096, 29871, 29906, 29892, 29871, 29896, 29929, 29953, 29946, 785, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 13, 5661, 2002, 27536, 744, 29920, 29892, 5046, 29871, 29945, 29945, 29892, 4502, 3448, 373, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 515, 752, 5795, 310, 25669, 333, 29899, 29896, 29929, 472, 25022, 287, 357, 29873, 4275, 29899, 29968, 264, 359, 2350, 20795, 7817, 29889, 13, 13468, 471, 263, 7408, 29871, 29946, 8104, 23900, 10503, 440, 272, 1058, 750, 385, 29403, 5360, 310, 4177, 29892, 902, 3942, 29892, 322, 7875, 29889, 13, 13468, 27849, 409, 16958, 322, 439, 309, 1259, 29892, 7984, 292, 29892, 289, 5086, 29892, 6025, 3277, 322, 5183, 278, 21958, 29889, 13, 13468, 2175, 5742, 902, 10216, 310, 29871, 29906, 29929, 2440, 435, 29889, 17323, 27536, 744, 29920, 29892, 1023, 29215, 29892, 11775, 29878, 1099, 313, 29967, 5340, 29897, 27536, 744, 29920, 322, 29860, 1113, 27536, 744, 29920, 29892, 1023, 21383, 29892, 2155, 29885, 6201, 6209, 284, 322, 382, 29888, 6038, 6209, 284, 29892, 263, 4930, 346, 3467, 1099, 6209, 284, 29892, 322, 1023, 4595, 29881, 6334, 2153, 29892, 25775, 9889, 365, 2300, 29920, 322, 405, 4170, 365, 2300, 29920, 29889, 13, 25394, 13537, 5786, 4207, 8253, 21671, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 4124, 358, 674, 2125, 2058, 297, 8991, 842, 390, 5525, 19722, 4815, 29889, 319, 6493, 362, 363, 21671, 674, 367, 4934, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 373, 27822, 29892, 5468, 29871, 29896, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29945, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 13, 12197, 559, 22736, 13811, 13537, 8778, 669, 315, 1745, 362, 15538, 13, 29941, 29955, 29906, 29900, 29871, 29941, 29929, 386, 18874, 29871, 29906, 29953, 29906, 29899, 29953, 29945, 29947, 29899, 29946, 29896, 29900, 29896, 13, 1636, 29889, 29968, 264, 359, 2350, 25394, 13537, 11184, 29889, 510, 13, 29923, 345, 478, 2987, 3123, 13, 29923, 345, 478, 2987, 3123, 29892, 5046, 29871, 29947, 29900, 29892, 471, 6345, 964, 634, 17196, 2834, 322, 23038, 1573, 411, 902, 12355, 292, 10216, 11546, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 22047, 491, 902, 12355, 292, 29215, 29889, 13, 1349, 852, 2175, 304, 6456, 382, 345, 526, 902, 4344, 29892, 5061, 8625, 478, 2987, 3123, 29892, 323, 945, 347, 313, 9802, 29897, 478, 8817, 29892, 14019, 347, 313, 29928, 279, 1267, 29897 ]	1,332,858	2,048	CommonCrawl	0	3
Couillard and Linda (Jim) Cooklin; her grandchildren, Mark Oelke II, Jon (Elizabeth) Oelke, Shelly (Kevin) Malkmus, Eric Garza, Laura Garza, Michael Warren, Jacob (Hillary) Warren, Katie Warren, Joshua (Samantha) Vaughn; her great grandchildren, Emmette Oelke, Sophie and Barrett Malkmus, Brodie and Calyx Vaughn; her brother, John (Kathleen) Greiser; and her sister, Jeanne (Jerry) Polden. A visitation for Eve will be held on Tuesday, July 14, 2020 from 3:00 p.m. until 6:00 p.m. at the Piasecki Funeral Home. Funeral services honoring Eve's life will be held privately. Inurnment will take place at a later date. In lieu of flowers, memorial remembrances to: Hospice Alliance Inc/Hospice House, 10220 Prairie Ridge Blvd, Pleasant Prairie, WI 53158, The Salvation Army, 3116-75th Street, Kenosha, WI 53142, or Women and Children's Horizon, 2525-63rd Street, Kenosha, WI 53143 would be appreciated by the family. Avanell Moore Salisbury September 19, 1931—July 5, 2020 Avanell Moore Salisbury passed away on July 5, 2020 in Kenosha, WI at the age of 88. She was born on September 19, 1931 in Coraopolis, PA to Arthur and Florence Moore. On April 11, 1953 she married the late John Salisbury and they had two sons. She was devoted to her grandchildren and she loved pets and F1 Racing. Avanell is survived by her children John (Lynn) Salisbury of Gurnee, IL and Scott (Mary) Salisbury of Los Alamos, NM; grandchildren Jenni, Austin, and Allison Salisbury; sister-in-laws Marjorie Fickley of FL and Janice Moore of PA; brother-in-law David (Linda) Salisbury of TX. She was proceeded in death by her husband John, parents Arthur and Florence Moore, brothers Bob, Skip, and Jim Moore. A visitation will be held on Friday, July 10, 2020 beginning at 10:00 a.m., concluding with a service at 11:00 a.m. at Marsh Funeral Home in Gurnee. Interment will follow at Highland Memorial Park in Libertyville. In lieu of flowers, donations can be made to Orphans of the Storm Animal Shelter in Riverwoods, IL at www.orphansofthestorm.org/donate. In consideration of the safety of our guests and associates, Marsh Funeral Home will adhere to the current gathering restrictions in the state of Illinois, which allow 50 or fewer guests at services. Proper social distancing must be practiced and all guests will be required to wear face masks at all times. Donald Dejno Donald Dejno unexpectedly passed away on July 4th, 2020 in Pleasant Prairie, WI after spending one of his fullest days enjoying his family. His heart stopped beating while he was at a neighbor's house enjoying fireworks. Born in Independence, WI on September 1, 1941. As the oldest child, Don grew up on the family farm with six other children. It was there he learned much from his father about care for equipment, smart farming, and hard work. Don landed his first job in 1959 and moved to Kenosha, WI to work for American Motors/Chrysler. He spoke frequently of the lessons learned while he swept floors and was later promoted to supervisor. He was also a corporal in the Armory National Guard from 1964-1971. He later met Carol Tate and dated for four years. They were married on October 2, 1965. The challenge to make his father-in-law proud motivated him to be	-0.322128	-1.151663	-1.606334	-1.769847	[ -0.28720133862925407, -0.35705478550819086 ]	[ -1.259100706509619, -1.0442252767524527 ]	[ -1.7559719764725568, -1.4566955354772129 ]	[ -1.842685530371982, -1.6970087953498205 ]	1,024	[ 512, 512 ]	[ 19565, 453, 538, 322, 365, 11054, 313, 29967, 326, 29897, 17278, 1915, 29936, 902, 4595, 11991, 29892, 4485, 438, 295, 446, 1944, 29892, 9937, 313, 6489, 466, 9394, 29897, 438, 295, 446, 29892, 1383, 14112, 313, 9598, 3845, 29897, 341, 2235, 8366, 29892, 14713, 7455, 1362, 29892, 21671, 7455, 1362, 29892, 5765, 24511, 29892, 10968, 313, 29950, 453, 653, 29897, 24511, 29892, 476, 9474, 24511, 29892, 22838, 3357, 313, 22966, 9716, 29874, 29897, 478, 2987, 3123, 29936, 902, 2107, 4595, 11991, 29892, 2812, 29885, 2353, 438, 295, 446, 29892, 19122, 347, 322, 2261, 13158, 341, 2235, 8366, 29892, 4358, 16217, 322, 3037, 29891, 29916, 478, 2987, 3123, 29936, 902, 8099, 29892, 2259, 313, 29968, 493, 280, 264, 29897, 4122, 7608, 29936, 322, 902, 9883, 29892, 4581, 484, 313, 29967, 261, 719, 29897, 349, 1025, 264, 29889, 13, 29909, 6493, 362, 363, 382, 345, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29941, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29953, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 13811, 13537, 5786, 4207, 8253, 382, 345, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 512, 595, 358, 674, 2125, 2058, 472, 263, 2678, 2635, 29889, 512, 13003, 310, 18281, 29892, 2626, 9020, 1083, 1590, 661, 778, 304, 29901, 379, 4705, 625, 29855, 9266, 29914, 29950, 4705, 625, 5619, 29892, 29871, 29896, 29900, 29906, 29906, 29900, 9002, 24135, 390, 5525, 3164, 27491, 29892, 19777, 13186, 9002, 24135, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29945, 29947, 29892, 450, 14964, 362, 8811, 29892, 29871, 29941, 29896, 29896, 29953, 29899, 29955, 29945, 386, 7103, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 29892, 470, 10152, 322, 20986, 29915, 29879, 6912, 18162, 29892, 29871, 29906, 29945, 29906, 29945, 29899, 29953, 29941, 5499, 7103, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29941, 723, 367, 7556, 491, 278, 3942, 29889, 13, 29909, 3703, 514, 18588, 3956, 275, 11059, 13, 2008, 3266, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29896, 30003, 29967, 11850, 29871, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 13, 29909, 3703, 514, 18588, 3956, 275, 11059, 4502, 3448, 373, 5468, 29871, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 297, 10015, 359, 2350, 29892, 399, 29902, 472, 278, 5046, 310, 29871, 29947, 29947, 29889, 13, 13468, 471, 6345, 373, 3839, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29896, 297, 315, 2207, 13242, 275, 29892, 17687, 304, 11498, 322, 23998, 18588, 29889, 1551, 3786, 29871, 29896, 29896, 29892, 29871, 29896, 29929, 29945, 29941, 1183, 8300, 278, 5683, 2259, 3956, 275, 11059, 322, 896, 750, 1023, 18025, 29889, 2296, 471, 24600, 304, 902, 4595, 11991, 322, 1183, 18012, 282, 1691, 322, 383, 29896, 22582, 29889, 13, 29909, 3703, 514, 338, 10503, 2347, 491, 902, 4344, 2259, 313, 29931, 948, 29876, 29897, 3956, 275, 11059, 310, 402, 332, 484, 29872, 29892, 17674, 322, 8075, 313, 29924, 653, 29897, 3956, 275, 11059, 310, 4602, 838, 14054, 29892, 405, 29924, 29936, 4595, 11991, 21116, 1240, 29892, 24518, 29892, 322, 2178, 2285, 3956, 275, 11059, 29936, 9883, 29899, 262, 29899, 433, 5652, 1085, 3418, 347, 383, 860, 2330, 310, 383, 29931, 322, 2627, 625, 18588, 310, 17687, 29936, 8099, 29899, 262, 29899, 10653, 4699, 313, 29931, 11054, 29897, 3956, 275, 11059, 310, 323, 29990, 29889, 13, 13468, 471, 24825, 297, 4892, 491, 902, 10216, 2259, 29892, 11825, 11498, 322, 23998, 18588, 29892, 21383, 7991, 29892, 4971, 666, 29892, 322, 8507, 18588, 29889, 13, 29909, 6493, 362, 674, 367, 4934, 373, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 6763, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 1696, 378, 22368, 411, 263, 2669, 472, 29871, 29896, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 13216, 13811, 13537, 8778, 297, 402, 332, 484, 29872, 29889, 4124, 358, 674, 1101, 472, 5057, 1049, 19722, 4815, 297, 10895, 1017, 4909, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 508, 367, 1754, 304, 1394, 561, 550, 310, 278, 24444, 22809, 1383, 21883, 297, 6163, 6115, 29879, 29892, 17674, 472, 7821, 29889, 5676, 550, 974, 386, 342, 555, 29889, 990, 29914, 9176, 403, 29889, 13, 797, 19220, 310, 278, 15332, 310, 1749, 28865, 322, 4067, 1078, 29892, 13216, 13811, 13537, 8778, 674, 594, 4150, 304, 278, 1857, 11705, 292, 25091, 297, 278, 2106, 310, 17066, 29892, 607, 2758, 29871, 29945, 29900, 470, 28145, 28865, 472, 5786, 29889, 1019, 546, 5264, 1320, 19985, 1818, 367, 4120, 7612, 322, 599, 28865, 674, 367, 3734, 304, 19531, 3700, 11105, 29879, 472, 599, 3064, 29889, 13, 28080, 897, 29926, 1217, 13, 28080, 897, 29926, 1217, 15668, 368, 4502, 3448, 373, 5468, 29871, 29946, 386, 29892, 29871, 29906, 29900, 29906, 29900, 297, 19777, 13186, 9002, 24135, 29892, 399, 29902, 1156, 805, 2548, 697, 310, 670, 2989, 342, 3841, 11418, 5414, 670, 3942, 29889, 3600, 5192, 11084, 367, 1218, 1550, 540, 471, 472, 263, 12307, 29915, 29879, 3699, 11418, 5414, 3974, 13129, 29889, 13, 29933, 1398, 297, 28052, 663, 29892, 399, 29902, 373, 3839, 29871, 29896, 29892, 29871, 29896, 29929, 29946, 29896, 29889, 1094, 278, 23947, 2278, 29892, 3872, 13631, 701, 373, 278, 3942, 17888, 411, 4832, 916, 4344, 29889, 739, 471, 727, 540, 10972, 1568, 515, 670, 4783, 1048, 2562, 363, 21083, 29892, 15040, 2215, 4056, 29892, 322, 2898, 664, 29889, 13, 10310, 2982, 287, 670, 937, 4982, 297, 29871, 29896, 29929, 29945, 29929, 322, 6153, 304, 10015, 359, 2350, 29892, 399, 29902, 304, 664, 363, 3082, 7142, 943, 29914, 1451, 18450, 1358, 29889, 940, 12707, 13672, 310, 278, 3109, 787, 10972, 1550, 540, 7901, 415, 5685, 943, 322, 471, 2678, 21201, 304, 2428, 19188, 29889, 940, 471, 884, 263, 17266, 284, 297, 278, 8481, 706, 3086, 13211, 515, 29871, 29896, 29929, 29953, 29946, 29899, 29896, 29929, 29955, 29896, 29889, 13, 3868, 2678, 1539, 8562, 323, 403, 322, 29797, 363, 3023, 2440, 29889, 2688, 892, 8300, 373, 5533, 29871, 29906, 29892, 29871, 29896, 29929, 29953, 29945, 29889, 13, 1576, 18766, 304, 1207, 670, 4783, 29899, 262, 29899, 10653, 22314, 17385, 630, 1075, 304, 367 ]	1,332,858	3,072	CommonCrawl	0	3
financially successful. Don had an entrepreneurial spirit and started a wood recycling business in 1975. Next he started a trucking company to haul both wood shavings and other freight. After seven years of marriage, Don's life changed. He understood and believed the gospel. He had a newfound love for Jesus, His wife, and marriage. Delighting in his marriage, teaching others concerning marriage, and talking to his children and grandchildren endlessly about marriage never got old for him. While a principled man with a work ethic second to none, he would always acknowledge that his success rested upon the hands of the good men around him and the goodness of God. His son, Larry Dejno, who worked with him most of his 40 years in business was his right arm whom he loved and valued dearly. His daughters, sons-in-laws, daughter-in-law, and grandchildren have been an integral part of the success of the ongoing family business. He was always dreaming and implementing business ideas, providing work for others, and thinking about his grandchildren. While always a productive man, he always found time to be there for you when you needed him most. He truly cared for people as well as productivity. Because he was most affected by the forgiveness that he received from His Savior Jesus, he was a man of both forgiveness and repentance. While a man of few words and strong convictions, he was a man with an emotional and tender heart. He would want you to know that there is forgiveness and acceptance in the person of Christ. He led a prayer group in 1972 that met in the basement of St. Mary's Catholic Church that eventually became Living Light Christian Church. At Living Light he faithfully and passionately served as an elder, marriage workshop leader, and encourager until the end. Don is survived by his wife, Carol June Dejno, son, Lawrence Lee Dejno and wife Lori, daughter Cindy Marie Auch with husband Mike, daughter Debbie Lynn Swift with husband Joel, daughter Christine Eckert, daughter Shelly Snyder with husband Joe, and daughter Kimberly Nelson with husband Edward. He has 19 grandchildren and one great grandchild. A visitation for Donald will be held on Friday, July 10, 2020 from 4:00 p.m. until 8:00 p.m. at the Piasecki Funeral Home. Funeral services honoring Donald's life will be held on Saturday, July 11, 2020 at 10:00 a.m. at The Encounter, 8900 34th Ave, Kenosha, WI 53142. Private burial will take place in Sunset Ridge Memorial Park. Darla Jean Yingling Kreuser Darla Jean Yingling Kreuser (79) died peacefully in her sleep at home in Clarksville, TN on 23 March, 2020. Funeral services for Darla will be held on Saturday, July 11, at 11:00 a.m. at the Bruch-Hansen Funeral Home. Interment will follow at Sunset Ridge Memorial Park. Visitation will be held on Friday evening from 5 p.m. to 7 p.m. at the funeral home and masks are encouraged. Bruch-Hansen Funeral Home 6019 – 7th Ave. Online Memorial Book www.bruchhansenfuneralhome.com James G. Loken James G. Loken, 60, of Genoa City, passed away Tuesday, June 30, 2020 at his home. Born in Clintonville, Wisconsin on October 6, 1959, he was the son of Gene and Donna (nee Phillips) Loken. He served in the U.S. Army from 1977 until 1980. On August 2, 2003, he was united in marriage to Brenda Quaid. Following marriage, they made Genoa City their home. He was a resident of Genoa City for 19 years. Jim retired from Ecolab in pest control. He loved hunting, camping and spending time with his family. Jim is survived by his wife, Brenda Loken; sister, Kathy (Larry) Preuss and family, as they had a special place	0.258614	-0.721688	-0.561402	-1.288594	[ 0.9948148629135857, -0.47758622326008177 ]	[ -0.3382699585710961, -1.1051066485169831 ]	[ 0.39983289510407205, -1.522637802137204 ]	[ -0.8021374230708285, -1.7750499033974072 ]	1,024	[ 512, 512 ]	[ 11782, 5584, 9150, 29889, 3872, 750, 385, 23440, 1600, 332, 616, 8548, 322, 4687, 263, 8112, 1162, 29891, 19914, 5381, 297, 29871, 29896, 29929, 29955, 29945, 29889, 8084, 540, 4687, 263, 534, 2707, 292, 5001, 304, 447, 352, 1716, 8112, 528, 485, 886, 322, 916, 3005, 523, 29889, 13, 13555, 9881, 2440, 310, 13718, 29892, 3872, 29915, 29879, 2834, 3939, 29889, 940, 11098, 322, 13112, 278, 330, 26265, 29889, 940, 750, 263, 716, 11940, 5360, 363, 13825, 29892, 3600, 6532, 29892, 322, 13718, 29889, 5556, 523, 292, 297, 670, 13718, 29892, 18819, 4045, 19813, 13718, 29892, 322, 9963, 304, 670, 4344, 322, 4595, 11991, 1095, 23769, 1048, 13718, 2360, 2355, 2030, 363, 1075, 29889, 13, 8809, 488, 263, 12502, 29881, 767, 411, 263, 664, 11314, 293, 1473, 304, 5642, 29892, 540, 723, 2337, 18145, 5485, 393, 670, 2551, 1791, 287, 2501, 278, 6567, 310, 278, 1781, 1757, 2820, 1075, 322, 278, 1781, 2264, 310, 4177, 29889, 3600, 1487, 29892, 26977, 897, 29926, 1217, 29892, 1058, 3796, 411, 1075, 1556, 310, 670, 29871, 29946, 29900, 2440, 297, 5381, 471, 670, 1492, 5075, 6029, 540, 18012, 322, 659, 6742, 9425, 368, 29889, 3600, 29215, 29892, 18025, 29899, 262, 29899, 433, 5652, 29892, 8750, 29899, 262, 29899, 10653, 29892, 322, 4595, 11991, 505, 1063, 385, 10160, 760, 310, 278, 2551, 310, 278, 373, 17696, 3942, 5381, 29889, 13, 3868, 471, 2337, 12561, 292, 322, 16049, 5381, 7014, 29892, 13138, 664, 363, 4045, 29892, 322, 7291, 1048, 670, 4595, 11991, 29889, 5806, 2337, 263, 3234, 573, 767, 29892, 540, 2337, 1476, 931, 304, 367, 727, 363, 366, 746, 366, 4312, 1075, 1556, 29889, 940, 19781, 274, 1965, 363, 2305, 408, 1532, 408, 3234, 2068, 29889, 7311, 540, 471, 1556, 15201, 491, 278, 18879, 20193, 393, 540, 4520, 515, 3600, 9583, 1611, 13825, 29892, 540, 471, 263, 767, 310, 1716, 18879, 20193, 322, 1634, 296, 749, 29889, 5806, 263, 767, 310, 2846, 3838, 322, 4549, 7602, 919, 1080, 29892, 540, 471, 263, 767, 411, 385, 23023, 1848, 322, 22707, 5192, 29889, 940, 723, 864, 366, 304, 1073, 393, 727, 338, 18879, 20193, 322, 3544, 749, 297, 278, 2022, 310, 2819, 29889, 13, 3868, 5331, 263, 27402, 2318, 297, 29871, 29896, 29929, 29955, 29906, 393, 1539, 297, 278, 2362, 882, 310, 624, 29889, 6182, 29915, 29879, 11865, 6291, 393, 10201, 3897, 26176, 12790, 6111, 6291, 29889, 2180, 26176, 12790, 540, 10847, 3730, 322, 15935, 2486, 6766, 408, 385, 27008, 29892, 13718, 664, 19032, 11822, 29892, 322, 13731, 336, 914, 2745, 278, 1095, 29889, 13, 10310, 338, 10503, 2347, 491, 670, 6532, 29892, 8562, 5306, 897, 29926, 1217, 29892, 1487, 29892, 19520, 9371, 897, 29926, 1217, 322, 6532, 365, 4170, 29892, 8750, 315, 513, 29891, 9932, 14307, 411, 10216, 12828, 29892, 8750, 7089, 10993, 18989, 29876, 14156, 411, 10216, 3650, 295, 29892, 8750, 2819, 457, 382, 384, 814, 29892, 8750, 1383, 14112, 317, 1460, 672, 411, 10216, 11131, 29892, 322, 8750, 12931, 495, 368, 19135, 411, 10216, 9300, 29889, 940, 756, 29871, 29896, 29929, 4595, 11991, 322, 697, 2107, 4595, 5145, 29889, 13, 29909, 6493, 362, 363, 18935, 674, 367, 4934, 373, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29947, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 13811, 13537, 5786, 4207, 8253, 18935, 29915, 29879, 2834, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 450, 11346, 5336, 29892, 29871, 29947, 29929, 29900, 29900, 29871, 29941, 29946, 386, 319, 345, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 29889, 12230, 6866, 616, 674, 2125, 2058, 297, 8991, 842, 390, 5525, 19722, 4815, 29889, 13, 29928, 279, 433, 4581, 612, 292, 1847, 7706, 1792, 13, 29928, 279, 433, 4581, 612, 292, 1847, 7706, 1792, 313, 29955, 29929, 29897, 6423, 10776, 3730, 297, 902, 8709, 472, 3271, 297, 17129, 4501, 1924, 29892, 323, 29940, 373, 29871, 29906, 29941, 4779, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 25394, 13537, 5786, 363, 7335, 433, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 472, 29871, 29896, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 278, 8135, 305, 29899, 29950, 29401, 13811, 13537, 8778, 29889, 4124, 358, 674, 1101, 472, 8991, 842, 390, 5525, 19722, 4815, 29889, 5741, 7018, 674, 367, 4934, 373, 28728, 11005, 515, 29871, 29945, 282, 29889, 29885, 29889, 304, 29871, 29955, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 322, 11105, 29879, 526, 18443, 287, 29889, 13, 29933, 582, 305, 29899, 29950, 29401, 13811, 13537, 8778, 13, 29953, 29900, 29896, 29929, 785, 29871, 29955, 386, 319, 345, 29889, 13, 2951, 1220, 19722, 6726, 13, 1636, 29889, 16670, 305, 29882, 29401, 7692, 13537, 5184, 29889, 510, 13, 29470, 402, 29889, 365, 4476, 13, 29470, 402, 29889, 365, 4476, 29892, 29871, 29953, 29900, 29892, 310, 5739, 19807, 4412, 29892, 4502, 3448, 323, 1041, 3250, 29892, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 2233, 16929, 4909, 29892, 22581, 373, 5533, 29871, 29953, 29892, 29871, 29896, 29929, 29945, 29929, 29892, 540, 471, 278, 1487, 310, 15350, 322, 3872, 1056, 313, 484, 29872, 21856, 4512, 29897, 365, 4476, 29889, 940, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 515, 29871, 29896, 29929, 29955, 29955, 2745, 29871, 29896, 29929, 29947, 29900, 29889, 1551, 3111, 29871, 29906, 29892, 29871, 29906, 29900, 29900, 29941, 29892, 540, 471, 443, 1573, 297, 13718, 304, 1771, 8395, 751, 29874, 333, 29889, 12206, 13718, 29892, 896, 1754, 5739, 19807, 4412, 1009, 3271, 29889, 940, 471, 263, 20201, 310, 5739, 19807, 4412, 363, 29871, 29896, 29929, 2440, 29889, 13, 29967, 326, 16528, 515, 382, 1054, 370, 297, 282, 342, 2761, 29889, 940, 18012, 29826, 29892, 4242, 292, 322, 805, 2548, 931, 411, 670, 3942, 29889, 13, 29967, 326, 338, 10503, 2347, 491, 670, 6532, 29892, 1771, 8395, 365, 4476, 29936, 9883, 29892, 19663, 29891, 313, 24105, 719, 29897, 4721, 1558, 322, 3942, 29892, 408, 896, 750, 263, 4266, 2058 ]	1,332,858	4,096	CommonCrawl	0	3
in Jim's heart; children, Sabra and Jeremy; and many nieces, nephews, other relatives and friends. He was preceded in death by his parents, The family would like to thank his caretakers, Diane and Keagan, for their care and concern during this time. Services for Jim will be held Friday, July 10, 2020 at 11AM at Schuette-Daniels Funeral Home. Relatives and friends may visit with the family from 10 until 11AM. Burial will be private. Shirley G. Haase Shirley G. Haase, age 92, of Genoa City, WI, passed away peacefully on Saturday morning, July 4, 2020 at the Aurora Burlington Medical Center in Burlington, WI. The former Shirley Gene Fields was born on May 2, 1928 in McGregor, IA the daughter of the late Everett A. and Olive S. Durr Fields. They moved to Madison, WI when she was a young girl where she worked as a secretary for State Farm Insurance. While in Madison, she met David E. Haase and they were married on November 17, 1948. They lived in Madison, WI and Dubuque, IA before moving to Genoa City in 1951 and purchased the Klement Funeral Home in 1953. This is when the Haase Funeral Home was started. Shirley worked alongside David for many years to build the business to what it is today. The family business has been serving the communities for almost 70 years. Shirley has been a member of the First Congregational United Church of Christ in Genoa City since 1951. She served as Supt. of Sunday School and was a teacher, served on the Church Council and the BYKOTA Circle. She volunteered at the Lakeland Medical Center since 1964 where she greeted people at the main entrance until 2 years ago when she retired from the hospital receiving an award for 53 years of dedicated service to the hospital volunteering. She was a member of the Election Board for Genoa City for over 50 years. She was a member and Treasurer of the Genoa City Garden Club. She volunteered and coordinated at the Blood Bank in Lake Geneva for many years. She was a Lifetime Member of the Order of Eastern Star, Genoa City, Walworth and Burlington Chapter. She was the 2003 Genoa City Lions Club, Citizen of the Year. She was a member of the Sponholtz-Deignan American Legion Post #183 Ladies Auxiliary and the Bloomfield VFW. She was an avid Green Bay Packer Fan. Shirley was always helping anyone in need. Shirley is survived by: her 4 children, Pamela (Kenneth ) Van Dyke, Sr. of Scandinavia, WI, Bruce (Nanette) Haase of Twin Lakes, WI, Bryan (Geri) Haase of Genoa City, WI and Cynthia (Bob Vail) Wilinski of Fontana, WI; 8 grandchildren, Dr. Kenneth (Jacqueline) Van Dyke, Jr., Ryan (Kayla) Van Dyke, Andrew (Suzanne) Haase, Kathryn (Matthew) Buchan, Jonathan (Rachael Otto) Haase, Jackie (John) Bettack, Sarah (Drew) Wellman and Matthew (Tausha) Wilinski; 16 great grandchildren, Olivia Van Dyke, Annaliese Van Dyke, Finn Van Dyke, Barrett Van Dyke, Sean Haase, Evan Haase, Emily Haase, Hunter Buchan, Kolt Buchan, Collin Bettack, Coltin Bettack, Isabella Bettack, Jenner Wellman, Quinn Wellman, Ellie Wilinski, Wade Haase and baby Wilinski to be born in December; 1 sister, Eleanor "Doll" Stanford of Madison, WI and a sister in law, Julie Fields of Morton, IL and many friends. Shirley was preceded in death by her husband David on September 23, 2000, 2 brothers Gary Fields in 2013 and Terry Fields in 1993. Brother in law Herbert Stanford. The Ha	-0.031072	-0.705125	-1.281695	-1.58515	[ -0.016690441401998893, -0.045453625410972864 ]	[ -1.2089631062329467, -0.20128687210090263 ]	[ -1.3501734124110736, -1.2132163970403231 ]	[ -1.7646444223243956, -1.4056553253054975 ]	1,024	[ 512, 512 ]	[ 297, 8507, 29915, 29879, 5192, 29936, 4344, 29892, 11775, 336, 322, 5677, 6764, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 916, 14576, 322, 7875, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29892, 13, 1576, 3942, 723, 763, 304, 6452, 670, 2562, 29873, 21079, 29892, 360, 16677, 322, 4813, 18939, 29892, 363, 1009, 2562, 322, 5932, 2645, 445, 931, 29889, 13, 13779, 363, 8507, 674, 367, 4934, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29896, 5194, 472, 1102, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 29889, 6376, 5056, 322, 7875, 1122, 6493, 411, 278, 3942, 515, 29871, 29896, 29900, 2745, 29871, 29896, 29896, 5194, 29889, 6640, 616, 674, 367, 2024, 29889, 13, 2713, 381, 2330, 402, 29889, 5952, 559, 13, 2713, 381, 2330, 402, 29889, 5952, 559, 29892, 5046, 29871, 29929, 29906, 29892, 310, 5739, 19807, 4412, 29892, 399, 29902, 29892, 4502, 3448, 10776, 3730, 373, 24211, 7250, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 23266, 2207, 6640, 1847, 880, 20795, 7817, 297, 6640, 1847, 880, 29892, 399, 29902, 29889, 13, 1576, 4642, 1383, 381, 2330, 15350, 8989, 29879, 471, 6345, 373, 2610, 29871, 29906, 29892, 29871, 29896, 29929, 29906, 29947, 297, 22805, 1727, 272, 29892, 306, 29909, 278, 8750, 310, 278, 5683, 18274, 1803, 319, 29889, 322, 438, 9258, 317, 29889, 360, 1038, 8989, 29879, 29889, 2688, 6153, 304, 4104, 2285, 29892, 399, 29902, 746, 1183, 471, 263, 4123, 7826, 988, 1183, 3796, 408, 263, 28274, 363, 4306, 23354, 512, 7610, 749, 29889, 5806, 297, 4104, 2285, 29892, 1183, 1539, 4699, 382, 29889, 5952, 559, 322, 896, 892, 8300, 373, 3979, 29871, 29896, 29955, 29892, 29871, 29896, 29929, 29946, 29947, 29889, 2688, 10600, 297, 4104, 2285, 29892, 399, 29902, 322, 11668, 29884, 802, 29892, 306, 29909, 1434, 8401, 304, 5739, 19807, 4412, 297, 29871, 29896, 29929, 29945, 29896, 322, 20848, 278, 476, 944, 13811, 13537, 8778, 297, 29871, 29896, 29929, 29945, 29941, 29889, 910, 338, 746, 278, 5952, 559, 13811, 13537, 8778, 471, 4687, 29889, 1383, 381, 2330, 3796, 19963, 4699, 363, 1784, 2440, 304, 2048, 278, 5381, 304, 825, 372, 338, 9826, 29889, 450, 3942, 5381, 756, 1063, 16330, 278, 23507, 363, 4359, 29871, 29955, 29900, 2440, 29889, 13, 2713, 381, 2330, 756, 1063, 263, 4509, 310, 278, 3824, 6005, 1727, 1288, 3303, 6291, 310, 2819, 297, 5739, 19807, 4412, 1951, 29871, 29896, 29929, 29945, 29896, 29889, 2296, 6766, 408, 2166, 415, 29889, 310, 16340, 4523, 322, 471, 263, 15703, 29892, 6766, 373, 278, 6291, 8831, 322, 278, 6770, 29968, 2891, 29909, 27927, 29889, 2296, 27886, 14561, 472, 278, 27229, 14045, 20795, 7817, 1951, 29871, 29896, 29929, 29953, 29946, 988, 1183, 1395, 300, 287, 2305, 472, 278, 1667, 19546, 2745, 29871, 29906, 2440, 8020, 746, 1183, 16528, 515, 278, 13457, 13442, 385, 9862, 363, 29871, 29945, 29941, 2440, 310, 16955, 2669, 304, 278, 13457, 27886, 3241, 29889, 2296, 471, 263, 4509, 310, 278, 382, 1464, 12590, 363, 5739, 19807, 4412, 363, 975, 29871, 29945, 29900, 2440, 29889, 2296, 471, 263, 4509, 322, 6479, 294, 9945, 310, 278, 5739, 19807, 4412, 19906, 5977, 29889, 2296, 27886, 14561, 322, 6615, 630, 472, 278, 25122, 10253, 297, 9459, 15350, 1564, 363, 1784, 2440, 29889, 2296, 471, 263, 365, 361, 5410, 19495, 310, 278, 8170, 310, 16162, 7828, 29892, 5739, 19807, 4412, 29892, 5260, 12554, 322, 6640, 1847, 880, 23040, 29889, 2296, 471, 278, 29871, 29906, 29900, 29900, 29941, 5739, 19807, 4412, 365, 1080, 5977, 29892, 21353, 19642, 310, 278, 8905, 29889, 2296, 471, 263, 4509, 310, 278, 317, 1112, 5391, 17559, 29899, 2772, 647, 273, 3082, 5682, 291, 4918, 396, 29896, 29947, 29941, 19955, 583, 319, 1314, 2638, 653, 322, 278, 11447, 290, 2671, 478, 29943, 29956, 29889, 2296, 471, 385, 1029, 333, 7646, 6211, 18744, 261, 383, 273, 29889, 1383, 381, 2330, 471, 2337, 19912, 5019, 297, 817, 29889, 13, 2713, 381, 2330, 338, 10503, 2347, 491, 29901, 902, 29871, 29946, 4344, 29892, 25281, 3100, 313, 29968, 2108, 621, 1723, 6556, 24526, 446, 29892, 26250, 29889, 310, 2522, 392, 262, 12751, 29892, 399, 29902, 29892, 18885, 313, 29940, 273, 2353, 29897, 5952, 559, 310, 323, 5080, 365, 6926, 29892, 399, 29902, 29892, 13307, 273, 313, 29954, 13613, 29897, 5952, 559, 310, 5739, 19807, 4412, 29892, 399, 29902, 322, 315, 948, 386, 423, 313, 29362, 478, 737, 29897, 4624, 262, 2574, 310, 10928, 1648, 29892, 399, 29902, 29936, 29871, 29947, 4595, 11991, 29892, 4942, 29889, 28576, 313, 24288, 339, 5570, 29897, 6556, 24526, 446, 29892, 13843, 1696, 20916, 313, 29968, 388, 433, 29897, 6556, 24526, 446, 29892, 11571, 313, 29903, 3365, 11276, 29897, 5952, 559, 29892, 19663, 719, 29876, 313, 29924, 1131, 13636, 29897, 10586, 273, 29892, 20983, 313, 29934, 496, 4271, 13832, 29897, 5952, 559, 29892, 5457, 347, 313, 11639, 29897, 350, 1803, 547, 29892, 19235, 313, 29928, 3973, 29897, 5674, 1171, 322, 22292, 313, 29911, 1485, 2350, 29897, 4624, 262, 2574, 29936, 29871, 29896, 29953, 2107, 4595, 11991, 29892, 19802, 423, 6556, 24526, 446, 29892, 8081, 284, 21928, 6556, 24526, 446, 29892, 21189, 6556, 24526, 446, 29892, 2261, 13158, 6556, 24526, 446, 29892, 922, 273, 5952, 559, 29892, 382, 3703, 5952, 559, 29892, 2812, 2354, 5952, 559, 29892, 25703, 10586, 273, 29892, 10451, 29873, 10586, 273, 29892, 1530, 1915, 350, 1803, 547, 29892, 1530, 29873, 262, 350, 1803, 547, 29892, 16543, 433, 350, 1803, 547, 29892, 21116, 1089, 5674, 1171, 29892, 751, 2559, 5674, 1171, 29892, 11001, 347, 4624, 262, 2574, 29892, 399, 1943, 5952, 559, 322, 24354, 4624, 262, 2574, 304, 367, 6345, 297, 5846, 29936, 29871, 29896, 9883, 29892, 8317, 273, 272, 376, 29928, 3028, 29908, 7813, 4006, 310, 4104, 2285, 29892, 399, 29902, 322, 263, 9883, 297, 4307, 29892, 2739, 347, 8989, 29879, 310, 15533, 265, 29892, 17674, 322, 1784, 7875, 29889, 13, 2713, 381, 2330, 471, 9399, 287, 297, 4892, 491, 902, 10216, 4699, 373, 3839, 29871, 29906, 29941, 29892, 29871, 29906, 29900, 29900, 29900, 29892, 29871, 29906, 21383, 23529, 8989, 29879, 297, 29871, 29906, 29900, 29896, 29941, 322, 27571, 8989, 29879, 297, 29871, 29896, 29929, 29929, 29941, 29889, 4358, 721, 297, 4307, 19116, 7813, 4006, 29889, 13, 1576, 5952 ]	1,332,858	5,120	CommonCrawl	0	3
ase Family would like to send a big Thank You to Golden Years in Lake Geneva, WI for taking such good care our Mother, Dr. Karls, Dr. Welka, Dr. Hobbs the Aurora Medical Center in Burlington and the many friends that have reached out. A public visitation will be held on Saturday, July 11, 2020 from 2:00PM until 7:00PM at the Haase-Lockwood & Assoc. Funeral Home, 113 Freeman St. Genoa City, WI. Due to the Covid-19 Pandemic, everyone is asked to be patient and abide by the number of visitors allowed inside the funeral home. Everyone is welcome, but we ask that you keep your visit short so that all who wish to pay their respects will be able to do so. A Private Family Service will be held at the First Congregational United church of Christ on Sunday. Entombment will follow at Hillside Cemetery. In lieu of other expressions of sympathy, Shirley has asked that memorials be made the First Congregational United Church of Christ, 624 Park St. Genoa City, WI 53128. For online guestbook: haaselockwoodfhs.com. The Haase-Lockwood & Assoc. Funeral Home of Genoa City is handling our mother's arrangements. Donald D. Dejno Donald D. Dejno, age 78, passed away on Saturday, July 4, 2020 at Froedtert South – Pleasant Prairie Campus. Complete obituary information will be available in the Wednesday, July 8, 2020 edition of the Kenosha News. Shelby Jean Nielsen Shelby Jean Nielsen, 81 of Lepanto, Arkansas departed this life on June 30, 2020 in Jonesboro, Arkansas. She was born on July 14, 1938 to William Howard and Anna Blanche Kemp Watts. She was a member of Lepanto First Baptist Church. Shelby is preceded in death by her parents and husband: Paul Nielsen. Shelby is survived by her special friend: Carlton Soden of Amory, Mississippi, 1 son: Robert Lawrence of Kenosha, Wisconsin, 2 daughters: Connie Massie of Salem, Wisconsin and Tami Voigt (Peter) of Salem, Wisconsin, 3 sisters: Shelia Dean Tyler (Harold) of Lepanto, Arkansas, Patricia Ann Taylor (Morris) of Lepanto, Arkansas and Paula Diane Laney (B.J.) of Fulton, Mississippi, 10 grandchildren , 9 great-grandchildren, several nieces, nephews and a host of family and friends. Funeral service will be held Monday, July 6, 2020 at 1:00 pm and visitation will be held from 11:00 am – 1:00 pm at First Baptist Church in Lepanto, Arkansas. Interment will be at Potter Memorial Cemetery in Lepanto, Arkansas. Arrangements are under the care of Delancey-Murphy Funeral Home On line registry: [email protected] Rudolph "Rudy" J. Schwamlien Rudolph J. "Rudy" Schwamlien, 77 years old of Lake Villa, IL passed away unexpectedly Thursday July 2, 2020. He was born November 25, 1942 in Harvey, IL the son of the late Rudolph J. and Mary V. (neé Shaffer) Schwamlien, living in Chicago, IL and Paddock Lake, WI before settling in Lake Villa in 1988. Rudy proudly served in the US Airforce and was a proud member of the American Legion Post #2910. Before his retirement in 2005, Rudy had worked as a Head Lab Technician for American Conveyor Systems, Evanston, IL for over 40 years. Rudy was the head of the Pioneer's program at Zion Lutheran Church, Bristol from 1973 until 1979, a member of the Paddock Lake Sportsman's Club and the NRA, and he enjoyed: hunting, fishing, and gunsmithing. Sur	-0.741934	-1.280588	-1.867567	-1.975355	[ -0.4241688815291301, -1.059698280584555 ]	[ -1.3450508784124853, -1.2161256205581856 ]	[ -1.6443773713556489, -2.0907557918232804 ]	[ -1.936334860029086, -2.0143759680766724 ]	1,024	[ 512, 512 ]	[ 559, 14662, 723, 763, 304, 3638, 263, 4802, 3374, 887, 304, 16108, 23857, 297, 9459, 15350, 1564, 29892, 399, 29902, 363, 5622, 1316, 1781, 2562, 1749, 21869, 29892, 4942, 29889, 3467, 3137, 29892, 4942, 29889, 10458, 1335, 29892, 4942, 29889, 25302, 5824, 278, 23266, 2207, 20795, 7817, 297, 6640, 1847, 880, 322, 278, 1784, 7875, 393, 505, 7450, 714, 29889, 13, 29909, 970, 6493, 362, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29906, 29901, 29900, 29900, 13427, 2745, 29871, 29955, 29901, 29900, 29900, 13427, 472, 278, 5952, 559, 29899, 16542, 6115, 669, 4007, 542, 29889, 13811, 13537, 8778, 29892, 29871, 29896, 29896, 29941, 3878, 11422, 624, 29889, 5739, 19807, 4412, 29892, 399, 29902, 29889, 16809, 304, 278, 25669, 333, 29899, 29896, 29929, 6518, 24552, 29892, 14332, 338, 4433, 304, 367, 16500, 322, 633, 680, 491, 278, 1353, 310, 26824, 6068, 2768, 278, 2090, 13537, 3271, 29889, 7569, 650, 338, 12853, 29892, 541, 591, 2244, 393, 366, 3013, 596, 6493, 3273, 577, 393, 599, 1058, 6398, 304, 5146, 1009, 3390, 29879, 674, 367, 2221, 304, 437, 577, 29889, 319, 12230, 14662, 6692, 674, 367, 4934, 472, 278, 3824, 6005, 1727, 1288, 3303, 6586, 310, 2819, 373, 16340, 29889, 4284, 3424, 358, 674, 1101, 472, 9143, 2975, 315, 22875, 29889, 512, 13003, 310, 916, 12241, 310, 29738, 29892, 1383, 381, 2330, 756, 4433, 393, 2626, 9020, 29879, 367, 1754, 278, 3824, 6005, 1727, 1288, 3303, 6291, 310, 2819, 29892, 29871, 29953, 29906, 29946, 4815, 624, 29889, 5739, 19807, 4412, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29906, 29947, 29889, 1152, 7395, 17838, 2909, 29901, 447, 294, 295, 1698, 6115, 29888, 9499, 29889, 510, 29889, 450, 5952, 559, 29899, 16542, 6115, 669, 4007, 542, 29889, 13811, 13537, 8778, 310, 5739, 19807, 4412, 338, 11415, 1749, 5637, 29915, 29879, 15196, 4110, 29889, 13, 28080, 360, 29889, 897, 29926, 1217, 13, 28080, 360, 29889, 897, 29926, 1217, 29892, 5046, 29871, 29955, 29947, 29892, 4502, 3448, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 357, 29873, 4275, 785, 19777, 13186, 9002, 24135, 7259, 375, 29889, 13, 17813, 704, 1981, 653, 2472, 674, 367, 3625, 297, 278, 15050, 4515, 3250, 29892, 5468, 29871, 29947, 29892, 29871, 29906, 29900, 29906, 29900, 12203, 310, 278, 10015, 359, 2350, 10130, 29889, 13, 2713, 295, 1609, 4581, 405, 709, 4881, 13, 2713, 295, 1609, 4581, 405, 709, 4881, 29892, 29871, 29947, 29896, 310, 951, 29886, 5361, 29892, 19444, 13353, 5840, 287, 445, 2834, 373, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 297, 10920, 4089, 29877, 29892, 19444, 13353, 29889, 2296, 471, 6345, 373, 5468, 29871, 29896, 29946, 29892, 29871, 29896, 29929, 29941, 29947, 304, 4667, 17430, 322, 11230, 3164, 20372, 476, 3451, 399, 1131, 29879, 29889, 2296, 471, 263, 4509, 310, 951, 29886, 5361, 3824, 23759, 391, 6291, 29889, 13, 2713, 295, 1609, 338, 9399, 287, 297, 4892, 491, 902, 11825, 322, 10216, 29901, 3739, 405, 709, 4881, 29889, 13, 2713, 295, 1609, 338, 10503, 2347, 491, 902, 4266, 5121, 29901, 8965, 880, 317, 13183, 310, 1913, 706, 29892, 24743, 29892, 29871, 29896, 1487, 29901, 4755, 19520, 310, 10015, 359, 2350, 29892, 22581, 29892, 29871, 29906, 29215, 29901, 1281, 2786, 7360, 347, 310, 317, 12698, 29892, 22581, 322, 323, 4479, 4785, 5523, 313, 23686, 29897, 310, 317, 12698, 29892, 22581, 29892, 29871, 29941, 9883, 29879, 29901, 1383, 18556, 23263, 9656, 1358, 313, 21972, 1025, 29897, 310, 951, 29886, 5361, 29892, 19444, 13353, 29892, 4121, 2200, 423, 8081, 12537, 313, 28581, 3780, 29897, 310, 951, 29886, 5361, 29892, 19444, 13353, 322, 2621, 2497, 360, 16677, 18273, 1032, 313, 29933, 29889, 29967, 1846, 310, 383, 499, 265, 29892, 24743, 29892, 29871, 29896, 29900, 4595, 11991, 1919, 29871, 29929, 2107, 29899, 27857, 11991, 29892, 3196, 4930, 778, 29892, 23446, 354, 5652, 322, 263, 3495, 310, 3942, 322, 7875, 29889, 13, 25394, 13537, 2669, 674, 367, 4934, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29901, 29900, 29900, 26354, 322, 6493, 362, 674, 367, 4934, 515, 29871, 29896, 29896, 29901, 29900, 29900, 626, 785, 29871, 29896, 29901, 29900, 29900, 26354, 472, 3824, 23759, 391, 6291, 297, 951, 29886, 5361, 29892, 19444, 13353, 29889, 13, 4074, 358, 674, 367, 472, 10173, 357, 19722, 315, 22875, 297, 951, 29886, 5361, 29892, 19444, 13353, 29889, 13, 16401, 574, 4110, 526, 1090, 278, 2562, 310, 5556, 749, 29891, 29899, 29924, 332, 11461, 13811, 13537, 8778, 13, 2951, 1196, 21235, 29901, 628, 749, 962, 332, 11461, 7692, 13537, 5184, 29992, 21980, 29889, 510, 13, 29934, 566, 22138, 376, 29934, 566, 29891, 29908, 435, 29889, 9234, 314, 492, 264, 13, 29934, 566, 22138, 435, 29889, 376, 29934, 566, 29891, 29908, 9234, 314, 492, 264, 29892, 29871, 29955, 29955, 2440, 2030, 310, 9459, 14439, 29892, 17674, 4502, 3448, 15668, 368, 498, 1295, 3250, 5468, 29871, 29906, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 940, 471, 6345, 3979, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29946, 29906, 297, 3536, 6950, 29892, 17674, 278, 1487, 310, 278, 5683, 10670, 22138, 435, 29889, 322, 6182, 478, 29889, 313, 484, 29948, 1383, 2142, 571, 29897, 9234, 314, 492, 264, 29892, 8471, 297, 10059, 29892, 17674, 322, 349, 1202, 1698, 9459, 29892, 399, 29902, 1434, 3604, 1847, 297, 9459, 14439, 297, 29871, 29896, 29929, 29947, 29947, 29889, 10670, 29891, 22314, 368, 6766, 297, 278, 3148, 5593, 10118, 322, 471, 263, 22314, 4509, 310, 278, 3082, 5682, 291, 4918, 396, 29906, 29929, 29896, 29900, 29889, 10949, 670, 3240, 19211, 297, 29871, 29906, 29900, 29900, 29945, 29892, 10670, 29891, 750, 3796, 408, 263, 12252, 12016, 8364, 8910, 363, 3082, 1281, 6950, 272, 23985, 29892, 382, 3703, 7352, 29892, 17674, 363, 975, 29871, 29946, 29900, 2440, 29889, 10670, 29891, 471, 278, 2343, 310, 278, 349, 1421, 261, 29915, 29879, 1824, 472, 796, 291, 24760, 273, 6291, 29892, 1771, 19639, 515, 29871, 29896, 29929, 29955, 29941, 2745, 29871, 29896, 29929, 29955, 29929, 29892, 263, 4509, 310, 278, 349, 1202, 1698, 9459, 12453, 1171, 29915, 29879, 5977, 322, 278, 405, 4717, 29892, 322, 540, 27849, 29901, 29826, 29892, 9427, 292, 29892, 322, 13736, 3844, 389, 292, 29889, 13, 18498 ]	1,332,858	6,144	CommonCrawl	0	3
vivors include five children: Lisa Baker of Jonesboro, IL, Randy Schwamlien of Lake Villa, IL, Dale (Kim) Johnson of Paddock Lake, WI, Laura (Thomas) Casper of Franksville, WI, and Ki Johnson of Burlington, WI; five grandchildren: Tristan Koeller, Michael (Kari) Corrigan, Matthew (Katie) Corrigan, Miles (Nicole) Corrigan, and Jennifer (Trevor) Gorn; 12 great-grandchildren; sister Carol A. Corrigan of Kenosha, WI; special nephew Robert (Margaret) Moll of Fredonia, KY; great-niece and great-nephews: Robert, Cody, Daniel, Julie, Matthew, and Zack; and many friends. In addition to his parents, Rudy was preceded in death by his life partner: Joanne Johnson on October 11, 2004, a son Timothy Johnson, and a brother Edward A Schwamlien. Funeral Services will be held at 4:00PM Saturday July 11, 2020 at the STRANG FUNERAL HOME OF ANTIOCH 1055 Main St. (Rte. 83) Antioch, IL 60002, with visitation beginning at 12 Noon. Interment will be private. In lieu of flowers, donations to St. Jude Children's Research Hospital are appreciated in Rudy's memory. Please sign the online guest book for Rudy at www.strangfh.com. Anne T. Kinsey Anne T. Kinsey, age 90 of Kenosha passed away peacefully on Friday, June 26, 2020 at Froedert Memorial Hospital, Pleasant Prairie. Beloved wife of the late Paul Kinsey, loving mother of MaryLynn (Jeff) Wedeward, Patricia (Norm) Linnell, and Paula Kinsey; dear grandmother of Allison Wedeward, Michael Wedeward, Kinsey (Quincy) Davis, Breita Linnell and Paul (Lisa) Linnell; great-grandmother of Annika, Chatman, Leo, and Quin. A private Mass of Christian Burial will be celebrated at a later date. 4600 Cty. Line Road, Racine, WI William J. Althaus, Associate Edwin L. Segerstrom Edwin L. Segerstrom, age 76, passed away on Thursday, July 2, 2020 at North Point Senior Living with his family by his side. Born in Eau Claire, WI on July 25, 1943, he was the son of Lloyd and Bertha (Schlitz) Segerstrom. Ed owned and operated his own company, A & J Tool Grinding in Kenosha for many years until his retirement in 1988. He was a remarkable man; not only a loving, devoted and supportive son, father and grandfather but a successful businessman. Ed was a private pilot and also a captain of 2 charter boats that he owned called "The Get Away" and "I dunno". Ed was a member of Midwest Street Machine Car Club. Those left to remember Ed are his mother, Bertha Kempin; his children, Kathy, David and Daniel Segerstrom; their mother and former wife, Patricia Gannaway; his four grandchildren; his siblings, Linda Kimpel, Sandy German, Gary Segerstrom and Donald Kempin Edwin was preceded in death by his father, Lloyd Segerstrom and his sister, Rosanne Willox. Funeral services honoring Edwin's life will be held on Tuesday, July 7, 2020 at 12:00 p.m. at the Piasecki Funeral Home. Interment will take place in All Saints Cemetery. A visitation for Edwin will be held on Tuesday from 10:00 a.m. until the time of the service at the funeral home. Walter J. Barthuly Walter J. Barthuly, age 94, a resident of Kenosha, WI died May 30th, 2020 in Gurnee IL, on the day of his birthday. The light of the world dimmed just	-0.401227	-0.960066	-1.654522	-1.767246	[ -0.5063494072690558, -0.296104228917746 ]	[ -0.850837389971003, -1.0692940768907888 ]	[ -1.654522335457186, -1.654522335457186 ]	[ -1.7802526439339128, -1.7542389412513841 ]	1,024	[ 512, 512 ]	[ 24759, 943, 3160, 5320, 4344, 29901, 29420, 22652, 310, 10920, 4089, 29877, 29892, 17674, 29892, 390, 13910, 9234, 314, 492, 264, 310, 9459, 14439, 29892, 17674, 29892, 360, 744, 313, 29968, 326, 29897, 11717, 310, 349, 1202, 1698, 9459, 29892, 399, 29902, 29892, 21671, 313, 1349, 18902, 29897, 6960, 546, 310, 1352, 2039, 4909, 29892, 399, 29902, 29892, 322, 16540, 11717, 310, 6640, 1847, 880, 29892, 399, 29902, 29936, 5320, 4595, 11991, 29901, 1605, 9777, 8224, 4539, 29892, 5765, 313, 29968, 1306, 29897, 2994, 8966, 273, 29892, 22292, 313, 29968, 9474, 29897, 2994, 8966, 273, 29892, 3833, 267, 313, 29940, 23249, 29897, 2994, 8966, 273, 29892, 322, 23774, 9633, 313, 29911, 276, 5267, 29897, 402, 1398, 29936, 29871, 29896, 29906, 2107, 29899, 27857, 11991, 29936, 9883, 8562, 319, 29889, 2994, 8966, 273, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 4266, 23446, 13636, 4755, 313, 29924, 1191, 10474, 29897, 341, 3028, 310, 12001, 6405, 29892, 476, 29979, 29936, 2107, 29899, 2786, 346, 322, 2107, 29899, 484, 28362, 5652, 29901, 4755, 29892, 315, 1486, 29892, 8432, 29892, 2739, 347, 29892, 22292, 29892, 322, 796, 547, 29936, 322, 1784, 7875, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 10670, 29891, 471, 9399, 287, 297, 4892, 491, 670, 2834, 18096, 29901, 3650, 11276, 11717, 373, 5533, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29900, 29946, 29892, 263, 1487, 7870, 20336, 11717, 29892, 322, 263, 8099, 9300, 319, 9234, 314, 492, 264, 29889, 13, 25394, 13537, 15538, 674, 367, 4934, 472, 29871, 29946, 29901, 29900, 29900, 13427, 24211, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 29486, 19453, 383, 3904, 1001, 1964, 29832, 2303, 8079, 13764, 29911, 5971, 3210, 29871, 29896, 29900, 29945, 29945, 4241, 624, 29889, 313, 29934, 371, 29889, 29871, 29947, 29941, 29897, 5459, 601, 305, 29892, 17674, 29871, 29953, 29900, 29900, 29900, 29906, 29892, 411, 6493, 362, 6763, 472, 29871, 29896, 29906, 1939, 265, 29889, 4124, 358, 674, 367, 2024, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 304, 624, 29889, 435, 1151, 20986, 29915, 29879, 10550, 15967, 526, 7556, 297, 10670, 29891, 29915, 29879, 3370, 29889, 3529, 1804, 278, 7395, 17838, 3143, 363, 10670, 29891, 472, 7821, 29889, 710, 574, 29888, 29882, 29889, 510, 29889, 13, 2744, 484, 323, 29889, 20311, 7759, 13, 2744, 484, 323, 29889, 20311, 7759, 29892, 5046, 29871, 29929, 29900, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 814, 19722, 15967, 29892, 19777, 13186, 9002, 24135, 29889, 13, 21140, 8238, 6532, 310, 278, 5683, 3739, 20311, 7759, 29892, 12355, 292, 5637, 310, 6182, 29931, 948, 29876, 313, 29967, 12352, 29897, 15050, 809, 538, 29892, 4121, 2200, 423, 313, 29940, 555, 29897, 365, 2559, 514, 29892, 322, 2621, 2497, 20311, 7759, 29936, 9425, 4595, 29885, 1228, 310, 2178, 2285, 15050, 809, 538, 29892, 5765, 15050, 809, 538, 29892, 20311, 7759, 313, 2182, 262, 1270, 29897, 15225, 29892, 5826, 2028, 365, 2559, 514, 322, 3739, 313, 29931, 8069, 29897, 365, 2559, 514, 29936, 2107, 29899, 27857, 29885, 1228, 310, 8081, 4106, 29892, 678, 271, 1171, 29892, 22533, 29892, 322, 751, 262, 29889, 13, 29909, 2024, 7360, 310, 6111, 6640, 616, 674, 367, 26301, 472, 263, 2678, 2635, 29889, 13, 29946, 29953, 29900, 29900, 315, 1017, 29889, 7407, 9321, 29892, 390, 562, 457, 29892, 399, 29902, 13, 12984, 2829, 435, 29889, 838, 386, 1485, 29892, 6853, 403, 13, 3853, 5080, 365, 29889, 6667, 15714, 456, 13, 3853, 5080, 365, 29889, 6667, 15714, 456, 29892, 5046, 29871, 29955, 29953, 29892, 4502, 3448, 373, 498, 1295, 3250, 29892, 5468, 29871, 29906, 29892, 29871, 29906, 29900, 29906, 29900, 472, 4644, 8984, 24260, 26176, 411, 670, 3942, 491, 670, 2625, 29889, 13, 29933, 1398, 297, 382, 585, 6015, 533, 29892, 399, 29902, 373, 5468, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29946, 29941, 29892, 540, 471, 278, 1487, 310, 27054, 322, 2292, 15457, 313, 4504, 29880, 2784, 29897, 6667, 15714, 456, 29889, 13, 3853, 15205, 322, 19623, 670, 1914, 5001, 29892, 319, 669, 435, 21704, 1632, 4015, 297, 10015, 359, 2350, 363, 1784, 2440, 2745, 670, 3240, 19211, 297, 29871, 29896, 29929, 29947, 29947, 29889, 13, 3868, 471, 263, 22567, 767, 29936, 451, 871, 263, 12355, 292, 29892, 24600, 322, 2304, 573, 1487, 29892, 4783, 322, 4595, 22212, 541, 263, 9150, 5381, 1171, 29889, 2155, 471, 263, 2024, 19840, 322, 884, 263, 15315, 310, 29871, 29906, 1373, 357, 25462, 393, 540, 15205, 2000, 376, 1576, 3617, 319, 1582, 29908, 322, 376, 29902, 270, 348, 1217, 1642, 2155, 471, 263, 4509, 310, 13370, 5933, 7103, 6189, 1704, 5977, 29889, 13, 1349, 852, 2175, 304, 6456, 2155, 526, 670, 5637, 29892, 2292, 15457, 476, 3451, 262, 29936, 670, 4344, 29892, 19663, 29891, 29892, 4699, 322, 8432, 6667, 15714, 456, 29936, 1009, 5637, 322, 4642, 6532, 29892, 4121, 2200, 423, 402, 812, 21694, 29936, 670, 3023, 4595, 11991, 29936, 670, 27767, 18964, 29892, 365, 11054, 476, 6574, 295, 29892, 8564, 29891, 5332, 29892, 23529, 6667, 15714, 456, 322, 18935, 476, 3451, 262, 13, 3853, 5080, 471, 9399, 287, 297, 4892, 491, 670, 4783, 29892, 27054, 6667, 15714, 456, 322, 670, 9883, 29892, 5678, 11276, 4624, 417, 29916, 29889, 13, 25394, 13537, 5786, 4207, 8253, 2155, 5080, 29915, 29879, 2834, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29955, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 4124, 358, 674, 2125, 2058, 297, 2178, 14342, 1372, 315, 22875, 29889, 319, 6493, 362, 363, 2155, 5080, 674, 367, 4934, 373, 323, 1041, 3250, 515, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 2745, 278, 931, 310, 278, 2669, 472, 278, 2090, 13537, 3271, 29889, 13, 29956, 13794, 435, 29889, 2261, 386, 11850, 13, 29956, 13794, 435, 29889, 2261, 386, 11850, 29892, 5046, 29871, 29929, 29946, 29892, 263, 20201, 310, 10015, 359, 2350, 29892, 399, 29902, 6423, 2610, 29871, 29941, 29900, 386, 29892, 29871, 29906, 29900, 29906, 29900, 297, 402, 332, 484, 29872, 17674, 29892, 373, 278, 2462, 310, 670, 12060, 3250, 29889, 450, 3578, 310, 278, 3186, 3964, 2168, 925 ]	1,332,858	7,168	CommonCrawl	0	3
a little bit but then brightened back up from all of the lives he touched. Walter's daughter Patricia was caring for her father at her home with the help of Star Hospice, Gurnee, IL. Walter's children were able to spend time with him throughout the week leading up to when our Heavenly Father took him home. Walter was born in Fond du Lac WI to John and Katherine (Bopp) Barthuly. He attended high school and the Fond du Lac Business College. He married his beautiful and loving wife Patricia Lardinois on February 18, 1947 in Fond du Lac, WI. They spent their honeymoon in Chicago after taking the train to the city. Walter and Patricia were married for 73 years. What Wally enjoyed most was spending time with family, visiting friends and was always willing to give a helping hand to those in need. Wally was drafted during World War II and went through basic training/tech school. He was inducted in August 1944. His military occupational specialty was a Radio Operator, High Speed. He served in the Southwest Pacific Theater of Operations and went on to serve during the Korean Conflict and Berlin Crisis on active duty, National Guard and Reserves. His military service time was just short of 30 years. He retired as an Army Captain in May 1986. As a civilian his occupation was a Locomotive Maintenance Mechanic helper. Medals and decorations Walter earned included WW II American Theater Campaign Ribbon, Army of Occupation Medal (Japan), Good Conduct Medal, WWII Victory Asiatic-Pacific Campaign Medal, Army of Occupation National Defense Service Medal, Armed Forces Reserve, Army Presidential Unit Citation with 1 Oak Leaf Cluster, Combat Infantryman Badge, Marksman Rifle & Pistol Badge, and Expert Rifle & Carbine Badge. He worked for the Department of Defense as a troubleshooter for 15 years. He was a member of the Veterans of Foreign Wars and was a Golden Gloves Boxer. Wally worked for the City of Kenosha Transit Department as a bus driver and training coordinator for 14 years until retiring in 1994. He drove tour bus for the Tommy Dorsey band and the Kenosha Twins baseball team. Walter was a die-hard Green Bay Packer and Milwaukee Brewer fan. Wally is a member of Journey Church, Kenosha, WI. He joined Gideons International in 1984 and he was a member of Light for the Lost. He touched many lives during his 32 years of working with the Royal Rangers. Walter is preceded in death by parents John and Katherine Barthuly, his siblings Alex (Betty) Barthuly, Otto (Vivian) Barthuly, Johnny (Jennifer) Barthuly, Nathalie (Adolph) Hunt, Esther (Herman) Burkhardt, and Dorothy (Gordy) Zwicky. Carrying on his legacy are his wife Patricia Barthuly, his children Walter (Bonnie) Barthuly, David (Holly) Barthuly, Brad (Lorreen) Barthuly, Patricia (Dan) Jimenez, Scott (Nancy) Barthuly, and Dawn (Chris) Maylath. Grandchildren: Rachel (Anthony), Aaron (Nicole), Rebekah (Jonathan), Jonathan, Bradley (Traci), Bret, Christopher, Andrew, Jacqueline (Paul), and Alex. Great Grandchildren: Juliana, Alejandra, Katelyn, Audrey, Benjamin, Gwynivere, Robert, and Mollie. A memorial service will be held on July 11, 2020 at Journey Church (10700 75th St, Kenosha, WI). Visitation with the family will be at 9:30am and the service will be at 10:00am with Military Honors to follow. If attending the visitation or memorial service we ask that you please be respectful of others and practice social distancing guidelines. Walter will be interred at Southern Wisconsin Veterans Memorial Cemetery in Union Grove, WI at a later date. To leave Memories & Condolences to the family go to www.CaseyFamilyOptions.com. Donations can be made in Walter	-0.157082	0.129532	-0.747182	-1.370537	[ 0.1113742112093852, -0.42553855695812887 ]	[ 0.6353843325160634, -0.37632081592392763 ]	[ -0.3293363996939053, -1.165027817558022 ]	[ -1.0908895228468987, -1.6501841305212688 ]	1,024	[ 512, 512 ]	[ 263, 2217, 2586, 541, 769, 11785, 6419, 1250, 701, 515, 599, 310, 278, 12080, 540, 23051, 29889, 10705, 29915, 29879, 8750, 4121, 2200, 423, 471, 1559, 292, 363, 902, 4783, 472, 902, 3271, 411, 278, 1371, 310, 7828, 379, 4705, 625, 29892, 402, 332, 484, 29872, 29892, 17674, 29889, 10705, 29915, 29879, 4344, 892, 2221, 304, 18864, 931, 411, 1075, 10106, 278, 4723, 8236, 701, 304, 746, 1749, 22977, 368, 17852, 3614, 1075, 3271, 29889, 13, 29956, 13794, 471, 6345, 297, 383, 898, 868, 21095, 399, 29902, 304, 2259, 322, 476, 16490, 313, 8431, 407, 29897, 2261, 386, 11850, 29889, 940, 14283, 1880, 3762, 322, 278, 383, 898, 868, 21095, 15197, 6346, 29889, 940, 8300, 670, 9560, 322, 12355, 292, 6532, 4121, 2200, 423, 365, 538, 12387, 373, 6339, 29871, 29896, 29947, 29892, 29871, 29896, 29929, 29946, 29955, 297, 383, 898, 868, 21095, 29892, 399, 29902, 29889, 2688, 10398, 1009, 298, 650, 962, 6150, 297, 10059, 1156, 5622, 278, 7945, 304, 278, 4272, 29889, 10705, 322, 4121, 2200, 423, 892, 8300, 363, 29871, 29955, 29941, 2440, 29889, 1724, 399, 635, 27849, 1556, 471, 805, 2548, 931, 411, 3942, 29892, 6493, 292, 7875, 322, 471, 2337, 17762, 304, 2367, 263, 19912, 1361, 304, 1906, 297, 817, 29889, 13, 29956, 635, 471, 18195, 287, 2645, 2787, 3362, 1944, 322, 3512, 1549, 6996, 6694, 29914, 11345, 3762, 29889, 940, 471, 22799, 287, 297, 3111, 29871, 29896, 29929, 29946, 29946, 29889, 3600, 9121, 6919, 1288, 4266, 1017, 471, 263, 9204, 6607, 1061, 29892, 5057, 24839, 29889, 940, 6766, 297, 278, 4275, 5933, 14328, 16150, 310, 6607, 800, 322, 3512, 373, 304, 9080, 2645, 278, 22467, 10811, 29176, 322, 5115, 29524, 275, 373, 6136, 13360, 29892, 3086, 13211, 322, 2538, 20098, 29889, 3600, 9121, 2669, 931, 471, 925, 3273, 310, 29871, 29941, 29900, 2440, 29889, 940, 16528, 408, 385, 8811, 10842, 297, 2610, 29871, 29896, 29929, 29947, 29953, 29889, 1094, 263, 7631, 713, 670, 26818, 471, 263, 4309, 23045, 573, 4241, 841, 749, 27439, 293, 16876, 29889, 3436, 1338, 322, 10200, 800, 10705, 20591, 5134, 399, 29956, 1944, 3082, 16150, 7259, 8729, 27461, 6718, 29892, 8811, 310, 16117, 786, 362, 18416, 313, 29967, 21419, 511, 7197, 1281, 2199, 18416, 29892, 399, 29956, 2687, 7229, 706, 319, 1039, 2454, 29899, 29925, 562, 928, 7259, 8729, 18416, 29892, 8811, 310, 16117, 786, 362, 3086, 5282, 1947, 6692, 18416, 29892, 826, 2168, 25571, 27811, 29892, 8811, 7178, 616, 13223, 315, 7018, 411, 29871, 29896, 24132, 951, 2142, 2233, 5402, 29892, 422, 10222, 26571, 1171, 9178, 479, 29892, 4485, 29879, 1171, 390, 361, 280, 669, 349, 19639, 9178, 479, 29892, 322, 1222, 10700, 390, 361, 280, 669, 1704, 26062, 9178, 479, 29889, 940, 3796, 363, 278, 10317, 310, 5282, 1947, 408, 263, 18835, 1251, 17084, 363, 29871, 29896, 29945, 2440, 29889, 940, 471, 263, 4509, 310, 278, 478, 1308, 550, 310, 19358, 9149, 322, 471, 263, 16108, 21806, 1960, 11773, 261, 29889, 13, 29956, 635, 3796, 363, 278, 4412, 310, 10015, 359, 2350, 4103, 277, 10317, 408, 263, 3593, 7156, 322, 6694, 6615, 1061, 363, 29871, 29896, 29946, 2440, 2745, 3240, 8491, 297, 29871, 29896, 29929, 29929, 29946, 29889, 940, 26603, 6282, 3593, 363, 278, 27036, 9579, 7759, 3719, 322, 278, 10015, 359, 2350, 8168, 1144, 21573, 3815, 29889, 10705, 471, 263, 762, 29899, 6800, 7646, 6211, 18744, 261, 322, 3833, 29893, 585, 23137, 5826, 556, 13524, 29889, 13, 29956, 635, 338, 263, 4509, 310, 435, 473, 3801, 6291, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 8772, 402, 680, 787, 4623, 297, 29871, 29896, 29929, 29947, 29946, 322, 540, 471, 263, 4509, 310, 12790, 363, 278, 25133, 29889, 940, 23051, 1784, 12080, 2645, 670, 29871, 29941, 29906, 2440, 310, 1985, 411, 278, 7021, 390, 13873, 29889, 13, 29956, 13794, 338, 9399, 287, 297, 4892, 491, 11825, 2259, 322, 476, 16490, 2261, 386, 11850, 29892, 670, 27767, 18964, 4827, 313, 29933, 300, 1017, 29897, 2261, 386, 11850, 29892, 13832, 313, 29963, 440, 713, 29897, 2261, 386, 11850, 29892, 20179, 313, 29967, 2108, 9633, 29897, 2261, 386, 11850, 29892, 405, 493, 284, 347, 313, 3253, 22138, 29897, 379, 1657, 29892, 2661, 2276, 313, 29950, 3504, 29897, 6640, 29895, 25603, 29892, 322, 9579, 20336, 313, 29954, 536, 29891, 29897, 796, 6669, 29891, 29889, 13, 8179, 719, 292, 373, 670, 25000, 526, 670, 6532, 4121, 2200, 423, 2261, 386, 11850, 29892, 670, 4344, 10705, 313, 29933, 265, 2786, 29897, 2261, 386, 11850, 29892, 4699, 313, 29950, 18368, 29897, 2261, 386, 11850, 29892, 15862, 313, 29931, 272, 2733, 29897, 2261, 386, 11850, 29892, 4121, 2200, 423, 313, 18529, 29897, 8507, 10281, 29892, 8075, 313, 29940, 6906, 29897, 2261, 386, 11850, 29892, 322, 7266, 1233, 313, 11626, 275, 29897, 2610, 29880, 493, 29889, 6265, 11991, 29901, 23647, 295, 313, 2744, 386, 2592, 511, 319, 5022, 313, 29940, 23249, 511, 12936, 1416, 801, 313, 29967, 265, 11385, 511, 20983, 29892, 15862, 2330, 313, 5323, 455, 511, 23132, 29892, 18888, 29892, 11571, 29892, 6044, 339, 5570, 313, 18275, 511, 322, 4827, 29889, 7027, 6265, 11991, 29901, 2739, 3857, 29892, 7801, 29926, 10738, 29892, 476, 2486, 29876, 29892, 8612, 8903, 29892, 20212, 29892, 402, 29893, 948, 2147, 29872, 29892, 4755, 29892, 322, 341, 3028, 347, 29889, 13, 29909, 2626, 9020, 2669, 674, 367, 4934, 373, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 435, 473, 3801, 6291, 313, 29896, 29900, 29955, 29900, 29900, 29871, 29955, 29945, 386, 624, 29892, 10015, 359, 2350, 29892, 399, 29902, 467, 5741, 7018, 411, 278, 3942, 674, 367, 472, 29871, 29929, 29901, 29941, 29900, 314, 322, 278, 2669, 674, 367, 472, 29871, 29896, 29900, 29901, 29900, 29900, 314, 411, 20080, 7906, 943, 304, 1101, 29889, 960, 1098, 2548, 278, 6493, 362, 470, 2626, 9020, 2669, 591, 2244, 393, 366, 3113, 367, 3390, 1319, 310, 4045, 322, 6944, 5264, 1320, 19985, 1410, 10652, 1475, 29889, 13, 29956, 13794, 674, 367, 1006, 1127, 472, 14234, 22581, 478, 1308, 550, 19722, 315, 22875, 297, 7761, 6070, 345, 29892, 399, 29902, 472, 263, 2678, 2635, 29889, 13, 1762, 5967, 8133, 3842, 669, 11790, 324, 2063, 304, 278, 3942, 748, 304, 7821, 29889, 8259, 29891, 27104, 5856, 29889, 510, 29889, 3872, 800, 508, 367, 1754, 297, 10705 ]	1,332,858	8,192	CommonCrawl	0	3
's name to Gideons International www.gideons.org. The family would like to thank Dr. Neil Shepler. Casey Family Options Funerals and Cremations Stephen P. Casey, Funeral Director and Owner 3016-75th Street, Kenosha WI 53142 www.CaseyFamilyOptions.com Barbara "Barb" M. Pofahl Barbara "Barb" M. Pofahl, 77, of Kenosha, passed away peacefully, Monday, June 29, 2020 at the Hospice Alliance Hospice House. Please see our webster for a complete obituary. Bruch Funeral Home Visit Barb's www.bruchfuneralhome.net Richard C. Smith Richard C. Smith, age 78 of Somers, WI, passed away on June 30, 2020 at his home. Born in Kenosha, WI on September 22, 1941, he was the son of the late Milton and Violet (Falk) Smith. Richard was a graduate of Bradford High School. Rich was employed as a Maintenance Mechanic with Chrysler. Prior to working at Chrysler, he was employed with Chevrolet Garage for 25 years and operated his own lawn service. He enjoyed spending time with his sons. Rich loved hunting, fishing, cribbage and most of all, his daily trips to play pull tabs with his black lab Sally. Rich is survived by his companion, Diane Gunderson; his children, Jeffrey (Tricia) Smith and Gregory Smith; his grandchildren, Ryan Dauster, Christopher Smith; his sister, Janann (Tom) Botzau; and his former wife Judy Smith. In addition to his parents, Rich was preceded in death by his daughter, Rhonda Smith. Services honoring Rich's life will be held privately. Inurnment will take place in St. George Cemetery. A Celebration of Rich's life will be held on Thursday, July 9, 2020 at 12 p.m. at Tina's Somers Inn, 8013-12th St, Somers, WI 53144. Laura Burke Laura Burke, of Camarillo, California, peacefully passed into heaven on May 14, 2020, at the age of 87. She was born in July of 1932, in Kenosha, Wisconsin, to Giuseppe (Joseph) Turco and Rose (Covelli) Turco, the second of their four children. As a child of the Depression she worked beside her parents to provide for the family, helping to plant crops, care for animals, preserve the harvest, and learned the value of a dollar. She often walked to town to do the family errands. Laura graduated from Mary D. Bradford High School in 1950. She worked at J.J. Newberry's and fondly remembered her days as a "soda jerk" at Mayer Drug in Kenosha. Later, she joined the work force at Great Lakes Naval Base in Illinois. One sunny day, when she was walking down the gravel road to add a letter to the mailbox, the boy next door, Hozie Burke, noticed her, and declared that they would be married one day. Laura told him that was "quite a line", but in October of 1953, they were joined in matrimony at Holy Rosary Catholic Church. They were married 64 years. In 1964 they moved to Oxnard, California, Hozie filling a position at Oxnard Air Force Base and Laura becoming a teller at the Bank of America branch serving the SeaBee base in Port Hueneme. They later relocated to Apple Valley, California. Laura worked for Bank of America for 23 years, becoming a loan officer, a branch manager and serving as a member of the regional staff. During those years she helped countless individuals buy their first homes, start businesses, realize goals, and overcome personal tragedy. She did this with skill, professionalism, grace, and compassion. Laura loved numbers—she actually enjoyed balancing her checkbook! But most of all, she treasured her faith, cherished her friends, and loved her family. Her thoughtfulness, the warmth of	0.027824	-0.687443	-0.935498	-1.741232	[ -0.7857631947848029, 0.8414112148657245 ]	[ -1.201800591907708, -0.17308447194527454 ]	[ -1.5480002123910466, -0.3229957971304447 ]	[ -1.9935650059306493, -1.4888991738895898 ]	1,024	[ 512, 512 ]	[ 29915, 29879, 1024, 304, 402, 680, 787, 4623, 7821, 29889, 29887, 680, 787, 29889, 990, 29889, 450, 3942, 723, 763, 304, 6452, 4942, 29889, 29334, 2296, 20069, 29889, 13, 8259, 29891, 14662, 25186, 13811, 261, 1338, 322, 315, 1745, 800, 13, 7789, 9789, 349, 29889, 11733, 29891, 29892, 13811, 13537, 15944, 322, 438, 23007, 13, 29941, 29900, 29896, 29953, 29899, 29955, 29945, 386, 7103, 29892, 10015, 359, 2350, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 13, 1636, 29889, 8259, 29891, 27104, 5856, 29889, 510, 13, 4297, 13839, 376, 4297, 29890, 29908, 341, 29889, 349, 974, 4494, 13, 4297, 13839, 376, 4297, 29890, 29908, 341, 29889, 349, 974, 4494, 29892, 29871, 29955, 29955, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 29892, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 379, 4705, 625, 29855, 379, 4705, 625, 5619, 29889, 13, 12148, 1074, 1749, 1856, 2475, 363, 263, 4866, 704, 1981, 653, 29889, 13, 29933, 582, 305, 13811, 13537, 8778, 13, 6116, 277, 21826, 29915, 29879, 13, 1636, 29889, 16670, 305, 7692, 13537, 5184, 29889, 1212, 13, 25627, 538, 315, 29889, 7075, 13, 25627, 538, 315, 29889, 7075, 29892, 5046, 29871, 29955, 29947, 310, 6254, 414, 29892, 399, 29902, 29892, 4502, 3448, 373, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 10015, 359, 2350, 29892, 399, 29902, 373, 3839, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29946, 29896, 29892, 540, 471, 278, 1487, 310, 278, 5683, 3833, 880, 322, 478, 601, 1026, 313, 29943, 2235, 29897, 7075, 29889, 6123, 471, 263, 10591, 403, 310, 15862, 4006, 5057, 4523, 29889, 13, 25627, 471, 15723, 408, 263, 4241, 841, 749, 27439, 293, 411, 678, 18450, 1358, 29889, 22096, 304, 1985, 472, 678, 18450, 1358, 29892, 540, 471, 15723, 411, 6561, 29894, 307, 1026, 7455, 482, 363, 29871, 29906, 29945, 2440, 322, 19623, 670, 1914, 425, 1233, 2669, 29889, 13, 3868, 27849, 805, 2548, 931, 411, 670, 18025, 29889, 4385, 18012, 29826, 29892, 9427, 292, 29892, 274, 1091, 17807, 322, 1556, 310, 599, 29892, 670, 14218, 3367, 567, 304, 1708, 8206, 18859, 411, 670, 4628, 9775, 317, 635, 29889, 13, 25627, 338, 10503, 2347, 491, 670, 18708, 29892, 360, 16677, 402, 870, 1330, 29936, 670, 4344, 29892, 12208, 8903, 313, 29911, 2200, 423, 29897, 7075, 322, 29094, 7075, 29936, 670, 4595, 11991, 29892, 20916, 7266, 5402, 29892, 18888, 7075, 29936, 670, 9883, 29892, 2627, 812, 313, 21599, 29897, 11273, 29920, 585, 29936, 322, 670, 4642, 6532, 8660, 29891, 7075, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 4385, 471, 9399, 287, 297, 4892, 491, 670, 8750, 29892, 7861, 14287, 7075, 29889, 13, 13779, 4207, 8253, 4385, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 512, 595, 358, 674, 2125, 2058, 297, 624, 29889, 5122, 315, 22875, 29889, 319, 315, 6146, 1182, 362, 310, 4385, 29915, 29879, 2834, 674, 367, 4934, 373, 498, 1295, 3250, 29892, 5468, 29871, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29906, 282, 29889, 29885, 29889, 472, 323, 1099, 29915, 29879, 6254, 414, 25408, 29892, 29871, 29947, 29900, 29896, 29941, 29899, 29896, 29906, 386, 624, 29892, 6254, 414, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29946, 29889, 13, 5661, 2002, 6640, 446, 13, 5661, 2002, 6640, 446, 29892, 310, 5500, 279, 9093, 29892, 8046, 29892, 10776, 3730, 4502, 964, 18356, 373, 2610, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 278, 5046, 310, 29871, 29947, 29955, 29889, 13, 13468, 471, 6345, 297, 5468, 310, 29871, 29896, 29929, 29941, 29906, 29892, 297, 10015, 359, 2350, 29892, 22581, 29892, 304, 18824, 313, 26473, 561, 29897, 5383, 1111, 322, 14008, 313, 29907, 586, 5481, 29897, 5383, 1111, 29892, 278, 1473, 310, 1009, 3023, 4344, 29889, 1094, 263, 2278, 310, 278, 897, 2590, 1183, 3796, 17620, 902, 11825, 304, 3867, 363, 278, 3942, 29892, 19912, 304, 8024, 8182, 567, 29892, 2562, 363, 15006, 29892, 19905, 278, 4023, 10147, 29892, 322, 10972, 278, 995, 310, 263, 11232, 279, 29889, 2296, 4049, 17096, 304, 4726, 304, 437, 278, 3942, 4589, 4167, 29889, 13, 5661, 2002, 23588, 515, 6182, 360, 29889, 15862, 4006, 5057, 4523, 297, 29871, 29896, 29929, 29945, 29900, 29889, 2296, 3796, 472, 435, 29889, 29967, 29889, 1570, 16344, 29915, 29879, 322, 6299, 368, 21832, 902, 3841, 408, 263, 376, 29879, 8887, 432, 5968, 29908, 472, 2610, 261, 360, 11124, 297, 10015, 359, 2350, 29889, 12699, 29892, 1183, 8772, 278, 664, 4889, 472, 7027, 365, 6926, 21590, 7399, 297, 17066, 29889, 13, 6716, 6575, 1460, 2462, 29892, 746, 1183, 471, 22049, 1623, 278, 2646, 955, 6520, 304, 788, 263, 5497, 304, 278, 10524, 1884, 29892, 278, 8023, 2446, 3050, 29892, 379, 2112, 347, 6640, 446, 29892, 10548, 902, 29892, 322, 8052, 393, 896, 723, 367, 8300, 697, 2462, 29889, 21671, 5429, 1075, 393, 471, 376, 339, 568, 263, 1196, 613, 541, 297, 5533, 310, 29871, 29896, 29929, 29945, 29941, 29892, 896, 892, 8772, 297, 1775, 5632, 2592, 472, 17733, 5678, 653, 11865, 6291, 29889, 2688, 892, 8300, 29871, 29953, 29946, 2440, 29889, 13, 797, 29871, 29896, 29929, 29953, 29946, 896, 6153, 304, 9471, 29876, 538, 29892, 8046, 29892, 379, 2112, 347, 27523, 263, 2602, 472, 9471, 29876, 538, 5593, 11004, 7399, 322, 21671, 14171, 263, 2649, 261, 472, 278, 10253, 310, 6813, 5443, 16330, 278, 14070, 3629, 29872, 2967, 297, 3371, 379, 3837, 2004, 29889, 2688, 2678, 337, 28809, 304, 12113, 13939, 29892, 8046, 29889, 21671, 3796, 363, 10253, 310, 6813, 363, 29871, 29906, 29941, 2440, 29892, 14171, 263, 24806, 12139, 29892, 263, 5443, 8455, 322, 16330, 408, 263, 4509, 310, 278, 14014, 13925, 29889, 7133, 1906, 2440, 1183, 9213, 2302, 2222, 15724, 15649, 1009, 937, 17774, 29892, 1369, 5381, 267, 29892, 16289, 14433, 29892, 322, 25688, 7333, 1020, 3192, 29891, 29889, 2296, 1258, 445, 411, 19911, 29892, 10257, 1608, 29892, 17659, 29892, 322, 752, 465, 291, 29889, 13, 5661, 2002, 18012, 3694, 30003, 11360, 2869, 27849, 6411, 19985, 902, 1423, 2909, 29991, 1205, 1556, 310, 599, 29892, 1183, 2578, 294, 2955, 902, 10847, 29892, 14954, 3276, 902, 7875, 29892, 322, 18012, 902, 3942, 29889, 2439, 2714, 1319, 2264, 29892, 278, 14294, 386, 310 ]	1,332,858	9,216	CommonCrawl	0	3
her home, and the hospitality she offered were legendary—the coffee, treats, and conversation were wonderful; there were amazing Italian dinners; and grandchildren and their friends could always count on a full cookie jar and her fabulous milkshakes. Laura is survived by her son, William Burke (Linda) of Camarillo; daughter, Laurie (Charles Vanoni) of Somis; five grandchildren, Matthew Vanoni, Mark (Gwyndolin) Vanoni, Michaela (Michael) Otani, Tierney (Michael) Meyer and Lee Burke; five great-grandchildren; brother, Guy Turco; and sister, Janet (Ewald) Weiss; as well as many much-loved in-laws, nieces and nephews. She was preceded in death by her husband, parents, and sister, Mary Jane Sorensen Due to restrictions imposed by COVID-19 mandates, funeral services and interment will be private. Arrangements are under the direction of Joseph P. Reardon Funeral Home, Ventura, California, and Proko Funeral Home, Kenosha, Wisconsin. Jon Buckingham January 21, 1939—June 25, 2020 Jon E. Buckingham, age 81 of Kenosha passed away peacefully on Thursday, June 25, 2020 at Burlington Memorial Hospital. Loving father of Ann Delaney; Dear grandfather of Jessica, Patrick, David, and Michael; brother of Tom (Mardell) Buckingham; special friend of Michael D. Klopp. A celebration of Jon's life will be held on Monday, July 6, 2020 at 2:00 p.m. at the funeral home. Friends are invited to meet with the family on Monday from 12:00 Noon until the time of the service. Memorial remembrances to Safe Harbor Humane Society, 7811 60th Ave., Kenosha, WI 53142 would be appreciated. Jon's complete obituary will be made available on the funeral home website on Wednesday, July 1, 2020. DRAEGER-LANGENDORF FUNERAL HOME & CREMATORY 4600 COUNTY LINE ROAD (corner of KR & 22nd Avenue) www.draeger-langendorf.com Ada DeBartolo Ada DeBartolo, 83, of Kenosha, passed away peacefully at her home on Monday, June 29, 2020, surrounded by her loving family. Born on April 9, 1937, in Marano Principato, Prov. of Cosenza, Italy, she was the daughter of the late Serafino and Maria (Filippelli) Bosco. In 1955, she came from Italy to Kenosha to make her home. On September 12, 1954, she married Ignazio DeBartolo in Italy. He preceded her in death on January 6, 2009. Ada and Ignazio owned and operated DeBartolo's Deli & Liquor from 1974 until 2000 when they retired. Ada was a member of Our Lady of Mt. Carmel Catholic Church. She greatly enjoyed cooking and entertaining family and friends, knitting blankets with love, baking and playing old maid with her grandchildren, telling stories of Italy while listening to Elvis and her Italian favorites, gardening and planting flowers, traveling all over the world with the love of her life, and her daily phone calls with her siblings. Above all else, she treasured her time spent being surrounded by her family. Surviving Ada are her six adoring children, Frank (Peggy) DeBartolo of Salem, Susan DeBartolo of Pleasant Prairie, Tina (John) Serpe of Pleasant Prairie, Carla (Scott) Lamos of Kenosha, Sandy (Robert) Morrone of Kenosha, and Tony (Katie) DeBartolo of Pleasant Prairie; her ten grandchildren, Nicole (Eddie) Briggs-Mulloy, Michael Briggs, Vincent (Charlotte) Morrone, Vanessa (Michael) Ambrosini, Francesca Ser	0.19471	-1.063922	-1.464304	-1.876503	[ 0.5510400239179873, -0.16161922273293022 ]	[ -0.9797626478253028, -1.1480817344684164 ]	[ -1.4110431970202961, -1.5175653200864354 ]	[ -1.8010636060799359, -1.9519430816386032 ]	1,024	[ 512, 512 ]	[ 902, 3271, 29892, 322, 278, 13457, 537, 1183, 12520, 892, 15983, 653, 30003, 1552, 26935, 29892, 2578, 1446, 29892, 322, 14983, 892, 20695, 29936, 727, 892, 21863, 292, 10545, 270, 16697, 29936, 322, 4595, 11991, 322, 1009, 7875, 1033, 2337, 2302, 373, 263, 2989, 15327, 14631, 322, 902, 10135, 352, 681, 27274, 845, 6926, 29889, 13, 5661, 2002, 338, 10503, 2347, 491, 902, 1487, 29892, 4667, 6640, 446, 313, 29931, 11054, 29897, 310, 5500, 279, 9093, 29936, 8750, 29892, 14019, 347, 313, 5914, 793, 6556, 5271, 29897, 310, 6254, 275, 29936, 5320, 4595, 11991, 29892, 22292, 6556, 5271, 29892, 4485, 313, 29954, 12822, 299, 22878, 29897, 6556, 5271, 29892, 3375, 29874, 3100, 313, 24083, 29897, 8540, 3270, 29892, 29088, 3801, 313, 24083, 29897, 26581, 322, 9371, 6640, 446, 29936, 5320, 2107, 29899, 27857, 11991, 29936, 8099, 29892, 15880, 5383, 1111, 29936, 322, 9883, 29892, 2627, 300, 313, 29923, 18370, 29897, 1334, 790, 29936, 408, 1532, 408, 1784, 1568, 29899, 417, 1490, 297, 29899, 433, 5652, 29892, 4930, 778, 322, 23446, 354, 5652, 29889, 13, 13468, 471, 9399, 287, 297, 4892, 491, 902, 10216, 29892, 11825, 29892, 322, 9883, 29892, 6182, 10447, 17784, 14762, 13, 29928, 434, 304, 25091, 527, 4752, 491, 19937, 29899, 29896, 29929, 9619, 1078, 29892, 2090, 13537, 5786, 322, 1006, 358, 674, 367, 2024, 29889, 13, 16401, 574, 4110, 526, 1090, 278, 5305, 310, 6936, 349, 29889, 830, 20342, 13811, 13537, 8778, 29892, 21141, 2002, 29892, 8046, 29892, 322, 1019, 2901, 13811, 13537, 8778, 29892, 10015, 359, 2350, 29892, 22581, 29889, 13, 29967, 265, 16281, 16094, 13, 29967, 15623, 653, 29871, 29906, 29896, 29892, 29871, 29896, 29929, 29941, 29929, 30003, 29967, 1540, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 13, 29967, 265, 382, 29889, 16281, 16094, 29892, 5046, 29871, 29947, 29896, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 498, 1295, 3250, 29892, 5306, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 472, 6640, 1847, 880, 19722, 15967, 29889, 13, 29931, 21081, 4783, 310, 8081, 5556, 273, 1032, 29936, 360, 799, 4595, 22212, 310, 23010, 983, 29892, 14875, 29892, 4699, 29892, 322, 5765, 29936, 8099, 310, 4335, 313, 29924, 538, 514, 29897, 16281, 16094, 29936, 4266, 5121, 310, 5765, 360, 29889, 476, 417, 407, 29889, 13, 29909, 10894, 362, 310, 9937, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 29889, 11169, 1975, 526, 23610, 304, 5870, 411, 278, 3942, 373, 27822, 515, 29871, 29896, 29906, 29901, 29900, 29900, 1939, 265, 2745, 278, 931, 310, 278, 2669, 29889, 19722, 1083, 1590, 661, 778, 304, 5701, 1725, 3536, 4089, 13863, 1662, 7765, 29892, 29871, 29955, 29947, 29896, 29896, 29871, 29953, 29900, 386, 319, 345, 1696, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 723, 367, 7556, 29889, 9937, 29915, 29879, 4866, 704, 1981, 653, 674, 367, 1754, 3625, 373, 278, 2090, 13537, 3271, 4700, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 29928, 4717, 11787, 1001, 29899, 29931, 19453, 11794, 1955, 29943, 383, 3904, 1001, 1964, 29832, 2303, 669, 315, 1525, 29924, 1299, 18929, 13, 29946, 29953, 29900, 29900, 21122, 29979, 365, 8895, 16641, 3035, 13, 29898, 2616, 1089, 310, 476, 29934, 669, 29871, 29906, 29906, 299, 18874, 29897, 13, 1636, 29889, 19811, 387, 261, 29899, 3893, 21466, 29889, 510, 13, 29909, 1388, 897, 29933, 442, 3543, 13, 29909, 1388, 897, 29933, 442, 3543, 29892, 29871, 29947, 29941, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 472, 902, 3271, 373, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 22047, 491, 902, 12355, 292, 3942, 29889, 13, 29933, 1398, 373, 3786, 29871, 29929, 29892, 29871, 29896, 29929, 29941, 29955, 29892, 297, 1085, 1562, 14771, 29886, 1219, 29892, 9133, 29889, 310, 13526, 5723, 29892, 12730, 29892, 1183, 471, 278, 8750, 310, 278, 5683, 317, 1572, 29888, 1789, 322, 6217, 313, 29943, 2638, 407, 5481, 29897, 10211, 1111, 29889, 512, 29871, 29896, 29929, 29945, 29945, 29892, 1183, 2996, 515, 12730, 304, 10015, 359, 2350, 304, 1207, 902, 3271, 29889, 1551, 3839, 29871, 29896, 29906, 29892, 29871, 29896, 29929, 29945, 29946, 29892, 1183, 8300, 18076, 834, 601, 897, 29933, 442, 3543, 297, 12730, 29889, 940, 9399, 287, 902, 297, 4892, 373, 5490, 29871, 29953, 29892, 29871, 29906, 29900, 29900, 29929, 29889, 13, 29909, 1388, 322, 18076, 834, 601, 15205, 322, 19623, 897, 29933, 442, 3543, 29915, 29879, 360, 5037, 669, 2718, 339, 272, 515, 29871, 29896, 29929, 29955, 29946, 2745, 29871, 29906, 29900, 29900, 29900, 746, 896, 16528, 29889, 13, 29909, 1388, 471, 263, 4509, 310, 8680, 10040, 310, 341, 29873, 29889, 1704, 12873, 11865, 6291, 29889, 2296, 11180, 27849, 7984, 292, 322, 22684, 292, 3942, 322, 7875, 29892, 889, 5367, 9654, 1691, 411, 5360, 29892, 289, 5086, 322, 8743, 2030, 611, 333, 411, 902, 4595, 11991, 29892, 14509, 15874, 310, 12730, 1550, 19866, 304, 1260, 1730, 322, 902, 10545, 7853, 3246, 29892, 16423, 292, 322, 8024, 292, 18281, 29892, 9850, 292, 599, 975, 278, 3186, 411, 278, 5360, 310, 902, 2834, 29892, 322, 902, 14218, 9008, 5717, 411, 902, 27767, 18964, 29889, 319, 29205, 599, 1683, 29892, 1183, 2578, 294, 2955, 902, 931, 10398, 1641, 22047, 491, 902, 3942, 29889, 13, 18498, 29894, 4357, 23255, 526, 902, 4832, 594, 8253, 4344, 29892, 4976, 313, 29925, 387, 1927, 29897, 897, 29933, 442, 3543, 310, 317, 12698, 29892, 25914, 897, 29933, 442, 3543, 310, 19777, 13186, 9002, 24135, 29892, 323, 1099, 313, 11639, 29897, 1816, 412, 310, 19777, 13186, 9002, 24135, 29892, 1704, 433, 313, 4421, 1501, 29897, 12718, 359, 310, 10015, 359, 2350, 29892, 8564, 29891, 313, 9588, 2151, 29897, 3879, 29878, 650, 310, 10015, 359, 2350, 29892, 322, 15293, 313, 29968, 9474, 29897, 897, 29933, 442, 3543, 310, 19777, 13186, 9002, 24135, 29936, 902, 3006, 4595, 11991, 29892, 405, 23249, 313, 29923, 1289, 347, 29897, 13051, 3174, 29899, 29924, 352, 2376, 29892, 5765, 13051, 3174, 29892, 19748, 313, 5914, 8276, 371, 29897, 3879, 29878, 650, 29892, 6556, 9297, 313, 24083, 29897, 15145, 1883, 2172, 29892, 10986, 1113, 1816 ]	1,332,858	10,240	CommonCrawl	0	3
pe, Ignazio (Diamond) DeBartolo, McKenzie Lamos, Luciano, Ava, and Enzo DeBartolo; one great-grandchild, Ignazio Francesco DeBartolo III; brother, Aldo (Connie) Bosco; sister, Iolanda (Mario) Sorrentino; two brothers-in-law, Eugenio "Gino" (Connie) DeBartolo and Orlando Bartello; and three sisters-in-law, Irma Bosco, Ersilia (Domenico) Casalena and Gloria Presta. She was preceded in death by her great-grandson, Benjamin Robert Morrone in infancy; brother, Francesco Bosco; two sisters-in-law, Carmella Ruffolo and Emma Bartello; and brother-in-law, Aldo Presta. The family would like to extend a special Thank You to Dr. Giuseppe Garretto and his staff, and the staff of Hospice Alliance and the staff at Society Assets for the wonderful care that was extended to Ada and her family during her illness. A visitation will be held on Monday, July 6, 2020, at Proko Funeral Home from 4:00 p.m. until 7:00 p.m. For the safety and security of our guests we will require those in attendance to wear a face covering. We thank everyone for their understanding and cooperation during this difficult time. A private Mass of Christian Burial will be celebrated at Our Lady of Mt. Carmel Catholic Church with entombment following at All Saints Mausoleum. Visit Ada's Online Memorial Book at: Stanley M. Widzins Stanley M. Widzins, 80 years old of Kenosha, WI passed away Monday, June 29, 2020, at his home surrounded by his family. He was born September 19, 1939, in Cambridge, NJ the son of the late John and Jane (Anderson) Widzins. He lived in Tomah, WI and Grayslake, IL before settling in Kenosha in 1996. Stan proudly served in the U.S. Army from 1966-1972 before being honorably discharged. On June 25, 1987, Stan married MaryAnn (Tokarz) in Tomah, WI. He went on to work as a civilian in engineering maintenance at Ft. McCoy and Ft. Sheridan before retiring in 1991. Stan was a member of Christian Life Church, Delavan, WI and participated in many mission trips to places like Guatemala, Costa Rica, and Peru, volunteering his time and devotion to others. He was also a chaplain at the Kenosha County Detention Center for several years. Stan was a family man and cherished the time he spent with his grandchildren and great-grandchildren. Survivors include his wife of 33 years, MaryAnn; his children, Michael Widzins, Ken (Laura) Widzins, Daniel (Karla) Widzins, Dawn (Lesley) Fitzgerald, Denny (Marcia) Steele, and Holly (Matt) Dufek; two brothers, Joseph Widzins and John Widzins; 18 grandchildren and 3 great-grandchildren. In addition to his parents, Stanley was preceded in death by a daughter, Jackie Widzins; and a brother, Walt Widzins. Funeral services will be held at a later date. Arrangements were entrusted to Proko Funeral Home. Visit & Sign Stan's Marilyn Emma Ehlen Marilyn Emma Ehlen, 90 years old of Nokomis, FL, passed away Wednesday, June 24, 2020. She was born April 5, 1930 in Kenosha, WI, the daughter of the late Reinhardt and Emma (Barth) Hoffmann. She attended Kenosha schools. On February 1, 1950, she married Jack Ehlen in Kenosha, WI. He preceded her in death in 1982. In 1985, Marilyn moved to Las Vegas, NV, to escape Wisconsin winters. She was employed by the City of Las Vegas until her retirement in 1998. She and	-0.2884	-0.731313	-1.322275	-1.657988	[ -0.4803255741180793, -0.0964740351411767 ]	[ -1.1051066485169831, -0.35751921582017554 ]	[ -1.7356820482694826, -0.9088674739942109 ]	[ -1.712617016959338, -1.6033594656927168 ]	1,024	[ 512, 512 ]	[ 412, 29892, 18076, 834, 601, 313, 29928, 2829, 898, 29897, 897, 29933, 442, 3543, 29892, 24053, 264, 3914, 12718, 359, 29892, 23817, 1562, 29892, 319, 1564, 29892, 322, 1174, 2502, 897, 29933, 442, 3543, 29936, 697, 2107, 29899, 27857, 5145, 29892, 18076, 834, 601, 16922, 897, 29933, 442, 3543, 4786, 29936, 8099, 29892, 18242, 29877, 313, 1168, 2786, 29897, 10211, 1111, 29936, 9883, 29892, 306, 324, 5863, 313, 29924, 2628, 29897, 17784, 7771, 1789, 29936, 1023, 21383, 29899, 262, 29899, 10653, 29892, 22864, 601, 376, 29954, 1789, 29908, 313, 1168, 2786, 29897, 897, 29933, 442, 3543, 322, 1394, 28514, 12245, 3156, 29936, 322, 2211, 9883, 29879, 29899, 262, 29899, 10653, 29892, 6600, 655, 10211, 1111, 29892, 1425, 29879, 11836, 313, 29928, 2770, 1417, 29897, 6960, 284, 2386, 322, 8467, 4108, 1588, 4405, 29889, 13, 13468, 471, 9399, 287, 297, 4892, 491, 902, 2107, 29899, 27857, 1100, 29892, 20212, 4755, 3879, 29878, 650, 297, 3041, 6906, 29936, 8099, 29892, 16922, 10211, 1111, 29936, 1023, 9883, 29879, 29899, 262, 29899, 10653, 29892, 1704, 29885, 3547, 390, 3096, 3543, 322, 26422, 12245, 3156, 29936, 322, 8099, 29899, 262, 29899, 10653, 29892, 18242, 29877, 1588, 4405, 29889, 13, 1576, 3942, 723, 763, 304, 10985, 263, 4266, 3374, 887, 304, 4942, 29889, 18824, 7455, 21161, 322, 670, 13925, 29892, 322, 278, 13925, 310, 379, 4705, 625, 29855, 322, 278, 13925, 472, 7765, 1094, 7224, 363, 278, 20695, 2562, 393, 471, 10410, 304, 23255, 322, 902, 3942, 2645, 902, 4486, 2264, 29889, 13, 29909, 6493, 362, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 1019, 2901, 13811, 13537, 8778, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 1152, 278, 15332, 322, 6993, 310, 1749, 28865, 591, 674, 1996, 1906, 297, 14333, 749, 304, 19531, 263, 3700, 21653, 29889, 1334, 6452, 14332, 363, 1009, 8004, 322, 1302, 16453, 2645, 445, 5189, 931, 29889, 319, 2024, 7360, 310, 6111, 6640, 616, 674, 367, 26301, 472, 8680, 10040, 310, 341, 29873, 29889, 1704, 12873, 11865, 6291, 411, 875, 3424, 358, 1494, 472, 2178, 14342, 1372, 341, 1485, 1772, 398, 29889, 13, 6116, 277, 23255, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 855, 273, 2330, 341, 29889, 399, 333, 29920, 1144, 13, 855, 273, 2330, 341, 29889, 399, 333, 29920, 1144, 29892, 29871, 29947, 29900, 2440, 2030, 310, 10015, 359, 2350, 29892, 399, 29902, 4502, 3448, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 670, 3271, 22047, 491, 670, 3942, 29889, 13, 3868, 471, 6345, 3839, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29929, 29892, 297, 12585, 29892, 405, 29967, 278, 1487, 310, 278, 5683, 2259, 322, 10447, 313, 2855, 1330, 29897, 399, 333, 29920, 1144, 29889, 940, 10600, 297, 4335, 801, 29892, 399, 29902, 322, 18956, 29879, 433, 446, 29892, 17674, 1434, 3604, 1847, 297, 10015, 359, 2350, 297, 29871, 29896, 29929, 29929, 29953, 29889, 13, 855, 273, 22314, 368, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 515, 29871, 29896, 29929, 29953, 29953, 29899, 29896, 29929, 29955, 29906, 1434, 1641, 10657, 2197, 766, 25389, 287, 29889, 1551, 5306, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29947, 29955, 29892, 7813, 8300, 6182, 2744, 29876, 313, 29911, 554, 11129, 29897, 297, 4335, 801, 29892, 399, 29902, 29889, 940, 3512, 373, 304, 664, 408, 263, 7631, 713, 297, 21639, 25413, 472, 383, 29873, 29889, 4052, 7967, 29891, 322, 383, 29873, 29889, 17375, 29219, 1434, 3240, 8491, 297, 29871, 29896, 29929, 29929, 29896, 29889, 13, 855, 273, 471, 263, 4509, 310, 6111, 4634, 6291, 29892, 5556, 29080, 29892, 399, 29902, 322, 25223, 297, 1784, 10655, 3367, 567, 304, 7600, 763, 2088, 17533, 2883, 29892, 17513, 29750, 29892, 322, 25493, 29892, 27886, 3241, 670, 931, 322, 2906, 8194, 304, 4045, 29889, 940, 471, 884, 263, 10708, 7420, 472, 278, 10015, 359, 2350, 5127, 5953, 2509, 7817, 363, 3196, 2440, 29889, 7813, 471, 263, 3942, 767, 322, 14954, 3276, 278, 931, 540, 10398, 411, 670, 4595, 11991, 322, 2107, 29899, 27857, 11991, 29889, 13, 18498, 24759, 943, 3160, 670, 6532, 310, 29871, 29941, 29941, 2440, 29892, 6182, 2744, 29876, 29936, 670, 4344, 29892, 5765, 399, 333, 29920, 1144, 29892, 10015, 313, 5661, 2002, 29897, 399, 333, 29920, 1144, 29892, 8432, 313, 24115, 433, 29897, 399, 333, 29920, 1144, 29892, 7266, 1233, 313, 24560, 2330, 29897, 22963, 914, 2741, 29892, 3384, 1460, 313, 7083, 1512, 29897, 2443, 6146, 29892, 322, 4168, 368, 313, 29924, 1131, 29897, 360, 1137, 1416, 29936, 1023, 21383, 29892, 6936, 399, 333, 29920, 1144, 322, 2259, 399, 333, 29920, 1144, 29936, 29871, 29896, 29947, 4595, 11991, 322, 29871, 29941, 2107, 29899, 27857, 11991, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 21631, 471, 9399, 287, 297, 4892, 491, 263, 8750, 29892, 5457, 347, 399, 333, 29920, 1144, 29936, 322, 263, 8099, 29892, 399, 1997, 399, 333, 29920, 1144, 29889, 13, 25394, 13537, 5786, 674, 367, 4934, 472, 263, 2678, 2635, 29889, 25681, 574, 4110, 892, 9953, 16656, 304, 1019, 2901, 13811, 13537, 8778, 29889, 13, 6116, 277, 669, 9954, 7813, 29915, 29879, 13, 7083, 309, 948, 26422, 382, 29785, 13, 7083, 309, 948, 26422, 382, 29785, 29892, 29871, 29929, 29900, 2440, 2030, 310, 405, 554, 290, 275, 29892, 383, 29931, 29892, 4502, 3448, 15050, 4515, 3250, 29892, 5306, 29871, 29906, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 2296, 471, 6345, 3786, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29900, 297, 10015, 359, 2350, 29892, 399, 29902, 29892, 278, 8750, 310, 278, 5683, 18334, 25603, 322, 26422, 313, 4297, 386, 29897, 22151, 4403, 29889, 2296, 14283, 10015, 359, 2350, 12462, 29889, 1551, 6339, 29871, 29896, 29892, 29871, 29896, 29929, 29945, 29900, 29892, 1183, 8300, 5457, 382, 29785, 297, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 9399, 287, 902, 297, 4892, 297, 29871, 29896, 29929, 29947, 29906, 29889, 512, 29871, 29896, 29929, 29947, 29945, 29892, 1085, 309, 948, 6153, 304, 7413, 17236, 294, 29892, 405, 29963, 29892, 304, 10169, 22581, 13851, 29879, 29889, 2296, 471, 15723, 491, 278, 4412, 310, 7413, 17236, 294, 2745, 902, 3240, 19211, 297, 29871, 29896, 29929, 29929, 29947, 29889, 2296, 322 ]	1,332,858	11,264	CommonCrawl	0	3
her sister Carol enjoyed many years in Las Vegas, welcoming family and friends into the home they shared. In 2013, Marilyn returned to Wisconsin to be close to her family. In 2016 she moved to Nokomis, FL, with John and Diane. Marilyn is survived by her brother John Hoffmann of Kenosha, WI; her children John (Diane) Ehlen of Nokomis, FL, and Douglas Ehlen of Fullerton, CA; her two granddaughters, Tanya Parent of Kenosha, WI, and Linda Ehlen of Milwaukee, WI; three grandchildren, Branden, Dean & Elizabeth Parent of Kenosha, WI; and many nieces, nephews, cousins and friends. In addition to her parents and her husband, she was preceded in death by eight siblings, Ruth Hoffmann, June Kubert, Hope Cole, Doris Bosman, Audrea VanArsdale, Raymond Hoffmann, Alice Theivagt and Carol LeMay. Memorial remembrances in Marilyn's name can be made to: Tidewell Hospice or the Alzheimer's Association There will be a memorial service for family and friends at a later date Full obituary information will appear in Sunday's newspaper. Visit Ada's Online Memorial Book at: Roger A. Nicholson Roger A. Nicholson, 80, of Kenosha, passed away peacefully, Tuesday, June 30, 2020 at Froedtert So. Kenosha Medical Center Campus. Private Family Services will be held. Visit Roger's Beverly J. DeSeife (Née: Seehafer) Beverly J (Néee: Seehafer) DeSeife, 74, of Marshfield, WI, peacefully passed away at her home June 26, 2020, in Kenosha WI. Beverly was born in Marshfield, WI, to the late Chester & Angeline (Luther) Seehafer on the June 19,1946. She graduated from Marshfield Sr. High class of 1964 and then moved to Kenosha, WI. She married David J. DeSeife of Kenosha, WI, on August 27, 1966. Beverly retired form American Motor Corporation / Chrysler with over 30 years of service. She also attended Gateway Technical Collage while obtaining her associates degree for Interior Design. Beverly was a hard worker who loved gardening to her last day. She loved her dear friends with all her heart. She enjoyed boating, golfing, bowling, softball and riding motorcycles. Beverly is preceded in death by her loving husband, David J DeSeife; parents, Chester & Angeline Seehafer; and one beloved brother, Charles Seehafer. Beverly is survived by two sons, Daniel DeSeife of Kenosha, WI, & Douglas (Elizabeth) DeSeife of Kenosha, WI; her beloved brothers and sisters, Rodney (Patty) Seehafer of Marshfield, WI, Carol (Ed) Schulze of Naples, FL, James (Pat) Seehafer of Marshfield, WI, Dian (Lloyd) Mueller of Marshfield, WI, Bruce (Kris) Seehafer of Marshfield, WI, Gary (Annie) Seehafer of Marshfield, WI, and Alan (Kathy) Seehafer of Marshfield, WI. Also surviving Beverly are her precious grandchildren, Jessica (Kyle) Worcester, Emily (Brandon) Prell, John DeSeife, Randy DeSeife, Leah DeSeife, Destini Elisasson and David, Derek, Nathaniel and Ryan DeSeife. She is further survived by many cousins, nieces, nephews and in-laws to whom she loved dearly. A celebration of Beverly's life will be held on Monday, July 6, 2020, 6:00pm, at Draeger-Langendorf Funeral Home and Crematory, 4600 County Line Road, Mount Pleasant. Visitation will be from 5:00pm until the time of the service. The service will be live streamed via YouTube	-0.050419	-0.904556	-1.274086	-1.684002	[ 0.12096193921237652, -0.22179933689456324 ]	[ -0.8759061901093391, -0.9332063047112501 ]	[ -1.2943761098526196, -1.2537962534464715 ]	[ -1.6605896115942802, -1.7074142764228322 ]	1,024	[ 512, 512 ]	[ 902, 9883, 8562, 27849, 1784, 2440, 297, 7413, 17236, 294, 29892, 5476, 11506, 3942, 322, 7875, 964, 278, 3271, 896, 7258, 29889, 512, 29871, 29906, 29900, 29896, 29941, 29892, 1085, 309, 948, 4133, 304, 22581, 304, 367, 3802, 304, 902, 3942, 29889, 512, 29871, 29906, 29900, 29896, 29953, 1183, 6153, 304, 405, 554, 290, 275, 29892, 383, 29931, 29892, 411, 2259, 322, 360, 16677, 29889, 13, 7083, 309, 948, 338, 10503, 2347, 491, 902, 8099, 2259, 22151, 4403, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 902, 4344, 2259, 313, 29928, 16677, 29897, 382, 29785, 310, 405, 554, 290, 275, 29892, 383, 29931, 29892, 322, 16721, 382, 29785, 310, 14846, 28634, 29892, 12766, 29936, 902, 1023, 4595, 29881, 6334, 2153, 29892, 323, 20912, 22280, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 322, 365, 11054, 382, 29785, 310, 3833, 29893, 585, 23137, 29892, 399, 29902, 29936, 2211, 4595, 11991, 29892, 1771, 7257, 29892, 23263, 669, 13061, 22280, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 274, 681, 1144, 322, 7875, 29889, 512, 6124, 304, 902, 11825, 322, 902, 10216, 29892, 1183, 471, 9399, 287, 297, 4892, 491, 9475, 27767, 18964, 29892, 23130, 22151, 4403, 29892, 5306, 29024, 814, 29892, 7963, 16816, 29892, 9579, 275, 10211, 1171, 29892, 8612, 5638, 6556, 1433, 4928, 744, 29892, 21380, 22151, 4403, 29892, 16308, 450, 440, 21416, 322, 8562, 951, 12703, 29889, 13, 11442, 9020, 1083, 1590, 661, 778, 297, 1085, 309, 948, 29915, 29879, 1024, 508, 367, 1754, 304, 29901, 13, 29911, 680, 5872, 379, 4705, 625, 470, 278, 838, 29920, 27400, 29915, 29879, 7993, 13, 8439, 674, 367, 263, 2626, 9020, 2669, 363, 3942, 322, 7875, 472, 263, 2678, 2635, 13, 13658, 704, 1981, 653, 2472, 674, 2615, 297, 16340, 29915, 29879, 19656, 29889, 13, 6116, 277, 23255, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 29934, 468, 261, 319, 29889, 16371, 324, 1100, 13, 29934, 468, 261, 319, 29889, 16371, 324, 1100, 29892, 29871, 29947, 29900, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 29892, 323, 1041, 3250, 29892, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 357, 29873, 1105, 29889, 10015, 359, 2350, 20795, 7817, 7259, 375, 29889, 13, 25207, 14662, 15538, 674, 367, 4934, 29889, 13, 6116, 277, 14159, 29915, 29879, 13, 29933, 1310, 368, 435, 29889, 897, 2008, 1607, 313, 29940, 1318, 29901, 2823, 2350, 571, 29897, 13, 29933, 1310, 368, 435, 313, 29940, 1318, 29872, 29901, 2823, 2350, 571, 29897, 897, 2008, 1607, 29892, 29871, 29955, 29946, 29892, 310, 13216, 2671, 29892, 399, 29902, 29892, 10776, 3730, 4502, 3448, 472, 902, 3271, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 297, 10015, 359, 2350, 399, 29902, 29889, 13, 29933, 1310, 368, 471, 6345, 297, 13216, 2671, 29892, 399, 29902, 29892, 304, 278, 5683, 678, 4156, 669, 3218, 5570, 313, 29931, 14107, 29897, 2823, 2350, 571, 373, 278, 5306, 29871, 29896, 29929, 29892, 29896, 29929, 29946, 29953, 29889, 2296, 23588, 515, 13216, 2671, 26250, 29889, 5057, 770, 310, 29871, 29896, 29929, 29953, 29946, 322, 769, 6153, 304, 10015, 359, 2350, 29892, 399, 29902, 29889, 2296, 8300, 4699, 435, 29889, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 373, 3111, 29871, 29906, 29955, 29892, 29871, 29896, 29929, 29953, 29953, 29889, 350, 1310, 368, 16528, 883, 3082, 16843, 15025, 847, 678, 18450, 1358, 411, 975, 29871, 29941, 29900, 2440, 310, 2669, 29889, 2296, 884, 14283, 22510, 1582, 8364, 936, 1530, 6184, 1550, 4017, 292, 902, 4067, 1078, 7426, 363, 4124, 1611, 12037, 29889, 350, 1310, 368, 471, 263, 2898, 15645, 1058, 18012, 16423, 292, 304, 902, 1833, 2462, 29889, 2296, 18012, 902, 9425, 7875, 411, 599, 902, 5192, 29889, 2296, 27849, 1045, 1218, 29892, 29416, 292, 29892, 12580, 1847, 29892, 4964, 2135, 322, 364, 4821, 10992, 1270, 7799, 29889, 13, 29933, 1310, 368, 338, 9399, 287, 297, 4892, 491, 902, 12355, 292, 10216, 29892, 4699, 435, 897, 2008, 1607, 29936, 11825, 29892, 678, 4156, 669, 3218, 5570, 2823, 2350, 571, 29936, 322, 697, 1339, 8238, 8099, 29892, 5322, 2823, 2350, 571, 29889, 13, 29933, 1310, 368, 338, 10503, 2347, 491, 1023, 18025, 29892, 8432, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 669, 16721, 313, 6489, 466, 9394, 29897, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 902, 1339, 8238, 21383, 322, 9883, 29879, 29892, 7733, 3801, 313, 11457, 1017, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 8562, 313, 3853, 29897, 12988, 911, 310, 8344, 793, 29892, 383, 29931, 29892, 5011, 313, 11457, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 360, 713, 313, 29931, 18966, 29897, 8229, 4539, 310, 13216, 2671, 29892, 399, 29902, 29892, 18885, 313, 29968, 3780, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 23529, 313, 2744, 2786, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 322, 17102, 313, 29968, 493, 29891, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29889, 3115, 10503, 4357, 350, 1310, 368, 526, 902, 758, 8802, 4595, 11991, 29892, 23010, 983, 313, 29968, 1508, 29897, 19662, 29883, 4156, 29892, 2812, 2354, 313, 12432, 9214, 29897, 4721, 645, 29892, 2259, 897, 2008, 1607, 29892, 390, 13910, 897, 2008, 1607, 29892, 951, 801, 897, 2008, 1607, 29892, 15435, 2172, 21279, 465, 265, 322, 4699, 29892, 360, 20400, 29892, 27650, 709, 322, 20916, 897, 2008, 1607, 29889, 2296, 338, 4340, 10503, 2347, 491, 1784, 274, 681, 1144, 29892, 4930, 778, 29892, 23446, 354, 5652, 322, 297, 29899, 433, 5652, 304, 6029, 1183, 18012, 9425, 368, 29889, 13, 29909, 10894, 362, 310, 350, 1310, 368, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 29871, 29953, 29901, 29900, 29900, 3358, 29892, 472, 16322, 387, 261, 29899, 29931, 574, 21466, 13811, 13537, 8778, 322, 315, 1745, 7606, 29892, 29871, 29946, 29953, 29900, 29900, 5127, 7407, 9321, 29892, 8040, 19777, 13186, 29889, 5741, 7018, 674, 367, 515, 29871, 29945, 29901, 29900, 29900, 3358, 2745, 278, 931, 310, 278, 2669, 29889, 450, 2669, 674, 367, 5735, 4840, 287, 3025, 14711 ]	1,332,858	12,288	CommonCrawl	0	3
. The link to the stream will be available on the funeral home website on the day of the service. Private burial will take place at Sunset Ridge Memorial Park. 4600 COUNTY LINE ROAD, MOUNT PLEASANT, WI 53403 Jon. E. Buckingham, age 81 of Kenosha passed away peacefully on Thursday, June 25, 2020 at Burlington Memorial Hospital. A celebration of Jon's life will be held on Monday, July 6, 2020 at 2:00 p.m. at the funeral home. Friends are invited to meet with the family on Monday from 12:00 Noon until the time of the service. Memorial remembrances to Safe Harbor Humane Society, 7811 60th Ave., Kenosha, WI 53142 would be appreciated. Jon's complete obituary will be made available on the funeral home webster on Wednesday, July 1, 2020. Timothy Pfaff On June 24, 2020, Tim Pfaff / Slim left his body to be in the arms of God, and the loved ones who have passed before him. Born in Kenosha, on December 16, 1971, he was the first-born child of Ralph and Michelle (St. John) Pfaff. He was a loving big brother to Steven and Kyle Pfaff. He was most proud of his two sons, Justin Timothy and Tyler Joseph Pfaff. Tim loved them to the moon and stars. And he was recently introduced to his wonderful new grandson, Kingston Ramsey Pfaff. Tim also leaves behind his sister, Michelle Moon, first best friend, Scott Anderson, and dear friend Jen; uncles Gary, John, and Rick and his auntie Cher and aunt Sharon. He has been blessed with many cousins, aunts, and uncles from both the Pfaff's and St. John's and kept contact with many of them on FB. Slim loved fishing and the Packers. He loved taking his boys camping and having cookouts with his many family and friends. He loved music; it filled his life wherever he was. Tim loved BIG. If he told you he loved you, he meant it. He was going to love you forever. He will be dearly missed by those who loved him back. 5111-60th Street Kenosha, WI 53144 Visit & Sign Tim's Online Memorial Book at: Mario Caira After 96 years, Mario Caira peacefully shed the bonds of this world on Friday, June 26, 202,0 for his life in eternity. A son of the late Gaspere and Raffaela Caira, Mario was born December 8, 1923, in Rende (Calabria) Italy. He was educated in local schools there. Following the war, in January 1947, he married his childhood sweetheart, Amelia Chiappetta in Rende. They shared some 71 wonderful years together before her death in 2018. Together they raised three children. In 1955, Mario and Amelia made their new home in the United States settling in Kenosha. Mario took an entry level position at the American Brass where he advanced to a pipefitter by his retirement, 30 years later. Always a hard worker and provider, Mario took side jobs delivering groceries, landscaping, and painting. After leaving the Brass, Mario started the Kenosha Antenna Services for Kenosha and Racine. He put up 100s of TV antennas and towers before taking his full retirement. Family came first for Mario. He had a keen mind, good sense of humor, and winning personality. He spent many hours in the garden and enjoyed sharing the harvest. Mario also would get away to his "secret" fishing spot. He served in the Italian Army before coming to this country. Mario was immensely proud to take U.S. citizenship in 1962. Mario was a member of St. Anthony's Church. Treasuring his memory are his daughter, Lena (Fred) Schlater; son, Reno Caira, both of Kenosha; and his son, Tony (Terry Hartnell) C	-0.163931	-0.974391	-1.319739	-1.85049	[ -0.5090887581270532, 0.181227658088322 ]	[ -1.194638077582469, -0.7541434465802782 ]	[ -1.532782766238741, -1.1066942739741839 ]	[ -1.8999156762735456, -1.8010636060799359 ]	1,024	[ 512, 512 ]	[ 29889, 450, 1544, 304, 278, 4840, 674, 367, 3625, 373, 278, 2090, 13537, 3271, 4700, 373, 278, 2462, 310, 278, 2669, 29889, 12230, 6866, 616, 674, 2125, 2058, 472, 8991, 842, 390, 5525, 19722, 4815, 29889, 13, 29946, 29953, 29900, 29900, 21122, 29979, 365, 8895, 16641, 3035, 29892, 16999, 10356, 349, 1307, 3289, 13566, 29892, 399, 29902, 29871, 29945, 29941, 29946, 29900, 29941, 13, 29967, 265, 29889, 382, 29889, 16281, 16094, 29892, 5046, 29871, 29947, 29896, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 498, 1295, 3250, 29892, 5306, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 472, 6640, 1847, 880, 19722, 15967, 29889, 13, 29909, 10894, 362, 310, 9937, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 29889, 11169, 1975, 526, 23610, 304, 5870, 411, 278, 3942, 373, 27822, 515, 29871, 29896, 29906, 29901, 29900, 29900, 1939, 265, 2745, 278, 931, 310, 278, 2669, 29889, 19722, 1083, 1590, 661, 778, 304, 5701, 1725, 3536, 4089, 13863, 1662, 7765, 29892, 29871, 29955, 29947, 29896, 29896, 29871, 29953, 29900, 386, 319, 345, 1696, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 723, 367, 7556, 29889, 9937, 29915, 29879, 4866, 704, 1981, 653, 674, 367, 1754, 3625, 373, 278, 2090, 13537, 3271, 1856, 2475, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 13711, 20336, 10022, 3470, 13, 2951, 5306, 29871, 29906, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 7870, 10022, 3470, 847, 317, 2576, 2175, 670, 3573, 304, 367, 297, 278, 10188, 310, 4177, 29892, 322, 278, 18012, 6743, 1058, 505, 4502, 1434, 1075, 29889, 13, 29933, 1398, 297, 10015, 359, 2350, 29892, 373, 5846, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29955, 29896, 29892, 540, 471, 278, 937, 29899, 4939, 2278, 310, 23438, 322, 3375, 1808, 313, 855, 29889, 2259, 29897, 10022, 3470, 29889, 13, 3868, 471, 263, 12355, 292, 4802, 8099, 304, 24703, 322, 476, 1508, 10022, 3470, 29889, 13, 3868, 471, 1556, 22314, 310, 670, 1023, 18025, 29892, 26408, 7870, 20336, 322, 9656, 1358, 6936, 10022, 3470, 29889, 7870, 18012, 963, 304, 278, 18786, 322, 10819, 29889, 1126, 540, 471, 10325, 9129, 304, 670, 20695, 716, 4595, 1100, 29892, 4088, 7352, 8292, 7759, 10022, 3470, 29889, 13, 13711, 884, 11308, 5742, 670, 9883, 29892, 3375, 1808, 17549, 29892, 937, 1900, 5121, 29892, 8075, 17483, 29892, 322, 9425, 5121, 21116, 29936, 443, 7799, 23529, 29892, 2259, 29892, 322, 24218, 322, 670, 263, 1657, 347, 23816, 322, 263, 1657, 1383, 5022, 29889, 13, 3868, 756, 1063, 1999, 11517, 411, 1784, 274, 681, 1144, 29892, 263, 348, 1372, 29892, 322, 443, 7799, 515, 1716, 278, 10022, 3470, 29915, 29879, 322, 624, 29889, 2259, 29915, 29879, 322, 8126, 6958, 411, 1784, 310, 963, 373, 28816, 29889, 13, 29903, 2576, 18012, 9427, 292, 322, 278, 18744, 414, 29889, 940, 18012, 5622, 670, 12544, 4242, 292, 322, 2534, 7984, 17718, 411, 670, 1784, 3942, 322, 7875, 29889, 940, 18012, 4696, 29936, 372, 10423, 670, 2834, 29693, 540, 471, 29889, 13, 13711, 18012, 350, 6259, 29889, 960, 540, 5429, 366, 540, 18012, 366, 29892, 540, 6839, 372, 29889, 940, 471, 2675, 304, 5360, 366, 22296, 29889, 13, 3868, 674, 367, 9425, 368, 13726, 491, 1906, 1058, 18012, 1075, 1250, 29889, 13, 29945, 29896, 29896, 29896, 29899, 29953, 29900, 386, 7103, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29946, 13, 6116, 277, 669, 9954, 7870, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 29924, 2628, 315, 1794, 336, 13, 13555, 29871, 29929, 29953, 2440, 29892, 16262, 315, 1794, 336, 10776, 3730, 28453, 278, 289, 13788, 310, 445, 3186, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29892, 29900, 363, 670, 2834, 297, 634, 824, 537, 29889, 13, 29909, 1487, 310, 278, 5683, 402, 4692, 406, 322, 390, 3470, 29874, 3100, 315, 1794, 336, 29892, 16262, 471, 6345, 5846, 29871, 29947, 29892, 29871, 29896, 29929, 29906, 29941, 29892, 297, 390, 3324, 313, 7856, 370, 2849, 29897, 12730, 29889, 940, 471, 27729, 297, 1887, 12462, 727, 29889, 12206, 278, 1370, 29892, 297, 5490, 29871, 29896, 29929, 29946, 29955, 29892, 540, 8300, 670, 2278, 6614, 14225, 23057, 29892, 1913, 18556, 678, 423, 7988, 941, 297, 390, 3324, 29889, 2688, 7258, 777, 29871, 29955, 29896, 20695, 2440, 4208, 1434, 902, 4892, 297, 29871, 29906, 29900, 29896, 29947, 29889, 323, 12966, 896, 10425, 2211, 4344, 29889, 13, 797, 29871, 29896, 29929, 29945, 29945, 29892, 16262, 322, 1913, 18556, 1754, 1009, 716, 3271, 297, 278, 3303, 3900, 3604, 1847, 297, 10015, 359, 2350, 29889, 16262, 3614, 385, 6251, 3233, 2602, 472, 278, 3082, 1771, 465, 988, 540, 12862, 304, 263, 14282, 29888, 5171, 491, 670, 3240, 19211, 29892, 29871, 29941, 29900, 2440, 2678, 29889, 29849, 263, 2898, 15645, 322, 13113, 29892, 16262, 3614, 2625, 17643, 12021, 292, 4071, 2265, 583, 29892, 2982, 1557, 21430, 29892, 322, 20413, 29889, 2860, 10124, 278, 1771, 465, 29892, 16262, 4687, 278, 10015, 359, 2350, 530, 841, 1056, 15538, 363, 10015, 359, 2350, 322, 390, 562, 457, 29889, 940, 1925, 701, 29871, 29896, 29900, 29900, 29879, 310, 5648, 25504, 22911, 322, 304, 17538, 1434, 5622, 670, 2989, 3240, 19211, 29889, 13, 27104, 2996, 937, 363, 16262, 29889, 940, 750, 263, 28430, 3458, 29892, 1781, 4060, 310, 27448, 29892, 322, 15613, 2022, 2877, 29889, 940, 10398, 1784, 6199, 297, 278, 16423, 322, 27849, 19383, 278, 4023, 10147, 29889, 16262, 884, 723, 679, 3448, 304, 670, 376, 19024, 29908, 9427, 292, 9758, 29889, 940, 6766, 297, 278, 10545, 8811, 1434, 6421, 304, 445, 4234, 29889, 16262, 471, 5198, 575, 873, 22314, 304, 2125, 501, 29889, 29903, 29889, 18363, 4034, 297, 29871, 29896, 29929, 29953, 29906, 29889, 13, 29924, 2628, 471, 263, 4509, 310, 624, 29889, 16477, 29915, 29879, 6291, 29889, 13, 29911, 12588, 3864, 670, 3370, 526, 670, 8750, 29892, 365, 2386, 313, 29943, 1127, 29897, 21262, 1008, 29936, 1487, 29892, 7493, 29877, 315, 1794, 336, 29892, 1716, 310, 10015, 359, 2350, 29936, 322, 670, 1487, 29892, 15293, 313, 29911, 261, 719, 12321, 18437, 29897, 315 ]	1,332,858	13,312	CommonCrawl	0	3
aira, of Boca Raton, FL. Mario leaves behind his brothers-in-law, Franchino (Olimpia) Chiappetta of Rende, and Leo (Marikay) Chiappetta of Kenosha. The blessings of a growing family were a joy to Mario. His grandchildren include, Peggy (Rodger) Kormylo and Reno Caira of Kenosha, Amy (Tommy) Cunningham of Atlanta, and Gina DiLeo of Orlando. Great-grandchildren surviving Mario are Cameron (Maddy) Kormylo & Katherine Kormylo, Gianna & Janessa DiLeo, and Joseph & Edison Cunningham. Surviving nieces and nephews include, Beniamino (Tina) Caira, Marisa (Enrico Bosco) Caira, and Gaspere Caira. Grand nieces and nephews include, Olympia, Francesco and Valerio Chiappetta, as well as Francesco (Federica) Petrasso and Paola Giovanna (Francesco Imbrogno) Petrasso; and a great-grandnephew, Peter Imbrogno. Mario was predeceased by his wife, Amelia; his parents; a brother, Ceaser Caira of Rende; and a brother, Aldo Caira of Buenos Aires, Argentina. The family expresses deep appreciation to Claridge House for their diligent care and Genesis Rehab Services for their continuous support and therapy for Mario. Visitation in celebration of the life of Mario Caira will be held Sunday, July 5th, from 1:00 a.m. to 4:00 p.m. at Proko Funeral Home. A Mass of Christian Burial will be held Monday, July 6th, at 10:00 a.m. at St. Anthony of Padua Catholic Church, 2223 – 51st St. Kenosha. Interment will follow at All Saints Cemetery & Mausoleum. Memorials for Masses will be appreciated by the family, in lieu of flowers. Visit Mario's Online Memorial Book at: Verle Roy Swenson Verle Roy Swenson, 98 years old of Camp Lake, WI passed away Saturday, June 27, 2020 at Aurora Medical Center, Kenosha, WI. He was born August 23, 1921 in Camp Lake, WI the son of the late Roy A. and Evelyn Mildred (nèe Orvis) Swenson. Verle served his country proudly in the United States Navy. He was a member of the United States Navy Reserves and was called to active duty on April 4, 1944 during World War II. His sea duty was on the USS Montauk LSV 6, where he was a Machinist Mate 1st Class. When he returned, he married, Dorothy E. Ott on June 11, 1949 in Ebenezer Lutheran Church, West Milwaukee, WI. After returning from their honeymoon, they began to build the house that they would live in for the next 66 years. Verle was then drafted into the United States Navy and sent to Korea for his second tour. He reported for active duty on September 9, 1950 and served on the USS Osprey AMS28 as an Engineman 1st Class. This vessel was a minesweeper in the Korean waters during the war. Verle was a 74-year active member of the Schultz-Hahn American Legion Post #293 in Silver Lake, WI. He was the Past Finance Officer, the Past Post Commander, Past Kenosha County Commander, and Lifetime Member of the Past Commanders of Wisconsin. Verle was also a member of the Naval Minewarfare Association, the Kenosha County Last Man's Club of WWII, Korean War Veterans and a 50-year member of the International Association of Machinists, with several years served as shop steward. He was a member of Peace Evangelical Lutheran Church in Wilmot, WI since 1950, where he sang in the choir and served on the church council. He also served 19 years on the school board of Wilmot Union High School. Verle spent a lot of his time in carpentry. He also enjoyed playing the mandolin, guitar, banjo, and electric organ with various groups at nurs	-0.035609	-0.322602	-1.228434	-1.387446	[ 0.040151088901449666, -0.11136925543153821 ]	[ -0.9511125905243473, 0.3059086735550752 ]	[ -1.5632176585433524, -0.8936500278419052 ]	[ -1.618967687302234, -1.1559237795532207 ]	1,024	[ 512, 512 ]	[ 1794, 336, 29892, 310, 350, 6400, 390, 14114, 29892, 383, 29931, 29889, 16262, 11308, 5742, 670, 21383, 29899, 262, 29899, 10653, 29892, 1352, 305, 1789, 313, 29949, 12552, 423, 29897, 678, 423, 7988, 941, 310, 390, 3324, 29892, 322, 22533, 313, 7083, 638, 388, 29897, 678, 423, 7988, 941, 310, 10015, 359, 2350, 29889, 13, 1576, 17065, 886, 310, 263, 15678, 3942, 892, 263, 15331, 304, 16262, 29889, 3600, 4595, 11991, 3160, 29892, 27281, 1927, 313, 29934, 397, 914, 29897, 476, 555, 29891, 417, 322, 7493, 29877, 315, 1794, 336, 310, 10015, 359, 2350, 29892, 28533, 313, 21599, 1357, 29897, 315, 27389, 3391, 310, 26484, 29892, 322, 402, 1099, 4671, 3226, 29877, 310, 1394, 28514, 29889, 7027, 29899, 27857, 11991, 10503, 4357, 16262, 526, 20939, 265, 313, 29924, 25644, 29897, 476, 555, 29891, 417, 669, 476, 16490, 476, 555, 29891, 417, 29892, 21569, 1056, 669, 2627, 9297, 4671, 3226, 29877, 29892, 322, 6936, 669, 2155, 2285, 315, 27389, 3391, 29889, 6298, 29894, 4357, 4930, 778, 322, 23446, 354, 5652, 3160, 29892, 4111, 2829, 1789, 313, 29911, 1099, 29897, 315, 1794, 336, 29892, 1085, 8069, 313, 2369, 24855, 10211, 1111, 29897, 315, 1794, 336, 29892, 322, 402, 4692, 406, 315, 1794, 336, 29889, 6265, 4930, 778, 322, 23446, 354, 5652, 3160, 29892, 6167, 423, 29892, 16922, 322, 2630, 261, 601, 678, 423, 7988, 941, 29892, 408, 1532, 408, 16922, 313, 29943, 2447, 983, 29897, 5879, 29878, 9979, 322, 2621, 2963, 11429, 9713, 313, 7675, 778, 1111, 1954, 6729, 29887, 1217, 29897, 5879, 29878, 9979, 29936, 322, 263, 2107, 29899, 27857, 484, 29886, 13636, 29892, 5310, 1954, 6729, 29887, 1217, 29889, 13, 29924, 2628, 471, 27978, 346, 1463, 491, 670, 6532, 29892, 1913, 18556, 29936, 670, 11825, 29936, 263, 8099, 29892, 7747, 29440, 315, 1794, 336, 310, 390, 3324, 29936, 322, 263, 8099, 29892, 18242, 29877, 315, 1794, 336, 310, 17882, 16981, 29892, 13798, 29889, 13, 1576, 3942, 4653, 267, 6483, 5108, 362, 304, 15183, 5525, 5619, 363, 1009, 21749, 25692, 2562, 322, 5739, 6656, 830, 7308, 15538, 363, 1009, 9126, 2304, 322, 29220, 27580, 363, 16262, 29889, 13, 6116, 7018, 297, 10894, 362, 310, 278, 2834, 310, 16262, 315, 1794, 336, 674, 367, 4934, 16340, 29892, 5468, 29871, 29945, 386, 29892, 515, 29871, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 304, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 1019, 2901, 13811, 13537, 8778, 29889, 319, 7360, 310, 6111, 6640, 616, 674, 367, 4934, 27822, 29892, 5468, 29871, 29953, 386, 29892, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 624, 29889, 16477, 310, 18011, 3357, 11865, 6291, 29892, 29871, 29906, 29906, 29906, 29941, 785, 29871, 29945, 29896, 303, 624, 29889, 10015, 359, 2350, 29889, 4124, 358, 674, 1101, 472, 2178, 14342, 1372, 315, 22875, 669, 341, 1485, 1772, 398, 29889, 13, 11442, 9020, 29879, 363, 7360, 267, 674, 367, 7556, 491, 278, 3942, 29892, 297, 13003, 310, 18281, 29889, 13, 6116, 277, 16262, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 6565, 280, 15793, 3925, 25151, 13, 6565, 280, 15793, 3925, 25151, 29892, 29871, 29929, 29947, 2440, 2030, 310, 7259, 9459, 29892, 399, 29902, 4502, 3448, 24211, 29892, 5306, 29871, 29906, 29955, 29892, 29871, 29906, 29900, 29906, 29900, 472, 23266, 2207, 20795, 7817, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 471, 6345, 3111, 29871, 29906, 29941, 29892, 29871, 29896, 29929, 29906, 29896, 297, 7259, 9459, 29892, 399, 29902, 278, 1487, 310, 278, 5683, 15793, 319, 29889, 322, 7298, 873, 29876, 341, 789, 1127, 313, 29876, 30000, 29872, 1394, 1730, 29897, 3925, 25151, 29889, 1798, 280, 6766, 670, 4234, 22314, 368, 297, 278, 3303, 3900, 13166, 29889, 940, 471, 263, 4509, 310, 278, 3303, 3900, 13166, 2538, 20098, 322, 471, 2000, 304, 6136, 13360, 373, 3786, 29871, 29946, 29892, 29871, 29896, 29929, 29946, 29946, 2645, 2787, 3362, 1944, 29889, 3600, 7205, 13360, 471, 373, 278, 17676, 4526, 585, 29895, 365, 7597, 29871, 29953, 29892, 988, 540, 471, 263, 17197, 262, 391, 29566, 29871, 29896, 303, 4134, 29889, 1932, 540, 4133, 29892, 540, 8300, 29892, 9579, 20336, 382, 29889, 13476, 373, 5306, 29871, 29896, 29896, 29892, 29871, 29896, 29929, 29946, 29929, 297, 26302, 1600, 3298, 24760, 273, 6291, 29892, 3122, 3833, 29893, 585, 23137, 29892, 399, 29902, 29889, 2860, 7863, 515, 1009, 298, 650, 962, 6150, 29892, 896, 4689, 304, 2048, 278, 3699, 393, 896, 723, 5735, 297, 363, 278, 2446, 29871, 29953, 29953, 2440, 29889, 1798, 280, 471, 769, 18195, 287, 964, 278, 3303, 3900, 13166, 322, 2665, 304, 19109, 363, 670, 1473, 6282, 29889, 940, 8967, 363, 6136, 13360, 373, 3839, 29871, 29929, 29892, 29871, 29896, 29929, 29945, 29900, 322, 6766, 373, 278, 17676, 438, 1028, 8903, 319, 4345, 29906, 29947, 408, 385, 2201, 262, 11422, 29871, 29896, 303, 4134, 29889, 910, 21239, 471, 263, 29086, 705, 11356, 297, 278, 22467, 19922, 2645, 278, 1370, 29889, 1798, 280, 471, 263, 29871, 29955, 29946, 29899, 6360, 6136, 4509, 310, 278, 1102, 499, 29920, 29899, 29950, 5422, 3082, 5682, 291, 4918, 396, 29906, 29929, 29941, 297, 16466, 9459, 29892, 399, 29902, 29889, 940, 471, 278, 19793, 4231, 749, 28288, 29892, 278, 19793, 4918, 27317, 29892, 19793, 10015, 359, 2350, 5127, 27317, 29892, 322, 365, 361, 5410, 19495, 310, 278, 19793, 10516, 414, 310, 22581, 29889, 1798, 280, 471, 884, 263, 4509, 310, 278, 21590, 26833, 4495, 24658, 7993, 29892, 278, 10015, 359, 2350, 5127, 9208, 2315, 29915, 29879, 5977, 310, 399, 29956, 2687, 29892, 22467, 3362, 478, 1308, 550, 322, 263, 29871, 29945, 29900, 29899, 6360, 4509, 310, 278, 4623, 7993, 310, 17197, 262, 2879, 29892, 411, 3196, 2440, 6766, 408, 18296, 1886, 1328, 29889, 13, 3868, 471, 263, 4509, 310, 24819, 21827, 936, 24760, 273, 6291, 297, 4624, 14817, 29892, 399, 29902, 1951, 29871, 29896, 29929, 29945, 29900, 29892, 988, 540, 13625, 297, 278, 3060, 381, 322, 6766, 373, 278, 6586, 18701, 29889, 940, 884, 6766, 29871, 29896, 29929, 2440, 373, 278, 3762, 7613, 310, 4624, 14817, 7761, 5057, 4523, 29889, 13, 6565, 280, 10398, 263, 3287, 310, 670, 931, 297, 1559, 29886, 8269, 29889, 940, 884, 27849, 8743, 278, 9619, 22878, 29892, 11210, 29892, 9892, 2212, 29892, 322, 12646, 2894, 411, 5164, 6471, 472, 302, 1295 ]	1,332,858	14,336	CommonCrawl	0	3
ing homes and many senior citizen get togethers. Verle is survived by his son, Dale (Laura) of Waukesha, WI; his grandchildren, Kelly (Jeremy) Brockwell and Adam Swenson; his great-grandchildren, Henry, Samuel, and Evelyn Brockwell; his brother-in-law, Don Bockman; his sister-in-law, Virginia Swenson; and many nieces, nephews, cousins, and friends. In addition to his parents and wife, Dorothy, he was preceded in death by his brother, Harry Swenson. Visitation will be held from 10:00 a.m. to 11:30 a.m. Friday, July 3, 2020 with a Funeral Service commencing at 11:30 a.m. at Strang Funeral Home, 1055 Main St., Antioch, IL 60002. Interment with Military Honors will immediately follow at Sunset Ridge Memorial Park, Kenosha, WI. For additional information, call 847-395-4000. In lieu of flowers, donations are appreciated to Peace Evangelical Lutheran Church, 11233 306th Avenue, Wilmot, WI 53192 or the Schultz-Hahn American Legion Post #293, Silver Lake, WI in Verle's memory. Please sign the online guestbook for Verle at www.strangfh.com. Joseph P. Cresto Joseph Philip Cresto, age 89, died in peace Sunday, June 21st in Raleigh, NC. Born on November 5, 1930 to Joseph and Margaret Cresto in Joliet, IL. He was a wonderful husband, father, grandfather, great grandfather, uncle and cousin. He is survived by his children; Susan (Nick) Berrong, Sally (Blake) Frodin, Michael, and Joseph (Kim) Cresto; grandchildren Erin (Ryan) McKevett, Reed and Margaret Frodin, Michael, Benjamin and Ava Cresto and great-granddaughter, Nora Maeve McKevett. Joe was preceded in death by his wife Marian, sister Marjorie Lyons and parents. In his later years, he found happiness again with Elizabeth Hund who passed in 2019. Joe will be fondly remembered by family and friends as a kind and caring man who was always the life of the party. He was a proud patriot and U.S. Marine Corps veteran. In lieu of flowers, the family requests a donation to a charity of your choice. Fredericksen remembered as a skilled officer, photographer and 'outstanding human being' As a law enforcement officer handling sensitive crimes, Cindy Fredericksen put away the wors… COLLECTION: Recent obituaries in the Kenosha News (June 24 - June 30, 2020) COLLECTION: Recent obituaries in the Kenosha News (June 17-23, 2020) COLLECTION: Recent obits in the Kenosha News (July 10-15, 2020) Mount Pleasant reaches settlement with couple on their property near Foxconn site UPDATE: A total of 13 KUSD schools switching to virtual learning protocols due to COVID-19 resurgence; more approaching threshold New felony charges filed against Kenosha man Baker Street eatery closes, owners cite staffing shortages for the decision Kenosha couple facing drug, child neglect charges COMING SOON: Get the latest Olympic Updates daily during the 2022 games Receive the latest local crime & courts coverage in your inbox every week. BEECH POINTE - Ad from 2022-01-09 Harbor Market c/o Kenosha Harbor Market - Ad from 2022-01-14 ON THE BORDER - Ad from 2022-01-12 St. Catherine Commons C/O Capri Communities, LLC - Ad from 2022-01-12 ADVOCATE AURORA HEALTH - Ad from 2022-01-12 BERKOTS SUPER FOODS /	-0.676874	-1.277007	-1.71032	-2.063802	[ -0.4912829775500694, -0.8624650188087335 ]	[ -1.2805882494853356, -1.2734257351600966 ]	[ -1.6393048893048803, -1.7813343867263993 ]	[ -1.9155238978830629, -2.2120801084638915 ]	1,024	[ 512, 512 ]	[ 292, 17774, 322, 1784, 16336, 14497, 264, 679, 3996, 621, 414, 29889, 13, 6565, 280, 338, 10503, 2347, 491, 670, 1487, 29892, 360, 744, 313, 5661, 2002, 29897, 310, 399, 585, 10794, 2350, 29892, 399, 29902, 29936, 670, 4595, 11991, 29892, 21872, 313, 29967, 261, 6764, 29897, 4358, 384, 5872, 322, 11783, 3925, 25151, 29936, 670, 2107, 29899, 27857, 11991, 29892, 6498, 29892, 15316, 29892, 322, 7298, 873, 29876, 4358, 384, 5872, 29936, 670, 8099, 29899, 262, 29899, 10653, 29892, 3872, 350, 1698, 1171, 29936, 670, 9883, 29899, 262, 29899, 10653, 29892, 11653, 3925, 25151, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 274, 681, 1144, 29892, 322, 7875, 29889, 512, 6124, 304, 670, 11825, 322, 6532, 29892, 9579, 20336, 29892, 540, 471, 9399, 287, 297, 4892, 491, 670, 8099, 29892, 10686, 3925, 25151, 29889, 13, 6116, 7018, 674, 367, 4934, 515, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 304, 29871, 29896, 29896, 29901, 29941, 29900, 263, 29889, 29885, 29889, 28728, 29892, 5468, 29871, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 411, 263, 13811, 13537, 6692, 844, 16750, 472, 29871, 29896, 29896, 29901, 29941, 29900, 263, 29889, 29885, 29889, 472, 3767, 574, 13811, 13537, 8778, 29892, 29871, 29896, 29900, 29945, 29945, 4241, 624, 1696, 5459, 601, 305, 29892, 17674, 29871, 29953, 29900, 29900, 29900, 29906, 29889, 4124, 358, 411, 20080, 7906, 943, 674, 7389, 1101, 472, 8991, 842, 390, 5525, 19722, 4815, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 1152, 5684, 2472, 29892, 1246, 29871, 29947, 29946, 29955, 29899, 29941, 29929, 29945, 29899, 29946, 29900, 29900, 29900, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 526, 7556, 304, 24819, 21827, 936, 24760, 273, 6291, 29892, 29871, 29896, 29896, 29906, 29941, 29941, 29871, 29941, 29900, 29953, 386, 18874, 29892, 4624, 14817, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29929, 29906, 470, 278, 1102, 499, 29920, 29899, 29950, 5422, 3082, 5682, 291, 4918, 396, 29906, 29929, 29941, 29892, 16466, 9459, 29892, 399, 29902, 297, 1798, 280, 29915, 29879, 3370, 29889, 3529, 1804, 278, 7395, 17838, 2909, 363, 1798, 280, 472, 7821, 29889, 710, 574, 29888, 29882, 29889, 510, 29889, 13, 26473, 561, 349, 29889, 6781, 4778, 13, 26473, 561, 14920, 6781, 4778, 29892, 5046, 29871, 29947, 29929, 29892, 6423, 297, 10776, 16340, 29892, 5306, 29871, 29906, 29896, 303, 297, 390, 744, 1141, 29892, 25166, 29889, 19298, 373, 3979, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29900, 304, 6936, 322, 18364, 6781, 4778, 297, 435, 324, 2035, 29892, 17674, 29889, 940, 471, 263, 20695, 10216, 29892, 4783, 29892, 4595, 22212, 29892, 2107, 4595, 22212, 29892, 22169, 322, 22618, 29889, 940, 338, 10503, 2347, 491, 670, 4344, 29936, 25914, 313, 29940, 860, 29897, 2292, 29373, 29892, 317, 635, 313, 29933, 433, 446, 29897, 383, 5964, 262, 29892, 5765, 29892, 322, 6936, 313, 29968, 326, 29897, 6781, 4778, 29936, 4595, 11991, 1425, 262, 313, 29934, 10094, 29897, 24053, 5750, 1803, 29892, 830, 287, 322, 18364, 383, 5964, 262, 29892, 5765, 29892, 20212, 322, 319, 1564, 6781, 4778, 322, 2107, 29899, 27857, 29881, 6334, 357, 29892, 405, 2207, 3219, 29872, 345, 24053, 5750, 1803, 29889, 11131, 471, 9399, 287, 297, 4892, 491, 670, 6532, 24236, 29892, 9883, 1085, 3418, 347, 8626, 787, 322, 11825, 29889, 512, 670, 2678, 2440, 29892, 540, 1476, 22722, 1449, 411, 13061, 379, 870, 1058, 4502, 297, 29871, 29906, 29900, 29896, 29929, 29889, 13, 29967, 7297, 674, 367, 6299, 368, 21832, 491, 3942, 322, 7875, 408, 263, 2924, 322, 1559, 292, 767, 1058, 471, 2337, 278, 2834, 310, 278, 6263, 29889, 940, 471, 263, 22314, 16967, 327, 322, 501, 29889, 29903, 29889, 15929, 16408, 25808, 273, 29889, 13, 797, 13003, 310, 18281, 29892, 278, 3942, 7274, 263, 1016, 362, 304, 263, 1373, 537, 310, 596, 7348, 29889, 13, 23923, 672, 860, 4881, 21832, 408, 263, 2071, 24455, 12139, 29892, 17739, 261, 322, 525, 449, 11235, 5199, 1641, 29915, 13, 2887, 263, 4307, 24555, 13561, 12139, 11415, 20502, 2181, 1355, 29892, 315, 513, 29891, 19769, 4881, 1925, 3448, 278, 281, 943, 30098, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 1540, 29871, 29906, 29946, 448, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 1540, 29871, 29896, 29955, 29899, 29906, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1169, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 11850, 29871, 29896, 29900, 29899, 29896, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 27648, 19777, 13186, 22170, 16493, 411, 7303, 373, 1009, 2875, 2978, 14802, 13082, 3268, 13, 14474, 29901, 319, 3001, 310, 29871, 29896, 29941, 476, 3308, 29928, 12462, 21293, 304, 6901, 6509, 9608, 29879, 2861, 304, 19937, 29899, 29896, 29929, 620, 2007, 663, 29936, 901, 28702, 16897, 13, 4373, 7995, 2592, 21090, 934, 29881, 2750, 10015, 359, 2350, 767, 13, 29933, 5790, 7103, 17545, 708, 4694, 267, 29892, 1914, 414, 274, 568, 13925, 292, 3273, 1179, 363, 278, 10608, 13, 29968, 264, 359, 2350, 7303, 14870, 15721, 29892, 2278, 22851, 21090, 13, 19795, 4214, 7791, 1164, 29901, 3617, 278, 9281, 19025, 5020, 15190, 14218, 2645, 278, 29871, 29906, 29900, 29906, 29906, 8090, 13, 24131, 278, 9281, 1887, 17268, 669, 28033, 23746, 297, 596, 297, 1884, 1432, 4723, 29889, 13, 15349, 29923, 3210, 349, 6992, 4330, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29900, 29929, 13, 21972, 4089, 28794, 274, 29914, 29877, 10015, 359, 2350, 3536, 4089, 28794, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29946, 13, 1164, 6093, 350, 22364, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 855, 29889, 21688, 3468, 315, 29914, 29949, 5915, 374, 20473, 1907, 29892, 365, 12182, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 3035, 29963, 20166, 3040, 319, 29965, 1672, 4717, 17714, 1964, 4690, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 13635, 29968, 2891, 29903, 317, 4897, 1001, 18322, 29949, 8452, 847 ]	1,332,858	15,360	CommonCrawl	0	3
\section{Introduction} \label{intro} Let $A_0$ be a self-adjoint operator in a separable Hilbert space $\gH$ and let $C=C^$ be a trace class operator in $\gH$, $C\in\mathfrak S_1(\gH)$. Recall, that according to the Kato-Rosenblum theorem, cf. \cite{Kat57,Ros57} the absolutely continuous parts $A^{ac}_0$ and ${\wt A}^{ac}$, { in short the $ac$-parts}, of the operators $A_0$ and ${\wt A}=A_0+C$ {are unitarily equivalent. In other words, the { absolutely continuous spectrum}, { in short $ac$-spectrum}, of $A_0$ and its spectral multiplicity { are} stable under { \emph{additive}} trace class perturbations. At the same time, the Weyl-von~Neumann-Kuroda theorem \cite[Theorem 94.2]{AG81}, \cite{Neu35}, \cite{Kur58} shows that the condition $C\in\mathfrak S_1(\gH)$ cannot be replaced by $C\in\mathfrak S_p(\gH)$ with $p\in (1,\infty]$ (where $\mathfrak S_p(\gH)$ denotes the Neumann-Schatten operator ideals). \begin{theorem}[{\cite[Theorem 10.2.1 and Theorem 10.2.3]{Ka76}}]\label{WNth} For any operator $A_0=A^_0$ in $\gH$ and any $p\in (1,\infty]$ there exists an operator $C= C^\in \mathfrak S_p(\gH)$ such that the perturbed operator ${\wt A} = A_0 + C$ has purely point spectrum. In particular, $\sigma_{ac}(A_0 + C)=\emptyset.$ \end{theorem} The Kato-Rosenblum theorem was generalized by Birman \cite{Bir63a} and Birman and Krein \cite{BirKrei62} to the case of \emph{non-additive} perturbations. Namely, it was shown that $A^{ac}_0$ and ${\wt A}^{ac}$ still remain unitary equivalent whenever \begin{displaymath} ({\wt A}-i)^{-1}-(A_0-i)^{-1}\in\mathfrak S_1(\gH). \end{displaymath} In particular, this is true if $A_0=A^_0$ and ${\wt A}={\wt A}^$ are self-adjoint extensions of a symmetric operator $A$ (in short $A_0, {\wt A}\in {\rm Ext\,}_A$). This rises the following Weyl-von~Neumann problem for extensions: Given $p \in (1,\infty]$ and a self-adjoint extension $A_0$ of $A.$ Does there exist a self-adjoint extension $\wt A$ of $A$ such that $\wt A$ has purely point spectrum and the difference $(\wt A - i)^{-1} - (A_0 - i)^{-1}$ belongs to $\mathfrak S_p(\gotH)$? To the best of our knowledge this problem was not investigated. In the present paper we show that the Weyl-von~Neumann theorem for extensions becomes false in general. We show that under an additional assumption on the symmetric operator $A$ the $ac$-part of a certain extension $A_0=A^_0$ is unitarily equivalent to the $ac$-part of any extension ${\wt A}={\wt A}^*$ of $A$ provided that their resolvent difference is compact, that is, \begin{equation}\label{0.2} K_{\wt A} := ({\wt A}-i)^{-1}-(A_0-i)^{-1}\in{\mathfrak S}_{\infty}(\gH). \end{equation} The additional assumption on the pair $\{A,A_0\}$ is formulated in terms of the Weyl function of the pair $\{A,A_0\}$. The latter is the main object in the boundary triplet approach to the extension theory developed in the last three decades	0.46749	-0.725493	0.526645	2.501603	[ 0.6113057427939328, 0.3236739027041931 ]	[ -0.825768589832667, -0.6252181887259785 ]	[ 0.7802690489117124, 0.2730208438348586 ]	[ 2.6576850337055076, 2.3455206015151613 ]	1,024	[ 512, 512 ]	[ 320, 2042, 29912, 25898, 29913, 320, 1643, 29912, 23333, 29913, 13, 13, 12024, 29871, 395, 29909, 29918, 29900, 29938, 367, 263, 1583, 29899, 328, 12090, 5455, 297, 263, 2903, 519, 12338, 2151, 2913, 13, 4535, 29887, 29950, 29938, 322, 1235, 395, 29907, 29922, 29907, 6622, 29938, 367, 263, 9637, 770, 5455, 297, 779, 29887, 29950, 1628, 13, 29938, 29907, 29905, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 4935, 3599, 497, 29892, 393, 5034, 304, 278, 13, 29968, 1219, 29899, 29934, 7749, 2204, 398, 9185, 29892, 274, 29888, 29889, 320, 2036, 29912, 29968, 271, 29945, 29955, 29892, 29934, 359, 29945, 29955, 29913, 278, 13312, 13, 20621, 681, 5633, 29871, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 7555, 14554, 319, 2844, 562, 4429, 426, 297, 3273, 278, 13, 29938, 562, 4388, 20895, 1118, 310, 278, 12768, 395, 29909, 29918, 29900, 29938, 322, 7555, 14554, 319, 5369, 29909, 29918, 29900, 29974, 29907, 29938, 426, 598, 13, 348, 3673, 2354, 7126, 29889, 512, 916, 3838, 29892, 278, 426, 13312, 9126, 13, 21494, 5848, 1118, 426, 297, 3273, 395, 562, 4388, 21494, 5848, 1118, 310, 395, 29909, 29918, 29900, 29938, 322, 967, 23161, 13, 18056, 17024, 426, 526, 29913, 13714, 1090, 426, 320, 7278, 29912, 1202, 3321, 930, 9637, 770, 13, 10700, 9265, 800, 29889, 2180, 278, 1021, 931, 29892, 278, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 29899, 29968, 2192, 1388, 13, 14648, 320, 2036, 29961, 28831, 29871, 29929, 29946, 29889, 29906, 3199, 10051, 29947, 29896, 1118, 320, 2036, 29912, 8139, 29884, 29941, 29945, 1118, 320, 2036, 29912, 29968, 332, 29945, 29947, 29913, 29871, 13, 845, 1242, 393, 278, 4195, 13, 29938, 29907, 29905, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 1262, 2609, 367, 8611, 491, 395, 29907, 29905, 262, 29905, 7237, 13, 29903, 29918, 29886, 1194, 29887, 29950, 1262, 411, 395, 29886, 29905, 262, 313, 29896, 2053, 3411, 9341, 313, 3062, 779, 7237, 317, 29918, 29886, 1194, 29887, 29950, 1262, 13, 1145, 4769, 278, 2448, 22553, 29899, 4504, 8606, 5455, 1957, 1338, 467, 13, 29905, 463, 29912, 14648, 4400, 741, 2036, 29961, 28831, 29871, 29896, 29900, 29889, 29906, 29889, 29896, 322, 10244, 29871, 29896, 29900, 29889, 29906, 29889, 29941, 3199, 29968, 29874, 29955, 29953, 930, 10725, 1643, 29912, 16048, 386, 29913, 13, 2831, 738, 5455, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 297, 779, 29887, 29950, 29938, 322, 738, 29871, 395, 29886, 29905, 262, 313, 29896, 2053, 3411, 9341, 13, 12711, 4864, 385, 5455, 395, 29907, 29922, 315, 6622, 29905, 262, 320, 7237, 317, 29918, 29886, 1194, 29887, 29950, 1262, 29871, 1316, 393, 13, 1552, 13499, 28179, 5455, 7555, 14554, 319, 29913, 353, 319, 29918, 29900, 718, 315, 29938, 756, 24837, 1298, 13, 21494, 5848, 29889, 512, 3153, 29892, 779, 3754, 648, 562, 2119, 29909, 29918, 29900, 718, 315, 7950, 26153, 7449, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 1576, 476, 1219, 29899, 29934, 7749, 2204, 398, 9185, 471, 28803, 491, 17853, 1171, 13, 29905, 2036, 29912, 29933, 381, 29953, 29941, 29874, 29913, 322, 17853, 1171, 322, 7706, 262, 320, 2036, 29912, 29933, 381, 29968, 5803, 29953, 29906, 29913, 13, 517, 278, 1206, 310, 320, 7278, 29912, 5464, 29899, 1202, 3321, 29913, 22786, 800, 29889, 13041, 873, 29892, 372, 471, 13, 845, 776, 393, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 7555, 14554, 319, 2844, 562, 1042, 1603, 3933, 5190, 653, 13, 1686, 27445, 10940, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 13670, 14554, 319, 7402, 29875, 21604, 29896, 7402, 29898, 29909, 29918, 29900, 29899, 29875, 21604, 29896, 1012, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 797, 3153, 29892, 445, 338, 1565, 565, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 322, 7555, 14554, 319, 5369, 741, 14554, 319, 2137, 29394, 13, 598, 1583, 29899, 328, 12090, 17752, 310, 263, 13, 11967, 16414, 5455, 395, 29909, 29938, 313, 262, 3273, 395, 29909, 29918, 29900, 29892, 29871, 2802, 14554, 319, 1012, 262, 2802, 1758, 7338, 5940, 2403, 29909, 18724, 13, 4013, 364, 4637, 278, 1494, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 1108, 363, 13, 24299, 29901, 11221, 29871, 395, 29886, 320, 262, 313, 29896, 2053, 3411, 9341, 322, 263, 1583, 29899, 328, 12090, 13, 29871, 6081, 259, 395, 29909, 29918, 29900, 29938, 310, 395, 29909, 7449, 29871, 5538, 29871, 727, 1863, 13, 263, 1583, 29899, 328, 12090, 6081, 29871, 779, 14554, 319, 29938, 310, 395, 29909, 29938, 1316, 393, 779, 14554, 319, 29938, 756, 13, 29886, 545, 368, 1298, 18272, 322, 278, 4328, 12211, 14554, 319, 448, 13, 29875, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 1042, 14393, 304, 779, 7237, 317, 29918, 29886, 1194, 7085, 29950, 1262, 29973, 1763, 13, 1552, 1900, 310, 1749, 7134, 445, 1108, 471, 451, 7405, 630, 29889, 13, 13, 797, 278, 2198, 5650, 591, 1510, 393, 278, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 9185, 363, 13, 24299, 7415, 2089, 297, 2498, 29889, 1334, 1510, 393, 1090, 385, 13, 1202, 3245, 11833, 373, 278, 18348, 5455, 395, 29909, 29938, 278, 395, 562, 4388, 1595, 310, 263, 13, 14082, 6081, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 29871, 338, 443, 3673, 2354, 7126, 304, 278, 395, 562, 4388, 1595, 310, 738, 13, 17588, 7555, 14554, 319, 5369, 741, 14554, 319, 2137, 29394, 310, 395, 29909, 29938, 4944, 393, 1009, 13, 9778, 794, 4328, 338, 11071, 29892, 393, 338, 29892, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29906, 29913, 13, 29968, 1665, 14554, 319, 29913, 3490, 313, 741, 14554, 319, 7402, 29875, 21604, 29896, 7402, 29898, 29909, 29918, 29900, 29899, 29875, 21604, 29896, 1012, 262, 741, 7237, 13, 29903, 6353, 3411, 4678, 29887, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1576, 5684, 11833, 373, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 338, 883, 7964, 297, 13, 357, 1516, 310, 278, 399, 1032, 29880, 740, 310, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 23699, 29871, 450, 13, 29880, 2620, 338, 278, 1667, 1203, 297, 278, 10452, 21954, 29873, 2948, 304, 278, 13, 17588, 6368, 8906, 297, 278, 1833, 2211, 1602, 3076 ]	1,332,863	0	ArXiv	-1	-1
, see \cite{DM91,DM95,GG91} and references therein. The core of this approach is the following abstract version of Green's formula \begin{equation}\label{0.3} (A^f,g) - (f,A^g) = ({\Gamma}_1f,{\Gamma}_0g)_{\cH} - ({\Gamma}_0f,{\Gamma}_1g)_{\cH}, \qquad f,g\in{\rm dom\,}(A^), \end{equation} where $\cH$ is an auxiliary Hilbert space and $\Gamma_0,\Gamma_1 : {\rm dom\,}(A^)\rightarrow \cH$ are linear mappings. A triplet $\Pi=\{\cH,\Gamma_0,\Gamma_1\}$ is called a boundary triplet for the operator $A^$ if \eqref{0.3} holds and the mapping $\Gamma:=\{\Gamma_0,\Gamma_1\}: {\rm dom\,}(A^)\rightarrow \cH\oplus \cH$ is surjective. With a boundary triplet ${\Pi}$ for $A^$ one associates in a natural way the Weyl function $M(\cdot)= M_{\Pi}(\cdot)$ (see Definition \ref{Weylfunc}), which is the key object of this approach. It is an operator-valued Nevanlinna function with values in $[\cH]$ (i.e. $R_{\cH}$-function) and its role in the extension theory is similar to that of the classical Weyl function in the spectral theory of Sturm-Liouville operators. In particular, if $A$ is simple, then $M(\cdot)$ determines the pair $\{A,A_0\}$, where $A_0 :=A^\upharpoonright {\xker\,}{\Gamma}_0$, uniquely, up to unitary equivalence. Moreover, $M(\cdot)$ is regular (holomorphic) precisely on the resolvent set $\varrho(A_0)$ of $A_0$ and the spectral properties of $A_0$ are described in terms of the limits $M(t+i0)$ at the real line (see \cite{BMN02}). One of our main results (Theorem \ref{V.5}) reads now as follows. \begin{theorem}\label{th0.1} Let $\Pi=\{\cH,\Gamma_0,\Gamma_1\}$ be a boundary triplet for $A^$ { such that} the corresponding Weyl function $M(\cdot)$ has weak limits \begin{equation}\label{0.2A} M(t+i0) :=\,\mbox{\rm w-}\hspace{-2pt} \lim_{y\downarrow 0}M(t+iy)\quad \text{for a.e. }\ t\in{\mathbb R}. \end{equation} If a self-adjoint extension $\wt A$ of $A$ satisfies condition \eqref{0.2}, then the { $ac$-parts} ${\wt A}^{ac}$ and $A^{ac}_0$ of ${\wt A}$ and { $A_0 \,(= A^\upharpoonright{\xker\,}({\Gamma}_0)$)} are unitarily equivalent. \end{theorem} We apply this result to direct sums $A :=\oplus^{\infty}_{n=1} S_n$ of symmetric operators $S_n$ { with equal and finite deficiency indices $n_\pm(S_n)$}. { Let $S_{0n}$ be a self-adjoint extension of $S_n$ for each $n \in \N$. We show that the $ac$-part of $A_0 :=\oplus^{\infty}_{n=1} S_{0n}$ is unitarily equivalent to the $ac$-part of any other extension $\wt A=\wt A^*\in {\rm Ext\,}_A$ provided that condition \eqref{0.2} is satisfied and the symmetric operators $S_n$ are unitarily equivalent to $S_1$ for any $n \in \N$.} The second part of the paper is concerned with a spectral extremal property of certain self-adjoint extensions of $A$ described by the following definition. \begin{	0.701704	-0.5236	0.737153	2.491197	[ 0.7482732856938088, 0.6551353565218931 ]	[ -0.45600378779221007, -0.5911962456810939 ]	[ 0.7041818181501843, 0.7701240848101754 ]	[ 2.6160631094134614, 2.3663315636611846 ]	1,024	[ 512, 512 ]	[ 29892, 1074, 13, 29905, 2036, 29912, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29892, 26788, 29929, 29896, 29913, 322, 9282, 727, 262, 29889, 13, 13, 1576, 7136, 310, 445, 2948, 338, 278, 1494, 9846, 1873, 310, 13, 24599, 29915, 29879, 7063, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29941, 29913, 13, 313, 29909, 6622, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 6622, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 741, 6642, 2403, 29900, 29887, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 29888, 29892, 741, 6642, 2403, 29896, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 6622, 511, 13, 418, 320, 355, 29912, 2573, 29913, 13, 3062, 779, 29883, 29950, 29938, 29871, 338, 385, 29587, 653, 12338, 2151, 2913, 322, 13, 4535, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 584, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29938, 29871, 526, 5608, 611, 27775, 29889, 29871, 319, 21954, 29873, 13, 4535, 12197, 2013, 741, 29883, 29950, 2053, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 11854, 338, 2000, 263, 10452, 21954, 29873, 29871, 363, 13, 1552, 5455, 395, 29909, 6622, 29938, 565, 320, 4915, 29912, 29900, 29889, 29941, 29913, 8640, 322, 278, 10417, 13, 4535, 6642, 29901, 2013, 741, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29905, 6177, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29905, 17201, 13, 29905, 29883, 29950, 29938, 338, 1190, 25674, 29889, 13, 13, 3047, 263, 10452, 21954, 29873, 7555, 12197, 1042, 363, 395, 29909, 6622, 29938, 697, 4067, 1078, 297, 263, 13, 25047, 982, 278, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 3892, 341, 1665, 12197, 4678, 3822, 1262, 313, 4149, 13, 14683, 320, 999, 29912, 29956, 1032, 29880, 9891, 9594, 607, 338, 278, 1820, 1203, 310, 445, 2948, 29889, 739, 13, 275, 385, 5455, 29899, 4387, 287, 2448, 3703, 1915, 1056, 740, 411, 1819, 297, 395, 7110, 29883, 29950, 9341, 13, 29898, 29875, 29889, 29872, 29889, 395, 29934, 1665, 29883, 29950, 23021, 2220, 29897, 322, 967, 6297, 297, 278, 6081, 6368, 338, 13, 29764, 304, 393, 310, 278, 14499, 399, 1032, 29880, 740, 297, 278, 23161, 13, 14138, 310, 624, 17095, 29899, 23410, 283, 4909, 12768, 29889, 512, 3153, 29892, 565, 395, 29909, 29938, 338, 13, 12857, 29892, 769, 395, 29924, 1194, 3822, 1262, 3683, 1475, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 28538, 988, 13, 29938, 29909, 29918, 29900, 3490, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 3331, 6642, 2403, 29900, 1628, 20498, 873, 29892, 701, 304, 13, 5441, 653, 24796, 29889, 12808, 29892, 395, 29924, 1194, 3822, 1262, 338, 4943, 13, 29898, 5391, 16898, 29897, 17503, 373, 278, 3770, 794, 731, 779, 1707, 4650, 29898, 29909, 29918, 29900, 1262, 310, 13, 29938, 29909, 29918, 29900, 29938, 29871, 322, 278, 23161, 4426, 310, 395, 29909, 29918, 29900, 29938, 526, 5439, 297, 4958, 13, 974, 278, 13071, 395, 29924, 29898, 29873, 29974, 29875, 29900, 1262, 472, 278, 1855, 1196, 313, 4149, 320, 2036, 29912, 29933, 29924, 29940, 29900, 29906, 7690, 13, 13, 6716, 310, 1749, 1667, 2582, 313, 28831, 320, 999, 29912, 29963, 29889, 29945, 1800, 13623, 1286, 408, 13, 23031, 29879, 29889, 13, 29905, 463, 29912, 14648, 1012, 1643, 29912, 386, 29900, 29889, 29896, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 2053, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 11854, 367, 263, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 29938, 29871, 426, 1316, 393, 29913, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 756, 29871, 8062, 13071, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29906, 29909, 29913, 13, 29924, 29898, 29873, 29974, 29875, 29900, 29897, 584, 2013, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 3204, 2936, 29871, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 2144, 3425, 320, 726, 29912, 1454, 263, 29889, 29872, 29889, 17704, 260, 29905, 262, 741, 1995, 390, 1836, 13, 320, 355, 29912, 2573, 29913, 13, 3644, 263, 1583, 29899, 328, 12090, 6081, 779, 14554, 319, 29938, 310, 395, 29909, 29938, 17150, 4195, 13, 29905, 4915, 29912, 29900, 29889, 29906, 1118, 769, 278, 426, 395, 562, 4388, 20895, 29913, 7555, 14554, 319, 2844, 562, 1042, 322, 13, 29938, 29909, 998, 562, 2403, 29900, 29938, 29871, 310, 29871, 7555, 14554, 319, 1042, 322, 426, 395, 29909, 29918, 29900, 7179, 29898, 29922, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 2915, 526, 443, 3673, 2354, 13, 1686, 27445, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 4806, 3394, 445, 1121, 304, 1513, 25470, 395, 29909, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 13, 29903, 29918, 29876, 29938, 310, 18348, 12768, 395, 29903, 29918, 29876, 29938, 426, 411, 5186, 322, 8093, 13, 1753, 293, 13396, 16285, 395, 29876, 3187, 3358, 29898, 29903, 29918, 29876, 1262, 1836, 426, 2803, 395, 29903, 648, 29900, 29876, 1042, 367, 263, 13, 1311, 29899, 328, 12090, 6081, 310, 395, 29903, 29918, 29876, 29938, 363, 1269, 395, 29876, 320, 262, 320, 29940, 1504, 1334, 1510, 29871, 393, 13, 1552, 395, 562, 4388, 1595, 310, 395, 29909, 29918, 29900, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317, 648, 29900, 29876, 1042, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 278, 395, 562, 4388, 1595, 310, 738, 916, 6081, 779, 14554, 13, 29909, 2013, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 29871, 4944, 393, 4195, 320, 4915, 29912, 29900, 29889, 29906, 29913, 338, 13, 29879, 27685, 1000, 322, 278, 18348, 12768, 395, 29903, 29918, 29876, 29938, 526, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29903, 29918, 29896, 29938, 363, 738, 395, 29876, 320, 262, 320, 29940, 1504, 29913, 13, 13, 1576, 1473, 760, 310, 278, 5650, 338, 15041, 411, 29871, 263, 23161, 13, 1062, 1745, 284, 2875, 310, 3058, 1583, 29899, 328, 12090, 17752, 310, 395, 29909, 29938, 13, 2783, 23059, 491, 278, 1494, 5023, 29889, 13, 29905, 463, 29912 ]	1,332,863	1,024	ArXiv	-1	-1
definition}\Label{0.3AA} {\em (i) Let $T_j=T_j^\in \cC(\gotH_j)$, $j = 1,2$. We say that $T_1$ is a part of $T_2$ if there is an isometry $V$ from $\gotH_1$ into $\gotH_2$ such that $VT_1V^ \subseteq T_2$. (ii) { Let $A_0=A^_0$ be an extension of $A$. We say that $A_0$ is $ac$-minimal if $A^{ac}_0$ is a part of any self-adjoint extension ${\wt A}$ of $A$.} (iii) Let ${\sigma}_0 :={\sigma}_{ac}(A_0)$. We say that $A_0$ is strictly $ac$-minimal if for any extension $\wt A=\wt A^$ of $A$ the parts $A^{ac}_0$ and $\wt A^{ac}E_{\wt A}(\sigma_0)$ are unitarily equivalent. } \end{definition} In particular, if $A_0$ is $ac$-minimal, then $\sigma_{ac}({\wt A})\supseteq \sigma_{ac}( A_0)$. Note that an $ac$-minimal extension of $A$ is not unique. For any two $ac$-minimal extensions their $ac$-parts are unitarily equivalent. We show (cf. Theorem \ref{VI.6}) that if $n_{\pm}(S_n)<\infty,$ then the $ac$-part $A^{ac}_0$ of any direct sum extension $A_0 =\oplus^{\infty}_{n=1} S_{0n}$ of $A :=\oplus^{\infty}_{n=1} S_{n}$ is $ac$-minimal. In particular, $\sigma_{ac}({\wt A})\supseteq \sigma_{ac}( A_0)$ for any ${\wt A}={\wt A}^\in {\rm Ext\,}_A.$ This result looks surprising with respect to Theorem \ref{WNth}. Indeed, in this case $A^{ac}_0$ is still a part of $\wt A^{ac}$ for any ${\wt A}\in {\rm Ext\,}_A$ though the resolvent difference $K_{\wt A}$ (see \eqref{0.2}) is not even compact. In other words, in this case the $ac$-spectrum of $A_0$ (but not its spectral multiplicity) remains stable under (non-additive) compact perturbations $K_{\wt A}$ though both $\sigma_{ac}( A_0)$ and its multiplicity can only increase, whenever} $K_{\wt A}\notin\gotS_{\infty}.$ Moreover, we apply our technique to minimal symmetric non-negative Sturm-Liouville operator $A$ with an unbounded operator potential \begin{eqnarray}\Label{0.4} (Af)(x) = -f''(x) + Tf(x). \end{eqnarray} We show that the Friedrichs extension $A^F$ is $ac$-minimal and under a simple additional assumption is even strictly $ac$-minimal. The paper is organized as follows. In Section 2 we give a short introduction into the theory of ordinary and generalized boundary triplets and the corresponding Weyl functions. In Section 3 we express the spectral multiplicity function of the { $ac$-part $\wt A^{ac}$ of $\wt A= \wt A^(\in {\rm Ext\,}_A)$} by means of the corresponding Weyl function. In Section 4 we apply this technique to prove Theorem \ref{th0.1} as well as to give a simple proof of the Kato-Rosenblum theorem. In Section 5 direct sums of boundary triplets ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for operators $S_n^$ adjoint to symmetric operators $S_n$ are investigated. We show that though, in general, ${\Pi} = \oplus^\infty_{n=1} {\Pi}_n$ is not a boundary triplet for the direct sum $A^ :=\oplus^{\infty}_{n=1} S	-0.035866	-0.931416	0.245122	2.158222	[ -0.3296612769282156, 0.2579294821122526 ]	[ -0.9797626478253028, -0.883068704434578 ]	[ 0.37954296690099787, 0.11070141821026537 ]	[ 2.0333561693248154, 2.2830877150770923 ]	1,024	[ 512, 512 ]	[ 16553, 1012, 4775, 29912, 29900, 29889, 29941, 6344, 29913, 13, 741, 331, 13, 29898, 29875, 29897, 13, 12024, 395, 29911, 29918, 29926, 29922, 29911, 29918, 29926, 6622, 29905, 262, 320, 29883, 29907, 1194, 7085, 29950, 29918, 29926, 5767, 395, 29926, 353, 29871, 29896, 29892, 29906, 1504, 1334, 13, 20834, 393, 395, 29911, 29918, 29896, 29938, 338, 263, 760, 310, 29871, 395, 29911, 29918, 29906, 29938, 29871, 565, 727, 338, 385, 338, 7843, 395, 29963, 29938, 13, 3166, 779, 7085, 29950, 29918, 29896, 29938, 964, 779, 7085, 29950, 29918, 29906, 29938, 1316, 393, 395, 29963, 29911, 29918, 29896, 29963, 6622, 320, 11725, 323, 29918, 29906, 1504, 13, 13, 13, 29898, 2236, 29897, 426, 2803, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 367, 385, 6081, 310, 395, 29909, 1504, 13, 4806, 1827, 393, 395, 29909, 29918, 29900, 29938, 338, 395, 562, 4388, 1195, 3039, 565, 395, 29909, 998, 562, 2403, 29900, 29938, 338, 263, 760, 310, 738, 13, 1311, 29899, 328, 12090, 6081, 7555, 14554, 319, 1042, 310, 395, 29909, 1504, 29913, 13, 13, 29898, 25609, 29897, 2803, 7555, 3754, 2403, 29900, 3490, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 4935, 1334, 1827, 393, 395, 29909, 29918, 29900, 29938, 338, 18719, 395, 562, 4388, 1195, 3039, 565, 363, 13, 1384, 6081, 779, 14554, 319, 2013, 14554, 319, 6622, 29938, 310, 395, 29909, 29938, 278, 5633, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 779, 14554, 13, 29909, 998, 562, 29913, 29923, 1665, 14554, 319, 4678, 3754, 29918, 29900, 1262, 526, 443, 3673, 2354, 7126, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 797, 3153, 29892, 565, 395, 29909, 29918, 29900, 29938, 338, 395, 562, 4388, 1195, 3039, 29892, 769, 13, 4535, 3754, 648, 562, 2119, 741, 14554, 319, 11606, 2146, 567, 300, 1837, 320, 3754, 648, 562, 2119, 319, 29918, 29900, 4935, 3940, 13, 5747, 385, 395, 562, 4388, 1195, 3039, 6081, 310, 395, 29909, 29938, 338, 451, 5412, 29889, 13, 2831, 738, 1023, 29871, 395, 562, 4388, 1195, 3039, 17752, 1009, 395, 562, 4388, 20895, 526, 13, 348, 3673, 2354, 7126, 29889, 13, 13, 4806, 1510, 313, 6854, 29889, 10244, 320, 999, 29912, 18118, 29889, 29953, 1800, 393, 565, 395, 29876, 1665, 3358, 2119, 29903, 29918, 29876, 29897, 13505, 3411, 8209, 13, 6098, 278, 395, 562, 4388, 1595, 395, 29909, 998, 562, 2403, 29900, 29938, 310, 738, 1513, 2533, 6081, 13, 29938, 29909, 29918, 29900, 17313, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317, 648, 29900, 29876, 1042, 310, 395, 29909, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 13, 29903, 648, 29876, 1042, 338, 395, 562, 4388, 1195, 3039, 29889, 512, 3153, 29892, 13, 4535, 3754, 648, 562, 2119, 741, 14554, 319, 11606, 2146, 567, 300, 1837, 320, 3754, 648, 562, 2119, 319, 29918, 29900, 1262, 363, 738, 7555, 14554, 13, 29909, 5369, 741, 14554, 319, 2137, 17710, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 4013, 1121, 3430, 26800, 411, 3390, 304, 10244, 320, 999, 29912, 16048, 386, 1836, 13, 2568, 12613, 29892, 297, 445, 1206, 395, 29909, 998, 562, 2403, 29900, 29938, 338, 1603, 29871, 263, 760, 310, 779, 14554, 13, 29909, 998, 562, 1042, 363, 738, 7555, 14554, 319, 1012, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 2466, 278, 3770, 794, 13, 29881, 17678, 395, 29968, 1665, 14554, 319, 1042, 313, 4149, 320, 4915, 29912, 29900, 29889, 29906, 1800, 338, 451, 1584, 11071, 29889, 13, 797, 916, 3838, 29892, 297, 445, 1206, 278, 395, 562, 4388, 21494, 5848, 310, 395, 29909, 29918, 29900, 29938, 13, 29898, 4187, 451, 967, 23161, 6674, 17024, 29897, 9242, 13714, 1090, 13, 29898, 5464, 29899, 1202, 3321, 29897, 11071, 22786, 800, 395, 29968, 1665, 14554, 319, 1042, 2466, 13, 20313, 779, 3754, 648, 562, 2119, 319, 29918, 29900, 1262, 322, 967, 6674, 17024, 29871, 508, 871, 7910, 29892, 13, 8256, 1310, 29913, 395, 29968, 1665, 14554, 319, 1012, 29842, 29905, 7085, 29903, 1665, 3411, 1836, 29938, 13, 13, 20761, 957, 29892, 591, 3394, 1749, 11043, 304, 29871, 13114, 18348, 13, 5464, 29899, 22198, 29871, 624, 17095, 29899, 23410, 283, 4909, 5455, 395, 29909, 29938, 411, 385, 443, 29306, 13, 6891, 7037, 13, 29905, 463, 29912, 9441, 1012, 4775, 29912, 29900, 29889, 29946, 29913, 13, 29898, 29909, 29888, 5033, 29916, 29897, 259, 353, 29871, 448, 29888, 4907, 29898, 29916, 29897, 718, 323, 29888, 29898, 29916, 467, 13, 29905, 355, 29912, 9441, 29913, 13, 4806, 1510, 393, 278, 9542, 29879, 6081, 395, 29909, 29985, 29943, 29938, 338, 395, 562, 4388, 1195, 3039, 13, 392, 1090, 263, 2560, 5684, 11833, 338, 1584, 18719, 13, 29938, 562, 4388, 1195, 3039, 29889, 13, 13, 1576, 5650, 338, 19098, 408, 4477, 29889, 512, 9779, 29871, 29906, 591, 2367, 263, 3273, 13, 524, 13210, 964, 278, 6368, 310, 15311, 322, 28803, 10452, 13, 3626, 552, 1372, 322, 29871, 278, 6590, 399, 1032, 29880, 3168, 29889, 512, 9779, 29871, 29941, 591, 13, 17073, 278, 23161, 6674, 17024, 740, 310, 278, 426, 395, 562, 4388, 1595, 13, 4535, 14554, 319, 998, 562, 1042, 310, 29871, 779, 14554, 319, 29922, 320, 14554, 319, 6622, 1194, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1262, 29913, 491, 2794, 310, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 29889, 512, 9779, 29871, 29946, 591, 3394, 445, 11043, 13, 517, 6356, 10244, 320, 999, 29912, 386, 29900, 29889, 29896, 29913, 408, 1532, 408, 304, 2367, 263, 2560, 5296, 310, 13, 1552, 476, 1219, 29899, 29934, 7749, 2204, 398, 9185, 29889, 13, 13, 797, 9779, 29871, 29945, 1513, 25470, 310, 10452, 21954, 1372, 7555, 12197, 2403, 29876, 353, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 29871, 363, 12768, 29871, 395, 29903, 29918, 29876, 6622, 29938, 594, 12090, 304, 13, 11967, 16414, 12768, 395, 29903, 29918, 29876, 29938, 526, 7405, 630, 29889, 29871, 1334, 1510, 393, 2466, 29892, 13, 262, 2498, 29892, 7555, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 2802, 12197, 2403, 29876, 29938, 338, 451, 263, 10452, 13, 3626, 552, 29873, 363, 278, 1513, 2533, 395, 29909, 6622, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317 ]	1,332,863	2,048	ArXiv	-1	-1
^_n,$ it is always possible to modify the triplets ${\Pi}_n$ in such a way that a new sequence $\wt {\Pi}_n= \{\cH_n,\wt{\Gamma}_{0n},\wt{\Gamma}_{1n}\}$ of boundary triplets for $S_n^$ satisfies the following properties: $\wt {\Pi} = \oplus^\infty_{n=1} \wt {\Pi}_n$ forms a boundary triplet for $A^$ { such that $S_{0n} := S^_n\upharpoonright {\xker\,}({\Gamma}_{0n}) = S^_n\upharpoonright {\xker\,}(\wt {\Gamma}_{0n}) =: {\wt S}_{0n},\ n \in \N$. In particular, the corresponding Weyl function $M(\cdot)$ is { block}-diagonal (see Theorem \ref{VI.3}). { Our spectral applications to direct sums are substantially based on this result. In particular, it is used in proving of Theorem \ref{VI.6} mentioned above}. Finally, in Section 6 we apply the technique (and abstract results) to operators \eqref{0.4} with { bounded and} unbounded operator potentials. { In particular, we investigate the $ac$-spectrum of self-adjoint realizations of Schr\"odinger operator \begin{displaymath} \cL = - \left(\frac{\partial^2}{\partial t^2} + \sum^n_{j=1}\frac{\partial^2}{\partial x^2_j}\right) + q(x). \quad (t,x) \in \R_+ \times \R^n, \quad q \in L^\infty(\R^n), \end{displaymath} in $L^2(\R_+\times\R^n)$, $n \ge 1$. For instance, we show that if $q(\cdot)\ge 0$ and} \begin{equation}\label{0.33} \lim_{\|x\|\to\infty}\int_{\|x-y\|\le 1}\|q(y)\|dy = 0, \end{equation} { then the Dirichlet realization $L^D$ is absolutely continuous, strictly $ac$-minimal and ${\sigma}(L^D) = {\sigma}_{ac}(L^D)= [0,\infty).$} {\bf Notations} In the following we consider only separable Hilbert spaces which are denoted by $\mathfrak H$, $\cH$ etc. { The symbols $\cC(\cH_1, \cH_2)$ and $[\mathfrak H_1, \mathfrak H_2]$ stand for the set of closed densely defined { linear} operators and the set of bounded linear operators from $\mathfrak H_1$ to $\mathfrak H_2,$ respectively}. { We set} $\cC(\cH):= \cC(\cH, \cH)$ and $[\mathfrak H] := [\mathfrak H, \mathfrak H]$. { The symbols ${\rm dom\,}(\cdot),$ ${\rm ran\,}(\cdot),$ $\varrho(T)$ and $\sigma(T)$ stand for the domain, the range, the resolvent set and the spectrum of an operator $T\in \cC(\cH),$ respectively}; $T^{ac}$ and $\sigma_{ac}(T)$ stand for the $ac$-part and the $ac$ spectrum of an operator $T=T^\in \cC(\cH).$ $\mathfrak S_p(\gH),$ $p\in [1,\infty],$ stand for the Schatten-von~Neumann ideals in $\gH$. { Denote by $\cB({\R})$ the Borel $\sigma$-algebra of the line $\R$ and by $\cB_b({\R})$ the algebra of bounded subsets in} $\cB_b(\R)$. The Lebesgue measure of a set ${\delta} \in \cB({\R})$ is denoted by $\|{\delta}\|$. \section{Preliminaries} \subsection{Operator measures} \begin{definition} {\em Let $\cH$ be a separable Hilbert space. A mapping ${\Sigma}(\cdot):\ \cB	0.039809	-1.318191	0.106897	1.94491	[ 0.3264132535621906, -0.24679591347379062 ]	[ -0.825768589832667, -1.8106143095530123 ]	[ 0.1817161669210249, 0.03207794642335302 ]	[ 2.3247096393691384, 1.5651095210392962 ]	1,024	[ 512, 512 ]	[ 6622, 29918, 29876, 8209, 372, 13, 275, 2337, 1950, 304, 6623, 278, 21954, 1372, 7555, 12197, 2403, 29876, 29938, 297, 1316, 263, 982, 13, 5747, 263, 716, 5665, 779, 14554, 2802, 12197, 2403, 29876, 29922, 320, 741, 29883, 29950, 29918, 29876, 2053, 14554, 741, 6642, 3227, 29900, 29876, 7570, 14554, 741, 6642, 3227, 29896, 29876, 1012, 1042, 13, 974, 10452, 21954, 1372, 363, 395, 29903, 29918, 29876, 6622, 29938, 17150, 278, 1494, 13, 11330, 29901, 779, 14554, 2802, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 14554, 2802, 12197, 2403, 29876, 29938, 7190, 263, 13, 9917, 653, 21954, 29873, 363, 395, 29909, 6622, 29938, 426, 1316, 393, 395, 29903, 648, 29900, 29876, 29913, 3490, 13, 29903, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 1800, 353, 317, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 13, 741, 29916, 3946, 5940, 4678, 14554, 2802, 6642, 3227, 29900, 29876, 1800, 353, 29901, 2802, 14554, 317, 3227, 29900, 29876, 7570, 29871, 302, 320, 262, 320, 29940, 1504, 512, 3153, 29892, 13, 1552, 6590, 399, 1032, 29880, 740, 29871, 395, 29924, 1194, 3822, 1262, 338, 426, 13, 1271, 7402, 6051, 351, 7177, 313, 4149, 29871, 10244, 320, 999, 29912, 18118, 29889, 29941, 7690, 29871, 426, 8680, 23161, 13, 932, 5795, 304, 1513, 25470, 526, 23228, 368, 2729, 373, 445, 13, 2914, 29889, 512, 3153, 29892, 372, 338, 1304, 297, 1326, 292, 310, 10244, 320, 999, 29912, 18118, 29889, 29953, 29913, 13, 358, 28487, 2038, 1836, 13, 13, 12881, 635, 29892, 297, 9779, 29871, 29953, 591, 3394, 278, 29871, 11043, 313, 392, 9846, 13, 9902, 29897, 304, 29871, 12768, 320, 4915, 29912, 29900, 29889, 29946, 29913, 29871, 411, 426, 12635, 322, 29913, 13, 348, 29306, 5455, 7037, 29879, 29889, 426, 512, 3153, 29892, 591, 13, 11569, 5286, 403, 278, 395, 562, 4388, 21494, 5848, 310, 1583, 29899, 328, 12090, 8869, 800, 310, 13, 4504, 29878, 5931, 3689, 261, 5455, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 29883, 29931, 353, 448, 320, 1563, 1194, 1154, 741, 3846, 29985, 29906, 3331, 3846, 260, 29985, 29906, 29913, 718, 13, 29905, 2083, 29985, 29876, 648, 29926, 29922, 29896, 1012, 1154, 741, 3846, 29985, 29906, 3331, 3846, 921, 29985, 29906, 29918, 29926, 1012, 1266, 29897, 718, 3855, 29898, 29916, 467, 320, 3425, 13, 29898, 29873, 29892, 29916, 29897, 320, 262, 320, 29934, 28842, 320, 3706, 320, 29934, 29985, 29876, 29892, 320, 3425, 3855, 320, 262, 365, 3823, 3411, 1194, 29934, 29985, 29876, 511, 13, 418, 320, 355, 29912, 4990, 755, 29913, 13, 262, 395, 29931, 29985, 29906, 1194, 29934, 29918, 3124, 3706, 29905, 29934, 29985, 29876, 5767, 395, 29876, 320, 479, 29871, 29896, 1504, 1152, 2777, 29892, 591, 1510, 393, 565, 13, 29938, 29939, 1194, 3822, 2144, 479, 29871, 29900, 29938, 322, 29913, 13, 1678, 320, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29941, 29941, 29913, 13, 29905, 2576, 648, 29989, 29916, 4295, 517, 29905, 3411, 1012, 524, 648, 29989, 29916, 29899, 29891, 4295, 280, 29871, 29896, 11079, 29939, 29898, 29891, 10531, 4518, 353, 29871, 29900, 29892, 13, 1678, 320, 355, 29912, 2573, 29913, 13, 29912, 769, 278, 19378, 436, 1026, 1855, 2133, 259, 395, 29931, 29985, 29928, 29938, 338, 13312, 13, 20621, 681, 29892, 29871, 18719, 395, 562, 4388, 1195, 3039, 322, 29871, 7555, 3754, 2119, 29931, 29985, 29928, 29897, 353, 2802, 3754, 3227, 562, 2119, 29931, 29985, 29928, 3892, 13, 29961, 29900, 2053, 3411, 467, 17133, 13, 13, 13, 13, 13, 741, 1635, 2216, 800, 29913, 29871, 512, 278, 1494, 591, 2050, 871, 2903, 519, 13, 29950, 309, 2151, 8162, 607, 526, 27291, 491, 779, 7237, 379, 1628, 779, 29883, 29950, 29938, 2992, 29889, 13, 29912, 450, 15072, 779, 29883, 29907, 1194, 29883, 29950, 29918, 29896, 29892, 320, 29883, 29950, 29918, 29906, 1262, 322, 395, 7110, 7237, 379, 29918, 29896, 29892, 13, 29905, 7237, 379, 29918, 29906, 9341, 2317, 363, 278, 731, 310, 5764, 6245, 873, 3342, 426, 13, 10660, 29913, 12768, 322, 278, 731, 310, 12635, 5608, 12768, 515, 13, 4535, 7237, 379, 29918, 29896, 29938, 304, 779, 7237, 379, 29918, 29906, 8209, 8307, 1836, 13, 29912, 1334, 731, 29913, 779, 29883, 29907, 1194, 29883, 29950, 1125, 29922, 320, 29883, 29907, 1194, 29883, 29950, 29892, 320, 29883, 29950, 1262, 322, 395, 7110, 7237, 379, 29962, 3490, 13, 7110, 7237, 379, 29892, 320, 7237, 379, 22689, 29871, 426, 450, 15072, 7555, 1758, 2432, 5940, 4678, 3822, 511, 29938, 13, 29938, 741, 1758, 6350, 5940, 4678, 3822, 511, 29938, 779, 1707, 4650, 29898, 29911, 1262, 322, 779, 3754, 29898, 29911, 1262, 2317, 363, 278, 5354, 29892, 13, 1552, 3464, 29892, 29871, 278, 3770, 794, 731, 322, 278, 18272, 310, 385, 5455, 13, 29938, 29911, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 511, 29938, 8307, 3400, 395, 29911, 998, 562, 1042, 322, 13, 4535, 3754, 648, 562, 2119, 29911, 1262, 2317, 363, 278, 395, 562, 4388, 1595, 322, 278, 395, 562, 29938, 13, 21494, 5848, 310, 385, 5455, 395, 29911, 29922, 29911, 6622, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 13, 13, 4535, 7237, 317, 29918, 29886, 1194, 29887, 29950, 511, 29938, 29871, 395, 29886, 29905, 262, 518, 29896, 2053, 3411, 1402, 29938, 2317, 363, 278, 13, 4504, 8606, 29899, 23696, 30022, 8139, 22553, 1957, 1338, 297, 779, 29887, 29950, 1504, 13, 29912, 3384, 866, 491, 779, 29883, 29933, 13670, 29934, 8435, 278, 6780, 295, 779, 3754, 4388, 15742, 310, 278, 13, 1220, 779, 29934, 29938, 29871, 322, 29871, 491, 779, 29883, 29933, 29918, 29890, 13670, 29934, 8435, 278, 9623, 310, 12635, 27639, 13, 262, 29913, 779, 29883, 29933, 29918, 29890, 1194, 29934, 4935, 450, 9388, 267, 13000, 5645, 310, 263, 731, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 13670, 29934, 8435, 13, 275, 27291, 491, 11892, 741, 4181, 11079, 1504, 13, 13, 29905, 2042, 29912, 6572, 2576, 262, 4314, 29913, 13, 13, 29905, 7235, 29912, 26486, 15366, 29913, 13, 29905, 463, 29912, 16553, 29913, 13, 741, 331, 13, 12024, 29871, 779, 29883, 29950, 29938, 367, 263, 2903, 519, 12338, 2151, 2913, 29889, 319, 29871, 10417, 13, 29938, 741, 10142, 4678, 3822, 1125, 29905, 29871, 320, 29883, 29933 ]	1,332,863	3,072	ArXiv	-1	-1
_b({\R})\to[\cH]$ is called an operator (operator-valued) measure if \item[\;\;{\rm (i)}] ${\Sigma}(\cdot)$ is ${\delta}$-additive in the strong sense and \item[\;\;{\rm (ii)}] ${\Sigma}({\delta})={\Sigma}({\delta})^\ge 0$ for ${\delta}\in \cB_b({\R})$. The operator measure ${\Sigma}({\cdot})$ is called bounded if it extends to the Borel algebra $\cB({\R})$ of $\R$, i.e. ${\Sigma}({\R})\in[\cH]$. Otherwise, it is called unbounded. A bounded operator measure ${\Sigma}(\cdot)=E(\cdot)$ is called orthogonal if, in addition the conditions \item[\;\;{\rm (iii)}] $E({\delta}_1)E({\delta}_2)=E({\delta}_1\cap{\delta}_2)$ for ${\delta}_1,{\delta}_2\in \cB({\R})$ and $E({\R})=I_{\cH}$ are satisfied. } \end{definition} Setting in (iii) ${\delta}_1={\delta}_2$, one gets that an orthogonal measure $E(\cdot)$ takes its values in the set of orthogonal projections on $\cH$. Every orthogonal measure $E(\cdot)$ defines an operator $T= T^= \int_{{\R}}{\lambda} d E({\lambda})$ in $\cH$ with $E(\cdot)$ being its spectral measure. Conversely, by the spectral theorem, every operator $T=T^$ in $\cH$ admits the above representation with the orthogonal spectral measure $E=:E_T$. By ${\Sigma}^{ac}$, ${\Sigma}^s$, ${\Sigma}^{sc}$ and ${\Sigma}^{pp}$ we denote absolutely continuous, singular, singular continuous and pure point parts of the measure ${\Sigma}$, respectively. The Lebesgue decomposition of ${\Sigma}$ is given by ${\Sigma} = {\Sigma}^{ac} + {\Sigma}^s = {\Sigma}^{ac} + {\Sigma}^{sc} + {\Sigma}^{pp}$. The operator measure ${\Sigma}_1$ is called subordinated to the operator measure ${\Sigma}_2$, in short ${\Sigma}_1 \prec {\Sigma}_2$, if ${\Sigma}_2({\delta}) = 0$ yields ${\Sigma}_1({\delta}) = 0$ for ${\delta} \in \cB_b(\R)$. If the measures ${\Sigma}_1$ and ${\Sigma}_2$ are mutually subordinated, then they are called equivalent, in short ${\Sigma}_1 \thicksim {\Sigma}_2$. Note, that there are always exists a scalar measure $\rho$ defined on $\cB_b(\R)$ such that ${\Sigma} \thicksim \rho$, see \cite[Remark 2.2]{MM03}. In particular, there is always a scalar measure such that ${\Sigma} \prec \rho$. Usually, with the operator-valued measure ${\Sigma}(\cdot)$ one associates a distribution operator-valued function ${\Sigma}(\cdot)$ defined by \begin{equation}\Label{a1} {\Sigma}(t) = \begin{cases} {\Sigma}([0,t)) & t > 0 \\ 0 & t = 0 \\ -{\Sigma}([t,0)) & t < 0 \end{cases} \end{equation} which is called the spectral function of ${\Sigma}$. Clearly, ${\Sigma}(\cdot)$ is strongly left continuous, ${\Sigma}(t-0)= {\Sigma}(t),$ and satisfies ${\Sigma}(t) = {\Sigma}(t)^, \quad {\Sigma}(s) \le {\Sigma}(t)$, $s \le t$. \begin{definition}[{\cite[Definition 4.5]{MM03}}] {\em Let ${\Sigma}$ be an operator measure in $\cH$ and let $\rho$ be a scalar measure on $\cB(\R)$ such that ${\Sigma} \prec \rho$. Further, let $e=\{e_j\}^{\infty}_{j=1}$ be an orthonormal basis in $\cH$. Let \begin{eqnarray*} {\Sigma}_{ij}(t):=\bigl({\Sigma}(t)e_i,e_j\bigr), \qquad \Psi_{ij}(t):=d	0.072338	-1.201801	0.318673	2.355926	[ 0.16068252665334057, -0.016005603687499512 ]	[ -0.9726001335000639, -1.4310010503153519 ]	[ 0.5266449463732855, 0.11070141821026537 ]	[ 2.4703863743912997, 2.241465790785046 ]	1,024	[ 512, 512 ]	[ 29918, 29890, 13670, 29934, 11606, 517, 7110, 29883, 29950, 9341, 338, 2000, 385, 5455, 13, 29898, 6891, 29899, 4387, 287, 29897, 5645, 565, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 29875, 2915, 29962, 7555, 10142, 4678, 3822, 1262, 338, 7555, 4181, 23021, 1202, 3321, 297, 278, 4549, 13, 1678, 4060, 322, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 2236, 2915, 29962, 7555, 10142, 2119, 741, 4181, 1800, 21854, 10142, 2119, 741, 4181, 1800, 6622, 29905, 479, 29871, 29900, 29938, 363, 7555, 4181, 1012, 262, 13, 29905, 29883, 29933, 29918, 29890, 13670, 29934, 23462, 13, 13, 1576, 5455, 5645, 7555, 10142, 2119, 741, 3822, 8435, 338, 2000, 12635, 565, 372, 13, 1062, 1975, 304, 278, 6780, 295, 9623, 779, 29883, 29933, 13670, 29934, 8435, 310, 779, 29934, 1628, 474, 29889, 29872, 29889, 13, 29938, 741, 10142, 2119, 741, 29934, 11606, 262, 7110, 29883, 29950, 22689, 13466, 29892, 29871, 372, 13, 275, 2000, 443, 29306, 29889, 319, 12635, 5455, 5645, 13, 29938, 741, 10142, 4678, 3822, 3892, 29923, 1194, 3822, 1262, 338, 2000, 28143, 565, 29892, 297, 6124, 278, 5855, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 25609, 2915, 29962, 395, 29923, 13670, 4181, 2403, 29896, 29897, 29923, 13670, 4181, 2403, 29906, 3892, 29923, 13670, 4181, 2403, 29896, 29905, 5030, 741, 4181, 2403, 29906, 1262, 363, 13, 29938, 741, 4181, 2403, 29896, 29892, 741, 4181, 2403, 29906, 29905, 262, 320, 29883, 29933, 13670, 29934, 8435, 322, 13, 29938, 29923, 13670, 29934, 1800, 29922, 29902, 1665, 29883, 29950, 1042, 13, 13, 598, 15787, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29020, 297, 313, 25609, 29897, 7555, 4181, 2403, 29896, 21854, 4181, 2403, 29906, 1628, 697, 4947, 393, 385, 28143, 13, 26658, 395, 29923, 1194, 3822, 1262, 4893, 967, 1819, 297, 278, 731, 310, 28143, 13, 771, 24247, 373, 779, 29883, 29950, 1504, 7569, 28143, 5645, 395, 29923, 1194, 3822, 1262, 13, 1753, 1475, 385, 5455, 395, 29911, 29922, 323, 6622, 29922, 320, 524, 24033, 29934, 12431, 2892, 29913, 29871, 270, 382, 13670, 2892, 8435, 297, 13, 4535, 29883, 29950, 29938, 411, 395, 29923, 1194, 3822, 1262, 1641, 967, 23161, 5645, 29889, 1281, 874, 873, 29892, 491, 13, 1552, 23161, 9185, 29892, 1432, 5455, 395, 29911, 29922, 29911, 6622, 29938, 297, 779, 29883, 29950, 29938, 7336, 1169, 278, 13, 27215, 8954, 411, 278, 28143, 23161, 5645, 13, 29938, 29923, 29922, 29901, 29923, 29918, 29911, 1504, 13, 13, 2059, 7555, 10142, 2844, 562, 4429, 7555, 10142, 2137, 29879, 1628, 7555, 10142, 2844, 1557, 1042, 322, 7555, 10142, 2844, 407, 1042, 29871, 591, 13530, 13, 370, 2929, 11579, 9126, 29892, 13512, 29892, 13512, 9126, 322, 8296, 13, 3149, 5633, 310, 278, 5645, 7555, 10142, 4429, 8307, 29889, 450, 9388, 267, 13000, 13, 311, 510, 3283, 310, 7555, 10142, 1042, 338, 2183, 491, 13, 29938, 741, 10142, 29913, 353, 2802, 10142, 2844, 562, 29913, 718, 2802, 10142, 2137, 29879, 353, 2802, 10142, 2844, 562, 29913, 718, 2802, 10142, 2844, 1557, 29913, 718, 2802, 10142, 2844, 407, 4311, 13, 13, 1576, 5455, 5645, 7555, 10142, 2403, 29896, 29938, 338, 2000, 1014, 4194, 630, 304, 13, 1552, 5455, 5645, 7555, 10142, 2403, 29906, 1628, 297, 3273, 7555, 10142, 2403, 29896, 320, 17990, 2802, 10142, 2403, 29906, 1628, 565, 13, 29938, 741, 10142, 2403, 29906, 13670, 4181, 1800, 353, 29871, 29900, 29938, 17498, 7555, 10142, 2403, 29896, 13670, 4181, 1800, 353, 29871, 29900, 29938, 363, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 4935, 960, 13, 1552, 15366, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 526, 5478, 1474, 1014, 4194, 630, 29892, 769, 13, 19562, 526, 2000, 7126, 29892, 297, 3273, 7555, 10142, 2403, 29896, 320, 27996, 3601, 2802, 10142, 2403, 29906, 1504, 13, 9842, 29892, 393, 29871, 727, 526, 2337, 4864, 263, 17336, 5645, 779, 4650, 29938, 13, 12119, 373, 779, 29883, 29933, 29918, 29890, 1194, 29934, 1262, 1316, 393, 7555, 10142, 29913, 320, 27996, 3601, 320, 4650, 1628, 1074, 13, 29905, 2036, 29961, 7301, 935, 29871, 29906, 29889, 29906, 3199, 7428, 29900, 29941, 1836, 512, 3153, 29892, 727, 338, 2337, 263, 17336, 13, 26658, 1316, 393, 7555, 10142, 29913, 320, 17990, 320, 4650, 1504, 13, 13, 15922, 1474, 29892, 411, 278, 5455, 29899, 4387, 287, 5645, 7555, 10142, 4678, 3822, 1262, 697, 13, 21264, 1078, 263, 4978, 5455, 29899, 4387, 287, 740, 7555, 10142, 4678, 3822, 1262, 13, 12119, 491, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29874, 29896, 29913, 13, 741, 10142, 2119, 29873, 29897, 353, 13, 29905, 463, 29912, 11436, 29913, 13, 741, 10142, 2119, 29961, 29900, 29892, 29873, 876, 669, 260, 1405, 29871, 29900, 2474, 13, 29900, 9651, 669, 260, 353, 29871, 29900, 2474, 13, 29899, 741, 10142, 2119, 29961, 29873, 29892, 29900, 876, 669, 260, 529, 29871, 29900, 13, 29905, 355, 29912, 11436, 29913, 13, 29905, 355, 29912, 2573, 29913, 13, 4716, 338, 2000, 278, 23161, 740, 310, 7555, 10142, 4311, 13, 18759, 368, 29892, 7555, 10142, 4678, 3822, 1262, 338, 13818, 2175, 9126, 29892, 7555, 10142, 2119, 29873, 29899, 29900, 3892, 13, 741, 10142, 2119, 29873, 511, 29938, 322, 17150, 13, 29938, 741, 10142, 2119, 29873, 29897, 353, 2802, 10142, 2119, 29873, 4887, 15966, 320, 3425, 2802, 10142, 2119, 29879, 29897, 320, 280, 2802, 10142, 2119, 29873, 5767, 395, 29879, 320, 280, 260, 1504, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29961, 14683, 29871, 29946, 29889, 29945, 3199, 7428, 29900, 29941, 930, 29962, 13, 741, 331, 13, 12024, 7555, 10142, 1042, 367, 385, 5455, 5645, 297, 13, 4535, 29883, 29950, 29938, 322, 1235, 779, 4650, 29938, 367, 263, 17336, 5645, 373, 779, 29883, 29933, 1194, 29934, 1262, 1316, 393, 13, 29938, 741, 10142, 29913, 320, 17990, 320, 4650, 1504, 8725, 29892, 1235, 395, 29872, 27805, 29872, 29918, 29926, 29905, 6292, 3411, 3227, 29926, 29922, 29896, 1042, 13, 915, 385, 14219, 265, 2759, 8405, 297, 779, 29883, 29950, 1504, 2803, 13, 29905, 463, 29912, 9441, 4044, 13, 741, 10142, 3227, 823, 2119, 29873, 1125, 2013, 3752, 29880, 13670, 10142, 2119, 29873, 29897, 29872, 29918, 29875, 29892, 29872, 29918, 29926, 29905, 3752, 29878, 511, 320, 12014, 13, 29905, 14118, 648, 823, 2119, 29873, 1125, 29922, 29881 ]	1,332,863	4,096	ArXiv	-1	-1
{\Sigma}_{ij}(t)/d\rho,\\ \Psi^e_n(t):=\bigl(\Psi_{ij}(t)\bigr)^n_{i,j=1}, \qquad \Psi^e(t):=\bigl(\Psi_{ij}(t)\bigr)^{\infty}_{i,j=1}. \end{eqnarray*} We call \begin{equation}\label{2.1A} N^e_{{\Sigma}}(t):={\rm rank\,}(\Psi^e(t)) := \sup_{n\ge 1} {\rm rank\,}(\Psi^e_n(t))\;({\rm mod}(\rho)) \end{equation} and \begin{displaymath} N_{\Sigma}(t) := {\rm ess\,}\!\sup_e N^e_{{\Sigma}}(t)\;({\rm mod}(\rho)) \end{displaymath} the multiplicity function and the total multiplicity of ${\Sigma}$, respectively. } \end{definition} By \cite[Proposition 4.6]{MM03} $N^e_{{\Sigma}}(\cdot)$ does not depend on the orthogonal basis $e$. Therefore one always has $N_{{\Sigma}}(t) := N^e_{{\Sigma}}(t)$ and one can omit the index $e$ in \eqref{2.1A}. When applying this definition to the absolutely continuous part ${\Sigma}^{ac}$ of ${\Sigma}$ the scalar measure $\rho^{ac}$ can be chosen to be the Lebesgue measure $\|\cdot\|$ on $\cB(\R)$. The concept of the multiplicity function allows one to introduce the following definitions. \begin{definition}\label{II.3} {\em Let ${\Sigma}_1$ and ${\Sigma}_2$ be two operator measures. \item[\;\;\rm (i)] The operator measure ${\Sigma}_1$ is called spectrally subordinate to the operator measure ${\Sigma}_2$, in short ${\Sigma}_1\prec\!\!\prec{\Sigma}_2$, if ${\Sigma}_1\prec{\Sigma}_2$ and $N_{{\Sigma}_1}(t)\le N_{{\Sigma}_2}(t)\;(\mbox{{\rm mod}}({\Sigma}_2))$. \item[\;\;\rm (ii)] The operator measures ${\Sigma}_1$ and ${\Sigma}_2$ are called spectrally equivalent, in short ${\Sigma}_1 \thickapprox {\Sigma}_2$, if ${\Sigma}_1 \thicksim {\Sigma}_2$ and $N_{{\Sigma}_1}(t)=N_{{\Sigma}_2}(t)(\mbox{{\rm mod}}({\Sigma}_2))$. } \end{definition} { Crucial for us in the sequel is the following theorem}. \begin{theorem}\Label{II.4a} { Let $T_j$ be self-adjoint operators acting in $\gotH_j$ with corresponding spectral measures $E_{T_j}(\cdot)$, $j =1,2$. Let $\cD \in \cB(\R)$. \item[\;\;\rm (i)] $T_1E_{T_1}(\cD)$ is a part of $T_2E_{T_2}(\cD)$ if and only if $E_{T_1,\cD} \prec\!\!\prec E_{T_2,\cD}$, where $E_{T_j,\cD}({\delta}) := E_{T_j}({\delta}\cap\cD), \ j = 1,2$. \item[\;\;\rm (ii)] The parts $T_1E_{T_1}(\cD)$ and $T_2E_{T_2}(\cD)$ are unitarily equivalent if and only if $E_{T_1,\cD} \thickapprox E_{T_2,\cD}$.} \end{theorem} The proof is immediate from \cite[Theorem 7.5.1]{BS87}. For $\cD = \R$ Theorem \ref{II.4a} gives conditions for $T_1$ to be unitarily equivalent either to a part of $T_2$ or to $T_2$ itself. \subsection{$R$-Functions} Let ${\cH}$ be a separable Hilbert space. We recall that an operator-valued function $F(\cdot)$ with values in $[{\cH}]$ is called to be a Her	-0.177114	-1.148082	0.162694	1.970923	[ -0.17728488545210352, -0.17694246659485385 ]	[ -1.1480817344684164, -1.1480817344684164 ]	[ -0.033864320236637976, 0.35925303869792374 ]	[ 2.0541671314708383, 1.8876794343026537 ]	1,024	[ 512, 512 ]	[ 741, 10142, 3227, 823, 2119, 29873, 6802, 29881, 29905, 4650, 29892, 1966, 13, 29905, 14118, 29985, 29872, 29918, 29876, 29898, 29873, 1125, 2013, 3752, 29880, 1194, 14118, 648, 823, 2119, 29873, 2144, 3752, 29878, 4887, 29876, 648, 29875, 29892, 29926, 29922, 29896, 1118, 320, 12014, 13, 29905, 14118, 29985, 29872, 29898, 29873, 1125, 2013, 3752, 29880, 1194, 14118, 648, 823, 2119, 29873, 2144, 3752, 29878, 21422, 3411, 3227, 29875, 29892, 29926, 29922, 29896, 1836, 13, 29905, 355, 29912, 9441, 4044, 13, 4806, 1246, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29909, 29913, 13, 29940, 29985, 29872, 24033, 10142, 12156, 29873, 1125, 21854, 1758, 7115, 5940, 4678, 14118, 29985, 29872, 29898, 29873, 876, 3490, 320, 12587, 648, 29876, 29905, 479, 29871, 29896, 29913, 2802, 1758, 7115, 5940, 4678, 14118, 29985, 29872, 29918, 29876, 29898, 29873, 876, 23891, 13670, 1758, 878, 4678, 4650, 876, 13, 29905, 355, 29912, 2573, 29913, 13, 392, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29940, 1665, 10142, 2119, 29873, 29897, 3490, 2802, 1758, 3686, 5940, 1012, 9903, 12587, 29918, 29872, 405, 29985, 29872, 24033, 10142, 12156, 29873, 2144, 29936, 13670, 1758, 878, 4678, 4650, 876, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1552, 6674, 17024, 740, 322, 278, 3001, 6674, 17024, 310, 7555, 10142, 4429, 8307, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 2059, 29871, 320, 2036, 29961, 1184, 3283, 29871, 29946, 29889, 29953, 3199, 7428, 29900, 29941, 29913, 395, 29940, 29985, 29872, 24033, 10142, 20828, 3822, 1262, 947, 13, 1333, 8839, 373, 278, 28143, 8405, 395, 29872, 1504, 7857, 697, 2337, 756, 13, 29938, 29940, 24033, 10142, 12156, 29873, 29897, 3490, 405, 29985, 29872, 24033, 10142, 12156, 29873, 1262, 29871, 322, 697, 508, 288, 2415, 278, 2380, 395, 29872, 29938, 297, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29909, 1836, 13, 13, 10401, 29871, 15399, 29871, 445, 5023, 304, 278, 13312, 13, 20621, 681, 760, 7555, 10142, 2844, 562, 1042, 310, 7555, 10142, 1042, 29871, 278, 17336, 5645, 13, 4535, 4650, 998, 562, 1042, 29871, 508, 367, 10434, 29871, 304, 367, 29871, 278, 9388, 267, 13000, 5645, 25984, 3822, 25183, 13, 265, 779, 29883, 29933, 1194, 29934, 4935, 13, 13, 1576, 6964, 310, 278, 6674, 17024, 740, 6511, 697, 304, 14944, 13, 1552, 1494, 15848, 29889, 13, 29905, 463, 29912, 16553, 1012, 1643, 29912, 2687, 29889, 29941, 29913, 13, 741, 331, 13, 12024, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 367, 1023, 5455, 15366, 29889, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 13, 1576, 5455, 5645, 7555, 10142, 2403, 29896, 29938, 338, 2000, 13, 21494, 29878, 635, 1014, 16065, 304, 278, 5455, 5645, 7555, 10142, 2403, 29906, 1628, 297, 3273, 13, 29938, 741, 10142, 2403, 29896, 29905, 17990, 29905, 9903, 9903, 17990, 741, 10142, 2403, 29906, 1628, 565, 7555, 10142, 2403, 29896, 29905, 17990, 741, 10142, 2403, 29906, 29938, 13, 392, 395, 29940, 24033, 10142, 2403, 29896, 2119, 29873, 2144, 280, 405, 24033, 10142, 2403, 29906, 2119, 29873, 2144, 29936, 1194, 8264, 16195, 1758, 878, 12156, 741, 10142, 2403, 29906, 876, 1504, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 13, 1576, 5455, 15366, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 526, 2000, 6683, 29878, 635, 13, 1686, 27445, 29892, 297, 3273, 7555, 10142, 2403, 29896, 320, 27996, 14850, 2802, 10142, 2403, 29906, 1628, 565, 7555, 10142, 2403, 29896, 320, 27996, 3601, 2802, 10142, 2403, 29906, 29938, 322, 13, 29938, 29940, 24033, 10142, 2403, 29896, 2119, 29873, 3892, 29940, 24033, 10142, 2403, 29906, 2119, 29873, 29897, 1194, 8264, 16195, 1758, 878, 12156, 741, 10142, 2403, 29906, 876, 1504, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29912, 11263, 1455, 363, 502, 297, 278, 8617, 295, 338, 278, 1494, 9185, 1836, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 2687, 29889, 29946, 29874, 29913, 13, 29912, 2803, 395, 29911, 29918, 29926, 29938, 367, 1583, 29899, 328, 12090, 12768, 16684, 297, 779, 7085, 29950, 29918, 29926, 29938, 13, 2541, 6590, 23161, 15366, 395, 29923, 648, 29911, 29918, 29926, 4678, 3822, 5767, 395, 29926, 353, 29896, 29892, 29906, 1504, 13, 12024, 779, 29883, 29928, 320, 262, 320, 29883, 29933, 1194, 29934, 4935, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 13, 29938, 29911, 29918, 29896, 29923, 648, 29911, 29918, 29896, 4678, 29883, 29928, 1262, 338, 263, 760, 310, 395, 29911, 29918, 29906, 29923, 648, 29911, 29918, 29906, 4678, 29883, 29928, 1262, 565, 322, 871, 565, 13, 29938, 29923, 648, 29911, 29918, 29896, 2053, 29883, 29928, 29913, 320, 17990, 29905, 9903, 9903, 17990, 29871, 382, 648, 29911, 29918, 29906, 2053, 29883, 29928, 4429, 988, 395, 29923, 648, 29911, 29918, 29926, 2053, 29883, 29928, 2119, 741, 4181, 1800, 3490, 13, 29923, 648, 29911, 29918, 29926, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 511, 320, 432, 353, 29871, 29896, 29892, 29906, 1504, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 13, 1576, 5633, 395, 29911, 29918, 29896, 29923, 648, 29911, 29918, 29896, 4678, 29883, 29928, 1262, 322, 395, 29911, 29918, 29906, 29923, 648, 29911, 29918, 29906, 4678, 29883, 29928, 1262, 526, 443, 3673, 2354, 7126, 13, 361, 322, 871, 565, 395, 29923, 648, 29911, 29918, 29896, 2053, 29883, 29928, 29913, 29871, 320, 27996, 14850, 382, 648, 29911, 29918, 29906, 2053, 29883, 29928, 4311, 29913, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 1576, 5296, 338, 16800, 515, 320, 2036, 29961, 28831, 29871, 29955, 29889, 29945, 29889, 29896, 3199, 9851, 29947, 29955, 1836, 13, 2831, 29871, 779, 29883, 29928, 353, 320, 29934, 29938, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 29913, 4076, 5855, 363, 13, 29938, 29911, 29918, 29896, 29938, 304, 367, 443, 3673, 2354, 7126, 2845, 304, 263, 760, 310, 395, 29911, 29918, 29906, 29938, 29871, 470, 304, 13, 29938, 29911, 29918, 29906, 29938, 3528, 29889, 13, 13, 29905, 7235, 8290, 29934, 4388, 6678, 29879, 29913, 13, 13, 12024, 7555, 29883, 29950, 1042, 367, 263, 2903, 519, 12338, 2151, 2913, 29889, 1334, 17386, 393, 385, 5455, 29899, 4387, 287, 13, 2220, 395, 29943, 1194, 3822, 1262, 411, 1819, 297, 11970, 741, 29883, 29950, 6525, 29938, 338, 2000, 304, 367, 263, 13, 18650 ]	1,332,863	5,120	ArXiv	-1	-1
glotz, Nevanlinna or $R$-function \cite{AG81,Ber68,GG91,KN77}, if it is holomorphic in $\C_+$ and its imaginary part is non-negative, i.e. $\im(F(z)) := (2i)^{-1}\bigl({F(z) - F(z)^}\bigr) \ge 0, \ z\in \C_+$. In what follows we prefer the notion of R-function. The class of R-functions with values in $[\cH]$ will be denoted by $(R_\cH)$. Any $(R_\cH)$-function $F(\cdot)$ admits an integral representation \begin{equation}\label{1.2} F(z) = C_0 + C_1 z + \int_{-\infty}^{\infty} \left(\frac{1}{t-z}- \frac{t}{1 + t^2}\right) d{\Sigma}_F,\quad z\in \C_+, \end{equation} (see, for instance, \cite{AG81, Ber68, KN77}), where $C_0 = C_0^, \ C_1\ge 0$ and ${\Sigma}_F$ is an operator-valued Borel measure on $\R$ satisfying $\int_\R (1+t^2)^{-1}d{\Sigma}_F \in [\cH]$. The integral is understood in the strong sense. In contrast to spectral measures of self-adjoint operators the measure ${\Sigma}_F$ is not necessarily orthogonal. However, the operator-valued measure ${\Sigma}_F$ is uniquely determined by the $R$-function $F(\cdot)$. It is called the spectral measure of $F(\cdot)$. The associated spectral function is denoted by ${\Sigma}_F(t)$, $t \in \R$, cf. { \eqref{a1}}. Let us calculate $N_{{\Sigma}^{ac}_F}(t)$, $t \in \R$. For any Hilbert-Schmidt operator ${ D} \in {\mathfrak S}_2(\cH)$ satisfying ${\xker\,}({D}) = {\xker\,}({D}^) = \{0\}$ let us consider the modified $R_\cH$-function \begin{displaymath} (F^{ D})(z) := { D}^F(z){ D}, \quad z \in \C_+. \end{displaymath} For $F^D(\cdot)$ the strong limit $F^D(t) := F^D(t+i0) :=\,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+\infty}F^D(t+iy)$ exists for a.e. $t \in \R$. We set \begin{equation}\Label{2.13} d_{F^D}(t):= {\rm dim}({\rm ran\,}(\im(F^D)(t))), \quad \mbox{for a.e.} \quad t \in \R. \end{equation} \begin{proposition}\Label{II.4} Let $F(\cdot)\in (R_\cH),$ \ $D \in {\mathfrak S}_2(\cH)$ and ${\xker\,}(D) = {\xker\,}(D^) = \{0\}.$ Then $N_{{\Sigma}^{ac}_F}(t) = d_{F^{ D}}(t)$ for a.e. $t \in \R$. \end{proposition} \begin{proof} It follows from \eqref{1.2} that \begin{equation}\label{2.12} \im(F({\lambda} + iy)) = y C_1 +\int^\infty_{-\infty}\frac{y}{(t-{\lambda})^2 +y^2}d{\Sigma}_F, \qquad {\lambda} \in \R. \end{equation} By Berezanskii-Gel'fand-Kostyuchenko theorem \cite{Ber68,BS87} the derivative $\Psi_{D^{\Sigma}_FD}(t) := \frac{d}{dt}D^{\Sigma}_F(t)D$ exists for a.e. $t \in \R$ and the representation \begin{displaymath} D^{\Sigma}^{ac}_F({\delta	0.143219	-1.080933	0.063781	2.298696	[ 0.5346039187700022, -0.2481655889027894 ]	[ -0.6377525887951465, -1.5241137365434572 ]	[ 0.40997785920560914, -0.2824159407242964 ]	[ 2.553630222975392, 2.043761650397827 ]	1,024	[ 512, 512 ]	[ 3820, 327, 29920, 29892, 2448, 3703, 1915, 1056, 470, 395, 29934, 4388, 2220, 13, 29905, 2036, 29912, 10051, 29947, 29896, 29892, 17104, 29953, 29947, 29892, 26788, 29929, 29896, 29892, 29968, 29940, 29955, 29955, 1118, 565, 372, 338, 8753, 16898, 297, 779, 29907, 29918, 24035, 322, 13, 1169, 6382, 3821, 760, 338, 1661, 29899, 22198, 29892, 474, 29889, 29872, 29889, 13, 4535, 326, 29898, 29943, 29898, 29920, 876, 3490, 313, 29906, 29875, 21604, 29896, 1012, 3752, 29880, 3319, 29943, 29898, 29920, 29897, 448, 383, 29898, 29920, 4887, 29930, 1012, 3752, 29878, 29897, 320, 479, 29871, 29900, 29892, 320, 29871, 503, 29905, 262, 13, 29905, 29907, 28842, 1504, 512, 825, 4477, 591, 5821, 278, 17837, 310, 390, 29899, 2220, 29889, 450, 770, 310, 13, 29934, 29899, 12171, 411, 1819, 297, 395, 7110, 29883, 29950, 9341, 674, 367, 27291, 491, 2427, 29934, 3187, 29883, 29950, 4935, 13, 10773, 2427, 29934, 3187, 29883, 29950, 26725, 2220, 395, 29943, 1194, 3822, 1262, 7336, 1169, 385, 10160, 13, 276, 26081, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29896, 29889, 29906, 29913, 13, 29943, 29898, 29920, 29897, 353, 315, 29918, 29900, 718, 315, 29918, 29896, 503, 718, 13, 29905, 524, 648, 2612, 3411, 6292, 3411, 29913, 320, 1563, 1194, 1154, 29912, 29896, 1157, 29873, 29899, 29920, 7402, 320, 1154, 29912, 29873, 1157, 29896, 718, 260, 29985, 29906, 1012, 1266, 29897, 270, 741, 10142, 2403, 29943, 2053, 3425, 503, 29905, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 29898, 4149, 29892, 363, 2777, 29892, 320, 2036, 29912, 10051, 29947, 29896, 29892, 2292, 29953, 29947, 29892, 476, 29940, 29955, 29955, 9594, 29871, 988, 395, 29907, 29918, 29900, 353, 315, 29918, 29900, 6622, 29892, 320, 315, 29918, 29896, 29905, 479, 29871, 29900, 29938, 322, 7555, 10142, 2403, 29943, 29938, 338, 385, 13, 6891, 29899, 4387, 287, 6780, 295, 5645, 373, 779, 29934, 29938, 24064, 779, 524, 3187, 29934, 13, 29898, 29896, 29974, 29873, 29985, 29906, 21604, 29896, 29913, 29881, 741, 10142, 2403, 29943, 320, 262, 12452, 29883, 29950, 22689, 450, 10160, 338, 11098, 297, 278, 13, 1110, 4060, 29889, 13, 13, 797, 12814, 304, 23161, 15366, 310, 1583, 29899, 328, 12090, 12768, 278, 13, 26658, 7555, 10142, 2403, 29943, 29938, 338, 451, 12695, 28143, 29889, 2398, 29892, 278, 13, 6891, 29899, 4387, 287, 5645, 7555, 10142, 2403, 29943, 29938, 338, 20498, 873, 10087, 491, 278, 13, 29938, 29934, 4388, 2220, 395, 29943, 1194, 3822, 4935, 29871, 739, 338, 2000, 278, 23161, 13, 26658, 310, 395, 29943, 1194, 3822, 4935, 450, 6942, 23161, 740, 338, 27291, 13, 1609, 7555, 10142, 2403, 29943, 29898, 29873, 5767, 395, 29873, 320, 262, 320, 29934, 1628, 274, 29888, 29889, 426, 320, 4915, 29912, 29874, 29896, 27243, 13, 13, 12024, 502, 29871, 8147, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 5767, 395, 29873, 320, 262, 320, 29934, 1504, 1152, 738, 13, 29950, 309, 2151, 29899, 4504, 19720, 5455, 6435, 360, 29913, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 13, 29879, 27685, 5414, 7555, 29916, 3946, 5940, 2119, 29912, 29928, 1800, 353, 2802, 29916, 3946, 5940, 2119, 29912, 29928, 2137, 7528, 353, 9991, 29900, 11854, 1235, 502, 2050, 278, 13, 1545, 2164, 395, 29934, 3187, 29883, 29950, 4388, 2220, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29943, 998, 360, 1800, 29898, 29920, 29897, 3490, 426, 360, 2137, 29930, 29943, 29898, 29920, 2597, 360, 1118, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 2831, 395, 29943, 29985, 29928, 1194, 3822, 1262, 278, 4549, 13, 13400, 395, 29943, 29985, 29928, 29898, 29873, 29897, 3490, 383, 29985, 29928, 29898, 29873, 29974, 29875, 29900, 29897, 584, 2013, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 3124, 3411, 29913, 29943, 29985, 29928, 29898, 29873, 29974, 19881, 1262, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29941, 29913, 13, 270, 648, 29943, 29985, 29928, 2119, 29873, 1125, 29922, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29943, 29985, 29928, 5033, 29873, 876, 511, 320, 3425, 320, 8264, 29912, 1454, 263, 29889, 29872, 5003, 29871, 320, 3425, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 2687, 29889, 29946, 29913, 13, 12024, 395, 29943, 1194, 3822, 2144, 262, 313, 29934, 3187, 29883, 29950, 511, 29938, 320, 395, 29928, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 13, 392, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 29905, 1836, 29938, 1987, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 29897, 353, 270, 648, 29943, 998, 360, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 3112, 4477, 515, 320, 4915, 29912, 29896, 29889, 29906, 29913, 393, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29906, 29913, 13, 320, 326, 29898, 29943, 13670, 2892, 29913, 718, 474, 29891, 876, 353, 343, 315, 29918, 29896, 17501, 524, 3823, 3411, 648, 2612, 3411, 1012, 1154, 29912, 29891, 19048, 29873, 29899, 741, 2892, 28813, 29906, 718, 29891, 29985, 29906, 29913, 29881, 741, 10142, 2403, 29943, 29892, 13, 29905, 12014, 2802, 2892, 29913, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 2059, 13143, 29920, 550, 1984, 29875, 29899, 29954, 295, 29915, 29888, 392, 29899, 29968, 520, 29891, 987, 264, 2901, 9185, 320, 2036, 29912, 17104, 29953, 29947, 29892, 9851, 29947, 29955, 29913, 278, 13, 672, 440, 1230, 779, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 29873, 29897, 3490, 320, 1154, 29912, 29881, 1157, 6008, 29913, 29928, 6622, 741, 10142, 2403, 29943, 29898, 29873, 29897, 29928, 29938, 4864, 363, 263, 29889, 29872, 29889, 13, 29938, 29873, 320, 262, 320, 29934, 29938, 322, 278, 8954, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 360, 6622, 741, 10142, 2844, 562, 2403, 29943, 13670, 4181 ]	1,332,863	6,144	ArXiv	-1	-1
})D = \int_{\delta} \Psi_{D^{\Sigma}_FD}(t) dt, \qquad {\delta} \in \cB_b(\R) \end{displaymath} holds. Applying the Fatou theorem (see \cite{KN77}) to \eqref{2.12} and using \eqref{2.13} we obtain \begin{equation}\Label{2.16} \im((F^D)({\lambda})) = \pi\Psi_{D^{\Sigma}_FD}({\lambda}) \quad \text{for a.e.}\quad {\lambda} \in \R. \end{equation} By \cite[Corollary 4.7]{MM03} $N_{{\Sigma}^{ac}_F}({\lambda}) = {\rm rank\,}(\Psi_{D^{\Sigma}_FD}({\lambda})) = {\rm dim}(\overline{{\rm ran\,}(\Psi_{D^{\Sigma}_FD}({\lambda}))})$ for a.e. ${\lambda} \in \R$. Finally, using \eqref{2.16} we get $N_{{\Sigma}^{ac}_F}({\lambda}) = d_{F^D}({\lambda})$ for a.e. ${\lambda} \in \R$. \end{proof} { Notice that Proposition \ref{II.4} implies that $D_{F^D}(t)$ does not dependent on $D$}. Assuming the existence of the limit $F(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}F(t + iy)$ for a.e. $t \in \R$, we set \begin{displaymath} d_F(t) := {\rm rank\,}(\im(F(t)) = {\rm dim}({\rm ran\,}(\im(F(t)))) \end{displaymath} for a.e. $t\in \R$. In this case Proposition \ref{II.4} can be modified as follows. \begin{corollary}\Label{II.5} Let $F(\cdot)\in (R_\cH)$. If the limit $F(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}F(t + iy)$ exists for a.e. $t \in \R$, then $N_{{\Sigma}^{ac}_F}(t) = d_F(t)$ for a.e. $t \in \R$. \end{corollary} \subsection{Boundary triplets and self-adjoint extensions} In this section we briefly recall the basic facts on boundary triplets and the corresponding Weyl functions, cf. \cite{DM87,DM91,DM95,GG91}. Let $A$ be a densely defined closed symmetric operator in the separable Hilbert space $\gH$ with equal deficiency indices $n_\pm(A)={\rm dim}({\xker\,}(A^\mp i)) \leq \infty$. \begin{definition}[\cite{GG91}]\Label{t1.9} {\em A triplet $\Pi = \{\cH, \Gamma_0, \Gamma_1\}$, where $\cH$ is an auxiliary Hilbert space and $\Gamma_0,\Gamma_1:\ {\rm dom\,}(A^)\rightarrow \cH$ are linear mappings, is called an (ordinary) boundary triplet for $A^$ if the "abstract Green's identity" \begin{equation}\Label{2.10A} (A^f,g) - (f,A^g) = ({\Gamma}_1f,{\Gamma}_0g)_{\cH} - ({\Gamma}_0f,{\Gamma}_1g)_{\cH}, \qquad f,g\in{\rm dom\,}(A^), \end{equation} holds and the mapping ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top: {\rm dom\,}(A^*) \rightarrow \cH \oplus \cH$ is surjective. } \end{definition} \begin{definition}[\cite{GG91}]\Label{def2.2} {\em A closed extension $A'$ of $A$ is called a proper extension, in short $A'\in {\rm Ext\,}_A,$	-0.380339	-1.452489	-0.213303	1.892882	[ -0.3419883557892045, -0.41869017981313505 ]	[ -1.6602015087229958, -1.2447756778591412 ]	[ -0.3293363996939053, -0.09727034587124471 ]	[ 2.012545207178792, 1.773219142499527 ]	1,024	[ 512, 512 ]	[ 1800, 29928, 353, 320, 524, 1665, 4181, 29913, 320, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 29873, 29897, 11636, 29892, 13, 29905, 12014, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 8640, 29889, 2401, 5890, 278, 29871, 383, 271, 283, 9185, 313, 4149, 320, 2036, 29912, 29968, 29940, 29955, 29955, 1800, 304, 320, 4915, 29912, 29906, 29889, 29896, 29906, 29913, 322, 773, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29941, 29913, 591, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29953, 29913, 13, 29905, 326, 3552, 29943, 29985, 29928, 5033, 741, 2892, 20073, 353, 320, 1631, 29905, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 1800, 320, 3425, 320, 726, 29912, 1454, 13, 29874, 29889, 29872, 29889, 1012, 3425, 2802, 2892, 29913, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 2059, 29871, 320, 2036, 29961, 12521, 21982, 29871, 29946, 29889, 29955, 3199, 7428, 29900, 29941, 29913, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 741, 2892, 1800, 353, 13, 741, 1758, 7115, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 20073, 353, 2802, 1758, 3964, 4678, 6875, 16195, 1758, 6350, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 20073, 8435, 363, 263, 29889, 29872, 29889, 13, 29938, 741, 2892, 29913, 320, 262, 320, 29934, 1504, 9788, 29892, 773, 320, 4915, 29912, 29906, 29889, 29896, 29953, 29913, 591, 679, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 741, 2892, 1800, 353, 13, 29881, 648, 29943, 29985, 29928, 2119, 741, 2892, 8435, 363, 263, 29889, 29872, 29889, 7555, 2892, 29913, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29912, 16393, 393, 22206, 320, 999, 29912, 2687, 29889, 29946, 29913, 10469, 393, 395, 29928, 648, 29943, 29985, 29928, 2119, 29873, 1262, 947, 451, 13, 18980, 373, 395, 29928, 29938, 1836, 17090, 13, 1552, 10379, 310, 278, 29871, 4046, 395, 29943, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29943, 29898, 29873, 718, 474, 29891, 1262, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 29871, 591, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29881, 29918, 29943, 29898, 29873, 29897, 3490, 2802, 1758, 7115, 5940, 4678, 326, 29898, 29943, 29898, 29873, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29943, 29898, 29873, 13697, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 29905, 262, 320, 29934, 1504, 512, 445, 1206, 22206, 320, 999, 29912, 2687, 29889, 29946, 29913, 13, 3068, 367, 9120, 408, 4477, 29889, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 2687, 29889, 29945, 29913, 13, 12024, 395, 29943, 1194, 3822, 2144, 262, 313, 29934, 3187, 29883, 29950, 4935, 960, 13, 1552, 4046, 395, 29943, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29943, 29898, 29873, 718, 474, 29891, 1262, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 29897, 353, 270, 29918, 29943, 29898, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 13, 29905, 7235, 29912, 17109, 653, 21954, 1372, 322, 1583, 29899, 328, 12090, 17752, 29913, 13, 13, 797, 445, 4004, 591, 23359, 13, 3757, 497, 278, 6996, 17099, 373, 29871, 10452, 21954, 1372, 322, 278, 6590, 13, 29956, 1032, 29880, 3168, 29892, 274, 29888, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29892, 26788, 29929, 29896, 1836, 13, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 278, 13, 25048, 519, 12338, 2151, 2913, 779, 29887, 29950, 29938, 411, 5186, 822, 293, 13396, 16285, 13, 29938, 29876, 3187, 3358, 29898, 29909, 3892, 741, 1758, 3964, 2119, 741, 29916, 3946, 5940, 2119, 29909, 6622, 29905, 1526, 474, 876, 320, 3797, 320, 3411, 1504, 13, 29905, 463, 29912, 16553, 4400, 29905, 2036, 29912, 26788, 29929, 29896, 6525, 29905, 4775, 29912, 29873, 29896, 29889, 29929, 29913, 13, 741, 331, 13, 29909, 21954, 29873, 779, 12197, 353, 320, 741, 29883, 29950, 29892, 320, 6642, 29918, 29900, 29892, 13, 29905, 6642, 29918, 29896, 28538, 988, 779, 29883, 29950, 29938, 338, 385, 29587, 653, 12338, 2151, 2913, 322, 13, 4535, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 3583, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29938, 526, 5608, 13, 655, 27775, 29892, 29871, 338, 2000, 385, 313, 24310, 29897, 10452, 21954, 29873, 363, 395, 29909, 6622, 29938, 565, 13, 1552, 376, 16595, 7646, 29915, 29879, 10110, 29908, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29900, 29909, 29913, 13, 29898, 29909, 6622, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 6622, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 741, 6642, 2403, 29900, 29887, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 29888, 29892, 741, 6642, 2403, 29896, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 6622, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 23177, 322, 278, 10417, 7555, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29901, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 13, 29905, 5211, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 29938, 338, 1190, 25674, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 29905, 463, 29912, 16553, 4400, 29905, 2036, 29912, 26788, 29929, 29896, 6525, 29905, 4775, 29912, 1753, 29906, 29889, 29906, 29913, 13, 741, 331, 13, 29909, 5764, 6081, 395, 29909, 13090, 310, 395, 29909, 29938, 338, 2000, 263, 1571, 6081, 29892, 13, 262, 3273, 395, 29909, 12764, 262, 2802, 1758, 7338, 5940, 2403, 29909, 8209 ]	1,332,863	7,168	ArXiv	-1	-1
if $A\subset A' \subset A^;$ Two proper extensions $A', A''$ are called disjoint if ${\rm dom\,}( A')\cap {\rm dom\,}( A'') = {\rm dom\,}( A)$ and transversal if in addition ${\rm dom\,}( A') + {\rm dom\,}( A'') = {\rm dom\,}( A^).$ } \end{definition} Clearly, any self-adjoint extension $\wt A= {\wt A}^$ is proper, $\wt A\in {\rm Ext\,}_A.$ A boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^$ exists whenever $n_+(A) = n_-(A)$. Moreover, the relations $n_\pm(A) = {\rm dim}(\cH)$ and ${\xker\,}(\Gamma_0) \cap {\xker\,}(\Gamma_1)={\rm dom\,}(A)$ are valid. Besides, $\Gamma_0, \Gamma_1\in [{\mathfrak H}_+, \cH]$, where ${\mathfrak H}_+$ denotes the Hilbert space { obtained by equipping} ${\rm dom\,}(A^)$ with the graph norm of $A^$. With any boundary triplet $\Pi$ one associates two extensions $A_j:=A^\!\upharpoonright{\xker\,}({\Gamma}_j), \ j\in \{0,1\}$, which are self-adjoint in view of Proposition \ref{prop2.1} below. Conversely, for any extension $A_0=A_0^\in {\rm Ext\,}_A$ there exists a (non-unique) boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^$ such that $A_0:=A^\!\upharpoonright{\xker\,}({\Gamma}_0)$. Using the concept of { boundary triplets} one can parameterize all proper, in particular, self-adjoint extensions of $A$. For this purpose denote by $\widetilde\cC(\cH)$ the set of closed linear relations in $\cH$, that is, the set of (closed) linear subspaces of $\cH\oplus\cH$. The adjoint relation $\Theta^\in\widetilde\cC(\cH)$ of a linear relation $\Theta$ in $\cH$ is defined by \begin{equation} \Theta^= \left\{ \begin{pmatrix} k\\k^\prime \end{pmatrix}: (h^\prime,k)=(h,k^\prime)\,\,\text{for all}\, \begin{pmatrix} h\\h^\prime\end{pmatrix} \in\Theta\right\}. \end{equation} A linear relation $\Theta$ is called {\it symmetric} if $\Theta\subset\Theta^$ and self-adjoint if $\Theta=\Theta^$. The multivalued part ${\rm mul\,}(\Theta)$ of { $\Theta\in \wt\cC(\cH)$ is} ${\rm mul\,}(\Theta) = \{h \in \cH: \{0,h\}\in \Theta\}.$ Setting $\cH_{\infty} :={\rm mul\,}(\Theta)$ and $\cH_{\rm op} :=\cH^{\perp}_{\infty}$ we get $\cH=\cH_{\rm op}\oplus\cH_{\infty}$. This decomposition yields an orthogonal { decomposition} $\Theta=\Theta_{\rm op}\oplus\Theta_{\infty}$ where $\Theta_{\infty}:= \{0\}\oplus{\rm mul\,}(\Theta)$ and $\Theta_{\rm op}:= \{\{f,g\}\in\Theta:\ f\in {\rm dom\,}(\Theta), g\perp{\rm mul\,}(\Theta)\}$. For the definition of the inverse and the resolvent set of a linear relation $\Theta$ we refer to \cite{DS87}. \begin{proposition}\label{prop2.1} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^*.$ Then the mapping \begin{equation}\label{bij} ({\rm Ext\,}_A\ni)\ \widetilde A \to \Gamma {\rm dom\,}(\widetilde A) =\{\{\Gamma_0 f,\Gamma_1f \} : \	0.182597	-1.092572	0.37447	2.345521	[ 0.24149337696426745, 0.12370129007037405 ]	[ -0.9761813906626834, -1.2089631062329467 ]	[ 0.5063550181702113, 0.24258595153024737 ]	[ 2.220654828639023, 2.4703863743912997 ]	1,024	[ 512, 512 ]	[ 565, 395, 29909, 29905, 6484, 319, 29915, 320, 6484, 319, 6622, 29936, 29938, 13, 13, 13985, 1571, 17752, 395, 29909, 742, 319, 4907, 29938, 526, 2000, 766, 12090, 565, 13, 29938, 741, 1758, 2432, 5940, 2119, 319, 1495, 29905, 5030, 2802, 1758, 2432, 5940, 2119, 319, 29915, 1495, 353, 2802, 1758, 2432, 5940, 2119, 319, 1262, 322, 29871, 1301, 874, 284, 565, 297, 13, 1202, 654, 7555, 1758, 2432, 5940, 2119, 319, 1495, 718, 2802, 1758, 2432, 5940, 2119, 319, 29915, 1495, 353, 2802, 1758, 2432, 5940, 2119, 319, 6622, 467, 29938, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 18759, 368, 29892, 738, 29871, 1583, 29899, 328, 12090, 6081, 779, 14554, 319, 29922, 2802, 14554, 319, 2137, 29394, 338, 1571, 29892, 13, 779, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 29909, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 4864, 13, 8256, 1310, 29871, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 4935, 12808, 29892, 278, 5302, 395, 29876, 3187, 3358, 29898, 29909, 29897, 353, 13, 741, 1758, 3964, 4678, 29883, 29950, 1262, 322, 7555, 29916, 3946, 5940, 4678, 6642, 29918, 29900, 29897, 320, 5030, 2802, 29916, 3946, 5940, 4678, 6642, 29918, 29896, 3892, 741, 1758, 2432, 5940, 2119, 29909, 1262, 526, 13, 3084, 29889, 19065, 29892, 779, 6642, 29918, 29900, 29892, 320, 6642, 29918, 29896, 29905, 262, 518, 741, 7237, 379, 2403, 29974, 29892, 320, 29883, 29950, 25473, 13, 3062, 7555, 7237, 379, 2403, 24035, 20169, 278, 12338, 2151, 2913, 426, 7625, 13, 1609, 1592, 17347, 29913, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 411, 278, 3983, 6056, 310, 395, 29909, 6622, 1504, 13, 13, 3047, 738, 10452, 21954, 29873, 779, 12197, 29938, 697, 4067, 1078, 29871, 1023, 17752, 13, 29938, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 511, 320, 432, 29905, 262, 9991, 29900, 29892, 29896, 28538, 607, 526, 13, 1311, 29899, 328, 12090, 297, 1776, 310, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 2400, 29889, 13, 1168, 874, 873, 29892, 363, 738, 6081, 395, 29909, 29918, 29900, 29922, 29909, 29918, 29900, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 727, 4864, 13, 29874, 313, 5464, 29899, 13092, 29897, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 13, 14565, 393, 395, 29909, 29918, 29900, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 13, 13, 15156, 278, 6964, 310, 426, 10452, 21954, 1372, 29913, 697, 508, 3443, 675, 599, 13, 771, 546, 29892, 297, 3153, 29892, 1583, 29899, 328, 12090, 17752, 310, 395, 29909, 1504, 1152, 445, 13, 15503, 4220, 13530, 491, 779, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 278, 731, 29871, 310, 5764, 5608, 13, 2674, 800, 297, 779, 29883, 29950, 1628, 393, 338, 29892, 278, 731, 310, 313, 15603, 29897, 5608, 1014, 22854, 13, 974, 779, 29883, 29950, 29905, 17201, 29905, 29883, 29950, 1504, 450, 594, 12090, 8220, 13, 4535, 17458, 6622, 29905, 262, 29905, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 310, 263, 5608, 8220, 779, 17458, 29938, 297, 13, 4535, 29883, 29950, 29938, 338, 3342, 491, 13, 29905, 463, 29912, 2573, 4044, 13, 29905, 17458, 6622, 29922, 320, 1563, 10045, 13, 29905, 463, 29912, 12571, 29913, 413, 1966, 29895, 3823, 10080, 13, 29905, 355, 29912, 12571, 6177, 313, 29882, 3823, 10080, 29892, 29895, 3892, 29898, 29882, 29892, 29895, 3823, 10080, 2144, 2053, 2053, 726, 29912, 1454, 599, 15379, 13, 29905, 463, 29912, 12571, 29913, 298, 1966, 29882, 3823, 10080, 29905, 355, 29912, 12571, 29913, 13, 29905, 262, 29905, 17458, 29905, 1266, 29905, 1836, 13, 29905, 355, 29912, 2573, 4044, 13, 29909, 5608, 8220, 779, 17458, 29938, 338, 2000, 2802, 277, 18348, 29913, 565, 13, 4535, 17458, 29905, 6484, 29905, 17458, 6622, 29938, 322, 1583, 29899, 328, 12090, 565, 779, 17458, 2013, 17458, 6622, 1504, 13, 13, 1576, 1773, 2561, 6742, 760, 7555, 1758, 15065, 5940, 4678, 17458, 1262, 310, 426, 779, 17458, 29905, 262, 13, 29905, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 338, 29913, 7555, 1758, 15065, 5940, 4678, 17458, 29897, 353, 9991, 29882, 320, 262, 320, 29883, 29950, 29901, 9991, 29900, 29892, 29882, 25848, 262, 13, 29905, 17458, 29905, 1836, 29938, 21605, 779, 29883, 29950, 1665, 3411, 29913, 3490, 741, 1758, 15065, 5940, 4678, 17458, 1262, 322, 779, 29883, 29950, 1665, 1758, 1015, 29913, 13, 29901, 2013, 29883, 29950, 3311, 24598, 6353, 3411, 1042, 591, 679, 779, 29883, 29950, 2013, 29883, 29950, 1665, 1758, 13, 459, 1012, 17201, 29905, 29883, 29950, 1665, 3411, 4311, 910, 26227, 17498, 385, 28143, 13, 29912, 26227, 29913, 13, 4535, 17458, 2013, 17458, 1665, 1758, 1015, 1012, 17201, 29905, 17458, 1665, 3411, 1042, 29871, 988, 13, 4535, 17458, 1665, 3411, 6177, 29922, 9991, 29900, 25848, 17201, 741, 1758, 15065, 5940, 4678, 17458, 1262, 322, 779, 17458, 1665, 1758, 1015, 6177, 29922, 13, 24976, 29912, 29888, 29892, 29887, 25848, 262, 29905, 17458, 3583, 285, 29905, 262, 2802, 1758, 2432, 5940, 4678, 17458, 511, 330, 29905, 24598, 741, 1758, 15065, 5940, 4678, 17458, 2144, 4311, 1152, 13, 1552, 5023, 310, 278, 16402, 322, 278, 3770, 794, 731, 310, 263, 5608, 13, 23445, 779, 17458, 29938, 591, 2737, 304, 320, 2036, 29912, 8452, 29947, 29955, 1836, 13, 29905, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29906, 29889, 29896, 29913, 13, 12024, 29871, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 367, 263, 13, 9917, 653, 21954, 29873, 363, 29871, 395, 29909, 6622, 7449, 29871, 1987, 278, 10417, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 19352, 29913, 13, 13670, 1758, 7338, 5940, 2403, 29909, 29905, 1240, 2144, 320, 10737, 319, 320, 517, 29871, 320, 6642, 2802, 1758, 2432, 5940, 4678, 10737, 319, 29897, 13, 2013, 741, 741, 6642, 29918, 29900, 285, 2053, 6642, 29918, 29896, 29888, 320, 29913, 584, 320, 29871 ]	1,332,863	8,192	ArXiv	-1	-1
f\in {\rm dom\,}(\widetilde A) \} =: \Theta \in \widetilde\cC(\cH) \end{equation} establishes a bijective correspondence between the sets ${\rm Ext\,}_A$ and $\widetilde\cC(\cH)$. We put $A_\Theta :=\widetilde A$ where $\Theta$ is defined by \eqref{bij}. { Moreover, the} following holds: \item[\;\;\rm (i)] $A_\Theta= A_\Theta^$ if and only if $\Theta= \Theta^;$ \item[\;\;\rm (ii)] The extensions $A_\Theta$ and $A_0$ are disjoint if and only if $\Theta\in \cC(\cH).$ In this case \eqref{bij} becomes \begin{displaymath} A_\Theta = A^\!\upharpoonright{\xker\,}({\Gamma}_1- \Theta{\Gamma}_0); \end{displaymath} \item[\;\;\rm (iii)] The extensions $A_\Theta$ and $A_0$ are transversal if and only if $\Theta = \Theta^\in [\cH].$ \end{proposition} In particular, $A_j:=A^\!\upharpoonright{\xker\,}({\Gamma}_j) = A_{\Theta_j},\ j\in \{0,1\}$ where ${\Theta}_0:= \{0\} \times \cH$ and ${\Theta}_1 := \cH \times \{0\}$. Hence $A_j= A_j^$ since ${\Theta}_j = {\Theta}^_j.$ In the sequel the extension $A_0$ is usually regarded as a reference self-adjoint extension. \subsection{Weyl functions and $\gamma$-fields}\label{weylsec} It is well known that Weyl functions give an important tool in the direct and inverse spectral theory of singular Sturm-Liouville operators. In \cite{DM87,DM91,DM95} the concept of Weyl function was generalized to the case of an arbitrary symmetric operator $A$ with $n_+(A) = n_-(A).$ Following \cite{DM87,DM91,DM95} we recall basic facts on Weyl functions and $\gamma$-fields associated with a boundary triplet $\Pi$. \begin{definition}[{\cite{DM87,DM91}}]\label{Weylfunc} {\em Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^.$ The functions $\gamma(\cdot): \varrho(A_0)\rightarrow [\cH,\gH]$ and $M(\cdot): \varrho(A_0)\rightarrow [\cH]$ defined by \begin{equation}\label{2.3A} \gamma(z):=\bigl(\Gamma_0\!\upharpoonright\mathfrak N_z\bigr)^{-1} \qquad\text{and}\qquad M(z):=\Gamma_1\gamma(z), \qquad z\in\varrho(A_0), \end{equation} are called the {\em $\gamma$-field} and the {\em Weyl function}, respectively, corresponding to $\Pi.$ } \end{definition} It follows from the identity ${\rm dom\,}(A^)={\xker\,}(\Gamma_0)\dot + {\mathfrak N}_z$, $z\in\varrho(A_0)$, where $A_0 = A^\!\upharpoonright{\xker\,}({\Gamma}_0)$, and ${\mathfrak N}_z :={\xker\,}(A^* - z)$, that the $\gamma$-field $\gamma(\cdot)$ is well defined and takes values in $[\cH,\gH]$. Since ${\Gamma}_1 \in [\gH_+, \cH]$, it follows from \eqref{2.3A} that $M(\cdot)$ is well defined too and takes values in $[\cH]$. Moreover, both $\gamma(\cdot)$ and $M(\cdot)$ are holomorphic on $\varrho(A_0)$ and satisfy the following relations (see \cite{DM91}) \begin{equation}\label{2.	0.178488	-0.833826	0.47592	2.407953	[ 0.312716499272203, 0.04426011518844594 ]	[ -1.194638077582469, -0.4730147593146524 ]	[ 0.2831658079363957, 0.6686744437948046 ]	[ 2.2830877150770923, 2.532819260829369 ]	1,024	[ 512, 512 ]	[ 285, 29905, 262, 2802, 1758, 2432, 5940, 4678, 10737, 319, 29897, 320, 29913, 353, 29901, 13, 29905, 17458, 320, 262, 320, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 342, 370, 1674, 267, 29871, 263, 4768, 25674, 3928, 663, 1546, 278, 6166, 7555, 1758, 7338, 5940, 2403, 29909, 29938, 13, 392, 29871, 779, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 4935, 1334, 1925, 395, 29909, 3187, 17458, 584, 2013, 10737, 319, 29938, 988, 13, 4535, 17458, 29938, 338, 3342, 491, 320, 4915, 29912, 19352, 1836, 426, 12808, 29892, 278, 29913, 1494, 8640, 29901, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 395, 29909, 3187, 17458, 29922, 319, 3187, 17458, 6622, 29938, 565, 322, 871, 565, 779, 17458, 29922, 13, 29905, 17458, 6622, 29936, 29938, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 450, 17752, 395, 29909, 3187, 17458, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 13, 2218, 12090, 565, 322, 871, 565, 779, 17458, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 512, 445, 1206, 13, 29905, 4915, 29912, 19352, 29913, 7415, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29909, 3187, 17458, 353, 319, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 29899, 13, 29905, 17458, 741, 6642, 2403, 29900, 416, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 25609, 4638, 450, 17752, 395, 29909, 3187, 17458, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 13, 3286, 874, 284, 565, 322, 871, 565, 779, 17458, 353, 320, 17458, 6622, 29905, 262, 12452, 29883, 29950, 1822, 29938, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 797, 3153, 29892, 13, 29938, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 29897, 353, 319, 1665, 17458, 29918, 29926, 7570, 432, 29905, 262, 13, 10045, 29900, 29892, 29896, 11854, 988, 7555, 17458, 2403, 29900, 9361, 9991, 29900, 18105, 320, 3706, 320, 29883, 29950, 29938, 322, 7555, 17458, 2403, 29896, 3490, 320, 29883, 29950, 320, 3706, 13, 10045, 29900, 23699, 10133, 395, 29909, 29918, 29926, 29922, 319, 29918, 29926, 6622, 29938, 1951, 7555, 17458, 2403, 29926, 13, 29922, 2802, 17458, 2137, 29930, 29918, 29926, 7449, 512, 278, 8617, 295, 278, 6081, 395, 29909, 29918, 29900, 29938, 13, 275, 5491, 17878, 408, 263, 3407, 13, 1311, 29899, 328, 12090, 6081, 29889, 13, 13, 29905, 7235, 29912, 29956, 1032, 29880, 3168, 322, 779, 4283, 4388, 9621, 1012, 1643, 29912, 705, 2904, 3471, 29913, 13, 13, 3112, 338, 1532, 2998, 393, 399, 1032, 29880, 3168, 2367, 385, 4100, 5780, 297, 278, 13, 11851, 322, 16402, 23161, 6368, 310, 13512, 624, 17095, 29899, 23410, 283, 4909, 13, 3372, 4097, 29889, 512, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29913, 278, 6964, 310, 399, 1032, 29880, 740, 13, 11102, 28803, 304, 278, 1206, 310, 385, 11472, 18348, 5455, 395, 29909, 29938, 13, 2541, 29871, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 467, 29938, 12206, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29913, 591, 17386, 13, 16121, 17099, 373, 399, 1032, 29880, 3168, 322, 779, 4283, 4388, 9621, 6942, 411, 13, 29874, 10452, 21954, 29873, 779, 12197, 1504, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 930, 10725, 1643, 29912, 29956, 1032, 29880, 9891, 29913, 13, 741, 331, 13, 2803, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 10452, 21954, 29873, 29871, 363, 395, 29909, 6622, 7449, 13, 1576, 3168, 779, 4283, 1194, 3822, 1125, 13, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5211, 12452, 29883, 29950, 2053, 29887, 29950, 9341, 322, 29871, 395, 29924, 1194, 3822, 1125, 13, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5211, 29871, 12452, 29883, 29950, 9341, 3342, 491, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29941, 29909, 29913, 13, 29905, 4283, 29898, 29920, 1125, 2013, 3752, 29880, 1194, 6642, 29918, 29900, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 29905, 7237, 405, 29918, 29920, 29905, 3752, 29878, 21604, 29896, 29913, 13, 29905, 12014, 29905, 726, 29912, 392, 1012, 12014, 341, 29898, 29920, 1125, 2013, 6642, 29918, 29896, 29905, 4283, 29898, 29920, 511, 320, 12014, 13, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 418, 320, 355, 29912, 2573, 29913, 13, 598, 2000, 278, 2802, 331, 779, 4283, 4388, 2671, 29913, 322, 278, 2802, 331, 399, 1032, 29880, 740, 1118, 13, 690, 1103, 3598, 29892, 6590, 304, 29871, 779, 12197, 7449, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 3112, 4477, 515, 278, 10110, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 3892, 741, 29916, 3946, 5940, 4678, 6642, 29918, 29900, 2144, 6333, 718, 13, 741, 7237, 405, 2403, 29920, 1628, 395, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 5767, 988, 29871, 395, 29909, 29918, 29900, 353, 13, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 322, 7555, 7237, 405, 2403, 29920, 3490, 741, 29916, 3946, 5940, 2119, 29909, 6622, 448, 13, 29920, 5767, 393, 278, 779, 4283, 4388, 2671, 779, 4283, 1194, 3822, 1262, 338, 1532, 3342, 322, 13, 29873, 6926, 1819, 297, 395, 7110, 29883, 29950, 2053, 29887, 29950, 22689, 4001, 7555, 6642, 2403, 29896, 320, 262, 12452, 29887, 29950, 28842, 29892, 320, 29883, 29950, 25473, 372, 13, 23031, 29879, 515, 320, 4915, 29912, 29906, 29889, 29941, 29909, 29913, 393, 29871, 395, 29924, 1194, 3822, 1262, 338, 1532, 3342, 2086, 322, 13, 29873, 6926, 1819, 297, 259, 395, 7110, 29883, 29950, 22689, 12808, 29892, 1716, 779, 4283, 1194, 3822, 1262, 322, 13, 29938, 29924, 1194, 3822, 1262, 526, 8753, 16898, 373, 779, 1707, 4650, 29898, 29909, 29918, 29900, 1262, 322, 15523, 278, 13, 23031, 292, 5302, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 1800, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889 ]	1,332,863	9,216	ArXiv	-1	-1
15} \gamma(z)=\bigl(I+(z-\zeta)(A_0 - z)^{-1}\bigr)\gamma(\zeta), \qquad z, \zeta\in\varrho(A_0), \end{equation} and \begin{equation}\label{mlambda} M(z) - M(\zeta)^= (z - \bar\zeta)\gamma(\zeta)^\gamma(z), \qquad z, \zeta\in\varrho(A_0). \end{equation} The last identity yields that $M(\cdot)$ is a $R_{\cH}$-function, that is, $M(\cdot)$ is a $[\cH]$-valued holomorphic function on $\C\backslash \R$ satisfying \begin{displaymath} M(z)=M(\overline z)^\qquad\text{and}\qquad \frac{{\rm Im\,}(M(z))}{{\rm Im\,}(z)}\geq 0, \qquad z\in\C\backslash\R. \end{displaymath} Moreover, it follows from \eqref{mlambda} that $M(\cdot)$ satisfies $0\in \varrho({\rm Im\,}(M(z))),\ z\in\C\backslash\R$. If $A$ is a simple symmetric operator, then the Weyl function $M(\cdot)$ determines the pair $\{A,A_0\}$ uniquely up to unitary equivalence (see \cite{DM95,KL71}). Therefore $M(\cdot)$ contains (implicitly) full information on spectral properties of $A_0$. We recall that a symmetric operator is said to be {\it simple} if there is no non-trivial subspace which reduces it to a self-adjoint operator. For a fixed $A_0 = A_0^$ a boundary triplet $\Pi =\{\cH, {\Gamma}_0,{\Gamma}_1\}$ satisfying ${\rm dom\,}(A_0)={\xker\,} (\Gamma_0)$ is not unique. Let $\Pi_j =\{\cH_j, {\Gamma}^j_0,{\Gamma}^j_1\}, \ j\in \{1,2\},$ be two such triplets. Then the corresponding Weyl functions $M_1(\cdot)$ and $M_2(\cdot)$ are related by \begin{equation}\label{2.11} M_2(z) = R^* M_1(z) R + R_0, \end{equation} where $R_0= R^_0 \in [{\cH}_2]$ and $R \in [{\cH}_2,{\cH}_1]$ is boundedly invertible. According to Proposition \ref{prop2.1} the extensions $A_{{\Theta}}$ and $A_0$ are not disjoint whenever ${\rm mul\,}(\Theta)\not = \{0\}.$ Considering $A_{{\Theta}}$ and $A_0$ as extensions of an intermediate extension $S := A_0\upharpoonright({\rm dom\,}(A_0) \cap {\rm dom\,}(A_{\Theta}))$ we can avoid this inconvenience. \begin{lemma}\Label{III.4} Let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^$, $M(\cdot)$ the corresponding Weyl function, ${\Theta}= {\Theta}^* \in \wt\cC(\cH)$ and ${\Theta} = \Theta_{op}\oplus \Theta_\infty $ its orthogonal decomposition. Further let $S := A_0\upharpoonright({\rm dom\,}(A_0) \cap {\rm dom\,}(A_{\Theta}))$. Then the triplet $\wh{\Pi} = \{\wh\cH,\wh{\Gamma}_0,\wh{\Gamma}_1\}$, defined by \begin{displaymath} \wh\cH := \cH_{\rm op} = \overline{{\rm dom\,}(\Theta)},\quad \wh{\Gamma}_0 := {\Gamma}_0\upharpoonright{\rm dom\,}( S^),\quad \wh{\Gamma}_1 := \pi_{\rm op}{\Gamma}_1\upharpoonright{\rm dom\,}(S^), \end{displaymath} is a	-0.010527	-1.149872	0.032078	2.210249	[ 0.1154832374963815, -0.13653704143939044 ]	[ -1.0191564766141166, -1.2805882494853356 ]	[ 0.09802021308334402, -0.033864320236637976 ]	[ 2.303898677223115, 2.1166000179089077 ]	1,024	[ 512, 512 ]	[ 29896, 29945, 29913, 13, 29905, 4283, 29898, 29920, 7950, 3752, 29880, 29898, 29902, 17108, 29920, 2612, 11327, 5033, 29909, 29918, 29900, 448, 503, 21604, 29896, 1012, 3752, 29878, 2144, 4283, 1194, 11327, 511, 13, 29905, 12014, 503, 29892, 320, 11327, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 392, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 828, 2269, 29913, 13, 29924, 29898, 29920, 29897, 448, 341, 1194, 11327, 4887, 29930, 29922, 313, 29920, 448, 320, 1646, 29905, 11327, 2144, 4283, 1194, 11327, 4887, 17710, 4283, 29898, 29920, 511, 320, 12014, 503, 29892, 13, 29905, 11327, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1576, 1833, 10110, 17498, 393, 395, 29924, 1194, 3822, 1262, 338, 263, 395, 29934, 1665, 29883, 29950, 23021, 2220, 29892, 13, 5747, 338, 29892, 395, 29924, 1194, 3822, 1262, 338, 263, 395, 7110, 29883, 29950, 29962, 4388, 4387, 287, 8753, 16898, 740, 373, 13, 4535, 29907, 29905, 1627, 17057, 320, 29934, 29938, 29871, 24064, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29898, 29920, 3892, 29924, 1194, 6875, 503, 4887, 17710, 12014, 29905, 726, 29912, 392, 1012, 12014, 13, 29905, 1154, 16195, 1758, 1954, 5940, 2119, 29924, 29898, 29920, 876, 1157, 741, 1758, 1954, 5940, 2119, 29920, 11383, 6279, 29871, 29900, 29892, 320, 12014, 503, 29905, 262, 29905, 29907, 29905, 1627, 17057, 29905, 29934, 29889, 13, 320, 355, 29912, 4990, 755, 29913, 13, 20761, 957, 29892, 372, 4477, 515, 320, 4915, 29912, 828, 2269, 29913, 393, 395, 29924, 1194, 3822, 1262, 17150, 13, 29938, 29900, 29905, 262, 320, 1707, 4650, 13670, 1758, 1954, 5940, 2119, 29924, 29898, 29920, 876, 20481, 29871, 503, 29905, 262, 29905, 29907, 29905, 1627, 17057, 29905, 29934, 1504, 13, 13, 13, 3644, 395, 29909, 29938, 338, 263, 2560, 18348, 5455, 29892, 769, 29871, 278, 399, 1032, 29880, 740, 13, 29938, 29924, 1194, 3822, 1262, 3683, 1475, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 20498, 873, 701, 304, 5190, 653, 13, 1686, 2561, 663, 313, 4149, 320, 2036, 29912, 23560, 29929, 29945, 29892, 29968, 29931, 29955, 29896, 7690, 7857, 395, 29924, 1194, 3822, 1262, 3743, 13, 29898, 6574, 4019, 368, 29897, 29871, 2989, 2472, 373, 23161, 4426, 310, 395, 29909, 29918, 29900, 1504, 13, 4806, 17386, 393, 263, 18348, 5455, 338, 13, 4977, 333, 304, 367, 2802, 277, 2560, 29913, 565, 727, 338, 694, 1661, 29899, 29873, 9473, 1014, 3493, 607, 13, 9313, 778, 372, 304, 263, 1583, 29899, 328, 12090, 5455, 29889, 13, 13, 2831, 263, 4343, 395, 29909, 29918, 29900, 353, 319, 29918, 29900, 6622, 29938, 263, 10452, 21954, 29873, 779, 12197, 17313, 741, 29883, 29950, 29892, 13, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 24064, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 3892, 741, 29916, 3946, 5940, 29913, 3441, 6642, 29918, 29900, 1262, 338, 451, 13, 13092, 29889, 2803, 779, 12197, 29918, 29926, 17313, 741, 29883, 29950, 29918, 29926, 29892, 2802, 6642, 2137, 29926, 29918, 29900, 29892, 741, 6642, 2137, 29926, 29918, 29896, 29905, 1118, 320, 432, 29905, 262, 9991, 29896, 29892, 29906, 29905, 1118, 29938, 13, 915, 1023, 1316, 21954, 1372, 29889, 1987, 278, 6590, 399, 1032, 29880, 3168, 13, 29938, 29924, 29918, 29896, 1194, 3822, 1262, 322, 395, 29924, 29918, 29906, 1194, 3822, 1262, 526, 4475, 491, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29896, 29913, 13, 29924, 29918, 29906, 29898, 29920, 29897, 353, 390, 6622, 341, 29918, 29896, 29898, 29920, 29897, 390, 718, 390, 29918, 29900, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29934, 29918, 29900, 29922, 390, 6622, 29918, 29900, 320, 262, 518, 741, 29883, 29950, 2403, 29906, 9341, 322, 395, 29934, 320, 262, 13, 29961, 741, 29883, 29950, 2403, 29906, 29892, 741, 29883, 29950, 2403, 29896, 9341, 338, 12635, 368, 21292, 1821, 29889, 13, 13, 7504, 3278, 304, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 278, 17752, 13, 29938, 29909, 24033, 17458, 7920, 322, 395, 29909, 29918, 29900, 29938, 526, 451, 766, 12090, 10940, 7555, 1758, 15065, 5940, 4678, 17458, 2144, 1333, 353, 13, 10045, 29900, 29905, 1836, 29938, 10056, 292, 395, 29909, 24033, 17458, 7920, 322, 395, 29909, 29918, 29900, 29938, 408, 17752, 310, 385, 13, 1639, 13847, 6081, 29871, 395, 29903, 3490, 319, 29918, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 13670, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 1665, 17458, 20073, 29938, 591, 508, 4772, 445, 22629, 854, 5597, 29889, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 5287, 29889, 29946, 29913, 13, 12024, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 29938, 29924, 1194, 3822, 1262, 278, 6590, 29871, 399, 1032, 29880, 740, 29892, 259, 7555, 17458, 5369, 2802, 17458, 2137, 29930, 320, 262, 13, 29905, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 322, 7555, 17458, 29913, 353, 320, 17458, 648, 459, 1012, 17201, 320, 17458, 3187, 3411, 13, 29938, 967, 28143, 26227, 29889, 8725, 1235, 29871, 395, 29903, 3490, 319, 29918, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 13670, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 1665, 17458, 20073, 1504, 1987, 278, 21954, 29873, 779, 1332, 741, 12197, 29913, 353, 13, 24976, 1332, 29905, 29883, 29950, 2053, 1332, 741, 6642, 2403, 29900, 2053, 1332, 741, 6642, 2403, 29896, 28538, 3342, 491, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 1332, 29905, 29883, 29950, 3490, 320, 29883, 29950, 1665, 1758, 1015, 29913, 353, 320, 6875, 16195, 1758, 2432, 5940, 4678, 17458, 29897, 7570, 3425, 13, 29905, 1332, 741, 6642, 2403, 29900, 3490, 2802, 6642, 2403, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 317, 6622, 20481, 3425, 320, 1332, 741, 6642, 2403, 29896, 3490, 13, 29905, 1631, 1665, 1758, 1015, 3331, 6642, 2403, 29896, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29903, 6622, 511, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 275, 263 ]	1,332,863	10,240	ArXiv	-1	-1
boundary triplet for $S^$, where $\pi_{\rm op}$ is the orthogonal projection from $\cH$ onto $\cH_{\rm op}$, $A_0 = S^\upharpoonright{\xker\,}(\wh {\Gamma}_0)$ and $A_{\Theta} = S_{{\Theta}_{\rm op}}$. The corresponding Weyl function is \begin{equation}\label{2.13a} \wh M(z) := \pi_{\rm op}M(z)\upharpoonright\cH_{\rm op}, \quad z \in \C_\pm. \end{equation} \end{lemma} The proof can be found in \cite{DHMS00}. Hence without loss of generality we can very often assume that the ``coordinate'' ${\Theta}:={\Gamma}\wt A$ of an extension $\wt A = A_{\Theta}=A_{\Theta}^* \in {\rm Ext\,}_A$ corresponds to the graph of a self-adjoint operator. In what follows, without loss of generality, we always assume that the closed symmetric $A$ is simple and, due to Lemma \ref{III.4}, the ``coordinate'' ${\Theta}$ of {\color{black} the extension $A_{\Theta} = A_{\Theta}^\in {{\rm Ext\,}}_A$ is the graph of a self-adjoint operator. \subsection{Krein type formula for resolvents and comparability} With any boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^$ and any proper (not necessarily self-adjoint) extension $A_{\Theta}\in {\rm Ext\,}_A$ it is naturally associated the following (unique) Krein type formula (cf. \cite{DM87,DM91,DM95}) \begin{equation}\label{2.30} (A_\Theta - z)^{-1} - (A_0 - z)^{-1} = \gamma(z) (\Theta - M(z))^{-1} \gamma({\overline z})^, \quad z\in \varrho(A_0)\cap \varrho(A_\Theta). \end{equation} Formula \eqref{2.30} is a generalization of the known Krein formula for resolvents. We note also, that all objects in \eqref{2.30} are expressed in terms of the boundary triplet $\Pi$ (cf. \cite{DM87,DM91,DM95}). In other words, \eqref{2.30} gives a relation between Krein-type formula for canonical resolvents and the theory of abstract boundary value problems (framework of boundary triplets). The following result is deduced from formula \eqref{2.30} (cf. \cite[Theorem 2]{DM91}). \begin{proposition}\label{prop2.9} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^$, $\Theta_i = \Theta_i^* \in \wt\cC(\cH), \ i\in \{1,2\}$. Then for any Schatten-von~Neumann ideal ${\mathfrak S}_p$, $p \in (0,\infty]$, and any $z \in \C\setminus\R$ the following equivalence holds \begin{displaymath} (A_{\Theta_1}-z)^{-1} - (A_{\Theta_2}-z)^{-1}\in{\mathfrak S}_p(\gH) \Longleftrightarrow \bigl(\Theta_1 - z\bigr)^{-1}- \bigl(\Theta_2 - z \bigr)^{-1}\in{\mathfrak S}_p(\cH) \end{displaymath} In particular, $(A_{{\Theta}_1} - z)^{-1} - (A_0 - z)^{-1} \in {\mathfrak S}_p(\gH) \Longleftrightarrow \bigl(\Theta_1 - i\bigr)^{-1} \in {\mathfrak S}_p(\cH)$. If in addition $\Theta_1, \Theta_2\in[\cH]$, then for any $p \in (0, \infty]$ the equivalence holds \begin{displaymath} (A_{\Theta_1}-z)^{-1	0.175407	-0.859791	0.204542	2.376737	[ 0.3784609198641435, -0.027647844833988976 ]	[ -0.9475313333617279, -0.7720497323933754 ]	[ 0.039686669499505826, 0.36939800279946083 ]	[ 2.595252147267438, 2.158221942200954 ]	1,024	[ 512, 512 ]	[ 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 988, 779, 1631, 1665, 1758, 1015, 1042, 338, 278, 13, 2072, 23419, 18246, 515, 779, 29883, 29950, 29938, 11480, 779, 29883, 29950, 1665, 1758, 1015, 4429, 395, 29909, 29918, 29900, 353, 13, 29903, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 4678, 1332, 2802, 6642, 2403, 29900, 1262, 322, 395, 29909, 1665, 17458, 29913, 353, 317, 24033, 17458, 6353, 1758, 1015, 26253, 13, 1576, 6590, 29871, 399, 1032, 29880, 740, 13, 275, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29941, 29874, 29913, 13, 29905, 1332, 341, 29898, 29920, 29897, 3490, 320, 1631, 1665, 1758, 1015, 29913, 29924, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 1665, 1758, 1015, 1118, 320, 3425, 503, 13, 29905, 262, 320, 29907, 3187, 3358, 29889, 320, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 13846, 29913, 13, 1576, 5296, 508, 367, 1476, 297, 320, 2036, 29912, 29928, 29950, 4345, 29900, 29900, 1836, 10133, 1728, 6410, 310, 13, 4738, 2877, 591, 508, 1407, 4049, 5251, 29871, 393, 278, 4954, 29302, 4907, 13, 29938, 741, 17458, 6177, 21854, 6642, 1012, 14554, 319, 29938, 310, 385, 6081, 779, 14554, 319, 353, 319, 1665, 17458, 5369, 29909, 1665, 17458, 2137, 29930, 320, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 16161, 304, 278, 29871, 3983, 310, 263, 1583, 29899, 328, 12090, 5455, 29889, 13, 13, 797, 825, 4477, 29892, 1728, 6410, 310, 2498, 537, 29892, 591, 2337, 13, 465, 2017, 393, 278, 5764, 18348, 395, 29909, 29938, 338, 2560, 322, 29892, 2861, 304, 29871, 11894, 13, 29905, 999, 29912, 5287, 29889, 29946, 1118, 278, 4954, 29302, 4907, 7555, 17458, 1042, 310, 2802, 2780, 29912, 8517, 29913, 278, 29871, 6081, 13, 29938, 29909, 1665, 17458, 29913, 353, 319, 1665, 17458, 2137, 17710, 262, 426, 741, 1758, 7338, 5940, 15609, 29909, 29938, 338, 278, 3983, 310, 263, 1583, 29899, 328, 12090, 13, 6891, 29889, 13, 13, 29905, 7235, 29912, 29968, 276, 262, 1134, 7063, 363, 3770, 794, 29879, 322, 5734, 3097, 29913, 13, 13, 3047, 29871, 738, 29871, 10452, 21954, 29873, 259, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 363, 395, 29909, 6622, 29938, 13, 392, 738, 1571, 313, 1333, 12695, 29871, 1583, 29899, 328, 12090, 29897, 29871, 6081, 395, 29909, 1665, 17458, 1012, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 372, 338, 18180, 29871, 6942, 29871, 278, 1494, 313, 13092, 29897, 7706, 262, 13, 1853, 7063, 313, 6854, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 1800, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29941, 29900, 29913, 13, 29898, 29909, 3187, 17458, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 353, 320, 4283, 29898, 29920, 29897, 3441, 17458, 448, 13, 29924, 29898, 29920, 876, 3426, 29896, 29913, 320, 4283, 13670, 6875, 503, 1800, 6622, 29892, 320, 3425, 503, 29905, 262, 320, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5030, 13, 29905, 1707, 4650, 29898, 29909, 3187, 17458, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 2500, 2497, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 338, 263, 2498, 2133, 310, 278, 2998, 7706, 262, 13, 689, 2497, 363, 3770, 794, 29879, 29889, 13, 4806, 4443, 884, 29892, 393, 599, 3618, 297, 13, 29905, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 526, 13384, 297, 4958, 310, 278, 10452, 21954, 29873, 779, 12197, 29938, 13, 29898, 6854, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 7690, 512, 916, 3838, 29892, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 4076, 263, 8220, 13, 14811, 7706, 262, 29899, 1853, 29871, 7063, 363, 24420, 3770, 794, 29879, 29871, 322, 278, 6368, 310, 9846, 13, 9917, 653, 995, 4828, 313, 4468, 310, 10452, 21954, 1372, 467, 13, 13, 1576, 1494, 1121, 338, 21049, 1133, 515, 29871, 7063, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 313, 6854, 29889, 13, 29905, 2036, 29961, 28831, 29871, 29906, 3199, 23560, 29929, 29896, 7690, 13, 29905, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29906, 29889, 29929, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 367, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 4535, 17458, 29918, 29875, 353, 320, 17458, 29918, 29875, 6622, 320, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 511, 320, 474, 29905, 262, 9991, 29896, 29892, 29906, 23699, 29871, 1987, 363, 13, 1384, 1102, 8606, 29899, 23696, 30022, 8139, 22553, 10839, 7555, 7237, 317, 2403, 29886, 1628, 395, 29886, 320, 262, 313, 29900, 2053, 3411, 25473, 322, 738, 395, 29920, 320, 262, 13, 29905, 29907, 29905, 15375, 29905, 29934, 29938, 278, 1494, 24796, 8640, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29918, 29896, 7402, 29920, 21604, 29896, 29913, 448, 313, 29909, 1665, 17458, 29918, 29906, 7402, 29920, 21604, 29896, 1012, 262, 741, 7237, 13, 29903, 2403, 29886, 1194, 29887, 29950, 29897, 13, 29905, 8208, 25874, 28751, 29871, 320, 3752, 29880, 1194, 17458, 29918, 29896, 448, 503, 29905, 3752, 29878, 21604, 29896, 7402, 13, 29905, 3752, 29880, 1194, 17458, 29918, 29906, 448, 503, 320, 3752, 29878, 21604, 29896, 1012, 262, 741, 7237, 317, 2403, 29886, 1194, 29883, 29950, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 797, 3153, 29892, 29871, 2427, 29909, 24033, 17458, 2403, 29896, 29913, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 320, 262, 13, 741, 7237, 317, 2403, 29886, 1194, 29887, 29950, 29897, 320, 8208, 25874, 28751, 320, 3752, 29880, 1194, 17458, 29918, 29896, 448, 474, 29905, 3752, 29878, 21604, 29896, 29913, 320, 262, 2802, 7237, 13, 29903, 2403, 29886, 1194, 29883, 29950, 4935, 13, 13, 3644, 297, 6124, 779, 17458, 29918, 29896, 29892, 320, 17458, 29918, 29906, 29905, 262, 7110, 29883, 29950, 25473, 769, 363, 738, 395, 29886, 320, 262, 13, 29898, 29900, 29892, 320, 3411, 9341, 278, 24796, 8640, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29918, 29896, 7402, 29920, 21604, 29896 ]	1,332,863	11,264	ArXiv	-1	-1
} - (A_{\Theta_2}-z)^{-1}\in{\mathfrak S}_p(\gH) \Longleftrightarrow \Theta_1 - \Theta_2 \in{\mathfrak S}_p(\cH). \end{displaymath} \end{proposition} \subsection{Generalized boundary triplets and proper extensions} In applications the concept of boundary triplets is too restrictive. Here we recall some facts on generalized boundary triplets following \cite{DM95}. \begin{definition}[{\cite[Definition 6.1]{DM95}}]\label{def3.1} {\em { A triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ is called a \emph{generalized boundary triplet for $A^$} if $\cH$ is an auxiliary Hilbert space and { ${\Gamma}_j: {\rm dom\,}(\Gamma_j) \to\cH$}, $j = 0,1$ are linear mappings such that { ${\rm dom\,}(\Gamma) := {\rm dom\,}({\Gamma}_0) \cap {\rm dom\,}({\Gamma}_1)$ is a core for $A^$}, ${\Gamma}_0$ is surjective, $A_0:= A^\upharpoonright{\xker\,}({\Gamma}_0)$ is self-adjoint and the following Green's formula holds} \begin{equation}\label{3.1} (A_f, g) - (f, A_g) = ({\Gamma}_1f, {\Gamma}_0 g)_{\cH} - ({\Gamma}_0 f, {\Gamma}_1 g)_{\cH}, \qquad f,g\in{\rm dom\,}(A_), \end{equation} where $A_:= A^\upharpoonright{\rm dom\,}(\Gamma).$ } \end{definition} { By definition, { $A_* := A^\upharpoonright{\rm dom\,}(\Gamma)$} and $A_ \subseteq A^* = \overline{A_}$ and $(A_)^=A.$} Clearly, every ordinary boundary triplet is a generalized boundary triplet. \begin{lemma}[{\cite[Proposition 6.1]{DM95}}]\label{lem3.2} Let $A$ be a densely defined closed symmetric operator and let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A^.$ Then the following assertions are true: \item[\;\;{\rm (i)}] ${\mathfrak N}^_{z}:={\rm dom\,}(A_)\cap{\N}_{z}$ is dense in $\mathfrak N_{z}$ and ${\rm dom\,}(A_) ={\rm dom\,}(A_0) + \mathfrak N^_{z}$; \item[\;\;{\rm (ii)}] $\overline{{\Gamma}_1{\rm dom\,}(A_0)}=\cH$; \item[\;\;{\rm (iii)}] ${\xker\,}({\Gamma}) = {\rm dom\,}(A)$ and ${\overline{{\rm ran\,}({\Gamma})}} = \cH \oplus \cH$. \end{lemma} \begin{lemma}\label{lem3.3} Let $A$ be a densely defined closed symmetric operator and let $\Pi = \{\cH, \Gamma_0, \Gamma_1\}$ be a generalized boundary triplet for $A^$. Then the mapping ${\Gamma} = \{{\Gamma}_0,{\Gamma}_1\}^\top$ is closable and $\overline{{\Gamma}} \in \cC(\gH_+, \cH)$. \end{lemma} \begin{proof} The Green's formula can be rewritten as $(A_f,g) - (f,A_g) = (J{\Gamma} f,{\Gamma} g)$ where ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top$ and $J := \begin{pmatrix} 0 & I\\ -I & 0 \end{pmatrix}$. Let $f_n\in{\rm dom\,}(\Gamma_0)\cap{\rm dom\,}(\Gamma_1)={\rm dom\,}(A_),$\ $\\|f_n\\|_{\gH_+}\to 0$ and $\Gamma	-0.246453	-0.990506	0.262242	2.220655	[ -0.4830649249760768, -0.009842064257005092 ]	[ -1.4310010503153519, -0.5500117883109703 ]	[ -0.3065102304654469, 0.8309938694193978 ]	[ 1.8668684721566307, 2.5744411851214153 ]	1,024	[ 512, 512 ]	[ 29913, 448, 13, 29898, 29909, 1665, 17458, 29918, 29906, 7402, 29920, 21604, 29896, 1012, 262, 741, 7237, 317, 2403, 29886, 1194, 29887, 29950, 29897, 320, 8208, 25874, 28751, 13, 29905, 17458, 29918, 29896, 448, 320, 17458, 29918, 29906, 320, 262, 741, 7237, 317, 2403, 29886, 1194, 29883, 29950, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 29905, 7235, 29912, 15263, 1891, 10452, 21954, 1372, 322, 1571, 17752, 29913, 13, 13, 797, 8324, 278, 6964, 310, 10452, 21954, 1372, 338, 2086, 13, 5060, 4146, 573, 29889, 2266, 591, 17386, 777, 17099, 373, 28803, 10452, 13, 3626, 552, 1372, 1494, 320, 2036, 29912, 23560, 29929, 29945, 1836, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29961, 14683, 29871, 29953, 29889, 29896, 3199, 23560, 29929, 29945, 930, 10725, 1643, 29912, 1753, 29941, 29889, 29896, 29913, 13, 741, 331, 13, 29912, 319, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 338, 2000, 263, 13, 29905, 7278, 29912, 17492, 1891, 10452, 21954, 29873, 363, 395, 29909, 6622, 17133, 565, 779, 29883, 29950, 29938, 338, 385, 13, 2993, 2638, 653, 12338, 2151, 2913, 322, 426, 7555, 6642, 2403, 29926, 29901, 2802, 1758, 2432, 5940, 4678, 6642, 29918, 29926, 29897, 320, 517, 29905, 29883, 29950, 29938, 1118, 395, 29926, 13, 29922, 29871, 29900, 29892, 29896, 29938, 526, 5608, 13, 655, 27775, 1316, 393, 426, 7555, 1758, 2432, 5940, 4678, 6642, 29897, 3490, 2802, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29900, 29897, 320, 5030, 2802, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29896, 1262, 13, 275, 263, 7136, 363, 395, 29909, 6622, 29938, 1118, 13, 29938, 741, 6642, 2403, 29900, 29938, 338, 1190, 25674, 29892, 395, 29909, 29918, 29900, 9361, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 338, 13, 1311, 29899, 328, 12090, 322, 278, 1494, 7646, 29915, 29879, 7063, 29871, 8640, 29913, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29896, 29913, 13, 29898, 29909, 24563, 29888, 29892, 330, 29897, 448, 313, 29888, 29892, 319, 24563, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 2802, 6642, 2403, 29900, 330, 29897, 1665, 29883, 29950, 29913, 448, 313, 741, 6642, 2403, 29900, 285, 29892, 2802, 6642, 2403, 29896, 13, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 24563, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 29871, 395, 29909, 24563, 9361, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 4678, 6642, 467, 29938, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29912, 2648, 5023, 29892, 426, 395, 29909, 24563, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 4678, 6642, 1262, 29913, 322, 395, 29909, 24563, 13, 29905, 11725, 319, 6622, 353, 320, 6875, 29912, 29909, 24563, 1042, 322, 2427, 29909, 24563, 4887, 29930, 29922, 29909, 7449, 29913, 29871, 17732, 368, 29892, 29871, 1432, 13, 24310, 10452, 21954, 29873, 338, 263, 28803, 10452, 21954, 29873, 29889, 13, 29905, 463, 29912, 13846, 4400, 741, 2036, 29961, 1184, 3283, 29871, 29953, 29889, 29896, 3199, 23560, 29929, 29945, 930, 10725, 1643, 29912, 2409, 29941, 29889, 29906, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 322, 1235, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29871, 263, 28803, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 7449, 1987, 278, 1494, 4974, 1080, 526, 1565, 29901, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 29875, 2915, 29962, 7555, 7237, 405, 2137, 29930, 648, 29920, 6177, 21854, 1758, 2432, 5940, 2119, 29909, 24563, 2144, 5030, 741, 29940, 3227, 29920, 1042, 338, 13, 1145, 344, 297, 779, 7237, 405, 648, 29920, 1042, 322, 7555, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 353, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 320, 7237, 405, 6622, 648, 29920, 1042, 29936, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 2236, 2915, 29962, 779, 6875, 16195, 6642, 2403, 29896, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 2915, 2013, 29883, 29950, 22073, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 25609, 2915, 29962, 7555, 29916, 3946, 5940, 2119, 741, 6642, 1800, 353, 2802, 1758, 2432, 5940, 2119, 29909, 1262, 322, 13, 29938, 741, 6875, 16195, 1758, 6350, 5940, 2119, 741, 6642, 1800, 930, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 13846, 1012, 1643, 29912, 2409, 29941, 29889, 29941, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 322, 1235, 13, 4535, 12197, 353, 320, 741, 29883, 29950, 29892, 320, 6642, 29918, 29900, 29892, 320, 6642, 29918, 29896, 11854, 367, 263, 28803, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 1504, 1987, 278, 10417, 7555, 6642, 29913, 353, 9991, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 29905, 10206, 3332, 29938, 13, 275, 4694, 519, 322, 779, 6875, 16195, 6642, 930, 320, 262, 320, 29883, 29907, 1194, 29887, 29950, 28842, 29892, 320, 29883, 29950, 4935, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1576, 7646, 29915, 29879, 7063, 508, 367, 337, 17625, 408, 2427, 29909, 24563, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 24563, 29887, 29897, 353, 13, 29898, 29967, 741, 6642, 29913, 285, 29892, 741, 6642, 29913, 330, 1262, 988, 29871, 7555, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29938, 322, 29871, 395, 29967, 3490, 13, 29905, 463, 29912, 12571, 29913, 13, 29900, 669, 306, 1966, 13, 29899, 29902, 669, 29871, 29900, 13, 29905, 355, 29912, 12571, 4311, 13, 12024, 395, 29888, 29918, 29876, 29905, 262, 741, 1758, 2432, 5940, 4678, 6642, 29918, 29900, 2144, 5030, 741, 1758, 2432, 5940, 4678, 6642, 29918, 29896, 3892, 741, 1758, 2432, 5940, 2119, 29909, 24563, 511, 4535, 13, 4535, 29989, 29888, 29918, 29876, 7893, 1665, 29887, 29950, 28842, 1012, 517, 29871, 29900, 29938, 322, 779, 6642 ]	1,332,863	12,288	ArXiv	-1	-1
f_n=\{\Gamma_0 f_n,\Gamma_1 f_n\}\to\{\varphi, \psi\}$ as $n\to\infty$. Hence \begin{displaymath} 0 = \lim_{n\to\infty}[(A_f_n, g) - (f_n, A_ g)] = \left(Jf_\infty,{\Gamma} g\right), \quad \mbox{where} \quad f_\infty := \{\varphi, \psi \}^\top. \end{displaymath} Since ${\rm ran\,}({\Gamma})$ is dense in $\cH \oplus \cH$ one has $Jf_\infty = 0$. Thus, $\varphi=\psi=0$ and $\Gamma$ is closable. \end{proof} For any generalized boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ we set $A_j:=A^\upharpoonright{\xker\,}({\Gamma}_j)$, $j \in \{0,1\}$. The extensions $A_0$ and $A_1$ are disjoint but not necessarily transversal. The latter holds if and only if $\Pi$ is an ordinary boundary triplet. In general, the extension $A_1$ is only essentially self-adjoint. Starting with Definition \ref{def3.1}, one easily extends the definitions of ${\gamma}$-field and Weyl function to the case of a generalized boundary triplet $\Pi$ by analogy with Definition \ref{Weylfunc} (cf. {\cite[Definition 6.2]{DM95}}). \begin{definition} \label{def3.2} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A^.$ Then the operator valued functions $\gamma(\cdot)$ and $M(\cdot)$ defined by \begin{equation}\label{3.3A} \gamma(z):=\bigl(\Gamma_0\!\upharpoonright\mathfrak N^_z\bigr)^{-1}:\ \cH\to \mathfrak N_{z} \;\;\text{and}\;\;M(z):=\Gamma_1\gamma(z), \;\;z\in\varrho(A_0), \end{equation} are called the (generalized) {\em $\gamma$-field} and the {\em Weyl function} associated with the generalized boundary triplet $\Pi$, { respectively}. \end{definition} It follows from Lemma \ref{lem3.2}(i) that $\gamma(\cdot)$ takes values in $[\cH, \gH]$, ${\rm ran\,}({\gamma}(z))=\mathfrak N^_{z} := {\rm dom\,}(A_*) \cap \mathfrak N_z$ and it satisfies the identity similar to that of \eqref{2.15} which shows that ${\gamma}(z)$ is a holomorphic operator valued function on $\varrho(A_0)$. Further, one has ${\rm dom\,} (M(z))= \cH$ since ${\rm ran\,}\gamma(z)\subset {\rm dom\,}({\Gamma}_1),\ z\in\varrho(A_0).$ By \eqref{3.3A} $M(z)$ is closable since $\gamma(z)$ is bounded and ${\Gamma}_1$ is closable, by Lemma \ref{lem3.3}. Hence, by the closed graph theorem $M(\cdot)$ takes values in $[\cH]$. Moreover, it is holomorphic on $\varrho(A_0)$, because so is $\gamma(\cdot)$, and satisfies the relation \eqref{mlambda}. It follows that ${\xker\,}(\im M(z)) =\{0\}, \ z\in \C_+,$ though the stronger condition $0 \in \varrho(\im M(i)) (\Longleftrightarrow {\rm ran\,}({\gamma}(i))=\mathfrak N_{i})$ is satisfied if and only if $\Pi$ is an ordinary boundary triplet (in the sense of Definition \ref{t1.9}). In the sequel we need the following simple but useful statement. \begin{proposition}\label{prop3.1} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1	0.102471	-1.137338	0.170303	2.137411	[ 0.04289043975944719, 0.16205220208233934 ]	[ -1.1803130489319913, -1.0943628770291247 ]	[ 0.0828027669310384, 0.25780339768255295 ]	[ 2.1374109800549306, 2.1374109800549306 ]	1,024	[ 512, 512 ]	[ 285, 29918, 29876, 2013, 741, 6642, 29918, 29900, 285, 29918, 29876, 2053, 6642, 29918, 29896, 13, 29888, 29918, 29876, 25848, 517, 24976, 6827, 29892, 320, 6134, 11854, 408, 395, 29876, 29905, 517, 29905, 3411, 1504, 10133, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29900, 353, 320, 2576, 648, 29876, 29905, 517, 29905, 3411, 4400, 29898, 29909, 24563, 29888, 29918, 29876, 29892, 330, 29897, 448, 313, 29888, 29918, 29876, 29892, 319, 24563, 330, 4638, 353, 13, 29905, 1563, 29898, 29967, 29888, 3187, 3411, 29892, 741, 6642, 29913, 330, 29905, 1266, 511, 320, 3425, 320, 8264, 29912, 3062, 29913, 320, 3425, 285, 3187, 3411, 3490, 13, 24976, 6827, 29892, 29871, 320, 6134, 320, 10206, 3332, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 7555, 1758, 6350, 5940, 2119, 741, 6642, 8435, 338, 20619, 297, 779, 29883, 29950, 320, 17201, 320, 29883, 29950, 29938, 697, 756, 395, 29967, 29888, 3187, 3411, 353, 29871, 29900, 1504, 13, 1349, 375, 29892, 779, 6827, 2013, 6134, 29922, 29900, 29938, 322, 779, 6642, 29938, 338, 4694, 519, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 2831, 738, 28803, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 591, 13, 842, 395, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 5767, 395, 29926, 320, 262, 9991, 29900, 29892, 29896, 23699, 450, 13, 24299, 395, 29909, 29918, 29900, 29938, 322, 395, 29909, 29918, 29896, 29938, 526, 766, 12090, 541, 451, 12695, 13, 3286, 874, 284, 29889, 450, 7480, 8640, 565, 322, 871, 565, 779, 12197, 29938, 338, 385, 15311, 13, 9917, 653, 21954, 29873, 29889, 512, 2498, 29892, 278, 6081, 395, 29909, 29918, 29896, 29938, 338, 871, 13674, 13, 1311, 29899, 328, 12090, 29889, 13, 13, 4763, 292, 411, 21940, 320, 999, 29912, 1753, 29941, 29889, 29896, 1118, 29871, 697, 5948, 29871, 4988, 278, 13, 25476, 2187, 310, 7555, 4283, 23021, 2671, 322, 399, 1032, 29880, 740, 13, 517, 278, 1206, 310, 263, 28803, 10452, 21954, 29873, 779, 12197, 29938, 491, 13, 7054, 6933, 411, 21940, 320, 999, 29912, 29956, 1032, 29880, 9891, 29913, 313, 6854, 29889, 2802, 2036, 29961, 14683, 13, 29953, 29889, 29906, 3199, 23560, 29929, 29945, 930, 467, 13, 29905, 463, 29912, 16553, 29913, 320, 1643, 29912, 1753, 29941, 29889, 29906, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29871, 263, 28803, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 7449, 259, 1987, 278, 5455, 659, 6742, 3168, 779, 4283, 1194, 3822, 1262, 13, 392, 395, 29924, 1194, 3822, 1262, 29871, 3342, 491, 13, 320, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29941, 29909, 29913, 13, 29905, 4283, 29898, 29920, 1125, 2013, 3752, 29880, 1194, 6642, 29918, 29900, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 29905, 7237, 405, 6622, 29918, 29920, 29905, 3752, 29878, 21604, 29896, 29913, 3583, 13, 29905, 29883, 29950, 29905, 517, 320, 7237, 405, 648, 29920, 29913, 320, 10436, 10436, 726, 29912, 392, 1012, 10436, 29936, 29924, 29898, 29920, 1125, 2013, 6642, 29918, 29896, 29905, 4283, 29898, 29920, 511, 13, 29905, 10436, 29936, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 598, 2000, 278, 313, 17492, 1891, 29897, 2802, 331, 779, 4283, 4388, 2671, 29913, 322, 278, 2802, 331, 13, 29956, 1032, 29880, 740, 29913, 6942, 411, 278, 28803, 13, 9917, 653, 21954, 29873, 779, 12197, 1628, 426, 8307, 1836, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 3112, 4477, 515, 29871, 11894, 320, 999, 29912, 2409, 29941, 29889, 29906, 2119, 29875, 29897, 393, 779, 4283, 1194, 3822, 1262, 4893, 13, 5975, 297, 395, 7110, 29883, 29950, 29892, 320, 29887, 29950, 25473, 7555, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29920, 876, 2013, 7237, 405, 6622, 648, 29920, 29913, 3490, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 13, 29905, 5030, 320, 7237, 405, 29918, 29920, 29938, 322, 372, 17150, 278, 10110, 2788, 304, 393, 310, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29945, 29913, 607, 3697, 393, 7555, 4283, 2119, 29920, 1262, 13, 275, 263, 8753, 16898, 5455, 659, 6742, 740, 373, 13, 4535, 1707, 4650, 29898, 29909, 29918, 29900, 4935, 13, 13, 29943, 332, 721, 29892, 697, 756, 7555, 1758, 2432, 5940, 29913, 313, 29924, 29898, 29920, 876, 29922, 320, 29883, 29950, 29938, 1951, 7555, 1758, 6350, 5940, 1012, 4283, 29898, 29920, 2144, 6484, 13, 741, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29896, 20481, 29871, 503, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 467, 29938, 2648, 320, 4915, 29912, 29941, 29889, 29941, 29909, 29913, 395, 29924, 29898, 29920, 1262, 13, 275, 4694, 519, 29871, 1951, 779, 4283, 29898, 29920, 1262, 338, 12635, 322, 7555, 6642, 2403, 29896, 29938, 338, 4694, 519, 29892, 13, 1609, 11894, 320, 999, 29912, 2409, 29941, 29889, 29941, 1836, 29871, 10133, 29892, 491, 278, 5764, 3983, 9185, 395, 29924, 1194, 3822, 1262, 13, 29873, 6926, 1819, 297, 395, 7110, 29883, 29950, 22689, 12808, 29892, 372, 338, 8753, 16898, 373, 13, 4535, 1707, 4650, 29898, 29909, 29918, 29900, 5767, 1363, 577, 338, 779, 4283, 1194, 3822, 5767, 322, 17150, 278, 13, 23445, 320, 4915, 29912, 828, 2269, 1836, 13, 3112, 4477, 393, 7555, 29916, 3946, 5940, 4678, 326, 341, 29898, 29920, 876, 353, 10045, 29900, 29905, 1118, 320, 29871, 503, 29905, 262, 320, 29907, 28842, 8209, 2466, 278, 13, 1110, 261, 4195, 395, 29900, 320, 262, 320, 1707, 4650, 1194, 326, 341, 29898, 29875, 876, 3441, 8208, 25874, 28751, 13, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 876, 2013, 7237, 405, 648, 29875, 8435, 338, 15787, 565, 322, 871, 565, 779, 12197, 29938, 13, 275, 385, 15311, 10452, 21954, 29873, 313, 262, 278, 4060, 310, 21940, 13, 29905, 999, 29912, 29873, 29896, 29889, 29929, 7690, 13, 13, 797, 278, 8617, 295, 591, 817, 278, 1494, 2560, 541, 5407, 3229, 29889, 13, 268, 320, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29941, 29889, 29896, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896 ]	1,332,863	13,312	ArXiv	-1	-1
\}$ be an ordinary boundary triplet for $A^$, $M(\cdot)$ the corresponding Weyl function, $B=B^ \in \cC(\cH)$ and $A_B = A^\upharpoonright {\xker\,}({\Gamma}_1 - B{\Gamma}_0)$. Let ${\Gamma}^B_1 :={\Gamma}_0$ and ${\Gamma}^B_0 := B{\Gamma}_0-{\Gamma}_1$. Then \item[\;\;\rm (i)] $\Pi_B=\{\cH,{\Gamma}^B_0,{\Gamma}^B_1\}$ is a generalized boundary triplet for $A^$ such that it holds ${\rm dom\,}(A_) := {\rm dom\,}({\Gamma}) := {\rm dom\,}(A_0) + {\rm dom\,}(A_B) \subseteq {\rm dom\,}(A^)$, $A^_ = A$; \item[\;\;\rm (ii)] the corresponding (generalized) Weyl function $M_B(\cdot)$ is \begin{displaymath} M_B(z)=\left(B-M(z)\right)^{-1}, \qquad z\in\C_\pm; \end{displaymath} \item[\;\;\rm (iii)] $\Pi_B$ is an (ordinary) boundary triplet if and only if $B = B^* \in[\cH]$. In this case $M_B(\cdot)$ is an ordinary Weyl function in the sense of Definition \ref{t1.9}. \end{proposition} Note, an analogon of Proposition \ref{prop2.1} does not hold for generalized boundary triplets. Nevertheless, since the corresponding Weyl function determines the pair $\{A,A_0\}$ uniquely, up to unitary equivalence, it is possible to describe the spectral properties of $A_0$ in terms of the (generalized) Weyl function $M(\cdot).$ \section{Weyl function and spectral multiplicity} Throughout of this section $A$ is a densely defined simple closed symmetric operator in $\gH$ with $n_+(A) = n_-(A).$ Let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized} boundary triplet for $A^$, and { let $M(\cdot)$ be} the corresponding generalized Weyl function. Since $M(\cdot)\in (R_{\cH})$ it admits representation \eqref{1.2}. Since $A$ is densely defined (see \cite{DM95, Ma92b}), one gets $C_1 = 0$, i.e. \begin{displaymath} M(z) = C_0 + \int^\infty_{-\infty} \left(\frac{1}{t-z} - \frac{t}{1+t^2}\right)d{\Sigma}_M. \end{displaymath} \begin{proposition}\Label{IV.6} Let $A$ be a densely defined, simple closed symmetric operator and let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A_ (\subseteq A^)$, $A^_* = A$, and { let} $M(\cdot)$ { be} the corresponding Weyl function. If $E_{A_0}$ is the spectral measure of $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$, then ${\Sigma}_M \thickapprox E_{A_0}$ and ${\Sigma}^{ac}_M \thickapprox E^{ac}_{A_0}$. \end{proposition} \begin{proof} Alongside ${\Sigma}_M(\cdot)$ we introduce the bounded operator measure ${\Sigma}^0_M(\cdot),$ \begin{displaymath} {\Sigma}^0_M({\delta}) = \int_{\delta} \frac{1}{1+t^2} \;d{\Sigma}_M, \qquad {\delta} \in \cB_b(\R). \end{displaymath} Clearly, ${\Sigma}^0_M(\cdot) \thickapprox {\Sigma}_M(\cdot)$. According to \cite[formula (2.16)]{ABMN05	0.162052	-1.067503	0.232441	2.459981	[ 0.2332753243902749, 0.0908290797744038 ]	[ -0.9045562474102946, -1.2304506492086633 ]	[ 0.3338906284440811, 0.1309913464133395 ]	[ 2.532819260829369, 2.3871425258072074 ]	1,024	[ 512, 512 ]	[ 11854, 367, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 1628, 395, 29924, 1194, 3822, 1262, 278, 6590, 399, 1032, 29880, 740, 29892, 259, 395, 29933, 29922, 29933, 6622, 320, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 322, 395, 29909, 29918, 29933, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 448, 350, 741, 6642, 2403, 29900, 4935, 2803, 13, 29938, 741, 6642, 2137, 29933, 29918, 29896, 3490, 741, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2137, 29933, 29918, 29900, 3490, 350, 741, 6642, 2403, 29900, 29899, 741, 6642, 2403, 29896, 1504, 1987, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 779, 12197, 29918, 29933, 2013, 741, 29883, 29950, 29892, 741, 6642, 2137, 29933, 29918, 29900, 29892, 741, 6642, 2137, 29933, 29918, 29896, 11854, 29871, 338, 263, 13, 17492, 1891, 10452, 21954, 29873, 363, 395, 29909, 6622, 29938, 1316, 393, 372, 8640, 13, 29938, 741, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 3490, 2802, 1758, 2432, 5940, 2119, 741, 6642, 1800, 3490, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29933, 29897, 320, 11725, 13, 741, 1758, 2432, 5940, 2119, 29909, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 22073, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 278, 6590, 29871, 313, 17492, 1891, 29897, 399, 1032, 29880, 740, 13, 29938, 29924, 29918, 29933, 1194, 3822, 1262, 338, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29918, 29933, 29898, 29920, 7950, 1563, 29898, 29933, 29899, 29924, 29898, 29920, 2144, 1266, 21604, 29896, 1118, 320, 12014, 503, 29905, 262, 29905, 29907, 3187, 3358, 29936, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 25609, 4638, 259, 779, 12197, 29918, 29933, 29938, 338, 385, 313, 24310, 29897, 10452, 21954, 29873, 565, 13, 392, 871, 565, 395, 29933, 353, 350, 6622, 320, 262, 7110, 29883, 29950, 22689, 512, 445, 1206, 395, 29924, 29918, 29933, 1194, 3822, 1262, 338, 385, 15311, 13, 29956, 1032, 29880, 740, 297, 278, 4060, 29871, 310, 21940, 320, 999, 29912, 29873, 29896, 29889, 29929, 1836, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 9842, 29892, 385, 15690, 265, 29871, 310, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 947, 451, 4808, 363, 13, 17492, 1891, 10452, 21954, 1372, 29889, 13, 29940, 1310, 16561, 29892, 1951, 278, 6590, 399, 1032, 29880, 740, 3683, 1475, 278, 13, 18784, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 20498, 873, 29892, 701, 304, 5190, 653, 24796, 29892, 29871, 372, 338, 13, 27338, 304, 8453, 278, 23161, 4426, 310, 395, 29909, 29918, 29900, 29938, 13, 262, 4958, 310, 278, 313, 17492, 1891, 29897, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 467, 29938, 13, 13, 29905, 2042, 29912, 29956, 1032, 29880, 740, 322, 23161, 6674, 17024, 29913, 13, 13, 29911, 1092, 820, 449, 310, 445, 4004, 395, 29909, 29938, 338, 263, 6245, 873, 3342, 13, 12857, 5764, 18348, 5455, 297, 779, 29887, 29950, 29938, 411, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 467, 29938, 13, 12024, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 28803, 29913, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 392, 29871, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 28803, 399, 1032, 29880, 740, 29889, 13, 23036, 395, 29924, 1194, 3822, 2144, 262, 313, 29934, 1665, 29883, 29950, 8435, 372, 7336, 1169, 8954, 13, 29905, 4915, 29912, 29896, 29889, 29906, 1836, 4001, 13, 395, 29909, 29938, 338, 6245, 873, 3342, 313, 4149, 320, 2036, 29912, 23560, 29929, 29945, 29892, 3219, 29929, 29906, 29890, 9594, 697, 4947, 395, 29907, 29918, 29896, 353, 29871, 29900, 1628, 474, 29889, 29872, 29889, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29898, 29920, 29897, 353, 315, 29918, 29900, 29871, 718, 320, 524, 3823, 3411, 648, 2612, 3411, 29913, 13, 29905, 1563, 1194, 1154, 29912, 29896, 1157, 29873, 29899, 29920, 29913, 448, 13, 29871, 320, 1154, 29912, 29873, 1157, 29896, 29974, 29873, 29985, 29906, 1012, 1266, 29897, 29881, 741, 10142, 2403, 29924, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 5667, 29889, 29953, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 29892, 2560, 5764, 18348, 5455, 322, 13, 1026, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 28803, 10452, 21954, 29873, 13, 1454, 395, 29909, 24563, 3441, 11725, 319, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 1628, 259, 322, 426, 1235, 29913, 13, 29938, 29924, 1194, 3822, 1262, 426, 367, 29913, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 960, 395, 29923, 648, 29909, 29918, 29900, 1042, 338, 278, 23161, 13, 26658, 310, 395, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 769, 7555, 10142, 2403, 29924, 13, 29905, 27996, 14850, 382, 648, 29909, 29918, 29900, 1042, 322, 7555, 10142, 2844, 562, 2403, 29924, 320, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29900, 4311, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2499, 549, 2975, 7555, 10142, 2403, 29924, 1194, 3822, 1262, 591, 14944, 278, 29871, 12635, 29871, 5455, 5645, 13, 29938, 741, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 511, 29938, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 10142, 2137, 29900, 29918, 29924, 13670, 4181, 1800, 353, 320, 524, 1665, 4181, 29913, 320, 1154, 29912, 29896, 1157, 29896, 29974, 29873, 29985, 29906, 29913, 18175, 29881, 741, 10142, 2403, 29924, 29892, 320, 12014, 13, 741, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 18759, 368, 29892, 7555, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 29897, 320, 27996, 14850, 29871, 2802, 10142, 2403, 29924, 1194, 3822, 4935, 13, 29871, 7579, 304, 320, 2036, 29961, 689, 2497, 313, 29906, 29889, 29896, 29953, 29897, 3199, 2882, 29924, 29940, 29900, 29945 ]	1,332,863	14,336	ArXiv	-1	-1
} one has \begin{equation}\label{2.15A} {\Sigma}^0_M({\delta}) = {\gamma}(i)^E_{A_0}({\delta}){\gamma}(i), \qquad {\delta} \in \cB(\R), \end{equation} where ${\gamma}(\cdot)$ is the generalized ${\gamma}$-field of ${\Pi}$. Note, that though formula \eqref{2.15A} is proved in \cite{ABMN05} for ordinary boundary triplets, the proof remains valid for generalized boundary triplets. Due to the simplicity of $A$ one has \begin{displaymath} {\rm span\,}\left\{(A_0 - z)^{-1}{\rm ran\,}({\gamma}(i)): \quad z \in \C_+ \cup \C_-\right\} = \gH. \end{displaymath} Hence the subspace $\mathfrak{N}_i := \overline{{\mathfrak N}^_i},$ where ${\mathfrak N}^_i := {\rm ran\,}({\gamma}(i))$ is cyclic for $A_0$. Next, let $P_i$ be the orthogonal projection from $\gH$ onto $\mathfrak{N}_i$. We set $\widetilde{{\Sigma}}^0_M(\cdot) := P_iE_{A_0}(\cdot)\upharpoonright{\mathfrak N}_i$. Clearly, $\widetilde{{\Sigma}}^0_M(\cdot)$ is an operator measure. Since the linear manifold ${\mathfrak N}^_i$ is cyclic for $A_0$, one gets from \cite[Theorem 4.15]{MM03} that the measures $\widetilde{{\Sigma}}^0_M$ and $E_{A_0}$ are spectrally equivalent. Note that ${\Sigma}^0_M(\cdot) = {\gamma}(i)^\widetilde{{\Sigma}}^0_M(\cdot){\gamma}(i)$. Since ${\rm ran\,}({\gamma}(i))$ is dense in ${\mathfrak N}_i$, the latter yields ${\Sigma}^0_M \thicksim \wt{\Sigma}^0_M$. Let $D\in {\mathfrak S}_2(\cH)$ and ${\xker\,}(D) = {\xker\,}(D^) = \{0\}$. We set \begin{displaymath} \Psi_{D^{\Sigma}^0_MD}(t) := \frac{dD^{\Sigma}^0_M(t)D}{d\rho(t)} \quad \mbox{and} \quad \Psi_{\wt D^\wt {\Sigma}^0_M\wt D}(t) := \frac{d\widetilde{D}^\widetilde{{\Sigma}}^0_M(t)\widetilde{D}}{d\rho(t)} \end{displaymath} where $\rho$ is a scalar measure such that $\widetilde{{\Sigma}}^0_M \thicksim \rho$ and $\widetilde{D} := {\gamma}(i)D: \cH \longrightarrow {\mathfrak N}_i$. We note that ${\xker\,}(\widetilde{D}) = {\xker\,}(\widetilde{D}^) = \{0\}$. By \cite[Corollary 4.7]{MM03} we have \begin{displaymath} N_{{\Sigma}^0_M}(t) = {\rm rank\,}(\Psi_{D^{\Sigma}^0_MD}(t)) \quad \mbox{and} \quad N_{\wt {\Sigma}^0_M}(t) = {\rm rank\,}(\Psi_{\wt D^\wt {\Sigma}^0_M\wt D}(t)) \end{displaymath} for a.e. $t \in \R$ (${\rm mod}(\rho)$). Since $\Psi_{D^{\Sigma}^0_MD}(t) = \Psi_{\wt D^*\wt {\Sigma}^0_M\wt D}(t)$ for a.e. $t \in \R$ (${\rm mod}(\rho)$) we get $N_{{\Sigma}^0_M}(t) = N_{\widetilde{{\Sigma}}^0_M}(t)$ for a.e. $t \in \R$ (${\rm mod}(\rho)$). Hence $\widetilde{{\Sigma}}^0_M$ and ${\Sigma}^0_M$ are spectrally equivalent. Since $\wt{\Sigma}^0_M$ and $E_{A_0}$ are spectrally equivalent the measures ${{\	-0.153658	-1.438164	-0.27988	2.127005	[ 0.13876771978936042, -0.44608368839311024 ]	[ -1.130175448655319, -1.7461516806258623 ]	[ 0.016860500271047407, -0.5766198996688716 ]	[ 2.241465790785046, 2.012545207178792 ]	1,024	[ 512, 512 ]	[ 29913, 697, 756, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29945, 29909, 29913, 2802, 10142, 2137, 29900, 29918, 29924, 13670, 4181, 1800, 353, 2802, 4283, 2119, 29875, 4887, 29930, 29923, 648, 29909, 29918, 29900, 2119, 741, 4181, 1800, 741, 4283, 2119, 29875, 511, 13, 29905, 12014, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 1194, 29934, 511, 320, 355, 29912, 2573, 29913, 13, 3062, 7555, 4283, 4678, 3822, 1262, 338, 278, 28803, 7555, 4283, 23021, 2671, 310, 13, 29938, 741, 12197, 4311, 3940, 29892, 393, 2466, 7063, 320, 4915, 29912, 29906, 29889, 29896, 29945, 29909, 29913, 13, 275, 11827, 297, 320, 2036, 29912, 2882, 29924, 29940, 29900, 29945, 29913, 363, 15311, 10452, 21954, 1372, 29892, 278, 5296, 9242, 2854, 13, 1454, 28803, 10452, 21954, 1372, 29889, 16809, 304, 278, 23205, 310, 395, 29909, 29938, 13, 650, 756, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 1758, 10638, 5940, 1012, 1563, 29905, 8001, 29909, 29918, 29900, 448, 503, 21604, 29896, 3331, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 22164, 320, 3425, 503, 320, 262, 320, 29907, 28842, 320, 5231, 13, 29905, 29907, 29918, 2612, 1266, 18105, 353, 320, 29887, 29950, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29950, 663, 278, 1014, 3493, 779, 7237, 29912, 29940, 2403, 29875, 3490, 13, 29905, 6875, 16195, 7237, 405, 2137, 29930, 29918, 29875, 1118, 29938, 988, 7555, 7237, 405, 2137, 29930, 29918, 29875, 3490, 13, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 23846, 338, 5094, 28746, 363, 395, 29909, 29918, 29900, 1504, 8084, 29892, 1235, 395, 29925, 29918, 29875, 29938, 367, 278, 13, 2072, 23419, 18246, 515, 779, 29887, 29950, 29938, 11480, 779, 7237, 29912, 29940, 2403, 29875, 1504, 13, 4806, 731, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 29897, 3490, 13, 29925, 29918, 29875, 29923, 648, 29909, 29918, 29900, 4678, 3822, 2144, 29884, 561, 279, 1129, 265, 1266, 741, 7237, 405, 2403, 29875, 1504, 13, 13, 18759, 368, 29892, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 1262, 338, 385, 5455, 5645, 29889, 13, 23036, 278, 5608, 25941, 7555, 7237, 405, 2137, 29930, 29918, 29875, 29938, 338, 5094, 28746, 13, 1454, 395, 29909, 29918, 29900, 1628, 697, 4947, 515, 320, 2036, 29961, 28831, 29871, 29946, 29889, 29896, 29945, 3199, 7428, 29900, 29941, 29913, 393, 278, 13, 1004, 25414, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 13, 13, 9842, 393, 7555, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 29897, 353, 13, 741, 4283, 2119, 29875, 4887, 17710, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 21964, 4283, 2119, 29875, 4935, 4001, 13, 29938, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 23846, 338, 20619, 297, 7555, 7237, 405, 2403, 29875, 1628, 278, 7480, 13, 17498, 7555, 10142, 2137, 29900, 29918, 29924, 320, 27996, 3601, 320, 14554, 741, 10142, 2137, 29900, 29918, 29924, 1504, 2803, 395, 29928, 29905, 262, 13, 741, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 322, 29871, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 13, 10045, 29900, 23699, 1334, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 29897, 3490, 320, 1154, 29912, 29881, 29928, 6622, 741, 10142, 2137, 29900, 29918, 29924, 29898, 29873, 29897, 29928, 1157, 29881, 29905, 4650, 29898, 29873, 2915, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29905, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 29897, 3490, 13, 29905, 1154, 29912, 29881, 29905, 10737, 29912, 29928, 2137, 17710, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29898, 29873, 2144, 10737, 29912, 29928, 7585, 29881, 29905, 4650, 29898, 29873, 2915, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 779, 4650, 29938, 338, 263, 17336, 5645, 1316, 13, 5747, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29871, 320, 27996, 3601, 320, 4650, 29938, 322, 13, 4535, 10737, 29912, 29928, 29913, 3490, 2802, 4283, 2119, 29875, 29897, 29928, 29901, 320, 29883, 29950, 320, 24225, 13, 741, 7237, 405, 2403, 29875, 1504, 1334, 4443, 393, 7555, 29916, 3946, 5940, 4678, 10737, 29912, 29928, 1800, 353, 13, 741, 29916, 3946, 5940, 4678, 10737, 29912, 29928, 2137, 7528, 353, 9991, 29900, 23699, 2648, 29871, 320, 2036, 29961, 12521, 21982, 13, 29946, 29889, 29955, 3199, 7428, 29900, 29941, 29913, 591, 505, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29940, 24033, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 2802, 1758, 7115, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 876, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29940, 1665, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 2802, 1758, 7115, 5940, 4678, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 876, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 3255, 741, 1758, 878, 4678, 4650, 1262, 467, 4001, 779, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 29897, 353, 13, 29905, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 13, 1566, 741, 1758, 878, 4678, 4650, 1262, 29897, 591, 679, 395, 29940, 24033, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 13, 29940, 1665, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 3255, 741, 1758, 878, 4678, 4650, 1262, 467, 13, 29950, 663, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29938, 322, 7555, 10142, 2137, 29900, 29918, 29924, 29938, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 4001, 779, 14554, 741, 10142, 2137, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 278, 15366, 6435, 741 ]	1,332,863	15,360	ArXiv	-1	-1
Sigma}}^0_M$ and $E_{A_0}$ are spectrally equivalent. This proves the first statement. The second statement follows from the equality ${\Sigma}^{0,ac}_M({\delta}) = {\gamma}(i)^E^{ac}_{A_0}({\delta}){\gamma}(i),$\ ${\delta} \in \mathcal \cB(\R)$ where ${\Sigma}^{0,ac}_M$ is the absolutely continuous part of ${\Sigma}^0_M$. \end{proof} The proof of Proposition \ref{IV.6} leads to the following computing procedure for $N_{{\Sigma}^{ac}_M}(t)$: choosing $D \in {\mathfrak S}_2(\cH) $ { such that} ${\xker\,}(D) = {\xker\,}(D^) = \{0\}$ we introduce the sandwiched Weyl function $M^D(\cdot)$, \begin{displaymath} (M^D)(z) := D^M(z)D, \quad z \in \C_+. \end{displaymath} It turns out that the limit $(M^D)(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M^D(t+iy)$ exists for a.e. $t \in \R$. We define in accordance with \eqref{2.13a} the function $d_{M^D}(\cdot): \R \to \N\cup\{\infty\}$, \begin{displaymath} d_{M^D}(t) := {\rm rank\,}(\im(M^D(t))) = {\rm dim}({\rm ran\,}(\im(M^D(t)))) \end{displaymath} which is well-defined for a.e. $t \in \R$. For a measurable non-negative function $\xi: \R \longrightarrow \R_+$ defined for a.e. $t \in \R$ we introduce its support ${\rm supp\,}(\xi) := \{t \in \R: \ \xi(t)>0\}$. By ${\rm cl}_{ac}(\cdot)$ we denote the absolutely continuous closure of a Borel set of $\R$., cf. Appendix. \begin{proposition}\Label{III.8} Let $A$ be as in Proposition \ref{IV.6}, { let} ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ { be} a generalized boundary triplet for $A_ (\subseteq A^)$, $A^_* = A$, and { let} $M(\cdot)$ { be} the corresponding Weyl function. Further, let $E_{A_0}(\cdot)$ be the spectral measure of $A_0 = A_\upharpoonright{\xker\,}({\Gamma}_0)= A_0^.$ If $D \in \gotS_2(\cH)$ { and} satisfies ${\xker\,}( D) = {\xker\,}(D^*) = \{0\}$, then $N_{E^{ac}_{A_0}}(t) = d_{M^D}(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_{M^D}))$. If, in addition, the limit $M(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ exists for a.e. $t \in \R$, then $N_{E^{ac}_{A_0}}(t) = d_M(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_M))$. \end{proposition} \begin{proof} The relation $N_{E^{ac}_{A_0}}(t) = d_{M^D}(t)$ follows from Theorem \ref{II.4} and Theorem \ref{IV.6}. Further, let $\{g_k\}^N_{k=1}$, $1 \le N \le \infty$, be a total set in $\cH$. We set $h_k := Dg_k$. One easily verifies that $\{h_n\}^N_{n=1}$	0.017209	-1.253729	0.110701	2.022951	[ 0.07439297462641867, -0.03997492369497782 ]	[ -1.3522133927377242, -1.1552442487936552 ]	[ 0.08533900795642267, 0.13606382846410806 ]	[ 1.8252465478645845, 2.220654828639023 ]	1,024	[ 512, 512 ]	[ 10142, 24251, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 910, 29871, 28281, 29871, 278, 937, 3229, 29889, 13, 13, 1576, 29871, 1473, 3229, 4477, 515, 278, 17193, 13, 29938, 741, 10142, 2844, 29900, 29892, 562, 2403, 29924, 13670, 4181, 1800, 353, 2802, 4283, 2119, 29875, 4887, 29930, 29923, 998, 562, 3227, 29909, 29918, 29900, 2119, 741, 4181, 1800, 741, 4283, 2119, 29875, 511, 4535, 29871, 7555, 4181, 29913, 13, 29905, 262, 320, 1942, 320, 29883, 29933, 1194, 29934, 1262, 988, 7555, 10142, 2844, 29900, 29892, 562, 2403, 29924, 29938, 338, 278, 13312, 13, 20621, 681, 760, 310, 7555, 10142, 2137, 29900, 29918, 29924, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 1576, 5296, 310, 22206, 320, 999, 29912, 5667, 29889, 29953, 29913, 11981, 304, 278, 1494, 13, 12097, 292, 8792, 363, 395, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 1262, 29901, 23906, 13, 29938, 29928, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 29897, 395, 426, 1316, 393, 29913, 13, 29938, 741, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 11854, 591, 14944, 13, 1552, 11982, 16416, 287, 399, 1032, 29880, 740, 395, 29924, 29985, 29928, 1194, 3822, 5767, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29924, 29985, 29928, 5033, 29920, 29897, 3490, 360, 6622, 29924, 29898, 29920, 29897, 29928, 29892, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3112, 12169, 714, 393, 278, 4046, 2427, 29924, 29985, 29928, 5033, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29985, 29928, 29898, 29873, 29974, 19881, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 1334, 4529, 13, 262, 15017, 749, 411, 320, 4915, 29912, 29906, 29889, 29896, 29941, 29874, 29913, 278, 740, 13, 29938, 29881, 648, 29924, 29985, 29928, 4678, 3822, 1125, 320, 29934, 320, 517, 320, 29940, 29905, 5231, 24976, 3411, 28538, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 3490, 2802, 1758, 7115, 5940, 4678, 326, 29898, 29924, 29985, 29928, 29898, 29873, 4961, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29985, 29928, 29898, 29873, 13697, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 4716, 338, 1532, 29899, 12119, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 13, 2831, 263, 7540, 21115, 1661, 29899, 22198, 740, 779, 5389, 29901, 320, 29934, 320, 24225, 13, 29905, 29934, 29918, 24035, 3342, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 591, 14944, 967, 2304, 13, 29938, 741, 1758, 1462, 5940, 4678, 5389, 29897, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 320, 29871, 320, 5389, 29898, 29873, 15410, 29900, 23699, 2648, 7555, 1758, 1067, 3227, 562, 4678, 3822, 1262, 13, 29871, 591, 13530, 278, 13312, 9126, 18424, 310, 263, 6780, 295, 731, 310, 13, 29871, 779, 29934, 1504, 29892, 274, 29888, 29889, 22871, 861, 29889, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 5287, 29889, 29947, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 22206, 320, 999, 29912, 5667, 29889, 29953, 1118, 426, 1235, 29913, 7555, 12197, 29913, 353, 13, 24976, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 426, 367, 29913, 263, 28803, 10452, 21954, 29873, 363, 13, 29938, 29909, 24563, 3441, 11725, 319, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 1628, 29871, 322, 426, 1235, 29913, 395, 29924, 1194, 3822, 1262, 13, 29912, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 8725, 29892, 1235, 13, 29938, 29923, 648, 29909, 29918, 29900, 4678, 3822, 1262, 367, 278, 23161, 5645, 310, 395, 29909, 29918, 29900, 353, 13, 29909, 29918, 17710, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 3892, 319, 29918, 29900, 6622, 7449, 960, 395, 29928, 320, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 13, 29912, 322, 29913, 17150, 7555, 29916, 3946, 5940, 2119, 360, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 28538, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 1504, 13, 13, 3644, 29892, 297, 6124, 29892, 278, 4046, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 4864, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 395, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 29918, 29924, 29898, 29873, 1262, 363, 263, 29889, 29872, 29889, 13, 29938, 29873, 320, 262, 320, 29934, 29938, 322, 7555, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 29918, 29924, 876, 1504, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1576, 8220, 395, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 4477, 13, 3166, 10244, 320, 999, 29912, 2687, 29889, 29946, 29913, 322, 10244, 320, 999, 29912, 5667, 29889, 29953, 1836, 8725, 29892, 1235, 13, 4535, 29912, 29887, 29918, 29895, 29905, 2137, 29940, 648, 29895, 29922, 29896, 4429, 395, 29896, 320, 280, 405, 320, 280, 320, 3411, 1628, 367, 263, 3001, 731, 297, 779, 29883, 29950, 1504, 13, 4806, 731, 395, 29882, 29918, 29895, 3490, 360, 29887, 29918, 29895, 1504, 3118, 5948, 1147, 11057, 393, 13, 4535, 29912, 29882, 29918, 29876, 29905, 2137, 29940, 648, 29876, 29922, 29896, 1042 ]	1,332,863	16,384	ArXiv	-1	-1
is a total set. We set $M_{h_n}(z) := (M(z)h_n,h_n)$, $z \in \C_+$. Clearly, $M_{h_n}(z)$ is $R$-function for {\color{black} every} $n \in \{ 1,2,\ldots,N\}$ and \begin{displaymath} M_{h_n}(t) := \lim_{y\to+0}M_{h_n}(t+iy) = (M(t)h_n,h_n) \end{displaymath} exists for a.e. $t \in \R$. Set \begin{displaymath} {\Omega}_{ac}(M_{h_n}) := \{t \in \R: \; 0 < \im(M_{h_n}(t)) < \infty\}. \end{displaymath} Combining \cite[Proposition 4.1]{BMN02} with Lemma \ref{III.7} we obtain \begin{equation}\Label{3.23} {\sigma}_{ac}(A_0) = \overline{\bigcup^N_{k=1}{\rm cl}_{ac}({\Omega}_{ac}(M_{h_n}))} = {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right). \end{equation} If $t \in {\rm supp\,}(d_{M^D})$, then $\im((M^D)(t)) \not= 0$. Hence $t \in {\Omega}_{ac}(M_{h_n})$ for some $n \in \{ 1,2,\dots,N\}.$ Therefore ${\rm supp\,}(d_{M^D}) \subseteq \bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})$ which yields \begin{equation}\Label{3.24} {\rm cl}_{ac}({\rm supp\,}(d_{M^D})) \subseteq {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right). \end{equation} Conversely, if $t \in {\Omega}_{ac}(M_{h_n}) \cap \cE_{M^D}$, where $\cE_{M^D} := \{t \in \R: \; \exists\;(M^D)(t)\}$, for some $n$, then $0 < d_{M^ D}(t)$. Hence ${\Omega}_{ac}(M_{h_n}) \cap \cE_{M^D} \subseteq {\rm supp\,}(d_{M^D})$ which yields $\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n}) \cap \;\cE_{M^D} \subseteq {\rm supp\,}(d_{M^D})$. Hence \begin{equation} {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n}) \cap \; \cE_M\right) = {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right) \subseteq {\rm cl}_{ac}({\rm supp\,}(d_{M^D})) \end{equation} Combining this equality with \eqref{3.23} and \eqref{3.24} we obtain ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_{M^D}))$. \end{proof} \begin{corollary}\Label{IV.9} Let $A$ be as in Proposition \ref{III.8}, { let }$\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ { be} an ordinary boundary triplet for $A^$ and { let} $M(\cdot)$ { be} the corresponding Weyl function. Further, let $B= B^ \in \cC(\cH)$, $A_B = A^*\upharpoonright {\xker\,}({\Gamma}_1 - B{\Gamma}_0)$ and $E_{A_B}(\cdot)$ the spectral measure of $A_B$. If $D\in \gotS_2(\cH)$ { and satisfies } ${\xker\,}(	-0.394036	-1.688852	-0.363893	1.825247	[ -0.32144322435422307, -0.4666288198280917 ]	[ -1.5169512222182184, -1.8607519098296845 ]	[ -0.28748842277506487, -0.4402969445544671 ]	[ 1.773219142499527, 1.8772739532296423 ]	1,024	[ 512, 512 ]	[ 338, 263, 3001, 731, 29889, 1334, 731, 395, 29924, 648, 29882, 29918, 29876, 2119, 29920, 29897, 3490, 13, 29898, 29924, 29898, 29920, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 5767, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 17732, 368, 29892, 395, 29924, 648, 29882, 29918, 29876, 2119, 29920, 1262, 338, 13, 29938, 29934, 4388, 2220, 363, 2802, 2780, 29912, 8517, 29913, 1432, 29913, 395, 29876, 320, 262, 9991, 29871, 29896, 29892, 29906, 2053, 7796, 29892, 29940, 11854, 29871, 322, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 648, 29882, 29918, 29876, 2119, 29873, 29897, 3490, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 648, 29882, 29918, 29876, 2119, 29873, 29974, 19881, 29897, 353, 313, 29924, 29898, 29873, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 3789, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 18175, 29871, 29900, 529, 320, 326, 29898, 29924, 648, 29882, 29918, 29876, 2119, 29873, 876, 529, 13, 29905, 3411, 29905, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1523, 2109, 292, 29871, 320, 2036, 29961, 1184, 3283, 29871, 29946, 29889, 29896, 3199, 29933, 29924, 29940, 29900, 29906, 29913, 411, 11894, 320, 999, 29912, 5287, 29889, 29955, 29913, 591, 13, 711, 2408, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29906, 29941, 29913, 13, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 13, 29905, 6875, 741, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 1758, 1067, 3227, 562, 2119, 741, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 20073, 29913, 353, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 467, 13, 320, 355, 29912, 2573, 29913, 13, 3644, 395, 29873, 320, 262, 2802, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 27394, 769, 779, 326, 3552, 29924, 29985, 29928, 5033, 29873, 876, 320, 1333, 29922, 29871, 29900, 1504, 10133, 13, 29938, 29873, 320, 262, 2802, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 8435, 363, 777, 29871, 395, 29876, 320, 262, 9991, 29871, 29896, 29892, 29906, 2053, 7778, 29892, 29940, 29905, 1836, 29938, 13, 8439, 1079, 7555, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 1800, 320, 11725, 13, 29905, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 8435, 607, 17498, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29906, 29946, 29913, 13, 741, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 320, 11725, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1168, 874, 873, 29892, 565, 395, 29873, 320, 262, 2802, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 29883, 29923, 648, 29924, 29985, 29928, 4429, 13, 3062, 779, 29883, 29923, 648, 29924, 29985, 29928, 29913, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 18175, 13, 29905, 9933, 23891, 29898, 29924, 29985, 29928, 5033, 29873, 2144, 4429, 363, 777, 395, 29876, 1628, 769, 395, 29900, 529, 270, 648, 29924, 29985, 13, 29928, 2119, 29873, 4935, 10133, 7555, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 29883, 29923, 648, 29924, 29985, 29928, 29913, 320, 11725, 13, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 8435, 607, 17498, 13, 4535, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 10436, 29883, 29923, 648, 29924, 29985, 29928, 29913, 13, 29905, 11725, 2802, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 23462, 10133, 13, 29905, 463, 29912, 2573, 4044, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 18175, 13, 29905, 29883, 29923, 29918, 29924, 29905, 1266, 29897, 353, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 29897, 320, 11725, 13, 741, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 13, 268, 320, 355, 29912, 2573, 4044, 13, 1523, 2109, 292, 445, 17193, 411, 29871, 320, 4915, 29912, 29941, 29889, 29906, 29941, 29913, 322, 320, 4915, 29912, 29941, 29889, 29906, 29946, 29913, 591, 13, 711, 2408, 7555, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 5667, 29889, 29929, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 22206, 320, 999, 29912, 5287, 29889, 29947, 1118, 29871, 426, 1235, 13, 1042, 29905, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 426, 29871, 367, 29913, 385, 15311, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 29938, 322, 426, 1235, 29913, 395, 29924, 1194, 3822, 1262, 426, 367, 29913, 278, 6590, 13, 29956, 1032, 29880, 740, 29889, 8725, 29892, 1235, 395, 29933, 29922, 350, 6622, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 5767, 395, 29909, 29918, 29933, 353, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 448, 350, 741, 6642, 2403, 29900, 1262, 322, 395, 29923, 648, 29909, 29918, 29933, 4678, 3822, 1262, 278, 13, 21494, 1705, 5645, 310, 395, 29909, 29918, 29933, 1504, 29871, 960, 395, 29928, 29905, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 426, 322, 13, 29879, 27685, 583, 500, 7555, 29916, 3946, 5940, 2119 ]	1,332,863	17,408	ArXiv	-1	-1
D) = {\xker\,}( D^) = \{0\}$, then $N_{E^{ac}_{A_B}}(t) = d_{M_B^D}(t)$ for a.e. $t\in \R$ and ${\sigma}_{ac}(A_B) = {\rm cl}_{ac}({\rm supp\,}(d_{M_B^D}))$. If, in addition, the limit $M_B(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M_B(t + iy)$ exists for a.e. $t \in \R$, then $N_{E^{ac}_{A_B}}(t) = d_{M_B}(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_B) = {\rm cl}_{ac}({\rm supp\,}(d_{M_B}))$. \end{corollary} \begin{proof} By Proposition \ref{prop3.1} ${\Pi}_B = \{\cH,{\Gamma}^B_0,{\Gamma}^B_1\}$ is a generalized boundary triplet for $A_ := A^\upharpoonright{\rm dom\,}(A_)$, ${\rm dom\,}(A_)= {\rm dom\,}(A_0) + {\rm dom\,}(A_B)$, and $M_B(z) = (B - M(z))^{-1}$, $z \in \C_+$, the corresponding generalized Weyl function. Clearly, $A_B = A_\upharpoonright{\xker\,}({\Gamma}^B_0)$. It remains to apply Proposition \ref{III.8}. \end{proof} This leads to the following theorem. \begin{theorem}\Label{IV.10} { Let $A$ be a densely defined closed symmetric operator, let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be an ordinary boundary triplet for $A^$ and let $M(\cdot)$ be the corresponding Weyl function. Further, let $A_B := A^\upharpoonright{\xker\,}({\Gamma}_1-B{\Gamma}_0)$, $B = B^* \in \cC(\cH)$, and $E_{A_B}(\cdot)$ the spectral measure of $A_B$. Let $D \in \gotS_2(\cH)$} { and } ${\xker\,}(D) = {\xker\,}(D^) = \{0\}$. Then \item[{\rm\;\;(i)}] { $A_0E^{ac}_{A_0}(\cD)$ is a part of $A_BE^{ac}_{A_B}(\cD)$} if and only if $d_{M^{ D}}(t) \le d_{M_B^{ D}}(t)$ for a.e. $t \in \cD.$ \item[{\rm\;\;(ii)}] $A_0E^{ac}_{A_0}(\cD)$ and $A_BE^{ac}_{A_B}(\cD)$ are unitarily equivalent if and only if $d_{M^D}(t) = d_{M_B^D}(t)$ for a.e. $t \in \cD.$ \end{theorem} \begin{proof} Without loss of generality we assume that $A$ is simple since the self-adjoint part of $A$ is contained as a direct summand in any self-adjoint extension of $A$. We to show that ${\Sigma}^{ac}_M({\delta}) = 0$ for some ${\delta} \in \cB_b(\R)$ if and only if $d_{M^D}(t) = 0$ for a.e $t \in {\delta}$. By the Berezanskii-Gel'fand-Kostyuchenko theorem \cite{Ber68,BS87} the derivative $\Psi_{{ D}^{\Sigma}_M{ D}}(t) :=\frac{d}{dt}{ D}^{\Sigma}(t){D}$ exists and the relation \begin{displaymath} {D}^{\Sigma}^{ac}_M({\delta}\cap\cD){ D} = \int_{{\delta}\cap\cD}	-0.345199	-1.491882	-0.344237	2.199844	[ -0.15665414930280971, -0.5337429158490309 ]	[ -1.4381635646405908, -1.5456012795191738 ]	[ -0.27353909713545144, -0.41493453430062444 ]	[ 2.241465790785046, 2.158221942200954 ]	1,024	[ 512, 512 ]	[ 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 360, 6622, 29897, 353, 9991, 29900, 28538, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 29905, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29933, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29918, 29933, 29985, 29928, 20073, 1504, 13, 13, 3644, 29892, 297, 6124, 29892, 278, 4046, 395, 29924, 29918, 29933, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29918, 29933, 29898, 29873, 13, 29974, 474, 29891, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29933, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29918, 29933, 20073, 1504, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 22206, 320, 999, 29912, 7728, 29941, 29889, 29896, 29913, 29871, 7555, 12197, 2403, 29933, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2137, 29933, 29918, 29900, 29892, 741, 6642, 2137, 29933, 29918, 29896, 11854, 338, 13, 29874, 28803, 10452, 21954, 29873, 363, 395, 29909, 24563, 29871, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29909, 24563, 5767, 7555, 1758, 2432, 5940, 2119, 29909, 24563, 3892, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29933, 5767, 13, 392, 29871, 395, 29924, 29918, 29933, 29898, 29920, 29897, 353, 313, 29933, 448, 341, 29898, 29920, 876, 3426, 29896, 4429, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 278, 6590, 13, 17492, 1891, 399, 1032, 29880, 740, 29889, 17732, 368, 29892, 395, 29909, 29918, 29933, 353, 13, 29909, 29918, 17710, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2137, 29933, 29918, 29900, 4935, 739, 9242, 304, 3394, 13, 1184, 3283, 320, 999, 29912, 5287, 29889, 29947, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 4013, 11981, 304, 278, 1494, 9185, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 5667, 29889, 29896, 29900, 29913, 13, 29912, 2803, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 29892, 1235, 13, 29938, 741, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 322, 1235, 395, 29924, 1194, 3822, 1262, 367, 278, 6590, 399, 1032, 29880, 740, 29889, 13, 29943, 332, 721, 29892, 1235, 395, 29909, 29918, 29933, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 29899, 29933, 741, 6642, 2403, 29900, 5767, 395, 29933, 353, 13, 29933, 6622, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 5767, 322, 395, 29923, 648, 29909, 29918, 29933, 4678, 3822, 1262, 278, 23161, 5645, 310, 13, 29938, 29909, 29918, 29933, 1504, 2803, 395, 29928, 320, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 29913, 426, 322, 500, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 13, 29922, 9991, 29900, 23699, 1987, 13, 13, 29905, 667, 29961, 741, 1758, 29905, 10436, 29936, 29898, 29875, 2915, 29962, 426, 395, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 13, 29874, 760, 310, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 29913, 565, 322, 871, 565, 13, 259, 395, 29881, 648, 29924, 998, 360, 12156, 29873, 29897, 320, 280, 270, 648, 29924, 29918, 29933, 998, 360, 12156, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 7449, 13, 13, 13, 29905, 667, 29961, 741, 1758, 29905, 10436, 29936, 29898, 2236, 2915, 29962, 395, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 13, 392, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 29871, 526, 443, 3673, 2354, 7126, 565, 322, 871, 565, 13, 29938, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 7449, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 3047, 449, 6410, 310, 2498, 537, 591, 5251, 393, 395, 29909, 29938, 338, 2560, 13, 16076, 278, 1583, 29899, 328, 12090, 760, 310, 395, 29909, 29938, 338, 11122, 408, 263, 1513, 13, 2083, 29885, 392, 297, 738, 1583, 29899, 328, 12090, 6081, 310, 395, 29909, 1504, 1334, 304, 1510, 13, 5747, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1800, 353, 29871, 29900, 29938, 363, 777, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 1262, 565, 322, 13, 6194, 565, 395, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 395, 29873, 320, 262, 2802, 4181, 4311, 2648, 278, 13, 29933, 406, 29920, 550, 1984, 29875, 29899, 29954, 295, 29915, 29888, 392, 29899, 29968, 520, 29891, 987, 264, 2901, 9185, 320, 2036, 29912, 17104, 29953, 29947, 29892, 9851, 29947, 29955, 29913, 13, 1552, 16291, 779, 14118, 648, 29912, 360, 2137, 29930, 741, 10142, 2403, 29924, 29912, 360, 12156, 29873, 29897, 584, 2013, 1154, 29912, 29881, 1157, 6008, 1157, 13, 29928, 2137, 29930, 741, 10142, 2119, 29873, 2597, 29928, 1042, 4864, 322, 278, 8220, 13, 29905, 463, 29912, 4990, 755, 29913, 426, 29928, 2137, 29930, 741, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 2597, 360, 29913, 353, 320, 524, 24033, 4181, 1012, 5030, 29905, 29883, 29928, 29913 ]	1,332,863	18,432	ArXiv	-1	-1
\Psi_{{ D}^{\Sigma}_M{D}}(t) dt, \quad {\delta} \in \cB_b, \end{displaymath} holds. One has ${\Sigma}^{ac}_M({\delta}) = 0$ if and only if $\Psi_{ D^{\Sigma}_MD}(t) = 0$ for a.e. $t \in {\delta}$. Since $d_{M^{ D}}(t) = {\rm dim}({\rm ran\,}(\Psi_{{D}^{\Sigma}_M{ D}}(t)))$ for a.e. $t \in \R$ we find that ${\Sigma}^{ac}_M({\delta}\cap\cD) = 0$ if and only if $d_{M^{ D}}(t) = 0$\ for a.e. $t \in {\delta}\cap\cD$. Similarly we prove that ${\Sigma}^{ac}_{M_B}({\delta}\cap\cD) = 0$ if and only if $d_{{ D}^{M_B}{ D}}(t) = 0$ for a.e. $t \in {\delta}\cap\cD$. (i) Since by assumption $d_{M^{D}}(t) \le d_{M_B^{ D}}(t)$ for a.e. $t \in \cD,$ one gets by the considerations above that ${\Sigma}^{ac}_M({\delta}\cap\cD) \prec {\Sigma}^{ac}_{M_B}({\delta}\cap\cD)$. By Theorem \ref{II.4} we have $N_{{\Sigma}^{ac}_M}(t) = d_{M^{D}}(t)$ and $N_{{\Sigma}^{ac}_{M_B}}(t) = d_{M_B^{D}}(t)$ for a.e $t \in \R$. Hence $N_{{\Sigma}^{ac}_M}(t) \le N_{{\Sigma}^{ac}_{M_B}}(t)$ for a.e. $t \in \cD$ which proves that the restricted measures ${\Sigma}^{ac}_M(\cdot\cap\cD)$ is spectrally subordinated to ${\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$, cf. Definition \ref{II.3}(i). Since ${\Sigma}^{ac}_M \thickapprox E^{ac}_{A_0}$ and ${\Sigma}^{ac}_{M_B} \thickapprox E^{ac}_{A_B},$ by Theorem \ref{IV.6}, we get that $E^{ac}_{A_0}(\cdot\cap\cD)$ is spectrally subordinated to $E^{ac}_{A_B}(\cdot\cap\cD)$. Applying Theorem \ref{II.4a}(i) we complete the proof. (ii) If $d_{M^{ D}}(t) = d_{{ D}^*{M_B}{ D}}(t)$ for a.e. $t \in \cD,$ then ${\Sigma}^{ac}_M(\cdot\cap\cD) \thicksim {\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$. By Theorem \ref{II.4}, $N_{{\Sigma}^{ac}_M}(t) = d_{M^D}(t)$ and $N_{{\Sigma}^{ac}_{M_B}}(t) = d_{M^D_B}(t)$ for a.e $t \in \R$ which implies that the operator measures ${\Sigma}^{ac}_M(\cdot\cap\cD)$ and ${\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$ are spectrally equivalent, cf. Definition \ref{II.3}(ii). By Theorem \ref{IV.6}, $E^{ac}_{A_0}(\cdot\cap\cD)$ and $E^{ac}_{A_B}(\cdot\cap\cD)$ are spectrally equivalent. Applying Theorem \ref{II.4a}(ii) we prove that the absolutely continuous parts $A_0E^{ac}_{A_0}(\cD)$ and $A_BE^{ac}_{A_B}(\cD)$ are unitarily equivalent. \end{proof} Theorem \ref{IV.10} reduces the problem of unitary equivalence of $ac$-parts of certain self-adjoint extensions of $A$ to investigation of the functions $d_{M^{D}}(\cdot)$ and $d_{M_B^{D	-0.416721	-1.674527	-0.218693	1.960518	[ -0.6789285113228996, -0.15451403144499917 ]	[ -1.8106143095530123, -1.538438765193935 ]	[ -0.46692747532100193, 0.029541705397968753 ]	[ 1.8460575100106076, 2.0749780936168616 ]	1,024	[ 512, 512 ]	[ 320, 14118, 648, 29912, 13, 29928, 2137, 29930, 741, 10142, 2403, 29924, 29912, 29928, 12156, 29873, 29897, 11636, 29892, 320, 3425, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 29892, 13, 320, 355, 29912, 4990, 755, 29913, 13, 23177, 29889, 3118, 756, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1800, 353, 29871, 29900, 29938, 565, 322, 871, 565, 779, 14118, 648, 13, 29928, 6622, 741, 10142, 2403, 5773, 2119, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 4311, 4001, 395, 29881, 648, 29924, 998, 13, 29928, 12156, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 14118, 648, 29912, 29928, 2137, 29930, 741, 10142, 2403, 29924, 29912, 360, 12156, 29873, 876, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 13, 705, 1284, 393, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 353, 29871, 29900, 29938, 565, 322, 871, 565, 395, 29881, 648, 29924, 998, 13, 29928, 12156, 29873, 29897, 353, 29871, 29900, 4535, 29871, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 1012, 5030, 29905, 29883, 29928, 1504, 20175, 591, 6356, 393, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 353, 29871, 29900, 29938, 565, 322, 871, 565, 395, 29881, 648, 29912, 360, 2137, 19740, 29924, 29918, 29933, 1157, 13, 29928, 12156, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 1012, 5030, 29905, 29883, 29928, 1504, 13, 13, 29898, 29875, 29897, 4001, 491, 11833, 395, 29881, 648, 29924, 998, 29928, 12156, 29873, 29897, 320, 280, 270, 648, 29924, 29918, 29933, 998, 360, 12156, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 8209, 29871, 697, 4947, 491, 278, 2050, 800, 2038, 393, 13, 29938, 741, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 320, 17990, 2802, 10142, 2844, 562, 3227, 29924, 29918, 29933, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 4935, 2648, 13, 28831, 320, 999, 29912, 2687, 29889, 29946, 29913, 591, 505, 395, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 353, 270, 648, 29924, 998, 29928, 12156, 29873, 1262, 322, 13, 29938, 29940, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 998, 29928, 12156, 29873, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 1504, 10133, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 320, 280, 405, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 29938, 13, 4716, 28281, 393, 278, 22078, 15366, 13, 29938, 741, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 338, 6683, 29878, 635, 1014, 4194, 630, 304, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 5767, 274, 29888, 29889, 21940, 320, 999, 29912, 2687, 29889, 29941, 2119, 29875, 467, 13, 23036, 7555, 10142, 2844, 562, 2403, 29924, 320, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29900, 1042, 322, 7555, 10142, 2844, 562, 3227, 29924, 29918, 29933, 29913, 13, 29905, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29933, 1118, 29938, 491, 10244, 320, 999, 29912, 5667, 29889, 29953, 1118, 591, 679, 393, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 338, 6683, 29878, 635, 1014, 4194, 630, 304, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 4935, 2401, 5890, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 2119, 29875, 29897, 591, 13, 8835, 278, 5296, 29889, 13, 13, 29898, 2236, 29897, 960, 395, 29881, 648, 29924, 998, 360, 12156, 29873, 29897, 353, 270, 648, 29912, 360, 2137, 19740, 29924, 29918, 29933, 1157, 360, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29883, 29928, 8209, 769, 7555, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 29897, 320, 27996, 3601, 13, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 4935, 2648, 10244, 320, 999, 29912, 2687, 29889, 29946, 1118, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 322, 395, 29940, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 29897, 13, 29922, 270, 648, 29924, 29985, 29928, 29918, 29933, 2119, 29873, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 29938, 607, 10469, 393, 13, 1552, 5455, 15366, 7555, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 322, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 526, 6683, 29878, 635, 7126, 29892, 274, 29888, 29889, 13, 14683, 320, 999, 29912, 2687, 29889, 29941, 2119, 2236, 467, 2648, 10244, 320, 999, 29912, 5667, 29889, 29953, 1118, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 322, 395, 29923, 998, 562, 3227, 29909, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 526, 13, 21494, 29878, 635, 7126, 29889, 29871, 2401, 5890, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 2119, 2236, 29897, 13, 705, 6356, 393, 278, 13312, 9126, 5633, 13, 29938, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 322, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 526, 443, 3673, 2354, 13, 1686, 27445, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 28831, 320, 999, 29912, 5667, 29889, 29896, 29900, 29913, 26830, 278, 1108, 310, 5190, 653, 13, 1686, 2561, 663, 310, 395, 562, 4388, 20895, 29871, 310, 3058, 1583, 29899, 328, 12090, 17752, 310, 13, 29938, 29909, 29938, 304, 22522, 310, 278, 3168, 395, 29881, 648, 29924, 998, 29928, 20828, 3822, 1262, 322, 13, 29938, 29881, 648, 29924, 29918, 29933, 998, 29928 ]	1,332,863	19,456	ArXiv	-1	-1
}}(\cdot).$ \begin{corollary} Let $A$ be as in Theorem \ref{IV.10}. { If the self-adjoint extensions { $\wt A$ and $\wt A'$ of $A$ are $ac$-minimal, then their $ac$-parts are unitarily equivalent.}} \end{corollary} \section{Unitary equivalence} \subsection{Preliminaries} In what follows we assume that $A$ is a densely defined simple closed symmetric operator in $\gotH$. By $A_0$ we denote a self-adjoint extension of $A$ which is fixed. Alongside $A_0$ we consider $\wt A = \wt A^\in {\rm Ext\,}_A$. Usually we assume that \begin{equation}\Label{5.0} (\wt A - i)^{-1} - (A_0 - i)^{-1} \in \gotS_\infty(\gotH). \end{equation} It is known (see \cite{DM91} that there exists a boundary triplet ${\Pi} := \{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^$ such that $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0)$. Of course, the boundary triplet ${\Pi}$ is not uniquely determined by the assumption $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0)$. { If $\Pi_1$ and $\Pi_2$ are two such boundary triplets of $A^$, then their Weyl functions $M_1(\cdot)$ and $M_2(\cdot)$ are related by \eqref{2.11} (cf. \cite{DM91})}. { Fix a boundary triplet ${\Pi} := \{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^$ such that $A_0 = A^{\xker\,}({\Gamma}_0)$. By Proposition \ref{prop2.1} there is a linear relation ${\Theta}= {\Theta}^ \in \wt\cC(\cH)$ such that $\wt A = A_{\Theta}$. In general, ${\Theta}$ is not the graph of an operator, ${\Theta} \not \in \cC(\cH)$. However, let us assume that ${\Theta}$ is the graph an operator $B$. By Proposition} \ref{prop2.9} { we get} that $(B - i)^{-1} \in \gotS_\infty(\gotH)$, that means, that $B$ is a self-adjoint operator with discrete spectrum. Hence, $\varrho(B)\cap \R \not = \emptyset.$ In what follows we assume without loss of generality that $0 \in \varrho(B).$ According to the polar decomposition { we have} $B^{-1} = DJD$ where \begin{equation}\label{4.2A} D := \|B\|^{-1/2} = D^* \in \gotS_\infty(\gotH) \quad \mbox{and} \quad J := {\rm sign}(B) = J^* = J^{-1}. \end{equation} Clearly, $D \in \gotS_\infty(\cH)$, ${\xker\,}(D) = \{0\}$, and $D$ commutes with $J$. We set \begin{equation}\label{4.2} G(z) := J - M^D(z), \quad z \in \C_+, \end{equation} { $M^D(z) := DM(z)D$, $z \in \C_+$, as usually}. Obviously, ${ M^D(z)}$ and $-G(z)$ are $R$-functions. We have ${\xker\,}(G(z)) = \{0\}$ for every $z \in \C_+$. Indeed, if $G(z)f = 0$, then $Jf = DM(z)Df.$ Hence, $\im(M(z)Df,Df) = \im(Jf,f) = 0$ which yields $Df = 0$ or $f = 0$. Since $J$ is a Fredholm operator satisfying ${\xker\,}(J) = {\xker\,}(J^*) = \{0\}$ we find by \	-0.199564	-1.345051	0.052368	2.012545	[ -0.26254718090727636, -0.13657984379654664 ]	[ -1.4310010503153519, -1.259100706509619 ]	[ 0.18678864897179345, -0.08205289971893909 ]	[ 1.9084903964486768, 2.1166000179089077 ]	1,024	[ 512, 512 ]	[ 20828, 3822, 467, 29938, 13, 29905, 463, 29912, 2616, 21982, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 1836, 426, 960, 278, 1583, 29899, 328, 12090, 13, 24299, 426, 779, 14554, 319, 29938, 322, 779, 14554, 319, 13090, 310, 395, 29909, 29938, 526, 395, 562, 4388, 1195, 3039, 29892, 13, 6098, 1009, 395, 562, 4388, 20895, 526, 443, 3673, 2354, 7126, 29889, 930, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 13, 13, 29905, 2042, 29912, 8325, 653, 24796, 29913, 13, 13, 29905, 7235, 29912, 6572, 2576, 262, 4314, 29913, 13, 13, 13, 797, 825, 29871, 4477, 591, 5251, 393, 395, 29909, 29938, 338, 263, 6245, 873, 3342, 13, 12857, 5764, 18348, 5455, 297, 779, 7085, 29950, 1504, 2648, 395, 29909, 29918, 29900, 29938, 591, 13530, 263, 13, 1583, 29899, 328, 12090, 6081, 310, 395, 29909, 29938, 607, 338, 4343, 29889, 13, 2499, 549, 2975, 395, 29909, 29918, 29900, 29938, 591, 2050, 29871, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1504, 13, 15922, 1474, 591, 5251, 393, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29900, 29913, 13, 1194, 14554, 319, 448, 474, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 3112, 338, 2998, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 29913, 393, 727, 4864, 263, 10452, 13, 3626, 552, 29873, 7555, 12197, 29913, 3490, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 1316, 393, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 4587, 3236, 29892, 278, 10452, 21954, 29873, 13, 29938, 741, 12197, 1042, 338, 451, 20498, 873, 10087, 491, 278, 11833, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 426, 960, 13, 4535, 12197, 29918, 29896, 29938, 322, 779, 12197, 29918, 29906, 29938, 526, 1023, 1316, 10452, 21954, 1372, 310, 395, 29909, 6622, 1628, 769, 13, 1552, 381, 399, 1032, 29880, 3168, 395, 29924, 29918, 29896, 1194, 3822, 1262, 322, 395, 29924, 29918, 29906, 1194, 3822, 1262, 526, 4475, 491, 320, 4915, 29912, 29906, 29889, 29896, 29896, 29913, 313, 6854, 29889, 13, 29905, 2036, 29912, 23560, 29929, 29896, 1800, 1836, 13, 13, 29912, 24778, 29871, 263, 10452, 21954, 29873, 7555, 12197, 29913, 3490, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 13, 29938, 29909, 6622, 29938, 1316, 393, 395, 29909, 29918, 29900, 353, 319, 6622, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 29871, 2648, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 727, 338, 263, 5608, 8220, 13, 29938, 741, 17458, 5369, 2802, 17458, 2137, 29930, 320, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 1316, 393, 779, 14554, 319, 353, 319, 1665, 17458, 4311, 13, 797, 2498, 29892, 29871, 7555, 17458, 1042, 338, 451, 278, 3983, 310, 385, 5455, 29892, 13, 29938, 741, 17458, 29913, 320, 1333, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 4935, 2398, 29892, 1235, 502, 5251, 393, 7555, 17458, 1042, 338, 13, 1552, 3983, 385, 5455, 395, 29933, 1504, 13, 2059, 22206, 29913, 320, 999, 29912, 7728, 29906, 29889, 29929, 29913, 426, 591, 679, 29913, 393, 2427, 29933, 448, 474, 21604, 29896, 29913, 320, 262, 13, 29905, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 5767, 393, 2794, 29892, 393, 395, 29933, 29938, 338, 263, 1583, 29899, 328, 12090, 13, 6891, 411, 19554, 18272, 29889, 10133, 29892, 779, 1707, 4650, 29898, 29933, 2144, 5030, 320, 29934, 13, 29905, 1333, 353, 320, 26153, 7449, 29871, 512, 825, 4477, 591, 5251, 1728, 6410, 310, 13, 4738, 2877, 393, 395, 29900, 320, 262, 320, 1707, 4650, 29898, 29933, 467, 29938, 7579, 304, 278, 16755, 13, 311, 510, 3283, 426, 591, 505, 29913, 395, 29933, 3426, 29896, 29913, 353, 23366, 29928, 29938, 988, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29906, 29909, 29913, 360, 3490, 891, 29933, 29989, 3426, 29896, 29914, 29906, 29913, 353, 360, 6622, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 29897, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 435, 3490, 2802, 1758, 1804, 2119, 29933, 29897, 353, 435, 6622, 353, 435, 3426, 29896, 1836, 320, 355, 29912, 2573, 29913, 13, 18759, 368, 29892, 395, 29928, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 29883, 29950, 5767, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 9991, 29900, 28538, 13, 392, 259, 395, 29928, 29938, 844, 2667, 411, 395, 29967, 1504, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29906, 29913, 13, 29954, 29898, 29920, 29897, 3490, 435, 448, 341, 29985, 29928, 29898, 29920, 511, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 27692, 29898, 29920, 29897, 29928, 1628, 29871, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 408, 5491, 1836, 25735, 29892, 13, 5303, 341, 29985, 29928, 29898, 29920, 15604, 322, 15727, 29954, 29898, 29920, 1262, 526, 395, 29934, 4388, 12171, 29889, 1334, 505, 7555, 29916, 3946, 5940, 2119, 29954, 29898, 29920, 876, 13, 29922, 9991, 29900, 11854, 363, 1432, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 14598, 29892, 565, 395, 29954, 29898, 29920, 29897, 29888, 353, 29871, 29900, 1628, 769, 395, 29967, 29888, 13, 29922, 27692, 29898, 29920, 29897, 29928, 29888, 7449, 10133, 29892, 779, 326, 29898, 29924, 29898, 29920, 29897, 29928, 29888, 29892, 29928, 29888, 29897, 353, 320, 326, 29898, 29967, 29888, 29892, 29888, 29897, 353, 29871, 29900, 29938, 607, 17498, 13, 29938, 29928, 29888, 353, 29871, 29900, 29938, 470, 395, 29888, 353, 29871, 29900, 1504, 4001, 395, 29967, 29938, 338, 263, 12001, 13376, 5455, 24064, 13, 29938, 741, 29916, 3946, 5940, 2119, 29967, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29967, 6622, 29897, 353, 9991, 29900, 11854, 591, 1284, 491, 320 ]	1,332,863	20,480	ArXiv	-1	-1
cite[Theorem 5.26]{Ka76} that $G(z)$ is boundedly invertible for $z \in \C_+$. We set $T(z) := G(z)^{-1}$, $z \in \cC_+$ { and note that $T(\cdot)$ is a Nevanlinna function because so is $M^D(\cdot).$} Moreover, $T(z) - J = T(z)M^D(z)J\in \gotS_\infty(\gotH)$ for $z \in \C_+$. \subsection{Trace class perturbations: Rosenblum-Kato theorem} Here we apply the Weyl function technique in order to obtain a simple and quite different proof of the classical Rosenblum-Kato theorem. In fact, we prove a generalization of the Rosenblum-Kato theorem due to Birman and Krein \cite{BirKrei62} which includes non-additive (trace class) perturbations. Our proof demonstrates the main idea of the proof of more general { results} contained in the next subsection. \begin{theorem}\Label{V.1} Let $A_0$ and $\wt A$ be self-adjoint operators in $\gH$ satisfying \begin{equation}\label{4.3} (\wt A - i)^{-1} - (A_0 - i)^{-1} \in \gotS_1(\gotH). \end{equation} Then the absolutely continuous parts $\wt A^{ac}$ and $A^{ac}_0$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{theorem} \begin{proof} To include the operators $\wt A^{ac}$ and $A^{ac}_0$ in the framework of extension theory we set \begin{displaymath} A:= { A_0}\upharpoonright {\rm dom\,}(A),\quad {\rm dom\,}(A)=\{f\in {\rm dom\,}({\wt A})\cap {\rm dom\,}(A_0):\ A_0f = {\wt A}f\}. \end{displaymath} { Obviously, we have $A := \wt A\upharpoonright{\rm dom\,}(A)$}. Clearly, $A$ is a closed symmetric operator in $\gH$ with equal deficiency indices and $A_0,\wt A\in {\rm Ext\,}_A$. { First we assume that $A$ is densely defined}. Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a (ordinary) boundary triplet for $A^,$ such that $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0)$, and { $M(\cdot)$ } the corresponding Weyl function. { By definition $\wt A = \wt A^\in {\rm Ext\,}_A$ and $\wt A$ and $A_0$ are disjoint, that is, ${\rm dom\,}(A) = {\rm dom\,}(A_0) \cap {\rm dom\,}(\wt A)$. Hence, by Proposition \ref{prop2.1}(ii), there exists an operator $B = B^\in \cC(\cH)$ such that $\wt A = A_B.$} It follows from \eqref{2.30} and \eqref{4.3} that $M_B(z) := (B - M(z))^{-1} \in \gotS_1(\cH)$ for $z \in \C_+$. In accordance with \cite[Lemma 2.4]{BirEnt67}, see also \cite{Yaf92}, the limits $M_B(t) := \lim_{y\to+0}M_B(t + iy)$ exist in $\gotS_2(\cH)$, for a.e $t \in \R$. By Theorem \ref{IV.10} it is { it suffices} to calculate the multiplicity function $d_{M_B}(t) := {\rm rank\,}(M_B(t)) = {\rm dim}({\rm ran\,}(\im(M_B(t))))$. { It follows from \eqref{4.2A} and \eqref{	0.315456	-0.866058	0.308528	2.303899	[ 0.381200270722141, 0.24971142953826003 ]	[ -0.609102531494191, -1.1230129343300803 ]	[ 0.49113757201790575, 0.125918864362571 ]	[ 2.3871425258072074, 2.220654828639023 ]	1,024	[ 512, 512 ]	[ 2036, 29961, 28831, 29871, 29945, 29889, 29906, 29953, 3199, 29968, 29874, 29955, 29953, 29913, 13, 5747, 395, 29954, 29898, 29920, 1262, 338, 12635, 368, 21292, 1821, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 1334, 731, 395, 29911, 29898, 29920, 29897, 13, 9361, 402, 29898, 29920, 21604, 29896, 4429, 395, 29920, 320, 262, 320, 29883, 29907, 29918, 24035, 426, 322, 4443, 393, 395, 29911, 1194, 3822, 1262, 338, 29871, 263, 13, 8139, 3703, 1915, 1056, 740, 1363, 577, 338, 29871, 395, 29924, 29985, 29928, 1194, 3822, 467, 17133, 12808, 29892, 29871, 395, 29911, 29898, 29920, 29897, 13, 29899, 435, 353, 323, 29898, 29920, 29897, 29924, 29985, 29928, 29898, 29920, 29897, 29967, 29905, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 1262, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 13, 13, 29905, 7235, 29912, 11591, 770, 22786, 800, 29901, 28929, 2204, 398, 29899, 29968, 1219, 9185, 29913, 13, 13, 10605, 591, 3394, 278, 399, 1032, 29880, 740, 11043, 297, 1797, 304, 13, 711, 2408, 263, 2560, 322, 3755, 1422, 5296, 310, 278, 14499, 13, 29934, 7749, 2204, 398, 29899, 29968, 1219, 9185, 29889, 13, 797, 2114, 29892, 591, 6356, 263, 2498, 2133, 310, 278, 28929, 2204, 398, 29899, 29968, 1219, 9185, 13, 29123, 304, 17853, 1171, 322, 7706, 262, 320, 2036, 29912, 29933, 381, 29968, 5803, 29953, 29906, 29913, 607, 7805, 13, 5464, 29899, 1202, 3321, 313, 15003, 770, 29897, 22786, 800, 29889, 8680, 5296, 9004, 1078, 13, 1552, 1667, 2969, 310, 278, 5296, 310, 901, 2498, 426, 2582, 29913, 11122, 297, 278, 13, 4622, 1014, 2042, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 29963, 29889, 29896, 29913, 13, 12024, 29871, 395, 29909, 29918, 29900, 29938, 322, 779, 14554, 319, 29938, 29871, 367, 29871, 1583, 29899, 328, 12090, 12768, 297, 779, 29887, 29950, 29938, 13, 29879, 27685, 5414, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29941, 29913, 13, 1194, 14554, 319, 448, 474, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 7085, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 11760, 278, 13312, 9126, 5633, 779, 14554, 319, 998, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 13, 974, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 1628, 8307, 29892, 29871, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1762, 3160, 278, 12768, 779, 14554, 319, 998, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 297, 278, 13, 4468, 310, 6081, 6368, 591, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29909, 9361, 426, 319, 29918, 29900, 1012, 29884, 561, 279, 1129, 265, 1266, 2802, 1758, 2432, 5940, 2119, 29909, 20481, 3425, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 7950, 29912, 29888, 29905, 262, 2802, 1758, 2432, 5940, 2119, 741, 14554, 319, 11606, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 1125, 29905, 29871, 319, 29918, 29900, 29888, 353, 2802, 14554, 319, 29913, 29888, 29905, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29912, 25735, 29892, 591, 505, 395, 29909, 3490, 320, 14554, 319, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29909, 1262, 1836, 13, 18759, 368, 29892, 395, 29909, 29938, 338, 263, 5764, 18348, 5455, 297, 779, 29887, 29950, 29938, 411, 13, 11745, 822, 293, 13396, 16285, 322, 29871, 395, 29909, 29918, 29900, 2053, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1504, 13, 13, 29912, 29871, 3824, 591, 5251, 393, 395, 29909, 29938, 338, 6245, 873, 3342, 1836, 2803, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 313, 24310, 29897, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 8209, 29871, 1316, 393, 395, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 322, 13, 29912, 29871, 395, 29924, 1194, 3822, 1262, 500, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 426, 2648, 13, 16553, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 13, 392, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 766, 12090, 29892, 393, 338, 29892, 7555, 1758, 2432, 5940, 2119, 29909, 29897, 353, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 13, 29905, 5030, 2802, 1758, 2432, 5940, 4678, 14554, 319, 4935, 10133, 29892, 491, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 2119, 2236, 511, 727, 13, 9933, 29871, 385, 5455, 395, 29933, 353, 350, 6622, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 1262, 1316, 393, 779, 14554, 319, 353, 319, 29918, 29933, 7449, 29913, 13, 13, 13, 3112, 4477, 515, 29871, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 322, 320, 4915, 29912, 29946, 29889, 29941, 29913, 393, 395, 29924, 29918, 29933, 29898, 29920, 29897, 3490, 313, 29933, 448, 13, 29924, 29898, 29920, 876, 3426, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 1262, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 29871, 512, 15017, 749, 411, 13, 29905, 2036, 29961, 29931, 331, 655, 29871, 29906, 29889, 29946, 3199, 29933, 381, 5292, 29953, 29955, 1118, 1074, 884, 320, 2036, 29912, 29979, 2142, 29929, 29906, 1118, 29871, 278, 13071, 13, 29938, 29924, 29918, 29933, 29898, 29873, 29897, 3490, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29918, 29933, 29898, 29873, 718, 474, 29891, 1262, 1863, 297, 779, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 5767, 29871, 363, 13, 29874, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 1504, 2648, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 29913, 372, 338, 426, 372, 9378, 1575, 29913, 13, 517, 8147, 278, 6674, 17024, 740, 395, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 3490, 13, 741, 1758, 7115, 5940, 2119, 29924, 29918, 29933, 29898, 29873, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29918, 29933, 29898, 29873, 13697, 1504, 13, 13, 29912, 739, 4477, 515, 29871, 320, 4915, 29912, 29946, 29889, 29906, 29909, 29913, 322, 320, 4915, 29912 ]	1,332,863	21,504	ArXiv	-1	-1
4.2} that} \begin{eqnarray} \lefteqn{ T(z) = G(z)^{-1} = \bigl(J - M^D(z)\bigr)^{-1} = \bigl(J - D M(z)D \bigr)^{-1} }\\ & & = D^{-1}\bigl(D^{-1}JD^{-1}-M(z)\bigr)^{-1}D^{-1} =\|B\|^{1/2}\bigl(B-M(z)\bigr)^{-1} \|B\|^{1/2}, \;\; z \in \C_+. \nonumber \end{eqnarray} { Combining this relation with \eqref{4.2A} yields} \begin{displaymath} M_B(z) := (B - M(z))^{-1} = DT(z)D, \qquad z \in \C_+. \end{displaymath} In turn, this equality implies \begin{equation}\label{4.5} \im(M_B(z)) = DT(z)^\im({ M^D(z)})T(z)D, \qquad z \in \C_+. \end{equation} { Moreover, since ${ M^D(z)} \in \gotS_1(\cH)$ and $T(z) - J \in \gotS_1$ for $z \in \C_+$, by \cite[Lemma 2.4]{BirEnt67} (see also \cite{Yaf92})}, { for a.e $t \in \R$ and $y\to 0$ there exist the limits $M^D(t)$ and $T(t)$ in $\gotS_2(\cH)$-norm of the Nevanlinna operator functions ${ M^D((t+iy))}$ and $T(t+iy)$, respectively.} Therefore passing to the limit in \eqref{4.5} as $y\to 0$ we get \begin{equation}\Label{5.3} \im(M_B(t)) = {D}T(t)^\im({ M^D(t)})T(t){D}\quad \text{for a.e.}\quad t \in \R. \end{equation} Therefore we find \begin{eqnarray}\Label{5.3a} \lefteqn{ d_{M_B}(t) = {\rm dim}({\rm ran\,}(\im(M_B(t)))) }\\ & & = {\rm dim}({\rm ran\,}(\sqrt{\im(M_B(t))}\,)) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}T(t)D)). \nonumber \end{eqnarray} Since $(J - { M^D(t)})T(t) = T(t)(J - { M^D(t)}) = I$ for a.e. $t \in \R,$ we find ${\rm ran\,}(T(t)) = \cH$ for a.e. $t \in \R$. Combining this relation with $\overline {{\rm ran\,}(D)} = \cH$ and \eqref{5.3a} we obtain \begin{equation}\Label{5.3b} d_{M_B}(t) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}\,)) = {\rm dim}({\rm ran\,}(\im({ M^D(t)}))) = d_{M^D}(t) \end{equation} for a.e. $t \in \R$. { Applying} Theorem \ref{IV.10}(ii) we complete this part of the proof. { If $A$ is not densely defined} { one can repeat the above reasonings applying only} the boundary triplet technique for non-densely defined symmetric operators developed in \cite{DM95, Ma92b}. It turns out that the proof above can easily be carried over to this case. \end{proof} In the following corollary we show that in proving of unitary equivalence of $A_0$ and $\wt A\in {\rm Ext\,}_A$ it suffices to { restrict the	-0.142701	-1.42742	0.019397	2.074978	[ -0.00573303797000881, -0.27966812376976086 ]	[ -1.3020757924610522, -1.5527637938444128 ]	[ -0.01864687408433236, 0.057440356677195714 ]	[ 2.1790329043469767, 1.9709232828867462 ]	1,024	[ 512, 512 ]	[ 29946, 29889, 29906, 29913, 393, 29913, 13, 29905, 463, 29912, 9441, 29913, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29911, 29898, 29920, 29897, 353, 402, 29898, 29920, 21604, 29896, 29913, 353, 320, 3752, 29880, 29898, 29967, 448, 341, 29985, 29928, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 353, 320, 3752, 29880, 29898, 29967, 448, 360, 341, 29898, 29920, 29897, 29928, 320, 3752, 29878, 21604, 29896, 29913, 500, 1966, 13, 29987, 669, 353, 360, 3426, 29896, 1012, 3752, 29880, 29898, 29928, 3426, 29896, 29913, 29967, 29928, 3426, 29896, 7402, 29924, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 29928, 3426, 29896, 29913, 13, 29922, 29989, 29933, 29989, 998, 29896, 29914, 29906, 1012, 3752, 29880, 29898, 29933, 29899, 29924, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 891, 29933, 29989, 998, 29896, 29914, 29906, 1118, 29871, 320, 10436, 29936, 13, 29871, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 13621, 13, 29905, 355, 29912, 9441, 29913, 13, 29912, 422, 2109, 292, 445, 8220, 411, 29871, 320, 4915, 29912, 29946, 29889, 29906, 29909, 29913, 17498, 29913, 13, 29871, 320, 463, 29912, 4990, 755, 29913, 13, 29924, 29918, 29933, 29898, 29920, 29897, 3490, 313, 29933, 448, 341, 29898, 29920, 876, 3426, 29896, 29913, 353, 360, 29911, 29898, 29920, 29897, 29928, 29892, 320, 12014, 13, 29871, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29871, 320, 355, 29912, 4990, 755, 29913, 13, 797, 2507, 29892, 29871, 445, 17193, 10469, 13, 418, 320, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29945, 29913, 13, 29905, 326, 29898, 29924, 29918, 29933, 29898, 29920, 876, 353, 360, 29911, 29898, 29920, 4887, 17710, 326, 3319, 341, 29985, 29928, 29898, 29920, 26972, 29911, 29898, 29920, 29897, 29928, 29892, 320, 12014, 503, 320, 262, 13, 29905, 29907, 28842, 29889, 13, 418, 320, 355, 29912, 2573, 29913, 13, 29912, 12808, 29892, 1951, 6435, 341, 29985, 29928, 29898, 29920, 2915, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 1262, 322, 395, 29911, 29898, 29920, 29897, 13, 29899, 435, 320, 262, 320, 7085, 29903, 29918, 29896, 29938, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 491, 320, 2036, 29961, 29931, 331, 655, 29871, 29906, 29889, 29946, 3199, 29933, 381, 5292, 29953, 29955, 29913, 13, 29898, 4149, 884, 320, 2036, 29912, 29979, 2142, 29929, 29906, 1800, 1118, 426, 29871, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 29938, 322, 395, 29891, 29905, 517, 29871, 29900, 29938, 13, 12711, 1863, 278, 13071, 395, 29924, 29985, 29928, 29898, 29873, 1262, 322, 395, 29911, 29898, 29873, 1262, 297, 779, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 26725, 12324, 13, 974, 278, 29871, 2448, 3703, 1915, 1056, 5455, 3168, 6435, 341, 29985, 29928, 3552, 29873, 29974, 19881, 876, 1042, 322, 13, 29938, 29911, 29898, 29873, 29974, 19881, 5767, 8307, 5003, 13, 8439, 1079, 6819, 304, 278, 4046, 297, 320, 4915, 29912, 29946, 29889, 29945, 29913, 408, 395, 29891, 29905, 517, 29871, 29900, 29938, 591, 679, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29941, 29913, 13, 29905, 326, 29898, 29924, 29918, 29933, 29898, 29873, 876, 353, 426, 29928, 29913, 29911, 29898, 29873, 4887, 17710, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 2597, 29928, 1012, 3425, 320, 726, 29912, 1454, 13, 29874, 29889, 29872, 29889, 1012, 3425, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 7857, 591, 1284, 13, 29905, 463, 29912, 9441, 1012, 4775, 29912, 29945, 29889, 29941, 29874, 29913, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29918, 29933, 29898, 29873, 13697, 29871, 500, 1966, 13, 29987, 669, 29871, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29918, 29933, 29898, 29873, 876, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 29913, 29911, 29898, 29873, 29897, 29928, 8106, 320, 13621, 320, 355, 29912, 9441, 29913, 13, 4001, 2427, 29967, 448, 13, 29912, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 29897, 353, 323, 29898, 29873, 5033, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 353, 306, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 8209, 591, 1284, 13, 29938, 741, 1758, 6350, 5940, 2119, 29911, 29898, 29873, 876, 353, 320, 29883, 29950, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 422, 2109, 292, 445, 8220, 13, 2541, 29871, 779, 6875, 426, 741, 1758, 6350, 5940, 2119, 29928, 2915, 353, 320, 29883, 29950, 29938, 322, 29871, 320, 4915, 29912, 29945, 29889, 29941, 29874, 29913, 29871, 591, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29941, 29890, 29913, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 3319, 341, 29985, 29928, 29898, 29873, 2915, 4961, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 426, 2401, 5890, 29913, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 591, 13, 8835, 445, 760, 310, 278, 5296, 29889, 13, 13, 29912, 960, 395, 29909, 29938, 338, 451, 6245, 873, 3342, 29913, 426, 697, 508, 12312, 278, 13, 27215, 2769, 886, 29871, 15399, 871, 29913, 29871, 278, 10452, 21954, 29873, 11043, 13, 1454, 1661, 29899, 21518, 873, 3342, 18348, 12768, 8906, 297, 13, 29905, 2036, 29912, 23560, 29929, 29945, 29892, 3219, 29929, 29906, 29890, 1836, 739, 12169, 714, 393, 278, 5296, 2038, 508, 29871, 5948, 13, 915, 8988, 975, 304, 445, 1206, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 797, 278, 1494, 29871, 1034, 21982, 591, 1510, 393, 297, 29871, 1326, 292, 310, 13, 5441, 653, 24796, 310, 29871, 395, 29909, 29918, 29900, 29938, 322, 779, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 372, 9378, 1575, 304, 13, 29912, 9250, 278 ]	1,332,863	22,528	ArXiv	-1	-1
consideration to disjoint extensions}. \begin{corollary}\Label{V.1A} Let $A$ be a densely defined closed symmetric operator in $\gH,$ { let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be} an ordinary boundary triplet for $A^$, and { let $M(\cdot)$ be} the corresponding Weyl function. Let also $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0)$ and $\cD \in \cB(\R)$. \item[\rm\;\;(i)] If $A^{ac}_0E_{A_0}(\cD)$ is a part { of} ${\wt A}^{ac} E_{\wt A}(\cD)$ for any extension $\wt A = {\wt A}^\in {\rm Ext\,}_A$ disjoint with $A_0,$ then $A^{ac}_0E_{A_0}(\cD)$ is a part { of} $\wt A^{ac}E_{\wt A}(\cD)$ for any extension $\wt A = \wt A^\in {\rm Ext\,}_A.$ \item[\rm\;\;(ii)] If $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $\wt A^{ac} E_{\wt A}(\cD)$ for any extension $\wt A = \wt A^\in {\rm Ext\,}_A$ disjoint with $A_0$, then $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to the absolutely continuous part $\wt A^{ac}E_{\wt A}(\cD)$ of any extension $\wt A = \wt A^\in {\rm Ext\,}_A.$ \end{corollary} \begin{proof} By Proposition \ref{prop2.1} an extension $\wt A\in {\rm Ext\,}_A$ which is not disjoint with $A_0$ admits a representation $\wt A_{\Theta}$ with ${\Theta}= {\Theta}^\in \wt\cC(\cH) \setminus \cC(\cH).$ { However}, ${\Theta}$ admits a decomposition $\cH = \cH_{\rm op} \oplus \cH_\infty,$ \ ${\Theta} = {\Theta}_{\rm op} \oplus {\Theta}_{\infty}$ where ${\Theta}_{\rm op}$ is the graph of the operator $B_{\rm op}= B_{\rm op}^\in \cC(\cH_{\rm op})$ (cf. Section 2). Denoting by $\pi_{\rm op}$ the orthogonal projection from $\cH$ onto $\cH_{\rm op}$ and $M_{\rm op}(z) := \pi_{\rm op}M(z)\upharpoonright\cH_{\rm op}$, we get $({\Theta} - M(z))^{-1} = (B_{\rm op} - M_{\rm op}(z))^{-1}\pi_{\rm op}.$ Therefore formula \eqref{2.30} takes the form \begin{displaymath} (A_{\Theta} - z)^{-1} - (A_0 - z)^{-1} = {\gamma}(z)(B_{\rm op} - M_{\rm op}(z))^{-1}\pi_{\rm op}{\gamma}(\overline{z})^, \quad z \in \C_\pm. \end{displaymath} Choose an operator $B_\infty = B_\infty^ \in \cC(\cH_\infty)$ such that $(B_\infty - i)^{-1} \in \gotS_1(\cH_\infty)$ and put $B = B_{\rm op} \oplus B_\infty.$ It follows from Proposition \ref{prop2.9} that \begin{displaymath} (A_{\Theta} - z)^{-1} - ({ A_B} - z)^{-1} \in \gotS_1(\gotH), \end{displaymath} since $(B_\infty - i)^{-1} \in \gotS_1(\cH_\infty).$ By Theorem \ref{V.1} the absolutely continuous parts $A^{ac}_{\Theta}$ and $A^{ac}_B$ of $A_{\Theta}$ and $A_B$, respectively, are unitarily equivalent. (i) Since by assumption $A^{ac}_0E_{A_0}(\cD)$ is	-0.100412	-1.287751	0.133528	2.376737	[ -0.21769031060756697, 0.016866606608470735 ]	[ -1.194638077582469, -1.3808634500386798 ]	[ 0.34910807459638665, -0.08205289971893909 ]	[ 2.303898677223115, 2.449575412245277 ]	1,024	[ 512, 512 ]	[ 19220, 304, 766, 12090, 17752, 1836, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 29963, 29889, 29896, 29909, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 779, 29887, 29950, 8209, 13, 29912, 1235, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29913, 29871, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 1628, 322, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 2803, 884, 13, 29938, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 322, 29871, 779, 29883, 29928, 320, 262, 320, 29883, 29933, 1194, 29934, 4935, 13, 13, 29905, 667, 7110, 1758, 29905, 10436, 29936, 29898, 29875, 4638, 960, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 760, 426, 310, 29913, 13, 29938, 741, 14554, 319, 2844, 562, 29913, 382, 1665, 14554, 319, 4678, 29883, 29928, 1262, 363, 738, 6081, 779, 14554, 319, 353, 2802, 14554, 13, 29909, 2137, 17710, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 766, 12090, 411, 395, 29909, 29918, 29900, 8209, 13, 6098, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 760, 426, 310, 29913, 779, 14554, 319, 998, 562, 29913, 29923, 1665, 14554, 13, 29909, 4678, 29883, 29928, 1262, 363, 738, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 13, 29905, 667, 7110, 1758, 29905, 10436, 29936, 29898, 2236, 4638, 960, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 29871, 779, 14554, 319, 998, 562, 29913, 382, 1665, 14554, 319, 4678, 29883, 29928, 1262, 13, 1454, 738, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 766, 12090, 411, 13, 29938, 29909, 29918, 29900, 1628, 769, 29871, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 278, 13312, 9126, 760, 29871, 779, 14554, 319, 998, 562, 29913, 29923, 1665, 14554, 13, 29909, 4678, 29883, 29928, 1262, 310, 738, 29871, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 385, 6081, 29871, 779, 14554, 319, 29905, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 607, 338, 451, 766, 12090, 411, 395, 29909, 29918, 29900, 29938, 7336, 1169, 263, 8954, 13, 4535, 14554, 319, 1665, 17458, 1042, 411, 29871, 7555, 17458, 5369, 2802, 17458, 2137, 17710, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 29897, 320, 15375, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 13, 29912, 2398, 1118, 7555, 17458, 1042, 29871, 7336, 1169, 263, 26227, 779, 29883, 29950, 353, 320, 29883, 29950, 1665, 1758, 1015, 29913, 320, 17201, 13, 29905, 29883, 29950, 3187, 3411, 8209, 320, 7555, 17458, 29913, 353, 2802, 17458, 6353, 1758, 1015, 29913, 320, 17201, 2802, 17458, 6353, 3411, 1042, 988, 13, 29938, 741, 17458, 6353, 1758, 1015, 1042, 338, 278, 3983, 310, 278, 5455, 395, 29933, 1665, 1758, 1015, 5369, 350, 1665, 1758, 13, 459, 2137, 17710, 262, 320, 29883, 29907, 1194, 29883, 29950, 1665, 1758, 1015, 8435, 313, 6854, 29889, 9779, 29871, 29906, 467, 3384, 11427, 491, 779, 1631, 1665, 1758, 13, 459, 1042, 278, 28143, 18246, 515, 779, 29883, 29950, 29938, 11480, 779, 29883, 29950, 1665, 1758, 1015, 1042, 322, 13, 29938, 29924, 1665, 1758, 1015, 2119, 29920, 29897, 3490, 320, 1631, 1665, 1758, 1015, 29913, 29924, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 1665, 1758, 1015, 4429, 591, 13, 657, 2427, 741, 17458, 29913, 448, 341, 29898, 29920, 876, 3426, 29896, 29913, 353, 313, 29933, 1665, 1758, 1015, 29913, 448, 341, 1665, 1758, 1015, 2119, 29920, 876, 3426, 29896, 1012, 1631, 1665, 1758, 13, 459, 1836, 29938, 7857, 7063, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 4893, 278, 883, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 29909, 1665, 17458, 29913, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 353, 2802, 4283, 2119, 29920, 5033, 29933, 1665, 1758, 1015, 29913, 448, 13, 29924, 1665, 1758, 1015, 2119, 29920, 876, 3426, 29896, 1012, 1631, 1665, 1758, 1015, 3331, 4283, 4678, 6875, 29912, 29920, 1800, 6622, 29892, 320, 3425, 503, 320, 262, 13, 29905, 29907, 3187, 3358, 29889, 320, 355, 29912, 4990, 755, 29913, 13, 15954, 852, 385, 5455, 395, 29933, 3187, 3411, 353, 350, 3187, 3411, 6622, 320, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 3187, 3411, 1262, 1316, 393, 2427, 29933, 3187, 3411, 448, 474, 21604, 29896, 29913, 320, 262, 13, 29905, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 3187, 3411, 1262, 322, 1925, 395, 29933, 353, 350, 1665, 1758, 1015, 29913, 320, 17201, 350, 3187, 3411, 7449, 739, 13, 23031, 29879, 515, 22206, 320, 999, 29912, 7728, 29906, 29889, 29929, 29913, 393, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29913, 448, 503, 21604, 29896, 29913, 448, 21313, 319, 29918, 29933, 29913, 448, 503, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 7085, 29950, 511, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 16076, 29871, 2427, 29933, 3187, 3411, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 3187, 3411, 467, 29938, 13, 2059, 10244, 320, 999, 29912, 29963, 29889, 29896, 29913, 278, 13312, 9126, 5633, 395, 29909, 998, 562, 6353, 17458, 1042, 13, 392, 395, 29909, 998, 562, 2403, 29933, 29938, 310, 29871, 395, 29909, 1665, 17458, 1042, 322, 395, 29909, 29918, 29933, 1628, 8307, 29892, 526, 13, 348, 3673, 2354, 7126, 29889, 13, 13, 29898, 29875, 29897, 4001, 491, 11833, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338 ]	1,332,863	23,552	ArXiv	-1	-1
a part of $A^{ac}_B E_{A_B}(\cD)$ and $A^{ac}_B$ is unitarily equivalent to $A_{\Theta}^{ac}$ we get that $A^{ac}_0E_{A_0}(\cD)$ is a part of $A^{ac}_{\Theta} E_{A_{\Theta}}(\cD)$. (ii) Since, by assumption, $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $A^{ac}_BE_{A_B}(\cD)$ and $A^{ac}_B$ is unitarily equivalent to $A_{\Theta}$, we get that $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $A^{ac}_{\Theta} E_{A_{\Theta}}(\cD)$. \end{proof} \subsection{Compact non-additive perturbations} Here we generalize the Rosenblum-Kato theorem for the case of compact perturbations. To this end we assume that the maximal normal function \begin{displaymath} m^+(t) := \sup_{0<y\le 1}\\|M(t+iy)\\| \end{displaymath} is finite for a.e. $t \in \R$. This is the case if and only if the normal limits $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t + iy)$ exist and are bounded operators for a.e. $t \in \R$. Indeed, let $D = D^$ be a Hilbert-Schmidt operator such that ${\xker\,}(D) = \{0\}$ and let $M^D(z) := DM(z)D$, $z \in \C_+$. Since the limit $M^D(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}M^D(t + iy)$ exists and is a bounded operator for a.e. $t \in \R$, see \cite{BirEnt67, Yaf92}, we find that \begin{displaymath} \lim_{y\to+0}(M(t+iy)Df,Dg) = ({ M^D(t)}f,g), \quad f,g \in \cH, \quad \text{for a.e.} \quad t \in \R. \end{displaymath} Hence the limit $\lim_{y\to+0}(M(t+iy)h,k)$ exists for a.e. $t \in \R$ and $h,k \in {\rm ran\,}(D)$ which yields the existence of $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ for a.e. $t \in \R$. The converse statement is obvious. Now we are ready to prove the main result of this section. \begin{theorem}\Label{V.5} Let $A$ be a densely defined, closed symmetric operator in $\gH$, { let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be} an ordinary boundary triplet for $A^$, and { let $M(\cdot)$ be} the corresponding Weyl function. Let $\wt A$ be a self-adjoint extension of $A$ and $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0)$. If the maximal normal function $m^+(t)$ is finite for a.e. $t \in \R$ and condition \eqref{5.0} is satisfied, then the absolutely continuous parts $\wt A^{ac}$ and $A^{ac}_0$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{theorem} \begin{proof} We divide the proof into several steps. (i) { First we assume that the extensions $\wt A$ and $A_0$ are disjoint, that is} $\wt A = A_B$ where $B = B^\in \cC(\cH).$ We { define} the operator $D\in \gotS_{\infty}(\cH)$ in accordance with \eqref{4.	-0.432387	-1.663783	-0.230582	1.898085	[ -0.7939812473587955, -0.07079262084744993 ]	[ -1.7819642522520567, -1.5456012795191738 ]	[ -0.5820094118478132, 0.12084638231180245 ]	[ 1.8252465478645845, 1.9709232828867462 ]	1,024	[ 512, 512 ]	[ 263, 760, 13, 974, 395, 29909, 998, 562, 2403, 29933, 382, 648, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 322, 395, 29909, 998, 562, 2403, 29933, 29938, 338, 443, 3673, 2354, 7126, 13, 517, 395, 29909, 1665, 17458, 2844, 562, 1042, 591, 679, 393, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 13, 1595, 310, 395, 29909, 998, 562, 6353, 17458, 29913, 382, 648, 29909, 1665, 17458, 20828, 29883, 29928, 4935, 13, 13, 29898, 2236, 29897, 4001, 29892, 491, 11833, 29892, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29909, 998, 562, 2403, 15349, 648, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 322, 395, 29909, 998, 562, 2403, 29933, 29938, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29909, 1665, 17458, 4429, 591, 679, 393, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 13, 348, 3673, 2354, 7126, 304, 395, 29909, 998, 562, 6353, 17458, 29913, 382, 648, 29909, 1665, 17458, 20828, 29883, 29928, 4935, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29905, 7235, 29912, 6843, 627, 1661, 29899, 1202, 3321, 22786, 800, 29913, 13, 13, 10605, 29871, 591, 29871, 2498, 675, 278, 28929, 2204, 398, 29899, 29968, 1219, 9185, 363, 278, 1206, 310, 13, 2388, 627, 22786, 800, 29889, 1763, 445, 1095, 591, 5251, 393, 278, 23183, 13, 8945, 740, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29885, 14747, 29898, 29873, 29897, 3490, 320, 12587, 648, 29900, 29966, 29891, 29905, 280, 29871, 29896, 1012, 29989, 29924, 29898, 29873, 29974, 19881, 2144, 29989, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 275, 8093, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 910, 338, 278, 1206, 565, 322, 871, 565, 278, 13, 8945, 13071, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 718, 474, 29891, 1262, 1863, 322, 526, 13, 29306, 12768, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 14598, 29892, 1235, 29871, 395, 29928, 353, 360, 6622, 29938, 367, 263, 13, 29950, 309, 2151, 29899, 4504, 19720, 5455, 1316, 393, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 9991, 29900, 11854, 322, 13, 1026, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 27692, 29898, 29920, 29897, 29928, 1628, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 4001, 278, 4046, 13, 29938, 29924, 29985, 29928, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29985, 29928, 29898, 29873, 718, 474, 29891, 1262, 4864, 322, 338, 263, 12635, 13, 6891, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 1074, 320, 2036, 29912, 29933, 381, 5292, 29953, 29955, 29892, 612, 2142, 29929, 29906, 1118, 591, 1284, 13, 5747, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29924, 29898, 29873, 29974, 19881, 29897, 29928, 29888, 29892, 29928, 29887, 29897, 353, 21313, 341, 29985, 29928, 29898, 29873, 2915, 29888, 29892, 29887, 511, 320, 3425, 285, 29892, 29887, 320, 262, 320, 29883, 29950, 29892, 13, 29905, 3425, 320, 726, 29912, 1454, 263, 29889, 29872, 5003, 320, 3425, 29871, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29950, 663, 278, 4046, 779, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29924, 29898, 29873, 29974, 19881, 29897, 29882, 29892, 29895, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29934, 29938, 322, 395, 29882, 29892, 29895, 320, 262, 2802, 1758, 6350, 5940, 2119, 29928, 1262, 607, 17498, 278, 10379, 310, 395, 29924, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 450, 378, 3901, 3229, 13, 275, 6924, 29889, 13, 13, 10454, 591, 526, 7960, 29871, 304, 6356, 278, 1667, 1121, 310, 445, 4004, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 29963, 29889, 29945, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 29892, 5764, 18348, 5455, 297, 779, 29887, 29950, 1628, 13, 29912, 1235, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29913, 385, 15311, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 392, 29871, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 2803, 779, 14554, 319, 29938, 367, 263, 13, 1311, 29899, 328, 12090, 6081, 310, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 960, 278, 23183, 4226, 740, 13, 29938, 29885, 14747, 29898, 29873, 1262, 338, 8093, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 13, 275, 15787, 29892, 769, 278, 13312, 9126, 5633, 779, 14554, 319, 998, 562, 1042, 13, 392, 395, 29909, 998, 562, 2403, 29900, 29938, 310, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 1628, 8307, 29892, 29871, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 4806, 16429, 278, 5296, 964, 3196, 6576, 29889, 13, 13, 29898, 29875, 29897, 426, 3824, 591, 5251, 393, 29871, 278, 17752, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 29938, 13, 598, 766, 12090, 29892, 393, 338, 29913, 29871, 779, 14554, 319, 353, 319, 29918, 29933, 29938, 29871, 988, 395, 29933, 353, 350, 6622, 29905, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 467, 29938, 1334, 426, 4529, 29913, 278, 5455, 395, 29928, 29905, 262, 13, 29905, 7085, 29903, 1665, 3411, 4678, 29883, 29950, 1262, 297, 15017, 749, 411, 320, 4915, 29912, 29946, 29889 ]	1,332,863	24,576	ArXiv	-1	-1
2A}, $D := \|B\|^{-1/2},$ and investigate the function $M^D(z) := M^D(z):= DM(z)D$, $z \in \C_+$. Let $ M^D(t) := DM(t)D.$ Since the (weak) limit $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ exists for a.e. $t \in \R,$ by \cite[Lemma 6.1.4]{Yaf92}, the following limit exists \begin{equation}\label{4.9} \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0} \\|{ M^D(}t+iy) - { M^D(t)}\\| = 0 \qquad\text {for a.e.} \quad t \in \R. \end{equation} Let ${\delta}_a := \{t \in \R: \\|M(t)\\| \le a\}$. Since $D = D^*$ is a { a non-negative } compact operator, it admits the spectral decomposition \begin{displaymath} D = \sum_{l \in \N} \mu_lQ_l \end{displaymath} where $\{\mu_l\}^\infty_{l=1}$, is the { decreasing } sequence of eigenvalues of $D$, $\{Q_l\}_{l \in \N}$ the corresponding sequence of eigenprojections, ${\rm dim}\{Q_l\}<\infty.$ Since $\mu_l\to 0$ as $l\to \infty,$ there exists a number $l_a\in \N$ such that $\mu_{l_a}< 1/\sqrt {2a}$. We put $\cH_1 := \bigoplus^\infty_{l=l_a+1}Q_l\cH$ and $\cH_2 := \bigoplus^{l_a}_{l=1}Q_l\cH.$ Clearly, $\cH = \cH_1 \oplus \cH_2$ and ${\rm dim}(\cH_2) <\infty.$ Moreover, the operator $D$ admits the following decomposition $D = D_1 \oplus D_2$ where \begin{displaymath} D_1 := \sum^\infty_{l = l_a + 1}\mu_lQ_l \quad \text{and}\quad D_2 := \sum^{l_a}_{l=1}\mu_lQ_l. \end{displaymath} Since $\mu_{l_a}< 1/\sqrt {2a},$ we have $\\|D_1\\|< 1/\sqrt {2a}.$ Hence \begin{equation}\Label{5.5} \\|D_1M(t)D_1\\| < 1/2, \qquad t \in {\delta}_a. \end{equation} Denote by $P_1$ and $P_2$ the orthogonal projections from $\cH$ onto $\cH_1$ and $\cH_2$, respectively. Note that $P_1J = JP_1$ and $P_2J = JP_2$. (ii) Our next aim is to show that the operator function $G(z) := J - { M^D(z)}$ is invertible in $\C_+$ and { that $T(z) := G(z)^{-1}$ has the limits $T(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}T(t+iy)$ for a.e. $t \in {\delta}_a$}. For this purpose we consider the decompositions \begin{displaymath} { M^D(z)} := \bigg(D_iM(z)D_j\bigg)_{i,j=1}^2 := \begin{pmatrix} M^D_{11}(z) & M^D_{12}(z)\\ M^D_{21}(z) & M^D_{22}(z) \end{pmatrix}: \begin{array}{c} \cH_1\\ \oplus \\ \cH_2 \end{array}	-0.339249	-1.169569	-0.271003	2.085384	[ -0.3337703032152119, -0.344727706647202 ]	[ -1.3808634500386798, -0.9582751048495861 ]	[ -0.3204595561050604, -0.2215461561150739 ]	[ 2.0749780936168616, 2.0957890557628844 ]	1,024	[ 512, 512 ]	[ 29906, 29909, 1118, 29871, 395, 29928, 3490, 13, 29989, 29933, 29989, 3426, 29896, 29914, 29906, 1118, 29938, 322, 23033, 278, 740, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 341, 29985, 29928, 29898, 29920, 1125, 29922, 13, 23560, 29898, 29920, 29897, 29928, 1628, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 2803, 395, 341, 29985, 29928, 29898, 29873, 29897, 3490, 27692, 29898, 29873, 29897, 29928, 7449, 4001, 278, 313, 25129, 29897, 13, 13400, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 8209, 13, 1609, 320, 2036, 29961, 29931, 331, 655, 29871, 29953, 29889, 29896, 29889, 29946, 3199, 29979, 2142, 29929, 29906, 1118, 278, 1494, 4046, 4864, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29929, 29913, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 29898, 29913, 29873, 29974, 19881, 29897, 448, 426, 341, 29985, 29928, 29898, 29873, 11383, 29989, 353, 29871, 29900, 320, 12014, 29905, 726, 426, 1454, 263, 29889, 29872, 5003, 320, 3425, 13, 29873, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 12024, 7555, 4181, 2403, 29874, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 12926, 29924, 29898, 29873, 2144, 29989, 320, 280, 263, 23699, 4001, 395, 29928, 353, 360, 6622, 29938, 338, 263, 13, 29912, 263, 1661, 29899, 22198, 500, 29871, 11071, 5455, 29892, 372, 29871, 7336, 1169, 278, 23161, 13, 311, 510, 3283, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29928, 353, 320, 2083, 648, 29880, 320, 262, 320, 29940, 29913, 320, 2589, 29918, 29880, 29984, 29918, 29880, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 779, 741, 2589, 29918, 29880, 29905, 10206, 3411, 648, 29880, 29922, 29896, 4429, 29871, 338, 278, 426, 9263, 5832, 500, 13, 16506, 310, 25973, 310, 395, 29928, 1628, 12564, 29984, 29918, 29880, 29905, 3227, 29880, 320, 262, 320, 29940, 1042, 29871, 278, 13, 2616, 3636, 292, 5665, 310, 7388, 771, 24247, 29892, 7555, 1758, 3964, 1012, 29912, 29984, 29918, 29880, 18105, 13505, 3411, 7449, 13, 13, 23036, 29871, 779, 2589, 29918, 29880, 29905, 517, 29871, 29900, 29938, 408, 395, 29880, 29905, 517, 320, 3411, 8209, 727, 4864, 263, 1353, 13, 29938, 29880, 29918, 29874, 29905, 262, 320, 29940, 29938, 1316, 393, 259, 779, 2589, 648, 29880, 29918, 29874, 29913, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 4311, 1334, 1925, 779, 29883, 29950, 29918, 29896, 13, 9361, 320, 3752, 17201, 3823, 3411, 648, 29880, 29922, 29880, 29918, 29874, 29974, 29896, 29913, 29984, 29918, 29880, 29905, 29883, 29950, 29938, 322, 29871, 779, 29883, 29950, 29918, 29906, 3490, 13, 29905, 3752, 17201, 998, 29880, 29918, 29874, 3227, 29880, 29922, 29896, 29913, 29984, 29918, 29880, 29905, 29883, 29950, 7449, 259, 17732, 368, 29892, 29871, 779, 29883, 29950, 353, 320, 29883, 29950, 29918, 29896, 320, 17201, 13, 29905, 29883, 29950, 29918, 29906, 29938, 322, 29871, 7555, 1758, 3964, 4678, 29883, 29950, 29918, 29906, 29897, 529, 29905, 3411, 7449, 12808, 29892, 278, 5455, 395, 29928, 29938, 7336, 1169, 13, 1552, 1494, 26227, 395, 29928, 353, 360, 29918, 29896, 320, 17201, 360, 29918, 29906, 29938, 988, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29928, 29918, 29896, 3490, 320, 2083, 3823, 3411, 648, 29880, 353, 301, 29918, 29874, 718, 29871, 29896, 1012, 2589, 29918, 29880, 29984, 29918, 29880, 320, 3425, 13, 29905, 726, 29912, 392, 1012, 3425, 29871, 360, 29918, 29906, 3490, 320, 2083, 998, 29880, 29918, 29874, 3227, 29880, 29922, 29896, 1012, 2589, 29918, 29880, 29984, 29918, 29880, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 779, 2589, 648, 29880, 29918, 29874, 29913, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 1118, 29938, 591, 505, 29871, 779, 29989, 29928, 29918, 29896, 7893, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 1836, 29938, 13, 29950, 663, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29945, 29913, 13, 7893, 29928, 29918, 29896, 29924, 29898, 29873, 29897, 29928, 29918, 29896, 7893, 529, 29871, 29896, 29914, 29906, 29892, 320, 12014, 260, 320, 262, 13, 741, 4181, 2403, 29874, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29315, 866, 491, 395, 29925, 29918, 29896, 29938, 322, 395, 29925, 29918, 29906, 29938, 278, 28143, 410, 24247, 515, 779, 29883, 29950, 29938, 13, 10268, 779, 29883, 29950, 29918, 29896, 29938, 322, 779, 29883, 29950, 29918, 29906, 1628, 8307, 29889, 3940, 393, 395, 29925, 29918, 29896, 29967, 353, 435, 29925, 29918, 29896, 29938, 13, 392, 395, 29925, 29918, 29906, 29967, 353, 435, 29925, 29918, 29906, 1504, 13, 13, 29898, 2236, 29897, 8680, 2446, 12242, 338, 304, 1510, 393, 278, 5455, 740, 395, 29954, 29898, 29920, 29897, 3490, 435, 13, 29899, 426, 341, 29985, 29928, 29898, 29920, 15604, 338, 21292, 1821, 297, 779, 29907, 29918, 24035, 29871, 322, 426, 393, 395, 29911, 29898, 29920, 29897, 3490, 13, 29954, 29898, 29920, 21604, 29896, 1042, 29871, 756, 278, 13071, 395, 29911, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 29974, 19881, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 29938, 1836, 1152, 445, 6437, 591, 2050, 278, 13, 311, 22410, 2187, 13, 29905, 463, 29912, 4990, 755, 29913, 426, 341, 29985, 29928, 29898, 29920, 2915, 3490, 320, 17633, 29898, 29928, 29918, 29875, 29924, 29898, 29920, 29897, 29928, 29918, 29926, 29905, 17633, 20439, 29875, 29892, 29926, 29922, 29896, 2137, 29906, 3490, 13, 29905, 463, 29912, 12571, 29913, 13, 29924, 29985, 29928, 648, 29896, 29896, 2119, 29920, 29897, 669, 341, 29985, 29928, 648, 29896, 29906, 2119, 29920, 18775, 13, 29924, 29985, 29928, 648, 29906, 29896, 2119, 29920, 29897, 669, 341, 29985, 29928, 648, 29906, 29906, 2119, 29920, 29897, 13, 29905, 355, 29912, 12571, 6177, 13, 29905, 463, 29912, 2378, 1157, 29883, 29913, 13, 29905, 29883, 29950, 29918, 29896, 1966, 13, 29905, 17201, 2474, 13, 29905, 29883, 29950, 29918, 29906, 13, 29905, 355, 29912, 2378, 29913 ]	1,332,863	25,600	ArXiv	-1	-1
\longrightarrow \begin{array}{c} \cH_1\\ \oplus \\ \cH_2 \end{array}, \end{displaymath} $z \in \C_+$, and \begin{displaymath} G(z) = J - { M^D(z)} = \begin{pmatrix} J_1 - M^D_{11}(z) & -M^D_{12}(z)\\ -M^D_{21}(z) & J_2 - M^D_{22}(z) \end{pmatrix}, \qquad z \in \C_+, \end{displaymath} where $J_1 := JP_1$ and $J_2 := JP_2$. { ${\rm (ii)_1}$} Let us prove that ${\xker\,}(J_1 - { M^D_{11}}(z)) = \{0\}$ for $z \in \C_+$. Indeed, from $0= J_1g - { M^D_{11}}(z)g = J_1g - D_1M(z)D_1g $ one gets that $0 = \im({ M^D_{11}}(z)g,g) = (\im(M(z)D_1g,D_1g)$. Hence $0 = D_1g = Dg$ which yields $g = 0$. Since $0\in \varrho(J_1)$ and ${ M^D_{11}}(\cdot)\in{\gotS}_\infty,$ we obtain that the operator $J_1 - { M^D_{11}}(z) = J_1({ I_1} - J_1{ M^D_{11}}(z))$ is boundedly invertible for every $z \in \C_+$. Since ${ M^D_{11}}(z)$ is a $R_{\cH_1}$-function, we get that ${ \Xi}(z):= (J_1 - { M^D_{11}(z)})^{-1}$, $z \in \C_+$, is a $R_{\cH_1}$-function too. { ${\rm (ii)_2}$} We show that for a.e. $t \in {\delta}_a$, $a>0$, the limit ${ \Xi}(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}{ \Xi}(t + iy)$ exists in the operator norm and the following representation holds \begin{equation}\Label{5.6} { \Xi}(t) = (J_1 - { M^D_{11}}(t))^{-1}. \end{equation} First we note that $J_1 - { M^D_{11}}(z) = J_1(I_1 - J_1{ M^D_{11}}(z)$. Using \eqref{5.5} we get $\\|J_1{ M^D_{11}}(t)\\| <1$ for $t \in {\delta}_a$. Hence the inverse operator $(I_1 - J_1{ M^D_{11}}(t))^{-1}$ exists for $t \in {\delta}_a$. Using $(J_1 - { M^D_{11}}(t))^{-1} = (I_1 - J_1{ M^D_{11}}(t))^{-1}J_1$ we find that the inverse operator $(J_1 - { M^D_{11}}(t))^{-1}$ exist for $t \in {\delta}_a$. Since ${ M^D_{11}}(z)$ has limits ${ M^D_{11}}(t)$ for a.e. $t \in \R$ one gets that $J_1{ M^D_{11}}(t) = \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}J_1{ M^D_{11}}(t + iy)$ for a.e. $t \in \R$. Fix any such $t_0\in {\delta}_a.$ Then due to estimate \eqref{5.5} there exists $\eta =\eta(t_0)$ such that $\sup_{y \in (0,\eta)}\\|J_1{ M^D_{11}}(t_0 + iy)\\| \le 1/2$. Therefore, the family	-0.401569	-1.631551	-0.305559	1.94491	[ -0.4447140129641115, -0.3584244609371896 ]	[ -1.710339108999668, -1.5527637938444128 ]	[ -0.41239829327524014, -0.19871998688661546 ]	[ 1.9709232828867462, 1.9188958775216884 ]	1,024	[ 512, 512 ]	[ 13, 29905, 24225, 13, 29905, 463, 29912, 2378, 1157, 29883, 29913, 13, 29905, 29883, 29950, 29918, 29896, 1966, 13, 29905, 17201, 2474, 13, 29905, 29883, 29950, 29918, 29906, 13, 29905, 355, 29912, 2378, 1118, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29938, 29920, 320, 262, 320, 29907, 28842, 1628, 322, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29954, 29898, 29920, 29897, 353, 435, 448, 426, 341, 29985, 29928, 29898, 29920, 2915, 353, 13, 29905, 463, 29912, 12571, 29913, 13, 29967, 29918, 29896, 448, 341, 29985, 29928, 648, 29896, 29896, 2119, 29920, 29897, 29871, 669, 448, 29924, 29985, 29928, 648, 29896, 29906, 2119, 29920, 18775, 13, 29899, 29924, 29985, 29928, 648, 29906, 29896, 2119, 29920, 29897, 669, 435, 29918, 29906, 448, 341, 29985, 29928, 648, 29906, 29906, 2119, 29920, 29897, 13, 29905, 355, 29912, 12571, 1118, 320, 12014, 503, 320, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 395, 29967, 29918, 29896, 3490, 435, 29925, 29918, 29896, 29938, 322, 395, 29967, 29918, 29906, 3490, 435, 29925, 29918, 29906, 1504, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29896, 1042, 29913, 2803, 502, 6356, 393, 29871, 7555, 29916, 3946, 5940, 2119, 29967, 29918, 29896, 448, 426, 13, 29924, 29985, 29928, 648, 29896, 29896, 12156, 29920, 876, 353, 9991, 29900, 11854, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 14598, 29892, 515, 395, 29900, 29922, 435, 29918, 29896, 29887, 448, 13, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 29887, 353, 435, 29918, 29896, 29887, 448, 360, 29918, 29896, 29924, 29898, 29920, 29897, 29928, 29918, 29896, 29887, 395, 697, 4947, 393, 395, 29900, 353, 13, 29905, 326, 3319, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 29887, 29892, 29887, 29897, 353, 3441, 326, 29898, 29924, 29898, 29920, 29897, 29928, 29918, 29896, 29887, 29892, 29928, 29918, 29896, 29887, 4935, 10133, 395, 29900, 353, 360, 29918, 29896, 29887, 13, 29922, 360, 29887, 29938, 607, 17498, 29871, 395, 29887, 353, 29871, 29900, 1504, 4001, 395, 29900, 29905, 262, 320, 1707, 4650, 29898, 29967, 29918, 29896, 1262, 322, 6435, 13, 29924, 29985, 29928, 648, 29896, 29896, 20828, 3822, 2144, 262, 741, 7085, 29903, 12806, 3411, 8209, 29871, 591, 4017, 393, 278, 5455, 13, 29938, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 353, 435, 29918, 29896, 3319, 306, 29918, 29896, 29913, 448, 29871, 435, 29918, 29896, 29912, 13, 29924, 29985, 29928, 648, 29896, 29896, 12156, 29920, 23846, 338, 12635, 368, 21292, 1821, 363, 1432, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 13, 23036, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 1262, 338, 263, 395, 29934, 1665, 29883, 29950, 29918, 29896, 23021, 2220, 29892, 591, 679, 29871, 393, 13, 5303, 320, 29990, 29875, 2119, 29920, 1125, 29922, 313, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 2119, 29920, 26972, 3426, 29896, 4429, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 13, 275, 263, 395, 29934, 1665, 29883, 29950, 29918, 29896, 23021, 2220, 2086, 29889, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29906, 1042, 29913, 1334, 1510, 393, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1628, 395, 29874, 29958, 29900, 1628, 278, 4046, 13, 5303, 320, 29990, 29875, 2119, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 1157, 320, 29990, 29875, 2119, 29873, 718, 474, 29891, 1262, 4864, 297, 278, 5455, 6056, 13, 392, 278, 1494, 8954, 8640, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29953, 29913, 13, 29912, 320, 29990, 29875, 2119, 29873, 29897, 353, 313, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1836, 320, 355, 29912, 2573, 29913, 13, 6730, 591, 4443, 393, 395, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 353, 435, 29918, 29896, 29898, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 4935, 5293, 320, 4915, 29912, 29945, 29889, 29945, 29913, 591, 679, 779, 29989, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 2144, 29989, 529, 29896, 29938, 363, 13, 29938, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 10133, 278, 16402, 5455, 2427, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 4864, 363, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 5293, 2427, 29967, 29918, 29896, 448, 13, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 29913, 353, 313, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 29913, 29967, 29918, 29896, 29938, 591, 1284, 393, 278, 13, 262, 3901, 5455, 2427, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 1863, 363, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 23036, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 1262, 756, 13071, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29934, 29938, 697, 4947, 393, 395, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29897, 353, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 718, 474, 29891, 1262, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 24778, 29871, 738, 1316, 395, 29873, 29918, 29900, 29905, 262, 2802, 4181, 2403, 29874, 7449, 1987, 2861, 304, 13, 342, 6490, 320, 4915, 29912, 29945, 29889, 29945, 29913, 727, 4864, 779, 1187, 17313, 1187, 29898, 29873, 29918, 29900, 1262, 1316, 393, 13, 4535, 12587, 648, 29891, 320, 262, 313, 29900, 2053, 1187, 11383, 29989, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 2144, 29989, 320, 280, 29871, 29896, 29914, 29906, 1504, 7857, 29892, 13, 1552, 3942 ]	1,332,863	26,624	ArXiv	-1	-1
$\{\\|(I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1}\\|\}_{y \in (0,\eta)}$ is uniformly bounded for any fixed $t_0 \in {\delta}_a.$ Using this fact and \eqref{4.9} we can pass to the limit as $y \to 0$ in the identity \begin{eqnarray} \lefteqn{ (I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1} - (I_1 - J_1{ M^D_{11}}(t_0))^{-1} }\\ & & \hspace{-5mm} =(I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1} (J_1{ M^D_{11}}(t_0 + iy)) - J_1{ M^D_{11}}(t_0))(I_1 - J_1{ M^D_{11}}(t_0))^{-1}. \end{eqnarray} We obtain $\,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}((I_1 - J_1{ M^D_{11}}(t + iy))^{-1} = (I_1 - J_1{ M^D_{11}}(t))^{-1}$ for a.e. $t \in {\delta}_a$ which yields the existence of ${ \Xi}(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}{ \Xi}(t + iy)$ and proves representation \eqref{5.6}. { ${\rm (ii)_3}$} Next we set \begin{displaymath} {\Delta}(z) := { M^D_{22}}(z) + { M^D_{21}}(z)(J_1 - { M^D_{11}}(z))^{-1}{ M^D_{12}}(z), \quad z \in \C_+. \end{displaymath} and show that the function $T_2(\cdot) := (J_2 - {\Delta}(\cdot))^{-1}$ is $R_{\cH_2}$-function. Clearly, ${\Delta}(\cdot)$ is holomorphic in $\C_+$ and it acts in a finite dimensional Hilbert space $\cH_2$. Since $\det(J_2 - {\Delta}(\cdot))$ is also holomorphic in $\C_+,$ the determinant $\det(J_2 - {\Delta}(\cdot))$ has only a discrete set of zeros in $\C_+$. Hence the inverse operator $T_2(\cdot) := (J_2 - {\Delta}(\cdot))^{-1}$ exists for $z\in \Omega \subset\C_+$ where $\C_+ \setminus\Omega$ is at most countable discrete set, that is, $T_2(\cdot)$ is meromorphic in $\C_+$. As we just mentioned the inverse operator $(J_2 - {\Delta}(z))^{-1}$ exists for $z \in \Omega \subset \C_+$. Choose any $z \in \Omega.$ Then, by the { Frobenius} formula, \begin{equation}\Label{5.7} T(z) := (J - { M^D(z)})^{-1} = \begin{pmatrix} T_1(z) & { \Xi}(z){ M^D_{12}}(z)T_2(z)\\ T_2(z){ M^D_{21}}(z){ \Xi}(z) & T_2(z) \end{pmatrix} \end{equation} where \begin{equation}\Label{5.7A} T_1(z) := { \Xi}(z) + { \Xi}(z){ M^D_{12}}(z)T_2(z){ M^D_{21}}(z){ \Xi}(z). \end{equation} Hence \begin{displaymath} T_2(z) = P_2T(z)\upharpoonright\cH_2, \qquad z\in \Omega. \end{displaymath} Since $T(\cdot)$ is a $R	-0.23006	-1.509789	-0.2393	2.074978	[ -0.3337703032152119, -0.12635008043621215 ]	[ -1.7962892809025344, -1.2232881348834246 ]	[ -0.4903877048058064, 0.011788018220278867 ]	[ 1.9709232828867462, 2.1790329043469767 ]	1,024	[ 512, 512 ]	[ 779, 741, 29989, 29898, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 1012, 4295, 3227, 29891, 320, 262, 13, 29898, 29900, 2053, 1187, 15604, 338, 26018, 12635, 363, 738, 4343, 395, 29873, 29918, 29900, 320, 262, 2802, 4181, 2403, 29874, 7449, 13, 15156, 445, 2114, 322, 320, 4915, 29912, 29946, 29889, 29929, 29913, 259, 591, 508, 1209, 304, 278, 4046, 408, 395, 29891, 13, 29905, 517, 29871, 29900, 29938, 297, 278, 10110, 13, 29905, 463, 29912, 9441, 4044, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29898, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 29913, 448, 13, 29898, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 3426, 29896, 29913, 29871, 500, 1966, 13, 29987, 669, 29871, 320, 14158, 8499, 29945, 4317, 29913, 13, 7607, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 29913, 13, 29898, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 448, 29871, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 29898, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 3426, 29896, 1836, 13, 29905, 355, 29912, 9441, 4044, 13, 4806, 4017, 29871, 779, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29898, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 718, 474, 29891, 876, 3426, 29896, 29913, 13, 29922, 313, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 29938, 607, 13, 29891, 969, 29879, 278, 10379, 310, 6435, 320, 29990, 29875, 2119, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 1157, 320, 29990, 29875, 2119, 29873, 718, 474, 29891, 1262, 322, 13, 771, 1960, 8954, 320, 4915, 29912, 29945, 29889, 29953, 1836, 13, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29941, 1042, 29913, 8084, 591, 29871, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 5268, 2119, 29920, 29897, 3490, 426, 341, 29985, 29928, 648, 29906, 29906, 12156, 29920, 29897, 718, 13, 29912, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 5033, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 876, 3426, 29896, 1157, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 511, 320, 3425, 13, 29920, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 392, 29871, 1510, 393, 278, 740, 395, 29911, 29918, 29906, 1194, 3822, 29897, 3490, 313, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 876, 3426, 29896, 1042, 338, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29889, 13, 13, 18759, 368, 29892, 29871, 7555, 5268, 4678, 3822, 1262, 338, 8753, 16898, 297, 779, 29907, 29918, 24035, 322, 372, 14741, 297, 263, 13, 18925, 22112, 12338, 2151, 2913, 779, 29883, 29950, 29918, 29906, 1504, 4001, 779, 4801, 29898, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 23846, 338, 884, 8753, 16898, 297, 779, 29907, 28842, 8209, 278, 11806, 424, 13, 4535, 4801, 29898, 29967, 29918, 29906, 448, 2802, 5268, 4678, 3822, 23846, 756, 871, 263, 19554, 731, 310, 24786, 297, 13, 4535, 29907, 28842, 1504, 10133, 278, 16402, 5455, 395, 29911, 29918, 29906, 1194, 3822, 29897, 3490, 313, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 876, 3426, 29896, 1042, 4864, 363, 29871, 395, 29920, 29905, 262, 320, 5981, 320, 6484, 29905, 29907, 29918, 24035, 13, 3062, 779, 29907, 28842, 320, 15375, 29905, 5981, 29938, 29871, 338, 472, 1556, 2302, 519, 19554, 731, 29892, 13, 5747, 338, 29892, 395, 29911, 29918, 29906, 1194, 3822, 1262, 338, 2778, 16898, 297, 779, 29907, 28842, 1504, 13, 13, 2887, 591, 925, 29871, 5276, 278, 16402, 5455, 2427, 29967, 29918, 29906, 448, 2802, 5268, 2119, 29920, 876, 3426, 29896, 1042, 13, 9933, 363, 259, 395, 29920, 320, 262, 320, 5981, 320, 6484, 320, 29907, 28842, 1504, 29871, 14542, 852, 738, 29871, 395, 29920, 320, 262, 13, 29905, 5981, 7449, 1987, 29892, 491, 278, 426, 25022, 1785, 2482, 29913, 7063, 29892, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29955, 29913, 13, 29911, 29898, 29920, 29897, 3490, 313, 29967, 448, 426, 341, 29985, 29928, 29898, 29920, 26972, 3426, 29896, 29913, 353, 13, 29905, 463, 29912, 12571, 29913, 13, 29911, 29918, 29896, 29898, 29920, 29897, 669, 426, 320, 29990, 29875, 2119, 29920, 2597, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 29897, 29911, 29918, 29906, 29898, 29920, 18775, 13, 29911, 29918, 29906, 29898, 29920, 2597, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 2597, 320, 29990, 29875, 2119, 29920, 29897, 669, 323, 29918, 29906, 29898, 29920, 29897, 13, 29905, 355, 29912, 12571, 29913, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29955, 29909, 29913, 13, 323, 29918, 29896, 29898, 29920, 29897, 3490, 426, 320, 29990, 29875, 2119, 29920, 29897, 718, 13, 29912, 320, 29990, 29875, 2119, 29920, 2597, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 29897, 29911, 29918, 29906, 29898, 29920, 2597, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 2597, 320, 29990, 29875, 2119, 29920, 467, 13, 539, 320, 355, 29912, 2573, 29913, 13, 29950, 663, 13, 1678, 320, 463, 29912, 4990, 755, 29913, 13, 29911, 29918, 29906, 29898, 29920, 29897, 353, 349, 29918, 29906, 29911, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 29918, 29906, 29892, 320, 12014, 503, 29905, 262, 320, 5981, 29889, 13, 268, 320, 355, 29912, 4990, 755, 29913, 13, 23036, 395, 29911, 1194, 3822, 1262, 338, 263, 395, 29934 ]	1,332,863	27,648	ArXiv	-1	-1
_{\cH}$-function, we get that $\im {(T_2(z))}>0$ for $z\in \Omega.$ Since in addition $T_2(\cdot)$ is meromorphic in $\C_+$, we conclude that it is holomorphic. Thus, $T_2(\cdot) = (J_2 - {\Delta}(\cdot))^{-1}$ is $R_{\cH_2}$-function, too. { ${\rm (ii)_4}$} In this step we show that for any $a > 0$ the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exists in the operator norm for a.e. $t \in {\delta}_a$. Since $T_2(\cdot)$ is the matrix $R_{\cH_2}$-function, the limit $T_2(t) = \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T_2(t+iy)$ exists for { a.e.} $t \in \R$. Besides, \eqref{4.9} yields \begin{displaymath} \lim_{y\to+0} \\|{ M^D_{12}}(t+iy) - { M^D_{12}}(t)\\| = 0 \quad \text{and} \quad \lim_{y\to+0} \\|{ M^D_{21}}(t+iy) - { M^D_{21}}(t)\\| = 0 \end{displaymath} for { a.e.} $t \in \R$. { Combining} these relations with \eqref{5.6} and \eqref{5.7A} { yields} the existence of the limit $T_1(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T_1(t+iy)$ for a.e $t \in {\delta}_a$. Finally, combining all these relations with the block-matrix representation \eqref{5.7} we complete the proof of { (ii)}. { ${\rm (iii)}$} { Using the results of (ii) we are now going to complete the proof of the theorem}. We set ${\delta}_n := \{t \in \R:\ m^+(t) \le n\}$ { and } note that $\bigcup_{n \in \N}{\delta}_n$ differs from $\R$ by a set of Lebesgue measure zero. By step { (ii)} the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exists for a.e. $t \in \bigcup_{n \in \N}{\delta}_n$ in the operator norm. Hence the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exist for { a.e.} $t \in \R$. Combining this fact with \eqref{4.9} we can pass to the limit in the identity $(J - { M^D(}t+iy))T(t +iy) = I$ { as $y\to 0.$} We get \begin{equation}\label{4.13} (J - { M^D(t)})T(t) = T(t)(J - { M^D(t)}) = I \qquad \text{ for a.e.} \quad t \in \R \end{equation} The rest of the proof is similar to that of Theorem \ref{V.1}. First we assume that $\wt A$ is disjoint with $A_0$, hence, it admits a representation $\wt A = A_B$ with $B\in \cC(\cH)$. Therefore, setting $M_B(\cdot) := (B-M(\cdot))^{-1}$ and assuming without loss of generality that $0 \in \varrho(B)$ we arrive at the representation \eqref{5.3} with $D=\|B\|^{-1/2}$ for a.e. $t \in \R$. Moreover, \eqref{4.13} yields ${\rm ran\,}(T(t)) = \cH	0.009676	-1.362957	-0.018647	1.830449	[ -0.015320765973000134, 0.03467238718545462 ]	[ -1.4166760216648742, -1.309238306786291 ]	[ -0.06176297151586494, 0.024469223347200215 ]	[ 1.9293013585947, 1.7315972182074808 ]	1,024	[ 512, 512 ]	[ 1665, 29883, 29950, 23021, 2220, 29892, 591, 679, 393, 779, 326, 13, 8001, 29911, 29918, 29906, 29898, 29920, 876, 17428, 29900, 29938, 363, 395, 29920, 29905, 262, 320, 5981, 7449, 4001, 297, 6124, 395, 29911, 29918, 29906, 1194, 3822, 1262, 29871, 338, 13, 1050, 16898, 297, 779, 29907, 28842, 1628, 591, 17668, 29871, 393, 372, 338, 8753, 16898, 29889, 6549, 29892, 13, 395, 29911, 29918, 29906, 1194, 3822, 29897, 353, 313, 29967, 29918, 29906, 448, 2802, 5268, 4678, 3822, 876, 3426, 29896, 1042, 338, 29871, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29892, 13, 2086, 29889, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29946, 1042, 29913, 512, 445, 4331, 591, 1510, 393, 363, 738, 29871, 395, 29874, 1405, 29871, 29900, 29938, 278, 13, 13400, 395, 29911, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 4864, 297, 278, 5455, 13, 12324, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 23036, 395, 29911, 29918, 29906, 1194, 3822, 1262, 338, 278, 4636, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29892, 278, 13, 13400, 395, 29911, 29918, 29906, 29898, 29873, 29897, 353, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29918, 29906, 29898, 29873, 29974, 19881, 1262, 4864, 363, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 13, 29905, 29934, 1504, 19065, 29892, 320, 4915, 29912, 29946, 29889, 29929, 29913, 17498, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 648, 29896, 29906, 12156, 29873, 29974, 19881, 29897, 448, 426, 341, 29985, 29928, 648, 29896, 29906, 12156, 29873, 2144, 29989, 13, 29922, 29871, 29900, 320, 3425, 320, 726, 29912, 392, 29913, 320, 3425, 29871, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 648, 29906, 29896, 12156, 29873, 29974, 19881, 29897, 13, 29899, 426, 341, 29985, 29928, 648, 29906, 29896, 12156, 29873, 2144, 29989, 353, 29871, 29900, 320, 355, 29912, 4990, 755, 29913, 13, 1454, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 320, 29934, 1504, 426, 422, 2109, 292, 29913, 29871, 1438, 5302, 411, 13, 29905, 4915, 29912, 29945, 29889, 29953, 29913, 322, 320, 4915, 29912, 29945, 29889, 29955, 29909, 29913, 426, 29871, 17498, 29913, 278, 10379, 310, 278, 13, 13400, 395, 29911, 29918, 29896, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29918, 29896, 29898, 29873, 29974, 19881, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 12881, 635, 29892, 29299, 599, 1438, 5302, 411, 29871, 278, 2908, 29899, 5344, 13, 276, 26081, 320, 4915, 29912, 29945, 29889, 29955, 29913, 591, 4866, 278, 5296, 310, 426, 313, 2236, 29512, 13, 13, 29912, 7555, 1758, 313, 25609, 15604, 29913, 426, 5293, 278, 2582, 310, 313, 2236, 29897, 591, 526, 1286, 2675, 13, 29871, 304, 4866, 278, 5296, 310, 278, 9185, 1836, 1334, 731, 13, 29938, 741, 4181, 2403, 29876, 3490, 9991, 29873, 320, 262, 320, 29934, 3583, 286, 14747, 29898, 29873, 29897, 320, 280, 302, 11854, 426, 322, 500, 4443, 393, 13, 4535, 3752, 5231, 648, 29876, 320, 262, 320, 29940, 3331, 4181, 2403, 29876, 29938, 2923, 414, 515, 779, 29934, 29938, 491, 263, 731, 310, 9388, 267, 13000, 13, 26658, 5225, 29889, 2648, 4331, 426, 313, 2236, 2915, 29871, 278, 4046, 395, 29911, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 3752, 5231, 648, 29876, 320, 262, 13, 29905, 29940, 3331, 4181, 2403, 29876, 29938, 297, 278, 5455, 6056, 29889, 10133, 278, 4046, 395, 29911, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 1863, 363, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 320, 29934, 1504, 13, 1523, 2109, 292, 445, 2114, 411, 29871, 320, 4915, 29912, 29946, 29889, 29929, 29913, 591, 508, 1209, 304, 278, 4046, 297, 13, 1552, 10110, 2427, 29967, 448, 426, 341, 29985, 29928, 29898, 29913, 29873, 29974, 19881, 876, 29911, 29898, 29873, 718, 19881, 29897, 353, 306, 29938, 426, 29871, 408, 395, 29891, 29905, 517, 13, 29900, 7449, 29913, 1334, 679, 13, 320, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29896, 29941, 29913, 13, 29898, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 29897, 353, 323, 29898, 29873, 5033, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 353, 306, 320, 12014, 320, 726, 29912, 363, 263, 29889, 29872, 5003, 320, 3425, 13, 29873, 320, 262, 320, 29934, 13, 4706, 320, 355, 29912, 2573, 29913, 13, 1576, 1791, 310, 278, 5296, 338, 2788, 304, 393, 310, 10244, 13, 29905, 999, 29912, 29963, 29889, 29896, 1836, 3824, 591, 5251, 393, 779, 14554, 319, 29938, 338, 766, 12090, 411, 395, 29909, 29918, 29900, 1628, 13, 29882, 663, 29892, 372, 7336, 1169, 263, 8954, 259, 779, 14554, 319, 353, 319, 29918, 29933, 29938, 411, 395, 29933, 29905, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 4935, 7857, 29892, 4444, 29871, 395, 29924, 29918, 29933, 1194, 3822, 29897, 3490, 313, 29933, 29899, 29924, 1194, 3822, 876, 3426, 29896, 1042, 13, 392, 10241, 29871, 1728, 6410, 310, 2498, 537, 393, 395, 29900, 320, 262, 320, 1707, 4650, 29898, 29933, 1262, 13, 705, 18331, 472, 278, 8954, 320, 4915, 29912, 29945, 29889, 29941, 29913, 411, 395, 29928, 29922, 29989, 29933, 29989, 3426, 29896, 29914, 29906, 1042, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 12808, 29892, 320, 4915, 29912, 29946, 29889, 29896, 29941, 29913, 17498, 7555, 1758, 6350, 5940, 2119, 29911, 29898, 29873, 876, 353, 13, 29905, 29883, 29950 ]	1,332,863	28,672	ArXiv	-1	-1
$ for a.e. $t \in \R$. Therefore arguing as in \eqref{5.3a} and \eqref{5.3b} we obtain \begin{eqnarray} \lefteqn{ d_{M_B}(t) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}\,)) = {\rm dim}({\rm ran\,}(\sqrt{\im(M(t))}D\,)) }\\ & & = {\rm dim}({\rm ran\,}(\sqrt{\im(M(t))}\,)) = {\rm dim}({\rm ran\,}(\im(M(t)))) = d_M(t) \end{eqnarray} for a.e. $t \in \R$. Applying Theorem \ref{IV.10}(ii) we complete the proof. { Finally, we apply Corollary \ref{V.1A} to extend the proof for extensions $\wt A$ not disjoint with $A_0.$} \end{proof} \begin{remark} {\em { The result as well as the proof remains valid} if $A$ is { non-densely} defined. In this case { it suffices to use} the boundary triplet technique for non-densely defined operators developed in \cite{DM95,Ma92b}, cf. proof of Theorem \ref{V.1}. However, the assumptions on the Weyl function are indispensable. } \end{remark} { The following result is immediate from Theorem \ref{IV.10}(ii) and Theorem \ref{V.5}.} \begin{corollary}\Label{V.6} Let the assumptions of Theorem \ref{V.5} be satisfied and let \begin{equation} \cF := \{t \in \R: m^+(t) < \infty\}. \end{equation} If condition \eqref{5.0} holds, then the parts $\wt A^{ac} E_{\wt A^{ac}}(\cF)$ and $A^{ac}_0 E_{A^{ac}_0}(\cF)$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{corollary} \begin{remark}\Label{V.7} {\em { Let us} define the invariant maximal normal function \begin{equation}\label{4.12A}\hspace{-1.45mm} \gotm^+(t) := \sup_{y\in(0,1]} \left\\|{\im(M(i))}^{-1/2}\left(M(t+iy) - \re(M(i))\right){\im(M(i))}^{-1/2} \right\\|, \end{equation} for $t \in \R$. For Weyl functions one easily proves that $m^+(t)$ is finite if and only if $\gotm^+(t)$ is finite. \item[\;\;(i)] The quantity $\gotm^+(t)$ has the advantage that it is invariant: Let $A$ be a densely defined closed symmetric operator, ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ a boundary triplet for $A^,$ and $M(\cdot)$ the corresponding Weyl function. Further, let $\wt{\Pi} = \{\wt\cH,\wt{\Gamma}_0,\wt{\Gamma}_1\}$ be another boundary triplet for $A^$ with the Weyl function $\wt{M}(\cdot)$ and let $A_0 := A^\upharpoonright{\xker\,}({\Gamma}_0) = A^\upharpoonright{\xker\,}(\wt{\Gamma}_0)$. In this case $M(\cdot)$ and $\wt M(\cdot)$ are related by \eqref{2.11} However, $\wt \gotm^+(t) = \gotm^+(t)$ for $t \in \R$, where $\gotm^+(t)$ is obtained { by} replacing in \eqref{4.12A} $M(\cdot)$ by $\wt M(\cdot)$. \item[\;\;(ii)] Further, if the Weyl function $M(\cdot)$ satisfies $M(i) = i$, then $m^+(t) = \got	-0.032977	-1.294913	0.184252	1.804436	[ 0.08672005348740752, -0.15267353008728207 ]	[ -1.309238306786291, -1.2805882494853356 ]	[ 0.26794836178409004, 0.1005564541087283 ]	[ 2.1166000179089077, 1.4922711535282154 ]	1,024	[ 512, 512 ]	[ 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 7857, 1852, 26420, 408, 297, 320, 4915, 29912, 29945, 29889, 29941, 29874, 29913, 322, 13, 29905, 4915, 29912, 29945, 29889, 29941, 29890, 29913, 591, 4017, 13, 29905, 463, 29912, 9441, 4044, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29898, 29873, 876, 29913, 29928, 5940, 876, 500, 1966, 13, 29987, 669, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29898, 29873, 876, 15379, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29898, 29873, 13697, 353, 13, 29881, 29918, 29924, 29898, 29873, 29897, 320, 355, 29912, 9441, 4044, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 2401, 5890, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 591, 4866, 278, 13, 8017, 29889, 13, 13, 29912, 29871, 9788, 29892, 29871, 591, 3394, 29871, 2994, 21982, 320, 999, 29912, 29963, 29889, 29896, 29909, 29913, 304, 10985, 278, 13, 8017, 363, 17752, 779, 14554, 319, 29938, 451, 766, 12090, 411, 395, 29909, 29918, 29900, 7449, 29913, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 331, 13, 13, 29912, 29871, 450, 1121, 408, 1532, 408, 278, 5296, 9242, 2854, 29913, 565, 395, 29909, 29938, 338, 13, 29912, 1661, 29899, 21518, 873, 29913, 3342, 29889, 512, 445, 1206, 426, 29871, 372, 9378, 1575, 304, 13, 1509, 29913, 278, 10452, 21954, 29873, 11043, 363, 1661, 29899, 21518, 873, 3342, 13, 3372, 4097, 8906, 297, 320, 2036, 29912, 23560, 29929, 29945, 29892, 21870, 29929, 29906, 29890, 1118, 274, 29888, 29889, 5296, 310, 10244, 13, 29905, 999, 29912, 29963, 29889, 29896, 1836, 2398, 29892, 278, 20813, 373, 278, 399, 1032, 29880, 740, 526, 13, 513, 11936, 575, 519, 29889, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 13, 29912, 450, 1494, 1121, 13, 275, 16800, 515, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 322, 10244, 320, 999, 29912, 29963, 29889, 29945, 1836, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 29963, 29889, 29953, 29913, 13, 12024, 278, 20813, 310, 10244, 320, 999, 29912, 29963, 29889, 29945, 29913, 367, 15787, 322, 1235, 13, 29905, 463, 29912, 2573, 29913, 13, 29905, 29883, 29943, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 286, 14747, 29898, 29873, 29897, 529, 320, 3411, 29905, 1836, 13, 29905, 355, 29912, 2573, 29913, 13, 3644, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 8640, 29892, 769, 278, 5633, 779, 14554, 319, 998, 562, 29913, 382, 1665, 14554, 13, 29909, 998, 562, 20828, 29883, 29943, 1262, 322, 395, 29909, 998, 562, 2403, 29900, 382, 648, 29909, 998, 562, 2403, 29900, 4678, 29883, 29943, 1262, 310, 779, 14554, 319, 29938, 322, 13, 29938, 29909, 29918, 29900, 1628, 8307, 29892, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 26294, 1012, 4775, 29912, 29963, 29889, 29955, 29913, 13, 741, 331, 13, 29912, 2803, 502, 29913, 4529, 29871, 278, 22619, 23183, 4226, 740, 13, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29896, 29906, 29909, 1012, 14158, 8499, 29896, 29889, 29946, 29945, 4317, 29913, 13, 29905, 7085, 29885, 14747, 29898, 29873, 29897, 3490, 320, 12587, 648, 29891, 29905, 262, 29898, 29900, 29892, 29896, 12258, 13, 29905, 1563, 7893, 741, 326, 29898, 29924, 29898, 29875, 876, 19579, 29896, 29914, 29906, 1012, 1563, 29898, 29924, 29898, 29873, 29974, 19881, 29897, 448, 13, 29905, 276, 29898, 29924, 29898, 29875, 28986, 1266, 21964, 326, 29898, 29924, 29898, 29875, 876, 19579, 29896, 29914, 29906, 29913, 13, 29905, 1266, 7893, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 1454, 395, 29873, 320, 262, 320, 29934, 1504, 1152, 399, 1032, 29880, 3168, 697, 5948, 28281, 393, 13, 29938, 29885, 14747, 29898, 29873, 1262, 338, 8093, 565, 322, 871, 565, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 8093, 29889, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 29875, 4638, 450, 14728, 779, 7085, 29885, 14747, 29898, 29873, 1262, 756, 278, 10631, 393, 372, 338, 13, 262, 19365, 29901, 2803, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 29892, 13, 29938, 741, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 8209, 322, 13, 29938, 29924, 1194, 3822, 1262, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 8725, 29892, 1235, 779, 14554, 741, 12197, 29913, 13, 29922, 320, 741, 14554, 29905, 29883, 29950, 2053, 14554, 741, 6642, 2403, 29900, 2053, 14554, 741, 6642, 2403, 29896, 11854, 367, 1790, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 411, 278, 399, 1032, 29880, 740, 779, 14554, 29912, 29924, 4678, 3822, 1262, 322, 1235, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 29897, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 4678, 14554, 741, 6642, 2403, 29900, 4935, 13, 797, 445, 1206, 395, 29924, 1194, 3822, 1262, 322, 779, 14554, 341, 1194, 3822, 1262, 526, 4475, 491, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29896, 29913, 2398, 29892, 779, 14554, 320, 7085, 29885, 14747, 29898, 29873, 29897, 353, 320, 7085, 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 13, 29905, 29934, 1628, 988, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 7625, 426, 491, 29913, 15270, 297, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 395, 29924, 1194, 3822, 1262, 491, 779, 14554, 341, 1194, 3822, 4935, 13, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 2236, 4638, 8725, 29892, 29871, 565, 278, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 13, 29879, 27685, 583, 395, 29924, 29898, 29875, 29897, 353, 474, 1628, 769, 395, 29885, 14747, 29898, 29873, 29897, 353, 320, 7085 ]	1,332,863	29,696	ArXiv	-1	-1
m^+(t)$ for $t \in \R$. \item[\;\;(iii)] Let $\pi$ be an orthogonal projection onto a subspace $\wh\cH$ { of $\cH$}. If $\gotm^+(t)$ is finite, then the invariant maximal normal function $\wh \gotm^+(t)$, obtained from \eqref{4.12A} replacing $M(\cdot)$ by $\wh M(\cdot) := \pi M(\cdot)\upharpoonright \wh\cH$, is also finite and satisfies $\wh \gotm^+(t) \le \gotm^+(t)$ for $t \in \R$. } \end{remark} \section{Direct sums of symmetric operators} \subsection{Boundary triplets for direct sums} Let ${ S_n}$ be a closed densely defined symmetric { operators} in $\gotH_n,$ \ $n_+({ S_n})=n_-( S_n),$ and { let ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ be} a boundary triplet for $S_n^,\ n\in \N.$ Let \begin{equation}\Label{6.5a} A := \bigoplus^\infty_{n=1}{ S_n}, \quad {\rm dom\,}(A) := \bigoplus^\infty_{n=1}{\rm dom\,}({ S_n}). \end{equation} Clearly, $A$ is a closed densely defined symmetric operator in the Hilbert space $\gotH := \bigoplus^\infty_{n=1}\gotH_n$ with $n_\pm(A)= \infty.$ Consider the direct sum ${\Pi}:=\oplus_{n=1}^{\infty} {\Pi}_n=: \{\cH,{\Gamma}_{0},{\Gamma}_{1}\}$ of (ordinary) boundary triplets defined by \begin{equation}\Label{6.5} \cH := \bigoplus^\infty_{n=1}\cH_n, \quad {\Gamma}_0 := \bigoplus^\infty_{n=1}{\Gamma}_{0n} \quad \mbox{and} \quad {\Gamma}_1 := \bigoplus^\infty_{n=1}{\Gamma}_{1n}. \end{equation} { Clearly,} \begin{equation}\Label{6.5b} A^ = \bigoplus^\infty_{n=1}{ S}^_n, \quad {\rm dom\,}(A^) = \bigoplus^\infty_{n=1}{\rm dom\,}({ S}^_n). \end{equation} { We note that the Green's identity} \begin{displaymath} ( S_n^f_n, g_n) - (f_n, S_n^g_n) = ({\Gamma}_{1n}f_n,{\Gamma}_{0n}g_n)_{\cH_n} - ({\Gamma}_{0n}f_n, {\Gamma}_{1n}g_n)_{\cH_n}, \end{displaymath} { $f_n, g_n \in {\rm dom\,}( S_n^)$, holds for every $S^_n$, $n \in \N$. This yields the} Green's identity \eqref{3.1} for $A_:= A^\upharpoonright {\rm dom\,} ({\Gamma})$, ${\rm dom\,} ({\Gamma}) := {\rm dom\,} ({\Gamma}_0) \cap {\rm dom\,} ({\Gamma}_1) \subseteq {\rm dom\,} (A^)$, that is, for $f=\oplus_{n=1}^{\infty}f_n$, $g = \oplus_{n=1}^\infty g_n \in {\rm dom\,} ({\Gamma})$ we have \begin{equation}\label{3.1AA} (A_f, g) - (f, A_g) = ({\Gamma}_1f, {\Gamma}_0 g)_{\cH} - ({\Gamma}_0 f, {\Gamma}_1 g)_{\cH}, \qquad f,g\in{\rm dom\,}({\Gamma}), \end{equation} where $A^*$ and ${\Gamma}_j$ are defined by \eqref{6.5b} and \eqref{6.5}, respectively	-0.404309	-1.373701	-0.22218	1.846058	[ -0.42279920610013133, -0.3858179695171648 ]	[ -1.3880259643639186, -1.3593759070629632 ]	[ -0.11756027407431886, -0.3268001586685211 ]	[ 1.7628136614265153, 1.9293013585947 ]	1,024	[ 512, 512 ]	[ 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 320, 29934, 1504, 13, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 25609, 4638, 2803, 779, 1631, 29938, 367, 385, 28143, 18246, 11480, 263, 1014, 3493, 13, 4535, 1332, 29905, 29883, 29950, 29938, 426, 310, 779, 29883, 29950, 29938, 1836, 960, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 8093, 29892, 769, 278, 13, 262, 19365, 23183, 4226, 740, 779, 1332, 320, 7085, 29885, 14747, 29898, 29873, 5767, 29871, 7625, 515, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 15270, 395, 29924, 1194, 3822, 1262, 491, 779, 1332, 341, 1194, 3822, 29897, 3490, 320, 1631, 13, 29924, 1194, 3822, 2144, 29884, 561, 279, 1129, 265, 1266, 320, 1332, 29905, 29883, 29950, 1628, 338, 884, 8093, 322, 17150, 779, 1332, 13, 29905, 7085, 29885, 14747, 29898, 29873, 29897, 320, 280, 320, 7085, 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 29905, 2042, 29912, 17392, 25470, 310, 18348, 12768, 29913, 13, 13, 29905, 7235, 29912, 17109, 653, 21954, 1372, 363, 1513, 25470, 29913, 13, 13, 12024, 6435, 317, 29918, 29876, 1042, 367, 263, 5764, 6245, 873, 3342, 18348, 426, 13, 3372, 4097, 29913, 297, 779, 7085, 29950, 29918, 29876, 8209, 320, 395, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 17722, 317, 29918, 29876, 511, 29938, 322, 426, 1235, 13, 29938, 741, 12197, 2403, 29876, 353, 320, 741, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 29871, 367, 29913, 263, 10452, 21954, 29873, 363, 13, 29938, 29903, 29918, 29876, 6622, 2053, 302, 29905, 262, 320, 29940, 7449, 2803, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29874, 29913, 13, 29909, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 29918, 29876, 1118, 320, 3425, 2802, 1758, 2432, 5940, 2119, 29909, 29897, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 7690, 13, 29905, 355, 29912, 2573, 29913, 13, 18759, 368, 29892, 395, 29909, 29938, 338, 263, 5764, 6245, 873, 3342, 18348, 5455, 29871, 297, 13, 1552, 12338, 2151, 2913, 29871, 779, 7085, 29950, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 7085, 29950, 29918, 29876, 29938, 411, 13, 29938, 29876, 3187, 3358, 29898, 29909, 3892, 320, 3411, 7449, 10056, 278, 1513, 2533, 13, 29938, 741, 12197, 6177, 2013, 17201, 648, 29876, 29922, 29896, 6292, 3411, 29913, 2802, 12197, 2403, 29876, 29922, 29901, 320, 741, 29883, 29950, 29892, 741, 6642, 3227, 29900, 1118, 741, 6642, 3227, 29896, 1012, 1042, 310, 13, 29898, 24310, 29897, 10452, 21954, 1372, 3342, 491, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29913, 13, 29905, 29883, 29950, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 29883, 29950, 29918, 29876, 29892, 320, 3425, 2802, 6642, 2403, 29900, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 3227, 29900, 29876, 29913, 320, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 2802, 6642, 2403, 29896, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 3227, 29896, 29876, 1836, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 17732, 368, 29892, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29890, 29913, 13, 29909, 6622, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 2137, 29930, 29918, 29876, 29892, 320, 3425, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 353, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 317, 2137, 29930, 29918, 29876, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 1334, 4443, 393, 278, 7646, 29915, 29879, 10110, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 317, 29918, 29876, 6622, 29888, 29918, 29876, 29892, 330, 29918, 29876, 29897, 448, 313, 29888, 29918, 29876, 29892, 29871, 317, 29918, 29876, 6622, 29887, 29918, 29876, 29897, 353, 13, 13670, 6642, 3227, 29896, 29876, 29913, 29888, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 29913, 29887, 29918, 29876, 29897, 1665, 29883, 29950, 29918, 29876, 29913, 448, 313, 741, 6642, 3227, 29900, 29876, 29913, 29888, 29918, 29876, 29892, 13, 741, 6642, 3227, 29896, 29876, 29913, 29887, 29918, 29876, 29897, 1665, 29883, 29950, 29918, 29876, 1118, 320, 355, 29912, 4990, 755, 29913, 13, 29912, 395, 29888, 29918, 29876, 29892, 330, 29918, 29876, 320, 262, 2802, 1758, 2432, 5940, 2119, 317, 29918, 29876, 6622, 5767, 8640, 363, 1432, 395, 29903, 6622, 29918, 29876, 1628, 395, 29876, 320, 262, 13, 29905, 29940, 1504, 910, 17498, 278, 29913, 7646, 29915, 29879, 10110, 320, 4915, 29912, 29941, 29889, 29896, 29913, 363, 395, 29909, 24563, 9361, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 1758, 2432, 5940, 29913, 313, 741, 6642, 27394, 7555, 1758, 2432, 5940, 29913, 313, 741, 6642, 1800, 3490, 2802, 1758, 2432, 5940, 29913, 313, 741, 6642, 2403, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 29913, 313, 741, 6642, 2403, 29896, 29897, 320, 11725, 2802, 1758, 2432, 5940, 29913, 313, 29909, 6622, 5767, 393, 338, 29892, 363, 13, 29938, 29888, 2013, 17201, 648, 29876, 29922, 29896, 6292, 3411, 29913, 29888, 29918, 29876, 1628, 395, 29887, 353, 320, 17201, 648, 29876, 29922, 29896, 10206, 3411, 330, 29918, 29876, 320, 262, 13, 741, 1758, 2432, 5940, 29913, 313, 741, 6642, 8435, 591, 505, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29896, 6344, 29913, 13, 29898, 29909, 24563, 29888, 29892, 330, 29897, 448, 313, 29888, 29892, 319, 24563, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 2802, 6642, 2403, 29900, 330, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 285, 29892, 2802, 6642, 2403, 29896, 330, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 741, 6642, 9594, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29909, 6622, 29938, 322, 7555, 6642, 2403, 29926, 29938, 526, 3342, 491, 320, 4915, 29912, 29953, 29889, 29945, 29890, 29913, 322, 13, 29905, 4915, 29912, 29953, 29889, 29945, 1118, 8307 ]	1,332,863	30,720	ArXiv	-1	-1
. However, the Green's identity \eqref{3.1AA} cannot be extended to ${\rm dom\,}(A^)$ in general, since ${\rm dom\,}({\Gamma})$ is smaller than ${\rm dom\,}(A^)$ generically. It might even happen that ${\Gamma}_j$ are not bounded as mappings from ${\rm dom\,}(A^)$ equipped with the graph norm into $\cH.$ Counterexamples for the direct sum $\Pi=\oplus^\infty_{n=1} \Pi_n$, which { does not form} a boundary triplet, { firstly} appeared in \cite{Koch79}). In this section we show that it is always possible to modify the boundary triplets ${\Pi}_n$ in such a way that a new sequence $\wt {\Pi}_n= \{\cH_n,\wt{\Gamma}_{0},\wt{\Gamma}_{1}\}$ of boundary triplets for ${ S^_n}$ satisfies the following properties: $\wt {\Pi} = { \oplus^\infty_{n=1}} \wt {\Pi}_n$ { forms} a boundary triplet for $A^$ and the following relations { hold} \begin{equation}\Label{5.5A} { \wt S_{0n}} := { S^_n}\upharpoonright {\xker\,}(\wt{\Gamma}_{0n}) = { S^_n}\upharpoonright {\xker\,}({\Gamma}_{0n}) =: { S_{0n}}, \quad n\in \N. \end{equation} Hence $\wt A_{0} := { \oplus^\infty_{n=1} \wt S_{0n}} = { \oplus^\infty_{n=1}S_{0n}} =: A_0.$ { We note that the} existence of a boundary triplet ${\Pi}'= \{\cH, {\Gamma}'_{0}, {\Gamma}'_{1}\}$ for $A^$ satisfying ${\xker\,}({\Gamma}'_{0})= {\rm dom\,}(A_0) $ is known (see \cite{GG91, DM91}). However, we emphasize that in applications we need a special form \eqref{6.5} of a boundary triplet for $A^$ because it leads to the block-diagonal form of the corresponding Weyl function (cf. Sections 5.2, 5.3 below). We start with a simple technical lemma. \begin{lemma}\Label{VI.1} Let $S$ be a densely defined closed symmetric operator with equal deficiency indices, ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ a boundary triplet for $S^$, and $M(\cdot)$ the corresponding Weyl function. Then there exists a boundary triplet $\wt{{\Pi}} = \{\cH,\wt{{\Gamma}}_0,\wt{{\Gamma}}_1\}$ for $S^$ such that ${\xker\,}(\wt{{\Gamma}}_0) = {\xker\,}({\Gamma}_0)$ and the corresponding Weyl function $\wt{M}(\cdot)$ satisfies $\wt{M}(i) = i$. \end{lemma} \begin{proof} Let $M(i) = Q + iR^2$ where $Q := \re(M(i)),\ R := \sqrt{\im(M(i))}$. We set \begin{equation}\label{3.8} \wt{{\Gamma}}_0 := R{\Gamma}_0 \quad \mbox{and} \quad \wt{{\Gamma}}_1 := R^{-1}({\Gamma}_1 - Q{\Gamma}_0). \end{equation} A straightforward computation shows that $\wt{{\Pi}} : = \{\cH,\wt{{\Gamma}}_0,\wt{{\Gamma}}_1\}$ is a boundary triplet for $A^$. Clearly, ${\xker\,}(\wt{{\Gamma}}_0) = {\xker\,}({\Gamma}_0)$. The Weyl function $\wt{M}(\cdot)$ of $\wt{{\Pi}}$ is given by $\wt{M}(\cdot) = R^{-1}(M(\cdot) - Q)R^{-1}$ which yields $\wt{M}(i) = i$. \end{proof} If $S$ is a densely defined closed symmetric operator in $\gotH$, then by the first v. Neumann	0.522277	-0.71654	0.529181	2.43917	[ 0.29080169240822284, 0.7537519874098038 ]	[ -0.9153000188981529, -0.5177804738473953 ]	[ 0.1664987207687193, 0.8918636540286202 ]	[ 2.1374109800549306, 2.7409288822896 ]	1,024	[ 512, 512 ]	[ 29889, 2398, 29892, 278, 7646, 29915, 29879, 10110, 13, 29905, 4915, 29912, 29941, 29889, 29896, 6344, 29913, 2609, 367, 10410, 304, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 297, 2498, 29892, 1951, 13, 29938, 741, 1758, 2432, 5940, 2119, 741, 6642, 8435, 338, 7968, 1135, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 1176, 1711, 29889, 739, 1795, 1584, 13, 29882, 19934, 393, 7555, 6642, 2403, 29926, 29938, 526, 451, 12635, 408, 611, 27775, 515, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 13, 1686, 16242, 411, 278, 3983, 6056, 964, 779, 29883, 29950, 7449, 315, 5336, 19057, 363, 278, 13, 11851, 2533, 779, 12197, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 12197, 29918, 29876, 1628, 29871, 607, 426, 13, 13221, 451, 883, 29913, 263, 10452, 21954, 29873, 29892, 426, 937, 368, 29913, 7470, 297, 13, 29905, 2036, 29912, 29968, 2878, 29955, 29929, 7690, 13, 13, 797, 445, 4004, 591, 1510, 393, 372, 338, 2337, 1950, 304, 6623, 278, 13, 9917, 653, 21954, 1372, 7555, 12197, 2403, 29876, 29938, 297, 1316, 263, 982, 393, 263, 29871, 716, 5665, 779, 14554, 13, 741, 12197, 2403, 29876, 29922, 320, 741, 29883, 29950, 29918, 29876, 2053, 14554, 741, 6642, 3227, 29900, 7570, 14554, 741, 6642, 3227, 29896, 1012, 1042, 310, 10452, 21954, 1372, 363, 13, 5303, 317, 6622, 29918, 29876, 1042, 17150, 278, 1494, 4426, 29901, 29871, 779, 14554, 2802, 12197, 29913, 353, 13, 29912, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 930, 320, 14554, 2802, 12197, 2403, 29876, 29938, 426, 7190, 29913, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 29938, 322, 278, 1494, 5302, 426, 4808, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29945, 29909, 29913, 13, 29912, 320, 14554, 317, 648, 29900, 29876, 930, 3490, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 13, 741, 29916, 3946, 5940, 4678, 14554, 741, 6642, 3227, 29900, 29876, 1800, 353, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 1800, 353, 29901, 13, 29912, 317, 648, 29900, 29876, 11656, 320, 3425, 302, 29905, 262, 320, 29940, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29950, 663, 779, 14554, 319, 648, 29900, 29913, 3490, 426, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 14554, 317, 648, 29900, 29876, 930, 353, 426, 13, 29905, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29903, 648, 29900, 29876, 930, 353, 29901, 319, 29918, 29900, 7449, 426, 1334, 4443, 393, 278, 29913, 13, 735, 11416, 310, 263, 10452, 21954, 29873, 7555, 12197, 10162, 29922, 320, 741, 29883, 29950, 29892, 2802, 6642, 10162, 648, 29900, 1118, 13, 741, 6642, 10162, 648, 29896, 1012, 1042, 363, 395, 29909, 6622, 29938, 24064, 7555, 29916, 3946, 5940, 2119, 741, 6642, 10162, 648, 29900, 1800, 29922, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 395, 338, 13, 5203, 313, 4149, 320, 2036, 29912, 26788, 29929, 29896, 29892, 27692, 29929, 29896, 7690, 2398, 29892, 591, 19310, 675, 393, 297, 13, 932, 5795, 591, 817, 263, 4266, 883, 320, 4915, 29912, 29953, 29889, 29945, 29913, 310, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 29938, 1363, 372, 11981, 304, 278, 2908, 29899, 6051, 351, 7177, 883, 310, 13, 1552, 6590, 399, 1032, 29880, 740, 313, 6854, 29889, 922, 1953, 29871, 29945, 29889, 29906, 29892, 29871, 29945, 29889, 29941, 2400, 467, 13, 13, 4806, 1369, 411, 263, 2560, 16905, 10383, 29889, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 18118, 29889, 29896, 29913, 13, 12024, 395, 29903, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 411, 5186, 13, 1753, 293, 13396, 16285, 29892, 29871, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29903, 6622, 1628, 29871, 322, 395, 29924, 1194, 3822, 1262, 278, 6590, 399, 1032, 29880, 13, 2220, 29889, 1987, 727, 4864, 29871, 263, 10452, 21954, 29873, 779, 14554, 16195, 12197, 930, 353, 13, 24976, 29883, 29950, 2053, 14554, 16195, 6642, 15609, 29900, 2053, 14554, 16195, 6642, 15609, 29896, 11854, 363, 395, 29903, 6622, 29938, 1316, 393, 13, 29938, 741, 29916, 3946, 5940, 4678, 14554, 16195, 6642, 15609, 29900, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 322, 29871, 278, 6590, 399, 1032, 29880, 13, 2220, 779, 14554, 29912, 29924, 4678, 3822, 1262, 17150, 29871, 779, 14554, 29912, 29924, 2119, 29875, 29897, 353, 474, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 12024, 395, 29924, 29898, 29875, 29897, 353, 660, 718, 474, 29934, 29985, 29906, 29938, 988, 395, 29984, 3490, 320, 276, 29898, 29924, 29898, 29875, 8243, 29905, 390, 3490, 13, 29905, 3676, 741, 326, 29898, 29924, 29898, 29875, 876, 4311, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29947, 29913, 13, 29905, 14554, 16195, 6642, 15609, 29900, 3490, 390, 741, 6642, 2403, 29900, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29905, 14554, 16195, 6642, 15609, 29896, 3490, 390, 3426, 29896, 2119, 741, 6642, 2403, 29896, 448, 660, 741, 6642, 2403, 29900, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 29909, 20837, 16287, 3697, 393, 779, 14554, 16195, 12197, 930, 584, 353, 13, 24976, 29883, 29950, 2053, 14554, 16195, 6642, 15609, 29900, 2053, 14554, 16195, 6642, 15609, 29896, 11854, 338, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1504, 13, 18759, 368, 29892, 7555, 29916, 3946, 5940, 4678, 14554, 16195, 6642, 15609, 29900, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 450, 399, 1032, 29880, 740, 13, 4535, 14554, 29912, 29924, 4678, 3822, 1262, 310, 779, 14554, 16195, 12197, 7920, 338, 2183, 491, 779, 14554, 29912, 29924, 4678, 3822, 29897, 353, 13, 29934, 3426, 29896, 2119, 29924, 1194, 3822, 29897, 448, 660, 29897, 29934, 3426, 29896, 1042, 607, 17498, 779, 14554, 29912, 29924, 2119, 29875, 29897, 353, 474, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 3644, 395, 29903, 29938, 338, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 779, 7085, 29950, 1628, 13, 6098, 491, 278, 937, 325, 29889, 2448, 22553 ]	1,332,863	31,744	ArXiv	-1	-1
formula the direct decomposition ${\rm dom\,}(S^) = {\rm dom\,}(S) \stackrel{.}{+} \gotN_i \stackrel{.}{+} \gotN_{-i}$ holds where $\gotN_{\pm i} := {\xker\,}(S^\mp i)$. Equipping ${\rm dom\,}(S^)$ with the inner product \begin{equation}\Label{3.8b} (f,g)_+ := (S^f, S^g) + (f,g), \quad f,g \in {\rm dom\,}(S^), \end{equation} one obtains a Hilbert space denoted by $\gotH_+$. The first v. Neumann formula leads to the following orthogonal decomposition \begin{displaymath} \gotH_+ = {\rm dom\,}(S) \oplus \gotN_i \oplus \gotN_{-i}. \end{displaymath} \begin{lemma}\Label{VI.2} Let $S$ be as in Lemma \ref{VI.1}, let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a (ordinary) boundary triplet for $S^$, and $M(\cdot)$ the corresponding Weyl function. If $M(i) = i$, then the operator ${\Gamma}: \gotH_+ \longrightarrow \cH \oplus \cH$, ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top$ is a contraction. Moreover, ${\Gamma}$ isometrically maps $\gotN := \gotN_i\oplus \gotN_{-i}$ onto $\cH$. \end{lemma} \begin{proof} We show that \begin{equation}\Label{6.4} \\|{\Gamma}(f + f_i + f_{-i})\\|^2_{\cH \oplus \cH} = \\|f_i + f_{-i}\\|^2_+ \end{equation} where $f \stackrel{.}{+} f_i \stackrel{.}{+} f_{-i} \in {\rm dom\,}(S) \stackrel{.}{+} \gotN_i \stackrel{.}{+} \gotN_{-i} = {\rm dom\,}(S^)$. Indeed, { since ${\rm dom\,}(S) = {\xker\,}({\Gamma}_0) \cap {\xker\,}({\Gamma}_1)$, we find} \begin{displaymath} \\|{\Gamma}(f + f_i + f_{-i})\\|^2_{\cH \oplus \cH} = \\|{\Gamma}_0(f_i + f_{-i})\\|^2_\cH + \\|{\Gamma}_1(f_i + f_{-i})\\|^2_\cH. \end{displaymath} Clearly, \begin{equation}\Label{6.4A} \\|{\Gamma}_j(f_i + f_{-i})\\|^2_\cH = \\|{\Gamma}_jf_i\\|^2 + 2\re(({\Gamma}_jf_i,{\Gamma}_jf_{-i})) +\ \\|{\Gamma}_jf_{-i}\\|^2, \quad j\in \{0,1\}. \end{equation} Using ${\Gamma}_1f_i = M(i){\Gamma}_0f_i = i{\Gamma}_0f_i$ and ${\Gamma}_1f_{-i} = M(-i){\Gamma}_0f_{-i} = -i{\Gamma}_0f_{-i}$ we obtain \begin{equation}\Label{6.4B} \\|{\Gamma}_1(f_i + f_{-i})\\|^2_\cH = ({\Gamma}_0f_i,{\Gamma}_0f_i) - 2\re(({\Gamma}_0f_i,{\Gamma}_0f_{-i})) + ({\Gamma}_0f_{-i},{\Gamma}_0f_{-i}) \end{equation} Taking a sum of \eqref{6.4A} and \eqref{6.4B} we get \begin{equation}\Label{6.4BC} \\|{\Gamma}_0(f_i + f_{-i})\\|^2_\cH + \\|{\Gamma}_1(f_i + f_{-i})\\|^2_\cH = 2\\|{\Gamma}_0f_i\\|^2_\cH + 2\\|{\Gamma	0.084537	-1.094363	0.185521	2.428764	[ 0.3291526044201881, -0.16007833787530662 ]	[ -0.7720497323933754, -1.4166760216648742 ]	[ 0.5520073566271282, -0.18096629970892558 ]	[ 2.4703863743912997, 2.3871425258072074 ]	1,024	[ 512, 512 ]	[ 7063, 278, 1513, 26227, 13, 29938, 741, 1758, 2432, 5940, 2119, 29903, 6622, 29897, 353, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 13, 29905, 7085, 29940, 22631, 29875, 1042, 29871, 8640, 988, 779, 7085, 29940, 1665, 3358, 474, 29913, 3490, 2802, 29916, 3946, 5940, 2119, 29903, 6622, 29905, 1526, 474, 4935, 13, 6108, 17347, 29871, 7555, 1758, 2432, 5940, 2119, 29903, 6622, 1262, 411, 278, 6426, 29871, 3234, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29947, 29890, 29913, 13, 29898, 29888, 29892, 29887, 20344, 29974, 3490, 313, 29903, 6622, 29888, 29892, 317, 6622, 29887, 29897, 718, 313, 29888, 29892, 29887, 511, 320, 3425, 285, 29892, 29887, 320, 262, 2802, 1758, 2432, 5940, 2119, 29903, 6622, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 650, 4017, 29879, 263, 12338, 2151, 2913, 27291, 491, 779, 7085, 29950, 28842, 1504, 13, 1576, 937, 325, 29889, 2448, 22553, 7063, 11981, 304, 278, 1494, 13, 2072, 23419, 26227, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 7085, 29950, 28842, 353, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 320, 17201, 320, 7085, 29940, 29918, 29875, 320, 17201, 320, 7085, 29940, 22631, 29875, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 18118, 29889, 29906, 29913, 13, 12024, 395, 29903, 29938, 367, 408, 297, 11894, 320, 999, 29912, 18118, 29889, 29896, 1118, 1235, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 13, 915, 263, 313, 24310, 29897, 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 322, 395, 29924, 1194, 3822, 1262, 278, 13, 2616, 3636, 292, 29871, 399, 1032, 29880, 740, 29889, 29871, 960, 395, 29924, 29898, 29875, 29897, 353, 474, 1628, 769, 278, 5455, 13, 29938, 741, 6642, 6177, 320, 7085, 29950, 28842, 320, 24225, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1628, 13, 29938, 741, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29938, 29871, 338, 263, 6761, 428, 29889, 12808, 29892, 7555, 6642, 1042, 13, 275, 3297, 29878, 1711, 11053, 779, 7085, 29940, 3490, 320, 7085, 29940, 29918, 29875, 29905, 17201, 320, 7085, 29940, 22631, 29875, 1042, 11480, 779, 29883, 29950, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 4806, 1510, 393, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29913, 13, 7893, 741, 6642, 2119, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 1665, 29883, 29950, 320, 17201, 320, 29883, 29950, 29913, 353, 12926, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29888, 320, 1429, 2674, 26139, 1157, 29974, 29913, 285, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 285, 22631, 29875, 29913, 320, 262, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 13, 29905, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 22631, 29875, 29913, 353, 2802, 1758, 2432, 5940, 2119, 29903, 6622, 4935, 13, 2568, 12613, 29892, 426, 1951, 7555, 1758, 2432, 5940, 2119, 29903, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 29897, 320, 5030, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 5767, 591, 13, 2886, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 7893, 741, 6642, 2119, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 1665, 29883, 29950, 320, 17201, 320, 29883, 29950, 29913, 353, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 18759, 368, 29892, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29909, 29913, 12926, 741, 6642, 2403, 29926, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 12926, 741, 6642, 2403, 29926, 29888, 29918, 29875, 7893, 29985, 29906, 29871, 718, 13, 29906, 29905, 276, 3552, 741, 6642, 2403, 29926, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29926, 29888, 22631, 29875, 20073, 17501, 29871, 12926, 741, 6642, 2403, 29926, 29888, 22631, 29875, 1012, 15333, 29906, 29892, 320, 3425, 432, 29905, 262, 13, 10045, 29900, 29892, 29896, 29905, 1836, 320, 355, 29912, 2573, 29913, 13, 15156, 7555, 6642, 2403, 29896, 29888, 29918, 29875, 353, 341, 29898, 29875, 21964, 6642, 2403, 29900, 29888, 29918, 29875, 353, 474, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29938, 322, 7555, 6642, 2403, 29896, 29888, 22631, 29875, 29913, 353, 341, 6278, 29875, 21964, 6642, 2403, 29900, 29888, 22631, 29875, 29913, 353, 448, 29875, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1042, 13, 705, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29933, 29913, 13, 7893, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 13670, 6642, 2403, 29900, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29897, 448, 29871, 29906, 29905, 276, 3552, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29900, 29888, 22631, 29875, 20073, 718, 313, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1118, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1800, 13, 29905, 355, 29912, 2573, 29913, 13, 29911, 5086, 263, 2533, 310, 320, 4915, 29912, 29953, 29889, 29946, 29909, 29913, 322, 320, 4915, 29912, 29953, 29889, 29946, 29933, 29913, 591, 679, 13, 268, 320, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 5371, 29913, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 29906, 7893, 741, 6642, 2403, 29900, 29888, 29918, 29875, 7893, 29985, 29906, 3187, 29883, 29950, 718, 29871, 29906, 7893, 741, 6642 ]	1,332,863	32,768	ArXiv	-1	-1
}_0f_{-i}\\|^2_\cH. \end{equation} Combining equalities ${\Gamma}_1f_{\pm i}= \pm i {\Gamma}_0f_{\pm i}$ with Green's identity \eqref{2.10A} we obtain $\\|{\Gamma}_0f_i\\|_\cH = \\|f_i\\|$ and $\\|{\Gamma}_0f_{-i}\\|_\cH = \\|f_{-i}\\|$. { Therefore \eqref{6.4BC} takes the form} \begin{equation}\Label{6.4C} \\|{\Gamma}_0(f_i + f_{-i})\\|^2_\cH + \\|{\Gamma}_1(f_i + f_{-i})\\|^2_\cH = 2\\|f_i\\|^2 + 2\\|f_{-i}\\|^2. \end{equation} A straightforward computation shows $\\|f_i + f_{-i}\\|^2_+ = 2\\|f_i\\|^2 + 2\\|f_{-i}\\|^2$ which together with \eqref{6.4C} proves \eqref{6.4}. Since $\\|f_i + f_{-i}\\|^2_+ \le \\|f\\|^2_+ + \\|f_i + f_{-i}\\|^2_+ = \\|f + f_i + f_{-i}\\|^2_+$, we get from \eqref{6.4} that ${\Gamma}$ is a contraction. Obviously, ${\Gamma}$ is an isometry from $\gotN$ into $\cH \oplus \cH$. Since ${\Pi}$ is a boundary triplet for $S^$, ${\rm ran\,}({\Gamma}) = \cH \oplus \cH.$ { Hence} ${\Gamma}$ is an isometry from $\gotN$ onto $\cH \oplus \cH$. \end{proof} Passing to direct sum \eqref{6.5a}, we equip ${\rm dom\,}(A^_n)$ and ${\rm dom\,}(A^)$ with the graph's norms and obtain the Hilbert spaces $\gotH_{+n}$ and $\gotH_+$, respectively. Clearly, the corresponding inner products $(f,g)_{+n}$ and $(f,g)_+$ are defined by \eqref{3.8b} with $S$ replaced by ${ S_n}$ and $A$, respectively. Obviously, $\gotH_+ = \bigoplus^\infty_{n=1} \gotH_{+n}.$ \begin{theorem}\Label{VI.3} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let $A$ and $A_0$ be given by \eqref{6.5a} and \begin{equation}\Label{6.8} A_0 := \bigoplus^\infty_{n=1}{ S_{0n}}, \end{equation} respectively. Then there exist boundary triplets ${\Pi}_n := \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for ${ S^_n}$ such that ${ S_{0n}} = { S^_n}\upharpoonright{\xker\,}({\Gamma}_{0n})$, $n \in \N$, and the direct sum ${ {\Pi} = \oplus^\infty_{n=1} {\Pi}_n}$ defined by \eqref{6.5} forms an ordinary boundary triplet for $A^$ satisfying $A_0 = A^\upharpoonright{\xker\,}({\Gamma}_0)$. Moreover, the corresponding Weyl function $M(\cdot)$ and the ${\gamma}$-field ${\gamma}(\cdot)$ are { given by} \begin{equation}\Label{6.7} M(z) = \bigoplus^\infty_{n=1}M_n(z) \quad \mbox{and} \quad {\gamma}(z) = \bigoplus^\infty_{n=1}{\gamma}_n(z) \end{equation} where $M_n(\cdot)$ and ${\gamma}_n(\cdot	-0.016519	-1.405932	0.021933	2.199844	[ 0.17163993008533066, -0.20467839403207874 ]	[ -1.5169512222182184, -1.2949132781358133 ]	[ 0.024469223347200215, 0.019396741296431676 ]	[ 2.1374109800549306, 2.262276752931069 ]	1,024	[ 512, 512 ]	[ 2403, 29900, 29888, 22631, 29875, 1012, 15333, 29906, 3187, 29883, 29950, 29889, 13, 539, 320, 355, 29912, 2573, 29913, 13, 1523, 2109, 292, 5186, 1907, 7555, 6642, 2403, 29896, 29888, 1665, 3358, 474, 5369, 320, 3358, 474, 2802, 6642, 2403, 29900, 29888, 1665, 3358, 474, 1042, 411, 13, 24599, 29915, 29879, 29871, 10110, 320, 4915, 29912, 29906, 29889, 29896, 29900, 29909, 29913, 29871, 591, 4017, 779, 29989, 741, 6642, 2403, 29900, 29888, 29918, 29875, 7893, 3187, 29883, 29950, 353, 13, 7893, 29888, 29918, 29875, 7893, 29938, 322, 779, 29989, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1012, 29989, 3187, 29883, 29950, 353, 12926, 29888, 22631, 29875, 1012, 29989, 1504, 426, 7857, 13, 29905, 4915, 29912, 29953, 29889, 29946, 5371, 29913, 4893, 278, 883, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29907, 29913, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 29906, 7893, 29888, 29918, 29875, 7893, 29985, 29906, 718, 29871, 29906, 7893, 29888, 22631, 29875, 1012, 15333, 29906, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29909, 20837, 16287, 3697, 13, 4535, 29989, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 353, 29871, 29906, 7893, 29888, 29918, 29875, 7893, 29985, 29906, 718, 29871, 29906, 7893, 29888, 22631, 29875, 1012, 15333, 29906, 29938, 13, 4716, 4208, 411, 320, 4915, 29912, 29953, 29889, 29946, 29907, 29913, 28281, 320, 4915, 29912, 29953, 29889, 29946, 1836, 13, 23036, 779, 29989, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 320, 280, 12926, 29888, 7893, 29985, 29906, 28842, 718, 12926, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 353, 13, 7893, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 1628, 591, 679, 515, 320, 4915, 29912, 29953, 29889, 29946, 29913, 393, 7555, 6642, 1042, 338, 263, 6761, 428, 29889, 13, 13, 6039, 16604, 29892, 7555, 6642, 1042, 338, 385, 338, 7843, 515, 779, 7085, 29940, 29938, 964, 779, 29883, 29950, 320, 17201, 13, 29905, 29883, 29950, 1504, 4001, 7555, 12197, 1042, 338, 263, 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 13, 7555, 1758, 6350, 5940, 2119, 741, 6642, 1800, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 7449, 426, 10133, 29913, 7555, 6642, 1042, 13, 275, 385, 338, 7843, 515, 779, 7085, 29940, 29938, 11480, 779, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 7129, 292, 304, 29871, 1513, 2533, 320, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 591, 29871, 7462, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 29918, 29876, 1262, 322, 13, 29938, 741, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 411, 278, 3983, 29915, 29879, 6056, 29879, 322, 4017, 278, 12338, 2151, 8162, 13, 4535, 7085, 29950, 648, 29974, 29876, 1042, 322, 779, 7085, 29950, 28842, 1628, 8307, 29889, 17732, 368, 29892, 278, 13, 2616, 3636, 292, 6426, 9316, 2427, 29888, 29892, 29887, 20439, 29974, 29876, 1042, 13, 392, 2427, 29888, 29892, 29887, 20344, 24035, 526, 3342, 491, 320, 4915, 29912, 29941, 29889, 29947, 29890, 29913, 411, 395, 29903, 29938, 8611, 491, 13, 5303, 317, 29918, 29876, 1042, 322, 395, 29909, 1628, 8307, 29889, 25735, 29892, 779, 7085, 29950, 28842, 353, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 7085, 29950, 648, 29974, 29876, 1836, 29938, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 18118, 29889, 29941, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 13, 15603, 18348, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 13, 29903, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 8725, 29892, 1235, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 29938, 367, 13, 29887, 5428, 491, 320, 4915, 29912, 29953, 29889, 29945, 29874, 29913, 322, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29947, 29913, 13, 29909, 29918, 29900, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 648, 29900, 29876, 11656, 13, 29905, 355, 29912, 2573, 29913, 13, 690, 1103, 3598, 29889, 1987, 727, 1863, 10452, 21954, 1372, 7555, 12197, 2403, 29876, 3490, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 363, 6435, 317, 6622, 29918, 29876, 1042, 1316, 393, 6435, 13, 29903, 648, 29900, 29876, 930, 353, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 395, 29876, 320, 262, 320, 29940, 1628, 13, 392, 278, 1513, 2533, 6435, 2802, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 2802, 12197, 2403, 29876, 1042, 13, 12119, 491, 320, 4915, 29912, 29953, 29889, 29945, 29913, 7190, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 24064, 395, 29909, 29918, 29900, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 12808, 29892, 13, 1552, 6590, 29871, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 322, 278, 7555, 4283, 23021, 2671, 13, 29938, 741, 4283, 4678, 3822, 1262, 526, 426, 2183, 491, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29955, 29913, 13, 29924, 29898, 29920, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29924, 29918, 29876, 29898, 29920, 29897, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 741, 4283, 2119, 29920, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 4283, 2403, 29876, 29898, 29920, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29924, 29918, 29876, 1194, 3822, 1262, 322, 7555, 4283, 2403, 29876, 1194, 3822 ]	1,332,863	33,792	ArXiv	-1	-1
)$ are the Weyl functions and the ${\gamma}$-field corresponding to ${\Pi}_n, \ n\in \N$. In addition, the condition { $M(i) = iI$} { holds}. \end{theorem} \begin{proof} For every ${ S_{0n}} = { S^_{0n}}\in {\rm Ext\,} { S_n}$ there exists a boundary triplet ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for $S_n^$ such that ${ S_{0n}} := A^_n\upharpoonright{\xker\,}({\Gamma}_{0n})$ (see \cite{DM91}). By Lemma \ref{VI.1} we can assume without loss of generality that the corresponding Weyl function $M_{n}(\cdot)$ satisfies $M_n(i) = i$. By Lemma \ref{VI.2} the mapping ${\Gamma}^n:=(\Gamma_{0n},\Gamma_{1n})^\top: \gotH_{+n} \longrightarrow \cH_n \oplus \cH_n$, is contractive { for each} $n\in \N$. Hence $\\|{\Gamma}_j\\| = \sup_{n}\\|{\Gamma}_{jn}\\|\le 1, j\in \{0,1\}$, where ${\Gamma}_0$ and ${\Gamma}_1$ are defined by \eqref{6.5}. It follows that the mappings ${\Gamma}_0$ and ${\Gamma}_1$ are well-defined on ${\rm dom\,}({\Gamma}) = {\rm dom\,}(A^) = \bigoplus^\infty_{n=1}{\rm dom\,}({ S^_n})$. Thus, { the Green's} identity \eqref{3.1AA} holds for all $f,g \in {\rm dom\,}(A^).$ Further, we set $\gotN_{\pm in} := {\xker\,}({ S^_n} \mp i)$,\ $\gotN_n := \gotN_{in} \stackrel{.}{+} \gotN_{-in}$, $\gotN_{\pm i} := {\xker\,}(A^ \mp i)$ and $\gotN := \gotN_i \stackrel{.}{+} \gotN_{-i}.$ By Lemma \ref{VI.2} the restriction ${\Gamma}^n\upharpoonright\gotN_n$ is an isometry from $\gotN_n,$ regarded as a subspace of $\gotH_{+n},$ onto $\cH_n \oplus \cH_n$. Since $\gotN$ regarded as a subspace of $\gotH_+$ admits the representation $\gotN = \bigoplus^\infty_{n=1}\gotN_n$, the restriction ${\Gamma}\upharpoonright\gotN$, ${\Gamma} := \bigoplus^\infty_{n=1}{\Gamma}^n$, isometrically maps $\gotN$ onto $\cH \oplus \cH$. Hence ${\rm ran\,}({\Gamma}) = \cH \oplus \cH$. Equalities \eqref{6.7} are immediate from Definition \ref{Weylfunc}. \end{proof} \begin{remark} {\rm Kochubei \cite{Koch79} proved that $\Pi=\oplus^{\infty}_{n=1}\Pi_n$ forms a boundary triplet whenever any pair $\{{ S_n},{ S_{0n}}\},$\ ${ S_{0n}} := S^*_n\upharpoonright{\xker\,}({\Gamma}_{0n})$, ${n\in\N}$, is unitarily equivalent to { $\{S_1,S_{01}\}$}. } \end{remark} Recall, that for any non-negative symmetric operator { $A$} the set of its non-negative self-adjoint extensions { ${\rm Ext\,}_A(0,\infty)$} is non-empty (see \cite{AG81, Ka76}). The set ${\rm Ext\,}_A(0,\infty)$ contains the Friedrichs (the biggest) extension $A^F$ and the Krein (the smallest) extension $A^K$. These extensions are uniquely determined by the following extremal property in the class ${\rm Ext	-0.051275	-1.081828	-0.075712	2.168627	[ -0.2591229923347795, 0.1565735003663443 ]	[ -1.1230129343300803, -1.0406440195898332 ]	[ -0.09727034587124471, -0.05415424843971213 ]	[ 2.0541671314708383, 2.2830877150770923 ]	1,024	[ 512, 512 ]	[ 1262, 526, 278, 399, 1032, 29880, 3168, 322, 13, 1552, 7555, 4283, 23021, 2671, 6590, 304, 7555, 12197, 2403, 29876, 29892, 320, 302, 29905, 262, 320, 29940, 1504, 512, 6124, 29892, 13, 1552, 4195, 426, 395, 29924, 29898, 29875, 29897, 353, 474, 29902, 17133, 29871, 426, 8640, 1836, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2831, 1432, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 29913, 426, 317, 29918, 29876, 1042, 13, 12711, 4864, 263, 10452, 21954, 29873, 7555, 12197, 2403, 29876, 353, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 363, 395, 29903, 29918, 29876, 6622, 29938, 1316, 393, 6435, 317, 648, 29900, 29876, 930, 13, 9361, 319, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 8435, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 7690, 2648, 11894, 13, 29905, 999, 29912, 18118, 29889, 29896, 29913, 591, 508, 5251, 1728, 6410, 310, 2498, 537, 393, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 395, 29924, 648, 29876, 4678, 3822, 1262, 17150, 395, 29924, 29918, 29876, 29898, 29875, 29897, 353, 474, 1504, 13, 2059, 11894, 320, 999, 29912, 18118, 29889, 29906, 29913, 278, 10417, 13, 29938, 741, 6642, 2137, 29876, 9361, 1194, 6642, 648, 29900, 29876, 7570, 6642, 648, 29896, 29876, 1800, 3823, 3332, 29901, 320, 7085, 29950, 648, 29974, 29876, 29913, 320, 24225, 13, 29905, 29883, 29950, 29918, 29876, 320, 17201, 320, 29883, 29950, 29918, 29876, 1628, 338, 8078, 573, 426, 363, 1269, 29913, 395, 29876, 29905, 262, 320, 29940, 1504, 13, 29950, 663, 779, 29989, 741, 6642, 2403, 29926, 7893, 353, 320, 12587, 648, 29876, 1012, 29989, 741, 6642, 3227, 29926, 29876, 1012, 4295, 280, 29871, 29896, 29892, 29871, 432, 29905, 262, 9991, 29900, 29892, 29896, 28538, 13, 3062, 7555, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2403, 29896, 29938, 526, 3342, 491, 320, 4915, 29912, 29953, 29889, 29945, 1836, 739, 4477, 13, 5747, 278, 611, 27775, 7555, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2403, 29896, 29938, 526, 1532, 29899, 12119, 373, 13, 29938, 741, 1758, 2432, 5940, 2119, 741, 6642, 1800, 353, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 13, 29903, 6622, 29918, 29876, 23462, 6549, 29892, 426, 278, 7646, 29915, 29879, 29913, 10110, 320, 4915, 29912, 29941, 29889, 29896, 6344, 29913, 8640, 13, 1454, 599, 395, 29888, 29892, 29887, 320, 262, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 467, 29938, 13, 13, 29943, 332, 721, 29892, 591, 731, 779, 7085, 29940, 1665, 3358, 297, 29913, 3490, 2802, 29916, 3946, 5940, 2119, 29912, 317, 6622, 29918, 29876, 29913, 320, 1526, 474, 1262, 2053, 29871, 779, 7085, 29940, 29918, 29876, 13, 9361, 320, 7085, 29940, 648, 262, 29913, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 22631, 262, 4429, 779, 7085, 29940, 1665, 3358, 474, 29913, 3490, 13, 741, 29916, 3946, 5940, 2119, 29909, 6622, 320, 1526, 474, 1262, 322, 779, 7085, 29940, 3490, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 13, 29905, 7085, 29940, 22631, 29875, 1836, 29938, 29871, 2648, 11894, 320, 999, 29912, 18118, 29889, 29906, 29913, 29871, 278, 24345, 13, 29938, 741, 6642, 2137, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 29905, 7085, 29940, 29918, 29876, 29938, 338, 385, 338, 7843, 515, 779, 7085, 29940, 29918, 29876, 8209, 13, 1727, 25600, 408, 263, 1014, 3493, 310, 779, 7085, 29950, 648, 29974, 29876, 1118, 29938, 11480, 779, 29883, 29950, 29918, 29876, 320, 17201, 320, 29883, 29950, 29918, 29876, 1504, 13, 23036, 779, 7085, 29940, 29938, 17878, 408, 263, 1014, 3493, 310, 779, 7085, 29950, 29918, 24035, 7336, 1169, 278, 13, 276, 26081, 779, 7085, 29940, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 7085, 29940, 29918, 29876, 1628, 278, 13, 5060, 19902, 7555, 6642, 1012, 29884, 561, 279, 1129, 265, 1266, 29905, 7085, 29940, 1628, 7555, 6642, 29913, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 2137, 29876, 1628, 338, 3297, 29878, 1711, 11053, 779, 7085, 29940, 29938, 11480, 779, 29883, 29950, 13, 29905, 17201, 320, 29883, 29950, 1504, 10133, 7555, 1758, 6350, 5940, 2119, 741, 6642, 1800, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 11243, 284, 1907, 13, 29905, 4915, 29912, 29953, 29889, 29955, 29913, 526, 16800, 515, 29871, 21940, 320, 999, 29912, 29956, 1032, 29880, 9891, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 1758, 13, 29968, 2878, 4003, 29875, 320, 2036, 29912, 29968, 2878, 29955, 29929, 29913, 11827, 393, 13, 4535, 12197, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 1012, 12197, 29918, 29876, 29938, 7190, 263, 10452, 21954, 29873, 10940, 13, 1384, 29871, 5101, 779, 6224, 317, 29918, 29876, 29087, 317, 648, 29900, 29876, 4229, 1118, 4535, 6435, 317, 648, 29900, 29876, 930, 3490, 13, 29903, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 6435, 29876, 29905, 262, 29905, 29940, 4429, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 426, 12564, 29903, 29918, 29896, 29892, 29903, 648, 29900, 29896, 1012, 1042, 1836, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 13, 4789, 497, 29892, 393, 363, 738, 1661, 29899, 22198, 18348, 5455, 426, 395, 29909, 17133, 13, 1552, 731, 310, 967, 1661, 29899, 22198, 1583, 29899, 328, 12090, 17752, 426, 13, 29938, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1262, 29913, 338, 1661, 29899, 6310, 313, 4149, 320, 2036, 29912, 10051, 29947, 29896, 29892, 13680, 29955, 29953, 7690, 450, 731, 13, 29938, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1262, 3743, 278, 9542, 29879, 313, 1552, 24842, 29897, 6081, 13, 29938, 29909, 29985, 29943, 29938, 322, 278, 7706, 262, 313, 1552, 19087, 29897, 6081, 395, 29909, 29985, 29968, 1504, 4525, 13, 24299, 526, 20498, 873, 10087, 491, 278, 1494, 9413, 284, 13, 6799, 297, 278, 770, 7555, 1758, 7338 ]	1,332,863	34,816	ArXiv	-1	-1
\,}_A(0,\infty):$ \begin{displaymath} (A^F + x)^{-1}\le(\wt A+x)^{-1}\le(A^K + x)^{-1},\quad x>0,\quad \wt A\in{\rm Ext\,}_A(0,\infty). \end{displaymath} \begin{corollary}\label{cor5.5} Assume conditions of Theorem \ref{VI.3}. Let $S_n\ge 0$, $n\in{\N},$ and let $S^F_n$ and $S^K_n$ be the { Friedrichs} and the { Krein} extensions of $S_n$, respectively. Then \begin{equation}\label{5.14} A^F=\oplus^\infty_{n=1}S_n^F \qquad \text{and}\qquad A^K=\oplus^\infty_{n=1} S^K_n. \end{equation} \end{corollary} \begin{proof} Let us prove the second of relations \eqref{5.14}. The first one is proved similarly. By Theorem \ref{VI.3} there exists { a} boundary triplet $\Pi_n=\{\cH_n,\Gamma_{0n},\Gamma_{1n}\}$ for $S^_n$ such that $S^K_n = S_{0n}$ and $\Pi=\oplus^{\infty}_{n=1}\Pi_n$ is a boundary triplet for $A^$. Fix any $x_2\in\R_+$ and put $C_2:=\\|M(-x_2)\\|$. Then any $h=\oplus^{\infty}_{n=1} h_n \in \cH$ can be decomposed by $h=h^{(1)}\oplus h^{(2)}$ with $h^{(1)}\in\oplus^p_{n=1} \cH_n$ { and} $h^{(2)}\in\oplus^{\infty}_{n=p+1}\cH_n$ {such that $\\|h^{(2)}\\| < C^{-1/2}_2$}. Hence $\|(M(-x_2)h^{(2)},h^{(2)})\| < 1$. { Due to the monotonicity of $M(\cdot)$ we get} \begin{displaymath} \bigg(M(-x)h^{(2)},h^{(2)}\bigg)>\bigg(M(-x_2)h^{(2)},h^{(2)}\bigg)>-1,\qquad x\in (0, x_2). \end{displaymath} Since $S_{0n} = S^K_n$, the Weyl function $M_n(\cdot)$ satisfies \begin{equation}\label{5.16} \lim_{{ x\downarrow 0}}\bigg(M_n(-x)g_n, g_n\bigg)=+\infty, \qquad g_n\in\cH_n\setminus\{0\}, \end{equation} { cf. \cite[Proposition 4]{DM91}}. Since $M(\cdot)= \oplus^\infty_{n=1} M_n(\cdot)$ { is block-diagonal}, cf. \eqref{6.7}, we get from \eqref{5.16} that for any $N>0$ there exists $x_1>0$ such that \begin{equation}\label{5.17} \bigg(M(-x)h^{(1)},h^{(1)}\bigg)=\sum^p_{n=1}\bigg(M_n(-x)h_n,h_n\bigg)> N \quad \text{for}\quad x\in (0, x_1). \end{equation} Combining \eqref{5.16} with \eqref{5.17} and using the diagonal form of $M(\cdot)$, we get \begin{displaymath} (M(-x)h,h) = (M(-x)h^{(1)}, h^{(1)}) + (M(-x)h^{(2)},h^{(2)}) > N-1 \end{displaymath} for $0<x\le\min(x_1,x_2)$. Thus, $\lim_{{x\downarrow 0}}(M(-x)h,h) = + \infty$ for $h\in \cH\setminus\{0\}.$	-0.544015	-1.495464	-0.360722	1.752408	[ -0.45293206553810406, -0.6350988975949392 ]	[ -1.3737009357134409, -1.6172264227715627 ]	[ -0.26719849457199074, -0.4542462701940806 ]	[ 1.9605178018137346, 1.5442985588932732 ]	1,024	[ 512, 512 ]	[ 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1125, 29938, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 29985, 29943, 718, 921, 21604, 29896, 1012, 280, 1194, 14554, 319, 29974, 29916, 21604, 29896, 1012, 280, 29898, 29909, 29985, 29968, 718, 921, 21604, 29896, 7570, 3425, 921, 29958, 29900, 2053, 3425, 13, 29905, 14554, 319, 29905, 262, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 1643, 29912, 2616, 29945, 29889, 29945, 29913, 13, 7900, 2017, 5855, 310, 10244, 320, 999, 29912, 18118, 29889, 29941, 1836, 2803, 395, 29903, 29918, 29876, 29905, 479, 29871, 29900, 1628, 13, 29938, 29876, 29905, 262, 741, 29940, 1118, 29938, 322, 1235, 395, 29903, 29985, 29943, 29918, 29876, 29938, 322, 395, 29903, 29985, 29968, 29918, 29876, 29938, 367, 278, 426, 9542, 29879, 29913, 322, 13, 1552, 426, 7706, 262, 29913, 29871, 17752, 310, 395, 29903, 29918, 29876, 1628, 8307, 29889, 1987, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29946, 29913, 13, 29909, 29985, 29943, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29903, 29918, 29876, 29985, 29943, 13, 29905, 12014, 320, 726, 29912, 392, 1012, 12014, 13, 29909, 29985, 29968, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 317, 29985, 29968, 29918, 29876, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 12024, 502, 6356, 278, 1473, 310, 5302, 320, 4915, 29912, 29945, 29889, 29896, 29946, 1836, 450, 937, 697, 13, 275, 11827, 22829, 29889, 29871, 2648, 10244, 320, 999, 29912, 18118, 29889, 29941, 29913, 727, 4864, 426, 263, 29913, 13, 9917, 653, 21954, 29873, 779, 12197, 29918, 29876, 2013, 741, 29883, 29950, 29918, 29876, 2053, 6642, 648, 29900, 29876, 7570, 6642, 648, 29896, 29876, 1012, 1042, 363, 13, 29938, 29903, 6622, 29918, 29876, 29938, 1316, 393, 395, 29903, 29985, 29968, 29918, 29876, 353, 317, 648, 29900, 29876, 1042, 322, 13, 4535, 12197, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 1012, 12197, 29918, 29876, 29938, 338, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1504, 13, 13, 29943, 861, 738, 395, 29916, 29918, 29906, 29905, 262, 29905, 29934, 29918, 24035, 322, 1925, 395, 29907, 29918, 29906, 29901, 2013, 29989, 29924, 6278, 29916, 29918, 29906, 2144, 29989, 1504, 1987, 738, 13, 29938, 29882, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 298, 29918, 29876, 320, 262, 320, 29883, 29950, 29938, 508, 367, 17753, 4752, 491, 13, 29938, 29882, 29922, 29882, 7650, 29896, 11383, 17201, 298, 7650, 29906, 15604, 411, 395, 29882, 7650, 29896, 11383, 262, 29905, 17201, 29985, 29886, 648, 29876, 29922, 29896, 29913, 320, 29883, 29950, 29918, 29876, 29938, 426, 13, 392, 29913, 395, 29882, 7650, 29906, 11383, 262, 29905, 17201, 3311, 3411, 3227, 29876, 29922, 29886, 29974, 29896, 1012, 29883, 29950, 29918, 29876, 29938, 426, 14565, 393, 13, 4535, 29989, 29882, 7650, 29906, 11383, 29989, 529, 315, 3426, 29896, 29914, 29906, 2403, 29906, 29938, 1836, 10133, 11892, 29898, 29924, 6278, 29916, 29918, 29906, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 26972, 29989, 529, 13, 29896, 1504, 426, 29871, 16809, 304, 278, 21196, 8927, 537, 310, 395, 29924, 1194, 3822, 1262, 591, 679, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 17633, 29898, 29924, 6278, 29916, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 11383, 17633, 29897, 14247, 17633, 29898, 29924, 6278, 29916, 29918, 29906, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 11383, 17633, 15410, 29899, 29896, 2053, 12014, 13, 29916, 29905, 262, 313, 29900, 29892, 921, 29918, 29906, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 395, 29903, 648, 29900, 29876, 29913, 353, 317, 29985, 29968, 29918, 29876, 1628, 278, 399, 1032, 29880, 740, 395, 29924, 29918, 29876, 1194, 3822, 1262, 17150, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29953, 29913, 13, 29905, 2576, 648, 29912, 921, 29905, 3204, 2936, 29871, 29900, 4229, 17633, 29898, 29924, 29918, 29876, 6278, 29916, 29897, 29887, 29918, 29876, 29892, 330, 29918, 29876, 29905, 17633, 3892, 3124, 3411, 29892, 320, 12014, 13, 29887, 29918, 29876, 29905, 262, 29905, 29883, 29950, 29918, 29876, 29905, 15375, 10045, 29900, 29905, 1118, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 274, 29888, 29889, 320, 2036, 29961, 1184, 3283, 29871, 29946, 3199, 23560, 29929, 29896, 27243, 4001, 395, 29924, 1194, 3822, 3892, 13, 29905, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 341, 29918, 29876, 1194, 3822, 1262, 426, 338, 2908, 29899, 6051, 351, 7177, 1118, 274, 29888, 29889, 13, 29905, 4915, 29912, 29953, 29889, 29955, 1118, 591, 679, 515, 320, 4915, 29912, 29945, 29889, 29896, 29953, 29913, 393, 363, 738, 395, 29940, 29958, 29900, 29938, 727, 13, 9933, 395, 29916, 29918, 29896, 29958, 29900, 29938, 1316, 393, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29955, 29913, 13, 29905, 17633, 29898, 29924, 6278, 29916, 29897, 29882, 7650, 29896, 19230, 29882, 7650, 29896, 11383, 17633, 7950, 2083, 29985, 29886, 648, 29876, 29922, 29896, 1012, 17633, 29898, 29924, 29918, 29876, 6278, 29916, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 29905, 17633, 15410, 13, 29940, 320, 3425, 320, 726, 29912, 1454, 1012, 3425, 921, 29905, 262, 313, 29900, 29892, 921, 29918, 29896, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1523, 2109, 292, 320, 4915, 29912, 29945, 29889, 29896, 29953, 29913, 411, 320, 4915, 29912, 29945, 29889, 29896, 29955, 29913, 322, 773, 278, 19640, 13, 689, 310, 395, 29924, 1194, 3822, 5767, 591, 679, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 29924, 6278, 29916, 29897, 29882, 29892, 29882, 29897, 353, 313, 29924, 6278, 29916, 29897, 29882, 7650, 29896, 19230, 298, 7650, 29896, 26972, 718, 313, 29924, 6278, 29916, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 26972, 13, 29958, 405, 29899, 29896, 320, 355, 29912, 4990, 755, 29913, 13, 1454, 395, 29900, 29966, 29916, 29905, 280, 29905, 1195, 29898, 29916, 29918, 29896, 29892, 29916, 29918, 29906, 4935, 6549, 29892, 779, 2576, 648, 29912, 29916, 29905, 3204, 2936, 29871, 29900, 12156, 29924, 6278, 29916, 29897, 29882, 29892, 29882, 29897, 13, 29922, 718, 320, 3411, 29938, 363, 395, 29882, 29905, 262, 320, 29883, 29950, 29905, 15375, 10045, 29900, 29905, 1836, 29938 ]	1,332,863	35,840	ArXiv	-1	-1
Applying \cite[Proposition 4]{DM91} we {prove the second relation of} \eqref{5.14}. \end{proof} \begin{remark} {\em Another proof can be obtained by using characterization of $A^F$ and $A^K$ by means of the respective quadratic forms. } \end{remark} \subsection{Summands with arbitrary equal deficiency indices} Here we apply Theorem \ref{V.5} to direct sums of symmetric operators \eqref{6.5a}, allowing summands ${ S_n}$ to have arbitrary (finite or infinite) equal deficiency indices. We start with a simple general proposition. \begin{proposition}\Label{VI.5b} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let $A$ and $A_0$ be given by \eqref{6.5a} and \eqref{6.8}, respectively. If $\wt A$ is a self-adjoint extension of $A$ such that condition \eqref{5.0} is satisfied, then \begin{equation}\label{5.13} {\sigma}_{ac}(A_{0}) = \overline{\bigcup {\sigma}_{ac}({ S_{0n}})} \subseteq {\sigma}(\wt A) \quad \mbox{and} \quad {\sigma}_{ac}(\wt A) \subseteq \overline{\bigcup {\sigma}({ S_{0n}})} = {\sigma}(A_{0}). \end{equation} \end{proposition} \begin{proof} By the Weyl theorem, condition \eqref{5.0} yields ${\sigma}_{\rm ess}(\wt A) = {\sigma}_{\rm ess}(A_0)$. Hence \begin{displaymath} \overline{\bigcup {\sigma}_{ac}({ S_{0n}})} = {\sigma}_{ac}(A_0) \subseteq {\sigma}_{\rm ess}(A_0) = {\sigma}_{\rm ess}(\wt A) \subseteq {\sigma}(\wt A) \end{displaymath} and \begin{displaymath} {\sigma}_{ac}(\wt A) \subseteq {\sigma}_{\rm ess}(\wt A) = {\sigma}_{\rm ess}(A_0) \subseteq {\sigma}(A_0) = \overline{\bigcup {\sigma}({ S_{0n}})}. \end{displaymath} \end{proof} Our further considerations are substantially based on Theorem \ref{VI.3}. \begin{theorem}\Label{VI.4} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ be an ordinary boundary triplet for ${ S^_n}$ such that ${ S_{0n}} = { S^_n}\upharpoonright{\xker\,}({\Gamma}_{0n})$, $n \in \N$, and let $M_n(\cdot)$ be the corresponding Weyl function. Moreover, let $\gotm^+_n(t)$, $n \in \N$, be the { invariant maximal normal function} obtained from \eqref{4.12A} by replacing $M(\cdot)$ by $M_n(\cdot)$. If $\sup_{n\in\N}\gotm^+_n(t) < +\infty$ for a.e. $t \in \R$, then for any self-adjoint extension $\wt{A}$ of $A$ defined by \eqref{6.5a}, which satisfies { the} condition \eqref{5.0}, the absolutely continuous parts $\wt{A}^{ac}$ and $A^{ac}_0$ are	-0.441975	-1.389817	-0.108366	1.721192	[ -0.21049951460532348, -0.6734498096069045 ]	[ -1.1552442487936552, -1.6243889370968014 ]	[ 0.22229602332717321, -0.43902882404177496 ]	[ 1.700380774988446, 1.7420026992804922 ]	1,024	[ 512, 512 ]	[ 29871, 2401, 5890, 13, 29905, 2036, 29961, 1184, 3283, 29871, 29946, 3199, 23560, 29929, 29896, 29913, 591, 426, 771, 345, 278, 1473, 8220, 310, 29913, 13, 29905, 4915, 29912, 29945, 29889, 29896, 29946, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 331, 13, 2744, 1228, 5296, 508, 367, 7625, 491, 773, 2931, 2133, 310, 395, 29909, 29985, 29943, 29938, 13, 392, 395, 29909, 29985, 29968, 29938, 491, 2794, 310, 278, 18067, 25904, 7190, 29889, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 29905, 7235, 29912, 11139, 29885, 4167, 411, 11472, 5186, 822, 293, 13396, 16285, 29913, 13, 13, 10605, 591, 3394, 10244, 320, 999, 29912, 29963, 29889, 29945, 29913, 304, 1513, 25470, 310, 18348, 13, 3372, 4097, 320, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 14372, 22792, 4167, 6435, 317, 29918, 29876, 1042, 304, 505, 11472, 13, 29898, 18925, 470, 10362, 29897, 5186, 822, 293, 13396, 16285, 29889, 1334, 1369, 411, 263, 13, 12857, 2498, 26619, 29889, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 18118, 29889, 29945, 29890, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 5764, 13, 11967, 16414, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 13, 29943, 332, 721, 29892, 1235, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 29938, 367, 2183, 491, 320, 4915, 29912, 29953, 29889, 29945, 29874, 29913, 322, 13, 29905, 4915, 29912, 29953, 29889, 29947, 1118, 8307, 29889, 960, 779, 14554, 319, 29938, 338, 263, 1583, 29899, 328, 12090, 6081, 13, 974, 395, 29909, 29938, 1316, 393, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 338, 15787, 29892, 769, 13, 1678, 320, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29941, 29913, 13, 741, 3754, 3227, 562, 2119, 29909, 648, 29900, 1800, 353, 320, 6875, 741, 3752, 5231, 2802, 3754, 3227, 562, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 320, 11725, 13, 741, 3754, 4678, 14554, 319, 29897, 320, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 2802, 3754, 3227, 562, 4678, 14554, 319, 29897, 320, 11725, 13, 29905, 6875, 741, 3752, 5231, 2802, 3754, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 353, 2802, 3754, 2119, 29909, 648, 29900, 7690, 13, 418, 320, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 278, 399, 1032, 29880, 9185, 29892, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 17498, 29871, 7555, 3754, 6353, 1758, 3686, 4678, 14554, 13, 29909, 29897, 353, 2802, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 4935, 10133, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 6875, 741, 3752, 5231, 2802, 3754, 3227, 562, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 353, 2802, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 320, 11725, 13, 741, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 29897, 353, 2802, 3754, 6353, 1758, 3686, 4678, 14554, 319, 29897, 320, 11725, 2802, 3754, 4678, 14554, 319, 29897, 320, 355, 29912, 4990, 755, 29913, 13, 392, 13, 29905, 463, 29912, 4990, 755, 29913, 2802, 3754, 3227, 562, 4678, 14554, 319, 29897, 320, 11725, 2802, 3754, 6353, 1758, 3686, 4678, 14554, 319, 29897, 353, 2802, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 29897, 13, 29905, 11725, 2802, 3754, 2119, 29909, 29918, 29900, 29897, 353, 320, 6875, 741, 3752, 5231, 2802, 3754, 2119, 29912, 317, 648, 29900, 29876, 24289, 1836, 320, 355, 29912, 4990, 755, 29913, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29949, 332, 4340, 2050, 800, 526, 23228, 368, 2729, 373, 10244, 13, 29905, 999, 29912, 18118, 29889, 29941, 1836, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 18118, 29889, 29946, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 5764, 13, 11967, 16414, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 13, 29943, 332, 721, 29892, 1235, 7555, 12197, 2403, 29876, 353, 320, 741, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 367, 385, 15311, 13, 9917, 653, 21954, 29873, 363, 6435, 317, 6622, 29918, 29876, 1042, 29871, 1316, 393, 6435, 317, 648, 29900, 29876, 930, 353, 13, 29912, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 395, 29876, 320, 262, 320, 29940, 1628, 322, 1235, 13, 29938, 29924, 29918, 29876, 1194, 3822, 1262, 367, 278, 6590, 399, 1032, 29880, 740, 29889, 12808, 29892, 1235, 13, 4535, 7085, 29885, 14747, 29918, 29876, 29898, 29873, 5767, 395, 29876, 320, 262, 320, 29940, 1628, 367, 278, 426, 22619, 23183, 4226, 740, 29913, 7625, 515, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 491, 15270, 395, 29924, 1194, 3822, 1262, 491, 395, 29924, 29918, 29876, 1194, 3822, 4935, 960, 13, 4535, 12587, 648, 29876, 29905, 262, 29905, 29940, 1012, 7085, 29885, 14747, 29918, 29876, 29898, 29873, 29897, 529, 17501, 3411, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 13, 1454, 738, 29871, 1583, 29899, 328, 12090, 6081, 779, 14554, 29912, 29909, 1042, 310, 395, 29909, 29938, 3342, 491, 13, 29905, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 607, 17150, 426, 278, 29913, 4195, 320, 4915, 29912, 29945, 29889, 29900, 1118, 278, 13, 370, 2929, 11579, 9126, 5633, 779, 14554, 29912, 29909, 2844, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 526 ]	1,332,863	36,864	ArXiv	-1	-1

Polyacrylonitrile (PAN) fibers were pre-oxidized in a temperature range of 180-275℃. The effects of positive and negative stretching on the structure and morphology of PAN fiber in the pre-oxidation process were studied by FTIR spectroscopy, XRD, and SEM. Mechanical property changes were also investigated. No changes in the movement and intensity of functional groups of PAN fibers were caused by positive stretching of up to 10% and negative stretching down to -8%. The crystal structure can be affected by the positive stretching and negative stretching. The maximum strength is 479.81 MPa when the stretching is positive,and the maximum strength is 420.55 MPa when the stretching is negative. It has been well established that polyacrylonitrile (PAN) fibers are one of the most suitable and widely used precursors for making high-performance carbon fiber, and PAN-based carbon fiber is stronger than other types precursor-based carbon fibers . Developing carbon fiber from PAN based fiber generally involves three processes, namely stabilization, carbonization, and graphitization under controlled conditions. Among those processes, pre-oxidation is a very important step because it largely governs the final structure and mechanical properties of the carbon fiber. During this process in a temperature range of 180-280℃, PAN precursors are converted into infusible and nonflammable fibers with a ladder structure suitable for further carbonization . Important factors such as temperature, time, and stretching have been studied previously [3 - 9] ; however, systematic investigations of the effects of positive and negative stretching have never been reported relating to the structure and properties of PAN fibers in the pre-oxidation process. In this work, the effects of positive and negative stretching on the structure and properties of PAN fibers in the pre-oxidation process were systematically investigated by using FTIR spectroscopy, XRD, and SEM observations. The PAN fiber used in this experiment was supplied by Zhongfu Shenying Carbon Fiber Co., Ltd. (Lianyungang, People's Republic of China) in tows of 1,000 fibers with an average density of 1.19 g/cm 3 and a mean diameter of 12.4 ㎛. Pre-oxidation was carried out in a furnace divided into nine temperature zones in a range of 180-300℃. Temperature gradually increased so as to control pre-oxidation temperature gradient. The stretching ratio was achieved by controlling the speed difference between the feed (v 1 ) and take-up rollers (v 2 ). The stretching ratio is determined by the follow equation: τ = [(v 2 -v 1 )/v 1 ] × 100%, where if τ = 0, it means no stretching, if τ > 0, it means positive stretching,and if τ < 0, it means negative stretching. Table 1 shows various stretching ratios during the increase of the pre-oxidation temperature. τ 1 means stretching ratio was 2% at 180℃, and it was increased 2% at 200℃ and then constantly sustained until 275℃. Therefore, the total positive stretching ratio was 4%. On the other hand, in the case of τ 5 , the fiber was relaxed 2% by supplying negative stretching at 270℃. Therefore, the total stretching ratio was also 4%; however, τ 5 contained negative stretching. where I C=N is the measured intensity of the conjugated band at 1630 cm -1 associated with the developing structure and I C≡N is the measured intensity of the nitrile band at 2240 cm -1 belonging to the unmodified PAN molecule. where λ is the wavelength of the X-rays. where I a is the intensity of diffraction at 2θ = 25.5°, which is given by the ladder structure and I p is the intensity of diffraction at 2θ = 17°. The mechanical properties of the PAN pre-oxidized fibers were measured with a single fiber strength machine (YG004E

-0.102295

1.312242

0.866501

1.461055

[ 0.3976363758701262, -0.602226687298969 ]

[ 1.8064554246926194, 0.8180284478096547 ]

[ 1.3483870385977887, 0.3846154489517664 ]

[ 1.7524081803535039, 1.1697012402648579 ]

1,024

[ 512, 512 ]

[ 21755, 562, 719, 12957, 277, 13816, 313, 29925, 2190, 29897, 18755, 414, 892, 758, 29899, 2251, 333, 1891, 297, 263, 10430, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29906, 29955, 29945, 229, 135, 134, 29889, 450, 9545, 310, 6374, 322, 8178, 16116, 292, 373, 278, 3829, 322, 18131, 3002, 310, 349, 2190, 5713, 495, 297, 278, 758, 29899, 2251, 333, 362, 1889, 892, 12399, 491, 383, 29911, 8193, 6683, 307, 1557, 2270, 29892, 1060, 29934, 29928, 29892, 322, 3725, 29924, 29889, 27439, 936, 2875, 3620, 892, 884, 7405, 630, 29889, 1939, 3620, 297, 278, 10298, 322, 26171, 310, 13303, 6471, 310, 349, 2190, 18755, 414, 892, 8581, 491, 6374, 16116, 292, 310, 701, 304, 29871, 29896, 29900, 29995, 322, 8178, 16116, 292, 1623, 304, 448, 29947, 15543, 450, 10901, 11195, 3829, 508, 367, 15201, 491, 278, 6374, 16116, 292, 322, 8178, 16116, 292, 29889, 450, 7472, 9324, 338, 29871, 29946, 29955, 29929, 29889, 29947, 29896, 341, 11868, 746, 278, 16116, 292, 338, 6374, 29892, 392, 278, 7472, 9324, 338, 29871, 29946, 29906, 29900, 29889, 29945, 29945, 341, 11868, 746, 278, 16116, 292, 338, 8178, 29889, 13, 3112, 756, 1063, 1532, 7841, 393, 15680, 562, 719, 12957, 277, 13816, 313, 29925, 2190, 29897, 18755, 414, 526, 697, 310, 278, 1556, 13907, 322, 17644, 1304, 8303, 1295, 943, 363, 3907, 1880, 29899, 546, 13390, 22004, 5713, 495, 29892, 322, 349, 2190, 29899, 6707, 22004, 5713, 495, 338, 23505, 1135, 916, 4072, 8303, 5966, 29899, 6707, 22004, 18755, 414, 29871, 869, 10682, 292, 22004, 5713, 495, 515, 349, 2190, 2729, 5713, 495, 6892, 20789, 2211, 10174, 29892, 18451, 16160, 2133, 29892, 22004, 2133, 29892, 322, 3983, 277, 2133, 1090, 20704, 5855, 29889, 17302, 1906, 10174, 29892, 758, 29899, 2251, 333, 362, 338, 263, 1407, 4100, 4331, 1363, 372, 18425, 14765, 1983, 278, 2186, 3829, 322, 28310, 4426, 310, 278, 22004, 5713, 495, 29889, 7133, 445, 1889, 297, 263, 10430, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29906, 29947, 29900, 229, 135, 134, 29892, 349, 2190, 8303, 1295, 943, 526, 11543, 964, 3041, 375, 1821, 322, 1661, 1579, 4850, 519, 18755, 414, 411, 263, 11979, 672, 3829, 13907, 363, 4340, 22004, 2133, 29871, 869, 16032, 424, 13879, 1316, 408, 10430, 29892, 931, 29892, 322, 16116, 292, 505, 1063, 12399, 9251, 518, 29941, 448, 29871, 29929, 29962, 2056, 3138, 29892, 1788, 2454, 7405, 800, 310, 278, 9545, 310, 6374, 322, 8178, 16116, 292, 505, 2360, 1063, 8967, 1104, 1218, 304, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 297, 278, 758, 29899, 2251, 333, 362, 1889, 29889, 13, 797, 445, 664, 29892, 278, 9545, 310, 6374, 322, 8178, 16116, 292, 373, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 297, 278, 758, 29899, 2251, 333, 362, 1889, 892, 1788, 19574, 7405, 630, 491, 773, 383, 29911, 8193, 6683, 307, 1557, 2270, 29892, 1060, 29934, 29928, 29892, 322, 3725, 29924, 13917, 29889, 13, 1576, 349, 2190, 5713, 495, 1304, 297, 445, 7639, 471, 19056, 491, 27134, 549, 21154, 1383, 264, 5414, 1704, 6718, 383, 12347, 3189, 1696, 19806, 29889, 313, 29931, 713, 29891, 686, 574, 29892, 11647, 29915, 29879, 8063, 310, 7551, 29897, 297, 304, 5652, 310, 29871, 29896, 29892, 29900, 29900, 29900, 18755, 414, 411, 385, 6588, 9027, 310, 29871, 29896, 29889, 29896, 29929, 330, 29914, 4912, 29871, 29941, 322, 263, 2099, 24235, 310, 29871, 29896, 29906, 29889, 29946, 29871, 230, 145, 158, 29889, 13, 6572, 29899, 2251, 333, 362, 471, 8988, 714, 297, 263, 15252, 815, 13931, 964, 14183, 10430, 20542, 297, 263, 3464, 310, 29871, 29896, 29947, 29900, 29899, 29941, 29900, 29900, 229, 135, 134, 29889, 6789, 546, 1535, 22020, 11664, 577, 408, 304, 2761, 758, 29899, 2251, 333, 362, 10430, 16030, 29889, 450, 16116, 292, 11959, 471, 14363, 491, 640, 22155, 278, 6210, 4328, 1546, 278, 8343, 313, 29894, 29871, 29896, 1723, 322, 2125, 29899, 786, 9679, 414, 313, 29894, 29871, 29906, 13742, 450, 16116, 292, 11959, 338, 10087, 491, 278, 1101, 6306, 29901, 29871, 30137, 353, 17288, 29894, 29871, 29906, 448, 29894, 29871, 29896, 1723, 29914, 29894, 29871, 29896, 4514, 13105, 29871, 29896, 29900, 29900, 13667, 988, 565, 29871, 30137, 353, 29871, 29900, 29892, 372, 2794, 694, 16116, 292, 29892, 565, 29871, 30137, 1405, 29871, 29900, 29892, 372, 2794, 6374, 16116, 292, 29892, 392, 565, 29871, 30137, 529, 29871, 29900, 29892, 372, 2794, 8178, 16116, 292, 29889, 13, 3562, 29871, 29896, 3697, 5164, 16116, 292, 364, 2219, 359, 2645, 278, 7910, 310, 278, 758, 29899, 2251, 333, 362, 10430, 29889, 29871, 30137, 29871, 29896, 2794, 16116, 292, 11959, 471, 29871, 29906, 29995, 472, 29871, 29896, 29947, 29900, 229, 135, 134, 29892, 322, 372, 471, 11664, 29871, 29906, 29995, 472, 29871, 29906, 29900, 29900, 229, 135, 134, 322, 769, 21003, 15075, 7114, 2745, 29871, 29906, 29955, 29945, 229, 135, 134, 29889, 7857, 29892, 278, 3001, 6374, 16116, 292, 11959, 471, 29871, 29946, 15543, 1551, 278, 916, 1361, 29892, 297, 278, 1206, 310, 29871, 30137, 29871, 29945, 1919, 278, 5713, 495, 471, 26681, 287, 29871, 29906, 29995, 491, 1462, 5890, 8178, 16116, 292, 472, 29871, 29906, 29955, 29900, 229, 135, 134, 29889, 7857, 29892, 278, 3001, 16116, 292, 11959, 471, 884, 29871, 29946, 8874, 3138, 29892, 29871, 30137, 29871, 29945, 11122, 8178, 16116, 292, 29889, 13, 3062, 306, 315, 29922, 29940, 338, 278, 17005, 26171, 310, 278, 25482, 630, 3719, 472, 29871, 29896, 29953, 29941, 29900, 7477, 448, 29896, 6942, 411, 278, 14338, 3829, 322, 306, 315, 30616, 29940, 338, 278, 17005, 26171, 310, 278, 21767, 13816, 3719, 472, 29871, 29906, 29906, 29946, 29900, 7477, 448, 29896, 23329, 304, 278, 443, 1545, 2164, 349, 2190, 13206, 29883, 1297, 29889, 13, 3062, 29871, 30142, 338, 278, 281, 6447, 1477, 310, 278, 1060, 29899, 764, 29879, 29889, 13, 3062, 306, 263, 338, 278, 26171, 310, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29906, 29945, 29889, 29945, 30073, 29892, 607, 338, 2183, 491, 278, 11979, 672, 3829, 322, 306, 282, 338, 278, 26171, 310, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29896, 29955, 30073, 29889, 13, 1576, 28310, 4426, 310, 278, 349, 2190, 758, 29899, 2251, 333, 1891, 18755, 414, 892, 17005, 411, 263, 2323, 5713, 495, 9324, 4933, 313, 29979, 29954, 29900, 29900, 29946, 29923 ]

1,332,813

0

C4

7

9

, Ningbo Textile Machinery Co., China). In each case, at least 40 samples were tested. Discarding the top 5 and bottom 5, the average value of the remaining 30 can be automatically obtained. The diameter of each fiber was measured with a (Olympus) microscope before the tensile test. The fractured surface of PAN pre-oxidized fibers were observed by using a field emission-SEM (Hitachi S-4700, Japan) with a revolution of 15 kV. Before observation, the samples were embedded in an epoxy resin and sputter-coated using Pt (JEOL JFC-1200, USA). Fig. 1 shows the FTIR spectroscopy of the pre-oxidized PAN fibers at different positive stretching ratios. The positive stretching ratio did not show any influence on the movement and intensity of the functional groups until 10%. There were weak absorption bands at 2243 cm -1 assigned to the nitrile group and, at 1581 cm -1 , were assigned to the vibration of carboxyl groups, which indicated that oxidation has occurred. The cyclization rate was calculated according to Eq. (1) based on Fig. 1 and is listed in Table 2 . Fig. 1 shows there is no obvious influence on the movement and intensity of functional groups of FTIR, and the cyclization rate is also affected less, which indicates that positive stretching cannot affect the chemical structure. Fourier transform infrared spectroscopy of pre-oxidized polyacrylonitrile fibers at different positive stretching ratios. X-ray diffraction patterns of the pre-oxidized polyacrylonitrile fibers at different positive stretching ratios. values increased with an increase in the stretching ratio, indicating that stretching promoted the reactions. In fact, stretching affected the readjustment of the molecular chains (involving the rotation of nitrile groups around the C-C single bond) not only in the ordered domains but also and especially in the disordered domains. This might have brought more nitrile groups into a suitable position for cyclization. So, one can conclude that stretching offers molecular chains additional energy to readjust and pack into an ordered phase, which is accordant to the results of Wu et al . It was also found that stretching had a significant influence on the physical structure of PAN fibers . Structural parameters at different positive stretching ratiosAI: aromatization index. Structural parameters at different positive stretching ratios AI: aromatization index. Mechanical properties of pre-oxidized PAN fibers at different positive stretching ratiosPAN: polyacrylonitrile. Mechanical properties of pre-oxidized PAN fibers at different positive stretching ratios PAN: polyacrylonitrile. PAN fibers for the 4% stretching ratio were higher than those of the other three samples and had a decreasing trend. However, there was no obvious difference among the elongation to break. Tensile power stands for the work involved in breaking the fibers and could be defined in terms of the product of strength and tensile power. Fig. 3 shows the SEM images of pre-oxidized PAN fibers at different positive stretching ratios. When the stretching ratio is at 4% ( Fig. 3 a), the fractured surface radiates from the center to the surrounding is and distributes equally, indicating that the internal binding force of fibers are large and the tensile strength and tensile power are larger. When the stretching ratio was at 6% ( Fig. 3 b), the toughness decreased and the fractured surface became smooth, resulting in a dramatically drop in tensile strength and tensile power. When the stretching ratio was at 8% ( Fig. 3 c), the fractured surface of pre-oxidized PAN fibers became rough, and the tensile strength increased a little. When the stretching ratio was at 10%, it prevented penetration into the PAN molecule and broke the molecular order and orientation so that the pre-oxidation was insufficient with large radial differences, resulting in uneven molecular structure and decreased tensile strength. As shown in Fig. 3 d, the fractured surface is quite rough, implying that the internal stress was not equal and bonding force decreased, and then the tensile strength

-0.386503

0.785797

0.430268

1.159296

[ -0.4899133021210706, -0.2830923123422578 ]

[ 0.9612787343144322, 0.6103155323777273 ]

[ 0.44041275151022036, 0.4201228233071462 ]

[ 1.2217286456299155, 1.096862872753777 ]

1,024

[ 512, 512 ]

[ 29892, 405, 292, 833, 3992, 488, 17197, 262, 708, 3189, 1696, 7551, 467, 512, 1269, 1206, 29892, 472, 3203, 29871, 29946, 29900, 11916, 892, 9528, 29889, 3295, 7543, 292, 278, 2246, 29871, 29945, 322, 5970, 29871, 29945, 29892, 278, 6588, 995, 310, 278, 9886, 29871, 29941, 29900, 508, 367, 6336, 7625, 29889, 450, 24235, 310, 1269, 5713, 495, 471, 17005, 411, 263, 313, 29949, 4960, 375, 29897, 20710, 1883, 4338, 1434, 278, 25187, 488, 1243, 29889, 13, 1576, 285, 1461, 2955, 7101, 310, 349, 2190, 758, 29899, 2251, 333, 1891, 18755, 414, 892, 8900, 491, 773, 263, 1746, 25477, 29899, 1660, 29924, 313, 29950, 277, 26213, 317, 29899, 29946, 29955, 29900, 29900, 29892, 5546, 29897, 411, 263, 19479, 310, 29871, 29896, 29945, 413, 29963, 29889, 10949, 15500, 29892, 278, 11916, 892, 15685, 297, 385, 21502, 3594, 620, 262, 322, 269, 649, 357, 29899, 1111, 630, 773, 349, 29873, 313, 29967, 29923, 5607, 435, 8610, 29899, 29896, 29906, 29900, 29900, 29892, 8278, 467, 13, 13080, 29889, 29871, 29896, 3697, 278, 383, 29911, 8193, 6683, 307, 1557, 2270, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 450, 6374, 16116, 292, 11959, 1258, 451, 1510, 738, 9949, 373, 278, 10298, 322, 26171, 310, 278, 13303, 6471, 2745, 29871, 29896, 29900, 15543, 1670, 892, 8062, 17977, 683, 22706, 472, 29871, 29906, 29906, 29946, 29941, 7477, 448, 29896, 9859, 304, 278, 21767, 13816, 2318, 322, 29892, 472, 29871, 29896, 29945, 29947, 29896, 7477, 448, 29896, 1919, 892, 9859, 304, 278, 325, 26218, 310, 1559, 1884, 2904, 6471, 29892, 607, 18694, 393, 19100, 333, 362, 756, 10761, 29889, 450, 24502, 2133, 6554, 471, 12833, 5034, 304, 12345, 29889, 313, 29896, 29897, 2729, 373, 5104, 29889, 29871, 29896, 322, 338, 9904, 297, 6137, 29871, 29906, 869, 13, 13080, 29889, 29871, 29896, 3697, 727, 338, 694, 6924, 9949, 373, 278, 10298, 322, 26171, 310, 13303, 6471, 310, 383, 29911, 8193, 29892, 322, 278, 24502, 2133, 6554, 338, 884, 15201, 3109, 29892, 607, 14088, 393, 6374, 16116, 292, 2609, 6602, 278, 22233, 3829, 29889, 13, 29943, 283, 4336, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 13, 29990, 29899, 764, 2923, 13857, 15038, 310, 278, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 13, 5975, 11664, 411, 385, 7910, 297, 278, 16116, 292, 11959, 29892, 23941, 393, 16116, 292, 21201, 278, 337, 7387, 29889, 512, 2114, 29892, 16116, 292, 15201, 278, 1303, 5143, 358, 310, 278, 13206, 16637, 521, 2708, 313, 262, 1555, 1747, 278, 13733, 310, 21767, 13816, 6471, 2820, 278, 315, 29899, 29907, 2323, 21224, 29897, 451, 871, 297, 278, 10372, 21904, 541, 884, 322, 7148, 297, 278, 766, 21693, 21904, 29889, 910, 1795, 505, 6296, 901, 21767, 13816, 6471, 964, 263, 13907, 2602, 363, 24502, 2133, 29889, 1105, 29892, 697, 508, 17668, 393, 16116, 292, 16688, 13206, 16637, 521, 2708, 5684, 5864, 304, 1303, 5143, 322, 4870, 964, 385, 10372, 8576, 29892, 607, 338, 15017, 424, 304, 278, 2582, 310, 29624, 634, 394, 29871, 869, 739, 471, 884, 1476, 393, 16116, 292, 750, 263, 7282, 9949, 373, 278, 9128, 3829, 310, 349, 2190, 18755, 414, 29871, 869, 13, 19560, 3631, 4128, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 12, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 12, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 29925, 2190, 18755, 414, 363, 278, 29871, 29946, 29995, 16116, 292, 11959, 892, 6133, 1135, 1906, 310, 278, 916, 2211, 11916, 322, 750, 263, 9263, 5832, 534, 355, 29889, 2398, 29892, 727, 471, 694, 6924, 4328, 4249, 278, 560, 549, 362, 304, 2867, 29889, 323, 575, 488, 3081, 15028, 363, 278, 664, 9701, 297, 16679, 278, 18755, 414, 322, 1033, 367, 3342, 297, 4958, 310, 278, 3234, 310, 9324, 322, 25187, 488, 3081, 29889, 5104, 29889, 29871, 29941, 3697, 278, 3725, 29924, 4558, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29889, 1932, 278, 16116, 292, 11959, 338, 472, 29871, 29946, 29995, 313, 5104, 29889, 29871, 29941, 263, 511, 278, 285, 1461, 2955, 7101, 17937, 1078, 515, 278, 4818, 304, 278, 18830, 338, 322, 1320, 5026, 18018, 29892, 23941, 393, 278, 7463, 9956, 4889, 310, 18755, 414, 526, 2919, 322, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 526, 7200, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29953, 29995, 313, 5104, 29889, 29871, 29941, 289, 511, 278, 260, 820, 2264, 9263, 1463, 322, 278, 285, 1461, 2955, 7101, 3897, 10597, 29892, 9819, 297, 263, 8541, 19574, 5768, 297, 25187, 488, 9324, 322, 25187, 488, 3081, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29947, 29995, 313, 5104, 29889, 29871, 29941, 274, 511, 278, 285, 1461, 2955, 7101, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 3897, 12164, 29892, 322, 278, 25187, 488, 9324, 11664, 263, 2217, 29889, 1932, 278, 16116, 292, 11959, 471, 472, 29871, 29896, 29900, 13667, 372, 5557, 287, 6584, 18184, 362, 964, 278, 349, 2190, 13206, 29883, 1297, 322, 14455, 278, 13206, 16637, 1797, 322, 19843, 577, 393, 278, 758, 29899, 2251, 333, 362, 471, 1663, 29884, 4543, 411, 2919, 28373, 12651, 29892, 9819, 297, 1597, 854, 13206, 16637, 3829, 322, 9263, 1463, 25187, 488, 9324, 29889, 1094, 4318, 297, 5104, 29889, 29871, 29941, 270, 29892, 278, 285, 1461, 2955, 7101, 338, 3755, 12164, 29892, 2411, 5890, 393, 278, 7463, 22884, 471, 451, 5186, 322, 21224, 292, 4889, 9263, 1463, 29892, 322, 769, 278, 25187, 488, 9324 ]

1,332,813

1,024

C4

12

5

and tensile power decreased. In a word, the tensile strength and tensile power have the same performance. It is necessary to consider the tensile strength and tensile power to obtain both the elongation and strength so that it performs well when it is used; meanwhile, the stretching ratio should not be too large so as to avoid performance degradation . Except for the results above, the evolution of structure and the changes of properties during the pre-oxidation on other important aspects have been studied by Zhang et al . Scanning electron microscope images of pre-oxidized polyacrylonitrile fibers at different positive stretching ratios: (a) 4 (b) 6 (c) 8 and (d) 10%. Fourier transform infrared spectroscopy of pre-oxidative polyacrylonitrile fibers at different negative stretching ratios. Wang et al has investigated the structure and properties of PAN fibers from the negative stretching in the high temperature zone. Fig. 4 shows the FTIR spectroscopy of the pre-oxidized PAN fibers at different negative stretching ratios. As with positive stretching, the FTIR spectra showed that negative stretching still has no influence on the movement and intensity of functional groups. The cyclization rate has been calculated according to Eq. (1) based on Fig. 4 and is listed in Table 5 . The effect of the cyclization rate by negative stretching is not obvious, just as with positive stretching. Fig. 5 shows WAXRD patterns of pre-oxidized PAN fibers at different negative stretching ratios. In general, the spectra of pre-oxidized PAN fibers showed weak diffraction at 2θ = 17° and a broad diffraction around 2θ = 25.5°. There are no obvious differences the ratios decrease. Relative cyclization rate based on FTIR spectroscopy inFig. 4FTIR: Fourier transform infrared spectroscopy. Relative cyclization rate based on FTIR spectroscopy in Fig. 4 FTIR: Fourier transform infrared spectroscopy. Wide-angle X-ray diffraction patterns of pre-oxidized polyacrylonitrile fibers at different negative stretching ratios. Structural parameters at different negative stretching ratiosAI: aromatization index. Structural parameters at different negative stretching ratios AI: aromatization index. Structural parameters were calculated according to Eqs. (2) and (3) and were listed in Table 6 . When the stretching ratio was -4%, the d-spacing diffraction at 17° and around 25.5° were the higher and lower than the other three samples, respectively; however, the AI values increased with an increase in the negative stretching ratio. Mechanical properties of pre-oxidized PAN d fibers at different negative stretching ratiosPAN: polyacrylonitrile. Mechanical properties of pre-oxidized PAN d fibers at different negative stretching ratios PAN: polyacrylonitrile. Scanning electron microscope images of pre-oxidized polyacrylonitrile fibers at different negative stretching ratios: (e) -2 (f ) -4 (g) -6 and (h) -8%. oxidation, it was difficult for oxygen to enter the PAN molecule, and this resistance caused the oxidation to not occur easily, resulting in the uneven structure of the pre-oxidized PAN fibers. Fig. 6 shows SEM images of pre-oxidized PAN fibers at different negative stretching ratios. When the stretching ratio was -2% ( Fig. 6 e), the fractured surface showed an uneven stress of internal molecules and could not spread after the tensile force; therefore, the tensile strength was not very high. When the stretching ratio was -4%, this was helpful for oxygen to penetrate into PAN molecular chains to oxidize and form an equal structure of pre-oxidized PAN fibers. The SEM image ( Fig. 6 f) also showed a better fractured surface than the other three groups of samples. As the stretching ratio was increased to -6%, oxygen molecules could penetrate into PAN molecular chains to peroxide and result in a decrease in tensile strength, but the

-0.743303

0.204738

0.188057

1.138485

[ -0.613184090730959, -0.8734224222407236 ]

[ 0.1644490156316074, 0.24502730179054474 ]

[ 0.36939800279946083, 0.00671553616951033 ]

[ 1.0240245052426962, 1.2529450888489502 ]

1,024

[ 512, 512 ]

[ 322, 25187, 488, 3081, 9263, 1463, 29889, 512, 263, 1734, 29892, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 505, 278, 1021, 4180, 29889, 739, 338, 5181, 304, 2050, 278, 25187, 488, 9324, 322, 25187, 488, 3081, 304, 4017, 1716, 278, 560, 549, 362, 322, 9324, 577, 393, 372, 23233, 1532, 746, 372, 338, 1304, 29936, 2099, 8000, 29892, 278, 16116, 292, 11959, 881, 451, 367, 2086, 2919, 577, 408, 304, 4772, 4180, 316, 5105, 362, 29871, 869, 1222, 1547, 363, 278, 2582, 2038, 29892, 278, 14675, 310, 3829, 322, 278, 3620, 310, 4426, 2645, 278, 758, 29899, 2251, 333, 362, 373, 916, 4100, 21420, 505, 1063, 12399, 491, 796, 11895, 634, 394, 29871, 869, 13, 4421, 9450, 11966, 20710, 1883, 4338, 4558, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 6374, 16116, 292, 364, 2219, 359, 29901, 313, 29874, 29897, 29871, 29946, 313, 29890, 29897, 29871, 29953, 313, 29883, 29897, 29871, 29947, 322, 313, 29881, 29897, 29871, 29896, 29900, 15543, 13, 29943, 283, 4336, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 310, 758, 29899, 2251, 333, 1230, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 13, 29956, 574, 634, 394, 29871, 756, 7405, 630, 278, 3829, 322, 4426, 310, 349, 2190, 18755, 414, 515, 278, 8178, 16116, 292, 297, 278, 1880, 10430, 10640, 29889, 5104, 29889, 29871, 29946, 3697, 278, 383, 29911, 8193, 6683, 307, 1557, 2270, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 1094, 411, 6374, 16116, 292, 29892, 278, 383, 29911, 8193, 6683, 336, 10018, 393, 8178, 16116, 292, 1603, 756, 694, 9949, 373, 278, 10298, 322, 26171, 310, 13303, 6471, 29889, 450, 24502, 2133, 6554, 756, 1063, 12833, 5034, 304, 12345, 29889, 313, 29896, 29897, 2729, 373, 5104, 29889, 29871, 29946, 322, 338, 9904, 297, 6137, 29871, 29945, 869, 450, 2779, 310, 278, 24502, 2133, 6554, 491, 8178, 16116, 292, 338, 451, 6924, 29892, 925, 408, 411, 6374, 16116, 292, 29889, 13, 13080, 29889, 29871, 29945, 3697, 399, 6604, 29934, 29928, 15038, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 512, 2498, 29892, 278, 6683, 336, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 10018, 8062, 2923, 13857, 472, 29871, 29906, 30209, 353, 29871, 29896, 29955, 30073, 322, 263, 7300, 2923, 13857, 2820, 29871, 29906, 30209, 353, 29871, 29906, 29945, 29889, 29945, 30073, 29889, 1670, 526, 694, 6924, 12651, 278, 364, 2219, 359, 23806, 29889, 13, 18278, 24502, 2133, 6554, 2729, 373, 383, 29911, 8193, 6683, 307, 1557, 2270, 297, 13080, 29889, 29871, 29946, 7818, 8193, 29901, 27506, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 29889, 13, 18278, 24502, 2133, 6554, 2729, 373, 383, 29911, 8193, 6683, 307, 1557, 2270, 297, 5104, 29889, 29871, 29946, 12, 7818, 8193, 29901, 27506, 4327, 3041, 336, 1127, 6683, 307, 1557, 2270, 29889, 13, 29956, 680, 29899, 2521, 1060, 29899, 764, 2923, 13857, 15038, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 13, 19560, 3631, 4128, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 12, 23869, 29901, 263, 456, 271, 2133, 2380, 29889, 13, 19560, 3631, 4128, 892, 12833, 5034, 304, 12345, 29879, 29889, 313, 29906, 29897, 322, 313, 29941, 29897, 322, 892, 9904, 297, 6137, 29871, 29953, 869, 1932, 278, 16116, 292, 11959, 471, 448, 29946, 13667, 278, 270, 29899, 1028, 9390, 2923, 13857, 472, 29871, 29896, 29955, 30073, 322, 2820, 29871, 29906, 29945, 29889, 29945, 30073, 892, 278, 6133, 322, 5224, 1135, 278, 916, 2211, 11916, 29892, 8307, 29936, 3138, 29892, 278, 319, 29902, 1819, 11664, 411, 385, 7910, 297, 278, 8178, 16116, 292, 11959, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 270, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 6816, 5083, 936, 4426, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 270, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 12, 29925, 2190, 29901, 15680, 562, 719, 12957, 277, 13816, 29889, 13, 4421, 9450, 11966, 20710, 1883, 4338, 4558, 310, 758, 29899, 2251, 333, 1891, 15680, 562, 719, 12957, 277, 13816, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29901, 313, 29872, 29897, 448, 29906, 313, 29888, 1723, 448, 29946, 313, 29887, 29897, 448, 29953, 322, 313, 29882, 29897, 448, 29947, 15543, 13, 2251, 333, 362, 29892, 372, 471, 5189, 363, 288, 28596, 304, 3896, 278, 349, 2190, 13206, 29883, 1297, 29892, 322, 445, 17711, 8581, 278, 19100, 333, 362, 304, 451, 6403, 5948, 29892, 9819, 297, 278, 1597, 854, 3829, 310, 278, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 29889, 5104, 29889, 29871, 29953, 3697, 3725, 29924, 4558, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 472, 1422, 8178, 16116, 292, 364, 2219, 359, 29889, 1932, 278, 16116, 292, 11959, 471, 448, 29906, 29995, 313, 5104, 29889, 29871, 29953, 321, 511, 278, 285, 1461, 2955, 7101, 10018, 385, 1597, 854, 22884, 310, 7463, 13206, 21337, 322, 1033, 451, 9677, 1156, 278, 25187, 488, 4889, 29936, 5480, 29892, 278, 25187, 488, 9324, 471, 451, 1407, 1880, 29889, 1932, 278, 16116, 292, 11959, 471, 448, 29946, 13667, 445, 471, 8444, 363, 288, 28596, 304, 6584, 300, 10492, 964, 349, 2190, 13206, 16637, 521, 2708, 304, 19100, 333, 675, 322, 883, 385, 5186, 3829, 310, 758, 29899, 2251, 333, 1891, 349, 2190, 18755, 414, 29889, 450, 3725, 29924, 1967, 313, 5104, 29889, 29871, 29953, 285, 29897, 884, 10018, 263, 2253, 285, 1461, 2955, 7101, 1135, 278, 916, 2211, 6471, 310, 11916, 29889, 1094, 278, 16116, 292, 11959, 471, 11664, 304, 448, 29953, 13667, 288, 28596, 13206, 21337, 1033, 6584, 300, 10492, 964, 349, 2190, 13206, 16637, 521, 2708, 304, 639, 2251, 680, 322, 1121, 297, 263, 23806, 297, 25187, 488, 9324, 29892, 541, 278 ]

1,332,813

2,048

C4

22

21

Everyday we hear about Artificial Intelligence (AI) and Machine learning in different contexts. Entrepreneurs like Elon Musk fear that it will doom the human race. Notably, the Russian President Mr Vladimir Putin was recently quoted telling students that whoever masters AI will rule the world. When ordinary people hear about A.I their thoughts immediately venture towards machine based programs encountered in movies like Star Trek and Star Wars. This is not the only form of AI that exists. We have previously covered Indian start-ups working in AI. In this post we will feature some start-ups in Europe who have incorporated artificial intelligence into their products and services. In computer science, AI refers to the study and demonstration of intelligent behaviour by machines. For a long time it was believed that machines will find it difficult to demonstrate human like intelligence. This has now been proven wrong because with each passing decade, technology has shown that machines can not only perform intelligent tasks but can also outperform humans in many areas. While humans still regain mastery over facial recognition, creativity and some aspects of visualisation, computers are catching up fast by learning to replicate human neural circuits digitally. You should check out Google's AI Experiments to know more. While the use of A.I will no doubt have disastrous consequences in military applications. It offers an edge to organisations when they use it for behavioural analytics and decision making. Given below are seven AI focused companies that are reshaping how corporations do business around the globe. Virtual Reality Worlds are powered by Artificial Intelligence. As these worlds become more complex, the AI's role will expand exponentially. This firm harness the power of cognitive computing to ensure computers understand data better and deliver accurate predictions. The company has built a suite of software that can learn and further build itself based on their environmental needs. Software that can learn in this manner is also called machine learning software and it is being used in a wide variety of sectors. By harnessing the power of cognitive computing, Digital Reasoning helps organisations and people make better decisions. The companies products are being used by government agencies, healthcare professionals and financial sector workers. Some of the users have reported enhanced productivity and large cost savings. These outcomes were a result of the timely decisions taken and insight garnered through their technology. Setting up a healthcare system for US Army Veterans. Members of the 40,000 strong Belgian Police force relies on systems built by Inter Systems for coordinating their policing activities. One of South Africa's largest NGO's fighting HIV/ AIDs has deployed their solution to support 4,400 clinics and hospitals. Money Hub provides financial solutions for employers, insurance companies and businesses. The company aims to drive customer and employee loyalty by harnessing personal analytics to offer financial solutions. The well being of employees is core concern of organisations and Money Hub can help your staff cope with financial issues facing them. With the Money Hub app users can see all their finances listed in one single platform. They can choose to get alerts when their balance dips below limits set by them. The company can also provide incentives which reduces financial worries and increases productivity. Studies have shown that regular usage of it's app can drive up productivity in the organisation and reduces employee abstentions. Cash rich companies have a niggling worry. How to generate optimum risk free returns on their cash holdings so that shareholder wealth is maximised. Interest rates offered by different banks on cash holdings is always changing and it is difficult for managers to get the best rate. Akoni helps such companies in cash management by re-balancing accounts automatically to ensure the maximum amount earns the highest interest rate. It's AI platform is integrated with multiple banks and you can personalise your saving options. The company was recently judged among the top ten fin-tech companies in Europe by the Spanish Wealth Management agency BBVA. A startup exhibiting it's AI products at a convention. Fixed income advisory is going digital with Bond It, which helps automate fixed income portfolio creation for its clients. By defining your yields and client constraints across 12 different variables, all it takes is 15 minutes to setup your client portfolio. Winner of several portfolio analytics awards, the company's products are being used by Private Wealth Managers and Institutional Banks. Their cloud based SaaS solution is today being used by investment managers to harness it'

0.608566

1.358798

1.17085

0.278732

[ 0.9509852491856253, 0.26614753468624514 ]

[ 1.5915799949354532, 1.1260165637949262 ]

[ 1.7338956744561975, 0.6078046591855821 ]

[ 0.534966894811154, 0.022496951965335868 ]

1,024

[ 512, 512 ]

[ 7569, 3250, 591, 8293, 1048, 3012, 928, 616, 3159, 28286, 313, 23869, 29897, 322, 6189, 6509, 297, 1422, 3030, 29879, 29889, 14447, 558, 1600, 1295, 763, 1260, 265, 3077, 29895, 8866, 393, 372, 674, 437, 290, 278, 5199, 8175, 29889, 2216, 2197, 29892, 278, 10637, 7178, 3237, 27880, 12065, 262, 471, 10325, 23153, 14509, 8041, 393, 1058, 1310, 5835, 29879, 319, 29902, 674, 5751, 278, 3186, 29889, 13, 10401, 15311, 2305, 8293, 1048, 319, 29889, 29902, 1009, 13133, 7389, 9712, 545, 7113, 4933, 2729, 11104, 18169, 297, 2351, 583, 763, 7828, 6479, 29895, 322, 7828, 9149, 29889, 910, 338, 451, 278, 871, 883, 310, 319, 29902, 393, 4864, 29889, 1334, 505, 9251, 10664, 7560, 1369, 29899, 14340, 1985, 297, 319, 29902, 29889, 512, 445, 1400, 591, 674, 4682, 777, 1369, 29899, 14340, 297, 4092, 1058, 505, 11039, 630, 23116, 21082, 964, 1009, 9316, 322, 5786, 29889, 13, 797, 6601, 10466, 29892, 319, 29902, 14637, 304, 278, 6559, 322, 9004, 362, 310, 13052, 296, 10468, 491, 14884, 29889, 1152, 263, 1472, 931, 372, 471, 13112, 393, 14884, 674, 1284, 372, 5189, 304, 22222, 5199, 763, 21082, 29889, 13, 4013, 756, 1286, 1063, 16413, 2743, 1363, 411, 1269, 6819, 316, 6332, 29892, 15483, 756, 4318, 393, 14884, 508, 451, 871, 2189, 13052, 296, 9595, 541, 508, 884, 714, 19826, 25618, 297, 1784, 10161, 29889, 5806, 25618, 1603, 1072, 475, 5835, 29891, 975, 2258, 1455, 19679, 29892, 907, 28157, 322, 777, 21420, 310, 7604, 4371, 29892, 23226, 526, 4380, 292, 701, 5172, 491, 6509, 304, 1634, 5926, 5199, 19677, 3449, 19544, 13615, 635, 29889, 887, 881, 1423, 714, 5087, 29915, 29879, 319, 29902, 28224, 7862, 304, 1073, 901, 29889, 13, 8809, 488, 278, 671, 310, 319, 29889, 29902, 674, 694, 7404, 505, 766, 7614, 681, 27721, 297, 9121, 8324, 29889, 739, 16688, 385, 7636, 304, 17459, 800, 746, 896, 671, 372, 363, 10468, 284, 16114, 1199, 322, 10608, 3907, 29889, 11221, 2400, 526, 9881, 319, 29902, 21309, 14582, 393, 526, 620, 29882, 21430, 920, 17266, 800, 437, 5381, 2820, 278, 15482, 915, 29889, 13, 21287, 830, 2877, 2787, 29879, 526, 3081, 287, 491, 3012, 928, 616, 3159, 28286, 29889, 1094, 1438, 3186, 29879, 4953, 901, 4280, 29892, 278, 319, 29902, 29915, 29879, 6297, 674, 7985, 18709, 9247, 29889, 13, 4013, 9226, 4023, 2264, 278, 3081, 310, 25323, 3321, 20602, 304, 9801, 23226, 2274, 848, 2253, 322, 12021, 16232, 27303, 29889, 450, 5001, 756, 4240, 263, 9460, 310, 7047, 393, 508, 5110, 322, 4340, 2048, 3528, 2729, 373, 1009, 29380, 4225, 29889, 18540, 393, 508, 5110, 297, 445, 8214, 338, 884, 2000, 4933, 6509, 7047, 322, 372, 338, 1641, 1304, 297, 263, 9377, 12875, 310, 409, 14359, 29889, 2648, 4023, 2264, 292, 278, 3081, 310, 25323, 3321, 20602, 29892, 15918, 830, 1658, 292, 6911, 17459, 800, 322, 2305, 1207, 2253, 1602, 12112, 29889, 13, 1576, 14582, 9316, 526, 1641, 1304, 491, 5874, 946, 15942, 29892, 9045, 18020, 6351, 1338, 322, 18161, 17535, 17162, 29889, 3834, 310, 278, 4160, 505, 8967, 427, 29308, 3234, 2068, 322, 2919, 3438, 4048, 886, 29889, 4525, 714, 26807, 892, 263, 1121, 310, 278, 5335, 873, 1602, 12112, 4586, 322, 25483, 7171, 1089, 287, 1549, 1009, 15483, 29889, 13, 29020, 701, 263, 9045, 18020, 1788, 363, 3148, 8811, 478, 1308, 550, 29889, 13, 29924, 13415, 310, 278, 29871, 29946, 29900, 29892, 29900, 29900, 29900, 4549, 9923, 713, 18923, 4889, 337, 3687, 373, 6757, 4240, 491, 4124, 23985, 363, 6615, 1218, 1009, 13665, 292, 14188, 29889, 13, 6716, 310, 4275, 10557, 29915, 29879, 10150, 405, 17080, 29915, 29879, 17770, 379, 5667, 29914, 319, 1367, 29879, 756, 21168, 1009, 1650, 304, 2304, 29871, 29946, 29892, 29946, 29900, 29900, 24899, 1199, 322, 29418, 277, 1338, 29889, 13, 29924, 4992, 14533, 8128, 18161, 6851, 363, 5703, 414, 29892, 1663, 18541, 14582, 322, 5381, 267, 29889, 450, 5001, 263, 9893, 304, 7899, 11962, 322, 19001, 28108, 1017, 491, 4023, 2264, 292, 7333, 16114, 1199, 304, 5957, 18161, 6851, 29889, 450, 1532, 1641, 310, 22873, 338, 7136, 5932, 310, 17459, 800, 322, 341, 4992, 14533, 508, 1371, 596, 13925, 1302, 412, 411, 18161, 5626, 14870, 963, 29889, 13, 3047, 278, 341, 4992, 14533, 623, 4160, 508, 1074, 599, 1009, 1436, 2925, 9904, 297, 697, 2323, 7481, 29889, 2688, 508, 6755, 304, 679, 6655, 29879, 746, 1009, 17346, 652, 567, 2400, 13071, 731, 491, 963, 29889, 450, 5001, 508, 884, 3867, 297, 1760, 3145, 607, 26830, 18161, 6365, 2722, 322, 16415, 3234, 2068, 29889, 16972, 505, 4318, 393, 4943, 8744, 310, 372, 29915, 29879, 623, 508, 7899, 701, 3234, 2068, 297, 278, 24788, 322, 26830, 19001, 633, 303, 296, 1080, 29889, 13, 29907, 1161, 8261, 14582, 505, 263, 302, 22817, 1847, 15982, 29889, 1128, 304, 5706, 5994, 398, 12045, 3889, 3639, 373, 1009, 274, 1161, 4808, 886, 577, 393, 6232, 7694, 17173, 338, 5256, 3368, 29889, 23829, 19257, 12520, 491, 1422, 24388, 373, 274, 1161, 4808, 886, 338, 2337, 6480, 322, 372, 338, 5189, 363, 767, 18150, 304, 679, 278, 1900, 6554, 29889, 10813, 5271, 6911, 1316, 14582, 297, 274, 1161, 10643, 491, 337, 29899, 5521, 19985, 15303, 6336, 304, 9801, 278, 7472, 5253, 2326, 1983, 278, 9939, 4066, 6554, 29889, 13, 3112, 29915, 29879, 319, 29902, 7481, 338, 23387, 411, 2999, 24388, 322, 366, 508, 7333, 895, 596, 14238, 3987, 29889, 450, 5001, 471, 10325, 6577, 3192, 4249, 278, 2246, 3006, 1436, 29899, 11345, 14582, 297, 4092, 491, 278, 10432, 1334, 4298, 15057, 946, 3819, 29449, 20449, 29889, 13, 29909, 20234, 10371, 11407, 372, 29915, 29879, 319, 29902, 9316, 472, 263, 15687, 29889, 13, 26262, 17869, 25228, 706, 338, 2675, 13436, 411, 26370, 739, 29892, 607, 6911, 3345, 403, 4343, 17869, 2011, 25648, 11265, 363, 967, 13154, 29889, 2648, 16184, 596, 17498, 322, 3132, 11938, 4822, 29871, 29896, 29906, 1422, 3651, 29892, 599, 372, 4893, 338, 29871, 29896, 29945, 6233, 304, 6230, 596, 3132, 2011, 25648, 29889, 399, 3993, 310, 3196, 2011, 25648, 16114, 1199, 24441, 29892, 278, 5001, 29915, 29879, 9316, 526, 1641, 1304, 491, 12230, 1334, 4298, 2315, 18150, 322, 28218, 284, 350, 1331, 29889, 13, 1576, 381, 9570, 2729, 5701, 29874, 29903, 1650, 338, 9826, 1641, 1304, 491, 13258, 358, 767, 18150, 304, 4023, 2264, 372, 29915 ]

1,332,815

0

C4

15

4

The IP legal regime in Hong Kong is well established and very similar to those of other modern and highly sophisticated economies such as the United Kingdom, Singapore and Australia. The IP laws of Hong Kong continue to be based on English legislation despite the change of sovereignty resulting from the handover of Hong Kong back to the People's Republic of China on July 1 1997; the common law will continue to be applicable until at least 2047 on the basis of the 'one country, two systems' policy. Hong Kong is a member of the World Intellectual Property Organization and a signatory to most of the important IP treaties, including the Paris Convention for the Protection of Industrial Property and the Agreement on Trade Related Aspects of Intellectual Property Rights. The two main statutes that govern the protection and enforcement of trademark rights in Hong Kong are the Trademarks Ordinance and the Trade Descriptions Ordinance. The latter protects consumers against false trade descriptions (which are defined as including trademarks under the ordinance) and false applications of trademarks registered in Hong Kong. as a result of such misrepresentation, it has suffered or is likely to suffer damage. litigation before the courts (in respect of civil disputes). We deal with these in turn in the paragraphs below, insofar as they relate to trademark and brand owners' rights. One of the key roles of Customs is the protection of the interests of IP rights owners in Hong Kong. Customs is made up of five branches, one of which is the Intellectual Property Investigation Bureau, which, as its name suggests, is focused on IP enforcement matters. Generally speaking, before Customs will take on an enforcement case, it is necessary for the relevant brand owner to register its rights and then file a complaint in respect of each particular case of infringement. (In Hong Kong, unlike in China, only trademark rights and copyrights may be registered with Customs. a letter of authorization issued by the trademark owner vesting the said examiner with the authority to act on its behalf in future cases led by Customs. Customs has wide powers of search and seizure, powers of arrest and discretion on whether to prosecute an infringer. Hence, the powers of Customs in Hong Kong exceed those of customs departments in other regions/countries, as Customs carries out all of the above procedures without encountering bureaucratic conflict with other government departments. It can seize counterfeit goods from anywhere in Hong Kong and not just in harbour or border areas. The Organized and Serious Crimes Ordinance confers extensive powers in certain appropriate circumstances on law enforcement officers (police and customs officers) for search and investigation in IP enforcement, including trademark infringement matters. The Trade Descriptions Ordinance contains criminal sanctions in respect of offences relating to false trade descriptions, trademark forgery and false application of trademarks registered in Hong Kong. Under the ordinance, any person who forges any trademark or falsely applies to any goods any trademark or any mark so nearly resembling a trademark as to be calculated to deceive commits an offence unless he or she proves that he or she acted without an intention to defraud. It is also an offence to sell or expose, or have in one's possession for sale or for any purpose of trade or manufacture, goods to which any forged trademark is applied, or to which any trademark or mark so nearly resembling a trademark as to be calculated to deceive is falsely applied. undertake personally, or through an authorized representative (who has good knowledge of the trademark), to assist Customs in the identification of infringing goods seized and testify in court as a prosecution witness if necessary. on summary conviction to a fine of HK$100,000 and to imprisonment for two years. there is a likelihood of irreparable damage to the plaintiff if the defendant's infringing activities are not stopped immediately. The timing of the application for an injunction is important, because any delay may prejudice the application. The plaintiff is also usually required to give a crossundertaking on damages in such cases. there is a real possibility that the defendant may destroy the evidence of infringement. Civil proceedings are instituted by filing a writ of summons with a general endorsement of claims or a detailed statement of claim,

0.484611

1.437586

0.886791

1.278959

[ 0.9400278457536352, 0.02919368546945958 ]

[ 1.6202300522364086, 1.254941821649226 ]

[ 1.257082361683955, 0.5164999822717484 ]

[ 1.367405380652077, 1.190512202410881 ]

1,024

[ 512, 512 ]

[ 450, 5641, 11706, 22384, 297, 12798, 12026, 338, 1532, 7841, 322, 1407, 2788, 304, 1906, 310, 916, 5400, 322, 10712, 269, 3021, 4695, 630, 7766, 583, 1316, 408, 278, 3303, 12626, 29892, 25960, 322, 8314, 29889, 450, 5641, 14243, 310, 12798, 12026, 6773, 304, 367, 2729, 373, 4223, 13332, 362, 15020, 278, 1735, 310, 577, 9359, 335, 593, 29891, 9819, 515, 278, 1361, 957, 310, 12798, 12026, 1250, 304, 278, 11647, 29915, 29879, 8063, 310, 7551, 373, 5468, 29871, 29896, 29871, 29896, 29929, 29929, 29955, 29936, 278, 3619, 4307, 674, 6773, 304, 367, 22903, 2745, 472, 3203, 29871, 29906, 29900, 29946, 29955, 373, 278, 8405, 310, 278, 525, 650, 4234, 29892, 1023, 6757, 29915, 8898, 29889, 13, 29950, 549, 12026, 338, 263, 4509, 310, 278, 2787, 18555, 781, 950, 9079, 9205, 2133, 322, 263, 1804, 7606, 304, 1556, 310, 278, 4100, 5641, 7539, 583, 29892, 3704, 278, 3681, 26774, 363, 278, 14409, 428, 310, 12157, 9315, 9079, 322, 278, 4059, 276, 882, 373, 27226, 6376, 630, 1094, 1103, 29879, 310, 18555, 781, 950, 9079, 26863, 29889, 13, 1576, 1023, 1667, 1002, 2667, 393, 4095, 278, 13047, 322, 24555, 13561, 310, 1020, 2310, 935, 10462, 297, 12798, 12026, 526, 278, 3201, 2310, 17862, 16557, 262, 749, 322, 278, 27226, 20355, 1980, 16557, 262, 749, 29889, 450, 7480, 12566, 29879, 11233, 414, 2750, 2089, 11302, 2342, 1980, 313, 4716, 526, 3342, 408, 3704, 1020, 2310, 17862, 1090, 278, 22420, 749, 29897, 322, 2089, 8324, 310, 1020, 2310, 17862, 15443, 297, 12798, 12026, 29889, 13, 294, 263, 1121, 310, 1316, 3984, 276, 26081, 29892, 372, 756, 17654, 470, 338, 5517, 304, 8812, 18658, 29889, 13, 19411, 335, 362, 1434, 278, 28033, 313, 262, 3390, 310, 7631, 8937, 267, 467, 13, 4806, 5376, 411, 1438, 297, 2507, 297, 278, 14880, 29879, 2400, 29892, 297, 578, 15641, 408, 896, 29279, 304, 1020, 2310, 935, 322, 14982, 1914, 414, 29915, 10462, 29889, 13, 6716, 310, 278, 1820, 16178, 310, 8701, 29879, 338, 278, 13047, 310, 278, 20017, 310, 5641, 10462, 1914, 414, 297, 12798, 12026, 29889, 8701, 29879, 338, 1754, 701, 310, 5320, 14202, 29892, 697, 310, 607, 338, 278, 18555, 781, 950, 9079, 28246, 362, 18903, 29892, 607, 29892, 408, 967, 1024, 14661, 29892, 338, 21309, 373, 5641, 24555, 13561, 13750, 29889, 13, 5631, 635, 13590, 29892, 1434, 8701, 29879, 674, 2125, 373, 385, 24555, 13561, 1206, 29892, 372, 338, 5181, 363, 278, 8018, 14982, 12271, 304, 6036, 967, 10462, 322, 769, 934, 263, 15313, 524, 297, 3390, 310, 1269, 3153, 1206, 310, 297, 1341, 292, 882, 29889, 313, 797, 12798, 12026, 29892, 25531, 297, 7551, 29892, 871, 1020, 2310, 935, 10462, 322, 3509, 1266, 29879, 1122, 367, 15443, 411, 8701, 29879, 29889, 13, 29874, 5497, 310, 28733, 16610, 491, 278, 1020, 2310, 935, 12271, 16779, 292, 278, 1497, 4392, 4983, 411, 278, 14329, 304, 1044, 373, 967, 2306, 3131, 297, 5434, 4251, 5331, 491, 8701, 29879, 29889, 13, 7281, 29879, 756, 9377, 10801, 310, 2740, 322, 409, 466, 545, 29892, 10801, 310, 22564, 322, 766, 4838, 291, 373, 3692, 304, 410, 3471, 1082, 385, 297, 1341, 5621, 29889, 10133, 29892, 278, 10801, 310, 8701, 29879, 297, 12798, 12026, 13461, 1906, 310, 2888, 29879, 5840, 1860, 297, 916, 12786, 29914, 2798, 2722, 29892, 408, 8701, 29879, 1559, 2722, 714, 599, 310, 278, 2038, 28648, 1728, 11735, 292, 289, 13411, 7283, 2454, 14529, 411, 916, 5874, 5840, 1860, 29889, 739, 508, 409, 675, 6795, 1725, 277, 22535, 515, 12214, 297, 12798, 12026, 322, 451, 925, 297, 4023, 6526, 470, 5139, 10161, 29889, 13, 1576, 9205, 1891, 322, 1816, 2738, 6781, 1355, 16557, 262, 749, 1970, 414, 20607, 10801, 297, 3058, 8210, 14209, 373, 4307, 24555, 13561, 13049, 313, 3733, 625, 322, 2888, 29879, 13049, 29897, 363, 2740, 322, 22522, 297, 5641, 24555, 13561, 29892, 3704, 1020, 2310, 935, 297, 1341, 292, 882, 13750, 29889, 13, 1576, 27226, 20355, 1980, 16557, 262, 749, 3743, 22161, 9753, 1953, 297, 3390, 310, 1283, 2063, 1104, 1218, 304, 2089, 11302, 2342, 1980, 29892, 1020, 2310, 935, 18879, 708, 322, 2089, 2280, 310, 1020, 2310, 17862, 15443, 297, 12798, 12026, 29889, 7634, 278, 22420, 749, 29892, 738, 2022, 1058, 363, 2710, 738, 1020, 2310, 935, 470, 285, 1338, 873, 16058, 304, 738, 22535, 738, 1020, 2310, 935, 470, 738, 2791, 577, 8886, 620, 1590, 1847, 263, 1020, 2310, 935, 408, 304, 367, 12833, 304, 23332, 573, 25741, 385, 1283, 663, 6521, 540, 470, 1183, 28281, 393, 540, 470, 1183, 27320, 1728, 385, 16392, 304, 822, 336, 566, 29889, 739, 338, 884, 385, 1283, 663, 304, 19417, 470, 24396, 29892, 470, 505, 297, 697, 29915, 29879, 17715, 363, 14686, 470, 363, 738, 6437, 310, 11302, 470, 12012, 545, 29892, 22535, 304, 607, 738, 363, 3192, 1020, 2310, 935, 338, 7436, 29892, 470, 304, 607, 738, 1020, 2310, 935, 470, 2791, 577, 8886, 620, 1590, 1847, 263, 1020, 2310, 935, 408, 304, 367, 12833, 304, 23332, 573, 338, 285, 1338, 873, 7436, 29889, 13, 7635, 1296, 22345, 29892, 470, 1549, 385, 4148, 1891, 21097, 313, 15970, 756, 1781, 7134, 310, 278, 1020, 2310, 935, 511, 304, 6985, 8701, 29879, 297, 278, 29769, 310, 297, 1341, 292, 292, 22535, 25291, 322, 1243, 1598, 297, 8973, 408, 263, 410, 3471, 918, 16277, 565, 5181, 29889, 13, 265, 15837, 7602, 2463, 304, 263, 2691, 310, 379, 29968, 29938, 29896, 29900, 29900, 29892, 29900, 29900, 29900, 322, 304, 29535, 358, 363, 1023, 2440, 29889, 13, 12711, 338, 263, 4188, 22342, 310, 19950, 862, 519, 18658, 304, 278, 2174, 524, 2593, 565, 278, 822, 5818, 29915, 29879, 297, 1341, 292, 292, 14188, 526, 451, 11084, 7389, 29889, 13, 1576, 28750, 310, 278, 2280, 363, 385, 10899, 651, 338, 4100, 29892, 1363, 738, 9055, 1122, 758, 17675, 625, 278, 2280, 29889, 450, 2174, 524, 2593, 338, 884, 5491, 3734, 304, 2367, 263, 4891, 7635, 5086, 373, 5625, 1179, 297, 1316, 4251, 29889, 13, 12711, 338, 263, 1855, 13331, 393, 278, 822, 5818, 1122, 8174, 278, 10757, 310, 297, 1341, 292, 882, 29889, 13, 29907, 5341, 8469, 886, 526, 25444, 3860, 491, 977, 292, 263, 2044, 310, 22792, 787, 411, 263, 2498, 1095, 943, 882, 310, 16726, 470, 263, 13173, 3229, 310, 5995, 29892 ]

1,332,817

0

C4

11

19

followed by the filing of pleadings according to certain statutorily prescribed time limits. Discovery follows the pleadings stage. Discovery is a process whereby the parties exchange and inspect documents and witness statements. Once this procedure is completed, matters are then set down for trial. It is possible to proceed by way of expedited procedures. In uncontested cases, default judgment may be applied for; on the other hand, in cases where the applicant can show that there are real prospects of success on a claim or part of a claim (or the defendant has no arguable case), it may seek Bird & Bird Anti-counterfeiting 2008 – A summary judgment of either the whole or that part of the claim without having to proceed to a full trial. Decisions handed down by the first instance court may be appealed. However, such appeals to the High Court must be filed by serving a notice of appeal on all the affected parties within 28 days of the date on which the judgment or order is sealed. This is subject to any application for leave to appeal out of time. A dissatisfied party can, with leave, appeal against a decision of the High Court to the Court of Appeal, whose decision shall be final. In Hong Kong, as in many jurisdictions worldwide, the sale of counterfeit goods through online channels poses a real threat to brand owners. Typically, online auction sites or trading platforms serve as a channel for individual sellers to sell their counterfeit goods. It is often difficult to track down such sellers as they provide limited identification information and are contactable only by email. However, there are practical measures that can be taken by trademark owners to counter the online sale of counterfeit products. If counterfeit goods are found to be offered for sale on auction websites, warning letters and demands for removal should be sent to the auction websites themselves, requiring that the offending offers for sale be removed from the websites and ceased forthwith. Further, as most of the goods sold on the online trading platforms are delivered to the purchasers by mail or courier, it is important for trademark owners to record their rights with Customs so that the counterfeit goods may be intercepted. In serious cases of infringement, trademark owners may consider applying to the courts for Norwich Pharmacal orders against internet service providers to disclose the IP address and the residential address (if the IP address originates from a residence) of the individuals behind the alleged acts of infringement. This then enables the trademark owner to take further action based on the information obtained. In addressing the threat of trademark infringements and trademark-related offences, brand owners may wish to adopt the measures and strategies outlined below. Clearly, there are numerous advantages in securing trademark registration rights, which are the strongest rights to rely upon in an enforcement scenario. As discussed above, one obvious advantage is the ability to record such registration rights with Customs to counter any possible infringement. To protect trademarks on the Internet, brand owners may wish to consider registering their key trademarks, trade names and company names as domain names, where appropriate. It is important to have a system to monitor trademarks that are being filed and/or used by third parties (on the Internet), in case these have an adverse impact on the brand owner's trademark rights. Brand owners may either subscribe to trademark watch services or conduct their own regular searches. The Intellectual Property Department of Hong Kong provides a free online search service at http://ipsearch.ipd.gov.hk. Trademark owners should also take care to look out for the illegitimate use of their trademarks by third parties and to retain the relevant evidence in support of any legal action that may be initiated as a result thereof. It is advisable for brand owners to work with local IP legal experts on trademark enforcement matters and in cases of infringement it is often helpful to hire local investigators who are sufficiently knowledgeable to be able to work closely with the legal team to help strategize on the gathering of relevant evidence in support of an enforcement action. If the trademark in question is used by parties other than the trademark owner through licensing or distributorship arrangements, the relevant arrangements should be devised bearing in mind the potential pitfalls that may result in potential trademark disputes – or worse still, inadvertently encouraging and permitting counterfeiting activity within the brand owner's authorized distribution network. Hence, the

0.429139

0.560178

0.983168

1.044835

[ 0.27436558726023774, 0.5839122342139575 ]

[ 0.542271646287958, 0.5780842179141524 ]

[ 0.9020086181301573, 1.0643280437547507 ]

[ 0.9511861377316155, 1.1384847970458232 ]

1,024

[ 512, 512 ]

[ 5643, 491, 278, 977, 292, 310, 5644, 328, 886, 5034, 304, 3058, 1002, 3406, 2354, 2225, 23059, 931, 13071, 29889, 8565, 22205, 4477, 278, 5644, 328, 886, 7408, 29889, 8565, 22205, 338, 263, 1889, 988, 1609, 278, 13973, 14523, 322, 16096, 10701, 322, 16277, 9506, 29889, 9038, 445, 8792, 338, 8676, 29892, 13750, 526, 769, 731, 1623, 363, 14260, 29889, 13, 3112, 338, 1950, 304, 8469, 491, 982, 310, 15310, 1573, 28648, 29889, 512, 443, 1285, 2868, 4251, 29892, 2322, 24284, 1122, 367, 7436, 363, 29936, 373, 278, 916, 1361, 29892, 297, 4251, 988, 278, 15576, 424, 508, 1510, 393, 727, 526, 1855, 27289, 29879, 310, 2551, 373, 263, 5995, 470, 760, 310, 263, 5995, 313, 272, 278, 822, 5818, 756, 694, 1852, 29884, 519, 1206, 511, 372, 1122, 16508, 17777, 669, 17777, 18473, 29899, 11808, 1725, 11407, 29871, 29906, 29900, 29900, 29947, 785, 319, 15837, 24284, 310, 2845, 278, 3353, 470, 393, 760, 310, 278, 5995, 1728, 2534, 304, 8469, 304, 263, 2989, 14260, 29889, 13, 6185, 12112, 29692, 1623, 491, 278, 937, 2777, 8973, 1122, 367, 5929, 7943, 29889, 2398, 29892, 1316, 5929, 1338, 304, 278, 5057, 9245, 1818, 367, 934, 29881, 491, 16330, 263, 8369, 310, 25530, 373, 599, 278, 15201, 13973, 2629, 29871, 29906, 29947, 3841, 310, 278, 2635, 373, 607, 278, 24284, 470, 1797, 338, 409, 7943, 29889, 910, 338, 4967, 304, 738, 2280, 363, 5967, 304, 25530, 714, 310, 931, 29889, 319, 16317, 27685, 1000, 6263, 508, 29892, 411, 5967, 29892, 25530, 2750, 263, 10608, 310, 278, 5057, 9245, 304, 278, 9245, 310, 2401, 29872, 284, 29892, 5069, 10608, 4091, 367, 2186, 29889, 13, 797, 12798, 12026, 29892, 408, 297, 1784, 24894, 8977, 1080, 3186, 8157, 29892, 278, 14686, 310, 6795, 1725, 277, 22535, 1549, 7395, 18196, 926, 267, 263, 1855, 28469, 304, 14982, 1914, 414, 29889, 14213, 1711, 29892, 7395, 782, 428, 11840, 470, 3534, 292, 21796, 9080, 408, 263, 8242, 363, 5375, 19417, 414, 304, 19417, 1009, 6795, 1725, 277, 22535, 29889, 739, 338, 4049, 5189, 304, 5702, 1623, 1316, 19417, 414, 408, 896, 3867, 9078, 29769, 2472, 322, 526, 6958, 519, 871, 491, 4876, 29889, 13, 17245, 29892, 727, 526, 15031, 15366, 393, 508, 367, 4586, 491, 1020, 2310, 935, 1914, 414, 304, 6795, 278, 7395, 14686, 310, 6795, 1725, 277, 9316, 29889, 960, 6795, 1725, 277, 22535, 526, 1476, 304, 367, 12520, 363, 14686, 373, 782, 428, 28007, 29892, 9177, 8721, 322, 1261, 4167, 363, 28744, 881, 367, 2665, 304, 278, 782, 428, 28007, 6053, 29892, 26795, 393, 278, 1283, 2548, 16688, 363, 14686, 367, 6206, 515, 278, 28007, 322, 24886, 11483, 2541, 29889, 8725, 29892, 408, 1556, 310, 278, 22535, 5239, 373, 278, 7395, 3534, 292, 21796, 526, 20115, 304, 278, 10596, 294, 414, 491, 10524, 470, 3581, 4336, 29892, 372, 338, 4100, 363, 1020, 2310, 935, 1914, 414, 304, 2407, 1009, 10462, 411, 8701, 29879, 577, 393, 278, 6795, 1725, 277, 22535, 1122, 367, 23404, 287, 29889, 13, 797, 10676, 4251, 310, 297, 1341, 292, 882, 29892, 1020, 2310, 935, 1914, 414, 1122, 2050, 15399, 304, 278, 28033, 363, 4186, 16416, 1963, 2817, 562, 284, 11299, 2750, 8986, 2669, 1326, 11376, 304, 2313, 2226, 278, 5641, 3211, 322, 278, 20201, 616, 3211, 313, 361, 278, 5641, 3211, 3978, 1078, 515, 263, 25488, 29897, 310, 278, 15724, 5742, 278, 16831, 287, 14741, 310, 297, 1341, 292, 882, 29889, 910, 769, 28936, 278, 1020, 2310, 935, 12271, 304, 2125, 4340, 3158, 2729, 373, 278, 2472, 7625, 29889, 13, 797, 3211, 292, 278, 28469, 310, 1020, 2310, 935, 297, 1341, 292, 4110, 322, 1020, 2310, 935, 29899, 12817, 1283, 2063, 29892, 14982, 1914, 414, 1122, 6398, 304, 9332, 278, 15366, 322, 16650, 583, 714, 21354, 2400, 29889, 13, 18759, 368, 29892, 727, 526, 12727, 25486, 297, 409, 2764, 292, 1020, 2310, 935, 22583, 10462, 29892, 607, 526, 278, 4549, 342, 10462, 304, 19104, 2501, 297, 385, 24555, 13561, 10483, 29889, 1094, 15648, 2038, 29892, 697, 6924, 10631, 338, 278, 11509, 304, 2407, 1316, 22583, 10462, 411, 8701, 29879, 304, 6795, 738, 1950, 297, 1341, 292, 882, 29889, 13, 1762, 12566, 1020, 2310, 17862, 373, 278, 4685, 29892, 14982, 1914, 414, 1122, 6398, 304, 2050, 6036, 292, 1009, 1820, 1020, 2310, 17862, 29892, 11302, 2983, 322, 5001, 2983, 408, 5354, 2983, 29892, 988, 8210, 29889, 13, 3112, 338, 4100, 304, 505, 263, 1788, 304, 11819, 1020, 2310, 17862, 393, 526, 1641, 934, 29881, 322, 29914, 272, 1304, 491, 4654, 13973, 313, 265, 278, 4685, 511, 297, 1206, 1438, 505, 385, 594, 3901, 10879, 373, 278, 14982, 12271, 29915, 29879, 1020, 2310, 935, 10462, 29889, 18007, 1914, 414, 1122, 2845, 1014, 13086, 304, 1020, 2310, 935, 6505, 5786, 470, 7512, 1009, 1914, 4943, 29645, 29889, 450, 18555, 781, 950, 9079, 10317, 310, 12798, 12026, 8128, 263, 3889, 7395, 2740, 2669, 472, 1732, 597, 666, 4478, 29889, 666, 29881, 29889, 13513, 29889, 29882, 29895, 29889, 3201, 2310, 935, 1914, 414, 881, 884, 2125, 2562, 304, 1106, 714, 363, 278, 980, 1397, 277, 6490, 671, 310, 1009, 1020, 2310, 17862, 491, 4654, 13973, 322, 304, 11551, 278, 8018, 10757, 297, 2304, 310, 738, 11706, 3158, 393, 1122, 367, 14511, 630, 408, 263, 1121, 727, 974, 29889, 13, 3112, 338, 25228, 519, 363, 14982, 1914, 414, 304, 664, 411, 1887, 5641, 11706, 2902, 1372, 373, 1020, 2310, 935, 24555, 13561, 13750, 322, 297, 4251, 310, 297, 1341, 292, 882, 372, 338, 4049, 8444, 304, 298, 533, 1887, 7405, 4097, 1058, 526, 18430, 7134, 519, 304, 367, 2221, 304, 664, 16467, 411, 278, 11706, 3815, 304, 1371, 16650, 675, 373, 278, 11705, 292, 310, 8018, 10757, 297, 2304, 310, 385, 24555, 13561, 3158, 29889, 13, 3644, 278, 1020, 2310, 935, 297, 1139, 338, 1304, 491, 13973, 916, 1135, 278, 1020, 2310, 935, 12271, 1549, 7794, 575, 292, 470, 22965, 3406, 3527, 15196, 4110, 29892, 278, 8018, 15196, 4110, 881, 367, 316, 11292, 24638, 297, 3458, 278, 7037, 22754, 12559, 393, 1122, 1121, 297, 7037, 1020, 2310, 935, 8937, 267, 785, 470, 15029, 1603, 29892, 297, 328, 1765, 2705, 18443, 292, 322, 3635, 5367, 6795, 1725, 11407, 6354, 2629, 278, 14982, 12271, 29915, 29879, 4148, 1891, 4978, 3564, 29889, 10133, 29892, 278 ]

1,332,817

1,024

C4

11

19

If men are good, you don't need government; if men are evil or ambivalent, you don't dare have one. ~ Robert LeFevre * Rethinking Hitler & National Socialism Author Topic: * Rethinking Hitler & National Socialism (Read 5054 times) Rethinking Hitler & National Socialism picture link I suppose it would eventually come to this: all the reading, investigating, and research I've done since discovering the truth about 9/11 would lead to a re-examination and re-learning of much of history, especially the mainstream version of WWI and WWII history. Since I began looking into 9/11, I've explored all sorts of "conspiracy theories", but lately, largely as a result of following the work of Deanna Spingola, ZionCrimeFactory, Carolyn Yeager, Veronica Clark, and others, I've began to delve deeper and deeper into revisionist history and what Adolf Hitler and the National Socialist German Workers' Party (NSDAP) really stood for. And today I'd like to share some of my thoughts with you about this subject. I've mentioned before that I once bought into Jim Condit, Jr.'s thesis about Adolf Hitler and the NSDAP, namely, that Hitler and many of the top Nazi leaders were either Jews themselves, or puppets of the international bankers and Jewish crime network, operating as part of the bankers controlled opposition in order to facilitate the establishment of the illegitimate, terrorist state of Israel as a safe haven and central headquarters for the global Jewish mafia, in the process fulfilling messianic Jewish prophecy in order to advance what is commonly known as "The New World Order", whose foundations are laid out in detail in the supremacist Jewish Talmud. However, I've always kept an open mind about this and many other subjects, and only recently (i.e., the past six months or so) began to really explore it in greater detail. And I'm now firmly convinced that Condit and others that promote this ridiculous theory about the NSDAP being puppets of the Rothschilds are 100% wrong in their assessment. I've concluded that all the other ridiculous theories and outright slanders against Adolf Hitler and National Socialist Germany are merely attempts to divert people's attention away from what Hitler and his movement actually stood for, what they represented, what they actually said, and what they actually did. By the way, Deanna Spingola and Veronica Clark refute many of these outlandish theories in a recent interview for those interested. One thing I want to make clear here: Hitler and the National Socialist movement were most definitely "anti-Semites", and used "anti-Semitism" in their political propaganda and messaging. After all, even critics of Hitler and the NSDAP recognize that their propaganda was based on truth, and in our ass-backwards, Jew-run world, the truth is fundamentally "anti-Semitic". So let's not get caught up in this childish meme of "Hitler and the Nazis were evil, racist anti-Semites'" nonsense, and simply refuse to investigate objectively what they stood for. Look at what they said, did, wrote about, and represented, and you will come to the obvious conclusion that I have: that this movement was the greatest threat the world has ever known to the parasitic, subversive, and destructive nature of the international Jewish criminal cabal largely controlling the West, pushing for their "New World Order" on every front imaginable. This is why Hitler and National Socialist Germany had to be destroyed. This is why Hitler and the NSDAP are constantly demonized, slandered, and blamed for every evil in the world. This is why the mass media, Hollywood and our educational system projects the crimes that the Jew-run Allies (the U.K., U.S. and Soviet Union) actually committed on to Hitler and National Socialist Germany. The Jews have completely flipped the script, blaming Hitler and the NSDAP for a fake "Holocaust" of European Jews and countless other alleged atrocities when in fact the Allies were responsible for the real holocausts and other crimes against humanity during WWII. Organized international Jewry, the primary network behind the push for a "New World Order", understand and recognize how dangerous Adolf Hitler and National Socialist ideology was – and potentially remains – to their totalitarian plan for world domination and subjugation. As

-0.114494

0.054102

-0.484681

0.649427

[ -0.1462103741566942, -0.08277728085118909 ]

[ -0.35886218725615787, 0.46706524587294984 ]

[ -0.3293363996939053, -0.6400259253034783 ]

[ 0.2644243869128541, 1.0344299863157078 ]

1,024

[ 512, 512 ]

[ 960, 1757, 526, 1781, 29892, 366, 1016, 29915, 29873, 817, 5874, 29936, 565, 1757, 526, 16126, 470, 3181, 27445, 29892, 366, 1016, 29915, 29873, 23222, 505, 697, 29889, 3695, 4755, 951, 29943, 5750, 276, 13, 29930, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 13720, 7488, 293, 29901, 334, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 313, 6359, 29871, 29945, 29900, 29945, 29946, 3064, 29897, 13, 29934, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 12095, 1544, 13, 29902, 7755, 372, 723, 10201, 2041, 304, 445, 29901, 599, 278, 5183, 29892, 7405, 1218, 29892, 322, 5925, 306, 29915, 345, 2309, 1951, 6523, 292, 278, 8760, 1048, 29871, 29929, 29914, 29896, 29896, 723, 3275, 304, 263, 337, 29899, 735, 314, 3381, 322, 337, 29899, 21891, 310, 1568, 310, 4955, 29892, 7148, 278, 1667, 5461, 1873, 310, 399, 22119, 322, 399, 29956, 2687, 4955, 29889, 4001, 306, 4689, 3063, 964, 29871, 29929, 29914, 29896, 29896, 29892, 306, 29915, 345, 3902, 4395, 599, 23551, 310, 376, 535, 1028, 29875, 10068, 25841, 613, 541, 301, 2486, 29892, 18425, 408, 263, 1121, 310, 1494, 278, 664, 310, 897, 9713, 1706, 292, 2963, 29892, 796, 291, 20647, 603, 5126, 29892, 8562, 948, 10134, 1875, 29892, 1798, 26082, 17129, 29892, 322, 4045, 29892, 306, 29915, 345, 4689, 304, 628, 345, 25871, 322, 25871, 964, 26554, 391, 4955, 322, 825, 21834, 23151, 322, 278, 3086, 10307, 391, 5332, 5244, 414, 29915, 9173, 313, 3059, 29928, 3301, 29897, 2289, 8389, 363, 29889, 1126, 9826, 306, 29915, 29881, 763, 304, 6232, 777, 310, 590, 13133, 411, 366, 1048, 445, 4967, 29889, 13, 29902, 29915, 345, 5276, 1434, 393, 306, 2748, 18093, 964, 8507, 11790, 277, 29892, 13843, 6169, 29879, 266, 6656, 1048, 21834, 23151, 322, 278, 3865, 29928, 3301, 29892, 18451, 29892, 393, 23151, 322, 1784, 310, 278, 2246, 11409, 29875, 20251, 892, 2845, 22057, 6053, 29892, 470, 2653, 27421, 310, 278, 6121, 9124, 414, 322, 16728, 17268, 3564, 29892, 13598, 408, 760, 310, 278, 9124, 414, 20704, 19626, 297, 1797, 304, 16089, 10388, 278, 25012, 310, 278, 980, 1397, 277, 6490, 29892, 15115, 391, 2106, 310, 11996, 408, 263, 9109, 7359, 322, 6555, 26463, 363, 278, 5534, 16728, 611, 29888, 423, 29892, 297, 278, 1889, 6095, 5589, 292, 4473, 713, 293, 16728, 3107, 354, 1270, 297, 1797, 304, 6564, 825, 338, 15574, 2998, 408, 376, 1576, 1570, 2787, 8170, 613, 5069, 1476, 800, 526, 12341, 714, 297, 9493, 297, 278, 22747, 8628, 391, 16728, 10288, 29885, 566, 29889, 2398, 29892, 306, 29915, 345, 2337, 8126, 385, 1722, 3458, 1048, 445, 322, 1784, 916, 17800, 29892, 322, 871, 10325, 313, 29875, 29889, 29872, 1696, 278, 4940, 4832, 7378, 470, 577, 29897, 4689, 304, 2289, 26987, 372, 297, 7621, 9493, 29889, 1126, 306, 29915, 29885, 1286, 9226, 368, 25617, 393, 11790, 277, 322, 4045, 393, 27391, 445, 8177, 12906, 681, 6368, 1048, 278, 3865, 29928, 3301, 1641, 2653, 27421, 310, 278, 21790, 816, 789, 29879, 526, 29871, 29896, 29900, 29900, 29995, 2743, 297, 1009, 24809, 358, 29889, 306, 29915, 345, 22834, 393, 599, 278, 916, 8177, 12906, 681, 25841, 322, 714, 1266, 269, 1049, 414, 2750, 21834, 23151, 322, 3086, 10307, 391, 9556, 526, 13586, 14734, 304, 652, 1765, 2305, 29915, 29879, 8570, 3448, 515, 825, 23151, 322, 670, 10298, 2869, 8389, 363, 29892, 825, 896, 9875, 29892, 825, 896, 2869, 1497, 29892, 322, 825, 896, 2869, 1258, 29889, 2648, 278, 982, 29892, 897, 9713, 1706, 292, 2963, 322, 1798, 26082, 17129, 2143, 1082, 1784, 310, 1438, 714, 1049, 728, 25841, 297, 263, 7786, 15593, 363, 1906, 8852, 29889, 13, 6716, 2655, 306, 864, 304, 1207, 2821, 1244, 29901, 23151, 322, 278, 3086, 10307, 391, 10298, 892, 1556, 11630, 376, 3656, 29899, 28516, 3246, 613, 322, 1304, 376, 3656, 29899, 29903, 21976, 1608, 29908, 297, 1009, 8604, 13089, 5863, 322, 4473, 6751, 29889, 2860, 599, 29892, 1584, 28431, 310, 23151, 322, 278, 3865, 29928, 3301, 18720, 393, 1009, 13089, 5863, 471, 2729, 373, 8760, 29892, 322, 297, 1749, 1223, 29899, 1627, 2935, 29892, 9576, 29899, 3389, 3186, 29892, 278, 8760, 338, 5220, 1166, 635, 376, 3656, 29899, 29903, 21976, 293, 1642, 1105, 1235, 29915, 29879, 451, 679, 12624, 701, 297, 445, 2278, 728, 286, 2004, 310, 376, 29950, 277, 1358, 322, 278, 11409, 275, 892, 16126, 29892, 11021, 391, 9418, 29899, 28516, 3246, 11838, 302, 787, 1947, 29892, 322, 3763, 26506, 304, 23033, 1203, 3598, 825, 896, 8389, 363, 29889, 7419, 472, 825, 896, 1497, 29892, 1258, 29892, 5456, 1048, 29892, 322, 9875, 29892, 322, 366, 674, 2041, 304, 278, 6924, 15997, 393, 306, 505, 29901, 393, 445, 10298, 471, 278, 14176, 28469, 278, 3186, 756, 3926, 2998, 304, 278, 610, 294, 277, 293, 29892, 1014, 874, 573, 29892, 322, 17912, 573, 5469, 310, 278, 6121, 16728, 22161, 7776, 284, 18425, 640, 22155, 278, 3122, 29892, 27556, 363, 1009, 376, 4373, 2787, 8170, 29908, 373, 1432, 4565, 6382, 262, 519, 29889, 13, 4013, 338, 2020, 23151, 322, 3086, 10307, 391, 9556, 750, 304, 367, 14416, 29889, 910, 338, 2020, 23151, 322, 278, 3865, 29928, 3301, 526, 21003, 8033, 1891, 29892, 269, 1049, 14561, 29892, 322, 1999, 2795, 363, 1432, 16126, 297, 278, 3186, 29889, 910, 338, 2020, 278, 4158, 5745, 29892, 19180, 322, 1749, 28976, 1788, 9279, 278, 2181, 1355, 393, 278, 9576, 29899, 3389, 838, 3687, 313, 1552, 501, 29889, 29968, 1696, 501, 29889, 29903, 29889, 322, 15308, 7761, 29897, 2869, 19355, 373, 304, 23151, 322, 3086, 10307, 391, 9556, 29889, 450, 22057, 505, 6446, 285, 492, 2986, 278, 2471, 29892, 1999, 11500, 23151, 322, 278, 3865, 29928, 3301, 363, 263, 25713, 376, 19984, 6400, 504, 29908, 310, 7824, 22057, 322, 2302, 2222, 916, 16831, 287, 472, 10198, 1907, 746, 297, 2114, 278, 838, 3687, 892, 14040, 363, 278, 1855, 8753, 6400, 504, 29879, 322, 916, 2181, 1355, 2750, 5199, 537, 2645, 399, 29956, 2687, 29889, 9205, 1891, 6121, 9576, 719, 29892, 278, 7601, 3564, 5742, 278, 5503, 363, 263, 376, 4373, 2787, 8170, 613, 2274, 322, 18720, 920, 18215, 21834, 23151, 322, 3086, 10307, 391, 1957, 3002, 471, 785, 322, 19998, 9242, 785, 304, 1009, 3001, 3673, 713, 3814, 363, 3186, 2432, 3381, 322, 1014, 29926, 688, 362, 29889, 13, 2887 ]

1,332,826

0

CommonCrawl

8

11

Veronica Clark explains in her must read article titled, Demystification of the Birth and Funding of the NSDAP, Hitler sought to overcome the class antagonism prevalent throughout Germany (and much of Europe) by establishing a political and social order based on merit, rather than class or wealth, and sought to unify German society around their common German heritage and Nordic race. Consider the following quote from Hitler, which underscores how he felt about the capitalist system that prevailed in Europe, Britain, and the United States: We are socialists, we are enemies of today's capitalistic economic system for the exploitation of the economically weak, with its unfair salaries, with its unseemly evaluation of a human being according to wealth and property instead of responsibility and performance, and we are all determined to destroy this system under all conditions. How true does that statement ring to you, especially in light of the criminal bailout of Wall Street and the absurd bonuses all the big shots were doling out for themselves and their crooked henchman following the (still on-going) financial collapse initiated in 2008? National Socialist ideology did have opinions about and openly discussed race and the "Jewish Problem", but it's far more nuanced than the mainstream version of history. For starters, National Socialism was more pro-German, pro-Aryan than anti-other races - except the Jewish "race". They cherished and sought to preserve their German race and identity, recognizing the destructive and subversive nature of Jewry, and their innate ability to corrupt society. They said and wrote some "extreme" things by today's Orwellian standards - but truthful things. The National Socialists were just being honest about the nature of organized Jewry, and their threat to Gentile societies. For instance, consider this excerpt from a 1935 bulletin published by the Reichspropagandaleitung, the Nazi Party's Central Propaganda office: Some believe that we are using methods in this battle that are too harsh. We reply that our attacks and methods in this battle cannot be determined by our way of thinking, by whether we find them ugly or harsh, but rather we must use methods in our attacks that are appropriate for the opponent that we are attacking. One cannot battle the Jews with the politeness of the noble Aryan soul, for which he as no understanding. We need only think back on the methods that the Jew used against our movement during the period of struggle. No lie or slander was too crude to be used, to be seized and passed on by the Jews and their Jewish lackeys with eagerness, enthusiasm, and Satanic joy. We would have had little success replying then with refined arguments. It is just as impossible today to combat this creeping, subterranean danger with methods that the Jew would only laugh at. The Führer's contribution has been to make the Jewish Question a matter for the entire people. The efforts völkisch groups, organizations, etc., made in the past to spread knowledge about the world enemy were never of great significance, since only a very limited circle was reached. With his movement, Adolf Hitler created an instrument that went far beyond these groups and made the nation see that the solution to this question was a prerequisite to changing Germany's fate. In answer to his brave act, all the powers at the command of the Jewish world were called on, including the mobilization of parties, of the press, of the radio, of finance, and of bloody terror. [...] I also recommend reading Those Damned Nazis, written by Joseph Goebbles in 1932, which explains National Socialist ideology in greater detail. Here are some excerpts that stand out to me: Why Are We Socialists? We are socialists because we see in socialism, that is the union of all citizens, the only chance to maintain our racial inheritance and to regain our political freedom and renew our German state. Socialism is the doctrine of liberation for the working class. It promotes the rise of the fourth class and its incorporation in the political organism of our Fatherland, and is inextricably bound to breaking the present slavery and regaining German freedom. Socialism, therefore, is not merely a matter of the oppressed class, but a matter for everyone, for freeing the German people from slavery is the goal of contemporary policy. [...] Why a Workers' Party? Work is not mankind's curse, but his blessing. A man becomes a man through labor. It elevates him, makes

0.904416

0.934419

0.437877

1.362203

[ 0.9016769337416699, 0.907155635457665 ]

[ 1.5700924519597366, 0.29874615922983633 ]

[ 0.5266449463732855, 0.34910807459638665 ]

[ 1.4714601913821923, 1.2529450888489502 ]

1,024

[ 512, 512 ]

[ 1798, 26082, 17129, 18568, 297, 902, 1818, 1303, 4274, 25278, 29892, 4432, 858, 2450, 310, 278, 350, 7515, 322, 13249, 292, 310, 278, 3865, 29928, 3301, 29892, 23151, 18365, 304, 25688, 278, 770, 3677, 12841, 1608, 758, 791, 296, 10106, 9556, 313, 392, 1568, 310, 4092, 29897, 491, 10127, 292, 263, 8604, 322, 5264, 1797, 2729, 373, 2778, 277, 29892, 3265, 1135, 770, 470, 17173, 29892, 322, 18365, 304, 443, 1598, 5332, 12459, 2820, 1009, 3619, 5332, 902, 16639, 322, 5245, 293, 8175, 29889, 10056, 278, 1494, 14978, 515, 23151, 29892, 607, 23400, 29883, 2361, 920, 540, 7091, 1048, 278, 7483, 391, 1788, 393, 758, 1564, 2356, 297, 4092, 29892, 14933, 29892, 322, 278, 3303, 3900, 29901, 13, 4806, 526, 5264, 2879, 29892, 591, 526, 22595, 310, 9826, 29915, 29879, 7483, 4695, 17407, 1788, 363, 278, 16035, 7018, 310, 278, 7766, 1711, 8062, 29892, 411, 967, 29395, 1466, 4497, 4314, 29892, 411, 967, 443, 344, 331, 368, 17983, 310, 263, 5199, 1641, 5034, 304, 17173, 322, 2875, 2012, 310, 23134, 322, 4180, 29892, 322, 591, 526, 599, 10087, 304, 8174, 445, 1788, 1090, 599, 5855, 29889, 13, 5328, 1565, 947, 393, 3229, 9228, 304, 366, 29892, 7148, 297, 3578, 310, 278, 22161, 289, 737, 449, 310, 14406, 7103, 322, 278, 6425, 18245, 10814, 6394, 599, 278, 4802, 528, 1862, 892, 8828, 292, 714, 363, 6053, 322, 1009, 8182, 12504, 19061, 305, 1171, 1494, 278, 313, 303, 453, 373, 29899, 17696, 29897, 18161, 24382, 14511, 630, 297, 29871, 29906, 29900, 29900, 29947, 29973, 13, 27325, 10307, 391, 1957, 3002, 1258, 505, 26971, 1048, 322, 1722, 368, 15648, 8175, 322, 278, 376, 29967, 809, 728, 11583, 613, 541, 372, 29915, 29879, 2215, 901, 4948, 8362, 1135, 278, 1667, 5461, 1873, 310, 4955, 29889, 1152, 5810, 2153, 29892, 3086, 10307, 1608, 471, 901, 410, 29899, 29954, 3504, 29892, 410, 29899, 29909, 719, 273, 1135, 9418, 29899, 1228, 19830, 448, 5174, 278, 16728, 376, 25525, 1642, 2688, 14954, 3276, 322, 18365, 304, 19905, 1009, 5332, 8175, 322, 10110, 29892, 5936, 5281, 278, 17912, 573, 322, 1014, 874, 573, 5469, 310, 9576, 719, 29892, 322, 1009, 7622, 403, 11509, 304, 1034, 6685, 12459, 29889, 2688, 1497, 322, 5456, 777, 376, 1062, 10291, 29908, 2712, 491, 9826, 29915, 29879, 1394, 29893, 5481, 273, 20801, 448, 541, 8760, 1319, 2712, 29889, 450, 3086, 10307, 2879, 892, 925, 1641, 15993, 1048, 278, 5469, 310, 19098, 9576, 719, 29892, 322, 1009, 28469, 304, 20655, 488, 5374, 20850, 29889, 13, 2831, 2777, 29892, 2050, 445, 429, 2265, 415, 515, 263, 29871, 29896, 29929, 29941, 29945, 24334, 262, 6369, 491, 278, 26981, 7728, 351, 392, 744, 10125, 29892, 278, 11409, 29875, 9173, 29915, 29879, 8068, 1019, 13573, 5863, 8034, 29901, 13, 9526, 4658, 393, 591, 526, 773, 3519, 297, 445, 10555, 393, 526, 2086, 4023, 845, 29889, 1334, 8908, 393, 1749, 16661, 322, 3519, 297, 445, 10555, 2609, 367, 10087, 491, 1749, 982, 310, 7291, 29892, 491, 3692, 591, 1284, 963, 22769, 470, 4023, 845, 29892, 541, 3265, 591, 1818, 671, 3519, 297, 1749, 16661, 393, 526, 8210, 363, 278, 23995, 296, 393, 591, 526, 5337, 292, 29889, 3118, 2609, 10555, 278, 22057, 411, 278, 2832, 18543, 310, 278, 15996, 319, 719, 273, 10752, 29892, 363, 607, 540, 408, 694, 8004, 29889, 1334, 817, 871, 1348, 1250, 373, 278, 3519, 393, 278, 9576, 1304, 2750, 1749, 10298, 2645, 278, 3785, 310, 21117, 29889, 1939, 3804, 470, 269, 1049, 261, 471, 2086, 7618, 311, 304, 367, 1304, 29892, 304, 367, 25291, 322, 4502, 373, 491, 278, 22057, 322, 1009, 16728, 425, 10055, 952, 411, 321, 351, 824, 404, 29892, 23644, 3173, 29885, 29892, 322, 12178, 273, 293, 15331, 29889, 1334, 723, 505, 750, 2217, 2551, 1634, 5890, 769, 411, 2143, 1312, 6273, 29889, 739, 338, 925, 408, 9301, 9826, 304, 15499, 445, 907, 26819, 29892, 1014, 357, 10800, 273, 9703, 411, 3519, 393, 278, 9576, 723, 871, 10569, 472, 29889, 13, 1576, 383, 4000, 261, 29915, 29879, 11896, 756, 1063, 304, 1207, 278, 16728, 894, 263, 4383, 363, 278, 4152, 2305, 29889, 450, 14231, 325, 5873, 29895, 783, 6471, 29892, 25700, 29892, 2992, 1696, 1754, 297, 278, 4940, 304, 9677, 7134, 1048, 278, 3186, 11103, 892, 2360, 310, 2107, 26002, 29892, 1951, 871, 263, 1407, 9078, 8607, 471, 7450, 29889, 2973, 670, 10298, 29892, 21834, 23151, 2825, 385, 11395, 393, 3512, 2215, 8724, 1438, 6471, 322, 1754, 278, 5233, 1074, 393, 278, 1650, 304, 445, 1139, 471, 263, 544, 406, 7680, 568, 304, 6480, 9556, 29915, 29879, 23779, 29889, 512, 1234, 304, 670, 26565, 1044, 29892, 599, 278, 10801, 472, 278, 1899, 310, 278, 16728, 3186, 892, 2000, 373, 29892, 3704, 278, 27227, 2133, 310, 13973, 29892, 310, 278, 3965, 29892, 310, 278, 7155, 29892, 310, 1436, 749, 29892, 322, 310, 6668, 1486, 15115, 29889, 21945, 13, 29902, 884, 6907, 5183, 16025, 9865, 9571, 11409, 275, 29892, 3971, 491, 6936, 2921, 774, 7586, 297, 29871, 29896, 29929, 29941, 29906, 29892, 607, 18568, 3086, 10307, 391, 1957, 3002, 297, 7621, 9493, 29889, 2266, 526, 777, 429, 2265, 16485, 393, 2317, 714, 304, 592, 29901, 3750, 4683, 1334, 10307, 2879, 29973, 13, 4806, 526, 5264, 2879, 1363, 591, 1074, 297, 5264, 1608, 29892, 393, 338, 278, 9833, 310, 599, 18363, 29892, 278, 871, 8825, 304, 7344, 1749, 1153, 1455, 20328, 322, 304, 1072, 475, 1749, 8604, 16082, 322, 23011, 1749, 5332, 2106, 29889, 13, 6295, 1455, 1608, 338, 278, 22542, 310, 7866, 362, 363, 278, 1985, 770, 29889, 739, 2504, 4769, 278, 14451, 310, 278, 11582, 770, 322, 967, 11039, 362, 297, 278, 8604, 2894, 1608, 310, 1749, 17852, 1049, 29892, 322, 338, 297, 1062, 2200, 2197, 3216, 304, 16679, 278, 2198, 8370, 1201, 322, 1072, 17225, 5332, 16082, 29889, 10307, 1608, 29892, 5480, 29892, 338, 451, 13586, 263, 4383, 310, 278, 4575, 1253, 287, 770, 29892, 541, 263, 4383, 363, 14332, 29892, 363, 3889, 292, 278, 5332, 2305, 515, 8370, 1201, 338, 278, 7306, 310, 24952, 8898, 29889, 21945, 13, 11008, 263, 5244, 414, 29915, 9173, 29973, 13, 5531, 338, 451, 767, 14380, 29915, 29879, 3151, 344, 29892, 541, 670, 17065, 292, 29889, 319, 767, 7415, 263, 767, 1549, 10212, 29889, 739, 11858, 1078, 1075, 29892, 3732 ]

1,332,826

1,024

CommonCrawl

6

2

him great and aware, raises him above all other creatures. It is in the deepest sense creative, productive, and culture-producing. Without labor, no food. Without food, no life. The idea that the dirtier one's hands get, the more degrading the work, is a Jewish, not a German, idea. [...] We call ourselves a workers' party because we want to rescue the word work from its current definition and give it back its original meaning. Anyone who creates value is a creator, that is, a worker. We refuse to distinguish kinds of work. Our only standard is whether the work serves the whole, or at least does not harm it, or if it is harmful. Work is service. If it works against the general welfare, then it is treason against the fatherland. [...] Why Do We Oppose the Jews? We oppose the Jews because we are defending the freedom of the German people. The Jew is the cause and beneficiary of our slavery. He has misused the social misery of the broad masses to deepen the dreadful split between the right and left of our people, to divide Germany into two halves thereby concealing the true reason for the loss of the Great War and falsifying the nature of the revolution. The Jew has no interest in solving the German question. He cannot have such an interest. He depends on it remaining unsolved. If the German people formed a united community and won back its freedom, there would be no place any longer for the Jew. His hand is strongest when a people lives in domestic and international slavery, not when it is free, industrious, self-aware and determined. The Jew caused our problems, and lives from them. That is why we oppose the Jew as nationalists and as socialists. He has ruined our race, corrupted our morals, hollowed out our customs and broken our strength. We owe it to him that we today are the Pariah of the world. He was the leper among as long as we were German. When we forgot our German nature, he triumphed over us and our future. The Jew is the plastic demon of decomposition. Where he finds filth and decay, he surfaces and begins his butcher's work among the nations. He hides behind a mask and presents himself as a friend to his victims, and before they know it he has broken their neck. The Jew is uncreative. He produces nothing, he only haggles with products. With rags, clothing, pictures, jewels, grain, stocks, cures, peoples and states. He has somehow stolen everything he deals in. When he attacks a state he is a revolutionary. As soon as he holds power, he preaches peace and order so that he can devour his conquests in comfort. What does anti-Semitism have to do with socialism? I would put the question this way: What does the Jew have to do with socialism? Socialism has to do with labor. When did one ever see him working instead of plundering, stealing and living from the sweat of others? As socialists we are opponents of the Jews because we see in the Hebrews the incarnation of capitalism, of the misuse of the nation's goods. What does anti-Semitism have to do with nationalism? I would put the question this way: What does the Jew have to do with nationalism? Nationalism has to do with blood and race. The Jew is the enemy and destroyer of the purity of blood, the conscious destroyer of our race. As nationalists we oppose the Jews because we see the Hebrews as the eternal enemy of our national honor and of our national freedom. But the Jew, after all, is also a human being. Certainly, none of us doubts that. We only doubt that he is a decent human being. He does not get along with us. He lives by other laws than we do. The fact that he is a human being is not sufficient reason for us to allow him to subject us in inhumane ways. He may be a human being — but what kind of a human being is he! If someone slaps your mother in the face, do you say: "Thank you! He is after all a human being!" That is not a human being, it is a monster. Yet how much worse has the Jew done to our mother Germany, and is still doing today! [...] Finally, consider Adolf Hitler's political testament he dictated shortly before he committed suicide: More than thirty years have passed since 1914 when I made my modest contribution as a volunteer in the

0.898938

0.261143

0.082803

1.008416

[ 1.1975268264054022, 0.6003483393619427 ]

[ 0.25577107327840304, 0.26651484476626136 ]

[ 0.323745664342544, -0.15814013048046716 ]

[ 1.0136190241696847, 1.003213543096673 ]

1,024

[ 512, 512 ]

[ 1075, 2107, 322, 9543, 29892, 1153, 4637, 1075, 2038, 599, 916, 907, 3698, 29889, 739, 338, 297, 278, 6483, 342, 4060, 907, 1230, 29892, 3234, 573, 29892, 322, 9257, 29899, 5498, 3277, 29889, 13932, 10212, 29892, 694, 9687, 29889, 13932, 9687, 29892, 694, 2834, 29889, 13, 1576, 2969, 393, 278, 270, 2728, 631, 697, 29915, 29879, 6567, 679, 29892, 278, 901, 316, 5105, 292, 278, 664, 29892, 338, 263, 16728, 29892, 451, 263, 5332, 29892, 2969, 29889, 21945, 13, 4806, 1246, 20278, 263, 17162, 29915, 6263, 1363, 591, 864, 304, 26429, 278, 1734, 664, 515, 967, 1857, 5023, 322, 2367, 372, 1250, 967, 2441, 6593, 29889, 26407, 1058, 10017, 995, 338, 263, 907, 1061, 29892, 393, 338, 29892, 263, 15645, 29889, 1334, 26506, 304, 20820, 17690, 310, 664, 29889, 8680, 871, 3918, 338, 3692, 278, 664, 19700, 278, 3353, 29892, 470, 472, 3203, 947, 451, 10311, 372, 29892, 470, 565, 372, 338, 10311, 1319, 29889, 5244, 338, 2669, 29889, 960, 372, 1736, 2750, 278, 2498, 281, 761, 598, 29892, 769, 372, 338, 2578, 1658, 2750, 278, 4783, 1049, 29889, 21945, 13, 11008, 1938, 1334, 438, 407, 852, 278, 22057, 29973, 13, 4806, 4575, 852, 278, 22057, 1363, 591, 526, 822, 2548, 278, 16082, 310, 278, 5332, 2305, 29889, 450, 9576, 338, 278, 4556, 322, 7795, 1654, 653, 310, 1749, 8370, 1201, 29889, 940, 756, 3984, 3880, 278, 5264, 3984, 708, 310, 278, 7300, 23063, 304, 6483, 264, 278, 21005, 1319, 6219, 1546, 278, 1492, 322, 2175, 310, 1749, 2305, 29892, 304, 16429, 9556, 964, 1023, 8870, 1960, 27999, 10628, 12818, 278, 1565, 2769, 363, 278, 6410, 310, 278, 7027, 3362, 322, 285, 1338, 9215, 278, 5469, 310, 278, 19479, 29889, 13, 1576, 9576, 756, 694, 4066, 297, 17069, 278, 5332, 1139, 29889, 940, 2609, 505, 1316, 385, 4066, 29889, 940, 7111, 373, 372, 9886, 443, 2929, 1490, 29889, 960, 278, 5332, 2305, 8429, 263, 443, 1573, 7881, 322, 2113, 1250, 967, 16082, 29892, 727, 723, 367, 694, 2058, 738, 5520, 363, 278, 9576, 29889, 3600, 1361, 338, 4549, 342, 746, 263, 2305, 12080, 297, 21849, 322, 6121, 8370, 1201, 29892, 451, 746, 372, 338, 3889, 29892, 21136, 681, 29892, 1583, 29899, 28327, 322, 10087, 29889, 450, 9576, 8581, 1749, 4828, 29892, 322, 12080, 515, 963, 29889, 13, 7058, 338, 2020, 591, 4575, 852, 278, 9576, 408, 4797, 2879, 322, 408, 5264, 2879, 29889, 940, 756, 5796, 1312, 1749, 8175, 29892, 1034, 14214, 1749, 3036, 1338, 29892, 298, 2952, 287, 714, 1749, 2888, 29879, 322, 9391, 1749, 9324, 29889, 1334, 288, 705, 372, 304, 1075, 393, 591, 9826, 526, 278, 1459, 21071, 310, 278, 3186, 29889, 940, 471, 278, 454, 546, 4249, 408, 1472, 408, 591, 892, 5332, 29889, 1932, 591, 9640, 1749, 5332, 5469, 29892, 540, 24124, 287, 975, 502, 322, 1749, 5434, 29889, 13, 1576, 9576, 338, 278, 715, 6288, 8033, 310, 26227, 29889, 6804, 540, 14061, 977, 386, 322, 20228, 29892, 540, 28001, 322, 16410, 670, 541, 4630, 29915, 29879, 664, 4249, 278, 19079, 29889, 940, 298, 2247, 5742, 263, 11105, 322, 22981, 3654, 408, 263, 5121, 304, 670, 6879, 9893, 29892, 322, 1434, 896, 1073, 372, 540, 756, 9391, 1009, 18873, 29889, 13, 1576, 9576, 338, 443, 1037, 1230, 29889, 940, 13880, 3078, 29892, 540, 871, 298, 16170, 793, 411, 9316, 29889, 2973, 1153, 3174, 29892, 1067, 6046, 29892, 14956, 29892, 432, 809, 1379, 29892, 2646, 262, 29892, 10961, 29879, 29892, 274, 1973, 29892, 1236, 459, 793, 322, 5922, 29889, 940, 756, 10431, 380, 18975, 4129, 540, 316, 1338, 297, 29889, 1932, 540, 16661, 263, 2106, 540, 338, 263, 19479, 653, 29889, 1094, 4720, 408, 540, 8640, 3081, 29892, 540, 758, 14520, 10776, 322, 1797, 577, 393, 540, 508, 2906, 473, 670, 378, 1119, 29879, 297, 13016, 29889, 13, 5618, 947, 9418, 29899, 29903, 21976, 1608, 505, 304, 437, 411, 5264, 1608, 29973, 306, 723, 1925, 278, 1139, 445, 982, 29901, 1724, 947, 278, 9576, 505, 304, 437, 411, 5264, 1608, 29973, 10307, 1608, 756, 304, 437, 411, 10212, 29889, 1932, 1258, 697, 3926, 1074, 1075, 1985, 2012, 310, 715, 870, 3241, 29892, 1886, 12818, 322, 8471, 515, 278, 7901, 271, 310, 4045, 29973, 1094, 5264, 2879, 591, 526, 23995, 1237, 310, 278, 22057, 1363, 591, 1074, 297, 278, 18472, 3973, 29879, 278, 5528, 2753, 362, 310, 7483, 1608, 29892, 310, 278, 3984, 1509, 310, 278, 5233, 29915, 29879, 22535, 29889, 13, 5618, 947, 9418, 29899, 29903, 21976, 1608, 505, 304, 437, 411, 4797, 1608, 29973, 306, 723, 1925, 278, 1139, 445, 982, 29901, 1724, 947, 278, 9576, 505, 304, 437, 411, 4797, 1608, 29973, 3086, 1608, 756, 304, 437, 411, 10416, 322, 8175, 29889, 450, 9576, 338, 278, 11103, 322, 8174, 261, 310, 278, 3708, 537, 310, 10416, 29892, 278, 19861, 8174, 261, 310, 1749, 8175, 29889, 1094, 4797, 2879, 591, 4575, 852, 278, 22057, 1363, 591, 1074, 278, 18472, 3973, 29879, 408, 278, 634, 17196, 11103, 310, 1749, 4797, 10657, 322, 310, 1749, 4797, 16082, 29889, 13, 6246, 278, 9576, 29892, 1156, 599, 29892, 338, 884, 263, 5199, 1641, 29889, 315, 13946, 368, 29892, 5642, 310, 502, 27455, 1372, 393, 29889, 1334, 871, 7404, 393, 540, 338, 263, 27189, 5199, 1641, 29889, 940, 947, 451, 679, 3412, 411, 502, 29889, 940, 12080, 491, 916, 14243, 1135, 591, 437, 29889, 450, 2114, 393, 540, 338, 263, 5199, 1641, 338, 451, 8002, 2769, 363, 502, 304, 2758, 1075, 304, 4967, 502, 297, 297, 16063, 1662, 5837, 29889, 940, 1122, 367, 263, 5199, 1641, 813, 541, 825, 2924, 310, 263, 5199, 1641, 338, 540, 29991, 960, 4856, 8370, 567, 596, 5637, 297, 278, 3700, 29892, 437, 366, 1827, 29901, 376, 25271, 366, 29991, 940, 338, 1156, 599, 263, 5199, 1641, 3850, 2193, 338, 451, 263, 5199, 1641, 29892, 372, 338, 263, 1601, 2475, 29889, 15175, 920, 1568, 15029, 756, 278, 9576, 2309, 304, 1749, 5637, 9556, 29892, 322, 338, 1603, 2599, 9826, 29991, 21945, 13, 12881, 635, 29892, 2050, 21834, 23151, 29915, 29879, 8604, 1243, 1166, 540, 9657, 630, 21734, 1434, 540, 19355, 23921, 680, 29901, 13, 20761, 1135, 17058, 2440, 505, 4502, 1951, 29871, 29896, 29929, 29896, 29946, 746, 306, 1754, 590, 878, 342, 11896, 408, 263, 27886, 261, 297, 278 ]

1,332,826

2,048

CommonCrawl

6

2

First World War, which was forced upon the Reich. In these three decades love and loyalty to my people have guided all my thoughts, actions and my life. They gave me the strength to make the most difficult decisions ever to confront mortal man. In these three decades I have spent my strength and my health. It is untrue that I or anyone else in Germany wanted war in 1939. It was wanted and provoked solely by international statesmen either of Jewish origin or working for Jewish interests. I have made too many offers for the limitation and control of armaments, which posterity will not be cowardly enough always to disregard, for responsibility for the outbreak of this war to be placed on me. Nor have I ever wished that, after the appalling First World War, there would ever be a second against either England or America. Centuries will go by, but from the ruins of our towns and monuments the hatred of those ultimately responsible will always grow anew against the people whom we have to thank for all this: international Jewry and its henchmen. [...] Hitler and the National Socialist movement in Germany, from what I can tell after honestly assessing the situation, were leaders and statesmen in the truest sense. They were true patriots that cared deeply about their country and their people, unlike the puppets, sell-outs and traitors in the West today that do nothing but lie to the people they allegedly represent, all the while serving a foreign criminal cabal. The National Socialists were honest with their fellow Germans, and treated them with respect by and large, certainly compared to governments in the West today. Is it any wonder then that Hitler specifically, and National Socialist Germany generally, are so demonized, slandered, and hated by the Jews, and thus much of Western society due to their control over the mass media and educational system? Hitler and the National Socialists not only spoke openly and honestly about important subjects, clearly identifying the enemy of all humanity – international Jewry – they made serious moves against this destructive, parasitic network of criminals that had wrecked their country and sought to destroy their people. Hitler and National Socialism were the anti-thesis to Jewish Communism and Jewish plutocratic capitalism, and it's time we recognize this fact. « Last Edit: August 17, 2012, 09:08:24 PM by sushigirl » "At any given moment there is an orthodoxy, a body of ideas which it is assumed all right-thinking people will accept without question. It is not exactly forbidden to state this or that or the other, but it is "not done". ...Anyone who challenges the prevailing orthodoxy finds himself silenced with. - * Rethinking Hitler & National Socialism I don't know if this is the appropriate place to post this, but concerning Hitler, my favorite quote from him about the jews is this one, concerning their method of argument (I used to post this a few times back in the Nolajbs days): The more I argued with them, the better I came to know their dialectic. First they counted on the stupidity of their adversary, and then, when there was no other way out, they themselves simply played stupid. If all this didn't help, they pretended not to understand, or, if challenged, they changed the subject in a hurry, quoted platitudes which, if you accepted them, they immediately related to entirely different matters, and then, if again attacked, gave ground and pretended not to know exactly what you were talking about. Whenever you tried to attack one of these apostles, your hand closed on a jelly-like slime which divided up and poured through your fingers, but in the next moment collected again. But if you really struck one of these fellows so telling a blow that, observed by the audience, he couldn't help but agree, and if you believed that this had taken you at least one step forward, your amazement was great the next day. The Jew had not the slightest recollection of the day before, he rattled off his same old nonsense as though nothing at all had happened, and, if indignantly challenged, affected amazement; he couldn't remember a thing, except that he had proved the correctness of his assertions the previous day. Sometimes I stood there thunderstruck. I didn't know what to be more amazed at: the agility of their tongues or their virtuosity at lying. Gradually I began to hate them. http://www.hitler.org/writings/Mein_

0.504129

-0.033415

-0.45488

0.428311

[ 1.0057722663455757, 0.002485014603983752 ]

[ 0.3846963311327028, -0.4515272163389358 ]

[ -0.1784300586835413, -0.7313306022173119 ]

[ 0.8991587323665579, -0.042537304740986236 ]

1,024

[ 512, 512 ]

[ 3824, 2787, 3362, 29892, 607, 471, 11826, 2501, 278, 9320, 29889, 13, 797, 1438, 2211, 1602, 3076, 5360, 322, 28108, 1017, 304, 590, 2305, 505, 1410, 2618, 599, 590, 13133, 29892, 8820, 322, 590, 2834, 29889, 2688, 4846, 592, 278, 9324, 304, 1207, 278, 1556, 5189, 1602, 12112, 3926, 304, 21751, 5758, 284, 767, 29889, 512, 1438, 2211, 1602, 3076, 306, 505, 10398, 590, 9324, 322, 590, 9045, 29889, 13, 3112, 338, 443, 3009, 393, 306, 470, 5019, 1683, 297, 9556, 5131, 1370, 297, 29871, 29896, 29929, 29941, 29929, 29889, 739, 471, 5131, 322, 1326, 12504, 14419, 368, 491, 6121, 5922, 1527, 2845, 310, 16728, 3978, 470, 1985, 363, 16728, 20017, 29889, 306, 505, 1754, 2086, 1784, 16688, 363, 278, 29485, 322, 2761, 310, 5075, 20060, 29892, 607, 10368, 537, 674, 451, 367, 21282, 538, 368, 3307, 2337, 304, 766, 1727, 538, 29892, 363, 23134, 363, 278, 714, 8690, 310, 445, 1370, 304, 367, 7180, 373, 592, 29889, 4186, 505, 306, 3926, 20024, 393, 29892, 1156, 278, 623, 27855, 3824, 2787, 3362, 29892, 727, 723, 3926, 367, 263, 1473, 2750, 2845, 5408, 470, 6813, 29889, 2895, 14886, 674, 748, 491, 29892, 541, 515, 278, 5796, 1144, 310, 1749, 20248, 322, 22586, 278, 3056, 1127, 310, 1906, 18973, 14040, 674, 2337, 6548, 385, 809, 2750, 278, 2305, 6029, 591, 505, 304, 6452, 363, 599, 445, 29901, 6121, 9576, 719, 322, 967, 19061, 305, 1527, 29889, 21945, 13, 29950, 277, 1358, 322, 278, 3086, 10307, 391, 10298, 297, 9556, 29892, 515, 825, 306, 508, 2649, 1156, 15993, 368, 24809, 292, 278, 6434, 29892, 892, 20251, 322, 5922, 1527, 297, 278, 534, 16139, 4060, 29889, 2688, 892, 1565, 16967, 1862, 393, 274, 1965, 24344, 1048, 1009, 4234, 322, 1009, 2305, 29892, 25531, 278, 2653, 27421, 29892, 19417, 29899, 17718, 322, 1020, 17259, 297, 278, 3122, 9826, 393, 437, 3078, 541, 3804, 304, 278, 2305, 896, 16831, 23244, 2755, 29892, 599, 278, 1550, 16330, 263, 9117, 22161, 7776, 284, 29889, 450, 3086, 10307, 2879, 892, 15993, 411, 1009, 10404, 7287, 550, 29892, 322, 14914, 963, 411, 3390, 491, 322, 2919, 29892, 8959, 9401, 304, 4095, 1860, 297, 278, 3122, 9826, 29889, 13, 3624, 372, 738, 4997, 769, 393, 23151, 10816, 29892, 322, 3086, 10307, 391, 9556, 6892, 29892, 526, 577, 8033, 1891, 29892, 269, 1049, 14561, 29892, 322, 298, 630, 491, 278, 22057, 29892, 322, 4550, 1568, 310, 10504, 12459, 2861, 304, 1009, 2761, 975, 278, 4158, 5745, 322, 28976, 1788, 29973, 23151, 322, 278, 3086, 10307, 2879, 451, 871, 12707, 1722, 368, 322, 15993, 368, 1048, 4100, 17800, 29892, 9436, 2893, 9215, 278, 11103, 310, 599, 5199, 537, 785, 6121, 9576, 719, 785, 896, 1754, 10676, 16229, 2750, 445, 17912, 573, 29892, 610, 294, 277, 293, 3564, 310, 15116, 19016, 393, 750, 281, 18217, 287, 1009, 4234, 322, 18365, 304, 8174, 1009, 2305, 29889, 23151, 322, 3086, 10307, 1608, 892, 278, 9418, 29899, 26533, 304, 16728, 20473, 1608, 322, 16728, 28185, 8415, 2454, 7483, 1608, 29892, 322, 372, 29915, 29879, 931, 591, 18720, 445, 2114, 29889, 13, 30009, 9208, 7641, 29901, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29929, 29901, 29900, 29947, 29901, 29906, 29946, 11278, 491, 269, 1878, 335, 5168, 2047, 13, 29908, 4178, 738, 2183, 3256, 727, 338, 385, 14219, 17324, 29891, 29892, 263, 3573, 310, 7014, 607, 372, 338, 12023, 599, 1492, 29899, 386, 18159, 2305, 674, 3544, 1728, 1139, 29889, 739, 338, 451, 3721, 19752, 4215, 304, 2106, 445, 470, 393, 470, 278, 916, 29892, 541, 372, 338, 376, 1333, 2309, 1642, 13, 856, 10773, 650, 1058, 18066, 267, 278, 12379, 737, 292, 14219, 17324, 29891, 14061, 3654, 4047, 9223, 411, 29889, 13, 29899, 334, 390, 621, 18159, 23151, 669, 3086, 10307, 1608, 13, 29902, 1016, 29915, 29873, 1073, 565, 445, 338, 278, 8210, 2058, 304, 1400, 445, 29892, 541, 19813, 23151, 29892, 590, 25448, 14978, 515, 1075, 1048, 278, 432, 809, 29879, 338, 445, 697, 29892, 19813, 1009, 1158, 310, 2980, 313, 29902, 1304, 304, 1400, 445, 263, 2846, 3064, 1250, 297, 278, 405, 324, 1175, 5824, 3841, 1125, 13, 1576, 901, 306, 28705, 411, 963, 29892, 278, 2253, 306, 2996, 304, 1073, 1009, 23725, 293, 29889, 3824, 896, 29115, 373, 278, 20239, 537, 310, 1009, 19901, 653, 29892, 322, 769, 29892, 746, 727, 471, 694, 916, 982, 714, 29892, 896, 6053, 3763, 5318, 20239, 29889, 960, 599, 445, 3282, 29915, 29873, 1371, 29892, 896, 14794, 2760, 451, 304, 2274, 29892, 470, 29892, 565, 18066, 287, 29892, 896, 3939, 278, 4967, 297, 263, 12166, 719, 29892, 23153, 18870, 20816, 607, 29892, 565, 366, 9259, 963, 29892, 896, 7389, 4475, 304, 9186, 1422, 13750, 29892, 322, 769, 29892, 565, 1449, 22630, 29892, 4846, 5962, 322, 14794, 2760, 451, 304, 1073, 3721, 825, 366, 892, 9963, 1048, 29889, 1932, 1310, 366, 1898, 304, 5337, 697, 310, 1438, 18115, 793, 29892, 596, 1361, 5764, 373, 263, 12736, 368, 29899, 4561, 2243, 603, 607, 13931, 701, 322, 7446, 1127, 1549, 596, 23915, 29892, 541, 297, 278, 2446, 3256, 16531, 1449, 29889, 1205, 565, 366, 2289, 15469, 697, 310, 1438, 8379, 1242, 577, 14509, 263, 13031, 393, 29892, 8900, 491, 278, 20026, 29892, 540, 8496, 29915, 29873, 1371, 541, 8661, 29892, 322, 565, 366, 13112, 393, 445, 750, 4586, 366, 472, 3203, 697, 4331, 6375, 29892, 596, 21863, 882, 471, 2107, 278, 2446, 2462, 29889, 450, 9576, 750, 451, 278, 7248, 342, 337, 10855, 310, 278, 2462, 1434, 29892, 540, 364, 1131, 839, 1283, 670, 1021, 2030, 302, 787, 1947, 408, 2466, 3078, 472, 599, 750, 9559, 29892, 322, 29892, 565, 1399, 647, 10835, 18066, 287, 29892, 15201, 21863, 882, 29936, 540, 8496, 29915, 29873, 6456, 263, 2655, 29892, 5174, 393, 540, 750, 11827, 278, 1959, 2264, 310, 670, 4974, 1080, 278, 3517, 2462, 29889, 13, 29903, 14618, 306, 8389, 727, 266, 5062, 10582, 384, 29889, 13, 29902, 3282, 29915, 29873, 1073, 825, 304, 367, 901, 21863, 287, 472, 29901, 278, 946, 1793, 310, 1009, 21861, 1041, 470, 1009, 4610, 29884, 359, 537, 472, 19214, 29889, 13, 25584, 1474, 306, 4689, 304, 26277, 963, 29889, 13, 1124, 597, 1636, 29889, 27342, 1358, 29889, 990, 29914, 8231, 886, 29914, 6816, 262, 29918 ]

1,332,826

3,072

CommonCrawl

8

11

Kampf/mkv1ch02.html All that said, Hitler really started to lose it mentally some time after America got involved in WWII. I don't know if it was the speed, the juice (steroids) he was shooting, and/or some ingrained mental illness. Not to say he wasn't brilliant, just crazy in his later life. "Divert, distort, denigrate, disrupt or destroy any discussion of the corruption of American liberty by the organized lobby of a foreign power." ~ WindRiverShoshoni Quote from: dominique on August 17, 2012, 08:20:28 PM Just to be fair, the realization that the USA had decided to enter the war against Germany had to be extremely unsettling. Insane - absolutely NOT - just deeply unsettled. Their war machinery was just too much, too overwhelming. More thoughts about Adolf Hitler and National Socialism I'd like to express a few more thoughts to follow up the post I wrote a couple weeks ago, Rethinking Adolf Hitler and National Socialism. First, Hitler and the NSDAP were not, I repeat, were not funded by Jews. They were not "Rothschild agents" or "puppets of the bankers" or "stooges for the Jews". They were diametrically opposed to the Jewish supremacist goal of a "New World Order", which is essentially Jewish domination and subjugation of the entire globe, a Jewish Utopia so to speak. I linked this article by Veronica Clark in the last post, which explains in great detail the rise of the NSDAP in Germany, dispelling all of these myths about Hitler being funded by Jews, or the Rothschilds, or the Illuminati, or the bankers, ect. Sit down and read it if you haven't yet. I'm also currently reading Heiki B. Gortemaker's Eva Braun: Life with Hitler, which succinctly summarizes the rise of the NSDAP in just a few pages. She discusses the central importance of the Munich beer halls as gathering places and recruitment centers (beer halls have a long history as political gathering places in Germany) of the NSDAP, the increase in popularity of the NSDAP following the economic crash of 1929, and Hitler's efforts to unite all segments of German society - industrialists, aristocrats, soldiers, civil servants, farmers, workers, teachers, students, mothers, fathers, children - under the banner of National Socialism. Just to further discredit this idea that Hitler and the NSDAP were funded by "the Jews", consider the following excerpt of Michael Collins Piper's must read book, The New Babylon: Those Who Reign Supreme - A Panoramic Overview of the Historical, Religious and Economic Origins of the New World Order: There is also the legend that "The Jewish bankers" or "The Zionist bankers" (used often interchangeably) financed Hitler. Not true. James Pool, in his authortative work, Who Financed Hitler?, demonstrates quite to the contrary. In one instance, a Jewish financier in Germany did give money to the Nazi Party–prior to the rise of Adolf Hitler–but those funds were designed to help Hitler's intra-party opposition to stop Hitler. But despite this fact, some "patriots" still say that "The Jews Backed Hitler." Many of those who worship at the altar of this nonsense cite a flagrantly-fraudulent document of shadowy origins entitled Hitler's Secret Bankers, ostensibly written by one "Sidney Warburg," one of those "Jewish bankers." But this document, as we've said, is a fraud. The late Dr. Anthony Sutton's Wall Street and the Rise of Hitler has promoted this theory, based in part on the Warburg travesty and has given further institutionalization to this mythology–truth be damned. American banks and corporations did work with the Hitler regime, usually a continuation of previous financial arrangements going back decades, but this was not part of any grand conspiracy to bring Hitler to power. The claim that the Bush family was integral to the rise of Hitler is another myth. Kevin Phillips–no admirer of the Bush dynasty–examines the actual circumstances surrounding the Bush-Hitler scenario in his book, American Dynasty: Aristocracy,

-0.087229

0.752671

-0.418105

0.554477

[ -0.6159234415889565, 0.4414659895980865 ]

[ 0.09282387237921866, 1.4125171368044813 ]

[ -0.9316936432226692, 0.09548397205795975 ]

[ -0.2168291127139295, 1.3257834563600308 ]

1,024

[ 512, 512 ]

[ 29968, 16817, 29914, 11256, 29894, 29896, 305, 29900, 29906, 29889, 1420, 13, 3596, 393, 1497, 29892, 23151, 2289, 4687, 304, 14074, 372, 6042, 635, 777, 931, 1156, 6813, 2355, 9701, 297, 399, 29956, 2687, 29889, 306, 1016, 29915, 29873, 1073, 565, 372, 471, 278, 6210, 29892, 278, 3623, 625, 313, 303, 1489, 4841, 29897, 540, 471, 27904, 29892, 322, 29914, 272, 777, 2348, 22042, 19119, 4486, 2264, 29889, 2216, 304, 1827, 540, 9007, 29915, 29873, 27592, 29892, 925, 12220, 1537, 297, 670, 2678, 2834, 29889, 13, 29908, 12130, 1765, 29892, 1320, 441, 29892, 972, 4481, 403, 29892, 766, 6685, 470, 8174, 738, 10679, 310, 278, 1034, 18953, 310, 3082, 24169, 491, 278, 19098, 658, 1327, 29891, 310, 263, 9117, 3081, 1213, 3695, 17311, 29934, 2147, 2713, 10578, 5271, 13, 2182, 866, 515, 29901, 8022, 1387, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29947, 29901, 29906, 29900, 29901, 29906, 29947, 11278, 13, 14084, 304, 367, 6534, 29892, 278, 1855, 2133, 393, 278, 8278, 750, 8459, 304, 3896, 278, 1370, 2750, 9556, 750, 304, 367, 14154, 443, 9915, 1847, 29889, 13377, 1662, 448, 13312, 6058, 448, 925, 24344, 443, 9915, 839, 29889, 11275, 1370, 7672, 262, 708, 471, 925, 2086, 1568, 29892, 2086, 975, 1332, 295, 4056, 29889, 13, 20761, 13133, 1048, 21834, 23151, 322, 3086, 10307, 1608, 13, 29902, 29915, 29881, 763, 304, 4653, 263, 2846, 901, 13133, 304, 1101, 701, 278, 1400, 306, 5456, 263, 7303, 11405, 8020, 29892, 390, 621, 18159, 21834, 23151, 322, 3086, 10307, 1608, 29889, 13, 6730, 29892, 23151, 322, 278, 3865, 29928, 3301, 892, 451, 29892, 306, 12312, 29892, 892, 451, 5220, 287, 491, 22057, 29889, 2688, 892, 451, 376, 29934, 720, 816, 789, 19518, 29908, 470, 376, 3746, 27421, 310, 278, 9124, 414, 29908, 470, 376, 7864, 468, 267, 363, 278, 22057, 1642, 2688, 892, 11502, 18184, 1711, 15869, 304, 278, 16728, 22747, 8628, 391, 7306, 310, 263, 376, 4373, 2787, 8170, 613, 607, 338, 13674, 16728, 2432, 3381, 322, 1014, 29926, 688, 362, 310, 278, 4152, 15482, 915, 29892, 263, 16728, 501, 3332, 423, 577, 304, 7726, 29889, 13, 29902, 9024, 445, 4274, 491, 1798, 26082, 17129, 297, 278, 1833, 1400, 29892, 607, 18568, 297, 2107, 9493, 278, 14451, 310, 278, 3865, 29928, 3301, 297, 9556, 29892, 12272, 7807, 599, 310, 1438, 22082, 29879, 1048, 23151, 1641, 5220, 287, 491, 22057, 29892, 470, 278, 21790, 816, 789, 29879, 29892, 470, 278, 8408, 9735, 2219, 29892, 470, 278, 9124, 414, 29892, 321, 312, 29889, 21988, 1623, 322, 1303, 372, 565, 366, 7359, 29915, 29873, 3447, 29889, 306, 29915, 29885, 884, 5279, 5183, 940, 10058, 350, 29889, 402, 441, 331, 5790, 29915, 29879, 27040, 23514, 29901, 4634, 411, 23151, 29892, 607, 8348, 5562, 368, 19138, 7093, 278, 14451, 310, 278, 3865, 29928, 3301, 297, 925, 263, 2846, 6515, 29889, 2296, 5353, 267, 278, 6555, 13500, 310, 278, 13564, 436, 367, 261, 298, 4293, 408, 11705, 292, 7600, 322, 1162, 9216, 358, 1644, 414, 313, 915, 261, 298, 4293, 505, 263, 1472, 4955, 408, 8604, 11705, 292, 7600, 297, 9556, 29897, 310, 278, 3865, 29928, 3301, 29892, 278, 7910, 297, 5972, 537, 310, 278, 3865, 29928, 3301, 1494, 278, 17407, 8095, 310, 29871, 29896, 29929, 29906, 29929, 29892, 322, 23151, 29915, 29879, 14231, 304, 443, 568, 599, 24611, 310, 5332, 12459, 448, 18408, 2879, 29892, 28672, 8415, 1446, 29892, 13936, 29892, 7631, 26202, 29892, 2215, 13269, 29892, 17162, 29892, 27335, 29892, 8041, 29892, 25550, 414, 29892, 285, 19467, 29892, 4344, 448, 1090, 278, 289, 7310, 310, 3086, 10307, 1608, 29889, 13, 14084, 304, 4340, 766, 11944, 277, 445, 2969, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 5220, 287, 491, 376, 1552, 22057, 613, 2050, 278, 1494, 429, 2265, 415, 310, 5765, 26410, 7362, 546, 29915, 29879, 1818, 1303, 3143, 29892, 450, 1570, 14525, 2904, 265, 29901, 16025, 11644, 830, 647, 22569, 448, 319, 6518, 272, 314, 293, 6811, 1493, 310, 278, 20315, 29892, 16221, 2738, 322, 12884, 293, 29766, 1144, 310, 278, 1570, 2787, 8170, 29901, 13, 8439, 338, 884, 278, 15983, 393, 376, 1576, 16728, 9124, 414, 29908, 470, 376, 1576, 796, 291, 391, 9124, 414, 29908, 313, 3880, 4049, 1006, 3167, 2197, 29897, 1436, 8362, 23151, 29889, 2216, 1565, 29889, 5011, 28625, 29892, 297, 670, 4817, 441, 1230, 664, 29892, 11644, 4231, 8362, 23151, 14579, 9004, 1078, 3755, 304, 278, 21138, 29889, 13, 797, 697, 2777, 29892, 263, 16728, 22347, 261, 297, 9556, 1258, 2367, 6909, 304, 278, 11409, 29875, 9173, 29994, 29886, 13479, 304, 278, 14451, 310, 21834, 23151, 29994, 4187, 1906, 29199, 892, 8688, 304, 1371, 23151, 29915, 29879, 938, 336, 29899, 22633, 19626, 304, 5040, 23151, 29889, 1205, 15020, 445, 2114, 29892, 777, 376, 5031, 374, 1862, 29908, 1603, 1827, 393, 376, 1576, 22057, 7437, 287, 23151, 1213, 13, 14804, 310, 1906, 1058, 26320, 472, 278, 5272, 279, 310, 445, 302, 787, 1947, 274, 568, 263, 7353, 29878, 10835, 29899, 20910, 566, 352, 296, 1842, 310, 15504, 29891, 1677, 1144, 23437, 23151, 29915, 29879, 10213, 10253, 414, 29892, 14750, 575, 14981, 3971, 491, 697, 376, 29903, 333, 3801, 3362, 3074, 1699, 697, 310, 1906, 376, 29967, 809, 728, 9124, 414, 1213, 1205, 445, 1842, 29892, 408, 591, 29915, 345, 1497, 29892, 338, 263, 5227, 566, 29889, 13, 1576, 5683, 4942, 29889, 16477, 317, 1851, 29915, 29879, 14406, 7103, 322, 278, 390, 895, 310, 23151, 756, 21201, 445, 6368, 29892, 2729, 297, 760, 373, 278, 3362, 3074, 6427, 14596, 322, 756, 2183, 4340, 12666, 284, 2133, 304, 445, 22082, 3002, 29994, 509, 2806, 367, 5625, 9571, 29889, 13, 14689, 24388, 322, 17266, 800, 1258, 664, 411, 278, 23151, 22384, 29892, 5491, 263, 3133, 362, 310, 3517, 18161, 15196, 4110, 2675, 1250, 1602, 3076, 29892, 541, 445, 471, 451, 760, 310, 738, 4595, 21588, 29875, 10068, 304, 6963, 23151, 304, 3081, 29889, 450, 5995, 393, 278, 24715, 3942, 471, 10160, 304, 278, 14451, 310, 23151, 338, 1790, 22082, 29889, 19323, 21856, 4512, 29994, 1217, 7336, 381, 261, 310, 278, 24715, 22337, 29891, 29994, 735, 314, 1475, 278, 3935, 14209, 18830, 278, 24715, 29899, 29950, 277, 1358, 10483, 297, 670, 3143, 29892, 3082, 360, 15290, 29891, 29901, 25068, 25804, 29892 ]

1,332,826

4,096

CommonCrawl

8

11

Fortune and the Politics of Deceit in the House of Bush and puts the facts in proper perspective. If Hitler and the NSDAP were "Rothschild agents" or "Jewish puppets", why on earth did they do things like this or this or this? Why did they make movies like this or the one shown below if they were in the pocket of the Rothschilds and other Jewish bankers? Why did Hitler perfectly describe the Big Lie technique (Holohoax & 9/11) used by the Jews to advance their "New World Order", deceive and rob Gentiles, and subvert their governments, economy, and culture if he was secretly working for them? But it remained for the Jews, with their unqualified capacity for falsehood, and their fighting comrades, the Marxists, to impute responsibility for the downfall precisely to the man who alone had shown a superhuman will and energy in his effort to prevent the catastrophe which he had foreseen and to save the nation from that hour of complete overthrow and shame. By placing responsibility for the loss of the world war on the shoulders of Ludendorff they took away the weapon of moral right from the only adversary dangerous enough to be likely to succeed in bringing the betrayers of the Fatherland to Justice. All this was inspired by the principle - which is quite true in itself - that in the big lie there is always a certain force of credibility; because the broad masses of a nation are always more easily corrupted in the deeper strata of their emotional nature than consciously or voluntarily; and thus in the primitive simplicity of their minds they more readily fall victims to the big lie than the small lie, since they themselves often tell small lies in little matters but would be ashamed to resort to large-scale falsehoods. It would never come into their heads to fabricate colossal untruths, and they would not believe that others could have the impudence to distort the truth so infamously. Even though the facts which prove this to be so may be brought clearly to their minds, they will still doubt and waver and will continue to think that there may be some other explanation. For the grossly impudent lie always leaves traces behind it, even after it has been nailed down, a fact which is known to all expert liars in this world and to all who conspire together in the art of lying. These people know only too well how to use falsehood for the basest purposes. From time immemorial; however, the Jews have known better than any others how falsehood and calumny can be exploited. Is not their very existence founded on one great lie, namely, that they are a religious community, whereas in reality they are a race? And what a race! One of the greatest thinkers that mankind has produced has branded the Jews for all time with a statement which is profoundly and exactly true. He (Schopenhauer) called the Jew "The Great Master of Lies". Those who do not realize the truth of that statement, or do not wish to believe it, will never be able to lend a hand in helping Truth to prevail. - Adolf Hitler, quote from Mein Kampf (page 184-185) Why did Joseph Goebbels and other NSDAP leaders say things like this if they weren't for real about their convictions? The historic responsibility of world Jewry for the outbreak and widening of this war has been proven so clearly that it does not need to be talked about any further. The Jews wanted war, and now they have it. But the Führer's prophecy of 30 January 1939 to the German Reichstag is also being fulfilled: If international finance Jewry should succeed in plunging the world into war once again, the result will be not the Bolshevization of the world and thereby the victory of the Jews, but rather the destruction of the Jewish race in Europe. We are seeing the fulfillment of the prophecy. The Jews are receiving a penalty that is certainly hard, but more than deserved. World Jewry erred in adding up the forces available to it for this war, and now is gradually experiencing the destructon that it planned for us, and would have carried out without a second thought if it had possessed the ability. It is perishing according its own law: "An eye for an eye, a tooth for a tooth." Every Jew is our enemy in this historic struggle, regardless of whether he vegetates in a Polish ghetto or carries on his parasitic existence in Berlin or Hamburg or blows the trumpets of war in New York or Washington

0.415442

0.350674

-0.520664

1.070849

[ 0.20862116666829722, 0.6222631462259228 ]

[ 0.44557770289723325, 0.25577107327840304 ]

[ -0.43902882404177496, -0.6022993400508873 ]

[ 0.9824025809506501, 1.1592957591918462 ]

1,024

[ 512, 512 ]

[ 7236, 1540, 322, 278, 6934, 1199, 310, 897, 346, 277, 297, 278, 5619, 310, 24715, 322, 15223, 278, 17099, 297, 1571, 18520, 29889, 13, 3644, 23151, 322, 278, 3865, 29928, 3301, 892, 376, 29934, 720, 816, 789, 19518, 29908, 470, 376, 29967, 809, 728, 2653, 27421, 613, 2020, 373, 8437, 1258, 896, 437, 2712, 763, 445, 470, 445, 470, 445, 29973, 13, 11008, 1258, 896, 1207, 2351, 583, 763, 445, 470, 278, 697, 4318, 2400, 565, 896, 892, 297, 278, 24589, 310, 278, 21790, 816, 789, 29879, 322, 916, 16728, 9124, 414, 29973, 13, 11008, 1258, 23151, 7970, 8453, 278, 7997, 7326, 11043, 313, 19984, 1148, 29877, 1165, 669, 29871, 29929, 29914, 29896, 29896, 29897, 1304, 491, 278, 22057, 304, 6564, 1009, 376, 4373, 2787, 8170, 613, 23332, 573, 322, 10832, 20655, 5475, 29892, 322, 1014, 1765, 1009, 4095, 1860, 29892, 26504, 29892, 322, 9257, 565, 540, 471, 7035, 368, 1985, 363, 963, 29973, 13, 6246, 372, 9488, 363, 278, 22057, 29892, 411, 1009, 443, 15380, 2164, 13284, 363, 2089, 6614, 29892, 322, 1009, 17770, 419, 29878, 3076, 29892, 278, 28579, 2879, 29892, 304, 527, 649, 29872, 23134, 363, 278, 1623, 11950, 17503, 304, 278, 767, 1058, 7432, 750, 4318, 263, 2428, 26029, 674, 322, 5864, 297, 670, 7225, 304, 5557, 278, 6635, 579, 1336, 354, 607, 540, 750, 363, 968, 264, 322, 304, 4078, 278, 5233, 515, 393, 7234, 310, 4866, 975, 20539, 322, 28503, 29889, 2648, 24421, 23134, 363, 278, 6410, 310, 278, 3186, 1370, 373, 278, 26671, 310, 8591, 12184, 600, 896, 3614, 3448, 278, 28639, 310, 14731, 1492, 515, 278, 871, 19901, 653, 18215, 3307, 304, 367, 5517, 304, 9269, 297, 20794, 278, 1010, 764, 414, 310, 278, 17852, 1049, 304, 17181, 29889, 2178, 445, 471, 20603, 491, 278, 12502, 448, 607, 338, 3755, 1565, 297, 3528, 448, 393, 297, 278, 4802, 3804, 727, 338, 2337, 263, 3058, 4889, 310, 6625, 4127, 29936, 1363, 278, 7300, 23063, 310, 263, 5233, 526, 2337, 901, 5948, 1034, 14214, 297, 278, 25871, 851, 532, 310, 1009, 23023, 1848, 5469, 1135, 1136, 455, 5794, 470, 27081, 6275, 29936, 322, 4550, 297, 278, 19269, 23205, 310, 1009, 27656, 896, 901, 28520, 6416, 6879, 9893, 304, 278, 4802, 3804, 1135, 278, 2319, 3804, 29892, 1951, 896, 6053, 4049, 2649, 2319, 12185, 297, 2217, 13750, 541, 723, 367, 23723, 2795, 304, 25362, 304, 2919, 29899, 7052, 2089, 6614, 29879, 29889, 739, 723, 2360, 2041, 964, 1009, 15883, 304, 18187, 403, 784, 2209, 284, 443, 509, 2806, 29879, 29892, 322, 896, 723, 451, 4658, 393, 4045, 1033, 505, 278, 2411, 566, 663, 304, 1320, 441, 278, 8760, 577, 3041, 314, 5794, 29889, 7753, 2466, 278, 17099, 607, 6356, 445, 304, 367, 577, 1122, 367, 6296, 9436, 304, 1009, 27656, 29892, 896, 674, 1603, 7404, 322, 11324, 369, 322, 674, 6773, 304, 1348, 393, 727, 1122, 367, 777, 916, 8252, 29889, 1152, 278, 22683, 368, 2411, 10385, 3804, 2337, 11308, 26695, 5742, 372, 29892, 1584, 1156, 372, 756, 1063, 1055, 2356, 1623, 29892, 263, 2114, 607, 338, 2998, 304, 599, 17924, 619, 1503, 297, 445, 3186, 322, 304, 599, 1058, 21588, 533, 4208, 297, 278, 1616, 310, 19214, 29889, 4525, 2305, 1073, 871, 2086, 1532, 920, 304, 671, 2089, 6614, 363, 278, 2362, 342, 11976, 29889, 13, 4591, 931, 5198, 331, 9020, 29936, 3138, 29892, 278, 22057, 505, 2998, 2253, 1135, 738, 4045, 920, 2089, 6614, 322, 1208, 1227, 29891, 508, 367, 16035, 1573, 29889, 1317, 451, 1009, 1407, 10379, 11091, 373, 697, 2107, 3804, 29892, 18451, 29892, 393, 896, 526, 263, 12962, 7881, 29892, 13452, 297, 16832, 896, 526, 263, 8175, 29973, 1126, 825, 263, 8175, 29991, 3118, 310, 278, 14176, 1348, 414, 393, 767, 14380, 756, 7371, 756, 14982, 287, 278, 22057, 363, 599, 931, 411, 263, 3229, 607, 338, 2600, 618, 368, 322, 3721, 1565, 29889, 940, 313, 4504, 3150, 29882, 7547, 29897, 2000, 278, 9576, 376, 1576, 7027, 9082, 310, 365, 583, 1642, 16025, 1058, 437, 451, 16289, 278, 8760, 310, 393, 3229, 29892, 470, 437, 451, 6398, 304, 4658, 372, 29892, 674, 2360, 367, 2221, 304, 301, 355, 263, 1361, 297, 19912, 1605, 2806, 304, 12379, 737, 29889, 13, 29899, 21834, 23151, 29892, 14978, 515, 2191, 262, 476, 16817, 313, 3488, 29871, 29896, 29947, 29946, 29899, 29896, 29947, 29945, 29897, 13, 11008, 1258, 6936, 2921, 27885, 1379, 322, 916, 3865, 29928, 3301, 20251, 1827, 2712, 763, 445, 565, 896, 2949, 264, 29915, 29873, 363, 1855, 1048, 1009, 7602, 919, 1080, 29973, 13, 1576, 22879, 23134, 310, 3186, 9576, 719, 363, 278, 714, 8690, 322, 281, 3615, 292, 310, 445, 1370, 756, 1063, 16413, 577, 9436, 393, 372, 947, 451, 817, 304, 367, 24867, 1048, 738, 4340, 29889, 450, 22057, 5131, 1370, 29892, 322, 1286, 896, 505, 372, 29889, 1205, 278, 383, 4000, 261, 29915, 29879, 3107, 354, 1270, 310, 29871, 29941, 29900, 5490, 29871, 29896, 29929, 29941, 29929, 304, 278, 5332, 9320, 24403, 338, 884, 1641, 6095, 26940, 29901, 960, 6121, 1436, 749, 9576, 719, 881, 9269, 297, 715, 686, 292, 278, 3186, 964, 1370, 2748, 1449, 29892, 278, 1121, 674, 367, 451, 278, 350, 3775, 354, 29894, 2133, 310, 278, 3186, 322, 27999, 278, 15354, 310, 278, 22057, 29892, 541, 3265, 278, 22104, 310, 278, 16728, 8175, 297, 4092, 29889, 13, 4806, 526, 8790, 278, 6095, 5589, 358, 310, 278, 3107, 354, 1270, 29889, 450, 22057, 526, 13442, 263, 27368, 393, 338, 8959, 2898, 29892, 541, 901, 1135, 553, 9841, 29889, 2787, 9576, 719, 604, 1127, 297, 4417, 701, 278, 8249, 3625, 304, 372, 363, 445, 1370, 29892, 322, 1286, 338, 22020, 10623, 3277, 278, 17912, 265, 393, 372, 20458, 363, 502, 29892, 322, 723, 505, 8988, 714, 1728, 263, 1473, 2714, 565, 372, 750, 25622, 278, 11509, 29889, 739, 338, 639, 14424, 5034, 967, 1914, 4307, 29901, 376, 2744, 10977, 363, 385, 10977, 29892, 263, 304, 720, 363, 263, 304, 720, 1213, 13, 26526, 9576, 338, 1749, 11103, 297, 445, 22879, 21117, 29892, 17126, 310, 3692, 540, 18655, 1078, 297, 263, 19919, 24170, 8563, 470, 1559, 2722, 373, 670, 610, 294, 277, 293, 10379, 297, 5115, 470, 14847, 470, 13031, 29879, 278, 534, 3427, 1691, 310, 1370, 297, 1570, 3088, 470, 7660 ]

1,332,826

5,120

CommonCrawl

8

11

. All Jews by virtue of their birth and their race are part of an international conspiracy against National Socialist Germany. They want its defeat and annihilation, and do all in their power to bring it about. That they can do nothing inside the Reich is hardly a sign of their loyalty, but rather of the appropriate measures we took against them. [...] If Hitler and the NSDAP were indeed "puppets of the bankers" or "stooges of the Jews", why on earth were they speaking openly and honestly about the Jews, publicly naming the enemy and exposing his agenda? And Hitler and the NSDAP were not only being honest with their fellow countryman (and world, really) about the Jews and the disgraceful Versailles Treaty, they made serious moves to counteract and redress these problems. Second, Hitler was not "the founder of Israel". This is absurd, and I'll explain why. It was Britain, through the Balfour Declaration, addressed to none other than Lord Rothschild himself, that initially facilitated the establishment of the illegitimate terrorist state of Israel, not Germany. Germany never supported or wanted a Jewish state in Palestine. Hitler and NSDAP policy were primarily concerned with getting the Jews out of Germany (and eventually all of Europe), and did in fact collaborate with Zionist organizations and factions that promoted Jewish emigration to Palestine. They even entered into economic agreements with these organizations to not only facilitate the emigration of Jews from Germany, but also bolster Germans exports. Mark Weber of the Institute for Historical Review lays this out quite clearly in an article titled, Zionism and the Third Reich: [...] German support for Zionism was not unlimited. Government and Party officials were very mindful of the continuing campaign by powerful Jewish communities in the United States, Britain and other countries to mobilize "their" governments and fellow citizens against Germany. As long as world Jewry remained implacably hostile toward National Socialist Germany, and as long as the great majority of Jews around the world showed little eagerness to resettle in the Zionist "promised land," a sovereign Jewish state in Palestine would not really "solve" the international Jewish question. Instead, German officials reasoned, it would immeasurably strengthen this dangerous anti-German campaign. German backing for Zionism was therefore limited to support for a Jewish homeland in Palestine under British control, not a sovereign Jewish state. A Jewish state in Palestine, the Foreign Minister informed diplomats in June 1937, would not be in Germany's interest because it would not be able to absorb all Jews around the world, but would only serve as an additional power base for international Jewry, in much the same way as Moscow served as a base for international Communism. Reflecting something of a shift in official policy, the German press expressed much greater sympathy in 1937 for Palestinian Arab resistance to Zionist ambitions, at a time when tension and conflict between Jews and Arabs in Palestine was sharply increasing. A Foreign Office circular bulletin of June 22, 1937, cautioned that in spite of support for Jewish settlement in Palestine, "it would nevertheless be a mistake to assume that Germany supports the formation of a state structure in Palestine under some form of Jewish control. In view of the anti-German agitation of international Jewry, Germany cannot agree that the formation of a Palestine Jewish state would help the peaceful development of the nations of the world." "The proclamation of a Jewish state or a Jewish-administrated Palestine," warned an internal memorandum by the Jewish affairs section of the SS, "would create for Germany a new enemy, one that would have a deep influence on developments in the Near East." Another SS agency predicted that a Jewish state "would work to bring special minority protection to Jews in every country, therefore giving legal protection to the exploitation activity of world Jewry." In January 1939, Hitler's new Foreign Minister, Joachim von Ribbentrop, likewise warned in another circular bulletin that "Germany must regard the formation of a Jewish state as dangerous" because it "would bring an international increase in power to world Jewry." Hitler and the NSDAP did not advocate for or support a Jewish state in Palestine. In fact, in Mein Kampf Hitler accurately described what a Jewish state would look like should the Gentile world allow it to happen: The Jew's domination in the state seems so assured that now not only can he call himself a Jew again,

0.712662

1.383867

0.281898

1.575515

[ 0.5017317084740319, 0.9235917406056501 ]

[ 1.1188540494696875, 1.6488801095373642 ]

[ 0.06251283872796425, 0.5012825361194428 ]

[ 1.4714601913821923, 1.679569812842423 ]

1,024

[ 512, 512 ]

[ 29889, 2178, 22057, 491, 27935, 310, 1009, 12060, 322, 1009, 8175, 526, 760, 310, 385, 6121, 21588, 29875, 10068, 2750, 3086, 10307, 391, 9556, 29889, 2688, 864, 967, 20653, 322, 6957, 29882, 8634, 29892, 322, 437, 599, 297, 1009, 3081, 304, 6963, 372, 1048, 29889, 2193, 896, 508, 437, 3078, 2768, 278, 9320, 338, 15155, 263, 1804, 310, 1009, 28108, 1017, 29892, 541, 3265, 310, 278, 8210, 15366, 591, 3614, 2750, 963, 29889, 21945, 13, 3644, 23151, 322, 278, 3865, 29928, 3301, 892, 6200, 376, 3746, 27421, 310, 278, 9124, 414, 29908, 470, 376, 7864, 468, 267, 310, 278, 22057, 613, 2020, 373, 8437, 892, 896, 13590, 1722, 368, 322, 15993, 368, 1048, 278, 22057, 29892, 970, 368, 22006, 278, 11103, 322, 14060, 292, 670, 946, 8395, 29973, 1126, 23151, 322, 278, 3865, 29928, 3301, 892, 451, 871, 1641, 15993, 411, 1009, 10404, 2613, 509, 21909, 313, 392, 3186, 29892, 2289, 29897, 1048, 278, 22057, 322, 278, 766, 3874, 346, 1319, 10138, 29874, 7545, 6479, 11156, 29892, 896, 1754, 10676, 16229, 304, 6795, 627, 322, 2654, 1253, 1438, 4828, 29889, 13, 11863, 29892, 23151, 471, 451, 376, 1552, 25331, 310, 11996, 1642, 910, 338, 6425, 18245, 29892, 322, 306, 29915, 645, 5649, 2020, 29889, 13, 3112, 471, 14933, 29892, 1549, 278, 350, 3131, 473, 3826, 23838, 29892, 20976, 304, 5642, 916, 1135, 6171, 21790, 816, 789, 3654, 29892, 393, 12919, 16089, 22731, 278, 25012, 310, 278, 980, 1397, 277, 6490, 15115, 391, 2106, 310, 11996, 29892, 451, 9556, 29889, 9556, 2360, 6969, 470, 5131, 263, 16728, 2106, 297, 22053, 457, 29889, 23151, 322, 3865, 29928, 3301, 8898, 892, 19434, 15041, 411, 2805, 278, 22057, 714, 310, 9556, 313, 392, 10201, 599, 310, 4092, 511, 322, 1258, 297, 2114, 11465, 403, 411, 796, 291, 391, 25700, 322, 2258, 1953, 393, 21201, 16728, 953, 16783, 304, 22053, 457, 29889, 2688, 1584, 7802, 964, 17407, 8571, 4110, 411, 1438, 25700, 304, 451, 871, 16089, 10388, 278, 953, 16783, 310, 22057, 515, 9556, 29892, 541, 884, 15772, 2475, 7287, 550, 29586, 29889, 13, 9802, 1334, 495, 310, 278, 8907, 363, 20315, 13957, 301, 1036, 445, 714, 3755, 9436, 297, 385, 4274, 25278, 29892, 796, 291, 1608, 322, 278, 18008, 9320, 29901, 13, 29961, 17361, 5332, 2304, 363, 796, 291, 1608, 471, 451, 443, 29044, 29889, 10354, 322, 9173, 24921, 892, 1407, 3458, 1319, 310, 278, 3133, 292, 11531, 491, 13988, 16728, 23507, 297, 278, 3303, 3900, 29892, 14933, 322, 916, 10916, 304, 27227, 675, 376, 1552, 381, 29908, 4095, 1860, 322, 10404, 18363, 2750, 9556, 29889, 1094, 1472, 408, 3186, 9576, 719, 9488, 2411, 4620, 2197, 3495, 488, 11183, 3086, 10307, 391, 9556, 29892, 322, 408, 1472, 408, 278, 2107, 13638, 310, 22057, 2820, 278, 3186, 10018, 2217, 321, 351, 824, 404, 304, 620, 1803, 280, 297, 278, 796, 291, 391, 376, 14032, 3368, 2982, 1699, 263, 577, 369, 7577, 16728, 2106, 297, 22053, 457, 723, 451, 2289, 376, 2929, 345, 29908, 278, 6121, 16728, 1139, 29889, 8669, 29892, 5332, 24921, 2769, 287, 29892, 372, 723, 527, 1004, 294, 332, 2197, 9324, 264, 445, 18215, 9418, 29899, 29954, 3504, 11531, 29889, 5332, 27436, 363, 796, 291, 1608, 471, 5480, 9078, 304, 2304, 363, 263, 16728, 3632, 14045, 297, 22053, 457, 1090, 4908, 2761, 29892, 451, 263, 577, 369, 7577, 16728, 2106, 29889, 13, 29909, 16728, 2106, 297, 22053, 457, 29892, 278, 19358, 7668, 23388, 13487, 1446, 297, 5306, 29871, 29896, 29929, 29941, 29955, 29892, 723, 451, 367, 297, 9556, 29915, 29879, 4066, 1363, 372, 723, 451, 367, 2221, 304, 6425, 11831, 599, 22057, 2820, 278, 3186, 29892, 541, 723, 871, 9080, 408, 385, 5684, 3081, 2967, 363, 6121, 9576, 719, 29892, 297, 1568, 278, 1021, 982, 408, 25820, 6766, 408, 263, 2967, 363, 6121, 20473, 1608, 29889, 9897, 781, 292, 1554, 310, 263, 9500, 297, 6221, 8898, 29892, 278, 5332, 3965, 13384, 1568, 7621, 29738, 297, 29871, 29896, 29929, 29941, 29955, 363, 22053, 262, 713, 10387, 17711, 304, 796, 291, 391, 3181, 2187, 29892, 472, 263, 931, 746, 260, 2673, 322, 14529, 1546, 22057, 322, 10387, 29879, 297, 22053, 457, 471, 15301, 368, 10231, 29889, 13, 29909, 19358, 11367, 19308, 24334, 262, 310, 5306, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 29892, 5777, 918, 287, 393, 297, 21100, 310, 2304, 363, 16728, 16493, 297, 22053, 457, 29892, 376, 277, 723, 2360, 16561, 367, 263, 10171, 304, 5251, 393, 9556, 11286, 278, 12409, 310, 263, 2106, 3829, 297, 22053, 457, 1090, 777, 883, 310, 16728, 2761, 29889, 512, 1776, 310, 278, 9418, 29899, 29954, 3504, 946, 7018, 310, 6121, 9576, 719, 29892, 9556, 2609, 8661, 393, 278, 12409, 310, 263, 22053, 457, 16728, 2106, 723, 1371, 278, 10776, 1319, 5849, 310, 278, 19079, 310, 278, 3186, 1213, 376, 1576, 410, 15719, 362, 310, 263, 16728, 2106, 470, 263, 16728, 29899, 6406, 2132, 630, 22053, 457, 1699, 1370, 9571, 385, 7463, 26959, 392, 398, 491, 278, 16728, 19469, 4004, 310, 278, 5886, 29892, 376, 29893, 483, 1653, 363, 9556, 263, 716, 11103, 29892, 697, 393, 723, 505, 263, 6483, 9949, 373, 2693, 1860, 297, 278, 26206, 6932, 1213, 7280, 5886, 946, 3819, 25383, 393, 263, 16728, 2106, 376, 29893, 483, 664, 304, 6963, 4266, 9461, 537, 13047, 304, 22057, 297, 1432, 4234, 29892, 5480, 6820, 11706, 13047, 304, 278, 16035, 7018, 6354, 310, 3186, 9576, 719, 1213, 512, 5490, 29871, 29896, 29929, 29941, 29929, 29892, 23151, 29915, 29879, 716, 19358, 7668, 29892, 3650, 24039, 1005, 27461, 29890, 296, 1336, 29892, 763, 3538, 1370, 9571, 297, 1790, 19308, 24334, 262, 393, 376, 29954, 837, 1384, 1818, 4880, 278, 12409, 310, 263, 16728, 2106, 408, 18215, 29908, 1363, 372, 376, 29893, 483, 6963, 385, 6121, 7910, 297, 3081, 304, 3186, 9576, 719, 1213, 13, 29950, 277, 1358, 322, 278, 3865, 29928, 3301, 1258, 451, 22545, 403, 363, 470, 2304, 263, 16728, 2106, 297, 22053, 457, 29889, 512, 2114, 29892, 297, 2191, 262, 476, 16817, 23151, 7913, 2486, 5439, 825, 263, 16728, 2106, 723, 1106, 763, 881, 278, 20655, 488, 3186, 2758, 372, 304, 3799, 29901, 13, 1576, 9576, 29915, 29879, 2432, 3381, 297, 278, 2106, 2444, 577, 28715, 393, 1286, 451, 871, 508, 540, 1246, 3654, 263, 9576, 1449, 29892 ]

1,332,826

6,144

CommonCrawl

8

11

but he ruthlessly admits his ultimate national and political designs. A section of his race openly owns itself to be a foreign people, yet even here they lie. For while the Zionists try to make the rest of the world believe that the national consciousness of the Jew finds its satisfaction in the creation of a Palestinian state, the Jews again slyly dupe the dumb Goyim. It doesn't even enter their heads to build up a Jewish state in Palestine for the purpose of living there; all they want is a central organization for their international world swindle, endowed with its own sovereign rights and removed from the intervention of other states: a haven for convicted scoundrels and a university for budding crooks. Bottom line is, the Jews were dead set on establishing their criminal, usurping state in Palestine, not only to fulfill their twisted messianic prophecies, but also to gain a safe haven and central headquarters for their global crime syndicate, a fact Hitler recognized. He wanted the Jews out of Germany in order to rebuild German society after the devastation of WWI. The Jews in Palestine perfected their use of terrorism and underhandedness and declared "independence" shortly after Germany's defeat in WWII, using their fake "Holocaust" story and agents of influence across the globe to sell their false narrative of history to the rest of the world. And who were the first governments to recognize the illegitimate, terrorist state of Israel? Two of international Jewry's biggest puppets: the United States and the Soviet Union. On May 14, 1948, the leaders of the Jewish organizations in Palestine, headed byDavid Ben-Gurion,proclaimed the establishment of the State of Israel, to take effect at midnight that night. At that point, the State of Israel came into existence. The United States recognized the provisional Jewish government as de facto authority of the Jewish state within minutes. The Soviet Union granted de jure recognition almost immediately in 1948 along with seven other states within the next five days (Guatemala, Byelorussia, the Ukraine, Poland, Czechoslovakia, Uruguay, and Yugoslavia). [Source] Hitler and National Socialist Germany's ultimate aim was the removal of the Jews from Germany and Europe, and they collaborated with the Zionist movement to accomplish this goal. After the Jews and their puppet Allies brutally destroyed Germany in WWII, which represented the greatest threat in history to the global Jewish crime network behind "The New World Order", it was only a matter of time before "Israel" would be officially established. Hitler was not "the founder of Israel" as many continue to claim, and was not responsible for the establishment of that illegitimate, criminal hellhole brutally occupying Palestine. Hitler and National Socialist Germany were destroyed to pave the way for the establishment of Israel. Blaming Hitler and National Socialist Germany for something the Jews were determined to do on their own – with the assistance of their puppets in the West – is a gross distortion of history. Third, Hitler did not start WWII, and he was not a war-monger. Hitler wanted work and peace, as he outlined in numerous speeches after he was elected Chancellor in 1933. He wanted to rebuild the German economy, and help the German worker and farmer. Read all about it here. Further, we have to remember that international Jewry declared war on Germany in 1933, and some Jewish leaders, while projecting their own tribe's long established goals of world domination onto the Germans, actually called for the total annihilation of Germany: For it must be patent by now that while all the Germans may not approve of the means being employed by the Nazis in achieving German-world-dominion, they are practically unanimous in agreeing that that goal must, now or in the future, be definitely achieved by Germany. Were the German nations to win this war, not one German would hesitate laying claim to a share in the loot … Yet defeat will on no account erase their desire to conquer and rule the world. There is only one way to frustrate such a desire: the goal of world-dominion must be removed from the reach of the German and the only way to accomplish that is to remove the German from the world! -Theodore Kaufman, Germany Must Perish! Organized Jewry has been and remains the inciter of global war and genocide, including WWII. Consider what Jewish

-0.198172

0.617478

-1.03568

1.330986

[ 0.3455887095681733, -0.7419335810568426 ]

[ 0.861003533761088, 0.3739525596448445 ]

[ -0.741475566318849, -1.3298834842079996 ]

[ 1.4714601913821923, 1.190512202410881 ]

1,024

[ 512, 512 ]

[ 541, 540, 364, 2806, 23769, 7336, 1169, 670, 8494, 6490, 4797, 322, 8604, 25517, 29889, 319, 4004, 310, 670, 8175, 1722, 368, 1914, 29879, 3528, 304, 367, 263, 9117, 2305, 29892, 3447, 1584, 1244, 896, 3804, 29889, 1152, 1550, 278, 796, 291, 2879, 1018, 304, 1207, 278, 1791, 310, 278, 3186, 4658, 393, 278, 4797, 19861, 2264, 310, 278, 9576, 14061, 967, 26470, 297, 278, 11265, 310, 263, 22053, 262, 713, 2106, 29892, 278, 22057, 1449, 269, 368, 368, 868, 412, 278, 270, 3774, 2921, 29891, 326, 29889, 739, 1838, 29915, 29873, 1584, 3896, 1009, 15883, 304, 2048, 701, 263, 16728, 2106, 297, 22053, 457, 363, 278, 6437, 310, 8471, 727, 29936, 599, 896, 864, 338, 263, 6555, 13013, 363, 1009, 6121, 3186, 2381, 513, 280, 29892, 1095, 20937, 411, 967, 1914, 577, 369, 7577, 10462, 322, 6206, 515, 278, 1006, 7316, 310, 916, 5922, 29901, 263, 7359, 363, 7602, 18186, 885, 618, 2674, 29879, 322, 263, 16372, 363, 8619, 8497, 8182, 12117, 29889, 13, 15342, 1196, 338, 29892, 278, 22057, 892, 7123, 731, 373, 10127, 292, 1009, 22161, 29892, 502, 332, 15702, 2106, 297, 22053, 457, 29892, 451, 871, 304, 6095, 5589, 1009, 3252, 12652, 4473, 713, 293, 3107, 354, 2478, 29892, 541, 884, 304, 11581, 263, 9109, 7359, 322, 6555, 26463, 363, 1009, 5534, 17268, 22898, 9593, 29892, 263, 2114, 23151, 14831, 29889, 940, 5131, 278, 22057, 714, 310, 9556, 297, 1797, 304, 337, 4282, 5332, 12459, 1156, 278, 2906, 579, 362, 310, 399, 22119, 29889, 450, 22057, 297, 22053, 457, 4922, 287, 1009, 671, 310, 15115, 1608, 322, 1090, 3179, 287, 2264, 322, 8052, 376, 262, 2716, 355, 663, 29908, 21734, 1156, 9556, 29915, 29879, 20653, 297, 399, 29956, 2687, 29892, 773, 1009, 25713, 376, 19984, 6400, 504, 29908, 5828, 322, 19518, 310, 9949, 4822, 278, 15482, 915, 304, 19417, 1009, 2089, 15474, 1230, 310, 4955, 304, 278, 1791, 310, 278, 3186, 29889, 1126, 1058, 892, 278, 937, 4095, 1860, 304, 18720, 278, 980, 1397, 277, 6490, 29892, 15115, 391, 2106, 310, 11996, 29973, 7803, 310, 6121, 9576, 719, 29915, 29879, 24842, 2653, 27421, 29901, 278, 3303, 3900, 322, 278, 15308, 7761, 29889, 13, 2951, 2610, 29871, 29896, 29946, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 278, 20251, 310, 278, 16728, 25700, 297, 22053, 457, 29892, 2343, 287, 491, 19504, 4111, 29899, 29954, 332, 291, 29892, 15439, 13190, 278, 25012, 310, 278, 4306, 310, 11996, 29892, 304, 2125, 2779, 472, 7145, 11147, 393, 4646, 29889, 13, 4178, 393, 1298, 29892, 278, 4306, 310, 11996, 2996, 964, 10379, 29889, 450, 3303, 3900, 14831, 278, 1326, 275, 1848, 16728, 5874, 408, 316, 2114, 29877, 14329, 310, 278, 16728, 2106, 2629, 6233, 29889, 450, 15308, 7761, 16896, 316, 432, 545, 19679, 4359, 7389, 297, 29871, 29896, 29929, 29946, 29947, 3412, 411, 9881, 916, 5922, 2629, 278, 2446, 5320, 3841, 313, 9485, 17533, 2883, 29892, 2648, 12779, 1558, 423, 29892, 278, 23961, 29892, 18898, 29892, 21489, 24022, 557, 423, 29892, 29233, 29892, 322, 612, 688, 17464, 423, 467, 518, 4435, 29962, 13, 29950, 277, 1358, 322, 3086, 10307, 391, 9556, 29915, 29879, 8494, 6490, 12242, 471, 278, 28744, 310, 278, 22057, 515, 9556, 322, 4092, 29892, 322, 896, 11465, 630, 411, 278, 796, 291, 391, 10298, 304, 12709, 445, 7306, 29889, 2860, 278, 22057, 322, 1009, 2653, 7988, 838, 3687, 26644, 635, 14416, 9556, 297, 399, 29956, 2687, 29892, 607, 9875, 278, 14176, 28469, 297, 4955, 304, 278, 5534, 16728, 17268, 3564, 5742, 376, 1576, 1570, 2787, 8170, 613, 372, 471, 871, 263, 4383, 310, 931, 1434, 376, 3624, 9058, 29908, 723, 367, 22444, 7841, 29889, 13, 29950, 277, 1358, 471, 451, 376, 1552, 25331, 310, 11996, 29908, 408, 1784, 6773, 304, 5995, 29892, 322, 471, 451, 14040, 363, 278, 25012, 310, 393, 980, 1397, 277, 6490, 29892, 22161, 23927, 29716, 26644, 635, 6919, 5414, 22053, 457, 29889, 23151, 322, 3086, 10307, 391, 9556, 892, 14416, 304, 282, 1351, 278, 982, 363, 278, 25012, 310, 11996, 29889, 3164, 11500, 23151, 322, 3086, 10307, 391, 9556, 363, 1554, 278, 22057, 892, 10087, 304, 437, 373, 1009, 1914, 785, 411, 278, 18872, 310, 1009, 2653, 27421, 297, 278, 3122, 785, 338, 263, 22683, 1320, 441, 291, 310, 4955, 29889, 13, 1349, 1823, 29892, 23151, 1258, 451, 1369, 399, 29956, 2687, 29892, 322, 540, 471, 451, 263, 1370, 29899, 29885, 549, 261, 29889, 23151, 5131, 664, 322, 10776, 29892, 408, 540, 714, 21354, 297, 12727, 12032, 267, 1156, 540, 471, 11467, 22433, 3729, 272, 297, 29871, 29896, 29929, 29941, 29941, 29889, 940, 5131, 304, 337, 4282, 278, 5332, 26504, 29892, 322, 1371, 278, 5332, 15645, 322, 2215, 1050, 29889, 7523, 599, 1048, 372, 1244, 29889, 13, 29943, 332, 721, 29892, 591, 505, 304, 6456, 393, 6121, 9576, 719, 8052, 1370, 373, 9556, 297, 29871, 29896, 29929, 29941, 29941, 29892, 322, 777, 16728, 20251, 29892, 1550, 2060, 292, 1009, 1914, 29563, 29915, 29879, 1472, 7841, 14433, 310, 3186, 2432, 3381, 11480, 278, 7287, 550, 29892, 2869, 2000, 363, 278, 3001, 6957, 29882, 8634, 310, 9556, 29901, 13, 2831, 372, 1818, 367, 2373, 296, 491, 1286, 393, 1550, 599, 278, 7287, 550, 1122, 451, 2134, 345, 310, 278, 2794, 1641, 15723, 491, 278, 11409, 275, 297, 3657, 15387, 5332, 29899, 11526, 29899, 24130, 291, 29892, 896, 526, 4120, 1711, 443, 11576, 681, 297, 8661, 292, 393, 393, 7306, 1818, 29892, 1286, 470, 297, 278, 5434, 29892, 367, 11630, 14363, 491, 9556, 29889, 399, 406, 278, 5332, 19079, 304, 5401, 445, 1370, 29892, 451, 697, 5332, 723, 19066, 10388, 6568, 292, 5995, 304, 263, 6232, 297, 278, 658, 327, 16088, 15175, 20653, 674, 373, 694, 3633, 604, 559, 1009, 13521, 304, 26474, 322, 5751, 278, 3186, 29889, 1670, 338, 871, 697, 982, 304, 1424, 4627, 403, 1316, 263, 13521, 29901, 278, 7306, 310, 3186, 29899, 24130, 291, 1818, 367, 6206, 515, 278, 6159, 310, 278, 5332, 322, 278, 871, 982, 304, 12709, 393, 338, 304, 3349, 278, 5332, 515, 278, 3186, 29991, 448, 1576, 29221, 29462, 1171, 29892, 9556, 19928, 2431, 728, 29991, 13, 27356, 1891, 9576, 719, 756, 1063, 322, 9242, 278, 5528, 1524, 310, 5534, 1370, 322, 2531, 29877, 8204, 29892, 3704, 399, 29956, 2687, 29889, 10056, 825, 16728 ]

1,332,826

7,168

CommonCrawl

8

11

writer Marcus Eli Ravage said in the January 1928 issue of Century Magazine: We [Jews] have been at the bottom not merely of the latest great war but of nearly all your wars, not only of the Russian but of every other major revolution in your history. We have brought discord and confusion and frustration into your personal and public life. We are still doing it. No one can tell how long we shall go on doing it. Fourth, I haven't bothered to read all of this or this, which allege that Hitler and the NSDAP were homosexuals. I think it's pretty ridiculous on its face. The demonization and slanders against this man are never ending it seems. Hitler is a Jew, Hitler is a Rothschild, Hitler is a puppet of the bankers, he's a homosexual, the Nazis secretly run the world, the Nazis have underground bases in Antarctica, the Nazis are on the moon… all of these ridiculous claims about Hitler and the NSDAP can't all be true, can they? Let's assume that Hitler and the NSDAP were in fact homosexuals. Can someone who supports this theory explain to me why that would matter? Would that change anything that Hitler said, wrote about, and accomplished? Finally, National Socialist Germany demonstrated how to effectively deal with the international Jewish conspiracy for a "New World Order", their subversion and perversion of the German culture, economy, and government, and their control of the mass media, at least temporarily. What are the prospects of a movement of this type gaining a foothold in American society? America today, as opposed to Germany in the 1920s and 30s, is essentially a multinational empire, a true melting pot of all races, nationalities, cultures, and lifestyles. National Socialism sought to unite all elements of Germany society on their common German heritage and Nordic (or Aryan or white, whatever term you want to use) race, and wasn't afraid or intimidated by organized Jewry, which long ago declared war on the Gentile world. How is that going to happen in America? What is going to unite all Americans to overcome and defeat the forces of the "New World Order", especially when there is (increasingly) no common race, no common culture, or no common ideology? Making matters worse, most Americans are abysmally ignorant and totally brainwashed by Jewish propaganda, "entertainment", and false history. I'd venture to say that most Americans don't even know how to use their brains properly. Not to mention the rise of harmful vaccines, pharmaceutical drugs, alcohol and other narcotics, poisonous foods and the general degeneracy of American society… we have a lot to overcome, anyone know where to start? http://johnfriendsblog.blogspot.ca/2012/06/more-thoughts-about-adolf-hitler-and.html laconas So, what lessons can be learned by studying the failed revolt against Jewish banking power by the rise of the NSDAP? Nobody censors what they agree with Quote from: laconas on August 17, 2012, 10:05:26 PM I'm dead tired and off to bed, I need to do some errands out of town early tomorrow. Meanwhile laconas, please do feel free to post YOUR thoughts, I would love to read them when I get back. Good night. Judson Great article sushigirl .... good info. 'Even if you didn't do it, we don't want you to do it again' jacob gold Quote from: sushigirl on August 17, 2012, 10:40:21 PM That film is what happened to america Quote from: jacob gold on August 18, 2012, 03:52:23 PM Precisely! I would choose a good dictator over this so-called democracy [with umpteen 'choices'] B.S. anytime. Whoever coined these words was correct: Democracy is "two wolves and a sheep deciding what to have for dinner." Quote from: sushigirl on August 19, 2012, 07:53:

-0.773094

-0.406762

-0.999538

0.041682

[ -0.0646290814169555, -1.4815583127161733 ]

[ 0.517202846149622, -1.3307258497620076 ]

[ -0.3902061843031278, -1.6088699970002691 ]

[ 0.8575368080745117, -0.7741726926871099 ]

1,024

[ 512, 512 ]

[ 9227, 27390, 26864, 28093, 482, 1497, 297, 278, 5490, 29871, 29896, 29929, 29906, 29947, 2228, 310, 24027, 17880, 29901, 13, 4806, 518, 29967, 809, 29879, 29962, 505, 1063, 472, 278, 5970, 451, 13586, 310, 278, 9281, 2107, 1370, 541, 310, 8886, 599, 596, 29129, 29892, 451, 871, 310, 278, 10637, 541, 310, 1432, 916, 4655, 19479, 297, 596, 4955, 29889, 1334, 505, 6296, 2313, 536, 322, 14679, 322, 1424, 11036, 964, 596, 7333, 322, 970, 2834, 29889, 1334, 526, 1603, 2599, 372, 29889, 1939, 697, 508, 2649, 920, 1472, 591, 4091, 748, 373, 2599, 372, 29889, 13, 29943, 473, 386, 29892, 306, 7359, 29915, 29873, 24738, 287, 304, 1303, 599, 310, 445, 470, 445, 29892, 607, 394, 4424, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 3632, 29438, 27101, 29889, 306, 1348, 372, 29915, 29879, 5051, 8177, 12906, 681, 373, 967, 3700, 29889, 450, 8033, 2133, 322, 269, 1049, 414, 2750, 445, 767, 526, 2360, 17140, 372, 2444, 29889, 13, 29950, 277, 1358, 338, 263, 9576, 29892, 23151, 338, 263, 21790, 816, 789, 29892, 23151, 338, 263, 2653, 7988, 310, 278, 9124, 414, 29892, 540, 29915, 29879, 263, 3632, 29438, 950, 29892, 278, 11409, 275, 7035, 368, 1065, 278, 3186, 29892, 278, 11409, 275, 505, 1090, 2057, 22561, 297, 5459, 27014, 983, 29892, 278, 11409, 275, 526, 373, 278, 18786, 30098, 599, 310, 1438, 8177, 12906, 681, 16726, 1048, 23151, 322, 278, 3865, 29928, 3301, 508, 29915, 29873, 599, 367, 1565, 29892, 508, 896, 29973, 13, 12024, 29915, 29879, 5251, 393, 23151, 322, 278, 3865, 29928, 3301, 892, 297, 2114, 3632, 29438, 27101, 29889, 1815, 4856, 1058, 11286, 445, 6368, 5649, 304, 592, 2020, 393, 723, 4383, 29973, 10878, 393, 1735, 3099, 393, 23151, 1497, 29892, 5456, 1048, 29892, 322, 24799, 29973, 13, 12881, 635, 29892, 3086, 10307, 391, 9556, 28585, 920, 304, 17583, 5376, 411, 278, 6121, 16728, 21588, 29875, 10068, 363, 263, 376, 4373, 2787, 8170, 613, 1009, 1014, 3259, 322, 639, 3259, 310, 278, 5332, 9257, 29892, 26504, 29892, 322, 5874, 29892, 322, 1009, 2761, 310, 278, 4158, 5745, 29892, 472, 3203, 5382, 6275, 29889, 1724, 526, 278, 27289, 29879, 310, 263, 10298, 310, 445, 1134, 11581, 292, 263, 1701, 720, 1025, 297, 3082, 12459, 29973, 13, 29048, 9826, 29892, 408, 15869, 304, 9556, 297, 278, 29871, 29896, 29929, 29906, 29900, 29879, 322, 29871, 29941, 29900, 29879, 29892, 338, 13674, 263, 1773, 262, 1288, 3710, 533, 29892, 263, 1565, 9232, 1259, 3104, 310, 599, 19830, 29892, 4797, 1907, 29892, 4185, 1973, 29892, 322, 301, 7004, 5577, 29889, 3086, 10307, 1608, 18365, 304, 443, 568, 599, 3161, 310, 9556, 12459, 373, 1009, 3619, 5332, 902, 16639, 322, 5245, 293, 313, 272, 319, 719, 273, 470, 4796, 29892, 6514, 1840, 366, 864, 304, 671, 29897, 8175, 29892, 322, 9007, 29915, 29873, 13421, 470, 938, 326, 333, 630, 491, 19098, 9576, 719, 29892, 607, 1472, 8020, 8052, 1370, 373, 278, 20655, 488, 3186, 29889, 13, 5328, 338, 393, 2675, 304, 3799, 297, 6813, 29973, 1724, 338, 2675, 304, 443, 568, 599, 23035, 304, 25688, 322, 20653, 278, 8249, 310, 278, 376, 4373, 2787, 8170, 613, 7148, 746, 727, 338, 313, 262, 1037, 5832, 368, 29897, 694, 3619, 8175, 29892, 694, 3619, 9257, 29892, 470, 694, 3619, 1957, 3002, 29973, 13, 29924, 5086, 13750, 15029, 29892, 1556, 23035, 526, 633, 952, 29885, 635, 16245, 424, 322, 14909, 17294, 29893, 25936, 491, 16728, 13089, 5863, 29892, 376, 296, 13946, 358, 613, 322, 2089, 4955, 29889, 306, 29915, 29881, 9712, 545, 304, 1827, 393, 1556, 23035, 1016, 29915, 29873, 1584, 1073, 920, 304, 671, 1009, 4105, 1144, 6284, 29889, 2216, 304, 3585, 278, 14451, 310, 10311, 1319, 325, 5753, 1475, 29892, 1374, 22824, 346, 329, 936, 5883, 3174, 29892, 27231, 5391, 322, 916, 302, 5666, 327, 1199, 29892, 27908, 681, 9687, 29879, 322, 278, 2498, 3587, 759, 4135, 310, 3082, 12459, 30098, 591, 505, 263, 3287, 304, 25688, 29892, 5019, 1073, 988, 304, 1369, 29973, 13, 1124, 597, 29926, 6547, 7932, 1975, 7312, 29889, 7312, 17500, 29889, 1113, 29914, 29906, 29900, 29896, 29906, 29914, 29900, 29953, 29914, 5514, 29899, 386, 1774, 29879, 29899, 12717, 29899, 328, 4369, 29899, 27342, 1358, 29899, 392, 29889, 1420, 13, 433, 535, 294, 13, 6295, 29892, 825, 3109, 787, 508, 367, 10972, 491, 23382, 278, 5229, 13819, 29873, 2750, 16728, 9124, 292, 3081, 491, 278, 14451, 310, 278, 3865, 29928, 3301, 29973, 13, 29940, 711, 1486, 19343, 943, 825, 896, 8661, 411, 13, 2182, 866, 515, 29901, 425, 535, 294, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29896, 29900, 29901, 29900, 29945, 29901, 29906, 29953, 11278, 13, 29902, 29915, 29885, 7123, 23407, 322, 1283, 304, 6592, 29892, 306, 817, 304, 437, 777, 4589, 4167, 714, 310, 4726, 4688, 6454, 22396, 29889, 25065, 425, 535, 294, 29892, 3113, 437, 4459, 3889, 304, 1400, 612, 22970, 13133, 29892, 306, 723, 5360, 304, 1303, 963, 746, 306, 679, 1250, 29889, 7197, 4646, 29889, 13, 29967, 566, 1100, 13, 25120, 271, 4274, 269, 1878, 335, 5168, 13035, 1781, 5235, 29889, 13, 29915, 29923, 854, 565, 366, 3282, 29915, 29873, 437, 372, 29892, 591, 1016, 29915, 29873, 864, 366, 304, 437, 372, 1449, 29915, 13, 29926, 562, 711, 7684, 13, 2182, 866, 515, 29901, 269, 1878, 335, 5168, 373, 3111, 29871, 29896, 29955, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29896, 29900, 29901, 29946, 29900, 29901, 29906, 29896, 11278, 13, 7058, 2706, 338, 825, 9559, 304, 7902, 983, 13, 2182, 866, 515, 29901, 432, 562, 711, 7684, 373, 3111, 29871, 29896, 29947, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29941, 29901, 29945, 29906, 29901, 29906, 29941, 11278, 13, 6572, 3476, 873, 29991, 13, 29902, 723, 6755, 263, 1781, 9657, 1061, 975, 445, 577, 29899, 13998, 1261, 25804, 518, 2541, 318, 1526, 9404, 525, 1859, 1575, 2033, 350, 29889, 29903, 29889, 738, 2230, 29889, 11644, 1310, 1302, 1312, 1438, 3838, 471, 1959, 29901, 4432, 25804, 338, 376, 10184, 20040, 1960, 322, 263, 29735, 1602, 4821, 825, 304, 505, 363, 17803, 1213, 13, 2182, 866, 515, 29901, 269, 1878, 335, 5168, 373, 3111, 29871, 29896, 29929, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29955, 29901, 29945, 29941, 29901 ]

1,332,826

8,192

CommonCrawl

8

11

17 AM I would choose a good dictator over this so-called democracy [with umpteen 'choices'] B.S. anytime. "Umpteen" 'choices'? No, more like two, if you're lucky. In many offices (particularly local), sometimes there is only one. That's why we desperately need NOTA on the ballot. If NOTA wins, it's a do-over with a clean slate of candidates. Quote from: dominique on August 19, 2012, 08:06:41 AM Sorry, I meant numerous ''candidates'' serving the elite and not the people. Carlin said it best. "The politicians are put there to give you the idea that you have freedom of choice. YOU DON'T. You have no choice. You have OWNERS. They OWN YOU.... " Best monologue of all time.... "It's called the American Dream...because you have to be asleep to believe it." I have seen this one, Carlin is great!!! Nazi Expert: 'I Have Proof Hitler Died In 1960s' Painting depicting an aged Adolf Hitler in his 70s By Terrence Aym ~ Thursday, September 29, 2011 18:00 source: http://beforeitsnews.com/conspiracy-theories/2011/09/nazi-expert-i-have-proof-hitler-died-in-1960s-1163749.html "The biggest revelation is an authenticated secret German document which lists Hitler as one of the passengers evacuated by plane from Austria to Barcelona on April 26, 1945." Although official history contends Hitler committed suicide with his newlywed wife, Eva Braun, on April, 30 1945 and their corpses were burned by others in the Berlin bunker, Abel Basti claims proof the story is a fabrication. According to Basti's meticulous research, the leader of the Third Reich spent his last years as an art dealer and had facial plastic surgery to change his appearance. Those are just two of the astounding revelations that respected Argentine journalist and historian Abel Basti documents in his book, Hitler's Exile. TIME magazine announces Hitler's death in 1945 While the book was a runaway bestseller across South America, it's been suppressed in the United States and the Russian Federation. Those two countries still maintain that Germany's Führer committed suicide during the last days of World War Two. World newspapers report Hitler dead…were they wrong? The claim that Hitler and some high-ranking Schutzstaffel (SS) officers escaped Germany and fled to South America is not new. Nil Nikandrov observes (Strategic Culture Foundation, "All the Leaders of the Third Reich Fled to Latin America"): "In his well-documented, The Hitler Survival Myth (1981), Donald McKale identifies the earliest source of the myth of Hitler's escape to the southern hemisphere as the unexpected surrender of a German submarine in early July 1945 at Mar del Plata, Argentina. "Several Buenos Aires newspapers, in defiance of Argentine Navy statements, said that rubber boats had been seen landing from it, and other submarines spotted in the area. "On July 16, 1945, the Chicago Times carried a sensational article on the Hitlers having slipped off to Argentina." July 16, 1945: Chicago Times reports Hitler fled to South America The Hitler-in-Argentina tale first surfaced in a book back in 1947 "Ladislao Zsabó, a Hungarian advertiser, witnessed the arrival of the U-530 and saw its crew disembarking. He had heard that the destination was the German Antarctica and, mistakenly, made a supposition that Hitler had escaped to Antarctica, and published the book Hitler está Vivo (Hitler is Alive), where he speaks about the possible location of Hitler, in Queen's Maud properties, opposite the Weddel Sea, that was then renamed Neuschwabenland, when the area was explored in 1938/39

-0.278983

0.893235

-0.847998

-0.31438

[ -1.2185806303484112, 0.6606140582378881 ]

[ -0.8078623040195698, 2.5943320004688952 ]

[ -1.7965518328787051, 0.1005564541087283 ]

[ -1.2677827010880947, 0.6390217055412695 ]

1,024

[ 512, 512 ]

[ 29896, 29955, 13862, 13, 29902, 723, 6755, 263, 1781, 9657, 1061, 975, 445, 577, 29899, 13998, 1261, 25804, 518, 2541, 318, 1526, 9404, 525, 1859, 1575, 2033, 350, 29889, 29903, 29889, 738, 2230, 29889, 13, 29908, 29965, 1526, 9404, 29908, 525, 1859, 1575, 29915, 29973, 1939, 29892, 901, 763, 1023, 29892, 565, 366, 29915, 276, 9885, 29891, 29889, 512, 1784, 25222, 313, 1595, 16311, 368, 1887, 511, 6041, 727, 338, 871, 697, 29889, 13, 7058, 29915, 29879, 2020, 591, 553, 546, 2486, 817, 6058, 29909, 373, 278, 8287, 327, 29889, 960, 6058, 29909, 21614, 29892, 372, 29915, 29879, 263, 437, 29899, 957, 411, 263, 5941, 2243, 403, 310, 21669, 29889, 13, 2182, 866, 515, 29901, 8022, 1387, 373, 3111, 29871, 29896, 29929, 29892, 29871, 29906, 29900, 29896, 29906, 29892, 29871, 29900, 29947, 29901, 29900, 29953, 29901, 29946, 29896, 13862, 13, 29903, 3818, 29892, 306, 6839, 12727, 6629, 29883, 5380, 1078, 4907, 16330, 278, 560, 568, 322, 451, 278, 2305, 29889, 13, 8179, 1915, 1497, 372, 1900, 29889, 13, 29908, 1576, 2832, 14722, 526, 1925, 727, 304, 2367, 366, 278, 2969, 393, 366, 505, 16082, 310, 7348, 29889, 612, 27269, 360, 1164, 29915, 29911, 29889, 887, 505, 694, 7348, 29889, 887, 505, 438, 29956, 13865, 29903, 29889, 2688, 438, 16048, 612, 27269, 3045, 376, 13, 25353, 1601, 1189, 434, 310, 599, 931, 3045, 376, 3112, 29915, 29879, 2000, 278, 3082, 16814, 856, 18103, 366, 505, 304, 367, 408, 5436, 304, 4658, 372, 1213, 13, 29902, 505, 3595, 445, 697, 29892, 1704, 1915, 338, 2107, 21004, 13, 29940, 18861, 1222, 10700, 29901, 525, 29902, 6975, 18319, 23151, 360, 1000, 512, 29871, 29896, 29929, 29953, 29900, 29879, 29915, 13, 29925, 475, 1259, 1401, 919, 292, 385, 26552, 21834, 23151, 297, 670, 29871, 29955, 29900, 29879, 13, 2059, 23707, 663, 319, 962, 3695, 498, 1295, 3250, 29892, 3839, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29896, 29896, 29871, 29896, 29947, 29901, 29900, 29900, 13, 4993, 29901, 1732, 597, 11083, 1169, 15753, 29889, 510, 29914, 535, 1028, 29875, 10068, 29899, 1552, 3842, 29914, 29906, 29900, 29896, 29896, 29914, 29900, 29929, 29914, 29876, 18861, 29899, 735, 10700, 29899, 29875, 29899, 17532, 29899, 8017, 29899, 27342, 1358, 29899, 29881, 1000, 29899, 262, 29899, 29896, 29929, 29953, 29900, 29879, 29899, 29896, 29896, 29953, 29941, 29955, 29946, 29929, 29889, 1420, 13, 29908, 1576, 24842, 20474, 362, 338, 385, 15585, 630, 7035, 5332, 1842, 607, 8857, 23151, 408, 13, 650, 310, 278, 28134, 3415, 22061, 630, 491, 10694, 515, 17362, 304, 12408, 373, 3786, 29871, 29906, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 1213, 13, 2499, 3592, 6221, 4955, 640, 1975, 23151, 19355, 23921, 680, 411, 670, 15141, 8734, 6532, 29892, 27040, 23514, 29892, 373, 3786, 29892, 29871, 29941, 29900, 29871, 29896, 29929, 29946, 29945, 322, 1009, 14913, 267, 892, 12138, 287, 491, 4045, 297, 278, 5115, 289, 27560, 29892, 1976, 295, 25315, 29875, 16726, 5296, 278, 5828, 338, 263, 18187, 362, 29889, 13, 7504, 3278, 304, 25315, 29875, 29915, 29879, 1539, 12906, 681, 5925, 29892, 278, 11822, 310, 278, 18008, 9320, 10398, 670, 1833, 2440, 408, 385, 1616, 5376, 261, 322, 750, 2258, 1455, 715, 6288, 25300, 708, 304, 1735, 670, 10097, 29889, 13, 1349, 852, 526, 925, 1023, 310, 278, 8717, 12449, 20474, 800, 393, 3390, 287, 9385, 457, 24452, 322, 27629, 1976, 295, 25315, 29875, 10701, 297, 670, 3143, 29892, 23151, 29915, 29879, 1222, 488, 29889, 13, 15307, 14853, 7475, 778, 23151, 29915, 29879, 4892, 297, 29871, 29896, 29929, 29946, 29945, 13, 8809, 488, 278, 3143, 471, 263, 1065, 21694, 1900, 29879, 4539, 4822, 4275, 6813, 29892, 372, 29915, 29879, 1063, 21301, 287, 297, 278, 3303, 3900, 322, 278, 10637, 20438, 29889, 16025, 1023, 10916, 1603, 7344, 393, 9556, 29915, 29879, 383, 4000, 261, 19355, 23921, 680, 2645, 278, 1833, 3841, 310, 2787, 3362, 7803, 29889, 13, 14058, 14578, 21321, 3461, 23151, 7123, 30098, 29893, 406, 896, 2743, 29973, 13, 1576, 5995, 393, 23151, 322, 777, 1880, 29899, 661, 9292, 27651, 303, 3470, 295, 313, 1799, 29897, 13049, 19824, 9556, 322, 27481, 304, 4275, 6813, 338, 451, 716, 29889, 13, 27823, 11535, 392, 10139, 5366, 1960, 313, 5015, 1845, 293, 14062, 10606, 29892, 376, 3596, 278, 951, 24574, 310, 278, 18008, 9320, 383, 839, 304, 13548, 6813, 29908, 1125, 376, 797, 670, 1532, 29899, 3225, 287, 29892, 450, 23151, 6298, 29894, 2561, 341, 1541, 313, 29896, 29929, 29947, 29896, 511, 18935, 24053, 744, 2893, 11057, 278, 24577, 2752, 310, 278, 22082, 310, 23151, 29915, 29879, 10169, 304, 278, 14841, 9736, 275, 9085, 408, 278, 15668, 27503, 310, 263, 5332, 1014, 24556, 297, 4688, 5468, 29871, 29896, 29929, 29946, 29945, 472, 1085, 628, 1858, 532, 29892, 13798, 29889, 13, 29908, 29903, 1310, 284, 17882, 16981, 14578, 21321, 29892, 297, 822, 8837, 310, 9385, 457, 13166, 9506, 29892, 1497, 393, 14051, 495, 25462, 750, 1063, 3595, 25325, 515, 372, 29892, 322, 916, 1014, 3034, 1475, 805, 15048, 297, 278, 4038, 29889, 13, 29908, 2951, 5468, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 278, 10059, 10277, 8988, 263, 4771, 1288, 4274, 373, 278, 14309, 9306, 2534, 20662, 2986, 1283, 304, 13798, 1213, 13, 29967, 11850, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29946, 29945, 29901, 10059, 10277, 13676, 23151, 27481, 304, 4275, 6813, 13, 1576, 23151, 29899, 262, 29899, 1433, 5362, 1099, 17694, 937, 1190, 17470, 287, 297, 263, 3143, 1250, 297, 29871, 29896, 29929, 29946, 29955, 13, 29908, 29931, 328, 275, 433, 29877, 796, 29879, 370, 29980, 29892, 263, 14198, 13956, 18811, 7608, 29892, 16277, 287, 278, 18517, 310, 278, 501, 29899, 29945, 29941, 29900, 322, 4446, 967, 17616, 766, 1590, 935, 292, 29889, 940, 750, 6091, 393, 278, 12551, 471, 278, 5332, 5459, 27014, 983, 322, 29892, 25257, 368, 29892, 1754, 263, 1462, 4490, 393, 23151, 750, 19824, 304, 5459, 27014, 983, 29892, 322, 6369, 278, 3143, 23151, 7919, 478, 4243, 313, 29950, 277, 1358, 338, 319, 9258, 511, 988, 540, 7726, 29879, 1048, 278, 1950, 4423, 310, 23151, 29892, 297, 10470, 29915, 29879, 3219, 566, 4426, 29892, 11564, 278, 15050, 6144, 14070, 29892, 393, 471, 769, 19533, 2448, 17974, 29893, 12792, 1049, 29892, 746, 278, 4038, 471, 3902, 4395, 297, 29871, 29896, 29929, 29941, 29947, 29914, 29941, 29929 ]

1,332,826

9,216

CommonCrawl

8

11

by the German expedition [led] by Captain Ritschter. Brick from wall of Nazi complex in Patagonia "Zsabó made the wrong assumption. "Had he read the book by Professor Hugo Fernandez Artucio published in 1940, Nazis en el Uruguay, (Nazis in Uruguay) he would had discovered that there actually was a plan referring to German Antarctica, but this was nothing but the term they used for the Patagonia and that this information had been made public in New York in 1939." [Nil Nikandrov] 'Eagle's Nest" stonework on wall of German complex, Argentina. Basti doggedly digs deeper When there's so much smoke there's usually a fire. Basti tracked down that fire during seven years of sometimes grueling investigations. Author-journalist Abel Basti holds copy of his bestselling book He personally visited German compounds surrounded by security and stern-faced guards, interviewed surviving witnesses in villages near the strongholds, and even obtained authenticated photographs of Hitler and Braun during their exile years. Alleged photo of Adolf and Eva with daughter Urich in Argentina "Basti wrote that A. Hitler, E. Braun, and Führer's closest aides flew from the burning Berlin to Spain…and then crossed the Atlantic Ocean by three submarines and reached Argentina. "In July-August, 1945 Hitler and his clique landed in the Rio Negro province near the Caleta de los Loros village and moved on further into Argentine. "Allegedly, the same secret route prepared by SS chief Himmler's staff was later used by Bormann, Mengele, and Eichmann. "Basti detailed the journey of A. Hitler and E. Braun across Argentina assisted by local Nazi sympathizers and described the couple's family life during which—despite the hardships of hiding—they even had children." Alleged photo of Hitler in disguise, Buenos Aires meeting, 1952 Stonewalling Soviets The Soviets weren't helpful on the matter of the German leader's death. "The Soviets continued to be difficult. They refused to allow Westerners into Berlin even after the surrender of Dönitz's government and the last armies in the field on May 7-9. On May 10, they announced the existence of the burned bodies in the Chancellory courtyard, but only allowed that one might be Hitler. The same report went on to say that his body might never be found. "On June 6, a spokesman for the Soviet army in Berlin announced unequivocally that Hitler had committed suicide and that his body had been identified. Three days later, Marshall Zhukov, the head of the Soviet army gave a press conference with Deputy Foreign Minister Andrei Vishinski looking over his shoulder. 'We did not identify the body of Hitler,' he said. 'I can say nothing definite about his fate. He could have flown away from Berlin at the very last moment.'" [Nil Nikandrov ] Interview with Basti In an interview on Deadline – Live, an Argentine news program, journalist Santiago Romero interviewed Abel Basti about Hitler's escape, life in Patagonia, and the events that followed World War Two. ["Hitler huyó a la Patagonia en un submarino que zarpó desde Vigo" Edited.] Romero: What is your opinion on Hitler's escape? Basti: "Hitler escaped via air from Austria to Barcelona. The last stage of his escape was in a submarine, from Vigo, heading straight to the coast of Patagonia. Finally, Hitler and Eva Braun, in a car with a chauffeur and bodyguard—a motorcade of at least three cars—drove to Bariloche (Argentina). "He took refuge in a place called San Ramon, about 15 miles east of that town. It is a property of about 250,000 acres with a lake-front view of Lake Nahuel Huapi, which had been German property since the early twentieth century, when it belonged to a German firm by the name of Schamburg-Lippe." An alleged Hitler family home: Hacienda San Ramon Romero: "On what basis do you claim that Hitler was in Spain after leaving his Berlin bunker?" Basti: "I was able to confirm the presence of Hitler in

0.394897

2.229044

0.062513

0.836726

[ 0.2771049381182352, 0.5126891119060221 ]

[ 2.4081066280126846, 2.049980911750741 ]

[ 0.14620879256564515, -0.02118311510971663 ]

[ 0.9719970998776386, 0.7014545919793387 ]

1,024

[ 512, 512 ]

[ 491, 278, 5332, 24431, 518, 839, 29962, 491, 10842, 390, 20641, 357, 29889, 13, 29933, 9131, 515, 10090, 310, 11409, 29875, 4280, 297, 4121, 351, 6405, 13, 29908, 29999, 29879, 370, 29980, 1754, 278, 2743, 11833, 29889, 13, 29908, 29950, 328, 540, 1303, 278, 3143, 491, 11386, 20650, 7139, 4182, 29920, 3012, 29884, 3934, 6369, 297, 29871, 29896, 29929, 29946, 29900, 29892, 11409, 275, 427, 560, 29233, 29892, 313, 29940, 834, 275, 297, 29233, 29897, 540, 723, 750, 10943, 393, 727, 2869, 471, 263, 3814, 16811, 304, 5332, 5459, 27014, 983, 29892, 541, 445, 471, 3078, 541, 278, 1840, 896, 1304, 363, 278, 4121, 351, 6405, 322, 393, 445, 2472, 750, 1063, 1754, 970, 297, 1570, 3088, 297, 29871, 29896, 29929, 29941, 29929, 1213, 518, 27823, 11535, 392, 10139, 29962, 13, 29915, 29923, 20860, 29915, 29879, 405, 342, 29908, 12565, 1287, 373, 10090, 310, 5332, 4280, 29892, 13798, 29889, 13, 29933, 579, 29875, 437, 1505, 23244, 4697, 29879, 25871, 13, 10401, 727, 29915, 29879, 577, 1568, 25158, 727, 29915, 29879, 5491, 263, 3974, 29889, 25315, 29875, 5702, 287, 1623, 393, 3974, 2645, 9881, 2440, 310, 6041, 4500, 14067, 7405, 800, 29889, 13, 13720, 29899, 29926, 4659, 391, 1976, 295, 25315, 29875, 8640, 3509, 310, 670, 1900, 29879, 7807, 3143, 13, 3868, 22345, 16669, 5332, 752, 3885, 22047, 491, 6993, 322, 27784, 29899, 17470, 287, 1410, 3163, 29892, 15593, 287, 10503, 4357, 16277, 267, 297, 18481, 2978, 278, 4549, 23177, 29892, 322, 1584, 7625, 15585, 630, 17739, 29879, 310, 23151, 322, 23514, 2645, 1009, 429, 488, 2440, 29889, 13, 2499, 1397, 287, 15373, 310, 21834, 322, 27040, 411, 8750, 501, 4018, 297, 13798, 13, 29908, 29933, 579, 29875, 5456, 393, 319, 29889, 23151, 29892, 382, 29889, 23514, 29892, 322, 383, 4000, 261, 29915, 29879, 21438, 263, 2247, 9115, 29893, 515, 278, 25535, 5115, 304, 13616, 30098, 392, 769, 21692, 278, 19948, 21091, 491, 2211, 1014, 3034, 1475, 322, 7450, 13798, 29889, 13, 29908, 797, 5468, 29899, 26197, 29892, 29871, 29896, 29929, 29946, 29945, 23151, 322, 670, 9335, 802, 2982, 287, 297, 278, 11611, 12610, 307, 12291, 2978, 278, 315, 744, 941, 316, 1232, 10980, 359, 5720, 322, 6153, 373, 4340, 964, 9385, 457, 29889, 13, 29908, 2499, 1397, 23244, 29892, 278, 1021, 7035, 5782, 13240, 491, 5886, 9087, 18136, 828, 261, 29915, 29879, 13925, 471, 2678, 1304, 491, 350, 555, 812, 29892, 7567, 28253, 29892, 322, 382, 436, 4403, 29889, 13, 29908, 29933, 579, 29875, 13173, 278, 16342, 310, 319, 29889, 23151, 322, 382, 29889, 23514, 4822, 13798, 6985, 287, 491, 1887, 11409, 29875, 17520, 19427, 322, 5439, 278, 7303, 29915, 29879, 3942, 2834, 2645, 607, 30003, 2783, 29886, 568, 278, 2898, 9981, 310, 25508, 30003, 19562, 1584, 750, 4344, 1213, 13, 2499, 1397, 287, 15373, 310, 23151, 297, 766, 2543, 895, 29892, 17882, 16981, 11781, 29892, 29871, 29896, 29929, 29945, 29906, 13, 855, 650, 11358, 292, 317, 6895, 1691, 13, 1576, 317, 6895, 1691, 2949, 264, 29915, 29873, 8444, 373, 278, 4383, 310, 278, 5332, 11822, 29915, 29879, 4892, 29889, 13, 29908, 1576, 317, 6895, 1691, 7572, 304, 367, 5189, 29889, 2688, 15964, 304, 2758, 10504, 414, 964, 5115, 1584, 1156, 278, 27503, 310, 360, 3042, 2784, 29915, 29879, 5874, 322, 278, 1833, 5075, 583, 297, 278, 1746, 373, 2610, 29871, 29955, 29899, 29929, 29889, 1551, 2610, 29871, 29896, 29900, 29892, 896, 9326, 278, 10379, 310, 278, 12138, 287, 17873, 297, 278, 22433, 3729, 706, 2085, 1017, 538, 29892, 541, 871, 6068, 393, 697, 1795, 367, 23151, 29889, 450, 1021, 3461, 3512, 373, 304, 1827, 393, 670, 3573, 1795, 2360, 367, 1476, 29889, 13, 29908, 2951, 5306, 29871, 29953, 29892, 263, 805, 23195, 1171, 363, 278, 15308, 9987, 297, 5115, 9326, 1597, 339, 440, 542, 635, 393, 23151, 750, 19355, 23921, 680, 322, 393, 670, 3573, 750, 1063, 15659, 29889, 12753, 3841, 2678, 29892, 23072, 27134, 2679, 586, 29892, 278, 2343, 310, 278, 15308, 9987, 4846, 263, 3965, 21362, 411, 26721, 29891, 19358, 7668, 1126, 5803, 478, 728, 262, 2574, 3063, 975, 670, 23468, 29889, 525, 4806, 1258, 451, 12439, 278, 3573, 310, 23151, 5501, 540, 1497, 29889, 525, 29902, 508, 1827, 3078, 24860, 1048, 670, 23779, 29889, 940, 1033, 505, 4972, 29876, 3448, 515, 5115, 472, 278, 1407, 1833, 3256, 6169, 29908, 518, 27823, 11535, 392, 10139, 4514, 13, 4074, 1493, 411, 25315, 29875, 13, 797, 385, 15593, 373, 16992, 1220, 785, 10782, 29892, 385, 9385, 457, 9763, 1824, 29892, 24452, 18135, 6033, 1489, 15593, 287, 1976, 295, 25315, 29875, 1048, 23151, 29915, 29879, 10169, 29892, 2834, 297, 4121, 351, 6405, 29892, 322, 278, 4959, 393, 5643, 2787, 3362, 7803, 29889, 6796, 29950, 277, 1358, 298, 8631, 29980, 263, 425, 4121, 351, 6405, 427, 443, 1014, 3034, 1789, 712, 503, 6834, 29980, 5125, 478, 5973, 29908, 2155, 1573, 5586, 13, 29934, 290, 1489, 29901, 1724, 338, 596, 9426, 373, 23151, 29915, 29879, 10169, 29973, 13, 29933, 579, 29875, 29901, 376, 29950, 277, 1358, 19824, 3025, 4799, 515, 17362, 304, 12408, 29889, 450, 1833, 7408, 310, 670, 10169, 471, 297, 263, 1014, 24556, 29892, 515, 478, 5973, 29892, 28435, 7812, 304, 278, 12180, 310, 4121, 351, 6405, 29889, 9788, 29892, 23151, 322, 27040, 23514, 29892, 297, 263, 1559, 411, 263, 521, 28411, 5411, 322, 3573, 17728, 30003, 29874, 10992, 6332, 310, 472, 3203, 2211, 18647, 30003, 26419, 345, 304, 2261, 7820, 1173, 313, 1433, 5362, 1099, 467, 13, 29908, 3868, 3614, 25447, 297, 263, 2058, 2000, 3087, 8292, 265, 29892, 1048, 29871, 29896, 29945, 7800, 9755, 310, 393, 4726, 29889, 739, 338, 263, 2875, 310, 1048, 29871, 29906, 29945, 29900, 29892, 29900, 29900, 29900, 23931, 411, 263, 19437, 29899, 8862, 1776, 310, 9459, 405, 801, 2491, 12895, 2754, 29892, 607, 750, 1063, 5332, 2875, 1951, 278, 4688, 3252, 7268, 621, 6462, 29892, 746, 372, 28911, 304, 263, 5332, 9226, 491, 278, 1024, 310, 1102, 1117, 2007, 29899, 23410, 4798, 1213, 13, 2744, 16831, 287, 23151, 3942, 3271, 29901, 5952, 455, 8395, 3087, 8292, 265, 13, 29934, 290, 1489, 29901, 376, 2951, 825, 8405, 437, 366, 5995, 393, 23151, 471, 297, 13616, 1156, 10124, 670, 5115, 289, 27560, 3026, 13, 29933, 579, 29875, 29901, 376, 29902, 471, 2221, 304, 9659, 278, 10122, 310, 23151, 297 ]

1,332,826

10,240

CommonCrawl

8

11

Spain thanks to a—now elderly—Jesuit priest, whose family members were friends of the Nazi leader. And I have witnesses that allude to meetings he had with his entourage at the place where they stayed in Cantabria. Mr. and Mrs Hitler in Spain before voyage to Patagonia "In addition, a document of the British secret services reveals that in those days, a Nazi submarine convoy left Spain, and after stopping in the Canary Islands, it continued its journey to the south of Argentina. "Hitler and Eva Braun traveled onboard one of these submarines, which later arrived in Patagonia between July and August of 1945, under the de facto President Edelmiro Farrell and later Juan Domingo Peron, then his Minister of War. There is also another important document mentioning that the FBI was looking for Hitler in Spain after World War II." Romero: "From where did he leave to Patagonia?" Basti: "All the evidence points to the Galician coast, which was a significant base of supplies for Nazi submarines during the Battle of the Atlantic, to the extent that Churchill considered the possibility of invading it—an action that was scrapped when they built the code-breaking "Enigma" machine and managed to decipher Nazi submarine fleet messages and the course of submarine warfare was reversed. "There is the possibility that he left from Vigo or Ferrol, but it is almost certain that he did from Vigo, according to Britain's MI6." Romero: "What was Hitler's life in Argentina like?" Basti: "Hitler lived as a fugitive with his wife and his bodyguard. His first years were in Patagonia, and then he lived in the more northern provinces [of Argentina]. "In the early years, he held meetings in different parts of Argentina, and with other Nazis in Paraguay, as well as with sympathizers from foreign countries. "He shaved his head and mustache, so he was not easily recognizable. He lived away from large urban areas, although he had a few meetings in Buenos Aires. He died in the sixties in Argentina. "I'm currently investigating where he was buried and how he lived his last days." Romero: "Did you have access to documents from the former Soviet Union?" Basti: "Until his death in 1953, Stalin always believed that Hitler had escaped. In 1945, Stalin told the Allies this same information. There are three different shorthand writings in which Stalin mentioned that the German leader had fled. "In Argentina, I have interviewed people who had seen and met with Hitler. In the Russian archives, there is abundant documentation that shows that Hitler had escaped." Romero: "How did your book impact the official story of Hitler's death?" Basti: "Despite the recent investigations that proved that Hitler's remains at the Kremlin in Russia did not belong to him, most Russians have always rejected the theory that he escaped. The same applies to the nations involved in the war. "The U.S. has just reclassified [under national security auspices] for 20 [more] years all official material related to this story, and when that deadline is met, it will probably be reclassified. "The British reclassified all related documentation for 60 more years. The researchers cannot access that information." Also read Before It's News': Irish Soldier: 'I Saved Hitler's Life In 1919' - In one of those odd quirks of history, World War II and the 70 million lives lost could have been averted if, on a fateful day during 1919, a young Irishman had let Adolf Hitler die … Instead he unwittingly saved the life of Germany's future Führer. Hitler and Eva with child One can only dream It is truly amazing how much stuff is actually out there in net-land. Facts, fictions, outright lies, you name it... Adolf Hitler's Secret FBI files Timothy W Maier For almost 30 years, J. Edgar Hoover and the FBI maintained a detailed dossier on Adolf Hitler and closely investigated any report that indicated he still was alive. ADOLF HITLER LIVES -- in cyberspace, that is, where 734 pages of Hitler's raw FBI file can be downloaded from the Internet

0.334631

2.408107

0.029542

0.930375

[ 0.5784335324979625, 0.0908290797744038 ]

[ 2.5370318858669845, 2.2791813701583847 ]

[ -0.02118311510971663, 0.08026652590565414 ]

[ 1.2737560509949732, 0.5869943001762118 ]

1,024

[ 512, 512 ]

[ 13616, 3969, 304, 263, 30003, 3707, 27008, 368, 30003, 29967, 267, 3121, 18781, 29892, 5069, 3942, 5144, 892, 7875, 310, 278, 11409, 29875, 11822, 29889, 1126, 306, 505, 16277, 267, 393, 599, 1151, 304, 5870, 886, 540, 750, 411, 670, 875, 283, 6617, 472, 278, 2058, 988, 896, 27661, 297, 15498, 370, 2849, 29889, 13, 20335, 29889, 322, 6285, 23151, 297, 13616, 1434, 17775, 304, 4121, 351, 6405, 13, 29908, 797, 6124, 29892, 263, 1842, 310, 278, 4908, 7035, 5786, 10320, 1338, 393, 297, 1906, 3841, 29892, 263, 11409, 29875, 1014, 24556, 378, 18644, 2175, 13616, 29892, 322, 1156, 25480, 297, 278, 1815, 653, 17839, 29892, 372, 7572, 967, 16342, 304, 278, 7062, 310, 13798, 29889, 13, 29908, 29950, 277, 1358, 322, 27040, 23514, 1020, 345, 839, 373, 3377, 697, 310, 1438, 1014, 3034, 1475, 29892, 607, 2678, 11977, 297, 4121, 351, 6405, 1546, 5468, 322, 3111, 310, 29871, 29896, 29929, 29946, 29945, 29892, 1090, 278, 316, 2114, 29877, 7178, 2155, 295, 2460, 307, 8413, 15044, 322, 2678, 8699, 7809, 20191, 2431, 265, 29892, 769, 670, 7668, 310, 3362, 29889, 1670, 338, 884, 1790, 4100, 1842, 3585, 292, 393, 278, 383, 12809, 471, 3063, 363, 23151, 297, 13616, 1156, 2787, 3362, 1944, 1213, 13, 29934, 290, 1489, 29901, 376, 4591, 988, 1258, 540, 5967, 304, 4121, 351, 6405, 3026, 13, 29933, 579, 29875, 29901, 376, 3596, 278, 10757, 3291, 304, 278, 5208, 8910, 12180, 29892, 607, 471, 263, 7282, 2967, 310, 28075, 363, 11409, 29875, 1014, 3034, 1475, 2645, 278, 12788, 310, 278, 19948, 29892, 304, 278, 15834, 393, 6291, 453, 5545, 278, 13331, 310, 2437, 9382, 372, 30003, 273, 3158, 393, 471, 24559, 2986, 746, 896, 4240, 278, 775, 29899, 1030, 5086, 376, 2369, 2934, 29908, 4933, 322, 8745, 304, 316, 455, 8096, 11409, 29875, 1014, 24556, 22338, 7191, 322, 278, 3236, 310, 1014, 24556, 1370, 24658, 471, 18764, 287, 29889, 13, 29908, 8439, 338, 278, 13331, 393, 540, 2175, 515, 478, 5973, 470, 7756, 1467, 29892, 541, 372, 338, 4359, 3058, 393, 540, 1258, 515, 478, 5973, 29892, 5034, 304, 14933, 29915, 29879, 341, 29902, 29953, 1213, 13, 29934, 290, 1489, 29901, 376, 5618, 471, 23151, 29915, 29879, 2834, 297, 13798, 763, 3026, 13, 29933, 579, 29875, 29901, 376, 29950, 277, 1358, 10600, 408, 263, 20924, 3321, 411, 670, 6532, 322, 670, 3573, 17728, 29889, 3600, 937, 2440, 892, 297, 4121, 351, 6405, 29892, 322, 769, 540, 10600, 297, 278, 901, 14622, 28058, 518, 974, 13798, 1822, 13, 29908, 797, 278, 4688, 2440, 29892, 540, 4934, 5870, 886, 297, 1422, 5633, 310, 13798, 29892, 322, 411, 916, 11409, 275, 297, 1459, 10617, 388, 29892, 408, 1532, 408, 411, 17520, 19427, 515, 9117, 10916, 29889, 13, 29908, 3868, 528, 10511, 670, 2343, 322, 1818, 1829, 29892, 577, 540, 471, 451, 5948, 5936, 13902, 29889, 940, 10600, 3448, 515, 2919, 17164, 10161, 29892, 5998, 540, 750, 263, 2846, 5870, 886, 297, 17882, 16981, 29889, 940, 6423, 297, 278, 1354, 486, 583, 297, 13798, 29889, 13, 29908, 29902, 29915, 29885, 5279, 7405, 1218, 988, 540, 471, 18550, 322, 920, 540, 10600, 670, 1833, 3841, 1213, 13, 29934, 290, 1489, 29901, 376, 9260, 366, 505, 2130, 304, 10701, 515, 278, 4642, 15308, 7761, 3026, 13, 29933, 579, 29875, 29901, 376, 29965, 20233, 670, 4892, 297, 29871, 29896, 29929, 29945, 29941, 29892, 624, 25977, 2337, 13112, 393, 23151, 750, 19824, 29889, 512, 29871, 29896, 29929, 29946, 29945, 29892, 624, 25977, 5429, 278, 838, 3687, 445, 1021, 2472, 29889, 1670, 526, 2211, 1422, 528, 2072, 392, 2044, 886, 297, 607, 624, 25977, 5276, 393, 278, 5332, 11822, 750, 27481, 29889, 13, 29908, 797, 13798, 29892, 306, 505, 15593, 287, 2305, 1058, 750, 3595, 322, 1539, 411, 23151, 29889, 512, 278, 10637, 3190, 3145, 29892, 727, 338, 18666, 424, 5106, 393, 3697, 393, 23151, 750, 19824, 1213, 13, 29934, 290, 1489, 29901, 376, 5328, 1258, 596, 3143, 10879, 278, 6221, 5828, 310, 23151, 29915, 29879, 4892, 3026, 13, 29933, 579, 29875, 29901, 376, 4002, 29886, 568, 278, 7786, 7405, 800, 393, 11827, 393, 23151, 29915, 29879, 9242, 472, 278, 7706, 828, 262, 297, 12710, 1258, 451, 6852, 304, 1075, 29892, 1556, 11688, 1039, 550, 505, 2337, 22225, 278, 6368, 393, 540, 19824, 29889, 450, 1021, 16058, 304, 278, 19079, 9701, 297, 278, 1370, 29889, 13, 29908, 1576, 501, 29889, 29903, 29889, 756, 925, 1162, 605, 2164, 518, 5062, 4797, 6993, 1770, 29886, 1575, 29962, 363, 29871, 29906, 29900, 518, 5514, 29962, 2440, 599, 6221, 5518, 4475, 304, 445, 5828, 29892, 322, 746, 393, 7123, 1220, 338, 1539, 29892, 372, 674, 3117, 367, 1162, 605, 2164, 29889, 13, 29908, 1576, 4908, 1162, 605, 2164, 599, 4475, 5106, 363, 29871, 29953, 29900, 901, 2440, 29889, 450, 5925, 414, 2609, 2130, 393, 2472, 1213, 13, 17351, 1303, 10949, 739, 29915, 29879, 10130, 2396, 12601, 19019, 631, 29901, 525, 29902, 9583, 287, 23151, 29915, 29879, 4634, 512, 29871, 29896, 29929, 29896, 29929, 29915, 448, 512, 697, 310, 1906, 7736, 439, 27064, 310, 4955, 29892, 2787, 3362, 1944, 322, 278, 29871, 29955, 29900, 7284, 12080, 5714, 1033, 505, 1063, 263, 1765, 287, 565, 29892, 373, 263, 285, 22279, 2462, 2645, 29871, 29896, 29929, 29896, 29929, 29892, 263, 4123, 12601, 1171, 750, 1235, 21834, 23151, 762, 16088, 8669, 540, 18500, 5367, 368, 7160, 278, 2834, 310, 9556, 29915, 29879, 5434, 383, 4000, 261, 29889, 13, 29950, 277, 1358, 322, 27040, 411, 2278, 13, 6716, 508, 871, 12561, 13, 3112, 338, 19781, 21863, 292, 920, 1568, 6433, 338, 2869, 714, 727, 297, 7787, 29899, 1049, 29889, 26748, 29879, 29892, 26797, 1080, 29892, 714, 1266, 12185, 29892, 366, 1024, 372, 856, 13, 3253, 4369, 23151, 29915, 29879, 10213, 383, 12809, 2066, 13, 13711, 20336, 399, 3219, 631, 13, 2831, 4359, 29871, 29941, 29900, 2440, 29892, 435, 29889, 2155, 5397, 8335, 957, 322, 278, 383, 12809, 19949, 263, 13173, 270, 2209, 631, 373, 21834, 23151, 322, 16467, 7405, 630, 738, 3461, 393, 18694, 540, 1603, 471, 18758, 29889, 13, 3035, 5607, 29943, 379, 1806, 29931, 1001, 365, 5667, 2890, 1192, 297, 5094, 2596, 3535, 29892, 393, 338, 29892, 988, 29871, 29955, 29941, 29946, 6515, 310, 23151, 29915, 29879, 10650, 383, 12809, 934, 508, 367, 16532, 515, 278, 4685 ]

1,332,826

11,264

CommonCrawl

8

11

. The files contain speeches, rare photographs, old newspaper clippings, details about discovery of the Führer's personal notes and chinaware and assassination plots -- as well as an extensive 11-year probe into the possibility that Hitler faked his own death with a bogus suicide in 1945. At times these files read like a supermarket tabloid, with outrageous conspiracy theories that remind readers that FBI Director J. Edgar Hoover was a suspicious man. At other times, the files reveal how serious the FBI considered allegations that one of this century's most evil despots may have escaped his Berlin Bunker. The records begin with President Franklin Roosevelt becoming enraged upon learning of a 1933 New York conspiracy to kill Hitler and continue into the fifties with a Western Union telegram declaring: I have positive proof that Hitler is living. There are seven volumes of these records. A photographic exhibit of Hitler in uniform dominates the final volume. Scattered throughout are clippings from newspapers. The last story is a 1956 article about the plans of Hitler's sister, Paula Wolf, to write a book about her brother to "set some facts straight" as soon as a Munich court declares her brother dead. "The readers will forgive me," she says, "if I abstain from depicting my brother at all costs as a wicked character just for the sake of profit." An accompanying Associated Press article noted boldly: He Is Officially Alive 'Til Court Issues Certificate. As for that Western Union tipster, the FBI never tracked down the sender nor did it ever identify the members of the 1933 conspiracy plot to kill Hitler. But that plot sure kept Hoover's G-men busy. The file reveals that the plot began when the German Embassy asked the State Department to initiate an investigation based upon a letter signed by a "Daniel Stern," which said that unless FDR rebuked Hitler for his outrages against Jews, then "I notify you that I shall go to Germany and assassinate Hitler." The State Department handed off the probe to the FBI, which never found Stern. But the probe opened the door for Hoover to look at pro-Nazi organizations. Don Whitehead, one of the few authors to research the plot, wrote about it in his book, The FBI Story, A Report to the People. He calls it a "diplomatic fumble" by the German ambassador in Washington, who probably wished he never had called the State Department. That's because Hoover's investigation ultimately became "a valuable reference when the Department of Justice requested additional investigations. And Hoover passed the information to the president," Whitehead observes. All of this is in Hitler's FBI file -- even Whitehead's observations. Between the poor copies -- some nearly impossible to read because, says FBI Freedom of Information Officer Linda Gloss, the copies were not made from originals -- and the heavy black ink blocking out what today still is considered classified, there rests a fascinating tale of the FBI's role during the World War II era. For example, deep in the files are a series of memos written by Hoover on Oct. 5, 1939, reviewing intelligence from a confidential informant. The Hoover memos to various U.S. military-intelligence agencies and the president's chief of staff warned of future Japanese aggression and Germany's attack on France. "The Japanese will attack British Indochina and other colonies without warning, simultaneously with the German advance on France," Hoover wrote. For the last nine years of his life Adolf Hitler, a lifelong hypochondriac had as his physician Dr Theodor Morell. Hitler's mood swings, Parkinson's disease, gastro-intestinal symptoms, skin problems and steady decline until his suicide in 1945 are documented by reliable observers and historians, and in Morell's diaries. The bizarre and unorthodox medications given to Hitler, often for undisclosed reasons, include topical cocaine, injected amphetamines, glucose, testosterone, estradiol, and corticosteroids. In addition, he was given a preparation made from a gun cleaner, a compound of strychnine and atropine, an extract of seminal vesicles, and numerous vitamins and 'tonics'. It seems possible

0.775667

2.837857

0.442949

1.14889

[ 0.9893361611975906, 0.5619974273499774 ]

[ 3.195983203788961, 2.4797317712650733 ]

[ 0.5266449463732855, 0.35925303869792374 ]

[ 1.2425396077759385, 1.0552409484617309 ]

1,024

[ 512, 512 ]

[ 29889, 450, 2066, 1712, 12032, 267, 29892, 10812, 17739, 29879, 29892, 2030, 19656, 9335, 27775, 29892, 4902, 1048, 20699, 310, 278, 383, 4000, 261, 29915, 29879, 7333, 11486, 322, 521, 1099, 2519, 322, 20105, 3381, 24580, 1192, 408, 1532, 408, 385, 20607, 29871, 29896, 29896, 29899, 6360, 410, 915, 964, 278, 13331, 393, 23151, 285, 12535, 670, 1914, 4892, 411, 263, 26652, 375, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 4178, 3064, 1438, 2066, 1303, 763, 263, 2428, 28549, 4434, 417, 333, 29892, 411, 714, 6617, 681, 21588, 29875, 10068, 25841, 393, 1083, 513, 22176, 393, 383, 12809, 15944, 435, 29889, 2155, 5397, 8335, 957, 471, 263, 8872, 14803, 767, 29889, 2180, 916, 3064, 29892, 278, 2066, 10320, 284, 920, 10676, 278, 383, 12809, 5545, 16831, 800, 393, 697, 310, 445, 6462, 29915, 29879, 1556, 16126, 8913, 1862, 1122, 505, 19824, 670, 5115, 350, 27560, 29889, 13, 1576, 6475, 3380, 411, 7178, 21504, 1528, 852, 955, 29873, 14171, 427, 1431, 287, 2501, 6509, 310, 263, 29871, 29896, 29929, 29941, 29941, 1570, 3088, 21588, 29875, 10068, 304, 12088, 23151, 322, 6773, 964, 278, 285, 2027, 583, 411, 263, 10504, 7761, 4382, 1393, 25136, 29901, 13, 29902, 505, 6374, 5296, 393, 23151, 338, 8471, 29889, 13, 8439, 526, 9881, 18167, 310, 1438, 6475, 29889, 319, 6731, 12122, 10371, 277, 310, 23151, 297, 9090, 8022, 1078, 278, 2186, 7977, 29889, 2522, 2620, 287, 10106, 526, 9335, 27775, 515, 14578, 21321, 29889, 450, 1833, 5828, 338, 263, 29871, 29896, 29929, 29945, 29953, 4274, 1048, 278, 13900, 310, 23151, 29915, 29879, 9883, 29892, 2621, 2497, 10441, 29892, 304, 2436, 263, 3143, 1048, 902, 8099, 304, 376, 842, 777, 17099, 7812, 29908, 408, 4720, 408, 263, 13564, 436, 8973, 4845, 5114, 902, 8099, 7123, 29889, 376, 1576, 22176, 674, 18879, 573, 592, 1699, 1183, 4083, 29892, 376, 361, 306, 633, 303, 475, 515, 1401, 919, 292, 590, 8099, 472, 599, 21544, 408, 263, 281, 17840, 2931, 925, 363, 278, 16563, 310, 21665, 1213, 530, 10259, 1384, 292, 6853, 630, 5254, 4274, 11682, 14288, 368, 29901, 13, 3868, 1317, 10564, 368, 319, 9258, 525, 29911, 309, 9245, 16982, 1041, 18410, 8021, 29889, 13, 2887, 363, 393, 10504, 7761, 6872, 2475, 29892, 278, 383, 12809, 2360, 5702, 287, 1623, 278, 10004, 3643, 1258, 372, 3926, 12439, 278, 5144, 310, 278, 29871, 29896, 29929, 29941, 29941, 21588, 29875, 10068, 6492, 304, 12088, 23151, 29889, 1205, 393, 6492, 1854, 8126, 8335, 957, 29915, 29879, 402, 29899, 1527, 19587, 29889, 450, 934, 10320, 1338, 393, 278, 6492, 4689, 746, 278, 5332, 28735, 465, 29891, 4433, 278, 4306, 10317, 304, 14511, 403, 385, 22522, 2729, 2501, 263, 5497, 8794, 491, 263, 376, 29866, 23413, 1699, 607, 1497, 393, 6521, 383, 8353, 337, 2423, 17713, 23151, 363, 670, 714, 22428, 2750, 22057, 29892, 769, 376, 29902, 26051, 366, 393, 306, 4091, 748, 304, 9556, 322, 20105, 16976, 23151, 1213, 13, 1576, 4306, 10317, 29692, 1283, 278, 410, 915, 304, 278, 383, 12809, 29892, 607, 2360, 1476, 23413, 29889, 1205, 278, 410, 915, 6496, 278, 3050, 363, 8335, 957, 304, 1106, 472, 410, 29899, 29940, 18861, 25700, 29889, 3872, 8037, 2813, 29892, 697, 310, 278, 2846, 15717, 304, 5925, 278, 6492, 29892, 5456, 1048, 372, 297, 670, 3143, 29892, 450, 383, 12809, 13740, 29892, 319, 13969, 304, 278, 11647, 29889, 940, 5717, 372, 263, 376, 6051, 8840, 2454, 285, 15563, 29908, 491, 278, 5332, 3181, 28760, 297, 7660, 29892, 1058, 3117, 20024, 540, 2360, 750, 2000, 278, 4306, 10317, 29889, 2193, 29915, 29879, 1363, 8335, 957, 29915, 29879, 22522, 18973, 3897, 376, 29874, 21114, 3407, 746, 278, 10317, 310, 17181, 13877, 5684, 7405, 800, 29889, 1126, 8335, 957, 4502, 278, 2472, 304, 278, 6673, 1699, 8037, 2813, 5366, 1960, 29889, 13, 3596, 310, 445, 338, 297, 23151, 29915, 29879, 383, 12809, 934, 1192, 1584, 8037, 2813, 29915, 29879, 13917, 29889, 13, 29933, 300, 1452, 278, 6460, 14591, 1192, 777, 8886, 9301, 304, 1303, 1363, 29892, 4083, 383, 12809, 3878, 11607, 310, 10343, 28288, 365, 11054, 402, 6758, 29892, 278, 14591, 892, 451, 1754, 515, 2441, 29879, 1192, 322, 278, 9416, 4628, 297, 29895, 23473, 714, 825, 9826, 1603, 338, 5545, 770, 2164, 29892, 727, 1791, 29879, 263, 21028, 262, 1218, 17694, 310, 278, 383, 12809, 29915, 29879, 6297, 2645, 278, 2787, 3362, 1944, 3152, 29889, 13, 2831, 1342, 29892, 6483, 297, 278, 2066, 526, 263, 3652, 310, 2626, 359, 3971, 491, 8335, 957, 373, 4756, 29889, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29929, 29892, 9076, 292, 21082, 515, 263, 24332, 616, 1871, 424, 29889, 450, 8335, 957, 2626, 359, 304, 5164, 501, 29889, 29903, 29889, 9121, 29899, 524, 28286, 946, 15942, 322, 278, 6673, 29915, 29879, 9087, 310, 13925, 1370, 9571, 310, 5434, 10369, 946, 11476, 322, 9556, 29915, 29879, 5337, 373, 3444, 29889, 376, 1576, 10369, 674, 5337, 4908, 1894, 2878, 1099, 322, 916, 8104, 583, 1728, 9177, 29892, 21699, 411, 278, 5332, 6564, 373, 3444, 1699, 8335, 957, 5456, 29889, 13, 2831, 278, 1833, 14183, 2440, 310, 670, 2834, 21834, 23151, 29892, 263, 11747, 295, 549, 7498, 1129, 305, 898, 374, 562, 750, 408, 670, 4824, 8910, 4942, 450, 17606, 3879, 514, 29889, 13, 29950, 277, 1358, 29915, 29879, 286, 2092, 2381, 886, 29892, 4815, 26803, 29915, 29879, 17135, 29892, 330, 23364, 29899, 524, 342, 979, 25828, 4835, 29892, 19309, 4828, 322, 27357, 4845, 457, 2745, 670, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 526, 23531, 491, 23279, 5366, 874, 322, 3603, 5834, 29892, 322, 297, 3879, 514, 29915, 29879, 652, 4314, 29889, 13, 1576, 289, 15356, 276, 322, 443, 2072, 17324, 13589, 800, 2183, 304, 23151, 29892, 4049, 363, 563, 275, 15603, 9590, 29892, 3160, 2246, 936, 274, 6400, 457, 29892, 11658, 287, 626, 561, 300, 314, 1475, 29892, 3144, 1682, 852, 29892, 1243, 15664, 650, 29892, 707, 3665, 29875, 324, 29892, 322, 13979, 293, 520, 1489, 4841, 29889, 13, 797, 6124, 29892, 540, 471, 2183, 263, 10223, 362, 1754, 515, 263, 13736, 27372, 29892, 263, 752, 618, 310, 380, 719, 3049, 457, 322, 472, 1336, 457, 29892, 385, 6597, 310, 3031, 979, 28999, 4027, 29892, 322, 12727, 13901, 314, 1144, 322, 525, 880, 1199, 4286, 13, 3112, 2444, 1950 ]

1,332,826

12,288

CommonCrawl

8

11

that some of Hitler's behaviour, illnesses and suffering can be attributed to his medical care. Whether he blindly accepted such unorthodox medications or demanded them is unclear. And there is ample evidence in the files to undermine rumors that Hitler's personal physician tried to poison him or "administer narcotics that might have contributed to the impairment of Hitler's health" or that "Hitler inherited certain [psychophysical] traits in his childhood and later on, and that these might account for his crimes and other actions," according to an FBI investigation into the matter. The FBI's Hitler files have been available for some time to anyone who cared to schedule an appointment at FBI headquarters in Washington, but few have done so. Two recent critically acclaimed books, Hitler: Diagnosis of a Destructive Prophet by Fritz Redlich and Explaining Hitler by Ron Rosenbaum, fail to mention the FBI files -- although some of the records used to support these authors' opinions, such as Hitler's medical records, are duplicated in the files from other sources. Redlich and Rosenbaum may have avoided Hitler's FBI file because some of the information there concerns allegations that border on the absurd -- for instance, that Hitler survived the war. Historians generally accept that Hitler committed suicide April 30, 1945, in a Berlin bunker as Allied troops closed in on him. The Soviets recently made available forensic proof of this in their possession since the war's end. But there was no such certainty in the West 50 years ago when opinion polls showed that two of every three Americans believed Hitler indeed was alive. Hoover didn't rule it out but never concluded that the Nazi dictator was dead. Besieged with letters from witnesses swearing they had spotted the defeated Nazi dictator, the files show, the Hitler hunt began. Some tips were considered credible. One of these came from a doctor who claimed to have treated Hitler for an intestinal disorder in St. Louis -- an alarming story because the FBI obtained Hitler's classified medical records and verified that Hitler suffered from a similar condition. That information was not publicly known at the time. Other reports simply were bizarre. A 77-year-old man claimed to have found a letter written by Hitler in 1947. "Call it a Hitler hoax, if you will," the man wrote Hoover, "and believe its delivery in German over a USA radio would be the most startling sensation since Orson Welles' attack of the Martians." During an FBI interview with the elderly man, he admitted to "perpetrating this hoax to create a sensation," according to the interrogating agent's notes. "He seemed to be a psychopathic case," the agent wrote. And that was far from the only nut to roll out of the barrel. Others told tales of Hitler dining in a Washington restaurant in 1946; jumping out of a New Orleans train in 1948; purchasing 8,960 acres of land near Kit Carson, Colo.; and finding work as a butler in London in 1946. Most of the letters had one thing in common: suspicions and allegations but no proof -- such as this Oct. 15, 1945, letter from a New York man who wrote: I'll bet a dollar to a doughnut that Hitler is located right in New York City. There's no other city in the world where he could so easily be absorbed. No doubt you have considered this possibility, but I mention it for what it is worth anyway. As incredible as all of this sounds now, the FBI treated such matters very seriously. If the G-men couldn't chase down the tip, they made every effort to find the tipster and either expose a mistake or identify a prankster or mental case. For instance, on Oct. 10, 1948, a Washington woman who operated a boardinghouse wrote to the FBI, claiming one of her borders was Hitler. She mostly was worried about whether she might be prosecuted for harboring him and wanted to know if any "action could possibly be taken against her." The FBI dismissed the complaint with the note: "She is obviously demented." But while some sightings were dismissed without an intense investigation, others weren't. The files show that Hoover's G-men conducted a massive manhunt for Hitler on a scale not seen since

0.740055

2.465407

0.480993

0.906963

[ 0.8523686182977145, 0.6277418479419179 ]

[ 2.3651315420612513, 2.56568194316794 ]

[ 0.8208489053178607, 0.1411363105148766 ]

[ 1.2841615320679847, 0.5297641542746483 ]

1,024

[ 512, 512 ]

[ 393, 777, 310, 23151, 29915, 29879, 10468, 29892, 4486, 2264, 267, 322, 23164, 508, 367, 29393, 304, 670, 16083, 2562, 29889, 26460, 540, 16842, 368, 9259, 1316, 443, 2072, 17324, 13589, 800, 470, 24432, 963, 338, 20871, 29889, 13, 2855, 727, 338, 626, 552, 10757, 297, 278, 2066, 304, 563, 837, 457, 16558, 943, 393, 23151, 29915, 29879, 7333, 4824, 8910, 1898, 304, 27908, 1075, 470, 376, 6406, 1531, 302, 5666, 327, 1199, 393, 1795, 505, 26869, 304, 278, 2411, 1466, 358, 310, 23151, 29915, 29879, 9045, 29908, 470, 393, 376, 29950, 277, 1358, 23878, 3058, 518, 567, 3376, 3021, 952, 936, 29962, 1020, 1169, 297, 670, 2278, 6614, 322, 2678, 373, 29892, 322, 393, 1438, 1795, 3633, 363, 670, 2181, 1355, 322, 916, 8820, 1699, 5034, 304, 385, 383, 12809, 22522, 964, 278, 4383, 29889, 13, 1576, 383, 12809, 29915, 29879, 23151, 2066, 505, 1063, 3625, 363, 777, 931, 304, 5019, 1058, 274, 1965, 304, 20410, 385, 28573, 472, 383, 12809, 26463, 297, 7660, 29892, 541, 2846, 505, 2309, 577, 29889, 7803, 7786, 3994, 1711, 1035, 13190, 8277, 29892, 23151, 29901, 4671, 4211, 19263, 310, 263, 15435, 1247, 573, 1019, 561, 300, 491, 22839, 4367, 1470, 322, 12027, 433, 2827, 23151, 491, 11546, 28929, 29602, 29892, 4418, 304, 3585, 278, 383, 12809, 2066, 1192, 5998, 777, 310, 278, 6475, 1304, 304, 2304, 1438, 15717, 29915, 26971, 29892, 1316, 408, 23151, 29915, 29879, 16083, 6475, 29892, 526, 5141, 9169, 297, 278, 2066, 515, 916, 8974, 29889, 13, 9039, 1470, 322, 28929, 29602, 1122, 505, 28305, 23151, 29915, 29879, 383, 12809, 934, 1363, 777, 310, 278, 2472, 727, 21838, 16831, 800, 393, 5139, 373, 278, 6425, 18245, 1192, 363, 2777, 29892, 393, 23151, 10503, 2347, 278, 1370, 29889, 4731, 5834, 6892, 3544, 393, 23151, 19355, 23921, 680, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 297, 263, 5115, 289, 27560, 408, 838, 2957, 13230, 5764, 297, 373, 1075, 29889, 450, 317, 6895, 1691, 10325, 1754, 3625, 363, 575, 293, 5296, 310, 445, 297, 1009, 17715, 1951, 278, 1370, 29915, 29879, 1095, 29889, 1205, 727, 471, 694, 1316, 3058, 1017, 297, 278, 3122, 29871, 29945, 29900, 2440, 8020, 746, 9426, 1248, 3137, 10018, 393, 1023, 310, 1432, 2211, 23035, 13112, 23151, 6200, 471, 18758, 29889, 8335, 957, 3282, 29915, 29873, 5751, 372, 714, 541, 2360, 22834, 393, 278, 11409, 29875, 9657, 1061, 471, 7123, 29889, 6952, 347, 3192, 411, 8721, 515, 16277, 267, 7901, 4362, 896, 750, 805, 15048, 278, 16235, 11409, 29875, 9657, 1061, 29892, 278, 2066, 1510, 29892, 278, 23151, 298, 1657, 4689, 29889, 13, 9526, 25562, 892, 5545, 6625, 1821, 29889, 3118, 310, 1438, 2996, 515, 263, 11619, 1058, 17049, 304, 505, 14914, 23151, 363, 385, 938, 342, 979, 766, 2098, 297, 624, 29889, 5899, 1192, 385, 21200, 292, 5828, 1363, 278, 383, 12809, 7625, 23151, 29915, 29879, 770, 2164, 16083, 6475, 322, 26834, 393, 23151, 17654, 515, 263, 2788, 4195, 29889, 2193, 2472, 471, 451, 970, 368, 2998, 472, 278, 931, 29889, 13, 16107, 13676, 3763, 892, 289, 15356, 276, 29889, 319, 29871, 29955, 29955, 29899, 6360, 29899, 1025, 767, 17049, 304, 505, 1476, 263, 5497, 3971, 491, 23151, 297, 29871, 29896, 29929, 29946, 29955, 29889, 376, 5594, 372, 263, 23151, 5089, 1165, 29892, 565, 366, 674, 1699, 278, 767, 5456, 8335, 957, 29892, 376, 392, 4658, 967, 28289, 297, 5332, 975, 263, 8278, 7155, 723, 367, 278, 1556, 1369, 1847, 4771, 362, 1951, 1394, 1100, 399, 4999, 29915, 5337, 310, 278, 3760, 5834, 1213, 13, 29928, 3864, 385, 383, 12809, 15593, 411, 278, 27008, 368, 767, 29892, 540, 20186, 304, 376, 546, 10963, 29741, 445, 5089, 1165, 304, 1653, 263, 4771, 362, 1699, 5034, 304, 278, 1006, 9102, 1218, 10823, 29915, 29879, 11486, 29889, 376, 3868, 6140, 304, 367, 263, 11643, 459, 493, 293, 1206, 1699, 278, 10823, 5456, 29889, 1126, 393, 471, 2215, 515, 278, 871, 18254, 304, 9679, 714, 310, 278, 2594, 2674, 29889, 438, 3341, 5429, 29763, 310, 23151, 270, 2827, 297, 263, 7660, 27144, 297, 29871, 29896, 29929, 29946, 29953, 29936, 12500, 292, 714, 310, 263, 1570, 26884, 7945, 297, 29871, 29896, 29929, 29946, 29947, 29936, 10596, 5832, 29871, 29947, 29892, 29929, 29953, 29900, 23931, 310, 2982, 2978, 26240, 1704, 1100, 29892, 1530, 29877, 8670, 322, 9138, 664, 408, 263, 541, 1358, 297, 4517, 297, 29871, 29896, 29929, 29946, 29953, 29889, 13, 29924, 520, 310, 278, 8721, 750, 697, 2655, 297, 3619, 29901, 8872, 293, 1080, 322, 16831, 800, 541, 694, 5296, 1192, 1316, 408, 445, 4756, 29889, 29871, 29896, 29945, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 5497, 515, 263, 1570, 3088, 767, 1058, 5456, 29901, 13, 29902, 29915, 645, 1010, 263, 11232, 279, 304, 263, 270, 820, 21305, 393, 23151, 338, 5982, 1492, 297, 1570, 3088, 4412, 29889, 1670, 29915, 29879, 694, 916, 4272, 297, 278, 3186, 988, 540, 1033, 577, 5948, 367, 17977, 2580, 29889, 1939, 7404, 366, 505, 5545, 445, 13331, 29892, 541, 306, 3585, 372, 363, 825, 372, 338, 7088, 8763, 29889, 13, 2887, 29811, 1821, 408, 599, 310, 445, 10083, 1286, 29892, 278, 383, 12809, 14914, 1316, 13750, 1407, 25798, 29889, 960, 278, 402, 29899, 1527, 8496, 29915, 29873, 521, 559, 1623, 278, 6872, 29892, 896, 1754, 1432, 7225, 304, 1284, 278, 6872, 2475, 322, 2845, 24396, 263, 10171, 470, 12439, 263, 544, 804, 2475, 470, 19119, 1206, 29889, 1152, 2777, 29892, 373, 4756, 29889, 29871, 29896, 29900, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 263, 7660, 6114, 1058, 19623, 263, 7613, 292, 8697, 5456, 304, 278, 383, 12809, 29892, 5995, 292, 697, 310, 902, 28199, 471, 23151, 29889, 2296, 11149, 471, 6365, 1255, 1048, 3692, 1183, 1795, 367, 410, 3471, 3860, 363, 4023, 4089, 292, 1075, 322, 5131, 304, 1073, 565, 738, 376, 2467, 1033, 10075, 367, 4586, 2750, 902, 1213, 450, 383, 12809, 18918, 287, 278, 15313, 524, 411, 278, 4443, 29901, 376, 13468, 338, 12879, 316, 358, 287, 1213, 13, 6246, 1550, 777, 11126, 886, 892, 18918, 287, 1728, 385, 17818, 344, 22522, 29892, 4045, 2949, 264, 29915, 29873, 29889, 450, 2066, 1510, 393, 8335, 957, 29915, 29879, 402, 29899, 1527, 18043, 263, 20364, 767, 29882, 1657, 363, 23151, 373, 263, 6287, 451, 3595, 1951 ]

1,332,826

13,312

CommonCrawl

8

11

Charles Lindbergh's baby was kidnapped and murdered, with agents trekking to the four corners of the globe in search of the Nazi leader. The most frequent sighting was in South America -- a notoriously safe haven for Nazi war criminals, according to the FBI files. And so the FBI dispatched a team of G-men to investigate reports from newspaper articles (many contained in the FBI file) and independent witnesses apparently claiming Hitler was in Argentina. The Argentina stories intrigued Hoover. In 1944, a year before Hitler's reported death, Hoover received a tip that Hitler would receive refuge in Argentina, according to a Sept. 4, 1944, memo written by an FBI agent. The memo noted that Argentine political leaders had plans to conduct clandestine meetings with Hitler "for the arranging of importing arms and technicians into Argentina." The memo notes that bicycle factories there had been converted to plants for manufacturing munitions and that a "large wealthy German colony in Argentina affords tremendous possibilities" as a refuge for Hitler and his henchmen. "One of the members [of the postwar German planners], Count Luxburg, has been mentioned as operating a ranch which would serve in providing a haven." Within a year witnesses began flooding the FBI with Hitler sightings in Argentina. Some of these, the FBI rationalized, resulted from tabloid press reports claiming Hitler had escaped and was waiting for war to break out between the Soviet Union and the United States before emerging as a leader in the new world. And there were outspoken Nazi sympathizers such as Otto Abetz, Germany's wartime ambassador to France, boasting that Hitler "is certainly not dead" and was "not a coward -- I believe one day he will return." The most sensational story appeared June 20, 1948, in El Tiempo, a Spanish newspaper published in Colombia, claiming Hitler had escaped via submarine to Bogotà. The paper provided a detailed account of Hitler's supposedly cowardly flight and fueled dozens of similar stories around the world. Many of those appeared in the FBI files as clippings ranging from obscure magazines to the Associated Press. One such story claimed that the Swedes observed a mysterious yacht moving in and out of inlets on the North Sea or a Brazilian ship reportedly sunk by an unidentified submarine transporting a woman some claimed to be Eva Braun, Hitler's wife. Braun landed from that submarine off the coast of Argentina, one article claimed. The same article suggested a Japanese navy staff officer had volunteered details of a plan to evacuate Hitler and Braun to Japan after the fall of Germany. Closer to home a mysterious submarine reportedly was seen about 1,300 miles north of Catalina, Calif., in a location where Theodore Donay, a wealthy Detroit importer, disappeared. According to wire reports, Donay was convicted in 1943 as a traitor for aiding Hans Peter Krug, an escaped Nazi, and never was found. But none of these reports apparently could be directly linked to Hitler and the FBI repeatedly concluded they were baseless rumors. One agent expressed shock in the files that the Chicago Times carried such rumor and innuendo and chastised an unnamed writer. His reputation is extremely poor and he is generally considered to be a journalist of the most sensational and unreliable nature. One reason that Hitler's death was not believed for so long was that the Russians deliberately withheld information, writes Redlich. In fact, it wasn't until Russian journalist Lev Bezymenski wrote a book translated into English in 1968 that the West learned that the Russians performed autopsies on corpses recovered May 2, 1945, in shallow graves in a garden near the Berlin bunker. The bodies were believed to be Hitler, his wife and their two dogs. The United States was angered by the slow Russian revelations -- but the Russian government defended its actions, saying 30 years was customary for declassification of secrets. Meanwhile, at the Yalta conference in 1945, Stalin declared that Hitler had escaped. Further adding to continuing suspicions are the autopsy reports concerning a missing testicle and superficial accounts of main body organs. Indeed, Bezymenski since has acknowledged that the autopsy reports were false, casting more mystery on Hitler's

0.737316

2.945295

0.234977

0.935578

[ 1.038644476641546, 0.43598728788209146 ]

[ 3.238958289740394, 2.6516321150708064 ]

[ 0.5367899104748226, -0.06683545356663348 ]

[ 1.1592957591918462, 0.7118600730523502 ]

1,024

[ 512, 512 ]

[ 5322, 17277, 2552, 29882, 29915, 29879, 24354, 471, 26397, 29876, 17280, 322, 13406, 287, 29892, 411, 19518, 2578, 6859, 292, 304, 278, 3023, 26995, 310, 278, 15482, 915, 297, 2740, 310, 278, 11409, 29875, 11822, 29889, 13, 1576, 1556, 17091, 11126, 292, 471, 297, 4275, 6813, 1192, 263, 451, 272, 17365, 9109, 7359, 363, 11409, 29875, 1370, 15116, 19016, 29892, 5034, 304, 278, 383, 12809, 2066, 29889, 1126, 577, 278, 383, 12809, 13916, 287, 263, 3815, 310, 402, 29899, 1527, 304, 23033, 13676, 515, 19656, 7456, 313, 13011, 11122, 297, 278, 383, 12809, 934, 29897, 322, 7417, 16277, 267, 13229, 5995, 292, 23151, 471, 297, 13798, 29889, 13, 1576, 13798, 15874, 11158, 5526, 287, 8335, 957, 29889, 512, 29871, 29896, 29929, 29946, 29946, 29892, 263, 1629, 1434, 23151, 29915, 29879, 8967, 4892, 29892, 8335, 957, 4520, 263, 6872, 393, 23151, 723, 7150, 25447, 297, 13798, 29892, 5034, 304, 263, 28742, 29889, 29871, 29946, 29892, 29871, 29896, 29929, 29946, 29946, 29892, 2626, 29877, 3971, 491, 385, 383, 12809, 10823, 29889, 450, 2626, 29877, 11682, 393, 9385, 457, 8604, 20251, 750, 13900, 304, 7512, 274, 1049, 342, 457, 5870, 886, 411, 23151, 376, 1454, 278, 3948, 9776, 310, 28348, 10188, 322, 5722, 14722, 964, 13798, 1213, 450, 2626, 29877, 11486, 393, 289, 4245, 2841, 2114, 3842, 727, 750, 1063, 11543, 304, 18577, 363, 12012, 3864, 286, 348, 2187, 322, 393, 263, 376, 16961, 17173, 29891, 5332, 784, 2592, 297, 13798, 2756, 4339, 14586, 355, 681, 24496, 29908, 408, 263, 25447, 363, 23151, 322, 670, 19061, 305, 1527, 29889, 376, 6716, 310, 278, 5144, 518, 974, 278, 1400, 4495, 5332, 715, 812, 414, 1402, 3917, 18624, 3074, 29892, 756, 1063, 5276, 408, 13598, 263, 6350, 305, 607, 723, 9080, 297, 13138, 263, 7359, 1213, 13, 3047, 262, 263, 1629, 16277, 267, 4689, 5685, 3689, 278, 383, 12809, 411, 23151, 11126, 886, 297, 13798, 29889, 3834, 310, 1438, 29892, 278, 383, 12809, 17903, 1891, 29892, 20601, 515, 4434, 417, 333, 3965, 13676, 5995, 292, 23151, 750, 19824, 322, 471, 10534, 363, 1370, 304, 2867, 714, 1546, 278, 15308, 7761, 322, 278, 3303, 3900, 1434, 11176, 3460, 408, 263, 11822, 297, 278, 716, 3186, 29889, 1126, 727, 892, 714, 1028, 4476, 11409, 29875, 17520, 19427, 1316, 408, 13832, 1976, 6618, 29892, 9556, 29915, 29879, 281, 442, 603, 3181, 28760, 304, 3444, 29892, 1045, 579, 292, 393, 23151, 376, 275, 8959, 451, 7123, 29908, 322, 471, 376, 1333, 263, 21282, 538, 1192, 306, 4658, 697, 2462, 540, 674, 736, 1213, 13, 1576, 1556, 4771, 1288, 5828, 7470, 5306, 29871, 29906, 29900, 29892, 29871, 29896, 29929, 29946, 29947, 29892, 297, 1260, 323, 3768, 1129, 29892, 263, 10432, 19656, 6369, 297, 21078, 29892, 5995, 292, 23151, 750, 19824, 3025, 1014, 24556, 304, 15872, 327, 30001, 29889, 450, 5650, 4944, 263, 13173, 3633, 310, 23151, 29915, 29879, 7424, 368, 21282, 538, 368, 16286, 322, 3576, 839, 437, 29920, 575, 310, 2788, 15874, 2820, 278, 3186, 29889, 9267, 310, 1906, 7470, 297, 278, 383, 12809, 2066, 408, 9335, 27775, 364, 9776, 515, 19726, 545, 2320, 834, 1475, 304, 278, 6853, 630, 5254, 29889, 13, 6716, 1316, 5828, 17049, 393, 278, 3925, 11696, 8900, 263, 22277, 2738, 343, 5860, 8401, 297, 322, 714, 310, 297, 10376, 373, 278, 4644, 14070, 470, 263, 16078, 713, 7751, 8967, 368, 269, 2960, 491, 385, 443, 1693, 2164, 1014, 24556, 8608, 292, 263, 6114, 777, 17049, 304, 367, 27040, 23514, 29892, 23151, 29915, 29879, 6532, 29889, 23514, 2982, 287, 515, 393, 1014, 24556, 1283, 278, 12180, 310, 13798, 29892, 697, 4274, 17049, 29889, 450, 1021, 4274, 7829, 263, 10369, 302, 5301, 13925, 12139, 750, 27886, 14561, 4902, 310, 263, 3814, 304, 3415, 22061, 403, 23151, 322, 23514, 304, 5546, 1156, 278, 6416, 310, 9556, 29889, 13, 29907, 5409, 261, 304, 3271, 263, 22277, 2738, 1014, 24556, 8967, 368, 471, 3595, 1048, 29871, 29896, 29892, 29941, 29900, 29900, 7800, 6641, 310, 11732, 1099, 29892, 3037, 361, 1696, 297, 263, 4423, 988, 450, 29221, 3872, 388, 29892, 263, 17173, 29891, 25749, 527, 18505, 29892, 24273, 29889, 7579, 304, 8014, 13676, 29892, 3872, 388, 471, 7602, 18186, 297, 29871, 29896, 29929, 29946, 29941, 408, 263, 1020, 2105, 363, 263, 4821, 6971, 5310, 476, 11124, 29892, 385, 19824, 11409, 29875, 29892, 322, 2360, 471, 1476, 29889, 13, 6246, 5642, 310, 1438, 13676, 13229, 1033, 367, 4153, 9024, 304, 23151, 322, 278, 383, 12809, 28424, 22834, 896, 892, 2362, 6393, 16558, 943, 29889, 3118, 10823, 13384, 19253, 297, 278, 2066, 393, 278, 10059, 10277, 8988, 1316, 16558, 272, 322, 297, 3433, 2765, 322, 521, 579, 3368, 385, 443, 17514, 9227, 29889, 13, 29950, 275, 19821, 338, 14154, 6460, 322, 540, 338, 6892, 5545, 304, 367, 263, 24452, 310, 278, 1556, 4771, 1288, 322, 443, 276, 492, 519, 5469, 29889, 13, 6716, 2769, 393, 23151, 29915, 29879, 4892, 471, 451, 13112, 363, 577, 1472, 471, 393, 278, 11688, 1039, 550, 23663, 2486, 411, 29882, 2495, 2472, 29892, 15873, 4367, 1470, 29889, 512, 2114, 29892, 372, 9007, 29915, 29873, 2745, 10637, 24452, 20708, 1522, 14022, 575, 1984, 5456, 263, 3143, 20512, 964, 4223, 297, 29871, 29896, 29929, 29953, 29947, 393, 278, 3122, 10972, 393, 278, 11688, 1039, 550, 8560, 1120, 3554, 583, 373, 14913, 267, 24776, 2610, 29871, 29906, 29892, 29871, 29896, 29929, 29946, 29945, 29892, 297, 4091, 340, 2646, 1960, 297, 263, 16423, 2978, 278, 5115, 289, 27560, 29889, 450, 17873, 892, 13112, 304, 367, 23151, 29892, 670, 6532, 322, 1009, 1023, 26361, 29889, 13, 1576, 3303, 3900, 471, 27343, 287, 491, 278, 5232, 10637, 20474, 800, 1192, 541, 278, 10637, 5874, 822, 2760, 967, 8820, 29892, 5934, 29871, 29941, 29900, 2440, 471, 2888, 653, 363, 1602, 605, 2450, 310, 22183, 1372, 29889, 25065, 29892, 472, 278, 612, 284, 941, 21362, 297, 29871, 29896, 29929, 29946, 29945, 29892, 624, 25977, 8052, 393, 23151, 750, 19824, 29889, 13, 29943, 332, 721, 4417, 304, 3133, 292, 8872, 293, 1080, 526, 278, 1120, 3554, 29891, 13676, 19813, 263, 4567, 1243, 2512, 322, 2428, 29888, 5611, 15303, 310, 1667, 3573, 1638, 550, 29889, 14598, 29892, 1522, 14022, 575, 1984, 1951, 756, 24084, 3192, 393, 278, 1120, 3554, 29891, 13676, 892, 2089, 29892, 23013, 901, 29236, 373, 23151, 29915, 29879 ]

1,332,826

14,336

CommonCrawl

8

11

death. Redlich says: This only confirms what Western historians and forensic experts suspected: that the Soviet investigation was fraught with deceit, secrecy and incompetence. Compounding the mystery was how Hitler died. It generally was believed by historians that Hitler bit down on a glass ampoule containing potassium cyanide while shooting himself in the head on April 30, 1945. But Redlich observes: The question can be raised as to whether Hitler's Parkinson's tremor would have allowed him to follow this procedure. Proving that theory ended after it was learned that Hitler's remains had been transferred nine times from one burial site to another and, finally, to the Lefortove prison in Moscow where they were cremated. It wasn't until 1973 when two Western experts in forensic dentistry compared Russian medical reports and X-rays of Hitler's teeth that it became evident that the corpse found outside the bunker indeed was the Führer. For Redlich and others that is enough proof. It is certain that Hitler, who at present would be over 100 years old, is dead and that he died by suicide. No serious student of history maintains that he escaped with the help of his paladins. Meanwhile, the definitive proof that the X-rays of the corpse provided by the Russians to that forensic dentistry team are legitimate, rests in a Russian classified vault. What's inside that archive? Hitler's lower jawbone. At least that's what the Russians claim. Such details no doubt are being added to Hitler's FBI file even now. The FBI believed that Nazi dictator Adolf Hitler faked his suicide in 1945, and tried to track him down for nearly 30 years after his death, according to de-classified files. On 29 April 1945, Hitler and his lover Eva Braun killed themselves in the Berlin bunker. Now, 66 years on, the FBI files reveal that the US agency had maintained a detailed dossier on the Fuhrer and closely investigated any report that indicated he still was alive. The files reveal how FBI agents ranch in Argentina, living in a hotel in Denmark and in New York City. He was bearded, clean-shaven, suffered from asthma and stomach ulcers, according to informants who wrote their sightings in to the then FBI director, J Edgar Hoover. The FBI office in Los Angeles noted on 21 Sept, 1945: "Hitler and 50 of his closest family landed approximately 10 days after the fall of Berlin in two submarines in southern Argentina. Hitler has grown a beard and is hiding on a ranch." One theory Hoover ordered his agents to pursue was an extensive 11-year probe into the possibility that Hitler faked his own death with a bogus suicide in 1945. One sighting came from a doctor in 1954 who claimed to have treated Hitler for an intestinal disorder in St Louis. Others told tales of Hitler dining in a Washington restaurant in 1946, The Scotsman reported. ~The Indian Express There always have been doubts as to Hitler's alleged suicide in his bunker in Berlin on April 30, 1945. The most authoritarian doubter was the Russian Dictator Josef Stalin who was convinced that Hitler escaped to Spain in April of 1945. Even if one takes the submitted Russian report on Hitler's autopsy at face value, there still remains the fact that there was no trace of the corpse of Eva Braun, Hitler's mistress and later wife. This alone disproves the double-suicide theory now part of German history. There never was an identifiable corpse of Adolf Hitler nor of Eva Braun. The whole suicide story of Hitler rests solely on the concocted testimony of four fanatical Nazis. The Russians found the buried (and un-burned) corpse of the double of Adolf Hitler near the bunker. An Argentinean researcher has now claimed that Adolf Hitler did not commit suicide in the bunker in Berlin, but in fact fled to Spain in 1945. Journalist Abel Basti is basing his claim on an FBI document published in 1947 saying the United States was looking for him in Spain, and says

0.354492

2.307831

0.049198

0.854935

[ 0.6058270410779377, 0.10315615863539264 ]

[ 2.451081713964118, 2.1645811409545628 ]

[ 0.43026778740868327, -0.3318726407192896 ]

[ 1.0448354673887195, 0.6650354082237983 ]

1,024

[ 512, 512 ]

[ 4892, 29889, 13, 9039, 1470, 4083, 29901, 13, 4013, 871, 12388, 1516, 825, 10504, 3603, 5834, 322, 363, 575, 293, 2902, 1372, 2858, 6021, 29901, 393, 278, 15308, 22522, 471, 5227, 688, 400, 411, 23332, 277, 29892, 22183, 1270, 322, 297, 2388, 300, 663, 29889, 13, 6843, 12449, 278, 29236, 471, 920, 23151, 6423, 29889, 739, 6892, 471, 13112, 491, 3603, 5834, 393, 23151, 2586, 1623, 373, 263, 12917, 21332, 283, 280, 6943, 3104, 465, 1974, 5094, 273, 680, 1550, 27904, 3654, 297, 278, 2343, 373, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29889, 1205, 4367, 1470, 5366, 1960, 29901, 13, 1576, 1139, 508, 367, 10425, 408, 304, 3692, 23151, 29915, 29879, 4815, 26803, 29915, 29879, 14586, 272, 723, 505, 6068, 1075, 304, 1101, 445, 8792, 29889, 13, 1184, 1747, 393, 6368, 9698, 1156, 372, 471, 10972, 393, 23151, 29915, 29879, 9242, 750, 1063, 18440, 14183, 3064, 515, 697, 6866, 616, 3268, 304, 1790, 322, 29892, 7146, 29892, 304, 278, 951, 3921, 994, 8475, 297, 25820, 988, 896, 892, 907, 29885, 630, 29889, 13, 3112, 9007, 29915, 29873, 2745, 29871, 29896, 29929, 29955, 29941, 746, 1023, 10504, 2902, 1372, 297, 363, 575, 293, 12042, 6020, 9401, 10637, 16083, 13676, 322, 1060, 29899, 764, 29879, 310, 23151, 29915, 29879, 25287, 393, 372, 3897, 13602, 393, 278, 1034, 27358, 1476, 5377, 278, 289, 27560, 6200, 471, 278, 383, 4000, 261, 29889, 1152, 4367, 1470, 322, 4045, 393, 338, 3307, 5296, 29889, 13, 3112, 338, 3058, 393, 23151, 29892, 1058, 472, 2198, 723, 367, 975, 29871, 29896, 29900, 29900, 2440, 2030, 29892, 338, 7123, 322, 393, 540, 6423, 491, 23921, 680, 29889, 1939, 10676, 8368, 310, 4955, 7344, 29879, 393, 540, 19824, 411, 278, 1371, 310, 670, 5112, 328, 1144, 29889, 13, 6816, 273, 8000, 29892, 278, 8422, 573, 5296, 393, 278, 1060, 29899, 764, 29879, 310, 278, 1034, 27358, 4944, 491, 278, 11688, 1039, 550, 304, 393, 363, 575, 293, 12042, 6020, 3815, 526, 25204, 6490, 29892, 1791, 29879, 297, 263, 10637, 770, 2164, 325, 1292, 29889, 1724, 29915, 29879, 2768, 393, 18871, 29973, 23151, 29915, 29879, 5224, 432, 1450, 15933, 29889, 2180, 3203, 393, 29915, 29879, 825, 278, 11688, 1039, 550, 5995, 29889, 10506, 4902, 694, 7404, 526, 1641, 2715, 304, 23151, 29915, 29879, 383, 12809, 934, 1584, 1286, 29889, 13, 1576, 383, 12809, 13112, 393, 11409, 29875, 9657, 1061, 21834, 23151, 285, 12535, 670, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29892, 322, 1898, 304, 5702, 1075, 1623, 363, 8886, 29871, 29941, 29900, 2440, 1156, 670, 4892, 29892, 5034, 304, 316, 29899, 1990, 2164, 2066, 29889, 13, 2951, 29871, 29906, 29929, 3786, 29871, 29896, 29929, 29946, 29945, 29892, 23151, 322, 670, 658, 369, 27040, 23514, 9445, 6053, 297, 278, 5115, 289, 27560, 29889, 2567, 29892, 29871, 29953, 29953, 2440, 373, 29892, 278, 383, 12809, 2066, 10320, 284, 393, 278, 3148, 946, 3819, 750, 19949, 263, 13173, 270, 2209, 631, 373, 278, 11871, 26768, 322, 16467, 7405, 630, 738, 3461, 393, 18694, 540, 1603, 471, 18758, 29889, 13, 1576, 2066, 10320, 284, 920, 383, 12809, 19518, 6350, 305, 297, 13798, 29892, 8471, 297, 263, 16730, 297, 3384, 3502, 322, 297, 1570, 3088, 4412, 29889, 940, 471, 367, 25600, 29892, 5941, 29899, 845, 3496, 29892, 17654, 515, 8717, 29882, 655, 322, 380, 290, 496, 9238, 22543, 29892, 5034, 304, 1871, 1934, 1058, 5456, 1009, 11126, 886, 297, 304, 278, 769, 383, 12809, 8881, 29892, 435, 2155, 5397, 8335, 957, 29889, 13, 1576, 383, 12809, 8034, 297, 4602, 10722, 11682, 373, 29871, 29906, 29896, 28742, 29892, 29871, 29896, 29929, 29946, 29945, 29901, 376, 29950, 277, 1358, 322, 29871, 29945, 29900, 310, 670, 21438, 3942, 2982, 287, 14235, 29871, 29896, 29900, 3841, 1156, 278, 6416, 310, 5115, 297, 1023, 1014, 3034, 1475, 297, 14841, 13798, 29889, 23151, 756, 21633, 263, 367, 538, 322, 338, 25508, 373, 263, 6350, 305, 1213, 13, 6716, 6368, 8335, 957, 10372, 670, 19518, 304, 12359, 434, 471, 385, 20607, 29871, 29896, 29896, 29899, 6360, 410, 915, 964, 278, 13331, 393, 23151, 285, 12535, 670, 1914, 4892, 411, 263, 26652, 375, 23921, 680, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 6716, 11126, 292, 2996, 515, 263, 11619, 297, 29871, 29896, 29929, 29945, 29946, 1058, 17049, 304, 505, 14914, 23151, 363, 385, 938, 342, 979, 766, 2098, 297, 624, 5899, 29889, 438, 3341, 5429, 29763, 310, 23151, 270, 2827, 297, 263, 7660, 27144, 297, 29871, 29896, 29929, 29946, 29953, 29892, 450, 2522, 1862, 1171, 8967, 29889, 13, 30022, 1576, 7560, 14657, 13, 8439, 2337, 505, 1063, 27455, 1372, 408, 304, 23151, 29915, 29879, 16831, 287, 23921, 680, 297, 670, 289, 27560, 297, 5115, 373, 3786, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29946, 29945, 29889, 450, 1556, 4148, 3673, 713, 27455, 357, 471, 278, 10637, 360, 919, 1061, 17374, 624, 25977, 1058, 471, 25617, 393, 23151, 19824, 304, 13616, 297, 3786, 310, 29871, 29896, 29929, 29946, 29945, 29889, 13, 29923, 854, 565, 697, 4893, 278, 18397, 10637, 3461, 373, 23151, 29915, 29879, 1120, 3554, 29891, 472, 3700, 995, 29892, 727, 1603, 9242, 278, 2114, 393, 727, 471, 694, 9637, 310, 278, 1034, 27358, 310, 27040, 23514, 29892, 23151, 29915, 29879, 5862, 1253, 322, 2678, 6532, 29889, 910, 7432, 766, 771, 1960, 278, 3765, 29899, 2146, 293, 680, 6368, 1286, 760, 310, 5332, 4955, 29889, 13, 8439, 2360, 471, 385, 2893, 28677, 1034, 27358, 310, 21834, 23151, 3643, 310, 27040, 23514, 29889, 450, 3353, 23921, 680, 5828, 310, 23151, 1791, 29879, 14419, 368, 373, 278, 378, 1111, 2954, 28523, 2592, 310, 3023, 13524, 271, 936, 11409, 275, 29889, 450, 11688, 1039, 550, 1476, 278, 18550, 313, 392, 443, 29899, 18712, 287, 29897, 1034, 27358, 310, 278, 3765, 310, 21834, 23151, 2978, 278, 289, 27560, 29889, 13, 2744, 9385, 457, 273, 5925, 261, 756, 1286, 17049, 393, 21834, 23151, 1258, 451, 9063, 23921, 680, 297, 278, 289, 27560, 297, 5115, 29892, 541, 297, 2114, 27481, 304, 13616, 297, 29871, 29896, 29929, 29946, 29945, 29889, 13, 29967, 4659, 391, 1976, 295, 25315, 29875, 338, 2362, 292, 670, 5995, 373, 385, 383, 12809, 1842, 6369, 297, 29871, 29896, 29929, 29946, 29955, 5934, 278, 3303, 3900, 471, 3063, 363, 1075, 297, 13616, 29892, 322, 4083 ]

1,332,826

15,360

CommonCrawl

8

11

Flexibility of deployment: challenges and policy options for retaining health workers during crisis in Zimbabwe Wilson Mashange1, Tim Martineau ORCID: orcid.org/0000-0003-4833-31492, Pamela Chandiwana1, Yotamu Chirwa1, Vongai Mildred Pepukai1, Shungu Munyati1 & Alvaro Alonso-Garbayo ORCID: orcid.org/0000-0002-4120-15412 Zimbabwe experienced a socio-economic crisis from 1997 to 2008 which heavily impacted all sectors. In this context, human resource managers were confronted with the challenge of health worker shortage in rural areas and, at the same time, had to operate under a highly centralised, government-centred system which defined health worker deployment policies. This study examines the implementation of deployment policies in Zimbabwe before, during and after the crisis in order to analyse how the official policy environment evolved over time, present the actual practices used by managers to cope with the crisis and draw lessons. 'Deployment' here was considered to include all the human resource management functions for getting staff into posts and managing subsequent movements: recruitment, bonding, transfer and secondment. The study contributes to address the existing paucity of evidence on flexibility on implementation of policies in crisis/conflict settings. This retrospective study investigates deployment policies in government and faith-based organisation health facilities in Zimbabwe before, during and after the crisis. A document review was done to understand the policy environment. In-depth interviews with key informant including policy makers, managers and health workers in selected facilities in three mainly rural districts in the Midlands province were conducted. Data generated was analysed using a framework approach. Before the crisis, health workers were allowed to look for jobs on their own, while during the crisis, they were given three choices and after the crisis the preference choice was withdrawn. The government froze recruitment in all sectors during the crisis which severely affected health workers' deployment. In practice, the implementation of the deployment policies was relatively flexible. In some cases, health workers were transferred to retain them, the recruitment freeze was temporarily lifted to fill priority vacancies, the length of the bonding period was reduced including relaxation of withholding certificates, and managers used secondment to relocate workers to priority areas. Flexibility in the implementation of deployment policies during crises may increase the resilience of the system and contribute to the retention of health workers. This, in turn, may assist in ensuring coverage of health services in hard-to-reach areas. Scaling up the healthcare workforce as well as improving distribution, management, performance and quality were solutions proposed to address human resources for health (HRH) crisis in the last decade [1, 2]. The inequitable distribution of HRH, especially between urban and rural areas, and the problems related to filling posts in remote areas have been identified as barriers in the provision of healthcare and the achievement of the health-related Sustainable Development Goal [3]. This is particularly prevalent in post conflict and crisis-affected settings [4, 5]. Much research has already been devoted to understanding health worker (HW) behaviour in relation to taking up and remaining in posts in rural/remote locations [6, 7]. Additionally, research has shown that the problem of mal-distribution of HRH is often made worse by the mismanagement of deployment systems [8, 9]. The term 'deployment' is frequently used in relation to distribution of staff, but rarely defined. More specifically, deployment is defined as 'the movement of staff from one's current assignment to another, to meet operational needs' [10] or simply 'the transfer of a person from one position to another' [11]. In this study, however, we define deployment as a 'bundle' of human resource management functions for getting staff into posts and managing subsequent movements including recruitment, reappointment, bonding, secondment and transfer [12]. Within a country's healthcare system and regulations, each of these human resource management (HRM) functions is governed by a set of policies which are sometimes official and explicit, but in other cases, they remain unwritten rules. In this paper, we explore the official policies and the informal practices that rule deployment of HWs in Zimbabwe, with

0.44626

0.989929

1.673026

1.102066

[ 0.08398070262941, 0.8085390045697542 ]

[ 0.7535658188825048, 1.2262917643482705 ]

[ 1.3280971103947146, 2.0179546692992356 ]

[ 1.0136190241696847, 1.190512202410881 ]

1,024

[ 512, 512 ]

[ 383, 2506, 4127, 310, 18209, 29901, 18066, 267, 322, 8898, 3987, 363, 11551, 292, 9045, 17162, 2645, 24161, 297, 796, 19977, 370, 705, 13, 29594, 1100, 341, 1161, 927, 29896, 29892, 13, 13711, 3760, 457, 585, 6323, 29907, 1367, 29901, 470, 25232, 29889, 990, 29914, 29900, 29900, 29900, 29900, 29899, 29900, 29900, 29900, 29941, 29899, 29946, 29947, 29941, 29941, 29899, 29941, 29896, 29946, 29929, 29906, 29892, 13, 29925, 314, 3100, 678, 392, 9429, 1648, 29896, 29892, 13, 29979, 327, 314, 29884, 678, 381, 2766, 29896, 29892, 13, 29963, 549, 1794, 341, 789, 1127, 349, 1022, 22971, 29875, 29896, 29892, 13, 2713, 686, 29884, 13564, 29891, 2219, 29896, 669, 13, 2499, 1707, 29877, 838, 16911, 29899, 29954, 279, 27495, 29877, 6323, 29907, 1367, 29901, 470, 25232, 29889, 990, 29914, 29900, 29900, 29900, 29900, 29899, 29900, 29900, 29900, 29906, 29899, 29946, 29896, 29906, 29900, 29899, 29896, 29945, 29946, 29896, 29906, 13, 29999, 19977, 370, 705, 18860, 263, 577, 3934, 29899, 29872, 4599, 293, 24161, 515, 29871, 29896, 29929, 29929, 29955, 304, 29871, 29906, 29900, 29900, 29947, 607, 20365, 10879, 287, 599, 409, 14359, 29889, 512, 445, 3030, 29892, 5199, 6503, 767, 18150, 892, 21751, 287, 411, 278, 18766, 310, 9045, 15645, 3273, 482, 297, 17692, 10161, 322, 29892, 472, 278, 1021, 931, 29892, 750, 304, 21994, 1090, 263, 10712, 6555, 3368, 29892, 5874, 29899, 1760, 1127, 1788, 607, 3342, 9045, 15645, 18209, 24833, 29889, 910, 6559, 4392, 1475, 278, 5314, 310, 18209, 24833, 297, 796, 19977, 370, 705, 1434, 29892, 2645, 322, 1156, 278, 24161, 297, 1797, 304, 16455, 344, 920, 278, 6221, 8898, 5177, 15220, 1490, 975, 931, 29892, 2198, 278, 3935, 23274, 1304, 491, 767, 18150, 304, 1302, 412, 411, 278, 24161, 322, 4216, 3109, 787, 29889, 525, 8498, 22812, 29915, 1244, 471, 5545, 304, 3160, 599, 278, 5199, 6503, 10643, 3168, 363, 2805, 13925, 964, 11803, 322, 767, 6751, 15352, 24147, 29901, 1162, 9216, 358, 29892, 21224, 292, 29892, 6782, 322, 1473, 358, 29889, 450, 6559, 640, 5026, 304, 3211, 278, 5923, 24571, 12690, 310, 10757, 373, 8525, 4127, 373, 5314, 310, 24833, 297, 24161, 29914, 5527, 29176, 6055, 29889, 13, 4013, 3240, 1883, 12645, 6559, 7405, 1078, 18209, 24833, 297, 5874, 322, 10847, 29899, 6707, 24788, 9045, 23330, 297, 796, 19977, 370, 705, 1434, 29892, 2645, 322, 1156, 278, 24161, 29889, 319, 1842, 9076, 471, 2309, 304, 2274, 278, 8898, 5177, 29889, 512, 29899, 19488, 1006, 7406, 411, 1820, 1871, 424, 3704, 8898, 2136, 414, 29892, 767, 18150, 322, 9045, 17162, 297, 4629, 23330, 297, 2211, 14364, 17692, 24172, 297, 278, 13370, 5252, 12291, 892, 18043, 29889, 3630, 5759, 471, 3483, 952, 287, 773, 263, 6890, 2948, 29889, 13, 18743, 278, 24161, 29892, 9045, 17162, 892, 6068, 304, 1106, 363, 17643, 373, 1009, 1914, 29892, 1550, 2645, 278, 24161, 29892, 896, 892, 2183, 2211, 19995, 322, 1156, 278, 24161, 278, 24583, 7348, 471, 411, 19811, 1233, 29889, 450, 5874, 14671, 911, 1162, 9216, 358, 297, 599, 409, 14359, 2645, 278, 24161, 607, 2775, 873, 15201, 9045, 17162, 29915, 18209, 29889, 512, 6944, 29892, 278, 5314, 310, 278, 18209, 24833, 471, 13774, 25706, 29889, 512, 777, 4251, 29892, 9045, 17162, 892, 18440, 304, 11551, 963, 29892, 278, 1162, 9216, 358, 3889, 911, 471, 5382, 6275, 26239, 304, 5445, 20136, 11757, 273, 2478, 29892, 278, 3309, 310, 278, 21224, 292, 3785, 471, 12212, 3704, 26681, 362, 310, 411, 8948, 292, 23199, 1078, 29892, 322, 767, 18150, 1304, 1473, 358, 304, 337, 2029, 403, 17162, 304, 20136, 10161, 29889, 13, 29943, 2506, 4127, 297, 278, 5314, 310, 18209, 24833, 2645, 2181, 4637, 1122, 7910, 278, 620, 2638, 663, 310, 278, 1788, 322, 29126, 304, 278, 3240, 2509, 310, 9045, 17162, 29889, 910, 29892, 297, 2507, 29892, 1122, 6985, 297, 5662, 3864, 23746, 310, 9045, 5786, 297, 2898, 29899, 517, 29899, 276, 496, 10161, 29889, 13, 29636, 292, 701, 278, 9045, 18020, 664, 10118, 408, 1532, 408, 4857, 1747, 4978, 29892, 10643, 29892, 4180, 322, 11029, 892, 6851, 7972, 304, 3211, 5199, 7788, 363, 9045, 313, 20938, 29950, 29897, 24161, 297, 278, 1833, 316, 6332, 518, 29896, 29892, 29871, 29906, 1822, 450, 297, 1686, 8270, 4978, 310, 379, 29934, 29950, 29892, 7148, 1546, 17164, 322, 17692, 10161, 29892, 322, 278, 4828, 4475, 304, 27523, 11803, 297, 7592, 10161, 505, 1063, 15659, 408, 2594, 26536, 297, 278, 25161, 310, 9045, 18020, 322, 278, 27012, 882, 310, 278, 9045, 29899, 12817, 317, 504, 475, 519, 14650, 2921, 284, 518, 29941, 1822, 910, 338, 10734, 758, 791, 296, 297, 1400, 14529, 322, 24161, 29899, 3470, 26458, 6055, 518, 29946, 29892, 29871, 29945, 1822, 13, 29924, 987, 5925, 756, 2307, 1063, 24600, 304, 8004, 9045, 15645, 313, 29950, 29956, 29897, 10468, 297, 8220, 304, 5622, 701, 322, 9886, 297, 11803, 297, 17692, 29914, 16674, 14354, 518, 29953, 29892, 29871, 29955, 1822, 19814, 29892, 5925, 756, 4318, 393, 278, 1108, 310, 4439, 29899, 27691, 310, 379, 29934, 29950, 338, 4049, 1754, 15029, 491, 278, 3984, 21895, 310, 18209, 6757, 518, 29947, 29892, 29871, 29929, 1822, 450, 1840, 525, 16519, 358, 29915, 338, 13672, 1304, 297, 8220, 304, 4978, 310, 13925, 29892, 541, 23703, 3342, 29889, 5853, 10816, 29892, 18209, 338, 3342, 408, 525, 1552, 10298, 310, 13925, 515, 697, 29915, 29879, 1857, 12827, 304, 1790, 29892, 304, 5870, 1751, 1288, 4225, 29915, 518, 29896, 29900, 29962, 470, 3763, 525, 1552, 6782, 310, 263, 2022, 515, 697, 2602, 304, 1790, 29915, 518, 29896, 29896, 1822, 512, 445, 6559, 29892, 3138, 29892, 591, 4529, 18209, 408, 263, 525, 16718, 29915, 310, 5199, 6503, 10643, 3168, 363, 2805, 13925, 964, 11803, 322, 767, 6751, 15352, 24147, 3704, 1162, 9216, 358, 29892, 337, 932, 2461, 358, 29892, 21224, 292, 29892, 1473, 358, 322, 6782, 518, 29896, 29906, 1822, 23732, 263, 4234, 29915, 29879, 9045, 18020, 1788, 322, 1072, 8250, 29892, 1269, 310, 1438, 5199, 6503, 10643, 313, 20938, 29924, 29897, 3168, 338, 4095, 287, 491, 263, 731, 310, 24833, 607, 526, 6041, 6221, 322, 6261, 29892, 541, 297, 916, 4251, 29892, 896, 3933, 443, 17625, 6865, 29889, 512, 445, 5650, 29892, 591, 26987, 278, 6221, 24833, 322, 278, 1871, 284, 23274, 393, 5751, 18209, 310, 379, 29956, 29879, 297, 796, 19977, 370, 705, 29892, 411 ]

1,332,829

0

CommonCrawl

6

2

the aim of reviewing the changes in deployment policies and the implementation practices during the crisis and post-crisis periods. Zimbabwe experienced a decade of severe economic, social and political crisis between 1997 and 2008. The crisis led to a reversal of gains made in key health indicators including immunisation, maternal mortality or infant mortality [13,14,15,16] and had an important impact on the health workforce. While out-migration of HWs was reported before 1997 [17, 18], it increased substantially during the crisis leaving the staffing situation severely deteriorated with high vacancy rates which peaked between 2008 and 2009 reaching up to 43% [13, 15, 19]. Prior to 2005, the health services in Zimbabwe were delivered through facilities run separately by government, faith-based organisations (FBOs) or private sector. Government hospitals and primary healthcare facilities are managed either by the Ministry of Health and Child Care (MOHCC) or Ministry of Local and Urban Development [20]. The Zimbabwe Association of Church Related Hospitals manages church-related health providers in coordination with the MOHCC particularly for issues related to their workforce. The majority of FBO facilities operate in rural settings [21] while government run facilities cover both urban and rural areas. In 2005, Government of Zimbabwe decided to unify health services provided by both government and FBOs. The Health Services Board (HSB) was established through the Health Act of 2004 which resulted in both government and FBO health service providers being under one central authority. Due to the enactment of the Health Services Regulations (HSR) in 2006, the deployment of government HWs employed in government and FBO facilities should be managed by MOHCC through the HSB. However, implementation of the new policy was uneven. Service contracts between MOHCC and FBOs were not implemented in all provinces simultaneously [14] which resulted in the uneven adoption of the terms comprised in the new regulation [22] particularly in those related to staff recruitment and deployment by health services managed by FBOs. This retrospective study looks at changes in deployment policies and practices in Zimbabwe's health sector during the pre-crisis period (1980–1997), crisis period (1997–2008) and the post-crisis period (2009–2013). There is little evidence of flexibility of these policies and practices in time of conflict or crisis [23] with the exception of post-conflict Timor Leste [24, 25]. This study sought to contribute to this evidence. This retrospective qualitative study was undertaken in two healthcare providers (FBOs and Government) in three largely rural districts in Zimbabwe where implementation of deployment policies and practices was explored. Data was collected through interviews with key informants involved in policy development and with managers and HWs involved in their implementation. Narratives about the life of HWs were used to generate data about the impact that changes in HRH deployment systems and practices have on their professional trajectory and experiences [26]. A total of 76 documents were extracted from published and unpublished literature and analysed using content analysis to explore the evolution of deployment policies including the rationale for changes. The study focuses on four main HRM functions related to deployment: recruitment, bonding, transfer and secondment. We define recruitment as the process of attracting the right people and selecting and offering employment to the best candidates. We have also included here appointment, which in this study refers to the allocation of a position to a HW when entering the health workforce for the first time. We consider bonding as the formal agreement with the government comprising compulsory service that newly graduated HWs who were beneficiaries of public financial support for their studies agree to provide after graduation to compensate for the government's investment. Transfer in this study refers to the process of moving HWs from one post to another and secondment, which is often considered as a modality of transfer, refers in this study to the temporary transfer of workers to another post for a limited period for a specific reason. The study was undertaken in three largely rural districts of the Midlands province. The districts are referred to numerically in this paper as districts 1, 2

0.437357

1.552186

1.693316

1.247742

[ 0.40585442844411873, 0.4688594981780617 ]

[ 1.4698172514063923, 1.6345550808868863 ]

[ 1.5614312847300673, 1.8252003513700312 ]

[ 1.1488902781188348, 1.3465944185060539 ]

1,024

[ 512, 512 ]

[ 278, 12242, 310, 9076, 292, 278, 3620, 297, 18209, 24833, 322, 278, 5314, 23274, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 29889, 13, 29999, 19977, 370, 705, 18860, 263, 316, 6332, 310, 22261, 17407, 29892, 5264, 322, 8604, 24161, 1546, 29871, 29896, 29929, 29929, 29955, 322, 29871, 29906, 29900, 29900, 29947, 29889, 450, 24161, 5331, 304, 263, 18764, 284, 310, 330, 2708, 1754, 297, 1820, 9045, 4221, 4097, 3704, 5198, 348, 4371, 29892, 1775, 17196, 5758, 2877, 470, 28056, 5758, 2877, 518, 29896, 29941, 29892, 29896, 29946, 29892, 29896, 29945, 29892, 29896, 29953, 29962, 322, 750, 385, 4100, 10879, 373, 278, 9045, 664, 10118, 29889, 5806, 714, 29899, 29885, 16783, 310, 379, 29956, 29879, 471, 8967, 1434, 29871, 29896, 29929, 29929, 29955, 518, 29896, 29955, 29892, 29871, 29896, 29947, 1402, 372, 11664, 23228, 368, 2645, 278, 24161, 10124, 278, 13925, 292, 6434, 2775, 873, 270, 1308, 1611, 630, 411, 1880, 11757, 6906, 19257, 607, 1236, 12535, 1546, 29871, 29906, 29900, 29900, 29947, 322, 29871, 29906, 29900, 29900, 29929, 20888, 701, 304, 29871, 29946, 29941, 29995, 518, 29896, 29941, 29892, 29871, 29896, 29945, 29892, 29871, 29896, 29929, 1822, 13, 29925, 13479, 304, 29871, 29906, 29900, 29900, 29945, 29892, 278, 9045, 5786, 297, 796, 19977, 370, 705, 892, 20115, 1549, 23330, 1065, 16949, 491, 5874, 29892, 10847, 29899, 6707, 17459, 800, 313, 29943, 8456, 29879, 29897, 470, 2024, 17535, 29889, 10354, 29418, 277, 1338, 322, 7601, 9045, 18020, 23330, 526, 8745, 2845, 491, 278, 20886, 310, 15202, 322, 10517, 10057, 313, 6720, 29950, 4174, 29897, 470, 20886, 310, 9959, 322, 22589, 14650, 518, 29906, 29900, 1822, 450, 796, 19977, 370, 705, 7993, 310, 6291, 6376, 630, 379, 4705, 277, 1338, 767, 1179, 6586, 29899, 12817, 9045, 1326, 11376, 297, 29311, 3381, 411, 278, 16999, 29950, 4174, 10734, 363, 5626, 4475, 304, 1009, 664, 10118, 29889, 450, 13638, 310, 383, 8456, 23330, 21994, 297, 17692, 6055, 518, 29906, 29896, 29962, 1550, 5874, 1065, 23330, 4612, 1716, 17164, 322, 17692, 10161, 29889, 13, 797, 29871, 29906, 29900, 29900, 29945, 29892, 10354, 310, 796, 19977, 370, 705, 8459, 304, 443, 1598, 9045, 5786, 4944, 491, 1716, 5874, 322, 383, 8456, 29879, 29889, 450, 15202, 15538, 12590, 313, 29950, 1744, 29897, 471, 7841, 1549, 278, 15202, 3185, 310, 29871, 29906, 29900, 29900, 29946, 607, 20601, 297, 1716, 5874, 322, 383, 8456, 9045, 2669, 1326, 11376, 1641, 1090, 697, 6555, 14329, 29889, 16809, 304, 278, 427, 627, 358, 310, 278, 15202, 15538, 2169, 8250, 313, 29950, 14098, 29897, 297, 29871, 29906, 29900, 29900, 29953, 29892, 278, 18209, 310, 5874, 379, 29956, 29879, 15723, 297, 5874, 322, 383, 8456, 23330, 881, 367, 8745, 491, 16999, 29950, 4174, 1549, 278, 379, 1744, 29889, 2398, 29892, 5314, 310, 278, 716, 8898, 471, 1597, 854, 29889, 6692, 8078, 29879, 1546, 16999, 29950, 4174, 322, 383, 8456, 29879, 892, 451, 8762, 297, 599, 28058, 21699, 518, 29896, 29946, 29962, 607, 20601, 297, 278, 1597, 854, 594, 3385, 310, 278, 4958, 7199, 3368, 297, 278, 716, 1072, 2785, 518, 29906, 29906, 29962, 10734, 297, 1906, 4475, 304, 13925, 1162, 9216, 358, 322, 18209, 491, 9045, 5786, 8745, 491, 383, 8456, 29879, 29889, 910, 3240, 1883, 12645, 6559, 3430, 472, 3620, 297, 18209, 24833, 322, 23274, 297, 796, 19977, 370, 705, 29915, 29879, 9045, 17535, 2645, 278, 758, 29899, 29883, 3780, 275, 3785, 313, 29896, 29929, 29947, 29900, 29994, 29896, 29929, 29929, 29955, 511, 24161, 3785, 313, 29896, 29929, 29929, 29955, 29994, 29906, 29900, 29900, 29947, 29897, 322, 278, 1400, 29899, 29883, 3780, 275, 3785, 313, 29906, 29900, 29900, 29929, 29994, 29906, 29900, 29896, 29941, 467, 13, 8439, 338, 2217, 10757, 310, 8525, 4127, 310, 1438, 24833, 322, 23274, 297, 931, 310, 14529, 470, 24161, 518, 29906, 29941, 29962, 411, 278, 3682, 310, 1400, 29899, 5527, 29176, 7870, 272, 365, 4196, 518, 29906, 29946, 29892, 29871, 29906, 29945, 1822, 910, 6559, 18365, 304, 29126, 304, 445, 10757, 29889, 13, 4013, 3240, 1883, 12645, 4021, 23378, 6559, 471, 22332, 9424, 297, 1023, 9045, 18020, 1326, 11376, 313, 29943, 8456, 29879, 322, 10354, 29897, 297, 2211, 18425, 17692, 24172, 297, 796, 19977, 370, 705, 988, 5314, 310, 18209, 24833, 322, 23274, 471, 3902, 4395, 29889, 3630, 471, 16531, 1549, 1006, 7406, 411, 1820, 1871, 1934, 9701, 297, 8898, 5849, 322, 411, 767, 18150, 322, 379, 29956, 29879, 9701, 297, 1009, 5314, 29889, 405, 2749, 5056, 1048, 278, 2834, 310, 379, 29956, 29879, 892, 1304, 304, 5706, 848, 1048, 278, 10879, 393, 3620, 297, 379, 29934, 29950, 18209, 6757, 322, 23274, 505, 373, 1009, 10257, 23324, 706, 322, 27482, 518, 29906, 29953, 1822, 13, 29909, 3001, 310, 29871, 29955, 29953, 10701, 892, 23892, 515, 6369, 322, 443, 5467, 3726, 12845, 322, 3483, 952, 287, 773, 2793, 7418, 304, 26987, 278, 14675, 310, 18209, 24833, 3704, 278, 364, 11464, 363, 3620, 29889, 13, 1576, 6559, 8569, 267, 373, 3023, 1667, 379, 29934, 29924, 3168, 4475, 304, 18209, 29901, 1162, 9216, 358, 29892, 21224, 292, 29892, 6782, 322, 1473, 358, 29889, 1334, 4529, 1162, 9216, 358, 408, 278, 1889, 310, 13978, 292, 278, 1492, 2305, 322, 18851, 322, 27032, 5703, 358, 304, 278, 1900, 21669, 29889, 1334, 505, 884, 5134, 1244, 28573, 29892, 607, 297, 445, 6559, 14637, 304, 278, 24082, 310, 263, 2602, 304, 263, 379, 29956, 746, 18055, 278, 9045, 664, 10118, 363, 278, 937, 931, 29889, 1334, 2050, 21224, 292, 408, 278, 11595, 17327, 411, 278, 5874, 7199, 5921, 752, 7273, 706, 2669, 393, 15141, 23588, 379, 29956, 29879, 1058, 892, 7795, 1654, 4314, 310, 970, 18161, 2304, 363, 1009, 11898, 8661, 304, 3867, 1156, 10591, 362, 304, 22874, 403, 363, 278, 5874, 29915, 29879, 13258, 358, 29889, 17934, 297, 445, 6559, 14637, 304, 278, 1889, 310, 8401, 379, 29956, 29879, 515, 697, 1400, 304, 1790, 322, 1473, 358, 29892, 607, 338, 4049, 5545, 408, 263, 878, 2877, 310, 6782, 29892, 14637, 297, 445, 6559, 304, 278, 13201, 6782, 310, 17162, 304, 1790, 1400, 363, 263, 9078, 3785, 363, 263, 2702, 2769, 29889, 13, 1576, 6559, 471, 22332, 9424, 297, 2211, 18425, 17692, 24172, 310, 278, 13370, 5252, 12291, 29889, 450, 24172, 526, 12992, 304, 4825, 1711, 297, 445, 5650, 408, 24172, 29871, 29896, 29892, 29871, 29906 ]

1,332,829

1,024

CommonCrawl

6

2

and 3. The major providers of healthcare in the selected districts are government and a large FBO which owns 52% of the faith-based hospitals in the country (Table 1). Government-run facilities in this study are comprised of those managed by HSB and rural district councils (RDC). Table 1 Population and numbers of facilities by ownership in study districts A total of 17 key informant interviews (KIIs) from national and local levels for both government and FBOs were purposively selected according to their knowledge and experience of policy development relating to deployment (Table 2). Table 2 Number of key informant interviews The overall manager and the officer responsible for HRM including deployment at facilities were selected in each study district for interviews and asked questions mainly about deployment practices. A total of 11 in-depth interviews (IDI) were carried out at both government and FBO institutions (Table 3). Table 3 Distribution of IDIs with facility managers by sector and gender A total of 67 interviews with midwives, nurses and environmental health practitioners (42 females and 25 males) working in the three different sectors with different lengths of service (11 < 5 years; 56 ≥ 5 years) were conducted (Table 4) using the 'life history' technique to elicit their views and perspectives [26]. Table 4 Distribution of IDIs with HWs by sector and gender Separate topic guides for semi-structured interviews for each group were developed and used flexibly as a guide for the interviewer allowing for new emerging thematic areas introduced by interviewees. The interviews for the KIIs lasted an average of 25 min while those for managers and health workers interviews with life histories lasted between 30 and 45 min. During data collection, researchers met on daily basis to discuss the emerging themes assessing whether research questions were being answered. Saturation was achieved with the initially planned interview schedule with no need for further additional interviews [27]. All interviews were transcribed verbatim and checked for accuracy by a second transcriber. Transcriptions of the combined set on interviews were analysed using a framework approach [28]. A coding framework was initially developed based on the document review, key research questions and new themes emerging during the analysis were added. All transcriptions were coded using the developed coding framework. The data was managed using NVIVO qualitative analysis software version 10. Recruitment and appointment Initial policies and further adaptations Recruitment in Zimbabwe is regulated through the Public Service Regulations (PSR), 2000 sections 2 and 3/1a-d [29]. These policies envisage that recruitment should be merit-based on the applicant's knowledge about their tasks and their ability to perform them. Appointments can be either under 'indefinite pensionable conditions' or 'temporary' to fill casual vacancies or supernumerary posts. All appointments should follow principles of equality of fair competition among candidates and need to be included in the Estimates of Expenditure approved by the Ministry of Finance each fiscal year. To confirm the suitability of new workers, they need to go through a probation period which initially was not less than 1 year after which and, if satisfactory, appointment was confirmed. With the introduction of HSR 2006, recruitment responsibility for the health sector was shifted to the HSB [22]. Besides merit, HSR 2006 introduced criteria of professional and moral standing and considered apprenticeship for individuals less than 18 years (previously not allowed under PSR 2000) as legal to allow health professional students to undertake their required internships to complete their studies. In order to address the high attrition from the public to the private sector observed after Independence, the new regulation provided greater flexibility for dual practice allowing HSB to authorise specific workers to devote part of their time to private practice and reducing the minimum probation period from 1 year to 6 months. Implementation practices During the pre-crisis period, HWs would search for jobs on their own after training. From 1992 to 1995 I did my nursing training as an RGN at Harare central hospital […] we were not being deployed. Each person would look for his/her own place (HW Gvt District 3).

-0.394721

0.889654

1.287517

0.971997

[ -0.5474396701390185, -0.24200204947229498 ]

[ 1.1689916497463595, 0.6103155323777273 ]

[ 1.388966895003937, 1.1860676129731955 ]

[ 1.096862872753777, 0.8471313270015002 ]

1,024

[ 512, 512 ]

[ 322, 29871, 29941, 29889, 450, 4655, 1326, 11376, 310, 9045, 18020, 297, 278, 4629, 24172, 526, 5874, 322, 263, 2919, 383, 8456, 607, 1914, 29879, 29871, 29945, 29906, 29995, 310, 278, 10847, 29899, 6707, 29418, 277, 1338, 297, 278, 4234, 313, 3562, 29871, 29896, 467, 10354, 29899, 3389, 23330, 297, 445, 6559, 526, 7199, 3368, 310, 1906, 8745, 491, 379, 1744, 322, 17692, 6474, 2613, 29883, 2719, 313, 29934, 12696, 467, 13, 3562, 29871, 29896, 24810, 322, 3694, 310, 23330, 491, 27428, 297, 6559, 24172, 13, 29909, 3001, 310, 29871, 29896, 29955, 1820, 1871, 424, 1006, 7406, 313, 29968, 2687, 29879, 29897, 515, 4797, 322, 1887, 11174, 363, 1716, 5874, 322, 383, 8456, 29879, 892, 3708, 1066, 3598, 4629, 5034, 304, 1009, 7134, 322, 7271, 310, 8898, 5849, 1104, 1218, 304, 18209, 313, 3562, 29871, 29906, 467, 13, 3562, 29871, 29906, 9681, 310, 1820, 1871, 424, 1006, 7406, 13, 1576, 12463, 8455, 322, 278, 12139, 14040, 363, 379, 29934, 29924, 3704, 18209, 472, 23330, 892, 4629, 297, 1269, 6559, 6474, 363, 1006, 7406, 322, 4433, 5155, 14364, 1048, 18209, 23274, 29889, 319, 3001, 310, 29871, 29896, 29896, 297, 29899, 19488, 1006, 7406, 313, 1367, 29902, 29897, 892, 8988, 714, 472, 1716, 5874, 322, 383, 8456, 21561, 313, 3562, 29871, 29941, 467, 13, 3562, 29871, 29941, 17740, 310, 3553, 3624, 411, 24454, 767, 18150, 491, 17535, 322, 23346, 13, 29909, 3001, 310, 29871, 29953, 29955, 1006, 7406, 411, 7145, 29893, 3145, 29892, 302, 1295, 267, 322, 29380, 9045, 4120, 654, 414, 313, 29946, 29906, 24473, 322, 29871, 29906, 29945, 25269, 29897, 1985, 297, 278, 2211, 1422, 409, 14359, 411, 1422, 27497, 310, 2669, 313, 29896, 29896, 529, 30080, 29945, 30080, 6360, 29879, 29936, 29871, 29945, 29953, 29871, 30386, 30080, 29945, 30080, 6360, 29879, 29897, 892, 18043, 313, 3562, 29871, 29946, 29897, 773, 278, 525, 19264, 4955, 29915, 11043, 304, 560, 293, 277, 1009, 8386, 322, 3736, 1103, 3145, 518, 29906, 29953, 1822, 13, 3562, 29871, 29946, 17740, 310, 3553, 3624, 411, 379, 29956, 29879, 491, 17535, 322, 23346, 13, 2008, 862, 403, 11261, 1410, 2247, 363, 12647, 29899, 4984, 2955, 1006, 7406, 363, 1269, 2318, 892, 8906, 322, 1304, 8525, 14981, 408, 263, 10754, 363, 278, 1006, 29894, 15580, 14372, 363, 716, 11176, 3460, 963, 2454, 10161, 9129, 491, 15593, 12712, 29889, 450, 1006, 7406, 363, 278, 476, 2687, 29879, 1833, 287, 385, 6588, 310, 29871, 29906, 29945, 30080, 1195, 1550, 1906, 363, 767, 18150, 322, 9045, 17162, 1006, 7406, 411, 2834, 3603, 583, 1833, 287, 1546, 29871, 29941, 29900, 322, 29871, 29946, 29945, 30080, 1195, 29889, 7133, 848, 4333, 29892, 5925, 414, 1539, 373, 14218, 8405, 304, 5353, 278, 11176, 3460, 963, 267, 24809, 292, 3692, 5925, 5155, 892, 1641, 7699, 29889, 317, 1337, 362, 471, 14363, 411, 278, 12919, 20458, 15593, 20410, 411, 694, 817, 363, 4340, 5684, 1006, 7406, 518, 29906, 29955, 1822, 2178, 1006, 7406, 892, 1301, 23059, 9750, 271, 326, 322, 7120, 363, 13600, 491, 263, 1473, 1301, 699, 495, 29889, 4103, 699, 1980, 310, 278, 12420, 731, 373, 1006, 7406, 892, 3483, 952, 287, 773, 263, 6890, 2948, 518, 29906, 29947, 1822, 319, 14137, 6890, 471, 12919, 8906, 2729, 373, 278, 1842, 9076, 29892, 1820, 5925, 5155, 322, 716, 963, 267, 11176, 3460, 2645, 278, 7418, 892, 2715, 29889, 2178, 1301, 699, 1980, 892, 274, 6797, 773, 278, 8906, 14137, 6890, 29889, 450, 848, 471, 8745, 773, 405, 29963, 5667, 29949, 4021, 23378, 7418, 7047, 1873, 29871, 29896, 29900, 29889, 13, 4789, 9216, 358, 322, 28573, 13, 15514, 24833, 322, 4340, 7744, 800, 13, 4789, 9216, 358, 297, 796, 19977, 370, 705, 338, 1072, 7964, 1549, 278, 5236, 6692, 2169, 8250, 313, 7024, 29934, 511, 29871, 29906, 29900, 29900, 29900, 13926, 29871, 29906, 322, 29871, 29941, 29914, 29896, 29874, 29899, 29881, 518, 29906, 29929, 1822, 4525, 24833, 427, 1730, 482, 393, 1162, 9216, 358, 881, 367, 2778, 277, 29899, 6707, 373, 278, 15576, 424, 29915, 29879, 7134, 1048, 1009, 9595, 322, 1009, 11509, 304, 2189, 963, 29889, 2401, 2461, 1860, 508, 367, 2845, 1090, 525, 262, 25476, 568, 282, 2673, 519, 5855, 29915, 470, 525, 1356, 1971, 653, 29915, 304, 5445, 3209, 950, 11757, 273, 2478, 470, 2428, 8058, 653, 11803, 29889, 2178, 8167, 1860, 881, 1101, 18671, 310, 17193, 310, 6534, 13888, 4249, 21669, 322, 817, 304, 367, 5134, 297, 278, 2661, 326, 1078, 310, 12027, 355, 17252, 23454, 491, 278, 20886, 310, 4231, 749, 1269, 16436, 1052, 1629, 29889, 1763, 9659, 278, 14726, 3097, 310, 716, 17162, 29892, 896, 817, 304, 748, 1549, 263, 2070, 362, 3785, 607, 12919, 471, 451, 3109, 1135, 29871, 29896, 1629, 1156, 607, 322, 29892, 565, 5119, 3832, 29892, 28573, 471, 16725, 29889, 13, 3047, 278, 18707, 310, 379, 14098, 29871, 29906, 29900, 29900, 29953, 29892, 1162, 9216, 358, 23134, 363, 278, 9045, 17535, 471, 9500, 287, 304, 278, 379, 1744, 518, 29906, 29906, 1822, 19065, 2778, 277, 29892, 379, 14098, 29871, 29906, 29900, 29900, 29953, 9129, 16614, 310, 10257, 322, 14731, 13407, 322, 5545, 623, 7771, 1575, 4034, 363, 15724, 3109, 1135, 29871, 29896, 29947, 30080, 6360, 29879, 313, 1457, 16604, 451, 6068, 1090, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29897, 408, 11706, 304, 2758, 9045, 10257, 8041, 304, 22332, 1296, 1009, 3734, 2836, 9981, 304, 4866, 1009, 11898, 29889, 512, 1797, 304, 3211, 278, 1880, 12421, 654, 515, 278, 970, 304, 278, 2024, 17535, 8900, 1156, 28052, 663, 29892, 278, 716, 1072, 2785, 4944, 7621, 8525, 4127, 363, 14581, 6944, 14372, 379, 1744, 304, 4148, 895, 2702, 17162, 304, 2906, 866, 760, 310, 1009, 931, 304, 2024, 6944, 322, 27668, 278, 9212, 2070, 362, 3785, 515, 29871, 29896, 1629, 304, 29871, 29953, 7378, 29889, 13, 1888, 14607, 23274, 13, 29928, 3864, 278, 758, 29899, 29883, 3780, 275, 3785, 29892, 379, 29956, 29879, 723, 2740, 363, 17643, 373, 1009, 1914, 1156, 6694, 29889, 13, 4591, 29871, 29896, 29929, 29929, 29906, 304, 29871, 29896, 29929, 29929, 29945, 306, 1258, 590, 302, 1295, 292, 6694, 408, 385, 390, 20728, 472, 3536, 598, 6555, 13457, 518, 30098, 29962, 591, 892, 451, 1641, 21168, 29889, 7806, 2022, 723, 1106, 363, 670, 29914, 2276, 1914, 2058, 313, 29950, 29956, 402, 21908, 7457, 29871, 29941, 467 ]

1,332,829

2,048

CommonCrawl

6

2

Before the crisis, recruitment of students was done by the relevant health service providers (government or FBO), drawing from their own training schools, but it was carried out in accordance to the MOHCC/HSB standards and criteria. Despite being regulated by the same framework, church-run nursing schools had the opportunity to retain the nurses they like at their facilities after completion of training: …the DNO [District Nursing Officer] will deploy them to us but [the nurse training school] can just say we need three here [at FBO facility] and they can even mention names preferably so and so […] (Manager FBO District 1) However, during the crisis period (1997–2008), they had the option to choose three priority provinces, both for students who had trained in government and in FBO-run training schools. Preference listing was withdrawn during the crisis period for nurses and paramedical staff mainly to address the shortage of HWs particularly in rural areas. On the other hand, doctors were still allowed to choose, although the human resources (HR) department at MOHCC head office would intervene to ensure even deployment in areas where majority of newly qualified doctors would have chosen one hospital. Most people (80%) would choose Harare and only 20% would choose Bulawayo but it was supposed to be 50-50. This meant that 30% of those who chose Harare were then forced to go and work in Bulawayo. To solve the issue there was a list that would come from the head office Human Resources Directorate of who would go where. (Manager Gvt District 1) Despite the establishment of the HSB which, in the views of the government, aimed at the unification of all health services, there were some differences in the implementation of HSR 2006 between government and FBO service providers. Some managers reported having two different and parallel processes for recruiting new workers: one triggered by the HSB and another one by the specific FBO: When we are recruiting [under the FBO process] we advertise the posts, and then people apply. When they are sent by the DNO [official HSB process] we just accept them. We sit down with them and do a bit of an interview but not as we do with those we recruit on our own because there is no option to say we want you or we don't because the person would have been already sent to us. We then ask them to fill the assumption of duty forms and other forms which are needed. (Manager FBO District 3) These overlapping recruitment systems with different degrees of thoroughness in terms of merit-based selection may have resulted in different recruitment outputs with a fairer system applied to these recruited through the FBO system (e.g. using interviews) as compared with these recruited through the HSB which may be more prone to patronage and weaker accountability. However, this was not substantiated by the study. Another factor that contributed to the poor staffing situation during the crisis was the recruitment freeze introduced as a response to an over-inflated civil service [30]. However, given its key role and its already precarious staffing situation, the freeze in the health sector was temporarily relaxed to allow for limited recruitment on a periodical basis to cover urgent needs [20]. This affected equally government and FBO-run facilities. When we have people, who qualify we wait for the unfreezing of posts. The HR [department] will allocate the posts to the provinces and provinces allocate to the districts. (National Manager Gvt) During the crisis, the number of absconders (i.e. workers leaving the workforce without prior notice or authorisation) increased substantially. While before the crisis the process of re-appointment of absconders was long and often unsuccessful, this was adjusted after the crisis to allow for fast-tracked re-appointment to mitigate the increasing vacancy rate. A new cadre, a primary care nurse (PCN), was introduced during the crisis to resolve staff shortages in rural areas and this cadre was meant to work at rural health centres/clinics only. In hospital [District Hospital] it [introduction of PCNs] did not help in any way, but it helped in the rural areas, that cadre was meant to work in the rural areas. They are not supposed to work at district hospitals or other upper hospitals. (Manager Gvt District 2) Bond

-0.463119

0.638966

0.605268

0.482939

[ -0.1706077177357346, -0.7556303353468302 ]

[ 0.9039786197125211, 0.3739525596448445 ]

[ 0.8715737258255462, 0.33896311049484956 ]

[ 0.7014545919793387, 0.2644243869128541 ]

1,024

[ 512, 512 ]

[ 13, 18743, 278, 24161, 29892, 1162, 9216, 358, 310, 8041, 471, 2309, 491, 278, 8018, 9045, 2669, 1326, 11376, 313, 29887, 6170, 358, 470, 383, 8456, 511, 11580, 515, 1009, 1914, 6694, 12462, 29892, 541, 372, 471, 8988, 714, 297, 15017, 749, 304, 278, 16999, 29950, 4174, 29914, 29950, 1744, 20801, 322, 16614, 29889, 19454, 1641, 1072, 7964, 491, 278, 1021, 6890, 29892, 6586, 29899, 3389, 302, 1295, 292, 12462, 750, 278, 15130, 304, 11551, 278, 302, 1295, 267, 896, 763, 472, 1009, 23330, 1156, 13285, 310, 6694, 29901, 13, 30098, 1552, 360, 6632, 518, 29928, 6801, 405, 1295, 292, 28288, 29962, 674, 7246, 963, 304, 502, 541, 518, 1552, 5595, 344, 6694, 3762, 29962, 508, 925, 1827, 591, 817, 2211, 1244, 518, 271, 383, 8456, 24454, 29962, 322, 896, 508, 1584, 3585, 2983, 5821, 2197, 577, 322, 577, 518, 30098, 29962, 313, 3260, 383, 8456, 7457, 29871, 29896, 29897, 13, 17245, 29892, 2645, 278, 24161, 3785, 313, 29896, 29929, 29929, 29955, 29994, 29906, 29900, 29900, 29947, 511, 896, 750, 278, 2984, 304, 6755, 2211, 20136, 28058, 29892, 1716, 363, 8041, 1058, 750, 16370, 297, 5874, 322, 297, 383, 8456, 29899, 3389, 6694, 12462, 29889, 4721, 1659, 18028, 471, 411, 19811, 1233, 2645, 278, 24161, 3785, 363, 302, 1295, 267, 322, 1828, 287, 936, 13925, 14364, 304, 3211, 278, 3273, 482, 310, 379, 29956, 29879, 10734, 297, 17692, 10161, 29889, 1551, 278, 916, 1361, 29892, 437, 14359, 892, 1603, 6068, 304, 6755, 29892, 5998, 278, 5199, 7788, 313, 20938, 29897, 14311, 472, 16999, 29950, 4174, 2343, 8034, 723, 26314, 29872, 304, 9801, 1584, 18209, 297, 10161, 988, 13638, 310, 15141, 18698, 437, 14359, 723, 505, 10434, 697, 13457, 29889, 13, 29924, 520, 2305, 313, 29947, 29900, 10997, 723, 6755, 3536, 598, 322, 871, 29871, 29906, 29900, 29995, 723, 6755, 8313, 21694, 29877, 541, 372, 471, 7424, 304, 367, 29871, 29945, 29900, 29899, 29945, 29900, 29889, 910, 6839, 393, 29871, 29941, 29900, 29995, 310, 1906, 1058, 12784, 3536, 598, 892, 769, 11826, 304, 748, 322, 664, 297, 8313, 21694, 29877, 29889, 1763, 4505, 278, 2228, 727, 471, 263, 1051, 393, 723, 2041, 515, 278, 2343, 8034, 12968, 27562, 15944, 403, 310, 1058, 723, 748, 988, 29889, 313, 3260, 402, 21908, 7457, 29871, 29896, 29897, 13, 4002, 29886, 568, 278, 25012, 310, 278, 379, 1744, 607, 29892, 297, 278, 8386, 310, 278, 5874, 29892, 12242, 287, 472, 278, 443, 2450, 310, 599, 9045, 5786, 29892, 727, 892, 777, 12651, 297, 278, 5314, 310, 379, 14098, 29871, 29906, 29900, 29900, 29953, 1546, 5874, 322, 383, 8456, 2669, 1326, 11376, 29889, 3834, 767, 18150, 8967, 2534, 1023, 1422, 322, 8943, 10174, 363, 1162, 9216, 292, 716, 17162, 29901, 697, 19799, 491, 278, 379, 1744, 322, 1790, 697, 491, 278, 2702, 383, 8456, 29901, 13, 10401, 591, 526, 1162, 9216, 292, 518, 5062, 278, 383, 8456, 1889, 29962, 591, 18811, 895, 278, 11803, 29892, 322, 769, 2305, 3394, 29889, 1932, 896, 526, 2665, 491, 278, 360, 6632, 518, 29877, 7880, 379, 1744, 1889, 29962, 591, 925, 3544, 963, 29889, 1334, 7845, 1623, 411, 963, 322, 437, 263, 2586, 310, 385, 15593, 541, 451, 408, 591, 437, 411, 1906, 591, 1162, 9216, 373, 1749, 1914, 1363, 727, 338, 694, 2984, 304, 1827, 591, 864, 366, 470, 591, 1016, 29915, 29873, 1363, 278, 2022, 723, 505, 1063, 2307, 2665, 304, 502, 29889, 1334, 769, 2244, 963, 304, 5445, 278, 11833, 310, 13360, 7190, 322, 916, 7190, 607, 526, 4312, 29889, 313, 3260, 383, 8456, 7457, 29871, 29941, 29897, 13, 1349, 968, 975, 433, 3262, 1162, 9216, 358, 6757, 411, 1422, 14496, 310, 17826, 2264, 297, 4958, 310, 2778, 277, 29899, 6707, 9262, 1122, 505, 20601, 297, 1422, 1162, 9216, 358, 14391, 411, 263, 6534, 261, 1788, 7436, 304, 1438, 1162, 582, 1573, 1549, 278, 383, 8456, 1788, 313, 29872, 29889, 29887, 29889, 773, 1006, 7406, 29897, 408, 9401, 411, 1438, 1162, 582, 1573, 1549, 278, 379, 1744, 607, 1122, 367, 901, 544, 650, 304, 18259, 482, 322, 591, 5790, 3633, 3097, 29889, 2398, 29892, 445, 471, 451, 5960, 3656, 630, 491, 278, 6559, 29889, 13, 2744, 1228, 7329, 393, 26869, 304, 278, 6460, 13925, 292, 6434, 2645, 278, 24161, 471, 278, 1162, 9216, 358, 3889, 911, 9129, 408, 263, 2933, 304, 385, 975, 29899, 13453, 630, 7631, 2669, 518, 29941, 29900, 1822, 2398, 29892, 2183, 967, 1820, 6297, 322, 967, 2307, 8303, 1306, 681, 13925, 292, 6434, 29892, 278, 3889, 911, 297, 278, 9045, 17535, 471, 5382, 6275, 26681, 287, 304, 2758, 363, 9078, 1162, 9216, 358, 373, 263, 3785, 936, 8405, 304, 4612, 5065, 5362, 4225, 518, 29906, 29900, 1822, 910, 15201, 18018, 5874, 322, 383, 8456, 29899, 3389, 23330, 29889, 13, 10401, 591, 505, 2305, 29892, 1058, 4021, 1598, 591, 4480, 363, 278, 443, 9021, 19583, 310, 11803, 29889, 450, 379, 29934, 518, 311, 8076, 29962, 674, 23632, 278, 11803, 304, 278, 28058, 322, 28058, 23632, 304, 278, 24172, 29889, 313, 27325, 15629, 402, 21908, 29897, 13, 29928, 3864, 278, 24161, 29892, 278, 1353, 310, 6425, 1116, 414, 313, 29875, 29889, 29872, 29889, 17162, 10124, 278, 664, 10118, 1728, 7536, 8369, 470, 4148, 4371, 29897, 11664, 23228, 368, 29889, 5806, 1434, 278, 24161, 278, 1889, 310, 337, 29899, 932, 2461, 358, 310, 6425, 1116, 414, 471, 1472, 322, 4049, 443, 8698, 1319, 29892, 445, 471, 10365, 287, 1156, 278, 24161, 304, 2758, 363, 5172, 29899, 11294, 287, 337, 29899, 932, 2461, 358, 304, 1380, 335, 403, 278, 10231, 11757, 6906, 6554, 29889, 13, 29909, 716, 25915, 29892, 263, 7601, 2562, 5595, 344, 313, 9026, 29940, 511, 471, 9129, 2645, 278, 24161, 304, 8814, 13925, 3273, 1179, 297, 17692, 10161, 322, 445, 25915, 471, 6839, 304, 664, 472, 17692, 9045, 1644, 690, 29914, 695, 262, 1199, 871, 29889, 13, 797, 13457, 518, 29928, 6801, 15967, 29962, 372, 518, 524, 13210, 310, 9609, 29940, 29879, 29962, 1258, 451, 1371, 297, 738, 982, 29892, 541, 372, 9213, 297, 278, 17692, 10161, 29892, 393, 25915, 471, 6839, 304, 664, 297, 278, 17692, 10161, 29889, 2688, 526, 451, 7424, 304, 664, 472, 6474, 29418, 277, 1338, 470, 916, 7568, 29418, 277, 1338, 29889, 313, 3260, 402, 21908, 7457, 29871, 29906, 29897, 13, 29933, 898 ]

1,332,829

3,072

CommonCrawl

6

2

ing policies were first adopted in Zimbabwe through the "Health for All Action Plan" in 1986. Initially bonding arrangements were between MOHCW and professional associations [13, 17, 31] by which all new HWs were to serve generally in the public sector for a period equivalent to the period of their training. However, bonding was not mentioned in the PSR 2000 or in the HSR 2006. This policy gap may be the cause behind recent research showing inconsistent implementation of this specific policy element [20]. New regulation was introduced in 2007 by which all newly graduated nurses had their certificates withheld until they completed their bonding obligations. However, after the introduction of the recruitment freeze and the subsequent difficulties for new professionals in finding a job in the public sector, the regulation was not enforced from 2010. Before the crisis, bonding regulations were well enforced with bonding playing a dual role: improving retention and providing a supervised induction after the training. Long back it [bonding] was there to retain nurses as the nurses were trained using public funds. It was also used to make sure that the nurse will be moulded through the supervision by the senior [staff] during the bonding period. (Provincial Manager Gvt). There was change in bonding policy in 2007 when it included withholding of certificates to mitigate the increasing attrition from the public to the private sector and through out-migration. Bonding rules were the same for staff working in both government and FBO sectors especially after the creation of the HSB. The nurses were bonded for a period equivalent to the training period and you would not get certificates for the three years you are bonded. (Provincial Manager Gvt) There were some exceptions in the application of bonding rules within the FBO sector for ordained staff who are directly managed by the church authorities through internal church policies Like after the training we used to know that a person will be bonded for a year before he/she can say I no longer want to be here, but for us, sisters [ordained staff], that rule doesn't apply, we stay at a place until we are told to move. (HW Gvt District 2) The introduction of the recruitment freeze led to discontinuation of withholding of certificates as the government could no longer guarantee employment to new graduates. At the moment because of the shortage of vacancies and the freezing of posts, the nurses are now being given their certificates immediately after qualifying. (Provincial Manager Gvt) Bonding for in-service training, particularly after the crisis, was perceived as fairer than for pre-service training, as it was reported by many HWs as a way of giving back to the system what the system invested in their education: It is good in the sense that you would have been sent by the facility, so you have to render back the service, if you think of going somewhere it would not be fair that after training you will just go without rendering the service. (HW Gvt District 3) Before 2006, transfer of civil servants was regulated through section 13 of PSR 2000. The policy reflects a compulsory top-down approach to transfer, for example stating, 'a member may at any time without his consent be transferred by the Commission or a delegated authority from the post which he occupies to any other post in the Public Service whether the post is inside or outside Zimbabwe' (page 16). Refusal to obey an instruction of transfer is treated as an act of misconduct. However, the regulations say that transfer should be planned to minimise discomfort to the member concerned and their family and that the member should be provided with all necessary information relating to the transfer and notified in time. Transfers cannot be used as a punitive measure except in cases of disciplinary procedures. The PSR 2000 was replaced by HSR 2006 and in the new regulation the length of a temporary posting was left to be determined by the HSB as opposed to the initial transfer for a limited period of maximum 3 years. During the pre-crisis period, managers were more in control of the processes of transferring workers, but during the crisis, due to substantial problems with attrition, they were less eager to allow transfers of staff. …as an HOD [Head of Department] I just realize

-0.374005

0.318443

0.655993

0.433513

[ -0.21426612203507006, -0.5337429158490309 ]

[ 0.5673404464262941, 0.06954570082219232 ]

[ 0.8309938694193978, 0.48099260791636866 ]

[ 0.7742929594904194, 0.09273394920816375 ]

1,024

[ 512, 512 ]

[ 292, 24833, 892, 937, 16356, 297, 796, 19977, 370, 705, 1549, 278, 376, 3868, 4298, 363, 2178, 9123, 8402, 29908, 297, 29871, 29896, 29929, 29947, 29953, 29889, 17250, 368, 21224, 292, 15196, 4110, 892, 1546, 16999, 19127, 29956, 322, 10257, 27733, 518, 29896, 29941, 29892, 29871, 29896, 29955, 29892, 29871, 29941, 29896, 29962, 491, 607, 599, 716, 379, 29956, 29879, 892, 304, 9080, 6892, 297, 278, 970, 17535, 363, 263, 3785, 7126, 304, 278, 3785, 310, 1009, 6694, 29889, 2398, 29892, 21224, 292, 471, 451, 5276, 297, 278, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 470, 297, 278, 379, 14098, 29871, 29906, 29900, 29900, 29953, 29889, 910, 8898, 17261, 1122, 367, 278, 4556, 5742, 7786, 5925, 6445, 22435, 9696, 5314, 310, 445, 2702, 8898, 1543, 518, 29906, 29900, 1822, 1570, 1072, 2785, 471, 9129, 297, 29871, 29906, 29900, 29900, 29955, 491, 607, 599, 15141, 23588, 302, 1295, 267, 750, 1009, 23199, 1078, 411, 29882, 2495, 2745, 896, 8676, 1009, 21224, 292, 10788, 800, 29889, 2398, 29892, 1156, 278, 18707, 310, 278, 1162, 9216, 358, 3889, 911, 322, 278, 15352, 23553, 363, 716, 6351, 1338, 297, 9138, 263, 4982, 297, 278, 970, 17535, 29892, 278, 1072, 2785, 471, 451, 24555, 1133, 515, 29871, 29906, 29900, 29896, 29900, 29889, 13, 18743, 278, 24161, 29892, 21224, 292, 1072, 8250, 892, 1532, 24555, 1133, 411, 21224, 292, 8743, 263, 14581, 6297, 29901, 4857, 1747, 3240, 2509, 322, 13138, 263, 2428, 11292, 21445, 1156, 278, 6694, 29889, 13, 8208, 1250, 372, 518, 29890, 898, 292, 29962, 471, 727, 304, 11551, 302, 1295, 267, 408, 278, 302, 1295, 267, 892, 16370, 773, 970, 29199, 29889, 739, 471, 884, 1304, 304, 1207, 1854, 393, 278, 5595, 344, 674, 367, 286, 483, 287, 1549, 278, 2428, 4924, 491, 278, 16336, 518, 303, 3470, 29962, 2645, 278, 21224, 292, 3785, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 467, 13, 8439, 471, 1735, 297, 21224, 292, 8898, 297, 29871, 29906, 29900, 29900, 29955, 746, 372, 5134, 411, 8948, 292, 310, 23199, 1078, 304, 1380, 335, 403, 278, 10231, 12421, 654, 515, 278, 970, 304, 278, 2024, 17535, 322, 1549, 714, 29899, 29885, 16783, 29889, 26370, 292, 6865, 892, 278, 1021, 363, 13925, 1985, 297, 1716, 5874, 322, 383, 8456, 409, 14359, 7148, 1156, 278, 11265, 310, 278, 379, 1744, 29889, 13, 1576, 302, 1295, 267, 892, 21224, 287, 363, 263, 3785, 7126, 304, 278, 6694, 3785, 322, 366, 723, 451, 679, 23199, 1078, 363, 278, 2211, 2440, 366, 526, 21224, 287, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 29897, 13, 8439, 892, 777, 15283, 297, 278, 2280, 310, 21224, 292, 6865, 2629, 278, 383, 8456, 17535, 363, 4356, 7114, 13925, 1058, 526, 4153, 8745, 491, 278, 6586, 21142, 1549, 7463, 6586, 24833, 13, 27552, 1156, 278, 6694, 591, 1304, 304, 1073, 393, 263, 2022, 674, 367, 21224, 287, 363, 263, 1629, 1434, 540, 29914, 11360, 508, 1827, 306, 694, 5520, 864, 304, 367, 1244, 29892, 541, 363, 502, 29892, 9883, 29879, 518, 536, 7114, 13925, 1402, 393, 5751, 1838, 29915, 29873, 3394, 29892, 591, 7952, 472, 263, 2058, 2745, 591, 526, 5429, 304, 4337, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29906, 29897, 13, 1576, 18707, 310, 278, 1162, 9216, 358, 3889, 911, 5331, 304, 766, 20621, 362, 310, 411, 8948, 292, 310, 23199, 1078, 408, 278, 5874, 1033, 694, 5520, 18818, 5703, 358, 304, 716, 10591, 1078, 29889, 13, 4178, 278, 3256, 1363, 310, 278, 3273, 482, 310, 11757, 273, 2478, 322, 278, 3889, 19583, 310, 11803, 29892, 278, 302, 1295, 267, 526, 1286, 1641, 2183, 1009, 23199, 1078, 7389, 1156, 4021, 9215, 29889, 313, 1184, 3845, 1455, 15629, 402, 21908, 29897, 13, 29933, 898, 292, 363, 297, 29899, 5509, 6694, 29892, 10734, 1156, 278, 24161, 29892, 471, 17189, 2347, 408, 6534, 261, 1135, 363, 758, 29899, 5509, 6694, 29892, 408, 372, 471, 8967, 491, 1784, 379, 29956, 29879, 408, 263, 982, 310, 6820, 1250, 304, 278, 1788, 825, 278, 1788, 2437, 2868, 297, 1009, 9793, 29901, 13, 3112, 338, 1781, 297, 278, 4060, 393, 366, 723, 505, 1063, 2665, 491, 278, 24454, 29892, 577, 366, 505, 304, 4050, 1250, 278, 2669, 29892, 565, 366, 1348, 310, 2675, 9051, 372, 723, 451, 367, 6534, 393, 1156, 6694, 366, 674, 925, 748, 1728, 15061, 278, 2669, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29941, 29897, 13, 18743, 29871, 29906, 29900, 29900, 29953, 29892, 6782, 310, 7631, 26202, 471, 1072, 7964, 1549, 4004, 29871, 29896, 29941, 310, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29889, 450, 8898, 9432, 29879, 263, 752, 7273, 706, 2246, 29899, 3204, 2948, 304, 6782, 29892, 363, 1342, 23659, 29892, 525, 29874, 4509, 1122, 472, 738, 931, 1728, 670, 20218, 367, 18440, 491, 278, 11444, 470, 263, 16000, 630, 14329, 515, 278, 1400, 607, 540, 6919, 583, 304, 738, 916, 1400, 297, 278, 5236, 6692, 3692, 278, 1400, 338, 2768, 470, 5377, 796, 19977, 370, 705, 29915, 313, 3488, 29871, 29896, 29953, 467, 9897, 375, 284, 304, 26449, 385, 15278, 310, 6782, 338, 14914, 408, 385, 1044, 310, 3984, 535, 2199, 29889, 2398, 29892, 278, 1072, 8250, 1827, 393, 6782, 881, 367, 20458, 304, 6260, 895, 766, 510, 3921, 304, 278, 4509, 15041, 322, 1009, 3942, 322, 393, 278, 4509, 881, 367, 4944, 411, 599, 5181, 2472, 1104, 1218, 304, 278, 6782, 322, 451, 2164, 297, 931, 29889, 4103, 25534, 2609, 367, 1304, 408, 263, 6035, 3321, 5645, 5174, 297, 4251, 310, 17119, 3821, 28648, 29889, 13, 1576, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 471, 8611, 491, 379, 14098, 29871, 29906, 29900, 29900, 29953, 322, 297, 278, 716, 1072, 2785, 278, 3309, 310, 263, 13201, 16742, 471, 2175, 304, 367, 10087, 491, 278, 379, 1744, 408, 15869, 304, 278, 2847, 6782, 363, 263, 9078, 3785, 310, 7472, 29871, 29941, 30080, 6360, 29879, 29889, 13, 29928, 3864, 278, 758, 29899, 29883, 3780, 275, 3785, 29892, 767, 18150, 892, 901, 297, 2761, 310, 278, 10174, 310, 6782, 5393, 17162, 29892, 541, 2645, 278, 24161, 29892, 2861, 304, 23228, 4828, 411, 12421, 654, 29892, 896, 892, 3109, 19888, 304, 2758, 1301, 25534, 310, 13925, 29889, 13, 30098, 294, 385, 379, 13668, 518, 5494, 310, 10317, 29962, 306, 925, 16289 ]

1,332,829

4,096

CommonCrawl

3

13

that if someone moves away there will be less [fewer] nurses here so I might refuse the person to move to another facility. (Manager Gvt District 3) These circumstances made it difficult for managers to deploy staff in a way that would improve geographical coverage. Managers also needed to balance carefully the requests from workers willing to be transferred as refusals may trigger greatly needed HRH to withdraw, abscond and go to private sector or leave the country. Transfers were easy during the crisis because there were more vacancies than HWs seeking those posts. One [a manager] had to be reasonable; it was either you let the cadre transfer to a preferred post or the system will lose the cadre altogether. (Manager Gvt District 1) In this regard, workers were allowed to transfer only when they found another worker in a similar position willing to exchange/swap positions. […] when I tried to talk to the DNO that I want to go to XXXX [Province] I was told that I should seek for a lateral transfer. I should convince somebody who is at a facility where I want to go so that he will come here, and I will go there. (HW Gvt District 1) The PSR 2000 states that a worker may at any time, with his/her consent and at the invitation of head of Ministry or the Commission, be seconded (a temporary form of transfer) by the Commission for a period not exceeding 3 years to a post in an approved service. Terms and conditions of services for seconded workers should be governed by the contract between the worker and the service concerned. The HSR 2006 revision points out that the period of secondment will be determined by the HSB without his/her consent while the rest of the terms and conditions are as stipulated by PSR 2000. During the crisis, because of the challenges of transferring staff explained above, managers used secondment to fill vacant posts, but it was unpopular among HWs as the legal terms for secondment were not appropriately applied. In some cases, HWs were seconded for a longer period of time than stipulated and sometimes communication about the secondment was not provided timely and it was not clear: I heard that the first group volunteered but as for our group we did not volunteer we were told to go. We were just told that you are going tomorrow, and we were not prepared to go. We could not even give excuses we were just told to go (HW FBO District 3) Some key positions within the FBO health services such as medical doctors were historically staffed through internal church-related networks and were never made explicit and included in the Public Service staffing norms when the HSB was introduced. During the crisis, when even FBO facilities faced problems with mobilisation of resources from external sources, many FBOs found themselves with shortage of this specific cadre. In these cases, secondment was used to allocate physicians to these facilities. My post is at XXX District Hospital [HSB]. When I came into the district, mission hospitals did not have posts for doctors from the government, so I was seconded here at XXX Hospital [FBO]. (Manager FBO District 1) This study was designed to review the changes and flexibility in deployment policies and the implementation practices during the crisis and post-crisis periods in Zimbabwe. Much of the response to the crisis and post-crisis situations relating to deployment was in the implementation of policies and in particular to transfer and secondment. The pragmatic response of the district-level managers was to be flexible in the use of the transfer rules aiming more at retaining HWs than to ensure equitable staffing of health facilities. Here, flexibility was used in a positive way, though elsewhere flexible interpretation of rules may be seen as negative [32]. However, secondment was used as an alternative and temporary way of filling vacancies. The aim of this, in the view of managers, was to at least retain staff. Interestingly, while we found that secondment (also known as deputation in some organisations) was driven by management in our study, elsewhere it is frequently used by employees as a means of changing their place of work through "side payments" to managers [33]. Several changes in the broader context that were highly relevant to understand the evolution of HRH deployment were identified. The first was the desire to improve equitable access to health services by bringing in and coordinating the then well-resourced FBO facilities in line with government plans and funding. The introduction of a blanket recruitment freeze

-0.266399

0.486762

0.5165

0.529764

[ -0.40636310095214623, -0.12643568515052458 ]

[ 0.37037130248222505, 0.6031530180524884 ]

[ 0.4454852335609889, 0.587514730982508 ]

[ 0.4673312678365791, 0.5921970407127175 ]

1,024

[ 512, 512 ]

[ 393, 565, 4856, 16229, 3448, 727, 674, 367, 3109, 518, 1725, 556, 29962, 302, 1295, 267, 1244, 577, 306, 1795, 26506, 278, 2022, 304, 4337, 304, 1790, 24454, 29889, 313, 3260, 402, 21908, 7457, 29871, 29941, 29897, 13, 1349, 968, 14209, 1754, 372, 5189, 363, 767, 18150, 304, 7246, 13925, 297, 263, 982, 393, 723, 11157, 1737, 19711, 23746, 29889, 2315, 18150, 884, 4312, 304, 17346, 16112, 278, 7274, 515, 17162, 17762, 304, 367, 18440, 408, 2143, 375, 1338, 1122, 7135, 11180, 4312, 379, 29934, 29950, 304, 28679, 29892, 6425, 1116, 322, 748, 304, 2024, 17535, 470, 5967, 278, 4234, 29889, 13, 4300, 25534, 892, 4780, 2645, 278, 24161, 1363, 727, 892, 901, 11757, 273, 2478, 1135, 379, 29956, 29879, 25738, 1906, 11803, 29889, 3118, 518, 29874, 8455, 29962, 750, 304, 367, 15590, 29936, 372, 471, 2845, 366, 1235, 278, 25915, 6782, 304, 263, 16389, 1400, 470, 278, 1788, 674, 14074, 278, 25915, 19148, 29889, 313, 3260, 402, 21908, 7457, 29871, 29896, 29897, 13, 797, 445, 4880, 29892, 17162, 892, 6068, 304, 6782, 871, 746, 896, 1476, 1790, 15645, 297, 263, 2788, 2602, 17762, 304, 14523, 29914, 26276, 11909, 29889, 13, 29961, 30098, 29962, 746, 306, 1898, 304, 5193, 304, 278, 360, 6632, 393, 306, 864, 304, 748, 304, 6193, 6247, 518, 1184, 29894, 1239, 29962, 306, 471, 5429, 393, 306, 881, 16508, 363, 263, 2678, 284, 6782, 29889, 306, 881, 7602, 1239, 18462, 1058, 338, 472, 263, 24454, 988, 306, 864, 304, 748, 577, 393, 540, 674, 2041, 1244, 29892, 322, 306, 674, 748, 727, 29889, 313, 29950, 29956, 402, 21908, 7457, 29871, 29896, 29897, 13, 1576, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 5922, 393, 263, 15645, 1122, 472, 738, 931, 29892, 411, 670, 29914, 2276, 20218, 322, 472, 278, 2437, 7018, 310, 2343, 310, 20886, 470, 278, 11444, 29892, 367, 1473, 287, 313, 29874, 13201, 883, 310, 6782, 29897, 491, 278, 11444, 363, 263, 3785, 451, 13461, 292, 29871, 29941, 2440, 304, 263, 1400, 297, 385, 23454, 2669, 29889, 11814, 29879, 322, 5855, 310, 5786, 363, 1473, 287, 17162, 881, 367, 4095, 287, 491, 278, 8078, 1546, 278, 15645, 322, 278, 2669, 15041, 29889, 450, 379, 14098, 29871, 29906, 29900, 29900, 29953, 26554, 3291, 714, 393, 278, 3785, 310, 1473, 358, 674, 367, 10087, 491, 278, 379, 1744, 1728, 670, 29914, 2276, 20218, 1550, 278, 1791, 310, 278, 4958, 322, 5855, 526, 408, 380, 666, 7964, 491, 11323, 29934, 29871, 29906, 29900, 29900, 29900, 29889, 13, 29928, 3864, 278, 24161, 29892, 1363, 310, 278, 18066, 267, 310, 6782, 5393, 13925, 10824, 2038, 29892, 767, 18150, 1304, 1473, 358, 304, 5445, 11757, 424, 11803, 29892, 541, 372, 471, 443, 7323, 1070, 4249, 379, 29956, 29879, 408, 278, 11706, 4958, 363, 1473, 358, 892, 451, 7128, 2486, 7436, 29889, 512, 777, 4251, 29892, 379, 29956, 29879, 892, 1473, 287, 363, 263, 5520, 3785, 310, 931, 1135, 380, 666, 7964, 322, 6041, 12084, 1048, 278, 1473, 358, 471, 451, 4944, 5335, 873, 322, 372, 471, 451, 2821, 29901, 13, 29902, 6091, 393, 278, 937, 2318, 27886, 14561, 541, 408, 363, 1749, 2318, 591, 1258, 451, 27886, 261, 591, 892, 5429, 304, 748, 29889, 1334, 892, 925, 5429, 393, 366, 526, 2675, 6454, 22396, 29892, 322, 591, 892, 451, 13240, 304, 748, 29889, 1334, 1033, 451, 1584, 2367, 5566, 6394, 591, 892, 925, 5429, 304, 748, 313, 29950, 29956, 383, 8456, 7457, 29871, 29941, 29897, 13, 9526, 1820, 11909, 2629, 278, 383, 8456, 9045, 5786, 1316, 408, 16083, 437, 14359, 892, 3603, 1711, 13925, 287, 1549, 7463, 6586, 29899, 12817, 14379, 322, 892, 2360, 1754, 6261, 322, 5134, 297, 278, 5236, 6692, 13925, 292, 6056, 29879, 746, 278, 379, 1744, 471, 9129, 29889, 7133, 278, 24161, 29892, 746, 1584, 383, 8456, 23330, 20050, 4828, 411, 27227, 4371, 310, 7788, 515, 7029, 8974, 29892, 1784, 383, 8456, 29879, 1476, 6053, 411, 3273, 482, 310, 445, 2702, 25915, 29889, 512, 1438, 4251, 29892, 1473, 358, 471, 1304, 304, 23632, 4824, 14722, 304, 1438, 23330, 29889, 13, 3421, 1400, 338, 472, 22615, 7457, 15967, 518, 29950, 1744, 1822, 1932, 306, 2996, 964, 278, 6474, 29892, 10655, 29418, 277, 1338, 1258, 451, 505, 11803, 363, 437, 14359, 515, 278, 5874, 29892, 577, 306, 471, 1473, 287, 1244, 472, 22615, 15967, 518, 29943, 8456, 1822, 313, 3260, 383, 8456, 7457, 29871, 29896, 29897, 13, 4013, 6559, 471, 8688, 304, 9076, 278, 3620, 322, 8525, 4127, 297, 18209, 24833, 322, 278, 5314, 23274, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 297, 796, 19977, 370, 705, 29889, 18927, 310, 278, 2933, 304, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 18845, 1104, 1218, 304, 18209, 471, 297, 278, 5314, 310, 24833, 322, 297, 3153, 304, 6782, 322, 1473, 358, 29889, 450, 282, 1431, 29885, 2454, 2933, 310, 278, 6474, 29899, 5563, 767, 18150, 471, 304, 367, 25706, 297, 278, 671, 310, 278, 6782, 6865, 12242, 292, 901, 472, 11551, 292, 379, 29956, 29879, 1135, 304, 9801, 1592, 8270, 13925, 292, 310, 9045, 23330, 29889, 2266, 29892, 8525, 4127, 471, 1304, 297, 263, 6374, 982, 29892, 2466, 17551, 25706, 19854, 310, 6865, 1122, 367, 3595, 408, 8178, 518, 29941, 29906, 1822, 2398, 29892, 1473, 358, 471, 1304, 408, 385, 8671, 322, 13201, 982, 310, 27523, 11757, 273, 2478, 29889, 450, 12242, 310, 445, 29892, 297, 278, 1776, 310, 767, 18150, 29892, 471, 304, 472, 3203, 11551, 13925, 29889, 23829, 11687, 29892, 1550, 591, 1476, 393, 1473, 358, 313, 15189, 2998, 408, 316, 14584, 297, 777, 17459, 800, 29897, 471, 18225, 491, 10643, 297, 1749, 6559, 29892, 17551, 372, 338, 13672, 1304, 491, 22873, 408, 263, 2794, 310, 6480, 1009, 2058, 310, 664, 1549, 376, 2975, 5146, 1860, 29908, 304, 767, 18150, 518, 29941, 29941, 1822, 13, 29903, 1310, 284, 3620, 297, 278, 2545, 1664, 3030, 393, 892, 10712, 8018, 304, 2274, 278, 14675, 310, 379, 29934, 29950, 18209, 892, 15659, 29889, 450, 937, 471, 278, 13521, 304, 11157, 1592, 8270, 2130, 304, 9045, 5786, 491, 20794, 297, 322, 6615, 1218, 278, 769, 1532, 29899, 690, 473, 1133, 383, 8456, 23330, 297, 1196, 411, 5874, 13900, 322, 5220, 292, 29889, 450, 18707, 310, 263, 9654, 300, 1162, 9216, 358, 3889, 911 ]

1,332,829

5,120

CommonCrawl

6

2

for the Civil Service represented a major challenge for district- and facility-level health service managers, particularly in rural areas. However, the system managed to mitigate some of the constraints by allowing flexibility on its implementation like temporarily lifting the freeze to allow recruitment and appointment for critical positions. Such exemptions for doctors and nurses were used during a lengthy recruitment freeze in Zambia in 2002 and 2004 [9]. Similarly, the policy on bonding was changed during the crisis and post-crisis periods, with for example the bonding period for nurses going from 3 to 2 years. With such a big staff shortage and a fluid labour market, the government could not afford to drive people away from the sector, so understandably they became more lenient. When even the reduced period of bonding was not being accepted by workers, the government initially used the common strategy of withholding graduation certificates during the bonding period [34] but following the recruitment freeze when jobs could no longer be guaranteed both the bonding policy and the policy of withholding of certificates were relaxed which also shows the flexibility of the system. On the other hand, the actions—or to some extent the lack of action—of policy makers in a crisis such as that experienced in Zimbabwe can be (at least partially) explained by the fact that it was difficult or impossible for them to predict how long the crisis would last, and, based on that, it was difficult to decide what changes to make to deployment policy even when the health workforce was clearly haemorrhaging. While the changes in response to the crisis in deployment-related policy might have been limited, adjustments and adaptations at the practice level, in particular in relation to transfer and secondment, were more prominent. In particular, the relaxation of transfer rules at the height of the crisis and the tactical use of secondment demonstrated the ability of managers' flexibility in implementing policy—what Bossert [35] refers to as 'decision space'—and to carry out actions to achieve their objectives, which in this case were to retain staff and to fill vacancies. Nevertheless, the bonding policies were clearly adapted at various stages of the crisis and post-crisis periods in response to the changing labour market situation. The shift on the policy of reappointment was clearly triggered by the window of opportunity as HWs who had left the sector were beginning to return in view of the apparent improvements in the overall situation. The timing of this window was fortunate, as such opportunities may be quite delayed as found by our research colleagues in Sierra Leone [36].The introduction of the PCN was also timely as it made sure posts were filled in rural areas. However, no official changes in the transfer and secondment policies were made specifically in response to the crisis and post-crisis situation. Though the deployment objectives might have been achieved reasonably successfully in the short term, the actions of FBO managers of preventing HWs from transferring and of government managers to force staff into short-term secondments meant that in the longer term staff in both cases may have left at the first opportunity. Hence, the longer-term objective of retention would not have been achieved, illustrating the challenge of developing coherent HR strategies [37, 38]. In these situations, managers should be supported to take the initiative to solve problems but should also be supported in understanding both the short- and longer-term implications of HRM actions. An ironic finding of this study is that although the reforms enacted through the Health Services Act of 2004 created a centralised system, in the context of crisis, district-level managers were able to push their degree of 'decision space' [39]—or 'room for manoeuvre'—more than in some stable but supposedly decentralised contexts [40, 41] with regard to staff deployment. In the absence of a central response to deployment policy, this must be seen as positive behaviour. However, without support on effective HRM, some decisions made run the risk of having negative longer-term consequences. This finding is an essential lesson for Zimbabwe as it deals with the aftermath of the peak of the economic crisis, as well as potentially for other countries facing similar situations. The policy should acknowledge that decision space must be increased for deployment managers in underserved rural areas. There were some limitations to this study. Documentation on policies and interviews with high-ranking key informants was difficult to obtain. Also, different accounts of the implementation of the policies were given between managers and between health

0.748273

0.660453

1.216503

1.138485

[ 0.8140177062857492, 0.6825288651018683 ]

[ 0.796540904833938, 0.5243653604748608 ]

[ 1.3078071821916404, 1.125197828363973 ]

[ 1.076051910607754, 1.2009176834838924 ]

1,024

[ 512, 512 ]

[ 363, 278, 12886, 6692, 9875, 263, 4655, 18766, 363, 6474, 29899, 322, 24454, 29899, 5563, 9045, 2669, 767, 18150, 29892, 10734, 297, 17692, 10161, 29889, 2398, 29892, 278, 1788, 8745, 304, 1380, 335, 403, 777, 310, 278, 11938, 491, 14372, 8525, 4127, 373, 967, 5314, 763, 5382, 6275, 11747, 1259, 278, 3889, 911, 304, 2758, 1162, 9216, 358, 322, 28573, 363, 12187, 11909, 29889, 10506, 11875, 1980, 363, 437, 14359, 322, 302, 1295, 267, 892, 1304, 2645, 263, 3309, 29891, 1162, 9216, 358, 3889, 911, 297, 796, 1117, 423, 297, 29871, 29906, 29900, 29900, 29906, 322, 29871, 29906, 29900, 29900, 29946, 518, 29929, 1822, 20175, 29892, 278, 8898, 373, 21224, 292, 471, 3939, 2645, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 29892, 411, 363, 1342, 278, 21224, 292, 3785, 363, 302, 1295, 267, 2675, 515, 29871, 29941, 304, 29871, 29906, 2440, 29889, 2973, 1316, 263, 4802, 13925, 3273, 482, 322, 263, 22576, 23390, 9999, 29892, 278, 5874, 1033, 451, 21750, 304, 7899, 2305, 3448, 515, 278, 17535, 29892, 577, 2274, 2197, 896, 3897, 901, 7431, 993, 29889, 1932, 1584, 278, 12212, 3785, 310, 21224, 292, 471, 451, 1641, 9259, 491, 17162, 29892, 278, 5874, 12919, 1304, 278, 3619, 13705, 310, 411, 8948, 292, 10591, 362, 23199, 1078, 2645, 278, 21224, 292, 3785, 518, 29941, 29946, 29962, 541, 1494, 278, 1162, 9216, 358, 3889, 911, 746, 17643, 1033, 694, 5520, 367, 22688, 1716, 278, 21224, 292, 8898, 322, 278, 8898, 310, 411, 8948, 292, 310, 23199, 1078, 892, 26681, 287, 607, 884, 3697, 278, 8525, 4127, 310, 278, 1788, 29889, 13, 2951, 278, 916, 1361, 29892, 278, 8820, 30003, 272, 304, 777, 15834, 278, 10225, 310, 3158, 30003, 974, 8898, 2136, 414, 297, 263, 24161, 1316, 408, 393, 18860, 297, 796, 19977, 370, 705, 508, 367, 313, 271, 3203, 22039, 29897, 10824, 491, 278, 2114, 393, 372, 471, 5189, 470, 9301, 363, 963, 304, 8500, 920, 1472, 278, 24161, 723, 1833, 29892, 322, 29892, 2729, 373, 393, 29892, 372, 471, 5189, 304, 11097, 825, 3620, 304, 1207, 304, 18209, 8898, 1584, 746, 278, 9045, 664, 10118, 471, 9436, 447, 28927, 19046, 6751, 29889, 13, 8809, 488, 278, 3620, 297, 2933, 304, 278, 24161, 297, 18209, 29899, 12817, 8898, 1795, 505, 1063, 9078, 29892, 10365, 1860, 322, 7744, 800, 472, 278, 6944, 3233, 29892, 297, 3153, 297, 8220, 304, 6782, 322, 1473, 358, 29892, 892, 901, 19555, 29889, 512, 3153, 29892, 278, 26681, 362, 310, 6782, 6865, 472, 278, 3171, 310, 278, 24161, 322, 278, 28476, 936, 671, 310, 1473, 358, 28585, 278, 11509, 310, 767, 18150, 29915, 8525, 4127, 297, 16049, 8898, 30003, 5816, 10211, 1940, 518, 29941, 29945, 29962, 14637, 304, 408, 525, 7099, 2459, 2913, 29915, 30003, 392, 304, 8677, 714, 8820, 304, 6176, 1009, 1203, 3145, 29892, 607, 297, 445, 1206, 892, 304, 11551, 13925, 322, 304, 5445, 11757, 273, 2478, 29889, 25678, 29892, 278, 21224, 292, 24833, 892, 9436, 23430, 472, 5164, 22950, 310, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 23704, 297, 2933, 304, 278, 6480, 23390, 9999, 6434, 29889, 450, 9500, 373, 278, 8898, 310, 337, 932, 2461, 358, 471, 9436, 19799, 491, 278, 3474, 310, 15130, 408, 379, 29956, 29879, 1058, 750, 2175, 278, 17535, 892, 6763, 304, 736, 297, 1776, 310, 278, 20295, 28473, 297, 278, 12463, 6434, 29889, 450, 28750, 310, 445, 3474, 471, 5162, 348, 403, 29892, 408, 1316, 28602, 1907, 1122, 367, 3755, 29801, 408, 1476, 491, 1749, 5925, 23056, 21628, 297, 24790, 951, 650, 518, 29941, 29953, 1822, 1576, 18707, 310, 278, 9609, 29940, 471, 884, 5335, 873, 408, 372, 1754, 1854, 11803, 892, 10423, 297, 17692, 10161, 29889, 2398, 29892, 694, 6221, 3620, 297, 278, 6782, 322, 1473, 358, 24833, 892, 1754, 10816, 297, 2933, 304, 278, 24161, 322, 1400, 29899, 29883, 3780, 275, 6434, 29889, 13, 1349, 820, 278, 18209, 1203, 3145, 1795, 505, 1063, 14363, 2769, 2197, 8472, 297, 278, 3273, 1840, 29892, 278, 8820, 310, 383, 8456, 767, 18150, 310, 5557, 292, 379, 29956, 29879, 515, 6782, 5393, 322, 310, 5874, 767, 18150, 304, 4889, 13925, 964, 3273, 29899, 8489, 1473, 1860, 6839, 393, 297, 278, 5520, 1840, 13925, 297, 1716, 4251, 1122, 505, 2175, 472, 278, 937, 15130, 29889, 10133, 29892, 278, 5520, 29899, 8489, 12091, 310, 3240, 2509, 723, 451, 505, 1063, 14363, 29892, 8632, 1218, 278, 18766, 310, 14338, 16165, 261, 296, 379, 29934, 16650, 583, 518, 29941, 29955, 29892, 29871, 29941, 29947, 1822, 512, 1438, 18845, 29892, 767, 18150, 881, 367, 6969, 304, 2125, 278, 14511, 1230, 304, 4505, 4828, 541, 881, 884, 367, 6969, 297, 8004, 1716, 278, 3273, 29899, 322, 5520, 29899, 8489, 2411, 5795, 310, 379, 29934, 29924, 8820, 29889, 13, 2744, 3805, 8927, 9138, 310, 445, 6559, 338, 393, 5998, 278, 337, 9514, 427, 627, 287, 1549, 278, 15202, 15538, 3185, 310, 29871, 29906, 29900, 29900, 29946, 2825, 263, 6555, 3368, 1788, 29892, 297, 278, 3030, 310, 24161, 29892, 6474, 29899, 5563, 767, 18150, 892, 2221, 304, 5503, 1009, 7426, 310, 525, 7099, 2459, 2913, 29915, 518, 29941, 29929, 29962, 30003, 272, 525, 8345, 363, 767, 7297, 4090, 276, 29915, 30003, 5514, 1135, 297, 777, 13714, 541, 7424, 368, 27189, 1705, 3368, 3030, 29879, 518, 29946, 29900, 29892, 29871, 29946, 29896, 29962, 411, 4880, 304, 13925, 18209, 29889, 512, 278, 18070, 310, 263, 6555, 2933, 304, 18209, 8898, 29892, 445, 1818, 367, 3595, 408, 6374, 10468, 29889, 2398, 29892, 1728, 2304, 373, 11828, 379, 29934, 29924, 29892, 777, 1602, 12112, 1754, 1065, 278, 12045, 310, 2534, 8178, 5520, 29899, 8489, 27721, 29889, 910, 9138, 338, 385, 18853, 3109, 265, 363, 796, 19977, 370, 705, 408, 372, 316, 1338, 411, 278, 1156, 755, 310, 278, 19224, 310, 278, 17407, 24161, 29892, 408, 1532, 408, 19998, 363, 916, 10916, 14870, 2788, 18845, 29889, 450, 8898, 881, 18145, 5485, 393, 10608, 2913, 1818, 367, 11664, 363, 18209, 767, 18150, 297, 23400, 9841, 17692, 10161, 29889, 1670, 892, 777, 27028, 304, 445, 6559, 29889, 10854, 362, 373, 24833, 322, 1006, 7406, 411, 1880, 29899, 661, 9292, 1820, 1871, 1934, 471, 5189, 304, 4017, 29889, 3115, 29892, 1422, 15303, 310, 278, 5314, 310, 278, 24833, 892, 2183, 1546, 767, 18150, 322, 1546, 9045 ]

1,332,829

6,144

CommonCrawl

6

2

workers. However, triangulation of data types and sources was used to ensure the credibility of the findings. We had initially planned to measure the impact of changing policies using routine staffing data. However, this was not finally possible as data was not available at the national level and insufficiently complete in the study districts to provide a representative sample across the categories of HWs. Nevertheless, the multi-method approach of this study allowed for qualitative data gathered through interviews with key informants, managers and staff—in particular the life histories [26]—to provide insights on the changing staffing situation. The 'uniqueness' of the situation in Zimbabwe makes these results very specific and therefore not directly transferable, but they add to the knowledge about how deployment policy and practice is or is not responsive to particular crises. How the crisis affected other HR policy and practice may be different and could be the subject of further study. Flexibility in implementing deployment policies is vital especially during changing conditions created by crisis in order to improve system responsiveness, retain HWs and manage their inequitable distribution in urban and rural areas. Managers at facilities and in provinces must be given mandate and support to be able to implement the policies for the interest of the HWs and facility at large. BRTI: Biomedical Research and Training Institute DFID: Department for International Development (UK Aid) DNO: District nursing officer FBO: Faith-based organisation Gvt: HOD: HRM: HSB: Health service board HSR: Health Services Regulations HW: IDI: Key informant interview MOHCC: Ministry of Health and Child Care MOHCW: Ministry of Health and Child Welfare PCN: Primary care nurse PSR: Public Service Regulation RDC: RGN: Chen L, Evans T, Anand S, Ivey Boufford J, Brown H, Chowdhury M, et al. Human resources for health: overcoming the crisis. Lancet. 2004;364(9449):1984–90. Scaling up, saving lives. Task force for scaling up education and training for health workers. Geneva: WHO/Global Health Workforce Alliance. 2008. Campbell J, Buchan J, Cometto G, David B, Dussault G, Fogstad H, et al. Human resources for health and universal health coverage : fostering equity and effective coverage. Policy Pract. 2013;(August:853–63. Varpilah ST, Safer M, Frenkel E, Baba D, Massaquoi M, Barrow G. Rebuilding human resources for health: a case study from Liberia. Hum Resour Health [Internet]. 2011;9(1):11. Available from: http://www.human-resources-health.com/content/9/1/11. Newbrander W, Yoder R, Debevoise AB. Rebuilding health systems in post-conflict countries: estimating the costs of basic services. Int J Heal Plan Manag. 2007;22(4):319–36. Lehmann U, Dieleman M, Martineau T. Staffing remote rural areas in middle- and low-income countries: a literature review of attraction and retention. BMC Health Serv Res [Internet]. 2008;8(1):19 Available from: http://bmchealthservres.biomedcentral.com/articles/10.1186/1472-6963-8-19. Dussault G, Franceschini MC. Not enough there, too many here: understanding geographical imbalances in the distribution of the health workforce. Hum Resour Health. 2006;4:12. Schaaf M, Freedman LP. Unmasking the open secret of posting and transfer practices in the health sector. Health Policy Plan. 2015;30(1):121–30. Vujicic M, Ohiri K, Sparkes S. Working in health. In: Financing and managing the public sector health workforce. Washington, DC: World Bank; 2009. Mponda JM, Biwot GK. The effects of deployment practices on employee performance among

-0.044769

0.918304

1.546214

0.951186

[ 0.42229053359210383, -0.5118281089850508 ]

[ 1.0902039921687319, 0.746403304557266 ]

[ 1.652735961643901, 1.4396917155116224 ]

[ 1.096862872753777, 0.805509402709454 ]

1,024

[ 512, 512 ]

[ 17162, 29889, 2398, 29892, 3367, 574, 2785, 310, 848, 4072, 322, 8974, 471, 1304, 304, 9801, 278, 6625, 4127, 310, 278, 1284, 886, 29889, 1334, 750, 12919, 20458, 304, 5645, 278, 10879, 310, 6480, 24833, 773, 26529, 13925, 292, 848, 29889, 2398, 29892, 445, 471, 451, 7146, 1950, 408, 848, 471, 451, 3625, 472, 278, 4797, 3233, 322, 1663, 29884, 4543, 368, 4866, 297, 278, 6559, 24172, 304, 3867, 263, 21097, 4559, 4822, 278, 13997, 310, 379, 29956, 29879, 29889, 25678, 29892, 278, 2473, 29899, 5696, 2948, 310, 445, 6559, 6068, 363, 4021, 23378, 848, 22229, 1549, 1006, 7406, 411, 1820, 1871, 1934, 29892, 767, 18150, 322, 13925, 30003, 262, 3153, 278, 2834, 3603, 583, 518, 29906, 29953, 29962, 30003, 517, 3867, 1663, 5861, 373, 278, 6480, 13925, 292, 6434, 29889, 450, 525, 3909, 339, 18543, 29915, 310, 278, 6434, 297, 796, 19977, 370, 705, 3732, 1438, 2582, 1407, 2702, 322, 5480, 451, 4153, 6782, 519, 29892, 541, 896, 788, 304, 278, 7134, 1048, 920, 18209, 8898, 322, 6944, 338, 470, 338, 451, 5544, 573, 304, 3153, 2181, 4637, 29889, 1128, 278, 24161, 15201, 916, 379, 29934, 8898, 322, 6944, 1122, 367, 1422, 322, 1033, 367, 278, 4967, 310, 4340, 6559, 29889, 13, 29943, 2506, 4127, 297, 16049, 18209, 24833, 338, 27131, 7148, 2645, 6480, 5855, 2825, 491, 24161, 297, 1797, 304, 11157, 1788, 5544, 20193, 29892, 11551, 379, 29956, 29879, 322, 10933, 1009, 297, 1686, 8270, 4978, 297, 17164, 322, 17692, 10161, 29889, 2315, 18150, 472, 23330, 322, 297, 28058, 1818, 367, 2183, 9619, 403, 322, 2304, 304, 367, 2221, 304, 2334, 278, 24833, 363, 278, 4066, 310, 278, 379, 29956, 29879, 322, 24454, 472, 2919, 29889, 13, 29933, 13079, 29902, 29901, 13, 29933, 14910, 287, 936, 10550, 322, 26101, 8907, 13, 4037, 1367, 29901, 13, 8498, 442, 358, 363, 4623, 14650, 313, 19960, 319, 333, 29897, 13, 29928, 6632, 29901, 13, 29928, 6801, 302, 1295, 292, 12139, 13, 29943, 8456, 29901, 13, 14206, 389, 29899, 6707, 24788, 13, 29954, 21908, 29901, 13, 8187, 29928, 29901, 13, 20938, 29924, 29901, 13, 29950, 1744, 29901, 13, 3868, 4298, 2669, 7613, 13, 29950, 14098, 29901, 13, 3868, 4298, 15538, 2169, 8250, 13, 29950, 29956, 29901, 13, 1367, 29902, 29901, 13, 2558, 1871, 424, 15593, 13, 6720, 29950, 4174, 29901, 13, 8140, 6020, 310, 15202, 322, 10517, 10057, 13, 6720, 19127, 29956, 29901, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 13, 9026, 29940, 29901, 13, 26666, 2562, 5595, 344, 13, 7024, 29934, 29901, 13, 19858, 6692, 2169, 2785, 13, 29934, 12696, 29901, 13, 29934, 20728, 29901, 13, 1451, 264, 365, 29892, 24056, 323, 29892, 530, 392, 317, 29892, 306, 6950, 12476, 600, 536, 435, 29892, 9817, 379, 29892, 678, 340, 12744, 2857, 341, 29892, 634, 394, 29889, 12968, 7788, 363, 9045, 29901, 975, 11506, 278, 24161, 29889, 24994, 300, 29889, 29871, 29906, 29900, 29900, 29946, 29936, 29941, 29953, 29946, 29898, 29929, 29946, 29946, 29929, 1125, 29896, 29929, 29947, 29946, 29994, 29929, 29900, 29889, 13, 29636, 292, 701, 29892, 14238, 12080, 29889, 9330, 4889, 363, 21640, 701, 9793, 322, 6694, 363, 9045, 17162, 29889, 15350, 1564, 29901, 399, 8187, 29914, 12756, 15202, 5244, 10118, 29855, 29889, 29871, 29906, 29900, 29900, 29947, 29889, 13, 29907, 1160, 12562, 435, 29892, 10586, 273, 435, 29892, 422, 8563, 402, 29892, 4699, 350, 29892, 360, 1558, 1292, 402, 29892, 383, 468, 17569, 379, 29892, 634, 394, 29889, 12968, 7788, 363, 9045, 322, 15968, 9045, 23746, 584, 9926, 3241, 1592, 537, 322, 11828, 23746, 29889, 25219, 29124, 29889, 29871, 29906, 29900, 29896, 29941, 29936, 29898, 26197, 29901, 29947, 29945, 29941, 29994, 29953, 29941, 29889, 13, 29963, 6834, 309, 801, 6850, 29892, 5701, 571, 341, 29892, 383, 1267, 10265, 382, 29892, 350, 5363, 360, 29892, 7360, 18463, 7768, 341, 29892, 2261, 798, 402, 29889, 12936, 29884, 789, 292, 5199, 7788, 363, 9045, 29901, 263, 1206, 6559, 515, 10895, 423, 29889, 13863, 2538, 473, 15202, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29896, 29936, 29929, 29898, 29896, 1125, 29896, 29896, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 26029, 29899, 13237, 29899, 354, 4298, 29889, 510, 29914, 3051, 29914, 29929, 29914, 29896, 29914, 29896, 29896, 29889, 13, 4373, 1182, 3825, 399, 29892, 612, 6119, 390, 29892, 7089, 29872, 1365, 895, 17571, 29889, 12936, 29884, 789, 292, 9045, 6757, 297, 1400, 29899, 5527, 29176, 10916, 29901, 4844, 1218, 278, 21544, 310, 6996, 5786, 29889, 3159, 435, 940, 284, 8402, 2315, 351, 29889, 29871, 29906, 29900, 29900, 29955, 29936, 29906, 29906, 29898, 29946, 1125, 29941, 29896, 29929, 29994, 29941, 29953, 29889, 13, 3226, 29882, 4403, 501, 29892, 1640, 280, 1171, 341, 29892, 3760, 457, 585, 323, 29889, 15351, 292, 7592, 17692, 10161, 297, 7256, 29899, 322, 4482, 29899, 262, 2763, 10916, 29901, 263, 12845, 9076, 310, 1098, 13857, 322, 3240, 2509, 29889, 350, 12513, 15202, 9635, 2538, 518, 26341, 1822, 29871, 29906, 29900, 29900, 29947, 29936, 29947, 29898, 29896, 1125, 29896, 29929, 7740, 3106, 515, 29901, 1732, 597, 5838, 1173, 4298, 2140, 690, 29889, 5365, 27067, 25171, 29889, 510, 29914, 18569, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29896, 29946, 29955, 29906, 29899, 29953, 29929, 29953, 29941, 29899, 29947, 29899, 29896, 29929, 29889, 13, 29928, 1558, 1292, 402, 29892, 10986, 305, 2172, 21271, 29889, 2216, 3307, 727, 29892, 2086, 1784, 1244, 29901, 8004, 1737, 19711, 527, 5521, 2925, 297, 278, 4978, 310, 278, 9045, 664, 10118, 29889, 13863, 2538, 473, 15202, 29889, 29871, 29906, 29900, 29900, 29953, 29936, 29946, 29901, 29896, 29906, 29889, 13, 4504, 29874, 2142, 341, 29892, 3878, 287, 1171, 23671, 29889, 853, 13168, 292, 278, 1722, 7035, 310, 16742, 322, 6782, 23274, 297, 278, 9045, 17535, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29896, 29945, 29936, 29941, 29900, 29898, 29896, 1125, 29896, 29906, 29896, 29994, 29941, 29900, 29889, 13, 29963, 8016, 293, 293, 341, 29892, 438, 2918, 374, 476, 29892, 20814, 267, 317, 29889, 24176, 297, 9045, 29889, 512, 29901, 4231, 19985, 322, 767, 6751, 278, 970, 17535, 9045, 664, 10118, 29889, 7660, 29892, 13681, 29901, 2787, 10253, 29936, 29871, 29906, 29900, 29900, 29929, 29889, 13, 29924, 2818, 29874, 435, 29924, 29892, 3457, 29893, 327, 402, 29968, 29889, 450, 9545, 310, 18209, 23274, 373, 19001, 4180, 4249 ]

1,332,829

7,168

CommonCrawl

14

10

the public banking institutions in Kenya a survey of post Bank coast. Region. 2015;5(9):1–13. Government of Canada. Public Service Employment Act; 2016. p. 5–8. Chirwa Y, Chandiwana P, Pepukai M, Mashange W, Buzuzi S, Munyati S, et al. Deployment of human resources for health in Zimbabwe : synthesis report. 2016. Ministry of Health and Child Welfare. Human resources for health policy. 2006; Ministry of Health and Child Welfare. National Health Strategy Zimbabwe 2009-2013. 2013; Osika J, Altman D, Ekbladh L, Katz I, Nguyen H, Rosenfeld J. Zimbabwe health system assessment, vol. 2011; 2010. ZIMSTATS. Zimbabwe population census 2012 [internet]. 2012. Available from: http://www.zimstat.co.zw/dmdocuments/Census/CensusResults2012/National_Report.pdf Chikanda A. Nurse migration from Zimbabwe: analysis of recent trends and impacts. Nurs Inq. 2005;12(3):162–74. Sikhosana PLN 2nd edition VT publishing. Challenges in reforming the health sector in Africa. 2nd editio. Victoria: Trafford publishing; 2005. Ministry of Health and Child Welfare. Human Resources for Health Strategic Plan 2010–2014; 2007. p. 83. Dieleman M, Watson M, Sisimayi C. Impact assessment of the Zimbabwe health worker retention scheme. Final Report. 2012. Mudyarabikwa O, Mbengwa A. Distribution of public sector health workers in Zimbabwe : a challenge for equity in health [Internet]. 2006. Available from: http://www.equinetafrica.org/bibl/docs/Diss34hresZim.pdf Government of Zimbabwe. Health service regulation 2006. Zimbabwe; 2006. Roome E, Raven J, Martineau T. Human resource management in post-conflict health systems: review of research and knowledge gaps. Confl Health [Internet]. 2014;8(1):18 Available from: http://conflictandhealth.biomedcentral.com/articles/10.1186/1752-1505-8-18. Alonso A, Brugha R. Rehabilitating the health system after conflict in East Timor : a shift from NGO to government leadership; September 1999. p. 2006. Bertone MP, Martins JS, Pereira SM, Martineau T, Alonso-Garbayo A. Understanding HRH recruitment in post- conflict settings : an analysis of central-level policies and processes in Timor-Leste ( 1999–2018 ), vol. 5; 2018. p. 1–12. Witter S, Namakula J, Alonso-Garbayo A, Wurie H, Theobald S, Mashange W, et al. Experiences of using life histories with health workers in post-conflict and crisis settings: methodological reflections. Health Policy Plan [Internet. 2017:czw166 Available from: https://academic.oup.com/heapol/article-lookup/doi/10.1093/heapol/czw166. Saunders B, Sim J, Kingstone T, Baker S, Waterfield J, Bartlam B, et al. Saturation in qualitative research : exploring its conceptualization and operationalization. Qual Quant. 2018;52(4):1893–907. Richie J, Spencer L. In: Burgess R, Bryman A, editors. Analyzing Qualitative Data. Rout

-1.00902

0.696266

0.803095

0.576589

[ -1.2514528406443814, -0.7665877387788202 ]

[ 0.8538410194358491, 0.5386903891253386 ]

[ 0.6331670694394248, 0.9730233668409168 ]

[ 0.41010112193501563, 0.7430765162713848 ]

1,024

[ 512, 512 ]

[ 278, 970, 9124, 292, 21561, 297, 10015, 3761, 263, 18994, 310, 1400, 10253, 12180, 29889, 11069, 29889, 29871, 29906, 29900, 29896, 29945, 29936, 29945, 29898, 29929, 1125, 29896, 29994, 29896, 29941, 29889, 13, 29954, 6170, 358, 310, 7400, 29889, 5236, 6692, 7361, 22812, 3185, 29936, 29871, 29906, 29900, 29896, 29953, 29889, 282, 29889, 29871, 29945, 29994, 29947, 29889, 13, 1451, 381, 2766, 612, 29892, 678, 392, 9429, 1648, 349, 29892, 349, 1022, 22971, 29875, 341, 29892, 341, 1161, 927, 399, 29892, 350, 3365, 29884, 2526, 317, 29892, 13564, 29891, 2219, 317, 29892, 634, 394, 29889, 10034, 22812, 310, 5199, 7788, 363, 9045, 297, 796, 19977, 370, 705, 584, 14710, 6656, 3461, 29889, 29871, 29906, 29900, 29896, 29953, 29889, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 12968, 7788, 363, 9045, 8898, 29889, 29871, 29906, 29900, 29900, 29953, 29936, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 3086, 15202, 3767, 8963, 796, 19977, 370, 705, 29871, 29906, 29900, 29900, 29929, 29899, 29906, 29900, 29896, 29941, 29889, 29871, 29906, 29900, 29896, 29941, 29936, 13, 24768, 4106, 435, 29892, 10790, 1171, 360, 29892, 16462, 2204, 328, 29882, 365, 29892, 476, 4101, 306, 29892, 405, 2543, 11771, 379, 29892, 28929, 10612, 435, 29889, 796, 19977, 370, 705, 9045, 1788, 24809, 358, 29892, 1700, 29889, 29871, 29906, 29900, 29896, 29896, 29936, 29871, 29906, 29900, 29896, 29900, 29889, 13, 29999, 7833, 17816, 29903, 29889, 796, 19977, 370, 705, 4665, 16411, 29871, 29906, 29900, 29896, 29906, 518, 14168, 300, 1822, 29871, 29906, 29900, 29896, 29906, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 29920, 326, 6112, 29889, 1111, 29889, 7659, 29914, 18933, 3225, 29879, 29914, 29907, 8841, 29914, 29907, 8841, 12191, 29906, 29900, 29896, 29906, 29914, 27325, 29918, 13020, 29889, 5140, 13, 1451, 638, 5863, 319, 29889, 25651, 344, 20332, 515, 796, 19977, 370, 705, 29901, 7418, 310, 7786, 534, 1975, 322, 10879, 29879, 29889, 405, 1295, 512, 29939, 29889, 29871, 29906, 29900, 29900, 29945, 29936, 29896, 29906, 29898, 29941, 1125, 29896, 29953, 29906, 29994, 29955, 29946, 29889, 13, 29903, 638, 15656, 1648, 16507, 29940, 29871, 29906, 299, 12203, 478, 29911, 27256, 29889, 678, 16047, 267, 297, 11736, 292, 278, 9045, 17535, 297, 10557, 29889, 29871, 29906, 299, 3863, 601, 29889, 14212, 29901, 3201, 600, 536, 27256, 29936, 29871, 29906, 29900, 29900, 29945, 29889, 13, 8140, 6020, 310, 15202, 322, 10517, 399, 761, 598, 29889, 12968, 27562, 363, 15202, 3767, 1845, 293, 8402, 29871, 29906, 29900, 29896, 29900, 29994, 29906, 29900, 29896, 29946, 29936, 29871, 29906, 29900, 29900, 29955, 29889, 282, 29889, 29871, 29947, 29941, 29889, 13, 29928, 9152, 1171, 341, 29892, 28284, 341, 29892, 317, 275, 326, 388, 29875, 315, 29889, 14305, 627, 24809, 358, 310, 278, 796, 19977, 370, 705, 9045, 15645, 3240, 2509, 11380, 29889, 9550, 13969, 29889, 29871, 29906, 29900, 29896, 29906, 29889, 13, 29924, 566, 8553, 370, 638, 2766, 438, 29892, 341, 29890, 996, 2766, 319, 29889, 17740, 310, 970, 17535, 9045, 17162, 297, 796, 19977, 370, 705, 584, 263, 18766, 363, 1592, 537, 297, 9045, 518, 26341, 1822, 29871, 29906, 29900, 29900, 29953, 29889, 7740, 3106, 515, 29901, 1732, 597, 1636, 29889, 1686, 262, 1187, 18961, 29889, 990, 29914, 18508, 29880, 29914, 2640, 29914, 29928, 790, 29941, 29946, 29882, 690, 29999, 326, 29889, 5140, 13, 29954, 6170, 358, 310, 796, 19977, 370, 705, 29889, 15202, 2669, 1072, 2785, 29871, 29906, 29900, 29900, 29953, 29889, 796, 19977, 370, 705, 29936, 29871, 29906, 29900, 29900, 29953, 29889, 13, 9588, 608, 382, 29892, 390, 3496, 435, 29892, 3760, 457, 585, 323, 29889, 12968, 6503, 10643, 297, 1400, 29899, 5527, 29176, 9045, 6757, 29901, 9076, 310, 5925, 322, 7134, 330, 2547, 29889, 1281, 1579, 15202, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29946, 29936, 29947, 29898, 29896, 1125, 29896, 29947, 7740, 3106, 515, 29901, 1732, 597, 5527, 29176, 392, 354, 4298, 29889, 5365, 27067, 25171, 29889, 510, 29914, 18569, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29896, 29955, 29945, 29906, 29899, 29896, 29945, 29900, 29945, 29899, 29947, 29899, 29896, 29947, 29889, 13, 2499, 16911, 319, 29892, 8135, 29887, 2350, 390, 29889, 830, 29882, 4427, 277, 1218, 278, 9045, 1788, 1156, 14529, 297, 6932, 7870, 272, 584, 263, 9500, 515, 405, 17080, 304, 5874, 26001, 29936, 3839, 29871, 29896, 29929, 29929, 29929, 29889, 282, 29889, 29871, 29906, 29900, 29900, 29953, 29889, 13, 29933, 814, 650, 16379, 29892, 3760, 1144, 7649, 29892, 23133, 3055, 13766, 29892, 3760, 457, 585, 323, 29892, 838, 16911, 29899, 29954, 279, 27495, 29877, 319, 29889, 7634, 11235, 379, 29934, 29950, 1162, 9216, 358, 297, 1400, 29899, 14529, 6055, 584, 385, 7418, 310, 6555, 29899, 5563, 24833, 322, 10174, 297, 7870, 272, 29899, 29931, 4196, 313, 29871, 29896, 29929, 29929, 29929, 29994, 29906, 29900, 29896, 29947, 10353, 1700, 29889, 29871, 29945, 29936, 29871, 29906, 29900, 29896, 29947, 29889, 282, 29889, 29871, 29896, 29994, 29896, 29906, 29889, 13, 29956, 5171, 317, 29892, 13041, 557, 2497, 435, 29892, 838, 16911, 29899, 29954, 279, 27495, 29877, 319, 29892, 399, 332, 347, 379, 29892, 450, 711, 2741, 317, 29892, 341, 1161, 927, 399, 29892, 634, 394, 29889, 28224, 819, 778, 310, 773, 2834, 3603, 583, 411, 9045, 17162, 297, 1400, 29899, 5527, 29176, 322, 24161, 6055, 29901, 1158, 5996, 2143, 5942, 29889, 15202, 25219, 8402, 518, 26341, 29889, 29871, 29906, 29900, 29896, 29955, 29901, 2067, 29893, 29896, 29953, 29953, 7740, 3106, 515, 29901, 2045, 597, 562, 1943, 13076, 29889, 1132, 29889, 510, 29914, 354, 481, 324, 29914, 7914, 29899, 20401, 29914, 1867, 29875, 29914, 29896, 29900, 29889, 29896, 29900, 29929, 29941, 29914, 354, 481, 324, 29914, 2067, 29893, 29896, 29953, 29953, 29889, 13, 29903, 585, 299, 414, 350, 29892, 3439, 435, 29892, 4088, 12734, 323, 29892, 22652, 317, 29892, 13062, 2671, 435, 29892, 12245, 5288, 350, 29892, 634, 394, 29889, 317, 1337, 362, 297, 4021, 23378, 5925, 584, 3902, 8253, 967, 6964, 950, 2133, 322, 1751, 1288, 2133, 29889, 15146, 22746, 29889, 29871, 29906, 29900, 29896, 29947, 29936, 29945, 29906, 29898, 29946, 1125, 29896, 29947, 29929, 29941, 29994, 29929, 29900, 29955, 29889, 13, 25627, 347, 435, 29892, 1706, 22687, 365, 29889, 512, 29901, 11202, 404, 390, 29892, 13307, 1171, 319, 29892, 3863, 943, 29889, 11597, 12339, 292, 15146, 23378, 3630, 29889, 20829 ]

1,332,829

8,192

CommonCrawl

9

22

ledge Qualitative data analysis for applied policy research; 1994. p. 173–94. Government of Zimbabwe. Public Service Regulation, 2000. 2000. International Monetary Fund. IMF. Zimbabwe 2012 article IV consultation. IMF country report no. 12/279. Washington, DC: International Monetary Fund; 2012. 2012. Mutizwa-Manziga D. The impact of health sector reform on public sector health worker motivation in Zimbabwe. Major applied research 5 working paper no. 4. Bethesda, MD: partnerships for health reform project: Abt Associates Inc; 1998. Purohit B, Martineau T, Sheikh K. Opening the black box of transfer systems in public sector health services in a Western state in India. BMC Health Serv Res. 2016;16(1):1–12. Available from. https://doi.org/10.1186/s12913-016-1675-0. Forgia G La, Raha S, Shaik S, Maheshwari S, Ali R. Parallel Systems and Human Resource Management in India's Public Health Services A View from the Front Lines. 2014;(June). Frehywot S, Mullan F, Payne W, Ross H. Compulsory service programmes for recruiting health workers in remote and rural areas : do they work ? Bull World Heal Organ. 2010:364–70. Bossert TJ. Analyzing the decentralization of health systems in developing countries: decision space, innovation and performance. Soc Sci Med. 1998;47:1513–27. Bertone MP, Samai M, Edem-hotah J, Witter S. A window of opportunity for reform in post-conflict settings ? The case of human resources for health policies in Sierra Leone , 2002 – 2012. Conflcit Heal. 2014;8(1):1–12. McCourt W, Eldridge D. Global human resource management: managing people in developing and transitional countries. Cheltenham: Edward Elgar; 2003. Fujita N, Zwi A, Nagai M, Akashi H. A comprehensive framework for human resources for health system development in fragile and post-conflict states. PLoS Med. 2011;8(12). Bossert TJ, Beauvais J. Decentralization of health systems in Ghana, Zambia, Uganda and the Philippines: a comparative analysis of decision space. Health Policy Plan. 2002;17(1):14–31 Available from: https://academic.oup.com/heapol/article-lookup/doi/10.1093/heapol/17.1.14. Bonenberger M, Aikins M, Akweongo P, Wyss K. Factors influencing the work efficiency of district health managers in low-resource settings : a qualitative study in Ghana. BMC Health Serv Res [Internet]. 2016;1–10. Available from: https://doi.org/10.1186/s12913-016-1271-3. Alonso-Garbayo A, Raven J, Theobald S, Ssengooba F, Nattimba M, Martineau T. Decision space for health workforce management in decentralized settings : a case study in Uganda. Health Policy Plan. 2017;32(suppl_3(August):iii59–66. This study is part of the ReBUILD consortium's work on health worker in crisis and conflicted-affected session and has a particular focus on deployment policies and practice during and post conflict or crisis. It contributes to the consortium's work on developing recommendations for strengthening health systems in such contexts. The ReBUILD consortium is funded by the UK Department for International Development (DFID). The authors are grateful to Dr. Maria Bertone for comments on a draft of this paper. This

-0.535455

1.05081

1.160705

0.998011

[ -0.8186354050807731, -0.25227461518978567 ]

[ 1.1403415924454041, 0.9612787343144322 ]

[ 0.8411388335209349, 1.4802715719177708 ]

[ 0.8471313270015002, 1.1488902781188348 ]

1,024

[ 512, 512 ]

[ 5485, 15146, 23378, 848, 7418, 363, 7436, 8898, 5925, 29936, 29871, 29896, 29929, 29929, 29946, 29889, 282, 29889, 29871, 29896, 29955, 29941, 29994, 29929, 29946, 29889, 13, 29954, 6170, 358, 310, 796, 19977, 370, 705, 29889, 5236, 6692, 2169, 2785, 29892, 29871, 29906, 29900, 29900, 29900, 29889, 29871, 29906, 29900, 29900, 29900, 29889, 13, 17579, 1288, 2598, 300, 653, 13249, 29889, 22313, 29943, 29889, 796, 19977, 370, 705, 29871, 29906, 29900, 29896, 29906, 4274, 6599, 8799, 362, 29889, 22313, 29943, 4234, 3461, 694, 29889, 29871, 29896, 29906, 29914, 29906, 29955, 29929, 29889, 7660, 29892, 13681, 29901, 4623, 2598, 300, 653, 13249, 29936, 29871, 29906, 29900, 29896, 29906, 29889, 29871, 29906, 29900, 29896, 29906, 29889, 13, 29924, 329, 466, 2766, 29899, 2517, 29920, 4324, 360, 29889, 450, 10879, 310, 9045, 17535, 11736, 373, 970, 17535, 9045, 15645, 17385, 362, 297, 796, 19977, 370, 705, 29889, 11019, 7436, 5925, 29871, 29945, 1985, 5650, 694, 29889, 29871, 29946, 29889, 23408, 267, 1388, 29892, 20672, 29901, 22056, 14587, 363, 9045, 11736, 2060, 29901, 1976, 29873, 6853, 1078, 9266, 29936, 29871, 29896, 29929, 29929, 29947, 29889, 13, 29925, 2192, 27342, 350, 29892, 3760, 457, 585, 323, 29892, 2296, 28464, 476, 29889, 4673, 292, 278, 4628, 3800, 310, 6782, 6757, 297, 970, 17535, 9045, 5786, 297, 263, 10504, 2106, 297, 7513, 29889, 350, 12513, 15202, 9635, 2538, 29889, 29871, 29906, 29900, 29896, 29953, 29936, 29896, 29953, 29898, 29896, 1125, 29896, 29994, 29896, 29906, 29889, 7740, 3106, 515, 29889, 2045, 597, 1867, 29875, 29889, 990, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29879, 29896, 29906, 29929, 29896, 29941, 29899, 29900, 29896, 29953, 29899, 29896, 29953, 29955, 29945, 29899, 29900, 29889, 13, 29943, 990, 423, 402, 997, 29892, 16790, 29874, 317, 29892, 1383, 29874, 638, 317, 29892, 10082, 12094, 29893, 1306, 317, 29892, 10785, 390, 29889, 1459, 6553, 23985, 322, 12968, 18981, 15057, 297, 7513, 29915, 29879, 5236, 15202, 15538, 319, 4533, 515, 278, 13960, 365, 1475, 29889, 29871, 29906, 29900, 29896, 29946, 29936, 29898, 29967, 1540, 467, 13, 29943, 9003, 5693, 327, 317, 29892, 341, 913, 273, 383, 29892, 14617, 484, 399, 29892, 13693, 379, 29889, 3831, 7273, 706, 2669, 1824, 4467, 363, 1162, 9216, 292, 9045, 17162, 297, 7592, 322, 17692, 10161, 584, 437, 896, 664, 1577, 20293, 2787, 940, 284, 9205, 29889, 29871, 29906, 29900, 29896, 29900, 29901, 29941, 29953, 29946, 29994, 29955, 29900, 29889, 13, 29933, 359, 1940, 323, 29967, 29889, 11597, 12339, 292, 278, 27189, 1705, 2133, 310, 9045, 6757, 297, 14338, 10916, 29901, 10608, 2913, 29892, 24233, 362, 322, 4180, 29889, 28239, 5636, 3436, 29889, 29871, 29896, 29929, 29929, 29947, 29936, 29946, 29955, 29901, 29896, 29945, 29896, 29941, 29994, 29906, 29955, 29889, 13, 29933, 814, 650, 16379, 29892, 3685, 1794, 341, 29892, 382, 2310, 29899, 8711, 801, 435, 29892, 399, 5171, 317, 29889, 319, 3474, 310, 15130, 363, 11736, 297, 1400, 29899, 5527, 29176, 6055, 1577, 450, 1206, 310, 5199, 7788, 363, 9045, 24833, 297, 24790, 951, 650, 1919, 29871, 29906, 29900, 29900, 29906, 785, 29871, 29906, 29900, 29896, 29906, 29889, 1281, 1579, 20752, 940, 284, 29889, 29871, 29906, 29900, 29896, 29946, 29936, 29947, 29898, 29896, 1125, 29896, 29994, 29896, 29906, 29889, 13, 27297, 29907, 14316, 399, 29892, 382, 430, 8605, 360, 29889, 12002, 5199, 6503, 10643, 29901, 767, 6751, 2305, 297, 14338, 322, 1301, 3245, 10916, 29889, 678, 295, 841, 3391, 29901, 9300, 1260, 5397, 29936, 29871, 29906, 29900, 29900, 29941, 29889, 13, 29943, 8016, 2028, 405, 29892, 796, 4353, 319, 29892, 14461, 1794, 341, 29892, 10813, 18321, 379, 29889, 319, 15171, 6270, 6890, 363, 5199, 7788, 363, 9045, 1788, 5849, 297, 13855, 488, 322, 1400, 29899, 5527, 29176, 5922, 29889, 349, 3410, 29903, 3436, 29889, 29871, 29906, 29900, 29896, 29896, 29936, 29947, 29898, 29896, 29906, 467, 13, 29933, 359, 1940, 323, 29967, 29892, 23826, 1564, 275, 435, 29889, 3826, 296, 1705, 2133, 310, 9045, 6757, 297, 13491, 1648, 29892, 796, 1117, 423, 29892, 501, 29887, 5863, 322, 278, 26260, 29901, 263, 5734, 1230, 7418, 310, 10608, 2913, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29900, 29906, 29936, 29896, 29955, 29898, 29896, 1125, 29896, 29946, 29994, 29941, 29896, 7740, 3106, 515, 29901, 2045, 597, 562, 1943, 13076, 29889, 1132, 29889, 510, 29914, 354, 481, 324, 29914, 7914, 29899, 20401, 29914, 1867, 29875, 29914, 29896, 29900, 29889, 29896, 29900, 29929, 29941, 29914, 354, 481, 324, 29914, 29896, 29955, 29889, 29896, 29889, 29896, 29946, 29889, 13, 29933, 19131, 15734, 341, 29892, 319, 638, 1144, 341, 29892, 10813, 705, 7443, 349, 29892, 10167, 893, 476, 29889, 26748, 943, 13787, 3277, 278, 664, 19201, 310, 6474, 9045, 767, 18150, 297, 4482, 29899, 10314, 6055, 584, 263, 4021, 23378, 6559, 297, 13491, 1648, 29889, 350, 12513, 15202, 9635, 2538, 518, 26341, 1822, 29871, 29906, 29900, 29896, 29953, 29936, 29896, 29994, 29896, 29900, 29889, 7740, 3106, 515, 29901, 2045, 597, 1867, 29875, 29889, 990, 29914, 29896, 29900, 29889, 29896, 29896, 29947, 29953, 29914, 29879, 29896, 29906, 29929, 29896, 29941, 29899, 29900, 29896, 29953, 29899, 29896, 29906, 29955, 29896, 29899, 29941, 29889, 13, 2499, 16911, 29899, 29954, 279, 27495, 29877, 319, 29892, 390, 3496, 435, 29892, 450, 711, 2741, 317, 29892, 317, 29879, 22260, 15330, 383, 29892, 405, 1131, 326, 2291, 341, 29892, 3760, 457, 585, 323, 29889, 3826, 2459, 2913, 363, 9045, 664, 10118, 10643, 297, 27189, 1705, 1891, 6055, 584, 263, 1206, 6559, 297, 501, 29887, 5863, 29889, 15202, 25219, 8402, 29889, 29871, 29906, 29900, 29896, 29955, 29936, 29941, 29906, 29898, 19303, 29880, 29918, 29941, 29898, 26197, 1125, 25609, 29945, 29929, 29994, 29953, 29953, 29889, 13, 4013, 6559, 338, 760, 310, 278, 830, 29933, 25282, 1136, 441, 1974, 29915, 29879, 664, 373, 9045, 15645, 297, 24161, 322, 9476, 9446, 29899, 3470, 26458, 4867, 322, 756, 263, 3153, 8569, 373, 18209, 24833, 322, 6944, 2645, 322, 1400, 14529, 470, 24161, 29889, 739, 640, 5026, 304, 278, 1136, 441, 1974, 29915, 29879, 664, 373, 14338, 6907, 800, 363, 9324, 8333, 9045, 6757, 297, 1316, 3030, 29879, 29889, 450, 830, 29933, 25282, 1136, 441, 1974, 338, 5220, 287, 491, 278, 10261, 10317, 363, 4623, 14650, 313, 4037, 1367, 467, 450, 15717, 526, 28656, 304, 4942, 29889, 6217, 16662, 650, 363, 6589, 373, 263, 18195, 310, 445, 5650, 29889, 13, 4013 ]

1,332,829

9,216

CommonCrawl

17

12

Understanding effects of nose-cone bluntness on hypersonic boundary layer transition using input-output analysis Cook, D. A., Thome, J. S., Brock, J. M., Nichols, J. W. & Candler, G. V., 2018, AIAA Aerospace Sciences Meeting. 210059 ed. American Institute of Aeronautics and Astronautics Inc, AIAA, (AIAA Aerospace Sciences Meeting, 2018; no. 210059). Understanding effects of personalized vs. aggregate ratings on user preferences Adomavicius, G., Bockstedt, J., Curley, S. & Zhang, J., Jan 1 2016, In: CEUR Workshop Proceedings. 1679, p. 14-21 8 p. Understanding elementary landscapes Whitley, L. D., Sutton, A. M. & Howe, A. E., 2008, GECCO'08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation 2008. Association for Computing Machinery, p. 585-592 8 p. (GECCO'08: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation 2008). Understanding emoji ambiguity in context: The role of text in emoji-related miscommunication Miller, H., Kluver, D., Thebault-Spieker, J., Terveen, L. & Hecht, B., 2017, Proceedings of the 11th International Conference on Web and Social Media, ICWSM 2017. AAAI press, p. 152-161 10 p. (Proceedings of the 11th International Conference on Web and Social Media, ICWSM 2017). Understanding employee awareness of health care quality information: How can employers benefit? Abraham, J., Feldman, R. & Carlin, C., Dec 2004, In: Health services research. 39, 6 I, p. 1799-1816 18 p. Understanding Environmental Public Opinion by Dimension: How Heuristic Processing Mitigates High Information Costs on Complex Issues Rugeley, C. R. & Gerlach, J. D., Jun 1 2012, In: Politics and Policy. 40, 3, p. 444-470 27 p. Understanding ethical concerns surrounding big data and learning analytics in higher education Duin, A. H. & Swenson, J., 2018, The Wiley Handbook of Education Policy. Papa, R. & Armfield, S. (eds.). Blackwell Publishing, p. 479-511 Understanding evolution in technology ecosystems Adomavicius, G., Bockstedt, J., Gupta, A. & Kauffman, R. J., Oct 1 2008, In: Communications of the ACM. 51, 10, p. 117-122 6 p. Understanding external and cascading benefits for HIV/AIDS control in a subsistence marketplace: Insights from Indonesia Arli, D. & Cadeaux, J., Mar 1 2017, In: Journal of Public Policy and Marketing. 36, 1, p. 117-136 20 p. Understanding factors affecting participation in online formative quizzes: An interview study Abney, A. J., Amin, S. & Kibble, J. D., Jan 1 2017, In: Advances in Physiology Education. 41, 3, p. 457-463 7 p. Understanding factors that trigger entrepreneurial behavior in established companies Morris, M. H., Zahra, S. A. & Schindehutte, M., 2000, Entrepreneurship and economic growth in the American economy. JAI Press, p. 133-159 27 p.

-1.01039

-0.619846

0.321209

0.264424

[ -0.9610816496966442, -1.059698280584555 ]

[ -0.4533178449202455, -0.7863747610438532 ]

[ 0.23751346947947882, 0.4049053771548406 ]

[ 0.3580737165699579, 0.17077505725575026 ]

1,024

[ 512, 512 ]

[ 7634, 11235, 9545, 310, 26414, 29899, 535, 29872, 1999, 1657, 2264, 373, 10163, 1330, 293, 10452, 7546, 9558, 773, 1881, 29899, 4905, 7418, 13, 19159, 29892, 360, 29889, 319, 1696, 498, 608, 29892, 435, 29889, 317, 1696, 4358, 384, 29892, 435, 29889, 341, 1696, 16371, 3775, 29892, 435, 29889, 399, 29889, 669, 28433, 1358, 29892, 402, 29889, 478, 1696, 29871, 29906, 29900, 29896, 29947, 29892, 319, 29902, 6344, 319, 9672, 3535, 17253, 2191, 15133, 29889, 29871, 29906, 29896, 29900, 29900, 29945, 29929, 1226, 29889, 3082, 8907, 310, 18682, 20546, 1199, 322, 319, 710, 20546, 1199, 9266, 29892, 319, 29902, 6344, 29892, 313, 23869, 6344, 319, 9672, 3535, 17253, 2191, 15133, 29892, 29871, 29906, 29900, 29896, 29947, 29936, 694, 29889, 29871, 29906, 29896, 29900, 29900, 29945, 29929, 467, 13, 29177, 11235, 9545, 310, 7333, 1891, 7186, 29889, 20431, 26838, 373, 1404, 5821, 2063, 13, 29909, 3129, 485, 1654, 375, 29892, 402, 1696, 350, 1698, 16470, 29873, 29892, 435, 1696, 10837, 2330, 29892, 317, 29889, 669, 796, 11895, 29892, 435, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 14645, 4574, 5244, 19032, 1019, 3947, 886, 29889, 29871, 29896, 29953, 29955, 29929, 29892, 282, 29889, 29871, 29896, 29946, 29899, 29906, 29896, 29871, 29947, 282, 29889, 13, 29177, 11235, 22470, 2982, 1557, 11603, 13, 8809, 1740, 29891, 29892, 365, 29889, 360, 1696, 317, 1851, 29892, 319, 29889, 341, 29889, 669, 1128, 29872, 29892, 319, 29889, 382, 1696, 29871, 29906, 29900, 29900, 29947, 29892, 402, 11206, 3217, 29915, 29900, 29947, 29901, 1019, 3947, 886, 310, 278, 29871, 29896, 29900, 386, 8081, 950, 16377, 373, 5739, 7492, 322, 382, 4068, 653, 11796, 362, 29871, 29906, 29900, 29900, 29947, 29889, 7993, 363, 11796, 292, 17197, 262, 708, 29892, 282, 29889, 29871, 29945, 29947, 29945, 29899, 29945, 29929, 29906, 29871, 29947, 282, 29889, 313, 1692, 29907, 3217, 29915, 29900, 29947, 29901, 1019, 3947, 886, 310, 278, 29871, 29896, 29900, 386, 8081, 950, 16377, 373, 5739, 7492, 322, 382, 4068, 653, 11796, 362, 29871, 29906, 29900, 29900, 29947, 467, 13, 29177, 11235, 953, 29877, 2397, 22363, 537, 297, 3030, 29901, 450, 6297, 310, 1426, 297, 953, 29877, 2397, 29899, 12817, 3984, 27820, 362, 13, 29924, 5495, 29892, 379, 1696, 476, 6092, 369, 29892, 360, 1696, 450, 29890, 1292, 29899, 5592, 347, 3946, 29892, 435, 1696, 5061, 345, 264, 29892, 365, 29889, 669, 940, 2570, 29892, 350, 1696, 29871, 29906, 29900, 29896, 29955, 29892, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 4623, 16377, 373, 2563, 322, 10307, 8213, 29892, 18340, 7811, 29924, 29871, 29906, 29900, 29896, 29955, 29889, 319, 6344, 29902, 3965, 29892, 282, 29889, 29871, 29896, 29945, 29906, 29899, 29896, 29953, 29896, 29871, 29896, 29900, 282, 29889, 313, 1184, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 4623, 16377, 373, 2563, 322, 10307, 8213, 29892, 18340, 7811, 29924, 29871, 29906, 29900, 29896, 29955, 467, 13, 29177, 11235, 19001, 3773, 8326, 404, 310, 9045, 2562, 11029, 2472, 29901, 1128, 508, 5703, 414, 14169, 29973, 13, 29909, 2634, 3391, 29892, 435, 1696, 21113, 1171, 29892, 390, 29889, 669, 1704, 1915, 29892, 315, 1696, 3826, 29871, 29906, 29900, 29900, 29946, 29892, 512, 29901, 15202, 5786, 5925, 29889, 29871, 29941, 29929, 29892, 29871, 29953, 306, 29892, 282, 29889, 29871, 29896, 29955, 29929, 29929, 29899, 29896, 29947, 29896, 29953, 29871, 29896, 29947, 282, 29889, 13, 29177, 11235, 16738, 284, 5236, 6461, 262, 291, 491, 4792, 2673, 29901, 1128, 940, 332, 4695, 10554, 292, 4573, 335, 1078, 5057, 10343, 9839, 29879, 373, 26596, 16982, 1041, 13, 29934, 5710, 2330, 29892, 315, 29889, 390, 29889, 669, 5681, 22617, 29892, 435, 29889, 360, 1696, 8378, 29871, 29896, 29871, 29906, 29900, 29896, 29906, 29892, 512, 29901, 6934, 1199, 322, 25219, 29889, 29871, 29946, 29900, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29946, 29946, 29946, 29899, 29946, 29955, 29900, 29871, 29906, 29955, 282, 29889, 13, 29177, 11235, 11314, 936, 21838, 18830, 4802, 848, 322, 6509, 16114, 1199, 297, 6133, 9793, 13, 29928, 29884, 262, 29892, 319, 29889, 379, 29889, 669, 3925, 25151, 29892, 435, 1696, 29871, 29906, 29900, 29896, 29947, 29892, 450, 399, 15168, 5166, 2909, 310, 13151, 25219, 29889, 27412, 29892, 390, 29889, 669, 8481, 2671, 29892, 317, 29889, 313, 5779, 6250, 6054, 5872, 19088, 29892, 282, 29889, 29871, 29946, 29955, 29929, 29899, 29945, 29896, 29896, 13, 29177, 11235, 14675, 297, 15483, 321, 3944, 973, 29879, 13, 29909, 3129, 485, 1654, 375, 29892, 402, 1696, 350, 1698, 16470, 29873, 29892, 435, 1696, 2088, 28363, 29892, 319, 29889, 669, 476, 28411, 1171, 29892, 390, 29889, 435, 1696, 4756, 29871, 29896, 29871, 29906, 29900, 29900, 29947, 29892, 512, 29901, 22365, 800, 310, 278, 14614, 29924, 29889, 29871, 29945, 29896, 29892, 29871, 29896, 29900, 29892, 282, 29889, 29871, 29896, 29896, 29955, 29899, 29896, 29906, 29906, 29871, 29953, 282, 29889, 13, 29177, 11235, 7029, 322, 3209, 29883, 9382, 23633, 363, 379, 5667, 29914, 29909, 1367, 29903, 2761, 297, 263, 11684, 11416, 9999, 6689, 29901, 13377, 5861, 515, 16704, 423, 13, 1433, 492, 29892, 360, 29889, 669, 315, 1943, 2993, 29892, 435, 1696, 1085, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 8237, 310, 5236, 25219, 322, 4485, 15133, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29896, 29896, 29955, 29899, 29896, 29941, 29953, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 13879, 6602, 292, 27577, 297, 7395, 883, 1230, 439, 4981, 267, 29901, 530, 15593, 6559, 13, 4920, 3801, 29892, 319, 29889, 435, 1696, 319, 1195, 29892, 317, 29889, 669, 476, 747, 569, 29892, 435, 29889, 360, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 25215, 2925, 297, 11661, 29875, 3002, 13151, 29889, 29871, 29946, 29896, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29946, 29945, 29955, 29899, 29946, 29953, 29941, 29871, 29955, 282, 29889, 13, 29177, 11235, 13879, 393, 7135, 23440, 1600, 332, 616, 6030, 297, 7841, 14582, 13, 28581, 3780, 29892, 341, 29889, 379, 1696, 796, 801, 336, 29892, 317, 29889, 319, 29889, 669, 1102, 25201, 29882, 329, 371, 29892, 341, 1696, 29871, 29906, 29900, 29900, 29900, 29892, 14447, 558, 1600, 332, 3527, 322, 17407, 14321, 297, 278, 3082, 26504, 29889, 435, 23869, 5254, 29892, 282, 29889, 29871, 29896, 29941, 29941, 29899, 29896, 29945, 29929, 29871, 29906, 29955, 282, 29889 ]

1,332,834

0

CommonCrawl

17

12

(Advances in the Study of Entrepreneurship, Innovation, and Economic Growth; vol. 12). Understanding family communication patterns and family functioning: The roles of conversation orientation and conformity orientation Koerner, A. F., Fitzpatrick, M. A. & Koerner, A. F., 2002, In: Communication Yearbook. p. 37-69 Understanding family interaction patterns in families with Alzheimer's disease Schaber, P., Blair, K., Jost, E., Schaffer, M. & Thurner, E., Jan 2016, In: OTJR Occupation, Participation and Health. 36, 1, p. 25-33 9 p. Understanding farmers' decision making processes and improving managerial assistance Öhlmér, B., Olson, K. & Brehmer, B., May 29 1998, In: Agricultural Economics. 18, 3, p. 273-290 18 p. Understanding farmscapes and their potential for improving IPM programs Rogers, M. A., Aug 4 2014, In: Journal of Integrated Pest Management. 5, 3 Understanding firewomen's fit problems with their coats and pants and its impact on mobility and safety Mckinney, E., Morris, K., Wu, Y., Griffin, L., Sokolowski, S., Carufel, R. & Park, J., Jun 24 2021, In: Work. 69, 2, p. 449-464 16 p. Understanding forced convective drying of apple tissue: Combining neutron radiography and numerical modelling Aregawi, W., Defraeye, T., Saneinejad, S., Vontobel, P., Lehmann, E., Carmeliet, J., Verboven, P., Derome, D. & Nicolai, B., Aug 2014, In: Innovative Food Science and Emerging Technologies. 24, p. 97-105 9 p. Understanding Galectin Structure-Function Relationships to Design Effective Antagonists Nesmelova, I. V., Dings, R. P. M. & Mayo, K. H., Jan 29 2008, Galectins. John Wiley & Sons, Inc., p. 33-69 37 p. Understanding gardening and dietary habits among youth garden program participants using the Theory of Planned Behavior Lautenschlager, L. & Smith, C., Jul 2007, In: Appetite. 49, 1, p. 122-130 9 p. Understanding gender roles in teen pregnancy prevention among American Indian youth Hanson, J. D., McMahon, T. R., Griese, E. R. & Kenyon, D. Y. B., Nov 1 2014, In: American journal of health behavior. 38, 6, p. 807-815 9 p. Understanding general and specific connections between psychopathology and marital distress: A model based approach South, S. C., Krueger, R. F. & Iacono, W. G., Nov 2011, In: Journal of abnormal psychology. 120, 4, p. 935-947 13 p. Understanding generational differences in financial literacy in Hmong immigrant families Solheim, C. A. & Yang, P. N. D., Jun 1 2010, In: Family and Consumer Sciences Research Journal. 38, 4, p. 435-454 20 p. Understanding genre through the lens of advocacy: The rhetorical work of the victim impact statement Propen, A. D. & Schuster, M. L., Jan 2010, In: Written Communication. 27, 1, p. 3-35 33 p. Understanding globalization Pesut, D. J. &

-0.996693

-0.550907

0.534254

0.062818

[ -0.9336881411166691, -1.059698280584555 ]

[ -0.49629293087167875, -0.6055212743315715 ]

[ 0.5114275002209799, 0.5570798386778968 ]

[ 0.03810517357485317, 0.08753120867165798 ]

1,024

[ 512, 512 ]

[ 313, 3253, 29894, 2925, 297, 278, 29301, 310, 14447, 558, 1600, 332, 3527, 29892, 512, 13715, 362, 29892, 322, 12884, 293, 402, 798, 386, 29936, 1700, 29889, 29871, 29896, 29906, 467, 13, 29177, 11235, 3942, 12084, 15038, 322, 3942, 740, 292, 29901, 450, 16178, 310, 14983, 19843, 322, 14670, 537, 19843, 13, 29968, 29877, 15479, 29892, 319, 29889, 383, 1696, 22963, 5031, 9131, 29892, 341, 29889, 319, 29889, 669, 8224, 15479, 29892, 319, 29889, 383, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 512, 29901, 22365, 362, 8905, 2909, 29889, 282, 29889, 29871, 29941, 29955, 29899, 29953, 29929, 13, 29177, 11235, 3942, 14881, 15038, 297, 13175, 411, 838, 29920, 27400, 29915, 29879, 17135, 13, 4504, 370, 261, 29892, 349, 1696, 10465, 381, 29892, 476, 1696, 435, 520, 29892, 382, 1696, 1102, 2142, 571, 29892, 341, 29889, 669, 498, 595, 261, 29892, 382, 1696, 2627, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 438, 29911, 29967, 29934, 16117, 786, 362, 29892, 3455, 12654, 362, 322, 15202, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29906, 29945, 29899, 29941, 29941, 29871, 29929, 282, 29889, 13, 29177, 11235, 2215, 13269, 29915, 10608, 3907, 10174, 322, 4857, 1747, 8455, 616, 18872, 13, 30094, 4415, 29885, 1064, 29892, 350, 1696, 7137, 1100, 29892, 476, 29889, 669, 5826, 29882, 1050, 29892, 350, 1696, 2610, 29871, 29906, 29929, 29871, 29896, 29929, 29929, 29947, 29892, 512, 29901, 27051, 3631, 12884, 1199, 29889, 29871, 29896, 29947, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29906, 29955, 29941, 29899, 29906, 29929, 29900, 29871, 29896, 29947, 282, 29889, 13, 29177, 11235, 2215, 1516, 5030, 267, 322, 1009, 7037, 363, 4857, 1747, 5641, 29924, 11104, 13, 29934, 468, 414, 29892, 341, 29889, 319, 1696, 22333, 29871, 29946, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 8237, 310, 17100, 630, 349, 342, 15057, 29889, 29871, 29945, 29892, 29871, 29941, 13, 29177, 11235, 3974, 29893, 2770, 29915, 29879, 6216, 4828, 411, 1009, 1302, 1446, 322, 282, 1934, 322, 967, 10879, 373, 22458, 1793, 322, 15332, 13, 29924, 384, 262, 3801, 29892, 382, 1696, 23112, 29892, 476, 1696, 29624, 29892, 612, 1696, 22990, 262, 29892, 365, 1696, 317, 554, 324, 11716, 29892, 317, 1696, 1704, 1137, 295, 29892, 390, 29889, 669, 4815, 29892, 435, 1696, 8378, 29871, 29906, 29946, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 5244, 29889, 29871, 29953, 29929, 29892, 29871, 29906, 29892, 282, 29889, 29871, 29946, 29946, 29929, 29899, 29946, 29953, 29946, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 11826, 378, 345, 312, 573, 15589, 292, 310, 26163, 260, 15118, 29901, 422, 2109, 292, 11553, 1617, 17937, 5275, 322, 16259, 878, 7807, 13, 29909, 1727, 1450, 29875, 29892, 399, 1696, 5282, 336, 1032, 29872, 29892, 323, 1696, 317, 1662, 457, 29926, 328, 29892, 317, 1696, 9299, 517, 6596, 29892, 349, 1696, 951, 29882, 4403, 29892, 382, 1696, 1704, 12873, 2035, 29892, 435, 1696, 26646, 9813, 29892, 349, 1696, 2452, 608, 29892, 360, 29889, 669, 13488, 1794, 29892, 350, 1696, 22333, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 512, 13715, 1230, 25453, 9327, 322, 27718, 3460, 8364, 11763, 29889, 29871, 29906, 29946, 29892, 282, 29889, 29871, 29929, 29955, 29899, 29896, 29900, 29945, 29871, 29929, 282, 29889, 13, 29177, 11235, 402, 744, 312, 262, 3767, 12425, 29899, 6678, 6376, 800, 14587, 304, 12037, 26475, 573, 530, 14103, 2879, 13, 29940, 267, 12873, 4273, 29892, 306, 29889, 478, 1696, 360, 886, 29892, 390, 29889, 349, 29889, 341, 29889, 669, 2610, 29877, 29892, 476, 29889, 379, 1696, 2627, 29871, 29906, 29929, 29871, 29906, 29900, 29900, 29947, 29892, 402, 744, 312, 1144, 29889, 2259, 399, 15168, 669, 317, 787, 29892, 9266, 1696, 282, 29889, 29871, 29941, 29941, 29899, 29953, 29929, 29871, 29941, 29955, 282, 29889, 13, 29177, 11235, 16423, 292, 322, 652, 300, 653, 2299, 1169, 4249, 12397, 16423, 1824, 27138, 773, 278, 24134, 310, 1858, 11310, 1522, 16300, 13, 29931, 1300, 3586, 29880, 1875, 29892, 365, 29889, 669, 7075, 29892, 315, 1696, 2739, 29871, 29906, 29900, 29900, 29955, 29892, 512, 29901, 2401, 300, 568, 29889, 29871, 29946, 29929, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29896, 29906, 29906, 29899, 29896, 29941, 29900, 29871, 29929, 282, 29889, 13, 29177, 11235, 23346, 16178, 297, 734, 264, 758, 5138, 6906, 5557, 291, 4249, 3082, 7560, 12397, 13, 29950, 16307, 29892, 435, 29889, 360, 1696, 4052, 29924, 801, 265, 29892, 323, 29889, 390, 1696, 402, 374, 968, 29892, 382, 29889, 390, 29889, 669, 10015, 29891, 265, 29892, 360, 29889, 612, 29889, 350, 1696, 2864, 29871, 29896, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 3082, 8955, 310, 9045, 6030, 29889, 29871, 29941, 29947, 29892, 29871, 29953, 29892, 282, 29889, 29871, 29947, 29900, 29955, 29899, 29947, 29896, 29945, 29871, 29929, 282, 29889, 13, 29177, 11235, 2498, 322, 2702, 12368, 1546, 11643, 459, 493, 3002, 322, 1766, 2410, 1320, 1253, 29901, 319, 1904, 2729, 2948, 13, 29903, 2438, 29892, 317, 29889, 315, 1696, 28499, 387, 261, 29892, 390, 29889, 383, 29889, 669, 306, 29874, 21441, 29892, 399, 29889, 402, 1696, 2864, 29871, 29906, 29900, 29896, 29896, 29892, 512, 29901, 8237, 310, 633, 8945, 11643, 3002, 29889, 29871, 29896, 29906, 29900, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29929, 29941, 29945, 29899, 29929, 29946, 29955, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 1176, 1288, 12651, 297, 18161, 4631, 4135, 297, 379, 29885, 549, 5198, 4481, 424, 13175, 13, 13296, 6391, 29892, 315, 29889, 319, 29889, 669, 27583, 29892, 349, 29889, 405, 29889, 360, 1696, 8378, 29871, 29896, 29871, 29906, 29900, 29896, 29900, 29892, 512, 29901, 14662, 322, 2138, 4680, 17253, 10550, 8237, 29889, 29871, 29941, 29947, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29946, 29941, 29945, 29899, 29946, 29945, 29946, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 16151, 1549, 278, 301, 575, 310, 22545, 4135, 29901, 450, 364, 9188, 272, 936, 664, 310, 278, 28985, 10879, 3229, 13, 1184, 2238, 29892, 319, 29889, 360, 29889, 669, 1102, 5402, 29892, 341, 29889, 365, 1696, 2627, 29871, 29906, 29900, 29896, 29900, 29892, 512, 29901, 16849, 841, 22365, 362, 29889, 29871, 29906, 29955, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29941, 29899, 29941, 29945, 29871, 29941, 29941, 282, 29889, 13, 29177, 11235, 5534, 2133, 13, 29925, 267, 329, 29892, 360, 29889, 435, 29889, 669 ]

1,332,834

1,024

CommonCrawl

17

12

Horton-Deutsch, S., 2002, In: Nursing outlook. 50, 3, p. 87-88 2 p. Understanding global teleconnections of climate to regional model estimates of Amazon ecosystem carbon fluxes Potter, C., Klooster, S., Steinbach, M., Tan, P. N., Kumar, V., Shekhar, S. & Reis de Carvalho, C., May 2004, In: Global change biology. 10, 5, p. 693-703 11 p. Understanding gradient clipping in private SGD: A geometric perspective Chen, X., Wu, S. & Hong, M., 2020, In: Advances in Neural Information Processing Systems. 2020-December Understanding horizontal Bridgman shelf growth of cadmium telluride and cadmium zinc telluride I. Heat and momentum transfer Edwards, K. & Derby, J. J., Aug 1997, In: Journal of Crystal Growth. 179, 1-2, p. 120-132 13 p. Understanding horizontal Bridgman shelf growth of cadmium telluride and cadmium zinc telluride II. Thermoelastic stresses Understanding How Acoustic Vibrations Modulate the Optical Response of Plasmonic Metal Nanoparticles Ahmed, A., Pelton, M. & Guest, J. R., Sep 26 2017, In: ACS nano. 11, 9, p. 9360-9369 10 p. Understanding 'How computing has changed the world' Misa, T. J., Oct 2007, In: IEEE Annals of the History of Computing. 29, 4, p. 52-63 12 p. Understanding how gay, bisexual, and other men who have sex with men in China cope with hiv care-related stressors Li, C., Giovenco, D., Dong, W., Smith, M. K., Golin, C. E., Fisher, E. B., Lei, G., Jiang, H., Tang, P. Y. & Muessig, K. E., Feb 1 2021, In: AIDS Education and Prevention. 33, 1, p. 46-61 16 p. Understanding how language matters Yang, K. K., Mar 15 2015, In: Index on Censorship. 44, 1, p. 64-66 3 p. Understanding How Language of Instruction Impacts Early Literacy Growth for Spanish-Speaking Children Wackerle-Hollman, A., Durán, L., Miranda, A., Chávez, C., Rodriguez, M. & Medina Morales, N., Jun 2 2021, In: School Psychology Review. Understanding how microbiomes influence the systems they inhabit Hall, E. K., Bernhardt, E. S., Bier, R. L., Bradford, M. A., Boot, C. M., Cotner, J. B., del Giorgio, P. A., Evans, S. E., Graham, E. B., Jones, S. E., Lennon, J. T., Locey, K. J., Nemergut, D., Osborne, B. B., Rocca, J. D., Schimel, J. P., Waldrop, M. P. & Wallenstein, M. D., Sep 1 2018, In: Nature Microbiology. 3, 9, p. 977-982 6 p. Understanding how people use natural language to ask for recommendations Kang, J., Condiff, K., Chang, S., Konstan, J. A., Terveen, L. & Harper, F. M., Aug 27 2017, RecSys 2017 - Proceedings of the 11th ACM Conference on Recommender Systems. Association for Computing Machinery, Inc, p. 229-237 9 p. (RecSys 2

-0.821375

-0.410063

0.437877

0.164272

[ -0.9665603514126393, -0.6761891604649021 ]

[ -0.2486266152192783, -0.571499331286687 ]

[ 0.0041792951441260605, 0.8715737258255462 ]

[ 0.37368193817947526, -0.04513867500923912 ]

1,024

[ 512, 512 ]

[ 379, 26342, 29899, 2772, 2434, 29892, 317, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 512, 29901, 405, 1295, 292, 714, 6914, 29889, 29871, 29945, 29900, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29947, 29955, 29899, 29947, 29947, 29871, 29906, 282, 29889, 13, 29177, 11235, 5534, 4382, 11958, 1953, 310, 23622, 304, 14014, 1904, 21875, 310, 16631, 321, 3944, 973, 22004, 19389, 267, 13, 29925, 327, 357, 29892, 315, 1696, 476, 417, 15664, 29892, 317, 1696, 14808, 6740, 29892, 341, 1696, 15066, 29892, 349, 29889, 405, 1696, 476, 24540, 29892, 478, 1696, 2296, 29895, 8222, 29892, 317, 29889, 669, 830, 275, 316, 1704, 791, 1251, 29892, 315, 1696, 2610, 29871, 29906, 29900, 29900, 29946, 29892, 512, 29901, 12002, 1735, 4768, 3002, 29889, 29871, 29896, 29900, 29892, 29871, 29945, 29892, 282, 29889, 29871, 29953, 29929, 29941, 29899, 29955, 29900, 29941, 29871, 29896, 29896, 282, 29889, 13, 29177, 11235, 16030, 9335, 3262, 297, 2024, 317, 29954, 29928, 29901, 319, 26224, 18520, 13, 1451, 264, 29892, 1060, 1696, 29624, 29892, 317, 29889, 669, 12798, 29892, 341, 1696, 29871, 29906, 29900, 29906, 29900, 29892, 512, 29901, 25215, 2925, 297, 2448, 3631, 10343, 10554, 292, 23985, 29889, 29871, 29906, 29900, 29906, 29900, 29899, 6185, 1096, 13, 29177, 11235, 14698, 1771, 333, 29887, 1171, 528, 761, 14321, 310, 13840, 29885, 1974, 2649, 332, 680, 322, 13840, 29885, 1974, 503, 3742, 2649, 332, 680, 306, 29889, 940, 271, 322, 19399, 6782, 13, 3853, 2935, 29892, 476, 29889, 669, 29520, 29892, 435, 29889, 435, 1696, 22333, 29871, 29896, 29929, 29929, 29955, 29892, 512, 29901, 8237, 310, 22121, 11195, 402, 798, 386, 29889, 29871, 29896, 29955, 29929, 29892, 29871, 29896, 29899, 29906, 29892, 282, 29889, 29871, 29896, 29906, 29900, 29899, 29896, 29941, 29906, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 14698, 1771, 333, 29887, 1171, 528, 761, 14321, 310, 13840, 29885, 1974, 2649, 332, 680, 322, 13840, 29885, 1974, 503, 3742, 2649, 332, 680, 1944, 29889, 498, 20772, 295, 6288, 851, 15322, 13, 29177, 11235, 1128, 7255, 18291, 293, 478, 4626, 800, 3382, 5987, 278, 20693, 936, 13291, 310, 1858, 294, 3712, 293, 24992, 25701, 459, 18569, 13, 17565, 2168, 29892, 319, 1696, 15549, 880, 29892, 341, 29889, 669, 2088, 342, 29892, 435, 29889, 390, 1696, 29639, 29871, 29906, 29953, 29871, 29906, 29900, 29896, 29955, 29892, 512, 29901, 319, 9295, 302, 1562, 29889, 29871, 29896, 29896, 29892, 29871, 29929, 29892, 282, 29889, 29871, 29929, 29941, 29953, 29900, 29899, 29929, 29941, 29953, 29929, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 525, 5328, 20602, 756, 3939, 278, 3186, 29915, 13, 29924, 8069, 29892, 323, 29889, 435, 1696, 4756, 29871, 29906, 29900, 29900, 29955, 29892, 512, 29901, 7159, 17896, 8081, 1338, 310, 278, 5298, 310, 11796, 292, 29889, 29871, 29906, 29929, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29945, 29906, 29899, 29953, 29941, 29871, 29896, 29906, 282, 29889, 13, 29177, 11235, 920, 23852, 29892, 2652, 735, 950, 29892, 322, 916, 1757, 1058, 505, 7916, 411, 1757, 297, 7551, 1302, 412, 411, 298, 440, 2562, 29899, 12817, 22884, 943, 13, 23410, 29892, 315, 1696, 4406, 9813, 1111, 29892, 360, 1696, 360, 549, 29892, 399, 1696, 7075, 29892, 341, 29889, 476, 1696, 20268, 262, 29892, 315, 29889, 382, 1696, 12030, 261, 29892, 382, 29889, 350, 1696, 951, 29875, 29892, 402, 1696, 18122, 574, 29892, 379, 1696, 27378, 29892, 349, 29889, 612, 29889, 669, 8229, 404, 335, 29892, 476, 29889, 382, 1696, 26319, 29871, 29896, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 319, 1367, 29903, 13151, 322, 4721, 7316, 29889, 29871, 29941, 29941, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29946, 29953, 29899, 29953, 29896, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 920, 4086, 13750, 13, 29979, 574, 29892, 476, 29889, 476, 1696, 1085, 29871, 29896, 29945, 29871, 29906, 29900, 29896, 29945, 29892, 512, 29901, 11374, 373, 315, 6073, 3527, 29889, 29871, 29946, 29946, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29953, 29946, 29899, 29953, 29953, 29871, 29941, 282, 29889, 13, 29177, 11235, 1128, 17088, 310, 2799, 4080, 14305, 627, 29879, 11095, 5449, 4135, 402, 798, 386, 363, 10432, 29899, 10649, 5086, 20986, 13, 29956, 28940, 280, 29899, 29950, 3028, 1171, 29892, 319, 1696, 7073, 1715, 29892, 365, 1696, 11612, 5863, 29892, 319, 1696, 678, 29976, 13325, 29892, 315, 1696, 7733, 8966, 24448, 29892, 341, 29889, 669, 3436, 1099, 3879, 2122, 29892, 405, 1696, 8378, 29871, 29906, 29871, 29906, 29900, 29906, 29896, 29892, 512, 29901, 4523, 16777, 3002, 13957, 29889, 13, 29177, 11235, 920, 9200, 5365, 290, 267, 9949, 278, 6757, 896, 14117, 277, 13, 29950, 497, 29892, 382, 29889, 476, 1696, 6209, 25603, 29892, 382, 29889, 317, 1696, 350, 631, 29892, 390, 29889, 365, 1696, 15862, 4006, 29892, 341, 29889, 319, 1696, 13760, 29892, 315, 29889, 341, 1696, 26783, 1089, 29892, 435, 29889, 350, 1696, 628, 25906, 601, 29892, 349, 29889, 319, 1696, 24056, 29892, 317, 29889, 382, 1696, 22196, 29892, 382, 29889, 350, 1696, 10920, 29892, 317, 29889, 382, 1696, 365, 2108, 265, 29892, 435, 29889, 323, 1696, 4309, 346, 29891, 29892, 476, 29889, 435, 1696, 18268, 15064, 329, 29892, 360, 1696, 6657, 4089, 484, 29892, 350, 29889, 350, 1696, 25111, 1113, 29892, 435, 29889, 360, 1696, 1102, 326, 295, 29892, 435, 29889, 349, 1696, 17721, 1336, 29892, 341, 29889, 349, 29889, 669, 399, 5442, 5465, 29892, 341, 29889, 360, 1696, 29639, 29871, 29896, 29871, 29906, 29900, 29896, 29947, 29892, 512, 29901, 17677, 20140, 5365, 3002, 29889, 29871, 29941, 29892, 29871, 29929, 29892, 282, 29889, 29871, 29929, 29955, 29955, 29899, 29929, 29947, 29906, 29871, 29953, 282, 29889, 13, 29177, 11235, 920, 2305, 671, 5613, 4086, 304, 2244, 363, 6907, 800, 13, 29968, 574, 29892, 435, 1696, 11790, 2593, 29892, 476, 1696, 678, 574, 29892, 317, 1696, 5250, 14411, 29892, 435, 29889, 319, 1696, 5061, 345, 264, 29892, 365, 29889, 669, 3536, 546, 29892, 383, 29889, 341, 1696, 22333, 29871, 29906, 29955, 29871, 29906, 29900, 29896, 29955, 29892, 3599, 29903, 952, 29871, 29906, 29900, 29896, 29955, 448, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 14614, 29924, 16377, 373, 830, 2055, 1581, 23985, 29889, 7993, 363, 11796, 292, 17197, 262, 708, 29892, 9266, 29892, 282, 29889, 29871, 29906, 29906, 29929, 29899, 29906, 29941, 29955, 29871, 29929, 282, 29889, 313, 4789, 29903, 952, 29871, 29906 ]

1,332,834

2,048

CommonCrawl

17

12

017 - Proceedings of the 11th ACM Conference on Recommender Systems). Understanding how product attributes influence product categorization: Development and validation of fuzzy set-based measures of gradedness in product categories Viswanathan, M. & Childers, T. L., Feb 1999, In: Journal of Marketing Research. 36, 1, p. 75-94 20 p. Understanding How Sustainability Initiatives Fail: A Framework to Aid Design of Effective Interventions Brough, A. R., Donnelly, G. E., Griskevicius, V., Markowitz, E. M., Raimi, K. T., Reeck, C., Trudel, R., Waldman, K. B., Winterich, K. P. & Wolske, K. S., Dec 2020, In: Social Marketing Quarterly. 26, 4, p. 309-324 16 p. Understanding how we talk about space: An examination of the meaning of English spatial prepositions: Cognitive and Computational Perspectives Manning, C., Sera, M. & Pick, H., 2002, Spatial Language: Cognitive and Computational Perspectives. Coventry, K. R. & Oliver, P. (eds.). Dordrecht, NL: Kluwer Academic Publishers, p. 147-164 Understanding human-landscape interactions in the "anthropocene" Harden, C. P., Chin, A., English, M. R., Fu, R., Galvin, K. A., Gerlak, A. K., McDowell, P. F., McNamara, D. E., Peterson, J. M., Poff, N. L., Rosa, E. A., Solecki, W. D. & Wohl, E. E., Jan 2014, In: Environmental management. 53, 1, p. 4-13 10 p. Understanding human motion and gestures for underwater human–robot collaboration Islam, M. J., Ho, M. & Sattar, J., Aug 2019, In: Journal of Field Robotics. 36, 5, p. 851-873 23 p. Understanding Humility and Its Role in Relational Therapy Rowden, T. J., Harris, S. M. & Wickel, K., Sep 2014, In: Contemporary Family Therapy. 36, 3, p. 380-391 12 p. Understanding identity integration: Theoretical, methodological, and applied issues Syed, M. & McLean, K. C., Feb 1 2016, In: Journal of Adolescence. 47, p. 109-118 10 p. Understanding immigrant college students: Applying a developmental ecology framework to the practice of academic advising Stebleton, M. J., 2011, In: NACADA Journal. 31, p. 42-54 Understanding implementation fidelity in a pragmatic randomized clinical trial in the nursing home setting:a mixed-methods examination Palmer, J. A., Parker, V. A., Barre, L. R., Mor, V., Volandes, A. E., Belanger, E., Loomer, L., McCreedy, E. & Mitchell, S. L., Nov 28 2019, In: Trials. 20, 1, 656. Understanding improved lifetime in mixed emissive layer organic light-emitting devices (OLEDs) Bangsund, J. S. & Holmes, R. J., Jan 1 2017, Solid-State Lighting, SSL 2017. OSA - The Optical Society, Vol. Part F72-SSL 2017. Understanding India's forest bureaucracy: a review Fleischman, F., Aug 1 2016, In: Regional Environmental Change. 16, p. 153-165 13 p. Understanding Infidelity Forgiveness

-0.60976

-0.420639

0.625558

0.303445

[ -0.4173205043841363, -0.802199299932788 ]

[ -0.10862184301812468, -0.7326559036045616 ]

[ 0.8715737258255462, 0.37954296690099787 ]

[ 0.4517230462270618, 0.15516683564623296 ]

1,024

[ 512, 512 ]

[ 29900, 29896, 29955, 448, 1019, 3947, 886, 310, 278, 29871, 29896, 29896, 386, 14614, 29924, 16377, 373, 830, 2055, 1581, 23985, 467, 13, 29177, 11235, 920, 3234, 8393, 9949, 3234, 11608, 2133, 29901, 14650, 322, 8845, 310, 285, 3365, 1537, 731, 29899, 6707, 15366, 310, 4656, 287, 2264, 297, 3234, 13997, 13, 6116, 11440, 11385, 29892, 341, 29889, 669, 10517, 414, 29892, 323, 29889, 365, 1696, 26319, 29871, 29896, 29929, 29929, 29929, 29892, 512, 29901, 8237, 310, 4485, 15133, 10550, 29889, 29871, 29941, 29953, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29955, 29945, 29899, 29929, 29946, 29871, 29906, 29900, 282, 29889, 13, 29177, 11235, 1128, 317, 504, 475, 3097, 512, 4812, 5056, 29098, 29901, 319, 16657, 304, 319, 333, 12037, 310, 26475, 573, 4124, 794, 1080, 13, 29933, 10573, 29892, 319, 29889, 390, 1696, 360, 3409, 14112, 29892, 402, 29889, 382, 1696, 1632, 19456, 29894, 1654, 375, 29892, 478, 1696, 4485, 340, 2784, 29892, 382, 29889, 341, 1696, 6981, 10233, 29892, 476, 29889, 323, 1696, 830, 29872, 384, 29892, 315, 1696, 1605, 566, 295, 29892, 390, 1696, 17721, 1171, 29892, 476, 29889, 350, 1696, 12267, 436, 29892, 476, 29889, 349, 29889, 669, 399, 3775, 446, 29892, 476, 29889, 317, 1696, 3826, 29871, 29906, 29900, 29906, 29900, 29892, 512, 29901, 10307, 4485, 15133, 751, 4254, 368, 29889, 29871, 29906, 29953, 29892, 29871, 29946, 29892, 282, 29889, 29871, 29941, 29900, 29929, 29899, 29941, 29906, 29946, 29871, 29896, 29953, 282, 29889, 13, 29177, 11235, 920, 591, 5193, 1048, 2913, 29901, 530, 4392, 3381, 310, 278, 6593, 310, 4223, 18652, 758, 1066, 2187, 29901, 315, 3811, 3321, 322, 11796, 1288, 9034, 1103, 3145, 13, 29924, 9450, 29892, 315, 1696, 317, 1572, 29892, 341, 29889, 669, 23868, 29892, 379, 1696, 29871, 29906, 29900, 29900, 29906, 29892, 1706, 15238, 17088, 29901, 315, 3811, 3321, 322, 11796, 1288, 9034, 1103, 3145, 29889, 25669, 8269, 29892, 476, 29889, 390, 29889, 669, 19731, 29892, 349, 29889, 313, 5779, 6250, 360, 536, 15320, 29892, 405, 29931, 29901, 476, 6092, 556, 16146, 293, 12904, 414, 29892, 282, 29889, 29871, 29896, 29946, 29955, 29899, 29896, 29953, 29946, 13, 29177, 11235, 5199, 29899, 5252, 5738, 22060, 297, 278, 376, 9716, 1336, 542, 1600, 29908, 13, 29950, 7879, 29892, 315, 29889, 349, 1696, 678, 262, 29892, 319, 1696, 4223, 29892, 341, 29889, 390, 1696, 11871, 29892, 390, 1696, 5208, 3845, 29892, 476, 29889, 319, 1696, 5681, 18170, 29892, 319, 29889, 476, 1696, 4052, 29928, 340, 514, 29892, 349, 29889, 383, 1696, 4052, 29940, 314, 2518, 29892, 360, 29889, 382, 1696, 5879, 1330, 29892, 435, 29889, 341, 1696, 349, 2696, 29892, 405, 29889, 365, 1696, 21974, 29892, 382, 29889, 319, 1696, 1105, 280, 22736, 29892, 399, 29889, 360, 29889, 669, 399, 10330, 29892, 382, 29889, 382, 1696, 2627, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 16738, 284, 10643, 29889, 29871, 29945, 29941, 29892, 29871, 29896, 29892, 282, 29889, 29871, 29946, 29899, 29896, 29941, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 5199, 10884, 322, 7737, 1973, 363, 1090, 13405, 5199, 29994, 307, 7451, 24771, 13, 29902, 2536, 314, 29892, 341, 29889, 435, 1696, 8335, 29892, 341, 29889, 669, 317, 1131, 279, 29892, 435, 1696, 22333, 29871, 29906, 29900, 29896, 29929, 29892, 512, 29901, 8237, 310, 8989, 6417, 327, 1199, 29889, 29871, 29941, 29953, 29892, 29871, 29945, 29892, 282, 29889, 29871, 29947, 29945, 29896, 29899, 29947, 29955, 29941, 29871, 29906, 29941, 282, 29889, 13, 29177, 11235, 13863, 1793, 322, 8011, 1528, 280, 297, 6376, 1288, 25451, 27580, 13, 4301, 1145, 29892, 323, 29889, 435, 1696, 20349, 29892, 317, 29889, 341, 29889, 669, 399, 860, 295, 29892, 476, 1696, 29639, 29871, 29906, 29900, 29896, 29946, 29892, 512, 29901, 27183, 653, 14662, 25451, 27580, 29889, 29871, 29941, 29953, 29892, 29871, 29941, 29892, 282, 29889, 29871, 29941, 29947, 29900, 29899, 29941, 29929, 29896, 29871, 29896, 29906, 282, 29889, 13, 29177, 11235, 10110, 13465, 29901, 450, 12116, 936, 29892, 1158, 5996, 29892, 322, 7436, 5626, 13, 29903, 28133, 29892, 341, 29889, 669, 4052, 3226, 273, 29892, 476, 29889, 315, 1696, 26319, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 8237, 310, 2087, 6544, 29883, 663, 29889, 29871, 29946, 29955, 29892, 282, 29889, 29871, 29896, 29900, 29929, 29899, 29896, 29896, 29947, 29871, 29896, 29900, 282, 29889, 13, 29177, 11235, 5198, 4481, 424, 12755, 8041, 29901, 2401, 5890, 263, 5849, 284, 321, 1054, 6933, 6890, 304, 278, 6944, 310, 21567, 25228, 292, 13, 7789, 569, 880, 29892, 341, 29889, 435, 1696, 29871, 29906, 29900, 29896, 29896, 29892, 512, 29901, 405, 2477, 3035, 29909, 8237, 29889, 29871, 29941, 29896, 29892, 282, 29889, 29871, 29946, 29906, 29899, 29945, 29946, 13, 29177, 11235, 5314, 285, 10652, 537, 297, 263, 282, 1431, 29885, 2454, 4036, 1891, 24899, 936, 14260, 297, 278, 302, 1295, 292, 3271, 4444, 29901, 29874, 12849, 29899, 23515, 4392, 3381, 13, 18210, 1050, 29892, 435, 29889, 319, 1696, 24239, 29892, 478, 29889, 319, 1696, 2261, 276, 29892, 365, 29889, 390, 1696, 3879, 29892, 478, 1696, 3684, 392, 267, 29892, 319, 29889, 382, 1696, 3741, 4600, 29892, 382, 1696, 4309, 12392, 29892, 365, 1696, 4052, 9832, 7584, 29892, 382, 29889, 669, 26676, 29892, 317, 29889, 365, 1696, 2864, 29871, 29906, 29947, 29871, 29906, 29900, 29896, 29929, 29892, 512, 29901, 8602, 1338, 29889, 29871, 29906, 29900, 29892, 29871, 29896, 29892, 29871, 29953, 29945, 29953, 29889, 13, 29177, 11235, 16710, 25423, 297, 12849, 953, 790, 573, 7546, 2894, 293, 3578, 29899, 331, 5367, 9224, 313, 29949, 20566, 29879, 29897, 13, 29933, 25128, 870, 29892, 435, 29889, 317, 29889, 669, 4168, 4467, 29892, 390, 29889, 435, 1696, 2627, 29871, 29896, 29871, 29906, 29900, 29896, 29955, 29892, 4956, 333, 29899, 2792, 12790, 292, 29892, 17122, 29871, 29906, 29900, 29896, 29955, 29889, 6570, 29909, 448, 450, 20693, 936, 7765, 29892, 3684, 29889, 3455, 383, 29955, 29906, 29899, 18641, 29871, 29906, 29900, 29896, 29955, 29889, 13, 29177, 11235, 7513, 29915, 29879, 13569, 289, 13411, 29883, 10068, 29901, 263, 9076, 13, 29943, 280, 783, 1171, 29892, 383, 1696, 22333, 29871, 29896, 29871, 29906, 29900, 29896, 29953, 29892, 512, 29901, 16208, 16738, 284, 10726, 29889, 29871, 29896, 29953, 29892, 282, 29889, 29871, 29896, 29945, 29941, 29899, 29896, 29953, 29945, 29871, 29896, 29941, 282, 29889, 13, 29177, 11235, 9969, 10652, 537, 383, 990, 20193 ]

1,332,834

3,072

CommonCrawl

17

12

Hidden Away – Part 2 Posted: February 21, 2016 in Book I Terror in Texas They drove deserted vehicles and abandoned stores. They passed a cluster of buildings in the distance but no one seemed to want to explore it. When Zack pointed toward the ranch, Steve frowned. "Too close to the road. Too many abandoned vehicles. There could be infected around." The pickup weaved around yet another abandoned vehicle while the light quickly began to fade as the sun dipped below the rim of a distant tree-covered ridge. A glimmer of light flashed against glass in the distance and they saw a small cabin on a high ridge. They neared a gravel road that turned to the right and disappeared into the trees. Zack stopped the truck. "Well, what do you think?" "It would be off the beaten path, for sure." Steve answered. "Let's try it." They turned onto the gravel road heading up trees. The path climbed the side of a hill. The further they drove, the steeper the slope at the side of the road and the narrower the path grew. Della sat up in the seat and whispered to Steve. "Are you sure about this?" "No but there's no place to turn around right, now." Steve answered. "Keep going, Zack." They drove another mile over deep ruts and washes then the path widened at a cattle pen and shed. Zack eased the truck to a stop. "What now? It looks like the wrong road." "No. I see the cabin through those trees. I think the road loops around the shed. Wait here." He stepped out of the truck and followed the path to the back of the shed. He disappeared for a few moments then came back to announce. "We're still going in the right direction. I can see a cabin. It looks pretty narrow ahead, but if we get beyond there the cabin is right ahead. Let me check it out." Steve retraced the narrow path to the back of the shed and then around a stand of trees. Ahead he could see the hunting cabin. It was a narrow trail that looked to be used by four wheeled ATVs in the past, but nothing recently. He limped farther down the track and saw an open yard in front of the cabin. He made his way back to the truck and climbed inside. On the way back he rolled half a dozen large rocks to the side of the trail. Steve limped back to the truck and announced. "It's doable." He climbed in the truck. "Around the back of the shed, head up the trail." Zack did as directed. When he pulled around the shed, he slammed on the breaks. "That's not wide enough!" He stared at the narrow trail with the rough drop off to the left and the steep rise of dirt and brush o the right. "I can't do this. We'll go over." Steve placed his hand on Zack's shoulder. "You can do this. Just keep your left tire on the trail. The slope on the inside is gentle enough that you can drive on it. It'll tilt the truck, but the tires are big enough to climb over a few rocks at the side of the road. The trail is wider around just beyond there." "You can do this Zack." Della echoed. Zack chuckled nervously. "Okay, at least ya'll get out, just in case." "Good idea. Della, you four get out. I'll ride with Zack." Stave answered. "We'll pick you up on the other side." The three women and child stepped out of the truck and waited as the vehicle pulled ahead. They watched as the massive vehicle rolled toward the narrowing of the trail. Zack shifted into low gear and the sound of the engine growled. The tires rolled forward with Steve urging Zack to guide the truck toward the upper slope. Zack turned the steering wheel to the right. The front tire climbed up the incline while the left tires rolled along-side the drop-off at the side of the trek. Zack's brow glistened with perspiration. "Am I good?" He asked. "I can't see the road." "You're doing fine." Steve leaned out the window judging the distance. "To the right. More to the right. The tire can roll up the rocks at the side. Slow and

0.290802

-0.3038

-0.096002

-0.795715

[ 0.24971142953826003, 0.33189195527818566 ]

[ 0.06954570082219232, -0.6771464175839603 ]

[ -0.18603878175969413, -0.005965668957411016 ]

[ -0.6019944980571221, -0.9894360823850361 ]

1,024

[ 512, 512 ]

[ 379, 4215, 319, 1582, 785, 3455, 29871, 29906, 13, 6747, 287, 29901, 6339, 29871, 29906, 29896, 29892, 29871, 29906, 29900, 29896, 29953, 297, 6726, 306, 323, 2704, 297, 10319, 13, 15597, 26603, 18197, 287, 24413, 322, 23181, 14422, 29889, 2688, 4502, 263, 9867, 310, 13814, 297, 278, 5418, 541, 694, 697, 6140, 304, 864, 304, 26987, 372, 29889, 1932, 796, 547, 11520, 11183, 278, 6350, 305, 29892, 13981, 285, 4708, 287, 29889, 376, 1762, 29877, 3802, 304, 278, 6520, 29889, 1763, 29877, 1784, 23181, 24413, 29889, 1670, 1033, 367, 3041, 26458, 2820, 1213, 13, 1576, 5839, 786, 591, 10511, 2820, 3447, 1790, 23181, 19716, 1550, 278, 3578, 9098, 4689, 304, 28747, 408, 278, 6575, 652, 2986, 2400, 278, 12726, 310, 263, 21188, 5447, 29899, 11911, 287, 364, 5525, 29889, 319, 330, 2576, 1050, 310, 3578, 11013, 287, 2750, 12917, 297, 278, 5418, 322, 896, 4446, 263, 2319, 28830, 373, 263, 1880, 364, 5525, 29889, 2688, 452, 1965, 263, 2646, 955, 6520, 393, 6077, 304, 278, 1492, 322, 24273, 964, 278, 10697, 29889, 13, 29999, 547, 11084, 278, 534, 2707, 29889, 376, 11284, 29892, 825, 437, 366, 1348, 3026, 13, 29908, 3112, 723, 367, 1283, 278, 367, 2579, 2224, 29892, 363, 1854, 1213, 13981, 7699, 29889, 376, 12024, 29915, 29879, 1018, 372, 1213, 13, 15597, 6077, 11480, 278, 2646, 955, 6520, 28435, 701, 10697, 29889, 450, 2224, 10784, 2580, 278, 2625, 310, 263, 17306, 29889, 450, 4340, 896, 26603, 29892, 278, 1886, 11356, 278, 24968, 472, 278, 2625, 310, 278, 6520, 322, 278, 17655, 307, 556, 278, 2224, 13631, 29889, 13, 29928, 3547, 3290, 701, 297, 278, 12949, 322, 21039, 287, 304, 13981, 29889, 376, 17506, 366, 1854, 1048, 445, 3026, 13, 29908, 3782, 541, 727, 29915, 29879, 694, 2058, 304, 2507, 2820, 1492, 29892, 1286, 1213, 13981, 7699, 29889, 376, 9598, 1022, 2675, 29892, 796, 547, 1213, 13, 15597, 26603, 1790, 17967, 975, 6483, 364, 8842, 322, 471, 13244, 769, 278, 2224, 281, 3615, 287, 472, 263, 27498, 6584, 322, 28453, 29889, 13, 29999, 547, 321, 1463, 278, 534, 2707, 304, 263, 5040, 29889, 376, 5618, 1286, 29973, 739, 3430, 763, 278, 2743, 6520, 1213, 13, 29908, 3782, 29889, 306, 1074, 278, 28830, 1549, 1906, 10697, 29889, 306, 1348, 278, 6520, 12104, 2820, 278, 28453, 29889, 20340, 1244, 1213, 940, 28996, 714, 310, 278, 534, 2707, 322, 5643, 278, 2224, 304, 278, 1250, 310, 278, 28453, 29889, 940, 24273, 363, 263, 2846, 19462, 769, 2996, 1250, 304, 7475, 346, 29889, 376, 4806, 29915, 276, 1603, 2675, 297, 278, 1492, 5305, 29889, 306, 508, 1074, 263, 28830, 29889, 739, 3430, 5051, 12474, 14432, 29892, 541, 565, 591, 679, 8724, 727, 278, 28830, 338, 1492, 14432, 29889, 2803, 592, 1423, 372, 714, 1213, 13, 7789, 345, 3240, 945, 287, 278, 12474, 2224, 304, 278, 1250, 310, 278, 28453, 322, 769, 2820, 263, 2317, 310, 10697, 29889, 319, 2813, 540, 1033, 1074, 278, 29826, 28830, 29889, 739, 471, 263, 12474, 26203, 393, 5148, 304, 367, 1304, 491, 3023, 21266, 29872, 839, 319, 8050, 29879, 297, 278, 4940, 29892, 541, 3078, 10325, 29889, 940, 2485, 9795, 26645, 1623, 278, 5702, 322, 4446, 385, 1722, 29413, 297, 4565, 310, 278, 28830, 29889, 940, 1754, 670, 982, 1250, 304, 278, 534, 2707, 322, 10784, 2580, 2768, 29889, 1551, 278, 982, 1250, 540, 29081, 4203, 263, 24231, 2919, 23150, 304, 278, 2625, 310, 278, 26203, 29889, 13, 7789, 345, 2485, 9795, 1250, 304, 278, 534, 2707, 322, 9326, 29889, 376, 3112, 29915, 29879, 437, 519, 1213, 940, 10784, 2580, 297, 278, 534, 2707, 29889, 376, 1433, 618, 278, 1250, 310, 278, 28453, 29892, 2343, 701, 278, 26203, 1213, 13, 29999, 547, 1258, 408, 10624, 29889, 1932, 540, 20043, 2820, 278, 28453, 29892, 540, 2243, 28913, 373, 278, 16706, 29889, 376, 7058, 29915, 29879, 451, 9377, 3307, 3850, 940, 380, 1965, 472, 278, 12474, 26203, 411, 278, 12164, 5768, 1283, 304, 278, 2175, 322, 278, 1886, 1022, 14451, 310, 270, 2728, 322, 1506, 1878, 288, 278, 1492, 29889, 376, 29902, 508, 29915, 29873, 437, 445, 29889, 1334, 29915, 645, 748, 975, 1213, 13, 7789, 345, 7180, 670, 1361, 373, 796, 547, 29915, 29879, 23468, 29889, 376, 3492, 508, 437, 445, 29889, 3387, 3013, 596, 2175, 260, 533, 373, 278, 26203, 29889, 450, 24968, 373, 278, 2768, 338, 9914, 3307, 393, 366, 508, 7899, 373, 372, 29889, 739, 29915, 645, 260, 2782, 278, 534, 2707, 29892, 541, 278, 260, 2658, 526, 4802, 3307, 304, 10784, 29890, 975, 263, 2846, 23150, 472, 278, 2625, 310, 278, 6520, 29889, 450, 26203, 338, 25734, 2820, 925, 8724, 727, 1213, 13, 29908, 3492, 508, 437, 445, 796, 547, 1213, 360, 3547, 2916, 287, 29889, 13, 29999, 547, 521, 2707, 839, 23547, 5794, 29889, 376, 20434, 388, 29892, 472, 3203, 9343, 29915, 645, 679, 714, 29892, 925, 297, 1206, 1213, 13, 29908, 18420, 2969, 29889, 360, 3547, 29892, 366, 3023, 679, 714, 29889, 306, 29915, 645, 22203, 411, 796, 547, 1213, 624, 1351, 7699, 29889, 376, 4806, 29915, 645, 5839, 366, 701, 373, 278, 916, 2625, 1213, 13, 1576, 2211, 5866, 322, 2278, 28996, 714, 310, 278, 534, 2707, 322, 25993, 408, 278, 19716, 20043, 14432, 29889, 2688, 20654, 408, 278, 20364, 19716, 29081, 11183, 278, 12474, 292, 310, 278, 26203, 29889, 796, 547, 9500, 287, 964, 4482, 330, 799, 322, 278, 6047, 310, 278, 6012, 6548, 839, 29889, 13, 1576, 260, 2658, 29081, 6375, 411, 13981, 5065, 3460, 796, 547, 304, 10754, 278, 534, 2707, 11183, 278, 7568, 24968, 29889, 796, 547, 6077, 278, 1886, 3241, 18875, 304, 278, 1492, 29889, 450, 4565, 260, 533, 10784, 2580, 701, 278, 1343, 457, 1550, 278, 2175, 260, 2658, 29081, 3412, 29899, 2975, 278, 5768, 29899, 2696, 472, 278, 2625, 310, 278, 2578, 29895, 29889, 796, 547, 29915, 29879, 3347, 330, 1761, 6419, 411, 3736, 29886, 12232, 29889, 13, 29908, 6833, 306, 1781, 3026, 940, 4433, 29889, 376, 29902, 508, 29915, 29873, 1074, 278, 6520, 1213, 13, 29908, 3492, 29915, 276, 2599, 2691, 1213, 13981, 20793, 287, 714, 278, 3474, 6577, 3460, 278, 5418, 29889, 376, 1762, 278, 1492, 29889, 5853, 304, 278, 1492, 29889, 450, 260, 533, 508, 9679, 701, 278, 23150, 472, 278, 2625, 29889, 317, 677, 322 ]

1,332,837

0

CommonCrawl

10

8

What is Fiscal Sponsorship? Fiscal Agency allows an organization without tax-exempt status to receive funds via an established nonprofit with 501[3] tax-exempt status. This is a great first step in fundraising. The historic water tower was originally consigned by the City of Brainerd's Water and Light Commission. It was constructed between 1919 & 1920; it is said to be the first ever poured in place concrete for municipal water storage in the United States. Over the past 100 years the tower has had its share of wear and tear. Efforts to maintain it have come to a pivotal point which is where the City of Brainerd's Citizens Historic Water Tower Committee began.The committee has spearheaded this enormous effort with the simple goal of preserving the heart of our community. To be a success we ask for any and all help from people just like you to save part of our rich collective history in the great state of Minnesota. You can follow the journey through their Facebook page and website at BrainerdWaterTower.com Have you ever wanted a fun, affordable and safe water experience for the whole family, without the added stress of watching multiple children at the lake or water park? The Brainerd Splash Pad project is all about family fun, in a safe environment with no risk of drowning. Together with Brainerd Community Action, Brainerd Splash Pad are gathering sponsorships representing Brainerd Lakes Area families and businesses. With YOUR help not only will they be providing an AWESOME addition to our green space, but you will also get to see your name on the pad for years to come! Please consider a donation today so we make a SPLASH in the BLA! 💦 Visit their website for more information www.brainerdsplashpad.com Crow Wing County Beyond the Yellow Ribbon Community (CWCBTYRC) is a volunteer organization that aims to continue Minnesota's proud history of supporting our nation's military. CWCBTYRC is a diverse group of citizens and community leaders uniting key areas within our communities to leverage existing support activities, build awareness and take action to recognize and support Service members, Veterans, military families and employers. For more information please email [email protected] Tummies is a collaboration between, The Baxter Cafe, The Raboin & Francis Law Firm, Pan-O-Gold Bakeries and Hubbard Radio. The program provides free kids' meals on weekends for hungry children in the Brainerd Lakes Area. The Brainerd Outreach Program also distributes family meal packets through this program. During the last two months, a number of other local businesses have volunteered to partner with Full Tummies to donate items families with children might find useful during these trying times. Brainerd Community Action has acted as their fiscal agent making donations to Full Tummies possible. Let's make sure no child goes hungry! Friends of the BLA Treatment Courts is made up of three Treatment Courts, Aitkin County Sobriety Court, Crow Wing County DWI Court, and Crow Wing County Drug Court, have been proud partners with Brainerd Community Action for the past 6 years. The Treatment Courts are grant funded, and work with high risk/high needs alcohol and drug offenders that are Aitkin and Crow Wing County residence. Their focus is to enhance public safety by increasing the supervision of the offenders, reducing recidivism rates and increasing the success of treatment. We work together to provide a safe and healthy community. Crow Wing Crow Wing Food Co-op is a cooperatively owned grocery store dedicated to sustaining a healthy and thriving community. Founded in 1979, Crow Wing Food Co-op is a trusted local source for natural, organic, local, and allergen-friendly foods. Crow Wing Food Co-op is owned and overseen by its member-owners; membership is open to everyone, and anyone can shop no matter if you're a member. Learn more at www.crowwingcoop.com. Since 2015, Brainerd Riverfront has been a city advisory committee advocating for equitable access to the Mississippi River through parks, overlooks, and trails. Over the past five years their 10 member community has worked with stakeholders including Central Lakes College, Brainerd YMCA and many others to

0.212045

0.384696

0.562152

-1.032359

[ 0.2853229906922278, 0.13876771978936042 ]

[ 0.3811150739700834, 0.3882775882953222 ]

[ 0.5773697668809709, 0.5469348745763597 ]

[ -1.0466662282865995, -1.0180511553358178 ]

1,024

[ 512, 512 ]

[ 1724, 338, 383, 275, 1052, 1706, 787, 272, 3527, 29973, 13, 29943, 275, 1052, 29353, 6511, 385, 13013, 1728, 8818, 29899, 735, 3456, 4660, 304, 7150, 29199, 3025, 385, 7841, 1661, 771, 9202, 411, 29871, 29945, 29900, 29896, 29961, 29941, 29962, 8818, 29899, 735, 3456, 4660, 29889, 910, 338, 263, 2107, 937, 4331, 297, 5220, 336, 5921, 29889, 13, 1576, 22879, 4094, 19372, 471, 10437, 1136, 12961, 491, 278, 4412, 310, 5032, 262, 2018, 29915, 29879, 13062, 322, 12790, 11444, 29889, 739, 471, 13319, 1546, 29871, 29896, 29929, 29896, 29929, 669, 29871, 29896, 29929, 29906, 29900, 29936, 372, 338, 1497, 304, 367, 278, 937, 3926, 7446, 1127, 297, 2058, 18387, 363, 11677, 4094, 8635, 297, 278, 3303, 3900, 29889, 6811, 278, 4940, 29871, 29896, 29900, 29900, 2440, 278, 19372, 756, 750, 967, 6232, 310, 19531, 322, 734, 279, 29889, 382, 600, 441, 29879, 304, 7344, 372, 505, 2041, 304, 263, 282, 440, 7288, 1298, 607, 338, 988, 278, 4412, 310, 5032, 262, 2018, 29915, 29879, 21353, 466, 575, 17939, 13062, 23615, 12930, 4689, 29889, 1576, 21118, 756, 961, 279, 2813, 287, 445, 18886, 681, 7225, 411, 278, 2560, 7306, 310, 2225, 29530, 278, 5192, 310, 1749, 7881, 29889, 1763, 367, 263, 2551, 591, 2244, 363, 738, 322, 599, 1371, 515, 2305, 925, 763, 366, 304, 4078, 760, 310, 1749, 8261, 6314, 573, 4955, 297, 278, 2107, 2106, 310, 20994, 29889, 887, 508, 1101, 278, 16342, 1549, 1009, 13327, 1813, 322, 4700, 472, 5032, 262, 2018, 29956, 1008, 29911, 1680, 29889, 510, 13, 25559, 366, 3926, 5131, 263, 2090, 29892, 21750, 519, 322, 9109, 4094, 7271, 363, 278, 3353, 3942, 29892, 1728, 278, 2715, 22884, 310, 21217, 2999, 4344, 472, 278, 19437, 470, 4094, 14089, 29973, 450, 5032, 262, 2018, 317, 572, 1161, 18011, 2060, 338, 599, 1048, 3942, 2090, 29892, 297, 263, 9109, 5177, 411, 694, 12045, 310, 270, 798, 1076, 29889, 323, 12966, 411, 5032, 262, 2018, 19184, 9123, 29892, 5032, 262, 2018, 317, 572, 1161, 18011, 526, 11705, 292, 21955, 272, 9981, 15783, 5032, 262, 2018, 365, 6926, 18320, 13175, 322, 5381, 267, 29889, 2973, 612, 22970, 1371, 451, 871, 674, 896, 367, 13138, 385, 319, 29956, 2890, 29949, 2303, 6124, 304, 1749, 7933, 2913, 29892, 541, 366, 674, 884, 679, 304, 1074, 596, 1024, 373, 278, 17132, 363, 2440, 304, 2041, 29991, 3529, 2050, 263, 1016, 362, 9826, 577, 591, 1207, 263, 317, 7390, 24943, 297, 278, 350, 4375, 29991, 29871, 243, 162, 149, 169, 5741, 277, 1009, 4700, 363, 901, 2472, 7821, 29889, 2634, 262, 2018, 23579, 1161, 8305, 29889, 510, 13, 29907, 798, 27792, 5127, 18502, 898, 278, 612, 4743, 27461, 6718, 19184, 313, 29907, 29956, 21685, 15631, 10363, 29897, 338, 263, 27886, 261, 13013, 393, 263, 9893, 304, 6773, 20994, 29915, 29879, 22314, 4955, 310, 20382, 1749, 5233, 29915, 29879, 9121, 29889, 315, 29956, 21685, 15631, 10363, 338, 263, 16984, 2318, 310, 18363, 322, 7881, 20251, 5190, 292, 1820, 10161, 2629, 1749, 23507, 304, 454, 19698, 5923, 2304, 14188, 29892, 2048, 3773, 8326, 404, 322, 2125, 3158, 304, 18720, 322, 2304, 6692, 5144, 29892, 478, 1308, 550, 29892, 9121, 13175, 322, 5703, 414, 29889, 1152, 901, 2472, 3113, 4876, 518, 5269, 6364, 29962, 13, 29911, 23824, 583, 338, 263, 24771, 1546, 29892, 450, 350, 1165, 357, 9243, 1725, 29892, 450, 16155, 28230, 669, 5845, 7927, 383, 3568, 29892, 6518, 29899, 29949, 29899, 29954, 1025, 22652, 583, 322, 14533, 29890, 538, 9204, 29889, 450, 1824, 8128, 3889, 413, 4841, 29915, 592, 1338, 373, 4723, 1975, 363, 9074, 14793, 4344, 297, 278, 5032, 262, 2018, 365, 6926, 18320, 29889, 450, 5032, 262, 2018, 4451, 276, 496, 7835, 884, 1320, 5026, 3942, 592, 284, 23912, 1549, 445, 1824, 29889, 7133, 278, 1833, 1023, 7378, 29892, 263, 1353, 310, 916, 1887, 5381, 267, 505, 27886, 14561, 304, 18096, 411, 14846, 323, 23824, 583, 304, 1016, 403, 4452, 13175, 411, 4344, 1795, 1284, 5407, 2645, 1438, 1811, 3064, 29889, 5032, 262, 2018, 19184, 9123, 756, 27320, 408, 1009, 16436, 1052, 10823, 3907, 1016, 800, 304, 14846, 323, 23824, 583, 1950, 29889, 2803, 29915, 29879, 1207, 1854, 694, 2278, 5771, 9074, 14793, 29991, 13, 27034, 1975, 310, 278, 350, 4375, 6479, 271, 358, 6325, 1372, 338, 1754, 701, 310, 2211, 6479, 271, 358, 6325, 1372, 29892, 319, 277, 9089, 5127, 25147, 374, 3305, 9245, 29892, 29445, 27792, 5127, 360, 22119, 9245, 29892, 322, 29445, 27792, 5127, 360, 11124, 9245, 29892, 505, 1063, 22314, 22056, 411, 5032, 262, 2018, 19184, 9123, 363, 278, 4940, 29871, 29953, 2440, 29889, 450, 6479, 271, 358, 6325, 1372, 526, 16690, 5220, 287, 29892, 322, 664, 411, 1880, 12045, 29914, 9812, 4225, 27231, 5391, 322, 15721, 1283, 21043, 393, 526, 319, 277, 9089, 322, 29445, 27792, 5127, 25488, 29889, 11275, 8569, 338, 304, 26371, 749, 970, 15332, 491, 10231, 278, 2428, 4924, 310, 278, 1283, 21043, 29892, 27668, 1162, 333, 440, 1608, 19257, 322, 10231, 278, 2551, 310, 14502, 29889, 1334, 664, 4208, 304, 3867, 263, 9109, 322, 9045, 29891, 7881, 29889, 13, 29907, 798, 27792, 29445, 27792, 25453, 3189, 29899, 459, 338, 263, 1302, 3372, 6703, 15205, 4071, 29883, 708, 3787, 16955, 304, 15075, 17225, 263, 9045, 29891, 322, 266, 1150, 292, 7881, 29889, 383, 7261, 297, 29871, 29896, 29929, 29955, 29929, 29892, 29445, 27792, 25453, 3189, 29899, 459, 338, 263, 9311, 287, 1887, 2752, 363, 5613, 29892, 2894, 293, 29892, 1887, 29892, 322, 16454, 1885, 29899, 18326, 368, 9687, 29879, 29889, 29445, 27792, 25453, 3189, 29899, 459, 338, 15205, 322, 975, 28026, 491, 967, 4509, 29899, 776, 414, 29936, 28512, 338, 1722, 304, 14332, 29892, 322, 5019, 508, 18296, 694, 4383, 565, 366, 29915, 276, 263, 4509, 29889, 19530, 29876, 901, 472, 7821, 29889, 29883, 798, 16958, 1111, 459, 29889, 510, 29889, 13, 23036, 29871, 29906, 29900, 29896, 29945, 29892, 5032, 262, 2018, 6163, 8862, 756, 1063, 263, 4272, 25228, 706, 21118, 22545, 1218, 363, 1592, 8270, 2130, 304, 278, 24743, 6163, 1549, 610, 2039, 29892, 975, 6914, 29879, 29892, 322, 1020, 2719, 29889, 6811, 278, 4940, 5320, 2440, 1009, 29871, 29896, 29900, 4509, 7881, 756, 3796, 411, 380, 1296, 8948, 414, 3704, 8068, 365, 6926, 6346, 29892, 5032, 262, 2018, 612, 29924, 5454, 322, 1784, 4045, 304 ]

1,332,838

0

CommonCrawl

1

6

DeMar: "It's Not Who Homosexuals Are … It's What They Do that Matters" Apr 16, 2019 American Vision, Gary DeMar, Hate groups Beyond all of that, the ultra-religious treat LGBTQ people as those who have made very bad choices. We are not just evil. We are presumed to have terrible judgment. Gary DeMar – American Vision via Southern Poverty Law Center Hate group leader Gary DeMar (American Vision) stopped targeting LGBT people for some time. Perhaps he was trying to get off the list compiled by the Southern Poverty Law Center which he admitted negatively affected institutional donations. Perhaps he no longer cares because he has reverted to form. Predictable certainty: There's a great deal of sloppy thinking going on about human sexuality. Many Christians have capitulated on the topic of same-sex sexuality. They've given into the premise that God's Word does not disapprove of such relationships. Students at some Christian colleges are the worst offenders. Students and alumni at Taylor University, a Christian College in Upland, Indiana, are denouncing the decision to have Vice President Mike Pence deliver this year's Commencement because of his opposition to same-sex sexuality. For the record, Taylor University is on Campus Pride's Shame List because of its Title IX exemption which permits the school to discriminate without losing federal student aid. Pence will be the commencement speaker. Some anti-Darwin rhetoric while he is at it: Sex is a good thing. It was created by God. It didn't evolve, and if it did, then any type of sex is OK, even rape. According to evolutionists, human beings, homo sapiens (wise man) to use the scientific vernacular, are evolved animals. Animals passed on their genes via rape and stopped genetic inferiors through "murder." Human primacy developed because of religious devotion. After all, they argued, only a human being has an immortal soul. Darwin and modern science changed all of that with the evolution continuum. Human beings have primacy because they are the most intelligent of animals. We also possess a level of emotional intelligence that does not exist in animals. I agree with DeMar that sex is, indeed, a good thing. Not only does it produce offspring but it feels great. Sex defines morality: People who engage in same-sex behavior must decide what side of the moral wall they are on. If they decide to abandon God, then homosexuality is just something evolved bags of meat and bones with an evolved monkey brain do. We do not have to make that decision. Gary DeMar has saved us the trouble of doing so. Note the absence of the phrase "gay people." They do not exist in DeMar's world. They are substituted with people who have gay sex. Otherwise, Mr. DeMar is in the uncomfortable position of having to explain why some people have a different sexual orientation than most people. If you believe in an omnipotent god then the continuum -of sexual orientation is god-given. It follows that we are sexual beings with sexual desires that we are compelled to act on. Why would the deity make people only to frustrate their sexual longings? Therefore, DeMar and others of similar mind are obligated to dispense with the entire concept of sexual orientation. Our sexuality is not defined by intersecting points of gender and orientation continua. Oh no. Out of convenience our sexuality is defined by the kind of sex that we engage in which, in turn, defines us. The entire narrative is intellectually dishonest at the outset because it seeks to redefine reality to suit the dogma of a belief system. Most assuredly morality is not defined by the kind of sex that we engage in. DeMar continues with the idea that if gay sex is acceptable then there are no guardrails: There is no right or wrong about anything. No hate crimes. No murder. No theft. No rape. No adultery. No prohibition against sex with children of any age. The above is ludicrous. Sex (gay and straight), for example, is only acceptable when the participants are consenting adults. DeMar is manufacturing a condition that does not exist. Our civil society can accept homosexuality while, at the same time, condem

-0.306783

-0.467195

-0.491656

0.155167

[ -0.47621654783108297, -0.13735028622535844 ]

[ -0.11936561450598299, -0.8150248183448087 ]

[ -0.4637571740392716, -0.5195544765977255 ]

[ 0.11874765189069258, 0.19158601940177333 ]

1,024

[ 512, 512 ]

[ 897, 7083, 29901, 376, 3112, 29915, 29879, 2216, 11644, 15089, 29438, 27101, 4683, 16088, 739, 29915, 29879, 1724, 2688, 1938, 393, 5345, 2153, 29908, 13, 29909, 558, 29871, 29896, 29953, 29892, 29871, 29906, 29900, 29896, 29929, 3082, 478, 2459, 29892, 23529, 897, 7083, 29892, 379, 403, 6471, 13, 29933, 1032, 898, 599, 310, 393, 29892, 278, 8494, 336, 29899, 2674, 335, 2738, 7539, 365, 7210, 29911, 29984, 2305, 408, 1906, 1058, 505, 1754, 1407, 4319, 19995, 29889, 1334, 526, 451, 925, 16126, 29889, 1334, 526, 2225, 21571, 304, 505, 16403, 24284, 29889, 13, 29954, 653, 897, 7083, 785, 3082, 478, 2459, 13, 6071, 14234, 349, 957, 1017, 7927, 7817, 13, 29950, 403, 2318, 11822, 23529, 897, 7083, 313, 14689, 478, 2459, 29897, 11084, 3646, 292, 365, 7210, 29911, 2305, 363, 777, 931, 29889, 11637, 540, 471, 1811, 304, 679, 1283, 278, 1051, 13126, 491, 278, 14234, 349, 957, 1017, 7927, 7817, 607, 540, 20186, 3480, 6703, 15201, 12666, 284, 1016, 800, 29889, 11637, 540, 694, 5520, 1559, 267, 1363, 540, 756, 29538, 287, 304, 883, 29889, 13, 23084, 919, 519, 3058, 1017, 29901, 13, 8439, 29915, 29879, 263, 2107, 5376, 310, 14216, 23717, 7291, 2675, 373, 1048, 5199, 18287, 537, 29889, 9267, 27353, 505, 11934, 7964, 373, 278, 11261, 310, 1021, 29899, 14167, 18287, 537, 29889, 2688, 29915, 345, 2183, 964, 278, 5188, 895, 393, 4177, 29915, 29879, 10803, 947, 451, 8796, 307, 345, 310, 1316, 21702, 29889, 5088, 1237, 472, 777, 6111, 18400, 267, 526, 278, 17322, 1283, 21043, 29889, 5088, 1237, 322, 394, 1227, 29875, 472, 12537, 3014, 29892, 263, 6111, 6346, 297, 501, 572, 392, 29892, 21817, 29892, 526, 972, 1309, 3277, 278, 10608, 304, 505, 21400, 7178, 12828, 349, 663, 12021, 445, 1629, 29915, 29879, 422, 1527, 13561, 1363, 310, 670, 19626, 304, 1021, 29899, 14167, 18287, 537, 29889, 13, 2831, 278, 2407, 29892, 12537, 3014, 338, 373, 7259, 375, 349, 2426, 29915, 29879, 1383, 420, 2391, 1363, 310, 967, 18527, 16841, 11875, 683, 607, 3635, 1169, 278, 3762, 304, 2313, 5632, 16976, 1728, 19035, 17097, 8368, 16226, 29889, 349, 663, 674, 367, 278, 844, 3977, 882, 25657, 29889, 13, 9526, 9418, 29899, 29928, 279, 5080, 364, 9188, 272, 293, 1550, 540, 338, 472, 372, 29901, 13, 29903, 735, 338, 263, 1781, 2655, 29889, 739, 471, 2825, 491, 4177, 29889, 739, 3282, 29915, 29873, 15220, 345, 29892, 322, 565, 372, 1258, 29892, 769, 738, 1134, 310, 7916, 338, 9280, 29892, 1584, 1153, 412, 29889, 7579, 304, 14675, 2879, 29892, 5199, 367, 886, 29892, 3632, 29877, 269, 2754, 575, 313, 3538, 767, 29897, 304, 671, 278, 16021, 24604, 562, 1070, 29892, 526, 15220, 1490, 15006, 29889, 24980, 1338, 4502, 373, 1009, 2531, 267, 3025, 1153, 412, 322, 11084, 2531, 7492, 10115, 18930, 1549, 376, 29885, 332, 672, 1213, 13, 29950, 7889, 1903, 4135, 8906, 1363, 310, 12962, 2906, 8194, 29889, 2860, 599, 29892, 896, 28705, 29892, 871, 263, 5199, 1641, 756, 385, 5198, 441, 284, 10752, 29889, 7335, 5080, 322, 5400, 10466, 3939, 599, 310, 393, 411, 278, 14675, 3133, 398, 29889, 12968, 367, 886, 505, 1903, 4135, 1363, 896, 526, 278, 1556, 13052, 296, 310, 15006, 29889, 1334, 884, 22592, 263, 3233, 310, 23023, 1848, 21082, 393, 947, 451, 1863, 297, 15006, 29889, 306, 8661, 411, 897, 7083, 393, 7916, 338, 29892, 6200, 29892, 263, 1781, 2655, 29889, 2216, 871, 947, 372, 7738, 1283, 4278, 541, 372, 23880, 2107, 29889, 13, 29903, 735, 17645, 3036, 2877, 29901, 13, 15666, 1991, 1058, 3033, 482, 297, 1021, 29899, 14167, 6030, 1818, 11097, 825, 2625, 310, 278, 14731, 10090, 896, 526, 373, 29889, 960, 896, 11097, 304, 11807, 4177, 29892, 769, 3632, 29438, 950, 537, 338, 925, 1554, 15220, 1490, 289, 810, 310, 27654, 322, 289, 2873, 411, 385, 15220, 1490, 1601, 1989, 17294, 437, 29889, 13, 4806, 437, 451, 505, 304, 1207, 393, 10608, 29889, 23529, 897, 7083, 756, 7160, 502, 278, 7458, 310, 2599, 577, 29889, 3940, 278, 18070, 310, 278, 16549, 376, 29887, 388, 2305, 1213, 2688, 437, 451, 1863, 297, 897, 7083, 29915, 29879, 3186, 29889, 2688, 526, 5960, 277, 3860, 411, 2305, 1058, 505, 23852, 7916, 29889, 13466, 29892, 3237, 29889, 897, 7083, 338, 297, 278, 443, 510, 3921, 519, 2602, 310, 2534, 304, 5649, 2020, 777, 2305, 505, 263, 1422, 18287, 19843, 1135, 1556, 2305, 29889, 960, 366, 4658, 297, 385, 2703, 29876, 666, 327, 296, 7339, 769, 278, 3133, 398, 448, 974, 18287, 19843, 338, 7339, 29899, 29887, 5428, 29889, 13, 3112, 4477, 393, 591, 526, 18287, 367, 886, 411, 18287, 553, 2658, 393, 591, 526, 752, 14356, 304, 1044, 373, 29889, 3750, 723, 278, 316, 537, 1207, 2305, 871, 304, 1424, 4627, 403, 1009, 18287, 1472, 886, 29973, 13, 8439, 1079, 29892, 897, 7083, 322, 4045, 310, 2788, 3458, 526, 10788, 630, 304, 12272, 1947, 411, 278, 4152, 6964, 310, 18287, 19843, 29889, 8680, 18287, 537, 338, 451, 3342, 491, 25869, 292, 3291, 310, 23346, 322, 19843, 3133, 29874, 29889, 6439, 694, 29889, 4451, 310, 29703, 1749, 18287, 537, 338, 3342, 491, 278, 2924, 310, 7916, 393, 591, 3033, 482, 297, 607, 29892, 297, 2507, 29892, 17645, 502, 29889, 450, 4152, 15474, 1230, 338, 18715, 1474, 270, 728, 265, 342, 472, 278, 714, 842, 1363, 372, 1074, 2039, 304, 337, 7922, 16832, 304, 14726, 278, 11203, 655, 310, 263, 17750, 1788, 29889, 13, 29924, 520, 28715, 368, 3036, 2877, 338, 451, 3342, 491, 278, 2924, 310, 7916, 393, 591, 3033, 482, 297, 29889, 13, 2772, 7083, 18172, 411, 278, 2969, 393, 565, 23852, 7916, 338, 22691, 769, 727, 526, 694, 8372, 9912, 29901, 13, 8439, 338, 694, 1492, 470, 2743, 1048, 3099, 29889, 1939, 26277, 2181, 1355, 29889, 1939, 13406, 29889, 1939, 278, 615, 29889, 1939, 1153, 412, 29889, 1939, 594, 352, 22005, 29889, 1939, 21460, 654, 2750, 7916, 411, 4344, 310, 738, 5046, 29889, 13, 1576, 2038, 338, 21615, 293, 29878, 681, 29889, 21703, 313, 29887, 388, 322, 7812, 511, 363, 1342, 29892, 338, 871, 22691, 746, 278, 27138, 526, 20218, 292, 16157, 29879, 29889, 897, 7083, 338, 12012, 3864, 263, 4195, 393, 947, 451, 1863, 29889, 8680, 7631, 12459, 508, 3544, 3632, 29438, 950, 537, 1550, 29892, 472, 278, 1021, 931, 29892, 24905 ]

1,332,839

0

CommonCrawl

19

18

ning murder, theft and rape. DeMar is actually providing us with examples of the limitations and constrictions of unquestioned obedience to religious dogma. In point of fact, some very moral people are gay or have had abortions. Some highly immoral people are — or at least claim to be — ultra-religious. As a society we have evolved past the point where religion defines morality. We are quite capable of differentiating between sin (my consumption of a lobster tail) and depravity (pedophiles). Lumping them together is dishonest. Rewriting the rules with a straw man: According to atheists, morality is a social construct foisted on humans based on religious myths. Atheistic materialism cannot account for any kind of morality since there is no ultimate lawgiver to pass judgment. "Foisted" means an unwelcome imposition. Morality is an important construct for society. Morality is not dependent upon religious belief nor is it related to materialism. The belief that morality is defined by an interpretation and presumption of a deity's judgment causes all sorts of problems. These include the ethnic cleansing of Native Americans, slavery and then segregation. They were all deemed to be moral on the premise that a god would approve. In a truly moral society the means are never justified by the end. In our society today we have a number of sanctimonious supposedly moral Christian leaders who are making excuses for Donald Trump's sociopathic behavior — past and present — to get some judges that they like appointed. As critical as I am of the Catholic Church, at least they condemned Trump for his cruel family separation policy. Evangelical Christians have not done so. Nor have they criticized the obvious greed and corruption in our government. None of that matters because they are obsessed with women's reproductive rights. In fact, evangelical Christians have enabled some of Trump's worst behavior towards Muslims and other minorities. Those good Christians do so without apology. None of it matters if they have a possibility of eroding abortion rights and if they can keep LGBTQ Americans in check. Our world is different. For example, we treat transgender people with dignity and kindness because it is the right thing to do. Conservative Christians treat them with inhumanity because their morality is defined — not by right and wrong — but, in this case, by a passage in Genesis. Where is the morality in treating children with savagery? Where is the morality in doing violence to people by the simple politeness of using appropriate pronouns in order to demonstrate their disapproval? Beyond all of that, the ultra-religious set treat LGBTQ people as those who have made very bad choices. We are not just evil. We are presumed to have terrible judgment. I am quite comfortable in my own skin. But LGBTQ children hear the same barbaric messages. Where is the morality in malice directed at vulnerable kids? In the end, opposition to Pete Buttigieg is not about him personally; it's about what he does. The same standard that's used against his sexual practices applies to everyone equally. It's the same moral law for everyone. No it is not the same moral law for everyone and who the hell appointed Mr. DeMar to be the arbiter of moral law? That passage in Leviticus that supposedly condemns gay sex is subject to the interpretations of people as scholarly as Mr. DeMar presumes to be. Many faithful Christians and Jews believe that the Hebrew Bible and Christian scripture reflect the times in which they were written. What was prohibited was the violation of young boy slaves by their owners. The slavery, however, was not a sin. Nor was it sinful to murder an insolent child or a bride who was not a virgin. At least not according to the same ancient screeds. In conclusion quoting a windbag: I happen to think that Everett Piper is an incoherent blowhard as evidenced by DeMar's quoted text regarding Pete Buttigieg: Your sexual appetites are your business. The thing about obedient and faithful Christians is this; we consider someone else's private life to be just that — Private. Please stop telling us what kind of sex you like. We don't want to know. If you want us to stay out of your bedroom, please shut the door. Stop opening it up and forcing us to applaud and celebrate. I think that

0.860587

-0.040578

0.217224

0.652029

[ 0.9838574594815955, 0.7373158822618187 ]

[ 0.2772586162541197, -0.3584145301108304 ]

[ 0.4962100540686743, -0.06176297151586494 ]

[ 0.7326710351983733, 0.5713860785666944 ]

1,024

[ 512, 512 ]

[ 1076, 13406, 29892, 278, 615, 322, 1153, 412, 29889, 897, 7083, 338, 2869, 13138, 502, 411, 6455, 310, 278, 27028, 322, 378, 710, 919, 1080, 310, 443, 12470, 287, 704, 287, 5597, 304, 12962, 11203, 655, 29889, 13, 797, 1298, 310, 2114, 29892, 777, 1407, 14731, 2305, 526, 23852, 470, 505, 750, 27450, 1080, 29889, 3834, 10712, 5198, 11251, 2305, 526, 813, 470, 472, 3203, 5995, 304, 367, 813, 8494, 336, 29899, 2674, 335, 2738, 29889, 1094, 263, 12459, 591, 505, 15220, 1490, 4940, 278, 1298, 988, 13433, 17645, 3036, 2877, 29889, 1334, 526, 3755, 15390, 310, 17473, 1218, 1546, 4457, 313, 1357, 27430, 310, 263, 658, 29890, 2475, 12464, 29897, 322, 1401, 5705, 537, 313, 9795, 3021, 5475, 467, 365, 3427, 292, 963, 4208, 338, 270, 728, 265, 342, 29889, 13, 29934, 809, 768, 292, 278, 6865, 411, 263, 380, 1610, 767, 29901, 13, 7504, 3278, 304, 472, 354, 2879, 29892, 3036, 2877, 338, 263, 5264, 3386, 1701, 12652, 373, 25618, 2729, 373, 12962, 22082, 29879, 29889, 319, 1552, 4695, 5518, 1608, 2609, 3633, 363, 738, 2924, 310, 3036, 2877, 1951, 727, 338, 694, 8494, 6490, 4307, 29887, 2147, 304, 1209, 24284, 29889, 13, 29908, 29943, 29877, 12652, 29908, 2794, 385, 18500, 295, 2763, 527, 3283, 29889, 3879, 2877, 338, 385, 4100, 3386, 363, 12459, 29889, 3879, 2877, 338, 451, 14278, 2501, 12962, 17750, 3643, 338, 372, 4475, 304, 5518, 1608, 29889, 450, 17750, 393, 3036, 2877, 338, 3342, 491, 385, 19854, 322, 2225, 28069, 310, 263, 316, 537, 29915, 29879, 24284, 9946, 599, 23551, 310, 4828, 29889, 4525, 3160, 278, 11314, 7823, 4531, 550, 292, 310, 19042, 23035, 29892, 8370, 1201, 322, 769, 2377, 1727, 362, 29889, 2688, 892, 599, 316, 22580, 304, 367, 14731, 373, 278, 5188, 895, 393, 263, 7339, 723, 2134, 345, 29889, 13, 797, 263, 19781, 14731, 12459, 278, 2794, 526, 2360, 925, 2164, 491, 278, 1095, 29889, 512, 1749, 12459, 9826, 591, 505, 263, 1353, 310, 9753, 312, 20170, 2738, 7424, 368, 14731, 6111, 20251, 1058, 526, 3907, 5566, 6394, 363, 18935, 27504, 29915, 29879, 5374, 459, 493, 293, 6030, 813, 4940, 322, 2198, 813, 304, 679, 777, 6577, 2710, 393, 896, 763, 10658, 29889, 1094, 12187, 408, 306, 626, 310, 278, 11865, 6291, 29892, 472, 3203, 896, 24905, 9571, 27504, 363, 670, 24116, 3942, 23683, 8898, 29889, 21827, 936, 27353, 505, 451, 2309, 577, 29889, 4186, 505, 896, 11164, 1891, 278, 6924, 1395, 287, 322, 1034, 18953, 297, 1749, 5874, 29889, 6213, 310, 393, 13750, 1363, 896, 526, 20881, 11517, 411, 5866, 29915, 29879, 337, 4704, 573, 10462, 29889, 13, 797, 2114, 29892, 23077, 936, 27353, 505, 9615, 777, 310, 27504, 29915, 29879, 17322, 6030, 7113, 23772, 29879, 322, 916, 9461, 1907, 29889, 16025, 1781, 27353, 437, 577, 1728, 3095, 3002, 29889, 6213, 310, 372, 13750, 565, 896, 505, 263, 13331, 310, 604, 3689, 27450, 291, 10462, 322, 565, 896, 508, 3013, 365, 7210, 29911, 29984, 23035, 297, 1423, 29889, 13, 29949, 332, 3186, 338, 1422, 29889, 1152, 1342, 29892, 591, 7539, 1301, 26098, 2305, 411, 18085, 537, 322, 2924, 2264, 1363, 372, 338, 278, 1492, 2655, 304, 437, 29889, 15312, 1230, 27353, 7539, 963, 411, 297, 26029, 537, 1363, 1009, 3036, 2877, 338, 3342, 813, 451, 491, 1492, 322, 2743, 813, 541, 29892, 297, 445, 1206, 29892, 491, 263, 13382, 297, 5739, 6656, 29889, 6804, 338, 278, 3036, 2877, 297, 2578, 1218, 4344, 411, 4048, 351, 708, 29973, 6804, 338, 278, 3036, 2877, 297, 2599, 21448, 304, 2305, 491, 278, 2560, 2832, 18543, 310, 773, 8210, 11504, 1309, 29879, 297, 1797, 304, 22222, 1009, 8796, 307, 791, 29973, 13, 29933, 1032, 898, 599, 310, 393, 29892, 278, 8494, 336, 29899, 2674, 335, 2738, 731, 7539, 365, 7210, 29911, 29984, 2305, 408, 1906, 1058, 505, 1754, 1407, 4319, 19995, 29889, 1334, 526, 451, 925, 16126, 29889, 1334, 526, 2225, 21571, 304, 505, 16403, 24284, 29889, 306, 626, 3755, 25561, 297, 590, 1914, 19309, 29889, 1205, 365, 7210, 29911, 29984, 4344, 8293, 278, 1021, 2594, 1646, 293, 7191, 29889, 6804, 338, 278, 3036, 2877, 297, 4439, 625, 10624, 472, 23180, 519, 413, 4841, 29973, 13, 797, 278, 1095, 29892, 19626, 304, 349, 2650, 1205, 29873, 335, 5876, 338, 451, 1048, 1075, 22345, 29936, 372, 29915, 29879, 1048, 825, 540, 947, 29889, 450, 1021, 3918, 393, 29915, 29879, 1304, 2750, 670, 18287, 23274, 16058, 304, 14332, 18018, 29889, 739, 29915, 29879, 278, 1021, 14731, 4307, 363, 14332, 29889, 13, 3782, 372, 338, 451, 278, 1021, 14731, 4307, 363, 14332, 322, 1058, 278, 23927, 10658, 3237, 29889, 897, 7083, 304, 367, 278, 564, 29890, 1524, 310, 14731, 4307, 29973, 2193, 13382, 297, 20708, 277, 12473, 393, 7424, 368, 24905, 1983, 23852, 7916, 338, 4967, 304, 278, 6613, 800, 310, 2305, 408, 21344, 368, 408, 3237, 29889, 897, 7083, 2225, 9351, 304, 367, 29889, 13, 14804, 27057, 27353, 322, 22057, 4658, 393, 278, 18472, 3973, 21958, 322, 6111, 2471, 545, 9432, 278, 3064, 297, 607, 896, 892, 3971, 29889, 1724, 471, 21460, 1573, 471, 278, 5537, 362, 310, 4123, 8023, 25569, 491, 1009, 1914, 414, 29889, 450, 8370, 1201, 29892, 3138, 29892, 471, 451, 263, 4457, 29889, 4186, 471, 372, 4457, 1319, 304, 13406, 385, 1663, 324, 296, 2278, 470, 263, 289, 2426, 1058, 471, 451, 263, 10636, 5359, 29889, 2180, 3203, 451, 5034, 304, 278, 1021, 12297, 885, 276, 5779, 29889, 13, 797, 15997, 439, 11427, 263, 8805, 23156, 29901, 13, 29902, 3799, 304, 1348, 393, 18274, 1803, 7362, 546, 338, 385, 297, 1111, 2276, 296, 13031, 6800, 408, 3415, 3615, 1133, 491, 897, 7083, 29915, 29879, 23153, 1426, 11211, 349, 2650, 1205, 29873, 335, 5876, 29901, 13, 10858, 18287, 623, 300, 3246, 526, 596, 5381, 29889, 450, 2655, 1048, 704, 287, 993, 322, 27057, 27353, 338, 445, 29936, 591, 2050, 4856, 1683, 29915, 29879, 2024, 2834, 304, 367, 925, 393, 813, 12230, 29889, 3529, 5040, 14509, 502, 825, 2924, 310, 7916, 366, 763, 29889, 1334, 1016, 29915, 29873, 864, 304, 1073, 29889, 960, 366, 864, 502, 304, 7952, 714, 310, 596, 6592, 8345, 29892, 3113, 12522, 278, 3050, 29889, 22303, 8718, 372, 701, 322, 28172, 502, 304, 623, 433, 566, 322, 10894, 403, 29889, 13, 29902, 1348, 393 ]

1,332,839

1,024

CommonCrawl

19

18

Over the course this year so far, you've seen my adoration for a certain button up sewing pattern (McCall's 6649 - now out of print) and then a couple of hacks of things I've made from it (here and here). I thought I would take a sec, stop down and say a little more about it. It's exciting. Well, at least I think so. Hopefully this post will help clear up some questions I've been getting and hopefully it will show you that you can take a pattern and hack it up and not have to re-invent the fitting wheel. This is a skill I've cultivated over several years and one that is well worth the time invested and when you get to the pattern drafting part, it's really quite fun to learn (in like a scrapbooking sort of way!). In my recent hack of my beloved McCall's 6649, I mentioned a Craftsy class I had taken. One Pattern, Many Looks with Sarah Holden. I enrolled in the class last year sometime and then it sat in my Craftsy cue for many months. One night, I was really tired and decided to watch this Craftsy class as I was sitting in bed. I watched all the episodes right there and then. I was riveted and I was so excited to get up and get started in the morning. Dreamt of pattern hacks all night! Yessssss! The class takes you through this pretty fascinating process. First you're supposed to fit the pattern. This process actually took a few weeks (the longest part of this whole business) because I wanted something that truly, was perfect and that usually means, for me, that I work out any and all kinks in a pattern by making it up at least 3 times. Seriously, 3 times is the charm. I have some more thoughts about the fitting process in my next post, but yeah, I made this shirt up a good 3 times (and then one more time, making that 4 times!!) before I moved on to the rest of the content of the class. Update: Just so you are aware, this Craftsy class does not cover anything about fitting! It's only about pattern drafting and manipulation. After a perfect fit, then it was time to reverse engineer the pattern back to sloper form. What is a sloper? In the most basic terms, a sloper is a base pattern, without seam allowances, from which other patterns can be created or hacked from. You can have different types of slopers. For example, you can have bodice, sleeve, dress, pants, etc. From there you can even have varying types of those basic patterns like a button-up shirt sloper or a raglan sleeve sloper. The idea is that you'll start forming an entire collection of base patterns that are closer in idea to what you want an end pattern to be. More colors in a crayon box if you will. Anyway, back to McCall's 6649. I created a sloper from this pattern and transferred all of the pertinent markings to posterboard. All of the seam allowances have been cut off here and there are holes and notches in specific places. Putting a pattern like this on posterboard is fantastic because then when I'm ready to create a new top from this pattern, I can just trace it off in a matter of seconds. The posterboard is stiff so you can just trace around it really easily. In the Craftsy class, Sarah shows you some really great hacks. And these are just starting points. I mean you really do have the entire world at your feet when you start creating your own patterns - from patterns that already fit you! Since you've already addressed the fit, that tends to not be a problem anymore. You might run into some issues here and there, but they are minimal by comparison. All in all, I'm very very pleased with how my hacks have turned out from this process. It took a lot of time, but was well worth the investment. Onward and upward from here. Have you gone through this process before? What kinds of slopers do you have? If you haven't, I can't recommend something like this enough. You learn a ton about fitting and about your body and what things you should be looking out for when you go to try a new sewing pattern. Plus then there's the creative gratification that comes from creating a pattern of your very own. Fun, fun! Thank you! I've had that class in my Crafty listing for ages and never "found"

0.619524

-0.726389

0.704182

-0.564762

[ 0.6496566548058981, 0.5893909359299526 ]

[ -0.9188812760607723, -0.5338961310791829 ]

[ 0.5063550181702113, 0.9020086181301573 ]

[ -0.8242490703509779, -0.30527570183452757 ]

1,024

[ 512, 512 ]

[ 6811, 278, 3236, 445, 1629, 577, 2215, 29892, 366, 29915, 345, 3595, 590, 594, 12418, 363, 263, 3058, 2826, 701, 409, 16958, 4766, 313, 27297, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 448, 1286, 714, 310, 1596, 29897, 322, 769, 263, 7303, 310, 447, 4684, 310, 2712, 306, 29915, 345, 1754, 515, 372, 313, 4150, 322, 1244, 467, 306, 2714, 306, 723, 2125, 263, 5226, 29892, 5040, 1623, 322, 1827, 263, 2217, 901, 1048, 372, 29889, 739, 29915, 29879, 5566, 11407, 29889, 5674, 29892, 472, 3203, 306, 1348, 577, 29889, 13, 29950, 2300, 3730, 445, 1400, 674, 1371, 2821, 701, 777, 5155, 306, 29915, 345, 1063, 2805, 322, 27581, 372, 674, 1510, 366, 393, 366, 508, 2125, 263, 4766, 322, 15833, 372, 701, 322, 451, 505, 304, 337, 29899, 262, 794, 278, 28221, 18875, 29889, 910, 338, 263, 19911, 306, 29915, 345, 18834, 630, 975, 3196, 2440, 322, 697, 393, 338, 1532, 7088, 278, 931, 2437, 2868, 322, 746, 366, 679, 304, 278, 4766, 18195, 292, 760, 29892, 372, 29915, 29879, 2289, 3755, 2090, 304, 5110, 313, 262, 763, 263, 885, 2390, 2909, 292, 2656, 310, 982, 29991, 467, 512, 590, 7786, 15833, 310, 590, 1339, 8238, 4052, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 29892, 306, 5276, 263, 315, 4154, 29879, 29891, 770, 306, 750, 4586, 29889, 3118, 25860, 29892, 9267, 19887, 411, 19235, 21771, 264, 29889, 306, 427, 24476, 297, 278, 770, 1833, 1629, 1047, 5410, 322, 769, 372, 3290, 297, 590, 315, 4154, 29879, 29891, 274, 434, 363, 1784, 7378, 29889, 3118, 4646, 29892, 306, 471, 2289, 23407, 322, 8459, 304, 6505, 445, 315, 4154, 29879, 29891, 770, 408, 306, 471, 16246, 297, 6592, 29889, 306, 20654, 599, 278, 23238, 1492, 727, 322, 769, 29889, 306, 471, 9050, 300, 287, 322, 306, 471, 577, 24173, 304, 679, 701, 322, 679, 4687, 297, 278, 7250, 29889, 16814, 29873, 310, 4766, 447, 4684, 599, 4646, 29991, 612, 404, 893, 893, 29991, 13, 1576, 770, 4893, 366, 1549, 445, 5051, 21028, 262, 1218, 1889, 29889, 3824, 366, 29915, 276, 7424, 304, 6216, 278, 4766, 29889, 910, 1889, 2869, 3614, 263, 2846, 11405, 313, 1552, 27217, 760, 310, 445, 3353, 5381, 29897, 1363, 306, 5131, 1554, 393, 19781, 29892, 471, 4922, 322, 393, 5491, 2794, 29892, 363, 592, 29892, 393, 306, 664, 714, 738, 322, 599, 413, 19363, 297, 263, 4766, 491, 3907, 372, 701, 472, 3203, 29871, 29941, 3064, 29889, 1816, 17365, 29892, 29871, 29941, 3064, 338, 278, 21192, 29889, 306, 505, 777, 901, 13133, 1048, 278, 28221, 1889, 297, 590, 2446, 1400, 29892, 541, 21915, 29892, 306, 1754, 445, 528, 2728, 701, 263, 1781, 29871, 29941, 3064, 313, 392, 769, 697, 901, 931, 29892, 3907, 393, 29871, 29946, 3064, 6824, 29897, 1434, 306, 6153, 373, 304, 278, 1791, 310, 278, 2793, 310, 278, 770, 29889, 10318, 29901, 3387, 577, 366, 526, 9543, 29892, 445, 315, 4154, 29879, 29891, 770, 947, 451, 4612, 3099, 1048, 28221, 29991, 739, 29915, 29879, 871, 1048, 4766, 18195, 292, 322, 11525, 2785, 29889, 13, 13555, 263, 4922, 6216, 29892, 769, 372, 471, 931, 304, 11837, 22055, 278, 4766, 1250, 304, 14216, 546, 883, 29889, 1724, 338, 263, 14216, 546, 29973, 512, 278, 1556, 6996, 4958, 29892, 263, 14216, 546, 338, 263, 2967, 4766, 29892, 1728, 409, 314, 2758, 2925, 29892, 515, 607, 916, 15038, 508, 367, 2825, 470, 15833, 287, 515, 29889, 887, 508, 505, 1422, 4072, 310, 269, 4757, 414, 29889, 1152, 1342, 29892, 366, 508, 505, 13004, 625, 29892, 12844, 29872, 345, 29892, 10714, 29892, 282, 1934, 29892, 2992, 29889, 3645, 727, 366, 508, 1584, 505, 24099, 4072, 310, 1906, 6996, 15038, 763, 263, 2826, 29899, 786, 528, 2728, 14216, 546, 470, 263, 1153, 3820, 273, 12844, 29872, 345, 14216, 546, 29889, 450, 2969, 338, 393, 366, 29915, 645, 1369, 25391, 385, 4152, 4333, 310, 2967, 15038, 393, 526, 17649, 297, 2969, 304, 825, 366, 864, 385, 1095, 4766, 304, 367, 29889, 5853, 11955, 297, 263, 274, 764, 265, 3800, 565, 366, 674, 29889, 13, 10773, 1582, 29892, 1250, 304, 4052, 5594, 29915, 29879, 29871, 29953, 29953, 29946, 29929, 29889, 306, 2825, 263, 14216, 546, 515, 445, 4766, 322, 18440, 599, 310, 278, 13499, 8946, 2791, 886, 304, 10368, 3377, 29889, 2178, 310, 278, 409, 314, 2758, 2925, 505, 1063, 5700, 1283, 1244, 322, 727, 526, 26532, 322, 451, 6609, 297, 2702, 7600, 29889, 12065, 1259, 263, 4766, 763, 445, 373, 10368, 3377, 338, 13568, 6288, 1363, 769, 746, 306, 29915, 29885, 7960, 304, 1653, 263, 716, 2246, 515, 445, 4766, 29892, 306, 508, 925, 9637, 372, 1283, 297, 263, 4383, 310, 6923, 29889, 450, 10368, 3377, 338, 380, 2593, 577, 366, 508, 925, 9637, 2820, 372, 2289, 5948, 29889, 13, 797, 278, 315, 4154, 29879, 29891, 770, 29892, 19235, 3697, 366, 777, 2289, 2107, 447, 4684, 29889, 1126, 1438, 526, 925, 6257, 3291, 29889, 306, 2099, 366, 2289, 437, 505, 278, 4152, 3186, 472, 596, 6900, 746, 366, 1369, 4969, 596, 1914, 15038, 448, 515, 15038, 393, 2307, 6216, 366, 29991, 4001, 366, 29915, 345, 2307, 20976, 278, 6216, 29892, 393, 29867, 304, 451, 367, 263, 1108, 15128, 29889, 887, 1795, 1065, 964, 777, 5626, 1244, 322, 727, 29892, 541, 896, 526, 13114, 491, 10230, 29889, 13, 3596, 297, 599, 29892, 306, 29915, 29885, 1407, 1407, 22301, 411, 920, 590, 447, 4684, 505, 6077, 714, 515, 445, 1889, 29889, 739, 3614, 263, 3287, 310, 931, 29892, 541, 471, 1532, 7088, 278, 13258, 358, 29889, 1551, 1328, 322, 701, 1328, 515, 1244, 29889, 6975, 366, 7695, 1549, 445, 1889, 1434, 29973, 1724, 17690, 310, 269, 4757, 414, 437, 366, 505, 29973, 960, 366, 7359, 29915, 29873, 29892, 306, 508, 29915, 29873, 6907, 1554, 763, 445, 3307, 29889, 887, 5110, 263, 15243, 1048, 28221, 322, 1048, 596, 3573, 322, 825, 2712, 366, 881, 367, 3063, 714, 363, 746, 366, 748, 304, 1018, 263, 716, 409, 16958, 4766, 29889, 15113, 769, 727, 29915, 29879, 278, 907, 1230, 20715, 2450, 393, 5304, 515, 4969, 263, 4766, 310, 596, 1407, 1914, 29889, 13811, 29892, 2090, 29991, 13, 25271, 366, 29991, 306, 29915, 345, 750, 393, 770, 297, 590, 14279, 3312, 18028, 363, 24646, 322, 2360, 376, 11940, 29908 ]

1,332,841

0

C4

4

1

the time to watch it. I am watching one class each morning this week. This is exactly what I want to do!Thank you! I've been interested in learning the sloper approach to sewing/pattern making and have been looking at books on slopers I could buy, but reviews seems to often be mixed on their quality, so I've been eyeing the bodice sloper class on Craftsy and the one you've mentionned (amongst so many others, I want to get them all..). It's good to know I'll get my moneys worth for the Many Shirts class when I buy it. I made some shirts in the past, but I see much room for emprouvement and would love to get (or make) a TNT shirt pattern. I've taken the sloper class on Craftsy, but this one seemed really interesting as well. The theory behind it sounds pretty fascinating! I like the concept of a sloper, but I just don't wear too many shirts, so I overlooked this class. I will take another look. Thanks, Sunni! I have a pants and a skirt sloper. I have really worked on the ginger jeans and archer shirt patterns into my idea of perfect jeans and button up patterns. They aren't slopers but now I am curious about doing that. I really believe in taking the time to fine tune patterns , it has been totally worth it for me. I got really tired of reinventing the wheel each go around with mixed results. Perfect timing on this topic! I was just doing some fitting through a new craftsy class (not the one you've mentioned but I will be checking it out now) and wondering if I could apply my new form fitting pattern as a sloper of sorts. Thanks for the insight. Amen! I hear ya sister! Trying to fit new sewing patterns gets so old. Gosh, I got so sick of starting at square zero everytime I wanted to make something a little different and so, it really was finally time to get some slopers done. They are a lot of work, but in the end, I'm so much happier with how these work instead of trying to fit a new sewing pattern. I have to weigh in because I've purchased several patternmaking books over the course of several years. While they are all good and they have wonderful information, drafting a sloper from your measurements is well, just as hard as getting a pattern to fit you. It's about a ton easier if you have a teacher there to help and hold your hand a bit, but if you're doing it on your own, I definitely say, take the Craftsy classes. It's so much easier to be guided by someone than try to decipher how to do it on your own! You'll go through about 1000 iterations of just the drafting trying to get it right - at least I did. I tried many, many different methods and books and found the same for all of them. Almost easier to just fit a sewing pattern from scratch. I think you would be glad you did once you were done. I've been taking my sloper out a TON and playing around with different ideas for different blouses from it - even dresses! It's getting a ton of play and use from me. I think the sloper class would be well worth the time - also have that one in my cue. I found this class really approachable. I like that she used a regular sewing pattern and then took that pattern and created a bunch of different blouses from it. It's really creative and fun! So many possibilities. I think there's one for pants too if I'm not mistaken. A Craftsy class I mean. Same idea. You take a pair of pants and create all the different pants patterns that you want from a single pattern. Makes it so you don't have to deal with fitting a new pattern. It's quite liberating and fun! I'm sure you can. Fitting is the #1 reason people don't sew their own clothes. When you start taking the fit out of the equation, it makes you want to sew more and believe me, you do! You can start cranking out patterns and projects left and right. I truly miss wearing shirts with buttons. Or even a shirtdress as the retro look is coming back. But my bust has a fuller shape from the sides so all RTW blouses get the gappies on me. Honestly, why sew a shirt I have to keep

0.354492

-1.176732

0.554544

-1.055771

[ 0.14698577236335297, 0.5619974273499774 ]

[ -1.5026261935677405, -0.850837389971003 ]

[ 0.4049053771548406, 0.7041818181501843 ]

[ -1.2755868118928533, -0.8359552365581159 ]

1,024

[ 512, 512 ]

[ 278, 931, 304, 6505, 372, 29889, 306, 626, 21217, 697, 770, 1269, 7250, 445, 4723, 29889, 910, 338, 3721, 825, 306, 864, 304, 437, 29991, 25271, 366, 29991, 13, 29902, 29915, 345, 1063, 8852, 297, 6509, 278, 14216, 546, 2948, 304, 409, 16958, 29914, 11037, 3907, 322, 505, 1063, 3063, 472, 8277, 373, 269, 4757, 414, 306, 1033, 15649, 29892, 541, 21804, 2444, 304, 4049, 367, 12849, 373, 1009, 11029, 29892, 577, 306, 29915, 345, 1063, 10977, 292, 278, 13004, 625, 14216, 546, 770, 373, 315, 4154, 29879, 29891, 322, 278, 697, 366, 29915, 345, 3585, 9571, 313, 314, 549, 303, 577, 1784, 4045, 29892, 306, 864, 304, 679, 963, 599, 636, 467, 739, 29915, 29879, 1781, 304, 1073, 306, 29915, 645, 679, 590, 286, 650, 952, 7088, 363, 278, 9267, 1383, 381, 1372, 770, 746, 306, 15649, 372, 29889, 306, 1754, 777, 528, 381, 1372, 297, 278, 4940, 29892, 541, 306, 1074, 1568, 5716, 363, 953, 558, 5128, 882, 322, 723, 5360, 304, 679, 313, 272, 1207, 29897, 263, 323, 20321, 528, 2728, 4766, 29889, 13, 29902, 29915, 345, 4586, 278, 14216, 546, 770, 373, 315, 4154, 29879, 29891, 29892, 541, 445, 697, 6140, 2289, 8031, 408, 1532, 29889, 450, 6368, 5742, 372, 10083, 5051, 21028, 262, 1218, 29991, 13, 29902, 763, 278, 6964, 310, 263, 14216, 546, 29892, 541, 306, 925, 1016, 29915, 29873, 19531, 2086, 1784, 528, 381, 1372, 29892, 577, 306, 975, 6914, 287, 445, 770, 29889, 306, 674, 2125, 1790, 1106, 29889, 1834, 29892, 8991, 1240, 29991, 13, 29902, 505, 263, 282, 1934, 322, 263, 2071, 2728, 14216, 546, 29889, 306, 505, 2289, 3796, 373, 278, 330, 5621, 1444, 550, 322, 3190, 261, 528, 2728, 15038, 964, 590, 2969, 310, 4922, 1444, 550, 322, 2826, 701, 15038, 29889, 2688, 9455, 29915, 29873, 269, 4757, 414, 541, 1286, 306, 626, 12758, 1048, 2599, 393, 29889, 306, 2289, 4658, 297, 5622, 278, 931, 304, 2691, 260, 1540, 15038, 1919, 372, 756, 1063, 14909, 7088, 372, 363, 592, 29889, 306, 2355, 2289, 23407, 310, 15561, 794, 292, 278, 18875, 1269, 748, 2820, 411, 12849, 2582, 29889, 13, 5894, 3647, 28750, 373, 445, 11261, 29991, 306, 471, 925, 2599, 777, 28221, 1549, 263, 716, 25554, 29879, 29891, 770, 313, 1333, 278, 697, 366, 29915, 345, 5276, 541, 306, 674, 367, 8454, 372, 714, 1286, 29897, 322, 9873, 565, 306, 1033, 3394, 590, 716, 883, 28221, 4766, 408, 263, 14216, 546, 310, 23551, 29889, 1834, 363, 278, 25483, 29889, 13, 29909, 1527, 29991, 306, 8293, 9343, 9883, 29991, 24428, 304, 6216, 716, 409, 16958, 15038, 4947, 577, 2030, 29889, 402, 10578, 29892, 306, 2355, 577, 17319, 310, 6257, 472, 6862, 5225, 1432, 2230, 306, 5131, 304, 1207, 1554, 263, 2217, 1422, 322, 577, 29892, 372, 2289, 471, 7146, 931, 304, 679, 777, 269, 4757, 414, 2309, 29889, 2688, 526, 263, 3287, 310, 664, 29892, 541, 297, 278, 1095, 29892, 306, 29915, 29885, 577, 1568, 2250, 631, 411, 920, 1438, 664, 2012, 310, 1811, 304, 6216, 263, 716, 409, 16958, 4766, 29889, 13, 29902, 505, 304, 591, 1141, 297, 1363, 306, 29915, 345, 20848, 3196, 4766, 28990, 8277, 975, 278, 3236, 310, 3196, 2440, 29889, 5806, 896, 526, 599, 1781, 322, 896, 505, 20695, 2472, 29892, 18195, 292, 263, 14216, 546, 515, 596, 20398, 338, 1532, 29892, 925, 408, 2898, 408, 2805, 263, 4766, 304, 6216, 366, 29889, 739, 29915, 29879, 1048, 263, 15243, 6775, 565, 366, 505, 263, 15703, 727, 304, 1371, 322, 4808, 596, 1361, 263, 2586, 29892, 541, 565, 366, 29915, 276, 2599, 372, 373, 596, 1914, 29892, 306, 11630, 1827, 29892, 2125, 278, 315, 4154, 29879, 29891, 4413, 29889, 739, 29915, 29879, 577, 1568, 6775, 304, 367, 1410, 2618, 491, 4856, 1135, 1018, 304, 316, 455, 8096, 920, 304, 437, 372, 373, 596, 1914, 29991, 887, 29915, 645, 748, 1549, 1048, 29871, 29896, 29900, 29900, 29900, 24372, 310, 925, 278, 18195, 292, 1811, 304, 679, 372, 1492, 448, 472, 3203, 306, 1258, 29889, 306, 1898, 1784, 29892, 1784, 1422, 3519, 322, 8277, 322, 1476, 278, 1021, 363, 599, 310, 963, 29889, 838, 3242, 6775, 304, 925, 6216, 263, 409, 16958, 4766, 515, 22728, 29889, 13, 29902, 1348, 366, 723, 367, 10932, 366, 1258, 2748, 366, 892, 2309, 29889, 306, 29915, 345, 1063, 5622, 590, 14216, 546, 714, 263, 323, 1164, 322, 8743, 2820, 411, 1422, 7014, 363, 1422, 1999, 23676, 515, 372, 448, 1584, 10714, 267, 29991, 739, 29915, 29879, 2805, 263, 15243, 310, 1708, 322, 671, 515, 592, 29889, 13, 29902, 1348, 278, 14216, 546, 770, 723, 367, 1532, 7088, 278, 931, 448, 884, 505, 393, 697, 297, 590, 274, 434, 29889, 306, 1476, 445, 770, 2289, 2948, 519, 29889, 306, 763, 393, 1183, 1304, 263, 4943, 409, 16958, 4766, 322, 769, 3614, 393, 4766, 322, 2825, 263, 14928, 310, 1422, 1999, 23676, 515, 372, 29889, 739, 29915, 29879, 2289, 907, 1230, 322, 2090, 29991, 1105, 1784, 24496, 29889, 13, 29902, 1348, 727, 29915, 29879, 697, 363, 282, 1934, 2086, 565, 306, 29915, 29885, 451, 25257, 29889, 319, 315, 4154, 29879, 29891, 770, 306, 2099, 29889, 19491, 2969, 29889, 887, 2125, 263, 5101, 310, 282, 1934, 322, 1653, 599, 278, 1422, 282, 1934, 15038, 393, 366, 864, 515, 263, 2323, 4766, 29889, 341, 6926, 372, 577, 366, 1016, 29915, 29873, 505, 304, 5376, 411, 28221, 263, 716, 4766, 29889, 739, 29915, 29879, 3755, 7866, 1218, 322, 2090, 29991, 13, 29902, 29915, 29885, 1854, 366, 508, 29889, 383, 5367, 338, 278, 396, 29896, 2769, 2305, 1016, 29915, 29873, 409, 29893, 1009, 1914, 22095, 29889, 1932, 366, 1369, 5622, 278, 6216, 714, 310, 278, 6306, 29892, 372, 3732, 366, 864, 304, 409, 29893, 901, 322, 4658, 592, 29892, 366, 437, 29991, 887, 508, 1369, 274, 661, 9292, 714, 15038, 322, 9279, 2175, 322, 1492, 29889, 13, 29902, 19781, 3052, 591, 4362, 528, 381, 1372, 411, 9828, 29889, 1394, 1584, 263, 528, 381, 1594, 1253, 408, 278, 24877, 1106, 338, 6421, 1250, 29889, 1205, 590, 289, 504, 756, 263, 2989, 261, 8267, 515, 278, 11192, 577, 599, 390, 16240, 1999, 23676, 679, 278, 330, 932, 583, 373, 592, 29889, 7906, 342, 368, 29892, 2020, 409, 29893, 263, 528, 2728, 306, 505, 304, 3013 ]

1,332,841

1,024

C4

4

1

closed with safety pins? This class is in my Crafty wish list but haven't taken the plunge yet. You've convinced me now that I may find my answer here. The idea of perfecting a pattern sloper has been brewing so I think on their next sale I'll get it. On a side note, I mentioned you and your Crafty class on zippers in my latest blog post. I reference that class ALL the time. Can you do a post about a dress with a lining and an invisible zipper? One that has that nice machine finish? Since I drafted my bodice, skirt and pant sloper from the book European Cut by Elizabeth Allemong, they have been invaluable to achieving fit that is 95% right the first time. The other 5% is the vagaries of the pattern and fabric I'm using which can be dealt with, with a muslin and then I'm good to go to make multiples :) I also use RTW items in my wardrobe to compare then tweak the patterns. I'm sure I could come up with something! Give me a bit and I'll see if I can't put this together! As for the Craftsy class I'm talking about here, I do want to state that it's not a fitting class by any means. Sarah Holden only talks and goes into depth about pattern drafting. But I still think the class would be worth everyone's while. The pattern drafting alone is great and it really does get you to think outside the box. I know exactly what you mean about wearing button-up shirts. I never did for a long time either because they never fit across the back. Couldn't put my arms in front of me! Now I can that I make my own. It's marvelous! Yes, I'm completely on board with you here! I feel the same way about the fit and I usually tend to make a muslin, if only just to check things like the neckline and such. Otherwise, the fit is so much easier and all I have to worry about is the design. Fun! I don't remember her using a lot of measurements, but sadly they are in inches. So sorry! We definitely need to convert over to the metric system! ugh! Someday I'll get to only 3 tries before fitting! It took me 8 Sorbettos before I got one that fit. Three sounds like a lovely goal! I am honestly still a little scared of the idea of a blank slate. I'm not familiar enough with my body and how clothes fit it yet to be able to envision something. I do look forward to that time, though, because frankly, I also find it hard to envision something from a pattern fitting me. It helps to troll the internet for someone similar to my body shape who has made the pattern, but it's still a wee bit exhausting. I have just finished fitting and putting together a dress sloper. But I don't know what to do with it now. Take it apart and trace it? Keep the darts closed? I used Vogue dress sloper pattern and really all it does is tell you to keep fitting it, but how do I use it against other patterns so that I will know they fit? This thing was a lot of work and I don't know how to use it now. Let me know if you have information on where to go from here. Hi Haze! Some great questions here. Hopefully I can answer them and give you some insight. The concept of using your sloper up against another sewing pattern to diagnose the fit before you make it is, well, a hard one. Additionally, I personally feel - since this is a method that I have tried - that it is full of holes and you end up still have to make a muslin and work out some fitting issues. If you are hell-bent on this method, I recommend Lynda Maynard's book Demystifying Fit. I would say that if you do want to do this method then you do need to take your muslin apart and copy it onto paper. You'll need to do this if you want to create sewing patterns from it, so I recommend that you do that step. If you want to create your own sewing patterns - which I find to be a much superior method to trying to use it to fit other sewing patterns - then I would recommend the Craftsy class above to give you a taste of how this works. You could still use your bodice section for most of the designs in the class or take the ideas and apply them to your sloper.

0.483926

-1.359376

0.271753

-0.945863

[ 0.5236465153380121, 0.444205340456084 ]

[ -1.2949132781358133, -1.423838535990113 ]

[ -0.07444417664278628, 0.6179496232871192 ]

[ -1.1585251498214735, -0.733201110962127 ]

1,024

[ 512, 512 ]

[ 5764, 411, 15332, 282, 1144, 29973, 910, 770, 338, 297, 590, 14279, 3312, 6398, 1051, 541, 7359, 29915, 29873, 4586, 278, 715, 19440, 3447, 29889, 887, 29915, 345, 25617, 592, 1286, 393, 306, 1122, 1284, 590, 1234, 1244, 29889, 450, 2969, 310, 4922, 292, 263, 4766, 14216, 546, 756, 1063, 2078, 16958, 577, 306, 1348, 373, 1009, 2446, 14686, 306, 29915, 645, 679, 372, 29889, 13, 2951, 263, 2625, 4443, 29892, 306, 5276, 366, 322, 596, 14279, 3312, 770, 373, 503, 8377, 414, 297, 590, 9281, 12618, 1400, 29889, 306, 3407, 393, 770, 15149, 278, 931, 29889, 1815, 366, 437, 263, 1400, 1048, 263, 10714, 411, 263, 301, 2827, 322, 385, 27597, 503, 29875, 2496, 29973, 3118, 393, 756, 393, 7575, 4933, 8341, 29973, 13, 23036, 306, 18195, 287, 590, 13004, 625, 29892, 2071, 2728, 322, 282, 424, 14216, 546, 515, 278, 3143, 7824, 315, 329, 491, 13061, 838, 2409, 549, 29892, 896, 505, 1063, 297, 4387, 519, 304, 3657, 15387, 6216, 393, 338, 29871, 29929, 29945, 29995, 1492, 278, 937, 931, 29889, 450, 916, 29871, 29945, 29995, 338, 278, 325, 351, 4314, 310, 278, 4766, 322, 18187, 306, 29915, 29885, 773, 607, 508, 367, 316, 1997, 411, 29892, 411, 263, 2301, 1915, 322, 769, 306, 29915, 29885, 1781, 304, 748, 304, 1207, 2473, 2701, 4248, 306, 884, 671, 390, 16240, 4452, 297, 590, 281, 538, 307, 915, 304, 7252, 769, 7780, 557, 278, 15038, 29889, 13, 29902, 29915, 29885, 1854, 306, 1033, 2041, 701, 411, 1554, 29991, 25538, 592, 263, 2586, 322, 306, 29915, 645, 1074, 565, 306, 508, 29915, 29873, 1925, 445, 4208, 29991, 13, 2887, 363, 278, 315, 4154, 29879, 29891, 770, 306, 29915, 29885, 9963, 1048, 1244, 29892, 306, 437, 864, 304, 2106, 393, 372, 29915, 29879, 451, 263, 28221, 770, 491, 738, 2794, 29889, 19235, 21771, 264, 871, 5969, 2039, 322, 5771, 964, 10809, 1048, 4766, 18195, 292, 29889, 1205, 306, 1603, 1348, 278, 770, 723, 367, 7088, 14332, 29915, 29879, 1550, 29889, 450, 4766, 18195, 292, 7432, 338, 2107, 322, 372, 2289, 947, 679, 366, 304, 1348, 5377, 278, 3800, 29889, 306, 1073, 3721, 825, 366, 2099, 1048, 591, 4362, 2826, 29899, 786, 528, 381, 1372, 29889, 306, 2360, 1258, 363, 263, 1472, 931, 2845, 1363, 896, 2360, 6216, 4822, 278, 1250, 29889, 6527, 29876, 29915, 29873, 1925, 590, 10188, 297, 4565, 310, 592, 29991, 2567, 306, 508, 393, 306, 1207, 590, 1914, 29889, 739, 29915, 29879, 1766, 955, 681, 29991, 13, 8241, 29892, 306, 29915, 29885, 6446, 373, 7613, 411, 366, 1244, 29991, 306, 4459, 278, 1021, 982, 1048, 278, 6216, 322, 306, 5491, 10331, 304, 1207, 263, 2301, 1915, 29892, 565, 871, 925, 304, 1423, 2712, 763, 278, 18873, 1220, 322, 1316, 29889, 13466, 29892, 278, 6216, 338, 577, 1568, 6775, 322, 599, 306, 505, 304, 15982, 1048, 338, 278, 2874, 29889, 13811, 29991, 13, 29902, 1016, 29915, 29873, 6456, 902, 773, 263, 3287, 310, 20398, 29892, 541, 14610, 368, 896, 526, 297, 22831, 29889, 1105, 7423, 29991, 1334, 11630, 817, 304, 3588, 975, 304, 278, 12714, 1788, 29991, 318, 12443, 29991, 13, 29903, 27067, 388, 306, 29915, 645, 679, 304, 871, 29871, 29941, 14335, 1434, 28221, 29991, 739, 3614, 592, 29871, 29947, 317, 11831, 1803, 359, 1434, 306, 2355, 697, 393, 6216, 29889, 12753, 10083, 763, 263, 12355, 873, 7306, 29991, 13, 29902, 626, 15993, 368, 1603, 263, 2217, 885, 1965, 310, 278, 2969, 310, 263, 9654, 2243, 403, 29889, 306, 29915, 29885, 451, 9985, 3307, 411, 590, 3573, 322, 920, 22095, 6216, 372, 3447, 304, 367, 2221, 304, 427, 4924, 1554, 29889, 306, 437, 1106, 6375, 304, 393, 931, 29892, 2466, 29892, 1363, 2524, 29895, 368, 29892, 306, 884, 1284, 372, 2898, 304, 427, 4924, 1554, 515, 263, 4766, 28221, 592, 29889, 739, 6911, 304, 260, 1245, 278, 8986, 363, 4856, 2788, 304, 590, 3573, 8267, 1058, 756, 1754, 278, 4766, 29892, 541, 372, 29915, 29879, 1603, 263, 591, 29872, 2586, 27096, 292, 29889, 13, 29902, 505, 925, 7743, 28221, 322, 10594, 4208, 263, 10714, 14216, 546, 29889, 13, 6246, 306, 1016, 29915, 29873, 1073, 825, 304, 437, 411, 372, 1286, 29889, 11190, 372, 12435, 322, 9637, 372, 29973, 19152, 278, 270, 5708, 5764, 29973, 306, 1304, 20797, 434, 10714, 14216, 546, 4766, 322, 2289, 599, 372, 947, 338, 2649, 366, 304, 3013, 28221, 372, 29892, 541, 920, 437, 306, 671, 372, 2750, 916, 15038, 577, 393, 306, 674, 1073, 896, 6216, 29973, 910, 2655, 471, 263, 3287, 310, 664, 322, 306, 1016, 29915, 29873, 1073, 920, 304, 671, 372, 1286, 29889, 13, 12024, 592, 1073, 565, 366, 505, 2472, 373, 988, 304, 748, 515, 1244, 29889, 13, 18567, 25606, 29872, 29991, 3834, 2107, 5155, 1244, 29889, 7963, 3730, 306, 508, 1234, 963, 322, 2367, 366, 777, 25483, 29889, 450, 6964, 310, 773, 596, 14216, 546, 701, 2750, 1790, 409, 16958, 4766, 304, 24876, 852, 278, 6216, 1434, 366, 1207, 372, 338, 29892, 1532, 29892, 263, 2898, 697, 29889, 19814, 29892, 306, 22345, 4459, 448, 1951, 445, 338, 263, 1158, 393, 306, 505, 1898, 448, 393, 372, 338, 2989, 310, 26532, 322, 366, 1095, 701, 1603, 505, 304, 1207, 263, 2301, 1915, 322, 664, 714, 777, 28221, 5626, 29889, 960, 366, 526, 23927, 29899, 29890, 296, 373, 445, 1158, 29892, 306, 6907, 8626, 299, 29874, 2610, 29876, 538, 29915, 29879, 3143, 4432, 858, 9215, 383, 277, 29889, 306, 723, 1827, 393, 565, 366, 437, 864, 304, 437, 445, 1158, 769, 366, 437, 817, 304, 2125, 596, 2301, 1915, 12435, 322, 3509, 372, 11480, 5650, 29889, 887, 29915, 645, 817, 304, 437, 445, 565, 366, 864, 304, 1653, 409, 16958, 15038, 515, 372, 29892, 577, 306, 6907, 393, 366, 437, 393, 4331, 29889, 13, 3644, 366, 864, 304, 1653, 596, 1914, 409, 16958, 15038, 448, 607, 306, 1284, 304, 367, 263, 1568, 11558, 1158, 304, 1811, 304, 671, 372, 304, 6216, 916, 409, 16958, 15038, 448, 769, 306, 723, 6907, 278, 315, 4154, 29879, 29891, 770, 2038, 304, 2367, 366, 263, 21779, 310, 920, 445, 1736, 29889, 887, 1033, 1603, 671, 596, 13004, 625, 4004, 363, 1556, 310, 278, 25517, 297, 278, 770, 470, 2125, 278, 7014, 322, 3394, 963, 304, 596, 14216, 546, 29889 ]

1,332,841

2,048

C4

4

1

Q: Rails server panic: repeating GET requests I was doing something unrelated to coding (and in a different Safari windows), when out of nowhere i see the logs generating a bunch of GET requests. The beginning looks like this: Started GET "/" for ::1 at 2015-06-28 18:19:41 -0400 Processing by StaticPagesController#home as HTML Rendered static_pages/home.html.erb within layouts/application (0.3ms) Rendered layouts/_shim.html.erb (0.1ms) Rendered layouts/_header.html.erb (3.0ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 375ms (Views: 373.9ms | ActiveRecord: 0.0ms) Started GET "/login" for ::1 at 2015-06-28 18:19:12 -0400 Processing by SessionsController#new as HTML Rendered sessions/new.html.erb within layouts/application (920.0ms) Rendered layouts/_shim.html.erb (0.1ms) Rendered layouts/_header.html.erb (101.4ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 1884ms (Views: 1883.2ms | ActiveRecord: 0.0ms) [2015-06-28 18:19:14] ERROR Errno::ECONNRESET: Connection reset by peer /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/httpserver.rb:80:in `eof?' /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/httpserver.rb:80:in `run' /System/Library/Frameworks/Ruby.framework/Versions/2.0/usr/lib/ruby/2.0.0/webrick/server.rb:295:in `block in start_thread' The first block then repeats again for n times until I stopped the server. The only anomaly is the following: Started GET "/" for ::1 at 2015-06-28 18:19:41 -0400 Processing by StaticPagesController#home as HTML Rendered static_pages/home.html.erb within layouts/application (0.3ms) Rendered layouts/_shim.html.erb (0.1ms) User Load (0.4ms) SELECT "users".* FROM "users" WHERE "users"."id" = ? LIMIT 1 [["id", 13]] Rendered layouts/_header.html.erb (4.5ms) Rendered layouts/_footer.html.erb (0.2ms) Completed 200 OK in 237ms (Views: 235.3ms | ActiveRecord: 0.4ms) ID:13 was the user_id i was working with. Any clue what might this be ? Looks suspicious. A: Does your app run any AJAX requests? Since this is on localhost, before assuming malice or hackery, I'd assume some rogue process related to your Rails server. In specific I'd make a checklist like the following: * *Does my app have any Javascript that might be sending an AJAX request? *Do the requests still occur when I disable all javascript? *Do I have any gems installed which might be triggering an AJAX request? *Do the requests occur when I don't have the site open in any browser? *Do the requests occur regardless of which browser I have open? (perhaps some strange browser add-on is causing the requests) *If I create a new empty / scaffolded Rails app, can I get the requests to occur on that one too? *Do the requests occur when I don't have any browsers open? *What other people / computers are on my network? Is

-1.613047

-1.167779

-1.139665

-0.524116

[ -1.7226211882199551, -1.5034731195801534 ]

[ -1.31640082111153, -1.0191564766141166 ]

[ -1.4516230534264445, -0.8277077611819142 ]

[ -0.7663685818823512, -0.2818633694202516 ]

1,024

[ 512, 512 ]

[ 660, 29901, 15144, 1923, 7243, 293, 29901, 28769, 12354, 7274, 306, 471, 2599, 1554, 443, 12817, 304, 14137, 313, 392, 297, 263, 1422, 24544, 5417, 511, 746, 714, 310, 1286, 4150, 474, 1074, 278, 10748, 14655, 263, 14928, 310, 12354, 7274, 29889, 450, 6763, 3430, 763, 445, 29901, 13, 4763, 287, 12354, 5591, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29946, 29896, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 624, 2454, 27514, 2956, 29937, 5184, 408, 4544, 13, 10716, 287, 2294, 29918, 12292, 29914, 5184, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29900, 29889, 29941, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29941, 29889, 29900, 1516, 29897, 13, 10716, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29941, 29955, 29945, 1516, 313, 23825, 29901, 29871, 29941, 29955, 29941, 29889, 29929, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29900, 1516, 29897, 13, 13, 4763, 287, 12354, 5591, 7507, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29896, 29906, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 317, 10964, 2956, 29937, 1482, 408, 4544, 13, 26000, 287, 21396, 29914, 1482, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29929, 29906, 29900, 29889, 29900, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29896, 29900, 29896, 29889, 29946, 1516, 29897, 13, 26000, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29896, 29947, 29947, 29946, 1516, 313, 23825, 29901, 29871, 29896, 29947, 29947, 29941, 29889, 29906, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29900, 1516, 29897, 13, 29961, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29896, 29946, 29962, 14431, 25361, 1217, 1057, 29923, 6007, 29940, 1525, 10490, 29901, 15160, 10092, 491, 23533, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 991, 261, 369, 29889, 6050, 29901, 29947, 29900, 29901, 262, 421, 29872, 974, 17901, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 991, 261, 369, 29889, 6050, 29901, 29947, 29900, 29901, 262, 421, 3389, 29915, 13, 29914, 3924, 29914, 12284, 29914, 4308, 13129, 29914, 29934, 4471, 29889, 4468, 29914, 29963, 414, 1080, 29914, 29906, 29889, 29900, 29914, 4855, 29914, 1982, 29914, 9754, 29914, 29906, 29889, 29900, 29889, 29900, 29914, 705, 1182, 860, 29914, 2974, 29889, 6050, 29901, 29906, 29929, 29945, 29901, 262, 421, 1271, 297, 1369, 29918, 7097, 29915, 13, 13, 1576, 937, 2908, 769, 5565, 1446, 1449, 363, 302, 3064, 2745, 306, 11084, 278, 1923, 29889, 450, 871, 29342, 14997, 338, 278, 1494, 29901, 13, 4763, 287, 12354, 5591, 29908, 363, 4761, 29896, 472, 29871, 29906, 29900, 29896, 29945, 29899, 29900, 29953, 29899, 29906, 29947, 29871, 29896, 29947, 29901, 29896, 29929, 29901, 29946, 29896, 448, 29900, 29946, 29900, 29900, 13, 7032, 292, 491, 624, 2454, 27514, 2956, 29937, 5184, 408, 4544, 13, 29871, 26000, 287, 2294, 29918, 12292, 29914, 5184, 29889, 1420, 29889, 23936, 2629, 5912, 29879, 29914, 6214, 313, 29900, 29889, 29941, 1516, 29897, 13, 29871, 26000, 287, 5912, 29879, 19891, 845, 326, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29896, 1516, 29897, 13, 29871, 4911, 16012, 313, 29900, 29889, 29946, 1516, 29897, 29871, 5097, 29871, 376, 7193, 1642, 29930, 3895, 376, 7193, 29908, 5754, 376, 7193, 29908, 1213, 333, 29908, 353, 1577, 27848, 29871, 29896, 29871, 518, 3366, 333, 613, 29871, 29896, 29941, 5262, 13, 29871, 26000, 287, 5912, 29879, 19891, 6672, 29889, 1420, 29889, 23936, 313, 29946, 29889, 29945, 1516, 29897, 13, 29871, 26000, 287, 5912, 29879, 19891, 21720, 29889, 1420, 29889, 23936, 313, 29900, 29889, 29906, 1516, 29897, 13, 26010, 29871, 29906, 29900, 29900, 9280, 297, 29871, 29906, 29941, 29955, 1516, 313, 23825, 29901, 29871, 29906, 29941, 29945, 29889, 29941, 1516, 891, 29058, 29901, 29871, 29900, 29889, 29946, 1516, 29897, 13, 13, 1367, 29901, 29896, 29941, 471, 278, 1404, 29918, 333, 474, 471, 1985, 411, 29889, 13, 10773, 23960, 825, 1795, 445, 367, 1577, 19887, 8872, 14803, 29889, 13, 13, 29909, 29901, 5538, 596, 623, 1065, 738, 18891, 7274, 29973, 4001, 445, 338, 373, 15683, 29892, 1434, 10241, 4439, 625, 470, 15833, 708, 29892, 306, 29915, 29881, 5251, 777, 696, 13000, 1889, 4475, 304, 596, 15144, 1923, 29889, 512, 2702, 306, 29915, 29881, 1207, 263, 1423, 1761, 763, 278, 1494, 29901, 13, 13, 13, 29930, 13, 13, 29930, 25125, 590, 623, 505, 738, 12728, 393, 1795, 367, 9348, 385, 18891, 2009, 29973, 13, 13, 29930, 6132, 278, 7274, 1603, 6403, 746, 306, 11262, 599, 3513, 29973, 13, 13, 29930, 6132, 306, 505, 738, 330, 1567, 5130, 607, 1795, 367, 7135, 292, 385, 18891, 2009, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 746, 306, 1016, 29915, 29873, 505, 278, 3268, 1722, 297, 738, 4714, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 17126, 310, 607, 4714, 306, 505, 1722, 29973, 313, 546, 4252, 777, 8515, 4714, 788, 29899, 265, 338, 10805, 278, 7274, 29897, 13, 13, 29930, 3644, 306, 1653, 263, 716, 4069, 847, 885, 3470, 1025, 287, 15144, 623, 29892, 508, 306, 679, 278, 7274, 304, 6403, 373, 393, 697, 2086, 29973, 13, 13, 29930, 6132, 278, 7274, 6403, 746, 306, 1016, 29915, 29873, 505, 738, 14376, 1722, 29973, 13, 13, 29930, 5618, 916, 2305, 847, 23226, 526, 373, 590, 3564, 29973, 1317 ]

1,332,842

0

StackExchange

-1

Need a Dumpster Rental in Rives Junction? We have the commercial and residential dumpster service you need in Rives Junction. At Royal Dumpster, we strive to bring you the best service at the best price available. We have a wide selection of dumpster sizes in stock in Rives Junction, MI, with flexible & timley pickup and delivery. Give us a call today for all your dumpster rental and roll off needs. Your roll-off dumpster in Rives Junction, MI is only a phone call away. Don't delay! Dumpsters are available* in Rives Junction. Most Rives Junction dumpster rental companies will take care of securing this permit for you if you rent from them. Make sure that if you're planning to put the dumpster on the street, the company has made the appropriate arrangements. You should also ensure that you get the permit in a timely manner and at the correct cost. If you thought the dumpster company was getting a permit and they did not, you will be the one who will have to pay the fine that is issued by the authorities. In the spring you may want to start school restorations that need to happen now. Increasingly more, schools are getting more and more jampacked. Additions are necessary as well as educational setting sizes created larger. In the course of spring break you possibly can have a contractor lined up to start your renovations. To acheive the restorations done swiftly you will need to find a person that the cost of rent next day dumpsters. Your contractors can readily do their work in addition to clean up subsequently with a dumpster right next to them. Make sure you cope with a company which includes dumpsters with wheels on the bottom. Your contractors can easily move the dumpster from one place to another whilst working. Dealing with these massive tons of junk on do it yourself would be a problem and requires lot of investment in terms of time and money. Your current painstaking research to find an inexpensive way of disposing the trash inside shortest moment possible could end up in 20 Yard Dumpster Rentals in Rives Junction, MI program. Dumpsters are usually easily obtainable in different your sizes in which range between 10 lawn and 45 yard. You need to be extra careful while picking out the size of dumpster simply because choosing the completely wrong sized dumpster aside from required will probably impose further charges as you have to go for multiple pickups to dispose your own trash when the dumpster is tiny in size. You'll be paying for the disposable space if you choose a dumpster that's large wide. A major cleanout might be stressful in addition to exhausting. Regardless of whether you're planning for an upcoming cross-country transfer to a smaller home, cleaning out a senior relative's home ahead of an real estate sale or perhaps foreclosure, or perhaps gut-renovating your office in addition to installing all-new fittings, all of the rubbish you pitch has to move somewhere. It is possible to divide the trash and rubbish up straight into small plenty and generate back and forth on the dump as well as the recycling center, wasting time, fuel, as well as. Or you can save the hassle by means of hiring a professional junk trucking team to perform the heavy lifting and discretion for you. Just what does a rubbish hauler do? All depends on the particular company, thus consider your requirements your budget before you make a hiring decision. Once you embark on an important cleaning, development, or remodelling project, not what you want to concern yourself with is getting rid of the producing debris. Executing it is hard plenty of. There's no reasons why you should be burdened with hand bags and lots of junk afterward. These may clutter your property, which regularly directly negates the intention of doing the work to begin with and can warrant special journeys to the remove or other discretion facility afterwards. Instead of dealing with your junk removal inside a piecemeal way, it could be worth your while to investigate renting a dumpster. While sporting a dumpster on your property may seem like a step backwards, this process simplifies your cleanup course of action. You can rent a new dumpster for as long as you'll need, you can put all your trash in addition to debris within it, and then you could get rid of all things in one fell swoop when you find yourself done. If you are doing a residence clean

-1.245974

-1.653039

-1.076893

-1.676198

[ -1.6459193641960246, -0.8460289136607484 ]

[ -1.653038994397757, -1.653038994397757 ]

[ -1.5074203559848984, -0.6463665278669389 ]

[ -1.9727540437846263, -1.3796416226229686 ]

1,024

[ 512, 512 ]

[ 20768, 263, 360, 3427, 2475, 390, 13703, 297, 390, 3145, 435, 651, 29973, 13, 4806, 505, 278, 12128, 322, 20201, 616, 16766, 2475, 2669, 366, 817, 297, 390, 3145, 435, 651, 29889, 13, 4178, 7021, 360, 3427, 2475, 29892, 591, 380, 4401, 304, 6963, 366, 278, 1900, 2669, 472, 278, 1900, 8666, 3625, 29889, 1334, 505, 263, 9377, 9262, 310, 16766, 2475, 15786, 297, 10961, 297, 390, 3145, 435, 651, 29892, 341, 29902, 29892, 411, 25706, 669, 5335, 2330, 5839, 786, 322, 28289, 29889, 25538, 502, 263, 1246, 9826, 363, 599, 596, 16766, 2475, 364, 13703, 322, 9679, 1283, 4225, 29889, 13, 10858, 9679, 29899, 2696, 16766, 2475, 297, 390, 3145, 435, 651, 29892, 341, 29902, 338, 871, 263, 9008, 1246, 3448, 29889, 3872, 29915, 29873, 9055, 29991, 13, 29928, 3427, 23080, 526, 3625, 29930, 297, 390, 3145, 435, 651, 29889, 13, 29924, 520, 390, 3145, 435, 651, 16766, 2475, 364, 13703, 14582, 674, 2125, 2562, 310, 409, 2764, 292, 445, 14257, 363, 366, 565, 366, 23990, 515, 963, 29889, 8561, 1854, 393, 565, 366, 29915, 276, 18987, 304, 1925, 278, 16766, 2475, 373, 278, 11952, 29892, 278, 5001, 756, 1754, 278, 8210, 15196, 4110, 29889, 887, 881, 884, 9801, 393, 366, 679, 278, 14257, 297, 263, 5335, 873, 8214, 322, 472, 278, 1959, 3438, 29889, 960, 366, 2714, 278, 16766, 2475, 5001, 471, 2805, 263, 14257, 322, 896, 1258, 451, 29892, 366, 674, 367, 278, 697, 1058, 674, 505, 304, 5146, 278, 2691, 393, 338, 16610, 491, 278, 21142, 29889, 13, 797, 278, 6709, 366, 1122, 864, 304, 1369, 3762, 1791, 272, 800, 393, 817, 304, 3799, 1286, 29889, 512, 1037, 5832, 368, 901, 29892, 12462, 526, 2805, 901, 322, 901, 432, 1160, 547, 287, 29889, 3462, 2187, 526, 5181, 408, 1532, 408, 28976, 4444, 15786, 2825, 7200, 29889, 512, 278, 3236, 310, 6709, 2867, 366, 10075, 508, 505, 263, 8078, 272, 301, 1312, 701, 304, 1369, 596, 25615, 800, 29889, 1763, 263, 1173, 573, 278, 1791, 272, 800, 2309, 12086, 368, 366, 674, 817, 304, 1284, 263, 2022, 393, 278, 3438, 310, 23990, 2446, 2462, 16766, 23080, 29889, 3575, 8078, 943, 508, 28520, 437, 1009, 664, 297, 6124, 304, 5941, 701, 17602, 411, 263, 16766, 2475, 1492, 2446, 304, 963, 29889, 8561, 1854, 366, 1302, 412, 411, 263, 5001, 607, 7805, 16766, 23080, 411, 21266, 1379, 373, 278, 5970, 29889, 3575, 8078, 943, 508, 5948, 4337, 278, 16766, 2475, 515, 697, 2058, 304, 1790, 21109, 1985, 29889, 13, 2772, 12818, 411, 1438, 20364, 23864, 310, 432, 2960, 373, 437, 372, 7535, 723, 367, 263, 1108, 322, 6858, 3287, 310, 13258, 358, 297, 4958, 310, 931, 322, 6909, 29889, 3575, 1857, 6788, 303, 5086, 5925, 304, 1284, 385, 297, 4548, 6270, 982, 310, 11549, 292, 278, 534, 1161, 2768, 3273, 342, 3256, 1950, 1033, 1095, 701, 297, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 29892, 341, 29902, 1824, 29889, 13, 29928, 3427, 23080, 526, 5491, 5948, 4017, 519, 297, 1422, 596, 15786, 297, 607, 3464, 1546, 29871, 29896, 29900, 425, 1233, 322, 29871, 29946, 29945, 29413, 29889, 887, 817, 304, 367, 4805, 16010, 1550, 5839, 292, 714, 278, 2159, 310, 16766, 2475, 3763, 1363, 23906, 278, 6446, 2743, 269, 1891, 16766, 2475, 17786, 515, 3734, 674, 3117, 2411, 852, 4340, 21090, 408, 366, 505, 304, 748, 363, 2999, 5839, 14340, 304, 27905, 596, 1914, 534, 1161, 746, 278, 16766, 2475, 338, 21577, 297, 2159, 29889, 887, 29915, 645, 367, 5146, 292, 363, 278, 11549, 519, 2913, 565, 366, 6755, 263, 16766, 2475, 393, 29915, 29879, 2919, 9377, 29889, 13, 29909, 4655, 5941, 449, 1795, 367, 22884, 1319, 297, 6124, 304, 27096, 292, 29889, 2169, 538, 2222, 310, 3692, 366, 29915, 276, 18987, 363, 385, 701, 11506, 4891, 29899, 13509, 6782, 304, 263, 7968, 3271, 29892, 5941, 292, 714, 263, 16336, 6198, 29915, 29879, 3271, 14432, 310, 385, 1855, 19989, 14686, 470, 6060, 29821, 5409, 545, 29892, 470, 6060, 22341, 29899, 1267, 586, 1218, 596, 8034, 297, 6124, 304, 15476, 599, 29899, 1482, 285, 986, 886, 29892, 599, 310, 278, 14051, 29890, 728, 366, 15905, 756, 304, 4337, 9051, 29889, 739, 338, 1950, 304, 16429, 278, 534, 1161, 322, 14051, 29890, 728, 701, 7812, 964, 2319, 20947, 322, 5706, 1250, 322, 11483, 373, 278, 16766, 408, 1532, 408, 278, 1162, 29891, 19914, 4818, 29892, 471, 1259, 931, 29892, 26413, 29892, 408, 1532, 408, 29889, 1394, 366, 508, 4078, 278, 298, 465, 280, 491, 2794, 310, 298, 8491, 263, 10257, 432, 2960, 534, 2707, 292, 3815, 304, 2189, 278, 9416, 11747, 1259, 322, 766, 4838, 291, 363, 366, 29889, 3387, 825, 947, 263, 14051, 29890, 728, 447, 8584, 437, 29973, 2178, 7111, 373, 278, 3153, 5001, 29892, 4550, 2050, 596, 11780, 596, 23562, 1434, 366, 1207, 263, 298, 8491, 10608, 29889, 13, 26222, 366, 7232, 935, 373, 385, 4100, 5941, 292, 29892, 5849, 29892, 470, 1083, 397, 7807, 2060, 29892, 451, 825, 366, 864, 304, 5932, 7535, 411, 338, 2805, 8177, 310, 278, 20811, 316, 1182, 275, 29889, 11080, 17068, 372, 338, 2898, 20947, 310, 29889, 1670, 29915, 29879, 694, 9590, 2020, 366, 881, 367, 6866, 1145, 287, 411, 1361, 289, 810, 322, 14568, 310, 432, 2960, 1156, 1328, 29889, 4525, 1122, 1067, 6463, 596, 2875, 29892, 607, 25704, 4153, 3480, 1078, 278, 16392, 310, 2599, 278, 664, 304, 3380, 411, 322, 508, 1370, 21867, 4266, 8694, 484, 952, 304, 278, 3349, 470, 916, 766, 4838, 291, 24454, 12335, 29889, 8669, 310, 16743, 411, 596, 432, 2960, 28744, 2768, 263, 5036, 29883, 2004, 284, 982, 29892, 372, 1033, 367, 7088, 596, 1550, 304, 23033, 23990, 292, 263, 16766, 2475, 29889, 5806, 7980, 292, 263, 16766, 2475, 373, 596, 2875, 1122, 2833, 763, 263, 4331, 28953, 29892, 445, 1889, 5466, 11057, 596, 5941, 786, 3236, 310, 3158, 29889, 887, 508, 23990, 263, 716, 16766, 2475, 363, 408, 1472, 408, 366, 29915, 645, 817, 29892, 366, 508, 1925, 599, 596, 534, 1161, 297, 6124, 304, 316, 1182, 275, 2629, 372, 29892, 322, 769, 366, 1033, 679, 8177, 310, 599, 2712, 297, 697, 8379, 16768, 459, 746, 366, 1284, 7535, 2309, 29889, 960, 366, 526, 2599, 263, 25488, 5941 ]

1,332,847

0

C4

0

3

-out, construction cleanup, or other redesigning or remodelling projects, renting a new dumpster can be a fantastic option. Dumpsters are workhorses in addition to aren't generally considered the celebs of the development or home renovation business. At the rear of every commercial business in the nation, there's normally a dumpster. These are generally under 15 yards, and the stars from the construction marketplace run 15, twenty, 30 or forty yards. How do you locate this sort of huge and incredibly heavy metal pack? By renting your own personal star dumpster from an online company - that's precisely how. Saving money in 20 Yard Dumpster Rentals in Rives Junctions is straightforward if you consider the above-mentioned tips. Simply by ensuring these pointers, you can easily obtain an affordable in addition to reliable services that can help you remove waste large quantities, without costing you a fortune. As soon as hiring a or maybe 20 Yard Dumpster Rentals in Rives Junction company to assistance with your property cleanout, look for someone who will address you having compassion in addition to care through what may be a difficult time. The speed and alleviate gained from professional property cleaning help will be made moot if the company's representatives tend to be pushy, rude or obnoxious, or disrespectful. Look at each company's Web site to see whether they listing estate cleaning as one of their particular specialties, or maybe call to speak to a customer services representative. The correct company can understand what you are heading through in addition to do whatever it takes to meet your needs. An alternative choice is to gather the bulk spend and carry it off with your car to any local disposal capability, one fill at a time. Many municipalities could accept this waste while others may not. Many may impose a fee for fingertips. Meanwhile, due to realize simply how much waste you've got until you try to fit all this in your auto. If you are a roofing contractor you know you will need to keep your roofer jobs moving. The time to top flies by with the moment you have thanks to the weather. Chances are you'll live in states that get passionate hot into the 90's in addition to 100's otherwise you may live in a state that possesses brutal winter months. With the times and thanks to time constraints, people are calling an individual left and right to acquire roof accomplished. Some of the consumer's roofs tend to be emergencies because they are leaking in addition to causing mould to form within the ceilings. You and your crew want to quickly give your customer an estimate. Once you increase the risk for time to evaluate the damage and exactly how much it will cost the customer to correct his or her top, you can warning the contract to practice it. When you start on a major cleaning, construction, or maybe renovation task, the last thing you need to worry about becomes rid of the particular resulting debris. Doing the work is challenging enough. There's no reason why you ought to be burdened having bags in addition to piles connected with trash later. These can clutter up your residence, which often right negates the purpose of working on the project in the first place and will necessitate specific trips to the particular dump or other disposal capability after the fact. Instead of tackling your own trash elimination in a piecemeal technique, it may be beneficial to look into hiring a dumpster. While wearing a dumpster on the property might appear to be a step back, it actually shortens the clean-up process. It is possible to rent a dumpster so long as you need, place all of your junk and debris in it, and you can get rid of everything in just one fell jump when you're accomplished. If you're carrying out a home clean-out, development cleaning, or other home improvement or maybe renovation tasks, renting a dumpster can be a great option. The idea of using a substantial bag to be able to load up and haul absent heavy junk items may seem like it could not work, but the Big Bag's layout is an clever fusion involving form and function that makes it a superb garbage removing choice. When you really need to get rid of plenty of trash, you can contact a crap remover that offers bag program, purchase a reusable Big Bag, and set this anywhere on your property. Then, you can get on with what ever work you should do. You can stock up the Big Bag with what you need to

-0.906295

-1.438164

-0.847998

-1.496703

[ -0.9172520359686839, -0.8953372291047038 ]

[ -1.2949132781358133, -1.5814138511453681 ]

[ -0.8124903150296086, -0.8835050637403682 ]

[ -1.5357238387181418, -1.4576827306705553 ]

1,024

[ 512, 512 ]

[ 29899, 449, 29892, 7632, 5941, 786, 29892, 470, 916, 2654, 267, 647, 292, 470, 1083, 397, 7807, 9279, 29892, 23990, 292, 263, 716, 16766, 2475, 508, 367, 263, 13568, 6288, 2984, 29889, 13, 29928, 3427, 23080, 526, 664, 29882, 943, 267, 297, 6124, 304, 9455, 29915, 29873, 6892, 5545, 278, 7793, 5824, 310, 278, 5849, 470, 3271, 25615, 362, 5381, 29889, 2180, 278, 18983, 310, 1432, 12128, 5381, 297, 278, 5233, 29892, 727, 29915, 29879, 12891, 263, 16766, 2475, 29889, 4525, 526, 6892, 1090, 29871, 29896, 29945, 17454, 29892, 322, 278, 10819, 515, 278, 7632, 9999, 6689, 1065, 29871, 29896, 29945, 29892, 10081, 29892, 29871, 29941, 29900, 470, 20949, 17454, 29889, 1128, 437, 366, 26694, 445, 2656, 310, 12176, 322, 29811, 14981, 9416, 11915, 4870, 29973, 2648, 23990, 292, 596, 1914, 7333, 5810, 16766, 2475, 515, 385, 7395, 5001, 448, 393, 29915, 29879, 17503, 920, 29889, 13, 29903, 5555, 6909, 297, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 29879, 338, 20837, 565, 366, 2050, 278, 2038, 29899, 358, 28487, 25562, 29889, 3439, 17632, 491, 5662, 3864, 1438, 12589, 29892, 366, 508, 5948, 4017, 385, 21750, 519, 297, 6124, 304, 23279, 5786, 393, 508, 1371, 366, 3349, 19863, 2919, 26855, 29892, 1728, 3438, 292, 366, 263, 19717, 29889, 13, 2887, 4720, 408, 298, 8491, 263, 470, 5505, 29871, 29906, 29900, 612, 538, 360, 3427, 2475, 390, 296, 1338, 297, 390, 3145, 435, 651, 5001, 304, 18872, 411, 596, 2875, 5941, 449, 29892, 1106, 363, 4856, 1058, 674, 3211, 366, 2534, 752, 465, 291, 297, 6124, 304, 2562, 1549, 825, 1122, 367, 263, 5189, 931, 29889, 450, 6210, 322, 4788, 1403, 403, 17515, 515, 10257, 2875, 5941, 292, 1371, 674, 367, 1754, 2730, 327, 565, 278, 5001, 29915, 29879, 2755, 5056, 10331, 304, 367, 5503, 29891, 29892, 364, 1151, 470, 704, 1217, 29916, 2738, 29892, 470, 766, 690, 1103, 1319, 29889, 7419, 472, 1269, 5001, 29915, 29879, 2563, 3268, 304, 1074, 3692, 896, 18028, 19989, 5941, 292, 408, 697, 310, 1009, 3153, 4266, 2938, 29892, 470, 5505, 1246, 304, 7726, 304, 263, 11962, 5786, 21097, 29889, 450, 1959, 5001, 508, 2274, 825, 366, 526, 28435, 1549, 297, 6124, 304, 437, 6514, 372, 4893, 304, 5870, 596, 4225, 29889, 13, 2744, 8671, 7348, 338, 304, 11705, 278, 21610, 18864, 322, 8677, 372, 1283, 411, 596, 1559, 304, 738, 1887, 11549, 284, 2117, 3097, 29892, 697, 5445, 472, 263, 931, 29889, 9267, 11677, 1907, 1033, 3544, 445, 19863, 1550, 4045, 1122, 451, 29889, 9267, 1122, 2411, 852, 263, 27684, 363, 285, 292, 814, 4512, 29889, 25065, 29892, 2861, 304, 16289, 3763, 920, 1568, 19863, 366, 29915, 345, 2355, 2745, 366, 1018, 304, 6216, 599, 445, 297, 596, 4469, 29889, 13, 3644, 366, 526, 263, 17526, 292, 8078, 272, 366, 1073, 366, 674, 817, 304, 3013, 596, 696, 29877, 571, 17643, 8401, 29889, 450, 931, 304, 2246, 285, 3687, 491, 411, 278, 3256, 366, 505, 3969, 304, 278, 14826, 29889, 678, 2925, 526, 366, 29915, 645, 5735, 297, 5922, 393, 679, 15935, 403, 7375, 964, 278, 29871, 29929, 29900, 29915, 29879, 297, 6124, 304, 29871, 29896, 29900, 29900, 29915, 29879, 6467, 366, 1122, 5735, 297, 263, 2106, 393, 3119, 15322, 26644, 284, 13851, 7378, 29889, 2973, 278, 3064, 322, 3969, 304, 931, 11938, 29892, 2305, 526, 5432, 385, 5375, 2175, 322, 1492, 304, 1274, 1548, 17526, 24799, 29889, 3834, 310, 278, 21691, 29915, 29879, 17526, 29879, 10331, 304, 367, 11176, 1885, 2478, 1363, 896, 526, 454, 5086, 297, 6124, 304, 10805, 286, 483, 304, 883, 2629, 278, 2257, 309, 886, 29889, 887, 322, 596, 17616, 864, 304, 9098, 2367, 596, 11962, 385, 12678, 29889, 9038, 366, 7910, 278, 12045, 363, 931, 304, 14707, 278, 18658, 322, 3721, 920, 1568, 372, 674, 3438, 278, 11962, 304, 1959, 670, 470, 902, 2246, 29892, 366, 508, 9177, 278, 8078, 304, 6944, 372, 29889, 13, 10401, 366, 1369, 373, 263, 4655, 5941, 292, 29892, 7632, 29892, 470, 5505, 25615, 362, 3414, 29892, 278, 1833, 2655, 366, 817, 304, 15982, 1048, 7415, 8177, 310, 278, 3153, 9819, 316, 1182, 275, 29889, 1938, 292, 278, 664, 338, 18066, 292, 3307, 29889, 1670, 29915, 29879, 694, 2769, 2020, 366, 12722, 304, 367, 6866, 1145, 287, 2534, 289, 810, 297, 6124, 304, 282, 5475, 6631, 411, 534, 1161, 2678, 29889, 4525, 508, 1067, 6463, 701, 596, 25488, 29892, 607, 4049, 1492, 3480, 1078, 278, 6437, 310, 1985, 373, 278, 2060, 297, 278, 937, 2058, 322, 674, 3520, 10388, 2702, 3367, 567, 304, 278, 3153, 16766, 470, 916, 11549, 284, 2117, 3097, 1156, 278, 2114, 29889, 8669, 310, 22002, 1847, 596, 1914, 534, 1161, 29007, 3381, 297, 263, 5036, 29883, 2004, 284, 11043, 29892, 372, 1122, 367, 7795, 5611, 304, 1106, 964, 298, 8491, 263, 16766, 2475, 29889, 5806, 591, 4362, 263, 16766, 2475, 373, 278, 2875, 1795, 2615, 304, 367, 263, 4331, 1250, 29892, 372, 2869, 3273, 575, 278, 5941, 29899, 786, 1889, 29889, 739, 338, 1950, 304, 23990, 263, 16766, 2475, 577, 1472, 408, 366, 817, 29892, 2058, 599, 310, 596, 432, 2960, 322, 316, 1182, 275, 297, 372, 29892, 322, 366, 508, 679, 8177, 310, 4129, 297, 925, 697, 8379, 12500, 746, 366, 29915, 276, 24799, 29889, 960, 366, 29915, 276, 19436, 714, 263, 3271, 5941, 29899, 449, 29892, 5849, 5941, 292, 29892, 470, 916, 3271, 20414, 470, 5505, 25615, 362, 9595, 29892, 23990, 292, 263, 16766, 2475, 508, 367, 263, 2107, 2984, 29889, 13, 1576, 2969, 310, 773, 263, 23228, 19548, 304, 367, 2221, 304, 2254, 701, 322, 447, 352, 29207, 9416, 432, 2960, 4452, 1122, 2833, 763, 372, 1033, 451, 664, 29892, 541, 278, 7997, 18341, 29915, 29879, 5912, 338, 385, 23455, 21736, 21677, 883, 322, 740, 393, 3732, 372, 263, 2428, 29890, 25861, 11077, 7348, 29889, 1932, 366, 2289, 817, 304, 679, 8177, 310, 20947, 310, 534, 1161, 29892, 366, 508, 6958, 263, 274, 2390, 1083, 957, 393, 16688, 19548, 1824, 29892, 20590, 263, 337, 27979, 7997, 18341, 29892, 322, 731, 445, 12214, 373, 596, 2875, 29889, 1987, 29892, 366, 508, 679, 373, 411, 825, 3926, 664, 366, 881, 437, 29889, 887, 508, 10961, 701, 278, 7997, 18341, 411, 825, 366, 817, 304 ]

1,332,847

1,024

C4

15

4

President Trump and Joe Biden Offer Study in Contrasts in Dueling Town Halls President Trump and Joe Biden offered starkly different visions for the country and a sharp contrast in leadership styles on Thursday as the presidential contenders took part in dueling town halls on NBC and ABC. NBC's hourlong event with Trump drew strong criticism from the entertainment industry and many others who saw it as a way of indulging Trump, who pulled out of a planned second presidential debate with his Democratic opponent. NBC was urged to move its event out of the 8 p.m. hour so as not to conflict with ABC's 90-minute session with Biden, which was announced first after Trump dropped out of the debate. "Today" anchor Savannah Guthrie sparred aggressively with Trump throughout the one-hour event. She set the tone early, asking him to disavow white supremacy and QAnon, the online conspiracy theory about a pedophile cult. Trump said he knew little about it, though he had heard they were "strongly against pedophilia." "I agree with that," he said. When she followed up, asking him to say there was no pedophile cult, he declined. "I don't know that," Trump said. "Neither do you know that. Why aren't you asking me about antifa?" Guthrie appeared ready for a fight. "You're not like someone's crazy uncle that can just retweet whatever," she said at one point. Guthrie also grilled Trump about his tax returns, asking if it was true — as the New York Times reported — that he paid only $750 a year. He said the figure was a "statutory number — a filing fee." "If they have my tax returns, they have to go to jail," Trump said. "It's illegal." Meanwhile on ABC, chief anchor George Stephanopoulos pressed Biden about whether Democrats will seek to add justices to the Supreme Court, assuming that conservatives take a 6-3 advantage with the confirmation of Judge Amy Coney Barrett. Biden declined to answer directly, but said he would offer "a clear position before Election Day pending on how they handle this." Biden said he wants to keep the focus on the inappropriate nature of Barrett's confirmation process, and that if he were to declare his position one way or another now, "that's the headline." He also advised viewers: "Presidents come and go. Justices stay and stay and stay." Speaking at Philadelphia's National Constitution Center, Biden fielded questions about racial justice, income inequality, infrastructure and police reform. His avuncular delivery and ease in discussing the nitty-gritty details of policy stood in sharp contrast to the more belligerent tone over on NBC. Biden offered some personal asides, such as his oft-repeated line that when he was a kid growing up in Clermont, Penn., most men "either became a cop, a firefighter or a priest. I wasn't qualified to do any of them." He made a point of asking each questioner whether he had sufficiently answered the query. He also castigated Trump's leadership during the pandemic. "The president has a responsibility to lead and he didn't do that," Biden said. "He didn't talk about what needed to be done. He kept worrying, in my view, about the (stock) market." On NBC, Trump bristled as Guthrie pressed hard on his administration's response to the virus. "I knew you'd be doing this," he said. "I know you very well." Biden made a strong statement about protecting LGBTQ rights, and he promised to end policies enacted by Trump that curb the rights of transgender people. He noted with dismay the recent rash of murders of transgender women of color. About 60 voters, all wearing masks, attended the event at the Pérez Art Museum in Miami. Several got to ask questions, many of which were quite pointed. One questioner complimented Trump on his smile, and then asked why he was trying to do away with DACA, the program that shields immigrant children from deportation. Trump responded that the pandemic had led to a clampdown on immigration. As for the third presidential debate, scheduled for Oct. 22, Biden said, "I expect to

0.445575

-0.320364

-0.071908

-0.339094

[ 0.27984428897623276, 0.6113057427939328 ]

[ -0.3396129300070784, -0.30111441550891943 ]

[ -0.1961837458612312, 0.052367874626427176 ]

[ -0.3481983112607001, -0.32998871938292995 ]

1,024

[ 512, 512 ]

[ 7178, 27504, 322, 11131, 350, 3615, 4587, 571, 29301, 297, 1281, 509, 19416, 297, 360, 2491, 292, 8421, 379, 4293, 13, 13504, 1693, 27504, 322, 11131, 350, 3615, 12520, 18561, 368, 1422, 1998, 1080, 363, 278, 4234, 322, 263, 15301, 12814, 297, 26001, 11949, 373, 498, 1295, 3250, 408, 278, 6673, 616, 640, 21043, 3614, 760, 297, 868, 14067, 4726, 298, 4293, 373, 405, 5371, 322, 16417, 29889, 13, 29940, 5371, 29915, 29879, 7234, 5426, 1741, 411, 27504, 15010, 4549, 29035, 515, 278, 22684, 358, 13661, 322, 1784, 4045, 1058, 4446, 372, 408, 263, 982, 310, 29156, 3460, 27504, 29892, 1058, 20043, 714, 310, 263, 20458, 1473, 6673, 616, 27836, 411, 670, 19083, 23995, 296, 29889, 405, 5371, 471, 5065, 3192, 304, 4337, 967, 1741, 714, 310, 278, 29871, 29947, 282, 29889, 29885, 29889, 7234, 577, 408, 451, 304, 14529, 411, 16417, 29915, 29879, 29871, 29929, 29900, 29899, 1195, 1082, 4867, 411, 350, 3615, 29892, 607, 471, 9326, 937, 1156, 27504, 13700, 714, 310, 278, 27836, 29889, 13, 29908, 29911, 397, 388, 29908, 17360, 9583, 812, 801, 24032, 1092, 347, 805, 279, 1127, 946, 3663, 3598, 411, 27504, 10106, 278, 697, 29899, 18721, 1741, 29889, 2296, 731, 278, 16225, 4688, 29892, 6721, 1075, 304, 766, 485, 340, 4796, 22747, 29885, 4135, 322, 660, 2744, 265, 29892, 278, 7395, 21588, 29875, 10068, 6368, 1048, 263, 8939, 3021, 488, 4185, 29889, 13, 2308, 3427, 1497, 540, 6363, 2217, 1048, 372, 29892, 2466, 540, 750, 6091, 896, 892, 376, 1110, 368, 2750, 8939, 3021, 11836, 1213, 13, 29908, 29902, 8661, 411, 393, 1699, 540, 1497, 29889, 13, 10401, 1183, 5643, 701, 29892, 6721, 1075, 304, 1827, 727, 471, 694, 8939, 3021, 488, 4185, 29892, 540, 4845, 1312, 29889, 13, 29908, 29902, 1016, 29915, 29873, 1073, 393, 1699, 27504, 1497, 29889, 376, 8139, 2121, 437, 366, 1073, 393, 29889, 3750, 9455, 29915, 29873, 366, 6721, 592, 1048, 3677, 26056, 3026, 13, 29954, 329, 1092, 347, 7470, 7960, 363, 263, 8589, 29889, 376, 3492, 29915, 276, 451, 763, 4856, 29915, 29879, 12220, 1537, 22169, 393, 508, 925, 3240, 16668, 6514, 1699, 1183, 1497, 472, 697, 1298, 29889, 13, 29954, 329, 1092, 347, 884, 867, 24455, 27504, 1048, 670, 8818, 3639, 29892, 6721, 565, 372, 471, 1565, 813, 408, 278, 1570, 3088, 10277, 8967, 813, 393, 540, 12530, 871, 395, 29955, 29945, 29900, 263, 1629, 29889, 940, 1497, 278, 4377, 471, 263, 376, 6112, 329, 706, 1353, 813, 263, 977, 292, 27684, 1213, 13, 29908, 3644, 896, 505, 590, 8818, 3639, 29892, 896, 505, 304, 748, 304, 432, 737, 1699, 27504, 1497, 29889, 376, 3112, 29915, 29879, 27302, 1213, 13, 6816, 273, 8000, 373, 16417, 29892, 9087, 17360, 5122, 2443, 16711, 459, 5059, 359, 15385, 350, 3615, 1048, 3692, 14189, 1446, 674, 16508, 304, 788, 925, 1575, 304, 278, 22569, 9245, 29892, 10241, 393, 8976, 5056, 2125, 263, 29871, 29953, 29899, 29941, 10631, 411, 278, 9659, 362, 310, 26817, 28533, 315, 4992, 2261, 13158, 29889, 13, 29933, 3615, 4845, 1312, 304, 1234, 4153, 29892, 541, 1497, 540, 723, 5957, 376, 29874, 2821, 2602, 1434, 382, 1464, 8373, 28235, 373, 920, 896, 4386, 445, 1213, 13, 29933, 3615, 1497, 540, 10753, 304, 3013, 278, 8569, 373, 278, 297, 932, 6649, 403, 5469, 310, 2261, 13158, 29915, 29879, 9659, 362, 1889, 29892, 322, 393, 565, 540, 892, 304, 9607, 670, 2602, 697, 982, 470, 1790, 1286, 29892, 376, 5747, 29915, 29879, 278, 2343, 1220, 1213, 13, 3868, 884, 594, 11292, 1776, 414, 29901, 376, 13504, 16719, 2041, 322, 748, 29889, 3387, 1575, 7952, 322, 7952, 322, 7952, 1213, 13, 10649, 5086, 472, 18292, 29915, 29879, 3086, 20063, 7817, 29892, 350, 3615, 1746, 287, 5155, 1048, 1153, 1455, 15426, 29892, 17869, 14585, 29892, 22035, 12425, 322, 10974, 11736, 29889, 3600, 1029, 4661, 1070, 28289, 322, 16326, 297, 5353, 292, 278, 302, 986, 29891, 29899, 629, 986, 29891, 4902, 310, 8898, 8389, 297, 15301, 12814, 304, 278, 901, 22623, 4087, 296, 16225, 975, 373, 405, 5371, 29889, 13, 29933, 3615, 12520, 777, 7333, 408, 2247, 29892, 1316, 408, 670, 18941, 29899, 276, 412, 630, 1196, 393, 746, 540, 471, 263, 26397, 15678, 701, 297, 2233, 837, 609, 29892, 349, 2108, 1696, 1556, 1757, 376, 29872, 2121, 3897, 263, 5614, 29892, 263, 3974, 1003, 29882, 357, 470, 263, 18781, 29889, 306, 9007, 29915, 29873, 18698, 304, 437, 738, 310, 963, 1213, 940, 1754, 263, 1298, 310, 6721, 1269, 1139, 261, 3692, 540, 750, 18430, 7699, 278, 2346, 29889, 13, 3868, 884, 4320, 335, 630, 27504, 29915, 29879, 26001, 2645, 278, 7243, 24552, 29889, 13, 29908, 1576, 6673, 756, 263, 23134, 304, 3275, 322, 540, 3282, 29915, 29873, 437, 393, 1699, 350, 3615, 1497, 29889, 376, 3868, 3282, 29915, 29873, 5193, 1048, 825, 4312, 304, 367, 2309, 29889, 940, 8126, 15982, 292, 29892, 297, 590, 1776, 29892, 1048, 278, 313, 17712, 29897, 9999, 1213, 13, 2951, 405, 5371, 29892, 27504, 1506, 391, 839, 408, 24032, 1092, 347, 15385, 2898, 373, 670, 17517, 29915, 29879, 2933, 304, 278, 24424, 29889, 13, 29908, 29902, 6363, 366, 29915, 29881, 367, 2599, 445, 1699, 540, 1497, 29889, 376, 29902, 1073, 366, 1407, 1532, 1213, 13, 29933, 3615, 1754, 263, 4549, 3229, 1048, 12566, 292, 365, 7210, 29911, 29984, 10462, 29892, 322, 540, 22399, 304, 1095, 24833, 427, 627, 287, 491, 27504, 393, 3151, 29890, 278, 10462, 310, 1301, 26098, 2305, 29889, 940, 11682, 411, 766, 13029, 278, 7786, 364, 1161, 310, 7167, 8623, 310, 1301, 26098, 5866, 310, 2927, 29889, 13, 28173, 29871, 29953, 29900, 9014, 414, 29892, 599, 591, 4362, 11105, 29879, 29892, 14283, 278, 1741, 472, 278, 28098, 3012, 6838, 297, 23740, 29889, 21882, 2355, 304, 2244, 5155, 29892, 1784, 310, 607, 892, 3755, 11520, 29889, 3118, 1139, 261, 13162, 2073, 287, 27504, 373, 670, 17819, 29892, 322, 769, 4433, 2020, 540, 471, 1811, 304, 437, 3448, 411, 360, 2477, 29909, 29892, 278, 1824, 393, 28761, 29879, 5198, 4481, 424, 4344, 515, 21455, 362, 29889, 27504, 10049, 287, 393, 278, 7243, 24552, 750, 5331, 304, 263, 1067, 1160, 3204, 373, 5198, 16783, 29889, 13, 2887, 363, 278, 4654, 6673, 616, 27836, 29892, 21467, 363, 4756, 29889, 29871, 29906, 29906, 29892, 350, 3615, 1497, 29892, 376, 29902, 2149, 304 ]

1,332,853

0

CommonCrawl

18

15

COLLECTION: Recent Obituaries in the Kenosha News (July 1-9, 2020) alert top story web only Here are the obituaries published online and in the print product of the Kenosha News between July 1 and July 9, 2020. Edmund F. Kretschmer Edmund F. Kretschmer, 92, of Wheatland, passed away Monday, July 6, 2020 at his home. Born in New Munster, Wisconsin on June 5, 1928, he was the son of John and Anna "Louise" (nee Epping) Kretschmer. His early life was spent in New Munster, where he attended St. Alphonsus Catholic School. He served in the U.S. Army during the Korean War. On June 30, 1956, he was united in marriage to Louise Gedemer. Following marriage, they made Burlington their home. Louise preceded him in death on April 12, 1994. Edmund worked for Lois Feedmill before working as a loader operator for and retiring from the Kenosha County Highway Department after over 30 years of service. He was a member of St. Alphonsus Catholic Church and treasurer for Catholic Order of Foresters for many years. He was a member of the VFW in Burlington and a volunteer firefighter for Wheatland. He was a hard worker who enjoyed gardening vegetables, lawn cutting and playing cards. Ed is survived by his children, Daniel (Elizabeth) Kretschmer, Ronald (Sandra) Kretschmer, Theresa (Dennis) Clapp, Kenneth (Johanna) Kretschmer, Susan (Tony) Pink and Judith (Kevin) Meyers; grandchildren, David Kretschmer, Matthew Kretschmer, Samantha Kretschmer, Ashley Kretschmer, Jessica (Chad) Birkholz, Kristina (Marc) Paprzyca, Gabrielle Clapp, Kristin (Daniel) Stroening, Brian Kretschmer, Adam Pink, Steven Pink, Lindsey Pink, Jordan Meyers, MacKenzie Meyers and Zachary Meyers; great-grandchildren, Emma Paprzyca, Audrey Paprzyca, Josephine Birkholz, Dylan Birkholz and Madison Stroening; sister, Armella Rossmiller; sister-in-laws, Eleanor Maller and Barbara Gedemer; along with many nieces, nephews, other relatives and friends. He was preceded in death by his parents; wife; infant son, Thomas; siblings, Joseph (Veronica) Kretschmer, Arthur Kretschmer, Father Albert Kretschmer, Henry Kretschmer, Agnes (Clem) Kerkman, Mary (Harold) Richter, Sister Martha Kretschmer and Rose Kretschmer; and brother-in-law, Harold Rossmiller. In lieu of flowers, memorial contributions may be made to St. Alphonsus Church or the Wheatland Fire Department. Visitation for Edmund will be held on Monday, July 13, 2020 from 4 until 7PM at Schuette-Daniels Funeral Home. Services will be held on Tuesday, July 14, 2020 at 11AM at St. Alphonsus Catholic Church with burial to follow at St. Alphonsus Cemetery. Schuette-Daniels Funeral Home & Crematory 625 S. Browns Lake Drive Burlington, WI 53105 www.danielsfamilyfuneral.com Renee Ann Galster Renee Ann Galster, 67, of Pleasant Prairie, passed away on Saturday, July 4, 2020, at Froedtert Hospital—Wauwatosa. Visitation will take place on Monday, July 13th, at Proko Funeral Home, from 5:00 p.m. until the time of service at 7:00 p.m. Interment will take place privately at St. George Cemetery at a later date. A full obituary will be published in Sunday's paper. Proko Funeral Home & Crematory 5111-60th Street Kenosha, WI 5

-0.466629

-1.059446

-1.494739

-1.840084

[ -0.45978044268309787, -0.4734771969730855 ]

[ -0.6449151031203854, -1.4739761362667851 ]

[ -1.1472741303803322, -1.8422041713356219 ]

[ -1.8843074546640282, -1.7958608655434303 ]

1,024

[ 512, 512 ]

[ 23958, 3281, 2725, 29901, 3599, 296, 4250, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 11850, 29871, 29896, 29899, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 12888, 2246, 5828, 1856, 871, 13, 10605, 526, 278, 704, 1981, 4314, 6369, 7395, 322, 297, 278, 1596, 3234, 310, 278, 10015, 359, 2350, 10130, 1546, 5468, 29871, 29896, 322, 5468, 29871, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 3853, 15282, 383, 29889, 476, 2267, 816, 1050, 13, 3853, 15282, 383, 29889, 476, 2267, 816, 1050, 29892, 29871, 29929, 29906, 29892, 310, 26286, 271, 1049, 29892, 4502, 3448, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 1570, 13564, 2475, 29892, 22581, 373, 5306, 29871, 29945, 29892, 29871, 29896, 29929, 29906, 29947, 29892, 540, 471, 278, 1487, 310, 2259, 322, 11230, 376, 20555, 895, 29908, 313, 484, 29872, 382, 3262, 29897, 476, 2267, 816, 1050, 29889, 3600, 4688, 2834, 471, 10398, 297, 1570, 13564, 2475, 29892, 988, 540, 14283, 624, 29889, 838, 561, 787, 375, 11865, 4523, 29889, 940, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 2645, 278, 22467, 3362, 29889, 1551, 5306, 29871, 29941, 29900, 29892, 29871, 29896, 29929, 29945, 29953, 29892, 540, 471, 443, 1573, 297, 13718, 304, 24417, 16836, 25154, 29889, 12206, 13718, 29892, 896, 1754, 6640, 1847, 880, 1009, 3271, 29889, 24417, 9399, 287, 1075, 297, 4892, 373, 3786, 29871, 29896, 29906, 29892, 29871, 29896, 29929, 29929, 29946, 29889, 13, 3853, 15282, 3796, 363, 4309, 275, 5169, 287, 19958, 1434, 1985, 408, 263, 23466, 5455, 363, 322, 3240, 8491, 515, 278, 10015, 359, 2350, 5127, 22080, 10317, 1156, 975, 29871, 29941, 29900, 2440, 310, 2669, 29889, 940, 471, 263, 4509, 310, 624, 29889, 838, 561, 787, 375, 11865, 6291, 322, 2578, 294, 9945, 363, 11865, 8170, 310, 17300, 414, 363, 1784, 2440, 29889, 940, 471, 263, 4509, 310, 278, 478, 29943, 29956, 297, 6640, 1847, 880, 322, 263, 27886, 261, 3974, 1003, 29882, 357, 363, 26286, 271, 1049, 29889, 940, 471, 263, 2898, 15645, 1058, 27849, 16423, 292, 18655, 1849, 29892, 425, 1233, 28967, 322, 8743, 15889, 29889, 13, 3853, 338, 10503, 2347, 491, 670, 4344, 29892, 8432, 313, 6489, 466, 9394, 29897, 476, 2267, 816, 1050, 29892, 11546, 2741, 313, 29903, 10738, 29897, 476, 2267, 816, 1050, 29892, 25451, 8625, 313, 29928, 9517, 29897, 6015, 407, 29892, 28576, 313, 29967, 1148, 9713, 29897, 476, 2267, 816, 1050, 29892, 25914, 313, 29911, 2592, 29897, 349, 682, 322, 8660, 389, 313, 9598, 3845, 29897, 18154, 414, 29936, 4595, 11991, 29892, 4699, 476, 2267, 816, 1050, 29892, 22292, 476, 2267, 816, 1050, 29892, 3685, 9716, 29874, 476, 2267, 816, 1050, 29892, 12835, 2330, 476, 2267, 816, 1050, 29892, 23010, 983, 313, 1451, 328, 29897, 350, 6793, 5391, 29920, 29892, 17773, 1099, 313, 29924, 5666, 29897, 8579, 29878, 1537, 1113, 29892, 9899, 374, 1808, 6015, 407, 29892, 17773, 262, 313, 29866, 29897, 624, 307, 8333, 29892, 15733, 476, 2267, 816, 1050, 29892, 11783, 349, 682, 29892, 24703, 349, 682, 29892, 17277, 7759, 349, 682, 29892, 18284, 18154, 414, 29892, 4326, 29968, 264, 3914, 18154, 414, 322, 29103, 653, 18154, 414, 29936, 2107, 29899, 27857, 11991, 29892, 26422, 8579, 29878, 1537, 1113, 29892, 8612, 8903, 8579, 29878, 1537, 1113, 29892, 6936, 457, 350, 6793, 5391, 29920, 29892, 360, 2904, 273, 350, 6793, 5391, 29920, 322, 4104, 2285, 624, 307, 8333, 29936, 9883, 29892, 8481, 3547, 13693, 29885, 5495, 29936, 9883, 29899, 262, 29899, 433, 5652, 29892, 8317, 273, 272, 341, 12572, 322, 18506, 16836, 25154, 29936, 3412, 411, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 916, 14576, 322, 7875, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29936, 6532, 29936, 28056, 1487, 29892, 5569, 29936, 27767, 18964, 29892, 6936, 313, 6565, 26082, 29897, 476, 2267, 816, 1050, 29892, 11498, 476, 2267, 816, 1050, 29892, 17852, 10537, 476, 2267, 816, 1050, 29892, 6498, 476, 2267, 816, 1050, 29892, 4059, 4515, 313, 29907, 2409, 29897, 476, 5968, 1171, 29892, 6182, 313, 21972, 1025, 29897, 4385, 357, 29892, 28088, 1085, 15457, 476, 2267, 816, 1050, 322, 14008, 476, 2267, 816, 1050, 29936, 322, 8099, 29899, 262, 29899, 10653, 29892, 25422, 13693, 29885, 5495, 29889, 13, 797, 13003, 310, 18281, 29892, 2626, 9020, 20706, 1122, 367, 1754, 304, 624, 29889, 838, 561, 787, 375, 6291, 470, 278, 26286, 271, 1049, 6438, 10317, 29889, 13, 6116, 7018, 363, 28925, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29896, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29946, 2745, 29871, 29955, 13427, 472, 1102, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 29889, 15538, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29896, 5194, 472, 624, 29889, 838, 561, 787, 375, 11865, 6291, 411, 6866, 616, 304, 1101, 472, 624, 29889, 838, 561, 787, 375, 315, 22875, 29889, 13, 4504, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 669, 315, 1745, 7606, 13, 29953, 29906, 29945, 317, 29889, 22415, 1983, 9459, 22850, 13, 29933, 332, 1847, 880, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29900, 29945, 13, 1636, 29889, 18386, 709, 4668, 1344, 29891, 7692, 13537, 29889, 510, 13, 29934, 1600, 29872, 8081, 5208, 2475, 13, 29934, 1600, 29872, 8081, 5208, 2475, 29892, 29871, 29953, 29955, 29892, 310, 19777, 13186, 9002, 24135, 29892, 4502, 3448, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 25022, 287, 357, 29873, 15967, 30003, 29956, 585, 29893, 271, 3628, 29889, 13, 6116, 7018, 674, 2125, 2058, 373, 27822, 29892, 5468, 29871, 29896, 29941, 386, 29892, 472, 1019, 2901, 13811, 13537, 8778, 29892, 515, 29871, 29945, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 278, 931, 310, 2669, 472, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 4124, 358, 674, 2125, 2058, 5999, 2486, 472, 624, 29889, 5122, 315, 22875, 472, 263, 2678, 2635, 29889, 319, 2989, 704, 1981, 653, 674, 367, 6369, 297, 16340, 29915, 29879, 5650, 29889, 13, 1184, 2901, 13811, 13537, 8778, 669, 315, 1745, 7606, 13, 29945, 29896, 29896, 29896, 29899, 29953, 29900, 386, 7103, 13, 29968, 264, 359, 2350, 29892, 399, 29902, 29871, 29945 ]

1,332,858

0

CommonCrawl

0

3

3144 Visit & Sign Renee's Online Memorial Book at: www.prokofuneralhome.com Robert R. Bonn Robert R. Bonn, 68, of Kenosha, passed away on Friday, June 26, 2020, at Froedtert South Pleasant Prairie. Born in Halifax Nova Scotia, on April 22, 1952, he was the son of the late Roy and Irene (Conrad) Bonn. On August 24, 1974, he married the love of his life, Michele Yung. Robert was an Athletic Director for 38 years. He enjoyed sports, golfing but most of all spending time with his family. Survivors include his wife, Michele Bonn; sons, Ryan (Christine) Bonn and Steven (Meaghan) Bonn; two grandchildren, Alec and Bradyn; siblings, Gary Bonn and Karen Bonn. He is further survived by other loving family and friends Due to the current health crisis, a private service was held. In lieu of flowers, memorials may be made to the Michele and Robert Bonn Athletic Endowment at Carthage College. Visit & Sign Robert's John Joseph Karnes September 22, 1937—July 03, 2020 John Joseph Karnes, age 82, of the Town of Three Lakes, died on July 3, 2020, at his home, with his family at his side. He was born on September 22, 1937 in Kenosha, Wisconsin to Ralph and Margaret (McQuestion) Karnes. He was raised in Kenosha and attended schools there graduating from the Kenosha High School in 1955. After his schooling he served his country as a member of the US Army. Upon his honorable discharge he returned to Kenosha where he was employed by AMC/Chrysler for 31 years as a die-setter in department 808. John retired in 1989 and moved to Three Lakes where he has lived since. In his retirement he drove for the Commission on Aging and also worked for 11 years at Trigs in Eagle River, or as he put it "a large corporation on Wall Street". He served his Lord and Savior as a member of St. Theresa Catholic Church in Three Lakes, Wisconsin. John is survived by his sister Margaret "Peggy" Bain, his nieces and nephews, Donnalee Bain, Jeanine Wolf, D Thomas Bain, Mike Bain, Patricia Johnson, Margaret "Maggie" Bain, Ralph Bain, Colleen "Kelly" Bain, Richard "Rick" Fanning, Leann Schuster, Maureen Modory, Erin Grimmer, Brian Fanning, Richelle "Shelly" Boslau, Lawrence "Larry" Fanning and his step son Michael Freeman and many great and great great nieces and nephews. He was preceded in death by his parents, his sister Alice Fanning and his brother Ralph Karnes. Graveside services and interment will be held at this time for John at the Three Lakes Cemetery. Due to the pandemic a Mass of Christian Burial will be held at a later date at the St. Theresa Catholic Church in Three Lakes. You may leave your private condolences for the Karnes family at www.carlsonfh.com. The Carlson Funeral Home (715-369-1414) is handling the arrangements for John's family. Michael D. Lamers MT. PLEASANT—Michael D. Lamers, 71, passed away at his beloved lake home in Lake Tomahawk on June 28, 2020. A memorial service celebrating his life will be held in the funeral home on Friday, July 10th at 6:00 p.m. Visitation will be in the funeral home on that Friday from 4:00 p.m. until the time of the service. Please see the funeral home website for the complete obituary. In accordance with Racine County mandate, only 50 people will be allowed to enter the funeral home at a time. You may be required to wait outside until others leave the building. For the safety and security of our guests we also require those

-0.434441

-1.090782

-1.553073

-1.782854

[ -0.5994873364409714, -0.26939555805227017 ]

[ -1.1086879056796026, -1.072875334053408 ]

[ -1.5429277303402782, -1.5632176585433524 ]

[ -1.9623485627116148, -1.6033594656927168 ]

1,024

[ 512, 512 ]

[ 29941, 29896, 29946, 29946, 13, 6116, 277, 669, 9954, 390, 1600, 29872, 29915, 29879, 13, 2951, 1220, 19722, 6726, 472, 29901, 13, 1636, 29889, 771, 29895, 974, 348, 13537, 5184, 29889, 510, 13, 9588, 2151, 390, 29889, 25056, 13, 9588, 2151, 390, 29889, 25056, 29892, 29871, 29953, 29947, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 25022, 287, 357, 29873, 4275, 19777, 13186, 9002, 24135, 29889, 13, 29933, 1398, 297, 8142, 361, 1165, 16216, 11032, 423, 29892, 373, 3786, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29945, 29906, 29892, 540, 471, 278, 1487, 310, 278, 5683, 15793, 322, 306, 28593, 313, 1168, 3665, 29897, 25056, 29889, 13, 2951, 3111, 29871, 29906, 29946, 29892, 29871, 29896, 29929, 29955, 29946, 29892, 540, 8300, 278, 5360, 310, 670, 2834, 29892, 341, 4070, 280, 612, 686, 29889, 13, 9588, 2151, 471, 385, 17183, 293, 15944, 363, 29871, 29941, 29947, 2440, 29889, 940, 27849, 14717, 29892, 29416, 292, 541, 1556, 310, 599, 805, 2548, 931, 411, 670, 3942, 29889, 13, 18498, 24759, 943, 3160, 670, 6532, 29892, 341, 4070, 280, 25056, 29936, 18025, 29892, 20916, 313, 18687, 457, 29897, 25056, 322, 24703, 313, 6816, 351, 5403, 29897, 25056, 29936, 1023, 4595, 11991, 29892, 7801, 29883, 322, 15862, 948, 29936, 27767, 18964, 29892, 23529, 25056, 322, 3467, 264, 25056, 29889, 940, 338, 4340, 10503, 2347, 491, 916, 12355, 292, 3942, 322, 7875, 13, 29928, 434, 304, 278, 1857, 9045, 24161, 29892, 263, 2024, 2669, 471, 4934, 29889, 512, 13003, 310, 18281, 29892, 2626, 9020, 29879, 1122, 367, 1754, 304, 278, 341, 4070, 280, 322, 4755, 25056, 17183, 293, 2796, 340, 358, 472, 13, 8179, 386, 482, 6346, 29889, 13, 6116, 277, 669, 9954, 4755, 29915, 29879, 13, 11639, 6936, 476, 2753, 267, 13, 2008, 3266, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 30003, 29967, 11850, 29871, 29900, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 13, 11639, 6936, 476, 2753, 267, 29892, 5046, 29871, 29947, 29906, 29892, 310, 278, 8421, 310, 12753, 365, 6926, 29892, 6423, 373, 5468, 29871, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 670, 3271, 29892, 411, 670, 3942, 472, 670, 2625, 29889, 940, 471, 6345, 373, 3839, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29941, 29955, 297, 10015, 359, 2350, 29892, 22581, 304, 23438, 322, 18364, 313, 27297, 16492, 29897, 476, 2753, 267, 29889, 940, 471, 10425, 297, 10015, 359, 2350, 322, 14283, 12462, 727, 10591, 1218, 515, 278, 10015, 359, 2350, 5057, 4523, 297, 29871, 29896, 29929, 29945, 29945, 29889, 2860, 670, 3762, 292, 540, 6766, 670, 4234, 408, 263, 4509, 310, 278, 3148, 8811, 29889, 19956, 670, 10657, 519, 766, 23367, 540, 4133, 304, 10015, 359, 2350, 988, 540, 471, 15723, 491, 319, 12513, 29914, 1451, 18450, 1358, 363, 29871, 29941, 29896, 2440, 408, 263, 762, 29899, 842, 357, 297, 14311, 29871, 29947, 29900, 29947, 29889, 13, 11639, 16528, 297, 29871, 29896, 29929, 29947, 29929, 322, 6153, 304, 12753, 365, 6926, 988, 540, 756, 10600, 1951, 29889, 512, 670, 3240, 19211, 540, 26603, 363, 278, 11444, 373, 319, 3460, 322, 884, 3796, 363, 29871, 29896, 29896, 2440, 472, 1605, 23379, 297, 382, 20860, 6163, 29892, 470, 408, 540, 1925, 372, 376, 29874, 2919, 17266, 362, 373, 14406, 7103, 1642, 940, 6766, 670, 6171, 322, 9583, 1611, 408, 263, 4509, 310, 624, 29889, 25451, 8625, 11865, 6291, 297, 12753, 365, 6926, 29892, 22581, 29889, 13, 11639, 338, 10503, 2347, 491, 670, 9883, 18364, 376, 29925, 387, 1927, 29908, 350, 475, 29892, 670, 4930, 778, 322, 23446, 354, 5652, 29892, 360, 3409, 744, 29872, 350, 475, 29892, 4581, 457, 10441, 29892, 360, 5569, 350, 475, 29892, 12828, 350, 475, 29892, 4121, 2200, 423, 11717, 29892, 18364, 376, 19095, 12053, 29908, 350, 475, 29892, 23438, 350, 475, 29892, 1530, 280, 264, 376, 29968, 14112, 29908, 350, 475, 29892, 6123, 376, 29934, 860, 29908, 383, 9450, 29892, 951, 812, 1102, 5402, 29892, 3219, 545, 264, 3382, 706, 29892, 1425, 262, 1632, 19400, 29892, 15733, 383, 9450, 29892, 4385, 1808, 376, 2713, 14112, 29908, 10211, 25855, 29892, 19520, 376, 24105, 719, 29908, 383, 9450, 322, 670, 4331, 1487, 5765, 3878, 11422, 322, 1784, 2107, 322, 2107, 2107, 4930, 778, 322, 23446, 354, 5652, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29892, 670, 9883, 16308, 383, 9450, 322, 670, 8099, 23438, 476, 2753, 267, 29889, 13, 29954, 336, 1960, 680, 5786, 322, 1006, 358, 674, 367, 4934, 472, 445, 931, 363, 2259, 472, 278, 12753, 365, 6926, 315, 22875, 29889, 16809, 304, 278, 7243, 24552, 263, 7360, 310, 6111, 6640, 616, 674, 367, 4934, 472, 263, 2678, 2635, 472, 278, 624, 29889, 25451, 8625, 11865, 6291, 297, 12753, 365, 6926, 29889, 887, 1122, 5967, 596, 2024, 2148, 324, 2063, 363, 278, 476, 2753, 267, 3942, 472, 7821, 29889, 4287, 29880, 1100, 29888, 29882, 29889, 510, 29889, 450, 8965, 1100, 13811, 13537, 8778, 313, 29955, 29896, 29945, 29899, 29941, 29953, 29929, 29899, 29896, 29946, 29896, 29946, 29897, 338, 11415, 278, 15196, 4110, 363, 2259, 29915, 29879, 3942, 29889, 13, 24083, 360, 29889, 12718, 414, 13, 11490, 29889, 349, 1307, 3289, 13566, 30003, 24083, 360, 29889, 12718, 414, 29892, 29871, 29955, 29896, 29892, 4502, 3448, 472, 670, 1339, 8238, 19437, 3271, 297, 9459, 4335, 801, 20011, 373, 5306, 29871, 29906, 29947, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 319, 2626, 9020, 2669, 10894, 1218, 670, 2834, 674, 367, 4934, 297, 278, 2090, 13537, 3271, 373, 28728, 29892, 5468, 29871, 29896, 29900, 386, 472, 29871, 29953, 29901, 29900, 29900, 282, 29889, 29885, 29889, 5741, 7018, 674, 367, 297, 278, 2090, 13537, 3271, 373, 393, 28728, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 278, 931, 310, 278, 2669, 29889, 13, 12148, 1074, 278, 2090, 13537, 3271, 4700, 363, 278, 4866, 704, 1981, 653, 29889, 13, 797, 15017, 749, 411, 390, 562, 457, 5127, 9619, 403, 29892, 871, 29871, 29945, 29900, 2305, 674, 367, 6068, 304, 3896, 278, 2090, 13537, 3271, 472, 263, 931, 29889, 887, 1122, 367, 3734, 304, 4480, 5377, 2745, 4045, 5967, 278, 5214, 29889, 1152, 278, 15332, 322, 6993, 310, 1749, 28865, 591, 884, 1996, 1906 ]

1,332,858

1,024

CommonCrawl

0

3

in attendance to wear a face covering. We thank everyone for their understanding and cooperation during this difficult time. DRAEGER-LANGENDORF FUNERAL HOME AND CREMATORY 4600 County Line Rd. draeger-langendorf.com Lynne Cleereman Lynne Cleereman (nee Drajkowski) Found peace on Wednesday, March 25, 2020, age 79. Cherished and devoted wife of Douglas P. Cleereman for 58 years. Loving mother of Kelly (Dr. Michael) Mindiola and Shannon Doberstein. Treasured grandmother of Madison, Marissa, Maxwell and Mikayla Mindiola and Matthew and Daniel Doberstein. Special sister-in-law of Bonnie Jean Becker Fronek (late Jerry). Special aunt to the Becker boys: David (Donna Misurelli), Daniel (Lisa Serpe), Darren (Angie Castellano) and Jimmy (Autumn Meyer) and other cherished nieces and nephews. Also survived by special, life-long friends from Kenosha and many sewing and quilting friends and the Skylark Ladies group. Lynne is preceded in death by her mother Elinor Drajkowski (nee Zwolinski) and her in-laws Charlie and Jean Cleereman, her brother Gary Drajkowski (Sharon), sister-in-law Shirley (Gene) Clippard, and devoted cousin and friend Dorothy Zeier. Lynne and Doug met at Allen-Bradley Company and were married in 1962. Lynne had a strong, quiet faith in God and practiced her religion beyond the church doors, within her circle of friends and through her generosity to many charitable causes and her special family. She loved connecting with her bible study group. Her devotion was immense; her warm, gentle giving spirit lives on in all the quilts she made. Her goal was to create a quilt for everyone important in her life and she left instructions on a few that she didn't finish. Kelly is now the family quilter and the times they spent on projects will be forever cherished. Memorials suggested to the Sarah Mindiola Barse Sunflower Endowment Fund at WCTC. Memorial services on Wednesday, July 15 at Carl's Catering, 5110 W. Loomis Rd, Greendale, WI. Visitation begins at 10:30 with service and luncheon to follow all at Carl's Catering. Please wear a mask to the visitation and service, thank you! December 2, 1964 – June 29, 2020 Laura Gonzalez, age 55, passed away on Monday, June 29, 2020 from complications of Covid-19 at Froedtert South-Kenosha Medical Center. She was a stage 4 colon cancer survivor who had an immense love of God, her family, and friends. She enjoyed sewing and quilting, cooking, baking, dancing and reading the Bible. She left behind her husband of 29 years J. Angel Gonzalez, two daughters, Sabrina (Jesse) Gonzalez and Bianca Gonzalez, two brothers, Edmundo Bernal and Efrain Bernal, a niece Karina Bernal, and two granddaughters, Arianni Lopez and Nori Lopez. Funeral services honoring Laura's life will be held privately. Interment will take place in Sunset Ridge Memorial Park. A visitation for Laura will be held at the Piasecki Funeral Home on Monday, July 13, 2020 from 5:00 p.m. until 7:00 p.m. Piasecki Funeral Home & Cremation Services 3720 39th Avenue 262-658-4101 www.KenoshaFuneralHome.com Eve Vaughn Eve Vaughn, age 80, was born into eternal life and reunited with her loving husband Ron on Saturday, July 4, 2020 surrounded by her loving daughters. Those left to remember Eve are her children, Teresa Vaughn, Tracie (Mark) Vidas, Laurie (Darren)

-0.142358

-1.253729

-1.296912

-1.923328

[ 0.005909203176480653, -0.29062552720175094 ]

[ -1.3880259643639186, -1.1194316771674608 ]

[ -1.2588687354972399, -1.334955966258768 ]

[ -1.9051184168100512, -1.9415376005655918 ]

1,024

[ 512, 512 ]

[ 297, 14333, 749, 304, 19531, 263, 3700, 21653, 29889, 1334, 6452, 14332, 363, 1009, 8004, 322, 1302, 16453, 2645, 445, 5189, 931, 29889, 13, 29928, 4717, 11787, 1001, 29899, 29931, 19453, 11794, 1955, 29943, 383, 3904, 1001, 1964, 29832, 2303, 5300, 315, 1525, 29924, 1299, 18929, 13, 29946, 29953, 29900, 29900, 5127, 7407, 390, 29881, 29889, 13, 19811, 387, 261, 29899, 3893, 21466, 29889, 510, 13, 29931, 948, 484, 21386, 261, 11422, 13, 29931, 948, 484, 21386, 261, 11422, 313, 484, 29872, 360, 10665, 7000, 2574, 29897, 7460, 10776, 373, 15050, 4515, 3250, 29892, 4779, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 5046, 29871, 29955, 29929, 29889, 23816, 3276, 322, 24600, 6532, 310, 16721, 349, 29889, 21386, 261, 11422, 363, 29871, 29945, 29947, 2440, 29889, 365, 21081, 5637, 310, 21872, 313, 25639, 29889, 5765, 29897, 341, 14108, 2963, 322, 1383, 23453, 1938, 495, 5465, 29889, 6479, 294, 2955, 4595, 29885, 1228, 310, 4104, 2285, 29892, 1085, 16343, 29892, 5918, 5872, 322, 13803, 388, 433, 341, 14108, 2963, 322, 22292, 322, 8432, 1938, 495, 5465, 29889, 12630, 9883, 29899, 262, 29899, 10653, 310, 8396, 2786, 4581, 1522, 4937, 4693, 650, 29895, 313, 9632, 23052, 467, 12630, 263, 1657, 304, 278, 1522, 4937, 12544, 29901, 4699, 313, 10310, 1056, 20929, 545, 29880, 492, 511, 8432, 313, 29931, 8069, 1816, 412, 511, 7335, 1267, 313, 9928, 347, 4834, 514, 1562, 29897, 322, 20636, 313, 6147, 1227, 26581, 29897, 322, 916, 14954, 3276, 4930, 778, 322, 23446, 354, 5652, 29889, 3115, 10503, 2347, 491, 4266, 29892, 2834, 29899, 5426, 7875, 515, 10015, 359, 2350, 322, 1784, 409, 16958, 322, 439, 309, 1259, 7875, 322, 278, 4971, 2904, 935, 19955, 583, 2318, 29889, 18989, 484, 338, 9399, 287, 297, 4892, 491, 902, 5637, 1260, 262, 272, 360, 10665, 7000, 2574, 313, 484, 29872, 12017, 22878, 2574, 29897, 322, 902, 297, 29899, 433, 5652, 20283, 322, 4581, 21386, 261, 11422, 29892, 902, 8099, 23529, 360, 10665, 7000, 2574, 313, 2713, 5022, 511, 9883, 29899, 262, 29899, 10653, 1383, 381, 2330, 313, 29954, 1600, 29897, 315, 492, 407, 538, 29892, 322, 24600, 22618, 322, 5121, 9579, 20336, 3091, 631, 29889, 13, 29931, 948, 484, 322, 13215, 1539, 472, 16092, 29899, 29933, 3665, 2330, 6938, 322, 892, 8300, 297, 29871, 29896, 29929, 29953, 29906, 29889, 13, 29931, 948, 484, 750, 263, 4549, 29892, 11813, 10847, 297, 4177, 322, 4120, 7612, 902, 13433, 8724, 278, 6586, 24189, 29892, 2629, 902, 8607, 310, 7875, 322, 1549, 902, 1176, 359, 537, 304, 1784, 1373, 8270, 9946, 322, 902, 4266, 3942, 29889, 2296, 18012, 16791, 411, 902, 289, 1821, 6559, 2318, 29889, 2439, 2906, 8194, 471, 29403, 29936, 902, 14294, 29892, 9914, 6820, 8548, 12080, 373, 297, 599, 278, 439, 309, 1372, 1183, 1754, 29889, 2439, 7306, 471, 304, 1653, 263, 439, 2782, 363, 14332, 4100, 297, 902, 2834, 322, 1183, 2175, 11994, 373, 263, 2846, 393, 1183, 3282, 29915, 29873, 8341, 29889, 21872, 338, 1286, 278, 3942, 439, 309, 357, 322, 278, 3064, 896, 10398, 373, 9279, 674, 367, 22296, 14954, 3276, 29889, 13, 11442, 9020, 29879, 7829, 304, 278, 19235, 341, 14108, 2963, 2261, 344, 8991, 1731, 261, 2796, 340, 358, 13249, 472, 399, 1783, 29907, 29889, 13, 11442, 9020, 5786, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29945, 472, 8965, 29915, 29879, 315, 1008, 292, 29892, 29871, 29945, 29896, 29896, 29900, 399, 29889, 4309, 290, 275, 390, 29881, 29892, 4122, 355, 744, 29892, 399, 29902, 29889, 5741, 7018, 16410, 472, 29871, 29896, 29900, 29901, 29941, 29900, 411, 2669, 322, 25081, 1173, 265, 304, 1101, 599, 472, 8965, 29915, 29879, 315, 1008, 292, 29889, 3529, 19531, 263, 11105, 304, 278, 6493, 362, 322, 2669, 29892, 6452, 366, 29991, 13, 6185, 1096, 29871, 29906, 29892, 29871, 29896, 29929, 29953, 29946, 785, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 13, 5661, 2002, 27536, 744, 29920, 29892, 5046, 29871, 29945, 29945, 29892, 4502, 3448, 373, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 515, 752, 5795, 310, 25669, 333, 29899, 29896, 29929, 472, 25022, 287, 357, 29873, 4275, 29899, 29968, 264, 359, 2350, 20795, 7817, 29889, 13, 13468, 471, 263, 7408, 29871, 29946, 8104, 23900, 10503, 440, 272, 1058, 750, 385, 29403, 5360, 310, 4177, 29892, 902, 3942, 29892, 322, 7875, 29889, 13, 13468, 27849, 409, 16958, 322, 439, 309, 1259, 29892, 7984, 292, 29892, 289, 5086, 29892, 6025, 3277, 322, 5183, 278, 21958, 29889, 13, 13468, 2175, 5742, 902, 10216, 310, 29871, 29906, 29929, 2440, 435, 29889, 17323, 27536, 744, 29920, 29892, 1023, 29215, 29892, 11775, 29878, 1099, 313, 29967, 5340, 29897, 27536, 744, 29920, 322, 29860, 1113, 27536, 744, 29920, 29892, 1023, 21383, 29892, 2155, 29885, 6201, 6209, 284, 322, 382, 29888, 6038, 6209, 284, 29892, 263, 4930, 346, 3467, 1099, 6209, 284, 29892, 322, 1023, 4595, 29881, 6334, 2153, 29892, 25775, 9889, 365, 2300, 29920, 322, 405, 4170, 365, 2300, 29920, 29889, 13, 25394, 13537, 5786, 4207, 8253, 21671, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 4124, 358, 674, 2125, 2058, 297, 8991, 842, 390, 5525, 19722, 4815, 29889, 319, 6493, 362, 363, 21671, 674, 367, 4934, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 373, 27822, 29892, 5468, 29871, 29896, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29945, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 13, 12197, 559, 22736, 13811, 13537, 8778, 669, 315, 1745, 362, 15538, 13, 29941, 29955, 29906, 29900, 29871, 29941, 29929, 386, 18874, 29871, 29906, 29953, 29906, 29899, 29953, 29945, 29947, 29899, 29946, 29896, 29900, 29896, 13, 1636, 29889, 29968, 264, 359, 2350, 25394, 13537, 11184, 29889, 510, 13, 29923, 345, 478, 2987, 3123, 13, 29923, 345, 478, 2987, 3123, 29892, 5046, 29871, 29947, 29900, 29892, 471, 6345, 964, 634, 17196, 2834, 322, 23038, 1573, 411, 902, 12355, 292, 10216, 11546, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 22047, 491, 902, 12355, 292, 29215, 29889, 13, 1349, 852, 2175, 304, 6456, 382, 345, 526, 902, 4344, 29892, 5061, 8625, 478, 2987, 3123, 29892, 323, 945, 347, 313, 9802, 29897, 478, 8817, 29892, 14019, 347, 313, 29928, 279, 1267, 29897 ]

1,332,858

2,048

CommonCrawl

0

3

Couillard and Linda (Jim) Cooklin; her grandchildren, Mark Oelke II, Jon (Elizabeth) Oelke, Shelly (Kevin) Malkmus, Eric Garza, Laura Garza, Michael Warren, Jacob (Hillary) Warren, Katie Warren, Joshua (Samantha) Vaughn; her great grandchildren, Emmette Oelke, Sophie and Barrett Malkmus, Brodie and Calyx Vaughn; her brother, John (Kathleen) Greiser; and her sister, Jeanne (Jerry) Polden. A visitation for Eve will be held on Tuesday, July 14, 2020 from 3:00 p.m. until 6:00 p.m. at the Piasecki Funeral Home. Funeral services honoring Eve's life will be held privately. Inurnment will take place at a later date. In lieu of flowers, memorial remembrances to: Hospice Alliance Inc/Hospice House, 10220 Prairie Ridge Blvd, Pleasant Prairie, WI 53158, The Salvation Army, 3116-75th Street, Kenosha, WI 53142, or Women and Children's Horizon, 2525-63rd Street, Kenosha, WI 53143 would be appreciated by the family. Avanell Moore Salisbury September 19, 1931—July 5, 2020 Avanell Moore Salisbury passed away on July 5, 2020 in Kenosha, WI at the age of 88. She was born on September 19, 1931 in Coraopolis, PA to Arthur and Florence Moore. On April 11, 1953 she married the late John Salisbury and they had two sons. She was devoted to her grandchildren and she loved pets and F1 Racing. Avanell is survived by her children John (Lynn) Salisbury of Gurnee, IL and Scott (Mary) Salisbury of Los Alamos, NM; grandchildren Jenni, Austin, and Allison Salisbury; sister-in-laws Marjorie Fickley of FL and Janice Moore of PA; brother-in-law David (Linda) Salisbury of TX. She was proceeded in death by her husband John, parents Arthur and Florence Moore, brothers Bob, Skip, and Jim Moore. A visitation will be held on Friday, July 10, 2020 beginning at 10:00 a.m., concluding with a service at 11:00 a.m. at Marsh Funeral Home in Gurnee. Interment will follow at Highland Memorial Park in Libertyville. In lieu of flowers, donations can be made to Orphans of the Storm Animal Shelter in Riverwoods, IL at www.orphansofthestorm.org/donate. In consideration of the safety of our guests and associates, Marsh Funeral Home will adhere to the current gathering restrictions in the state of Illinois, which allow 50 or fewer guests at services. Proper social distancing must be practiced and all guests will be required to wear face masks at all times. Donald Dejno Donald Dejno unexpectedly passed away on July 4th, 2020 in Pleasant Prairie, WI after spending one of his fullest days enjoying his family. His heart stopped beating while he was at a neighbor's house enjoying fireworks. Born in Independence, WI on September 1, 1941. As the oldest child, Don grew up on the family farm with six other children. It was there he learned much from his father about care for equipment, smart farming, and hard work. Don landed his first job in 1959 and moved to Kenosha, WI to work for American Motors/Chrysler. He spoke frequently of the lessons learned while he swept floors and was later promoted to supervisor. He was also a corporal in the Armory National Guard from 1964-1971. He later met Carol Tate and dated for four years. They were married on October 2, 1965. The challenge to make his father-in-law proud motivated him to be

-0.322128

-1.151663

-1.606334

-1.769847

[ -0.28720133862925407, -0.35705478550819086 ]

[ -1.259100706509619, -1.0442252767524527 ]

[ -1.7559719764725568, -1.4566955354772129 ]

[ -1.842685530371982, -1.6970087953498205 ]

1,024

[ 512, 512 ]

[ 19565, 453, 538, 322, 365, 11054, 313, 29967, 326, 29897, 17278, 1915, 29936, 902, 4595, 11991, 29892, 4485, 438, 295, 446, 1944, 29892, 9937, 313, 6489, 466, 9394, 29897, 438, 295, 446, 29892, 1383, 14112, 313, 9598, 3845, 29897, 341, 2235, 8366, 29892, 14713, 7455, 1362, 29892, 21671, 7455, 1362, 29892, 5765, 24511, 29892, 10968, 313, 29950, 453, 653, 29897, 24511, 29892, 476, 9474, 24511, 29892, 22838, 3357, 313, 22966, 9716, 29874, 29897, 478, 2987, 3123, 29936, 902, 2107, 4595, 11991, 29892, 2812, 29885, 2353, 438, 295, 446, 29892, 19122, 347, 322, 2261, 13158, 341, 2235, 8366, 29892, 4358, 16217, 322, 3037, 29891, 29916, 478, 2987, 3123, 29936, 902, 8099, 29892, 2259, 313, 29968, 493, 280, 264, 29897, 4122, 7608, 29936, 322, 902, 9883, 29892, 4581, 484, 313, 29967, 261, 719, 29897, 349, 1025, 264, 29889, 13, 29909, 6493, 362, 363, 382, 345, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29941, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29953, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 13811, 13537, 5786, 4207, 8253, 382, 345, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 512, 595, 358, 674, 2125, 2058, 472, 263, 2678, 2635, 29889, 512, 13003, 310, 18281, 29892, 2626, 9020, 1083, 1590, 661, 778, 304, 29901, 379, 4705, 625, 29855, 9266, 29914, 29950, 4705, 625, 5619, 29892, 29871, 29896, 29900, 29906, 29906, 29900, 9002, 24135, 390, 5525, 3164, 27491, 29892, 19777, 13186, 9002, 24135, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29945, 29947, 29892, 450, 14964, 362, 8811, 29892, 29871, 29941, 29896, 29896, 29953, 29899, 29955, 29945, 386, 7103, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 29892, 470, 10152, 322, 20986, 29915, 29879, 6912, 18162, 29892, 29871, 29906, 29945, 29906, 29945, 29899, 29953, 29941, 5499, 7103, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29941, 723, 367, 7556, 491, 278, 3942, 29889, 13, 29909, 3703, 514, 18588, 3956, 275, 11059, 13, 2008, 3266, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29896, 30003, 29967, 11850, 29871, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 13, 29909, 3703, 514, 18588, 3956, 275, 11059, 4502, 3448, 373, 5468, 29871, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 297, 10015, 359, 2350, 29892, 399, 29902, 472, 278, 5046, 310, 29871, 29947, 29947, 29889, 13, 13468, 471, 6345, 373, 3839, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29896, 297, 315, 2207, 13242, 275, 29892, 17687, 304, 11498, 322, 23998, 18588, 29889, 1551, 3786, 29871, 29896, 29896, 29892, 29871, 29896, 29929, 29945, 29941, 1183, 8300, 278, 5683, 2259, 3956, 275, 11059, 322, 896, 750, 1023, 18025, 29889, 2296, 471, 24600, 304, 902, 4595, 11991, 322, 1183, 18012, 282, 1691, 322, 383, 29896, 22582, 29889, 13, 29909, 3703, 514, 338, 10503, 2347, 491, 902, 4344, 2259, 313, 29931, 948, 29876, 29897, 3956, 275, 11059, 310, 402, 332, 484, 29872, 29892, 17674, 322, 8075, 313, 29924, 653, 29897, 3956, 275, 11059, 310, 4602, 838, 14054, 29892, 405, 29924, 29936, 4595, 11991, 21116, 1240, 29892, 24518, 29892, 322, 2178, 2285, 3956, 275, 11059, 29936, 9883, 29899, 262, 29899, 433, 5652, 1085, 3418, 347, 383, 860, 2330, 310, 383, 29931, 322, 2627, 625, 18588, 310, 17687, 29936, 8099, 29899, 262, 29899, 10653, 4699, 313, 29931, 11054, 29897, 3956, 275, 11059, 310, 323, 29990, 29889, 13, 13468, 471, 24825, 297, 4892, 491, 902, 10216, 2259, 29892, 11825, 11498, 322, 23998, 18588, 29892, 21383, 7991, 29892, 4971, 666, 29892, 322, 8507, 18588, 29889, 13, 29909, 6493, 362, 674, 367, 4934, 373, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 6763, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 1696, 378, 22368, 411, 263, 2669, 472, 29871, 29896, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 13216, 13811, 13537, 8778, 297, 402, 332, 484, 29872, 29889, 4124, 358, 674, 1101, 472, 5057, 1049, 19722, 4815, 297, 10895, 1017, 4909, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 508, 367, 1754, 304, 1394, 561, 550, 310, 278, 24444, 22809, 1383, 21883, 297, 6163, 6115, 29879, 29892, 17674, 472, 7821, 29889, 5676, 550, 974, 386, 342, 555, 29889, 990, 29914, 9176, 403, 29889, 13, 797, 19220, 310, 278, 15332, 310, 1749, 28865, 322, 4067, 1078, 29892, 13216, 13811, 13537, 8778, 674, 594, 4150, 304, 278, 1857, 11705, 292, 25091, 297, 278, 2106, 310, 17066, 29892, 607, 2758, 29871, 29945, 29900, 470, 28145, 28865, 472, 5786, 29889, 1019, 546, 5264, 1320, 19985, 1818, 367, 4120, 7612, 322, 599, 28865, 674, 367, 3734, 304, 19531, 3700, 11105, 29879, 472, 599, 3064, 29889, 13, 28080, 897, 29926, 1217, 13, 28080, 897, 29926, 1217, 15668, 368, 4502, 3448, 373, 5468, 29871, 29946, 386, 29892, 29871, 29906, 29900, 29906, 29900, 297, 19777, 13186, 9002, 24135, 29892, 399, 29902, 1156, 805, 2548, 697, 310, 670, 2989, 342, 3841, 11418, 5414, 670, 3942, 29889, 3600, 5192, 11084, 367, 1218, 1550, 540, 471, 472, 263, 12307, 29915, 29879, 3699, 11418, 5414, 3974, 13129, 29889, 13, 29933, 1398, 297, 28052, 663, 29892, 399, 29902, 373, 3839, 29871, 29896, 29892, 29871, 29896, 29929, 29946, 29896, 29889, 1094, 278, 23947, 2278, 29892, 3872, 13631, 701, 373, 278, 3942, 17888, 411, 4832, 916, 4344, 29889, 739, 471, 727, 540, 10972, 1568, 515, 670, 4783, 1048, 2562, 363, 21083, 29892, 15040, 2215, 4056, 29892, 322, 2898, 664, 29889, 13, 10310, 2982, 287, 670, 937, 4982, 297, 29871, 29896, 29929, 29945, 29929, 322, 6153, 304, 10015, 359, 2350, 29892, 399, 29902, 304, 664, 363, 3082, 7142, 943, 29914, 1451, 18450, 1358, 29889, 940, 12707, 13672, 310, 278, 3109, 787, 10972, 1550, 540, 7901, 415, 5685, 943, 322, 471, 2678, 21201, 304, 2428, 19188, 29889, 940, 471, 884, 263, 17266, 284, 297, 278, 8481, 706, 3086, 13211, 515, 29871, 29896, 29929, 29953, 29946, 29899, 29896, 29929, 29955, 29896, 29889, 13, 3868, 2678, 1539, 8562, 323, 403, 322, 29797, 363, 3023, 2440, 29889, 2688, 892, 8300, 373, 5533, 29871, 29906, 29892, 29871, 29896, 29929, 29953, 29945, 29889, 13, 1576, 18766, 304, 1207, 670, 4783, 29899, 262, 29899, 10653, 22314, 17385, 630, 1075, 304, 367 ]

1,332,858

3,072

CommonCrawl

0

3

financially successful. Don had an entrepreneurial spirit and started a wood recycling business in 1975. Next he started a trucking company to haul both wood shavings and other freight. After seven years of marriage, Don's life changed. He understood and believed the gospel. He had a newfound love for Jesus, His wife, and marriage. Delighting in his marriage, teaching others concerning marriage, and talking to his children and grandchildren endlessly about marriage never got old for him. While a principled man with a work ethic second to none, he would always acknowledge that his success rested upon the hands of the good men around him and the goodness of God. His son, Larry Dejno, who worked with him most of his 40 years in business was his right arm whom he loved and valued dearly. His daughters, sons-in-laws, daughter-in-law, and grandchildren have been an integral part of the success of the ongoing family business. He was always dreaming and implementing business ideas, providing work for others, and thinking about his grandchildren. While always a productive man, he always found time to be there for you when you needed him most. He truly cared for people as well as productivity. Because he was most affected by the forgiveness that he received from His Savior Jesus, he was a man of both forgiveness and repentance. While a man of few words and strong convictions, he was a man with an emotional and tender heart. He would want you to know that there is forgiveness and acceptance in the person of Christ. He led a prayer group in 1972 that met in the basement of St. Mary's Catholic Church that eventually became Living Light Christian Church. At Living Light he faithfully and passionately served as an elder, marriage workshop leader, and encourager until the end. Don is survived by his wife, Carol June Dejno, son, Lawrence Lee Dejno and wife Lori, daughter Cindy Marie Auch with husband Mike, daughter Debbie Lynn Swift with husband Joel, daughter Christine Eckert, daughter Shelly Snyder with husband Joe, and daughter Kimberly Nelson with husband Edward. He has 19 grandchildren and one great grandchild. A visitation for Donald will be held on Friday, July 10, 2020 from 4:00 p.m. until 8:00 p.m. at the Piasecki Funeral Home. Funeral services honoring Donald's life will be held on Saturday, July 11, 2020 at 10:00 a.m. at The Encounter, 8900 34th Ave, Kenosha, WI 53142. Private burial will take place in Sunset Ridge Memorial Park. Darla Jean Yingling Kreuser Darla Jean Yingling Kreuser (79) died peacefully in her sleep at home in Clarksville, TN on 23 March, 2020. Funeral services for Darla will be held on Saturday, July 11, at 11:00 a.m. at the Bruch-Hansen Funeral Home. Interment will follow at Sunset Ridge Memorial Park. Visitation will be held on Friday evening from 5 p.m. to 7 p.m. at the funeral home and masks are encouraged. Bruch-Hansen Funeral Home 6019 – 7th Ave. Online Memorial Book www.bruchhansenfuneralhome.com James G. Loken James G. Loken, 60, of Genoa City, passed away Tuesday, June 30, 2020 at his home. Born in Clintonville, Wisconsin on October 6, 1959, he was the son of Gene and Donna (nee Phillips) Loken. He served in the U.S. Army from 1977 until 1980. On August 2, 2003, he was united in marriage to Brenda Quaid. Following marriage, they made Genoa City their home. He was a resident of Genoa City for 19 years. Jim retired from Ecolab in pest control. He loved hunting, camping and spending time with his family. Jim is survived by his wife, Brenda Loken; sister, Kathy (Larry) Preuss and family, as they had a special place

0.258614

-0.721688

-0.561402

-1.288594

[ 0.9948148629135857, -0.47758622326008177 ]

[ -0.3382699585710961, -1.1051066485169831 ]

[ 0.39983289510407205, -1.522637802137204 ]

[ -0.8021374230708285, -1.7750499033974072 ]

1,024

[ 512, 512 ]

[ 11782, 5584, 9150, 29889, 3872, 750, 385, 23440, 1600, 332, 616, 8548, 322, 4687, 263, 8112, 1162, 29891, 19914, 5381, 297, 29871, 29896, 29929, 29955, 29945, 29889, 8084, 540, 4687, 263, 534, 2707, 292, 5001, 304, 447, 352, 1716, 8112, 528, 485, 886, 322, 916, 3005, 523, 29889, 13, 13555, 9881, 2440, 310, 13718, 29892, 3872, 29915, 29879, 2834, 3939, 29889, 940, 11098, 322, 13112, 278, 330, 26265, 29889, 940, 750, 263, 716, 11940, 5360, 363, 13825, 29892, 3600, 6532, 29892, 322, 13718, 29889, 5556, 523, 292, 297, 670, 13718, 29892, 18819, 4045, 19813, 13718, 29892, 322, 9963, 304, 670, 4344, 322, 4595, 11991, 1095, 23769, 1048, 13718, 2360, 2355, 2030, 363, 1075, 29889, 13, 8809, 488, 263, 12502, 29881, 767, 411, 263, 664, 11314, 293, 1473, 304, 5642, 29892, 540, 723, 2337, 18145, 5485, 393, 670, 2551, 1791, 287, 2501, 278, 6567, 310, 278, 1781, 1757, 2820, 1075, 322, 278, 1781, 2264, 310, 4177, 29889, 3600, 1487, 29892, 26977, 897, 29926, 1217, 29892, 1058, 3796, 411, 1075, 1556, 310, 670, 29871, 29946, 29900, 2440, 297, 5381, 471, 670, 1492, 5075, 6029, 540, 18012, 322, 659, 6742, 9425, 368, 29889, 3600, 29215, 29892, 18025, 29899, 262, 29899, 433, 5652, 29892, 8750, 29899, 262, 29899, 10653, 29892, 322, 4595, 11991, 505, 1063, 385, 10160, 760, 310, 278, 2551, 310, 278, 373, 17696, 3942, 5381, 29889, 13, 3868, 471, 2337, 12561, 292, 322, 16049, 5381, 7014, 29892, 13138, 664, 363, 4045, 29892, 322, 7291, 1048, 670, 4595, 11991, 29889, 5806, 2337, 263, 3234, 573, 767, 29892, 540, 2337, 1476, 931, 304, 367, 727, 363, 366, 746, 366, 4312, 1075, 1556, 29889, 940, 19781, 274, 1965, 363, 2305, 408, 1532, 408, 3234, 2068, 29889, 7311, 540, 471, 1556, 15201, 491, 278, 18879, 20193, 393, 540, 4520, 515, 3600, 9583, 1611, 13825, 29892, 540, 471, 263, 767, 310, 1716, 18879, 20193, 322, 1634, 296, 749, 29889, 5806, 263, 767, 310, 2846, 3838, 322, 4549, 7602, 919, 1080, 29892, 540, 471, 263, 767, 411, 385, 23023, 1848, 322, 22707, 5192, 29889, 940, 723, 864, 366, 304, 1073, 393, 727, 338, 18879, 20193, 322, 3544, 749, 297, 278, 2022, 310, 2819, 29889, 13, 3868, 5331, 263, 27402, 2318, 297, 29871, 29896, 29929, 29955, 29906, 393, 1539, 297, 278, 2362, 882, 310, 624, 29889, 6182, 29915, 29879, 11865, 6291, 393, 10201, 3897, 26176, 12790, 6111, 6291, 29889, 2180, 26176, 12790, 540, 10847, 3730, 322, 15935, 2486, 6766, 408, 385, 27008, 29892, 13718, 664, 19032, 11822, 29892, 322, 13731, 336, 914, 2745, 278, 1095, 29889, 13, 10310, 338, 10503, 2347, 491, 670, 6532, 29892, 8562, 5306, 897, 29926, 1217, 29892, 1487, 29892, 19520, 9371, 897, 29926, 1217, 322, 6532, 365, 4170, 29892, 8750, 315, 513, 29891, 9932, 14307, 411, 10216, 12828, 29892, 8750, 7089, 10993, 18989, 29876, 14156, 411, 10216, 3650, 295, 29892, 8750, 2819, 457, 382, 384, 814, 29892, 8750, 1383, 14112, 317, 1460, 672, 411, 10216, 11131, 29892, 322, 8750, 12931, 495, 368, 19135, 411, 10216, 9300, 29889, 940, 756, 29871, 29896, 29929, 4595, 11991, 322, 697, 2107, 4595, 5145, 29889, 13, 29909, 6493, 362, 363, 18935, 674, 367, 4934, 373, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29947, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 13811, 13537, 5786, 4207, 8253, 18935, 29915, 29879, 2834, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 450, 11346, 5336, 29892, 29871, 29947, 29929, 29900, 29900, 29871, 29941, 29946, 386, 319, 345, 29892, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 29889, 12230, 6866, 616, 674, 2125, 2058, 297, 8991, 842, 390, 5525, 19722, 4815, 29889, 13, 29928, 279, 433, 4581, 612, 292, 1847, 7706, 1792, 13, 29928, 279, 433, 4581, 612, 292, 1847, 7706, 1792, 313, 29955, 29929, 29897, 6423, 10776, 3730, 297, 902, 8709, 472, 3271, 297, 17129, 4501, 1924, 29892, 323, 29940, 373, 29871, 29906, 29941, 4779, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 25394, 13537, 5786, 363, 7335, 433, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 472, 29871, 29896, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 278, 8135, 305, 29899, 29950, 29401, 13811, 13537, 8778, 29889, 4124, 358, 674, 1101, 472, 8991, 842, 390, 5525, 19722, 4815, 29889, 5741, 7018, 674, 367, 4934, 373, 28728, 11005, 515, 29871, 29945, 282, 29889, 29885, 29889, 304, 29871, 29955, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 322, 11105, 29879, 526, 18443, 287, 29889, 13, 29933, 582, 305, 29899, 29950, 29401, 13811, 13537, 8778, 13, 29953, 29900, 29896, 29929, 785, 29871, 29955, 386, 319, 345, 29889, 13, 2951, 1220, 19722, 6726, 13, 1636, 29889, 16670, 305, 29882, 29401, 7692, 13537, 5184, 29889, 510, 13, 29470, 402, 29889, 365, 4476, 13, 29470, 402, 29889, 365, 4476, 29892, 29871, 29953, 29900, 29892, 310, 5739, 19807, 4412, 29892, 4502, 3448, 323, 1041, 3250, 29892, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 2233, 16929, 4909, 29892, 22581, 373, 5533, 29871, 29953, 29892, 29871, 29896, 29929, 29945, 29929, 29892, 540, 471, 278, 1487, 310, 15350, 322, 3872, 1056, 313, 484, 29872, 21856, 4512, 29897, 365, 4476, 29889, 940, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 515, 29871, 29896, 29929, 29955, 29955, 2745, 29871, 29896, 29929, 29947, 29900, 29889, 1551, 3111, 29871, 29906, 29892, 29871, 29906, 29900, 29900, 29941, 29892, 540, 471, 443, 1573, 297, 13718, 304, 1771, 8395, 751, 29874, 333, 29889, 12206, 13718, 29892, 896, 1754, 5739, 19807, 4412, 1009, 3271, 29889, 940, 471, 263, 20201, 310, 5739, 19807, 4412, 363, 29871, 29896, 29929, 2440, 29889, 13, 29967, 326, 16528, 515, 382, 1054, 370, 297, 282, 342, 2761, 29889, 940, 18012, 29826, 29892, 4242, 292, 322, 805, 2548, 931, 411, 670, 3942, 29889, 13, 29967, 326, 338, 10503, 2347, 491, 670, 6532, 29892, 1771, 8395, 365, 4476, 29936, 9883, 29892, 19663, 29891, 313, 24105, 719, 29897, 4721, 1558, 322, 3942, 29892, 408, 896, 750, 263, 4266, 2058 ]

1,332,858

4,096

CommonCrawl

0

3

in Jim's heart; children, Sabra and Jeremy; and many nieces, nephews, other relatives and friends. He was preceded in death by his parents, The family would like to thank his caretakers, Diane and Keagan, for their care and concern during this time. Services for Jim will be held Friday, July 10, 2020 at 11AM at Schuette-Daniels Funeral Home. Relatives and friends may visit with the family from 10 until 11AM. Burial will be private. Shirley G. Haase Shirley G. Haase, age 92, of Genoa City, WI, passed away peacefully on Saturday morning, July 4, 2020 at the Aurora Burlington Medical Center in Burlington, WI. The former Shirley Gene Fields was born on May 2, 1928 in McGregor, IA the daughter of the late Everett A. and Olive S. Durr Fields. They moved to Madison, WI when she was a young girl where she worked as a secretary for State Farm Insurance. While in Madison, she met David E. Haase and they were married on November 17, 1948. They lived in Madison, WI and Dubuque, IA before moving to Genoa City in 1951 and purchased the Klement Funeral Home in 1953. This is when the Haase Funeral Home was started. Shirley worked alongside David for many years to build the business to what it is today. The family business has been serving the communities for almost 70 years. Shirley has been a member of the First Congregational United Church of Christ in Genoa City since 1951. She served as Supt. of Sunday School and was a teacher, served on the Church Council and the BYKOTA Circle. She volunteered at the Lakeland Medical Center since 1964 where she greeted people at the main entrance until 2 years ago when she retired from the hospital receiving an award for 53 years of dedicated service to the hospital volunteering. She was a member of the Election Board for Genoa City for over 50 years. She was a member and Treasurer of the Genoa City Garden Club. She volunteered and coordinated at the Blood Bank in Lake Geneva for many years. She was a Lifetime Member of the Order of Eastern Star, Genoa City, Walworth and Burlington Chapter. She was the 2003 Genoa City Lions Club, Citizen of the Year. She was a member of the Sponholtz-Deignan American Legion Post #183 Ladies Auxiliary and the Bloomfield VFW. She was an avid Green Bay Packer Fan. Shirley was always helping anyone in need. Shirley is survived by: her 4 children, Pamela (Kenneth ) Van Dyke, Sr. of Scandinavia, WI, Bruce (Nanette) Haase of Twin Lakes, WI, Bryan (Geri) Haase of Genoa City, WI and Cynthia (Bob Vail) Wilinski of Fontana, WI; 8 grandchildren, Dr. Kenneth (Jacqueline) Van Dyke, Jr., Ryan (Kayla) Van Dyke, Andrew (Suzanne) Haase, Kathryn (Matthew) Buchan, Jonathan (Rachael Otto) Haase, Jackie (John) Bettack, Sarah (Drew) Wellman and Matthew (Tausha) Wilinski; 16 great grandchildren, Olivia Van Dyke, Annaliese Van Dyke, Finn Van Dyke, Barrett Van Dyke, Sean Haase, Evan Haase, Emily Haase, Hunter Buchan, Kolt Buchan, Collin Bettack, Coltin Bettack, Isabella Bettack, Jenner Wellman, Quinn Wellman, Ellie Wilinski, Wade Haase and baby Wilinski to be born in December; 1 sister, Eleanor "Doll" Stanford of Madison, WI and a sister in law, Julie Fields of Morton, IL and many friends. Shirley was preceded in death by her husband David on September 23, 2000, 2 brothers Gary Fields in 2013 and Terry Fields in 1993. Brother in law Herbert Stanford. The Ha

-0.031072

-0.705125

-1.281695

-1.58515

[ -0.016690441401998893, -0.045453625410972864 ]

[ -1.2089631062329467, -0.20128687210090263 ]

[ -1.3501734124110736, -1.2132163970403231 ]

[ -1.7646444223243956, -1.4056553253054975 ]

1,024

[ 512, 512 ]

[ 297, 8507, 29915, 29879, 5192, 29936, 4344, 29892, 11775, 336, 322, 5677, 6764, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 916, 14576, 322, 7875, 29889, 940, 471, 9399, 287, 297, 4892, 491, 670, 11825, 29892, 13, 1576, 3942, 723, 763, 304, 6452, 670, 2562, 29873, 21079, 29892, 360, 16677, 322, 4813, 18939, 29892, 363, 1009, 2562, 322, 5932, 2645, 445, 931, 29889, 13, 13779, 363, 8507, 674, 367, 4934, 28728, 29892, 5468, 29871, 29896, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29896, 5194, 472, 1102, 29884, 2353, 29899, 18529, 28119, 13811, 13537, 8778, 29889, 6376, 5056, 322, 7875, 1122, 6493, 411, 278, 3942, 515, 29871, 29896, 29900, 2745, 29871, 29896, 29896, 5194, 29889, 6640, 616, 674, 367, 2024, 29889, 13, 2713, 381, 2330, 402, 29889, 5952, 559, 13, 2713, 381, 2330, 402, 29889, 5952, 559, 29892, 5046, 29871, 29929, 29906, 29892, 310, 5739, 19807, 4412, 29892, 399, 29902, 29892, 4502, 3448, 10776, 3730, 373, 24211, 7250, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 23266, 2207, 6640, 1847, 880, 20795, 7817, 297, 6640, 1847, 880, 29892, 399, 29902, 29889, 13, 1576, 4642, 1383, 381, 2330, 15350, 8989, 29879, 471, 6345, 373, 2610, 29871, 29906, 29892, 29871, 29896, 29929, 29906, 29947, 297, 22805, 1727, 272, 29892, 306, 29909, 278, 8750, 310, 278, 5683, 18274, 1803, 319, 29889, 322, 438, 9258, 317, 29889, 360, 1038, 8989, 29879, 29889, 2688, 6153, 304, 4104, 2285, 29892, 399, 29902, 746, 1183, 471, 263, 4123, 7826, 988, 1183, 3796, 408, 263, 28274, 363, 4306, 23354, 512, 7610, 749, 29889, 5806, 297, 4104, 2285, 29892, 1183, 1539, 4699, 382, 29889, 5952, 559, 322, 896, 892, 8300, 373, 3979, 29871, 29896, 29955, 29892, 29871, 29896, 29929, 29946, 29947, 29889, 2688, 10600, 297, 4104, 2285, 29892, 399, 29902, 322, 11668, 29884, 802, 29892, 306, 29909, 1434, 8401, 304, 5739, 19807, 4412, 297, 29871, 29896, 29929, 29945, 29896, 322, 20848, 278, 476, 944, 13811, 13537, 8778, 297, 29871, 29896, 29929, 29945, 29941, 29889, 910, 338, 746, 278, 5952, 559, 13811, 13537, 8778, 471, 4687, 29889, 1383, 381, 2330, 3796, 19963, 4699, 363, 1784, 2440, 304, 2048, 278, 5381, 304, 825, 372, 338, 9826, 29889, 450, 3942, 5381, 756, 1063, 16330, 278, 23507, 363, 4359, 29871, 29955, 29900, 2440, 29889, 13, 2713, 381, 2330, 756, 1063, 263, 4509, 310, 278, 3824, 6005, 1727, 1288, 3303, 6291, 310, 2819, 297, 5739, 19807, 4412, 1951, 29871, 29896, 29929, 29945, 29896, 29889, 2296, 6766, 408, 2166, 415, 29889, 310, 16340, 4523, 322, 471, 263, 15703, 29892, 6766, 373, 278, 6291, 8831, 322, 278, 6770, 29968, 2891, 29909, 27927, 29889, 2296, 27886, 14561, 472, 278, 27229, 14045, 20795, 7817, 1951, 29871, 29896, 29929, 29953, 29946, 988, 1183, 1395, 300, 287, 2305, 472, 278, 1667, 19546, 2745, 29871, 29906, 2440, 8020, 746, 1183, 16528, 515, 278, 13457, 13442, 385, 9862, 363, 29871, 29945, 29941, 2440, 310, 16955, 2669, 304, 278, 13457, 27886, 3241, 29889, 2296, 471, 263, 4509, 310, 278, 382, 1464, 12590, 363, 5739, 19807, 4412, 363, 975, 29871, 29945, 29900, 2440, 29889, 2296, 471, 263, 4509, 322, 6479, 294, 9945, 310, 278, 5739, 19807, 4412, 19906, 5977, 29889, 2296, 27886, 14561, 322, 6615, 630, 472, 278, 25122, 10253, 297, 9459, 15350, 1564, 363, 1784, 2440, 29889, 2296, 471, 263, 365, 361, 5410, 19495, 310, 278, 8170, 310, 16162, 7828, 29892, 5739, 19807, 4412, 29892, 5260, 12554, 322, 6640, 1847, 880, 23040, 29889, 2296, 471, 278, 29871, 29906, 29900, 29900, 29941, 5739, 19807, 4412, 365, 1080, 5977, 29892, 21353, 19642, 310, 278, 8905, 29889, 2296, 471, 263, 4509, 310, 278, 317, 1112, 5391, 17559, 29899, 2772, 647, 273, 3082, 5682, 291, 4918, 396, 29896, 29947, 29941, 19955, 583, 319, 1314, 2638, 653, 322, 278, 11447, 290, 2671, 478, 29943, 29956, 29889, 2296, 471, 385, 1029, 333, 7646, 6211, 18744, 261, 383, 273, 29889, 1383, 381, 2330, 471, 2337, 19912, 5019, 297, 817, 29889, 13, 2713, 381, 2330, 338, 10503, 2347, 491, 29901, 902, 29871, 29946, 4344, 29892, 25281, 3100, 313, 29968, 2108, 621, 1723, 6556, 24526, 446, 29892, 26250, 29889, 310, 2522, 392, 262, 12751, 29892, 399, 29902, 29892, 18885, 313, 29940, 273, 2353, 29897, 5952, 559, 310, 323, 5080, 365, 6926, 29892, 399, 29902, 29892, 13307, 273, 313, 29954, 13613, 29897, 5952, 559, 310, 5739, 19807, 4412, 29892, 399, 29902, 322, 315, 948, 386, 423, 313, 29362, 478, 737, 29897, 4624, 262, 2574, 310, 10928, 1648, 29892, 399, 29902, 29936, 29871, 29947, 4595, 11991, 29892, 4942, 29889, 28576, 313, 24288, 339, 5570, 29897, 6556, 24526, 446, 29892, 13843, 1696, 20916, 313, 29968, 388, 433, 29897, 6556, 24526, 446, 29892, 11571, 313, 29903, 3365, 11276, 29897, 5952, 559, 29892, 19663, 719, 29876, 313, 29924, 1131, 13636, 29897, 10586, 273, 29892, 20983, 313, 29934, 496, 4271, 13832, 29897, 5952, 559, 29892, 5457, 347, 313, 11639, 29897, 350, 1803, 547, 29892, 19235, 313, 29928, 3973, 29897, 5674, 1171, 322, 22292, 313, 29911, 1485, 2350, 29897, 4624, 262, 2574, 29936, 29871, 29896, 29953, 2107, 4595, 11991, 29892, 19802, 423, 6556, 24526, 446, 29892, 8081, 284, 21928, 6556, 24526, 446, 29892, 21189, 6556, 24526, 446, 29892, 2261, 13158, 6556, 24526, 446, 29892, 922, 273, 5952, 559, 29892, 382, 3703, 5952, 559, 29892, 2812, 2354, 5952, 559, 29892, 25703, 10586, 273, 29892, 10451, 29873, 10586, 273, 29892, 1530, 1915, 350, 1803, 547, 29892, 1530, 29873, 262, 350, 1803, 547, 29892, 16543, 433, 350, 1803, 547, 29892, 21116, 1089, 5674, 1171, 29892, 751, 2559, 5674, 1171, 29892, 11001, 347, 4624, 262, 2574, 29892, 399, 1943, 5952, 559, 322, 24354, 4624, 262, 2574, 304, 367, 6345, 297, 5846, 29936, 29871, 29896, 9883, 29892, 8317, 273, 272, 376, 29928, 3028, 29908, 7813, 4006, 310, 4104, 2285, 29892, 399, 29902, 322, 263, 9883, 297, 4307, 29892, 2739, 347, 8989, 29879, 310, 15533, 265, 29892, 17674, 322, 1784, 7875, 29889, 13, 2713, 381, 2330, 471, 9399, 287, 297, 4892, 491, 902, 10216, 4699, 373, 3839, 29871, 29906, 29941, 29892, 29871, 29906, 29900, 29900, 29900, 29892, 29871, 29906, 21383, 23529, 8989, 29879, 297, 29871, 29906, 29900, 29896, 29941, 322, 27571, 8989, 29879, 297, 29871, 29896, 29929, 29929, 29941, 29889, 4358, 721, 297, 4307, 19116, 7813, 4006, 29889, 13, 1576, 5952 ]

1,332,858

5,120

CommonCrawl

0

3

ase Family would like to send a big Thank You to Golden Years in Lake Geneva, WI for taking such good care our Mother, Dr. Karls, Dr. Welka, Dr. Hobbs the Aurora Medical Center in Burlington and the many friends that have reached out. A public visitation will be held on Saturday, July 11, 2020 from 2:00PM until 7:00PM at the Haase-Lockwood & Assoc. Funeral Home, 113 Freeman St. Genoa City, WI. Due to the Covid-19 Pandemic, everyone is asked to be patient and abide by the number of visitors allowed inside the funeral home. Everyone is welcome, but we ask that you keep your visit short so that all who wish to pay their respects will be able to do so. A Private Family Service will be held at the First Congregational United church of Christ on Sunday. Entombment will follow at Hillside Cemetery. In lieu of other expressions of sympathy, Shirley has asked that memorials be made the First Congregational United Church of Christ, 624 Park St. Genoa City, WI 53128. For online guestbook: haaselockwoodfhs.com. The Haase-Lockwood & Assoc. Funeral Home of Genoa City is handling our mother's arrangements. Donald D. Dejno Donald D. Dejno, age 78, passed away on Saturday, July 4, 2020 at Froedtert South – Pleasant Prairie Campus. Complete obituary information will be available in the Wednesday, July 8, 2020 edition of the Kenosha News. Shelby Jean Nielsen Shelby Jean Nielsen, 81 of Lepanto, Arkansas departed this life on June 30, 2020 in Jonesboro, Arkansas. She was born on July 14, 1938 to William Howard and Anna Blanche Kemp Watts. She was a member of Lepanto First Baptist Church. Shelby is preceded in death by her parents and husband: Paul Nielsen. Shelby is survived by her special friend: Carlton Soden of Amory, Mississippi, 1 son: Robert Lawrence of Kenosha, Wisconsin, 2 daughters: Connie Massie of Salem, Wisconsin and Tami Voigt (Peter) of Salem, Wisconsin, 3 sisters: Shelia Dean Tyler (Harold) of Lepanto, Arkansas, Patricia Ann Taylor (Morris) of Lepanto, Arkansas and Paula Diane Laney (B.J.) of Fulton, Mississippi, 10 grandchildren , 9 great-grandchildren, several nieces, nephews and a host of family and friends. Funeral service will be held Monday, July 6, 2020 at 1:00 pm and visitation will be held from 11:00 am – 1:00 pm at First Baptist Church in Lepanto, Arkansas. Interment will be at Potter Memorial Cemetery in Lepanto, Arkansas. Arrangements are under the care of Delancey-Murphy Funeral Home On line registry: [email protected] Rudolph "Rudy" J. Schwamlien Rudolph J. "Rudy" Schwamlien, 77 years old of Lake Villa, IL passed away unexpectedly Thursday July 2, 2020. He was born November 25, 1942 in Harvey, IL the son of the late Rudolph J. and Mary V. (neé Shaffer) Schwamlien, living in Chicago, IL and Paddock Lake, WI before settling in Lake Villa in 1988. Rudy proudly served in the US Airforce and was a proud member of the American Legion Post #2910. Before his retirement in 2005, Rudy had worked as a Head Lab Technician for American Conveyor Systems, Evanston, IL for over 40 years. Rudy was the head of the Pioneer's program at Zion Lutheran Church, Bristol from 1973 until 1979, a member of the Paddock Lake Sportsman's Club and the NRA, and he enjoyed: hunting, fishing, and gunsmithing. Sur

-0.741934

-1.280588

-1.867567

-1.975355

[ -0.4241688815291301, -1.059698280584555 ]

[ -1.3450508784124853, -1.2161256205581856 ]

[ -1.6443773713556489, -2.0907557918232804 ]

[ -1.936334860029086, -2.0143759680766724 ]

1,024

[ 512, 512 ]

[ 559, 14662, 723, 763, 304, 3638, 263, 4802, 3374, 887, 304, 16108, 23857, 297, 9459, 15350, 1564, 29892, 399, 29902, 363, 5622, 1316, 1781, 2562, 1749, 21869, 29892, 4942, 29889, 3467, 3137, 29892, 4942, 29889, 10458, 1335, 29892, 4942, 29889, 25302, 5824, 278, 23266, 2207, 20795, 7817, 297, 6640, 1847, 880, 322, 278, 1784, 7875, 393, 505, 7450, 714, 29889, 13, 29909, 970, 6493, 362, 674, 367, 4934, 373, 24211, 29892, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 515, 29871, 29906, 29901, 29900, 29900, 13427, 2745, 29871, 29955, 29901, 29900, 29900, 13427, 472, 278, 5952, 559, 29899, 16542, 6115, 669, 4007, 542, 29889, 13811, 13537, 8778, 29892, 29871, 29896, 29896, 29941, 3878, 11422, 624, 29889, 5739, 19807, 4412, 29892, 399, 29902, 29889, 16809, 304, 278, 25669, 333, 29899, 29896, 29929, 6518, 24552, 29892, 14332, 338, 4433, 304, 367, 16500, 322, 633, 680, 491, 278, 1353, 310, 26824, 6068, 2768, 278, 2090, 13537, 3271, 29889, 7569, 650, 338, 12853, 29892, 541, 591, 2244, 393, 366, 3013, 596, 6493, 3273, 577, 393, 599, 1058, 6398, 304, 5146, 1009, 3390, 29879, 674, 367, 2221, 304, 437, 577, 29889, 319, 12230, 14662, 6692, 674, 367, 4934, 472, 278, 3824, 6005, 1727, 1288, 3303, 6586, 310, 2819, 373, 16340, 29889, 4284, 3424, 358, 674, 1101, 472, 9143, 2975, 315, 22875, 29889, 512, 13003, 310, 916, 12241, 310, 29738, 29892, 1383, 381, 2330, 756, 4433, 393, 2626, 9020, 29879, 367, 1754, 278, 3824, 6005, 1727, 1288, 3303, 6291, 310, 2819, 29892, 29871, 29953, 29906, 29946, 4815, 624, 29889, 5739, 19807, 4412, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29906, 29947, 29889, 1152, 7395, 17838, 2909, 29901, 447, 294, 295, 1698, 6115, 29888, 9499, 29889, 510, 29889, 450, 5952, 559, 29899, 16542, 6115, 669, 4007, 542, 29889, 13811, 13537, 8778, 310, 5739, 19807, 4412, 338, 11415, 1749, 5637, 29915, 29879, 15196, 4110, 29889, 13, 28080, 360, 29889, 897, 29926, 1217, 13, 28080, 360, 29889, 897, 29926, 1217, 29892, 5046, 29871, 29955, 29947, 29892, 4502, 3448, 373, 24211, 29892, 5468, 29871, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 357, 29873, 4275, 785, 19777, 13186, 9002, 24135, 7259, 375, 29889, 13, 17813, 704, 1981, 653, 2472, 674, 367, 3625, 297, 278, 15050, 4515, 3250, 29892, 5468, 29871, 29947, 29892, 29871, 29906, 29900, 29906, 29900, 12203, 310, 278, 10015, 359, 2350, 10130, 29889, 13, 2713, 295, 1609, 4581, 405, 709, 4881, 13, 2713, 295, 1609, 4581, 405, 709, 4881, 29892, 29871, 29947, 29896, 310, 951, 29886, 5361, 29892, 19444, 13353, 5840, 287, 445, 2834, 373, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 297, 10920, 4089, 29877, 29892, 19444, 13353, 29889, 2296, 471, 6345, 373, 5468, 29871, 29896, 29946, 29892, 29871, 29896, 29929, 29941, 29947, 304, 4667, 17430, 322, 11230, 3164, 20372, 476, 3451, 399, 1131, 29879, 29889, 2296, 471, 263, 4509, 310, 951, 29886, 5361, 3824, 23759, 391, 6291, 29889, 13, 2713, 295, 1609, 338, 9399, 287, 297, 4892, 491, 902, 11825, 322, 10216, 29901, 3739, 405, 709, 4881, 29889, 13, 2713, 295, 1609, 338, 10503, 2347, 491, 902, 4266, 5121, 29901, 8965, 880, 317, 13183, 310, 1913, 706, 29892, 24743, 29892, 29871, 29896, 1487, 29901, 4755, 19520, 310, 10015, 359, 2350, 29892, 22581, 29892, 29871, 29906, 29215, 29901, 1281, 2786, 7360, 347, 310, 317, 12698, 29892, 22581, 322, 323, 4479, 4785, 5523, 313, 23686, 29897, 310, 317, 12698, 29892, 22581, 29892, 29871, 29941, 9883, 29879, 29901, 1383, 18556, 23263, 9656, 1358, 313, 21972, 1025, 29897, 310, 951, 29886, 5361, 29892, 19444, 13353, 29892, 4121, 2200, 423, 8081, 12537, 313, 28581, 3780, 29897, 310, 951, 29886, 5361, 29892, 19444, 13353, 322, 2621, 2497, 360, 16677, 18273, 1032, 313, 29933, 29889, 29967, 1846, 310, 383, 499, 265, 29892, 24743, 29892, 29871, 29896, 29900, 4595, 11991, 1919, 29871, 29929, 2107, 29899, 27857, 11991, 29892, 3196, 4930, 778, 29892, 23446, 354, 5652, 322, 263, 3495, 310, 3942, 322, 7875, 29889, 13, 25394, 13537, 2669, 674, 367, 4934, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29901, 29900, 29900, 26354, 322, 6493, 362, 674, 367, 4934, 515, 29871, 29896, 29896, 29901, 29900, 29900, 626, 785, 29871, 29896, 29901, 29900, 29900, 26354, 472, 3824, 23759, 391, 6291, 297, 951, 29886, 5361, 29892, 19444, 13353, 29889, 13, 4074, 358, 674, 367, 472, 10173, 357, 19722, 315, 22875, 297, 951, 29886, 5361, 29892, 19444, 13353, 29889, 13, 16401, 574, 4110, 526, 1090, 278, 2562, 310, 5556, 749, 29891, 29899, 29924, 332, 11461, 13811, 13537, 8778, 13, 2951, 1196, 21235, 29901, 628, 749, 962, 332, 11461, 7692, 13537, 5184, 29992, 21980, 29889, 510, 13, 29934, 566, 22138, 376, 29934, 566, 29891, 29908, 435, 29889, 9234, 314, 492, 264, 13, 29934, 566, 22138, 435, 29889, 376, 29934, 566, 29891, 29908, 9234, 314, 492, 264, 29892, 29871, 29955, 29955, 2440, 2030, 310, 9459, 14439, 29892, 17674, 4502, 3448, 15668, 368, 498, 1295, 3250, 5468, 29871, 29906, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 940, 471, 6345, 3979, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29946, 29906, 297, 3536, 6950, 29892, 17674, 278, 1487, 310, 278, 5683, 10670, 22138, 435, 29889, 322, 6182, 478, 29889, 313, 484, 29948, 1383, 2142, 571, 29897, 9234, 314, 492, 264, 29892, 8471, 297, 10059, 29892, 17674, 322, 349, 1202, 1698, 9459, 29892, 399, 29902, 1434, 3604, 1847, 297, 9459, 14439, 297, 29871, 29896, 29929, 29947, 29947, 29889, 10670, 29891, 22314, 368, 6766, 297, 278, 3148, 5593, 10118, 322, 471, 263, 22314, 4509, 310, 278, 3082, 5682, 291, 4918, 396, 29906, 29929, 29896, 29900, 29889, 10949, 670, 3240, 19211, 297, 29871, 29906, 29900, 29900, 29945, 29892, 10670, 29891, 750, 3796, 408, 263, 12252, 12016, 8364, 8910, 363, 3082, 1281, 6950, 272, 23985, 29892, 382, 3703, 7352, 29892, 17674, 363, 975, 29871, 29946, 29900, 2440, 29889, 10670, 29891, 471, 278, 2343, 310, 278, 349, 1421, 261, 29915, 29879, 1824, 472, 796, 291, 24760, 273, 6291, 29892, 1771, 19639, 515, 29871, 29896, 29929, 29955, 29941, 2745, 29871, 29896, 29929, 29955, 29929, 29892, 263, 4509, 310, 278, 349, 1202, 1698, 9459, 12453, 1171, 29915, 29879, 5977, 322, 278, 405, 4717, 29892, 322, 540, 27849, 29901, 29826, 29892, 9427, 292, 29892, 322, 13736, 3844, 389, 292, 29889, 13, 18498 ]

1,332,858

6,144

CommonCrawl

0

3

vivors include five children: Lisa Baker of Jonesboro, IL, Randy Schwamlien of Lake Villa, IL, Dale (Kim) Johnson of Paddock Lake, WI, Laura (Thomas) Casper of Franksville, WI, and Ki Johnson of Burlington, WI; five grandchildren: Tristan Koeller, Michael (Kari) Corrigan, Matthew (Katie) Corrigan, Miles (Nicole) Corrigan, and Jennifer (Trevor) Gorn; 12 great-grandchildren; sister Carol A. Corrigan of Kenosha, WI; special nephew Robert (Margaret) Moll of Fredonia, KY; great-niece and great-nephews: Robert, Cody, Daniel, Julie, Matthew, and Zack; and many friends. In addition to his parents, Rudy was preceded in death by his life partner: Joanne Johnson on October 11, 2004, a son Timothy Johnson, and a brother Edward A Schwamlien. Funeral Services will be held at 4:00PM Saturday July 11, 2020 at the STRANG FUNERAL HOME OF ANTIOCH 1055 Main St. (Rte. 83) Antioch, IL 60002, with visitation beginning at 12 Noon. Interment will be private. In lieu of flowers, donations to St. Jude Children's Research Hospital are appreciated in Rudy's memory. Please sign the online guest book for Rudy at www.strangfh.com. Anne T. Kinsey Anne T. Kinsey, age 90 of Kenosha passed away peacefully on Friday, June 26, 2020 at Froedert Memorial Hospital, Pleasant Prairie. Beloved wife of the late Paul Kinsey, loving mother of MaryLynn (Jeff) Wedeward, Patricia (Norm) Linnell, and Paula Kinsey; dear grandmother of Allison Wedeward, Michael Wedeward, Kinsey (Quincy) Davis, Breita Linnell and Paul (Lisa) Linnell; great-grandmother of Annika, Chatman, Leo, and Quin. A private Mass of Christian Burial will be celebrated at a later date. 4600 Cty. Line Road, Racine, WI William J. Althaus, Associate Edwin L. Segerstrom Edwin L. Segerstrom, age 76, passed away on Thursday, July 2, 2020 at North Point Senior Living with his family by his side. Born in Eau Claire, WI on July 25, 1943, he was the son of Lloyd and Bertha (Schlitz) Segerstrom. Ed owned and operated his own company, A & J Tool Grinding in Kenosha for many years until his retirement in 1988. He was a remarkable man; not only a loving, devoted and supportive son, father and grandfather but a successful businessman. Ed was a private pilot and also a captain of 2 charter boats that he owned called "The Get Away" and "I dunno". Ed was a member of Midwest Street Machine Car Club. Those left to remember Ed are his mother, Bertha Kempin; his children, Kathy, David and Daniel Segerstrom; their mother and former wife, Patricia Gannaway; his four grandchildren; his siblings, Linda Kimpel, Sandy German, Gary Segerstrom and Donald Kempin Edwin was preceded in death by his father, Lloyd Segerstrom and his sister, Rosanne Willox. Funeral services honoring Edwin's life will be held on Tuesday, July 7, 2020 at 12:00 p.m. at the Piasecki Funeral Home. Interment will take place in All Saints Cemetery. A visitation for Edwin will be held on Tuesday from 10:00 a.m. until the time of the service at the funeral home. Walter J. Barthuly Walter J. Barthuly, age 94, a resident of Kenosha, WI died May 30th, 2020 in Gurnee IL, on the day of his birthday. The light of the world dimmed just

-0.401227

-0.960066

-1.654522

-1.767246

[ -0.5063494072690558, -0.296104228917746 ]

[ -0.850837389971003, -1.0692940768907888 ]

[ -1.654522335457186, -1.654522335457186 ]

[ -1.7802526439339128, -1.7542389412513841 ]

1,024

[ 512, 512 ]

[ 24759, 943, 3160, 5320, 4344, 29901, 29420, 22652, 310, 10920, 4089, 29877, 29892, 17674, 29892, 390, 13910, 9234, 314, 492, 264, 310, 9459, 14439, 29892, 17674, 29892, 360, 744, 313, 29968, 326, 29897, 11717, 310, 349, 1202, 1698, 9459, 29892, 399, 29902, 29892, 21671, 313, 1349, 18902, 29897, 6960, 546, 310, 1352, 2039, 4909, 29892, 399, 29902, 29892, 322, 16540, 11717, 310, 6640, 1847, 880, 29892, 399, 29902, 29936, 5320, 4595, 11991, 29901, 1605, 9777, 8224, 4539, 29892, 5765, 313, 29968, 1306, 29897, 2994, 8966, 273, 29892, 22292, 313, 29968, 9474, 29897, 2994, 8966, 273, 29892, 3833, 267, 313, 29940, 23249, 29897, 2994, 8966, 273, 29892, 322, 23774, 9633, 313, 29911, 276, 5267, 29897, 402, 1398, 29936, 29871, 29896, 29906, 2107, 29899, 27857, 11991, 29936, 9883, 8562, 319, 29889, 2994, 8966, 273, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 4266, 23446, 13636, 4755, 313, 29924, 1191, 10474, 29897, 341, 3028, 310, 12001, 6405, 29892, 476, 29979, 29936, 2107, 29899, 2786, 346, 322, 2107, 29899, 484, 28362, 5652, 29901, 4755, 29892, 315, 1486, 29892, 8432, 29892, 2739, 347, 29892, 22292, 29892, 322, 796, 547, 29936, 322, 1784, 7875, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 10670, 29891, 471, 9399, 287, 297, 4892, 491, 670, 2834, 18096, 29901, 3650, 11276, 11717, 373, 5533, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29900, 29946, 29892, 263, 1487, 7870, 20336, 11717, 29892, 322, 263, 8099, 9300, 319, 9234, 314, 492, 264, 29889, 13, 25394, 13537, 15538, 674, 367, 4934, 472, 29871, 29946, 29901, 29900, 29900, 13427, 24211, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 29486, 19453, 383, 3904, 1001, 1964, 29832, 2303, 8079, 13764, 29911, 5971, 3210, 29871, 29896, 29900, 29945, 29945, 4241, 624, 29889, 313, 29934, 371, 29889, 29871, 29947, 29941, 29897, 5459, 601, 305, 29892, 17674, 29871, 29953, 29900, 29900, 29900, 29906, 29892, 411, 6493, 362, 6763, 472, 29871, 29896, 29906, 1939, 265, 29889, 4124, 358, 674, 367, 2024, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 304, 624, 29889, 435, 1151, 20986, 29915, 29879, 10550, 15967, 526, 7556, 297, 10670, 29891, 29915, 29879, 3370, 29889, 3529, 1804, 278, 7395, 17838, 3143, 363, 10670, 29891, 472, 7821, 29889, 710, 574, 29888, 29882, 29889, 510, 29889, 13, 2744, 484, 323, 29889, 20311, 7759, 13, 2744, 484, 323, 29889, 20311, 7759, 29892, 5046, 29871, 29929, 29900, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 814, 19722, 15967, 29892, 19777, 13186, 9002, 24135, 29889, 13, 21140, 8238, 6532, 310, 278, 5683, 3739, 20311, 7759, 29892, 12355, 292, 5637, 310, 6182, 29931, 948, 29876, 313, 29967, 12352, 29897, 15050, 809, 538, 29892, 4121, 2200, 423, 313, 29940, 555, 29897, 365, 2559, 514, 29892, 322, 2621, 2497, 20311, 7759, 29936, 9425, 4595, 29885, 1228, 310, 2178, 2285, 15050, 809, 538, 29892, 5765, 15050, 809, 538, 29892, 20311, 7759, 313, 2182, 262, 1270, 29897, 15225, 29892, 5826, 2028, 365, 2559, 514, 322, 3739, 313, 29931, 8069, 29897, 365, 2559, 514, 29936, 2107, 29899, 27857, 29885, 1228, 310, 8081, 4106, 29892, 678, 271, 1171, 29892, 22533, 29892, 322, 751, 262, 29889, 13, 29909, 2024, 7360, 310, 6111, 6640, 616, 674, 367, 26301, 472, 263, 2678, 2635, 29889, 13, 29946, 29953, 29900, 29900, 315, 1017, 29889, 7407, 9321, 29892, 390, 562, 457, 29892, 399, 29902, 13, 12984, 2829, 435, 29889, 838, 386, 1485, 29892, 6853, 403, 13, 3853, 5080, 365, 29889, 6667, 15714, 456, 13, 3853, 5080, 365, 29889, 6667, 15714, 456, 29892, 5046, 29871, 29955, 29953, 29892, 4502, 3448, 373, 498, 1295, 3250, 29892, 5468, 29871, 29906, 29892, 29871, 29906, 29900, 29906, 29900, 472, 4644, 8984, 24260, 26176, 411, 670, 3942, 491, 670, 2625, 29889, 13, 29933, 1398, 297, 382, 585, 6015, 533, 29892, 399, 29902, 373, 5468, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29946, 29941, 29892, 540, 471, 278, 1487, 310, 27054, 322, 2292, 15457, 313, 4504, 29880, 2784, 29897, 6667, 15714, 456, 29889, 13, 3853, 15205, 322, 19623, 670, 1914, 5001, 29892, 319, 669, 435, 21704, 1632, 4015, 297, 10015, 359, 2350, 363, 1784, 2440, 2745, 670, 3240, 19211, 297, 29871, 29896, 29929, 29947, 29947, 29889, 13, 3868, 471, 263, 22567, 767, 29936, 451, 871, 263, 12355, 292, 29892, 24600, 322, 2304, 573, 1487, 29892, 4783, 322, 4595, 22212, 541, 263, 9150, 5381, 1171, 29889, 2155, 471, 263, 2024, 19840, 322, 884, 263, 15315, 310, 29871, 29906, 1373, 357, 25462, 393, 540, 15205, 2000, 376, 1576, 3617, 319, 1582, 29908, 322, 376, 29902, 270, 348, 1217, 1642, 2155, 471, 263, 4509, 310, 13370, 5933, 7103, 6189, 1704, 5977, 29889, 13, 1349, 852, 2175, 304, 6456, 2155, 526, 670, 5637, 29892, 2292, 15457, 476, 3451, 262, 29936, 670, 4344, 29892, 19663, 29891, 29892, 4699, 322, 8432, 6667, 15714, 456, 29936, 1009, 5637, 322, 4642, 6532, 29892, 4121, 2200, 423, 402, 812, 21694, 29936, 670, 3023, 4595, 11991, 29936, 670, 27767, 18964, 29892, 365, 11054, 476, 6574, 295, 29892, 8564, 29891, 5332, 29892, 23529, 6667, 15714, 456, 322, 18935, 476, 3451, 262, 13, 3853, 5080, 471, 9399, 287, 297, 4892, 491, 670, 4783, 29892, 27054, 6667, 15714, 456, 322, 670, 9883, 29892, 5678, 11276, 4624, 417, 29916, 29889, 13, 25394, 13537, 5786, 4207, 8253, 2155, 5080, 29915, 29879, 2834, 674, 367, 4934, 373, 323, 1041, 3250, 29892, 5468, 29871, 29955, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 7362, 559, 22736, 13811, 13537, 8778, 29889, 4124, 358, 674, 2125, 2058, 297, 2178, 14342, 1372, 315, 22875, 29889, 319, 6493, 362, 363, 2155, 5080, 674, 367, 4934, 373, 323, 1041, 3250, 515, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 2745, 278, 931, 310, 278, 2669, 472, 278, 2090, 13537, 3271, 29889, 13, 29956, 13794, 435, 29889, 2261, 386, 11850, 13, 29956, 13794, 435, 29889, 2261, 386, 11850, 29892, 5046, 29871, 29929, 29946, 29892, 263, 20201, 310, 10015, 359, 2350, 29892, 399, 29902, 6423, 2610, 29871, 29941, 29900, 386, 29892, 29871, 29906, 29900, 29906, 29900, 297, 402, 332, 484, 29872, 17674, 29892, 373, 278, 2462, 310, 670, 12060, 3250, 29889, 450, 3578, 310, 278, 3186, 3964, 2168, 925 ]

1,332,858

7,168

CommonCrawl

0

3

a little bit but then brightened back up from all of the lives he touched. Walter's daughter Patricia was caring for her father at her home with the help of Star Hospice, Gurnee, IL. Walter's children were able to spend time with him throughout the week leading up to when our Heavenly Father took him home. Walter was born in Fond du Lac WI to John and Katherine (Bopp) Barthuly. He attended high school and the Fond du Lac Business College. He married his beautiful and loving wife Patricia Lardinois on February 18, 1947 in Fond du Lac, WI. They spent their honeymoon in Chicago after taking the train to the city. Walter and Patricia were married for 73 years. What Wally enjoyed most was spending time with family, visiting friends and was always willing to give a helping hand to those in need. Wally was drafted during World War II and went through basic training/tech school. He was inducted in August 1944. His military occupational specialty was a Radio Operator, High Speed. He served in the Southwest Pacific Theater of Operations and went on to serve during the Korean Conflict and Berlin Crisis on active duty, National Guard and Reserves. His military service time was just short of 30 years. He retired as an Army Captain in May 1986. As a civilian his occupation was a Locomotive Maintenance Mechanic helper. Medals and decorations Walter earned included WW II American Theater Campaign Ribbon, Army of Occupation Medal (Japan), Good Conduct Medal, WWII Victory Asiatic-Pacific Campaign Medal, Army of Occupation National Defense Service Medal, Armed Forces Reserve, Army Presidential Unit Citation with 1 Oak Leaf Cluster, Combat Infantryman Badge, Marksman Rifle & Pistol Badge, and Expert Rifle & Carbine Badge. He worked for the Department of Defense as a troubleshooter for 15 years. He was a member of the Veterans of Foreign Wars and was a Golden Gloves Boxer. Wally worked for the City of Kenosha Transit Department as a bus driver and training coordinator for 14 years until retiring in 1994. He drove tour bus for the Tommy Dorsey band and the Kenosha Twins baseball team. Walter was a die-hard Green Bay Packer and Milwaukee Brewer fan. Wally is a member of Journey Church, Kenosha, WI. He joined Gideons International in 1984 and he was a member of Light for the Lost. He touched many lives during his 32 years of working with the Royal Rangers. Walter is preceded in death by parents John and Katherine Barthuly, his siblings Alex (Betty) Barthuly, Otto (Vivian) Barthuly, Johnny (Jennifer) Barthuly, Nathalie (Adolph) Hunt, Esther (Herman) Burkhardt, and Dorothy (Gordy) Zwicky. Carrying on his legacy are his wife Patricia Barthuly, his children Walter (Bonnie) Barthuly, David (Holly) Barthuly, Brad (Lorreen) Barthuly, Patricia (Dan) Jimenez, Scott (Nancy) Barthuly, and Dawn (Chris) Maylath. Grandchildren: Rachel (Anthony), Aaron (Nicole), Rebekah (Jonathan), Jonathan, Bradley (Traci), Bret, Christopher, Andrew, Jacqueline (Paul), and Alex. Great Grandchildren: Juliana, Alejandra, Katelyn, Audrey, Benjamin, Gwynivere, Robert, and Mollie. A memorial service will be held on July 11, 2020 at Journey Church (10700 75th St, Kenosha, WI). Visitation with the family will be at 9:30am and the service will be at 10:00am with Military Honors to follow. If attending the visitation or memorial service we ask that you please be respectful of others and practice social distancing guidelines. Walter will be interred at Southern Wisconsin Veterans Memorial Cemetery in Union Grove, WI at a later date. To leave Memories & Condolences to the family go to www.CaseyFamilyOptions.com. Donations can be made in Walter

-0.157082

0.129532

-0.747182

-1.370537

[ 0.1113742112093852, -0.42553855695812887 ]

[ 0.6353843325160634, -0.37632081592392763 ]

[ -0.3293363996939053, -1.165027817558022 ]

[ -1.0908895228468987, -1.6501841305212688 ]

1,024

[ 512, 512 ]

[ 263, 2217, 2586, 541, 769, 11785, 6419, 1250, 701, 515, 599, 310, 278, 12080, 540, 23051, 29889, 10705, 29915, 29879, 8750, 4121, 2200, 423, 471, 1559, 292, 363, 902, 4783, 472, 902, 3271, 411, 278, 1371, 310, 7828, 379, 4705, 625, 29892, 402, 332, 484, 29872, 29892, 17674, 29889, 10705, 29915, 29879, 4344, 892, 2221, 304, 18864, 931, 411, 1075, 10106, 278, 4723, 8236, 701, 304, 746, 1749, 22977, 368, 17852, 3614, 1075, 3271, 29889, 13, 29956, 13794, 471, 6345, 297, 383, 898, 868, 21095, 399, 29902, 304, 2259, 322, 476, 16490, 313, 8431, 407, 29897, 2261, 386, 11850, 29889, 940, 14283, 1880, 3762, 322, 278, 383, 898, 868, 21095, 15197, 6346, 29889, 940, 8300, 670, 9560, 322, 12355, 292, 6532, 4121, 2200, 423, 365, 538, 12387, 373, 6339, 29871, 29896, 29947, 29892, 29871, 29896, 29929, 29946, 29955, 297, 383, 898, 868, 21095, 29892, 399, 29902, 29889, 2688, 10398, 1009, 298, 650, 962, 6150, 297, 10059, 1156, 5622, 278, 7945, 304, 278, 4272, 29889, 10705, 322, 4121, 2200, 423, 892, 8300, 363, 29871, 29955, 29941, 2440, 29889, 1724, 399, 635, 27849, 1556, 471, 805, 2548, 931, 411, 3942, 29892, 6493, 292, 7875, 322, 471, 2337, 17762, 304, 2367, 263, 19912, 1361, 304, 1906, 297, 817, 29889, 13, 29956, 635, 471, 18195, 287, 2645, 2787, 3362, 1944, 322, 3512, 1549, 6996, 6694, 29914, 11345, 3762, 29889, 940, 471, 22799, 287, 297, 3111, 29871, 29896, 29929, 29946, 29946, 29889, 3600, 9121, 6919, 1288, 4266, 1017, 471, 263, 9204, 6607, 1061, 29892, 5057, 24839, 29889, 940, 6766, 297, 278, 4275, 5933, 14328, 16150, 310, 6607, 800, 322, 3512, 373, 304, 9080, 2645, 278, 22467, 10811, 29176, 322, 5115, 29524, 275, 373, 6136, 13360, 29892, 3086, 13211, 322, 2538, 20098, 29889, 3600, 9121, 2669, 931, 471, 925, 3273, 310, 29871, 29941, 29900, 2440, 29889, 940, 16528, 408, 385, 8811, 10842, 297, 2610, 29871, 29896, 29929, 29947, 29953, 29889, 1094, 263, 7631, 713, 670, 26818, 471, 263, 4309, 23045, 573, 4241, 841, 749, 27439, 293, 16876, 29889, 3436, 1338, 322, 10200, 800, 10705, 20591, 5134, 399, 29956, 1944, 3082, 16150, 7259, 8729, 27461, 6718, 29892, 8811, 310, 16117, 786, 362, 18416, 313, 29967, 21419, 511, 7197, 1281, 2199, 18416, 29892, 399, 29956, 2687, 7229, 706, 319, 1039, 2454, 29899, 29925, 562, 928, 7259, 8729, 18416, 29892, 8811, 310, 16117, 786, 362, 3086, 5282, 1947, 6692, 18416, 29892, 826, 2168, 25571, 27811, 29892, 8811, 7178, 616, 13223, 315, 7018, 411, 29871, 29896, 24132, 951, 2142, 2233, 5402, 29892, 422, 10222, 26571, 1171, 9178, 479, 29892, 4485, 29879, 1171, 390, 361, 280, 669, 349, 19639, 9178, 479, 29892, 322, 1222, 10700, 390, 361, 280, 669, 1704, 26062, 9178, 479, 29889, 940, 3796, 363, 278, 10317, 310, 5282, 1947, 408, 263, 18835, 1251, 17084, 363, 29871, 29896, 29945, 2440, 29889, 940, 471, 263, 4509, 310, 278, 478, 1308, 550, 310, 19358, 9149, 322, 471, 263, 16108, 21806, 1960, 11773, 261, 29889, 13, 29956, 635, 3796, 363, 278, 4412, 310, 10015, 359, 2350, 4103, 277, 10317, 408, 263, 3593, 7156, 322, 6694, 6615, 1061, 363, 29871, 29896, 29946, 2440, 2745, 3240, 8491, 297, 29871, 29896, 29929, 29929, 29946, 29889, 940, 26603, 6282, 3593, 363, 278, 27036, 9579, 7759, 3719, 322, 278, 10015, 359, 2350, 8168, 1144, 21573, 3815, 29889, 10705, 471, 263, 762, 29899, 6800, 7646, 6211, 18744, 261, 322, 3833, 29893, 585, 23137, 5826, 556, 13524, 29889, 13, 29956, 635, 338, 263, 4509, 310, 435, 473, 3801, 6291, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 8772, 402, 680, 787, 4623, 297, 29871, 29896, 29929, 29947, 29946, 322, 540, 471, 263, 4509, 310, 12790, 363, 278, 25133, 29889, 940, 23051, 1784, 12080, 2645, 670, 29871, 29941, 29906, 2440, 310, 1985, 411, 278, 7021, 390, 13873, 29889, 13, 29956, 13794, 338, 9399, 287, 297, 4892, 491, 11825, 2259, 322, 476, 16490, 2261, 386, 11850, 29892, 670, 27767, 18964, 4827, 313, 29933, 300, 1017, 29897, 2261, 386, 11850, 29892, 13832, 313, 29963, 440, 713, 29897, 2261, 386, 11850, 29892, 20179, 313, 29967, 2108, 9633, 29897, 2261, 386, 11850, 29892, 405, 493, 284, 347, 313, 3253, 22138, 29897, 379, 1657, 29892, 2661, 2276, 313, 29950, 3504, 29897, 6640, 29895, 25603, 29892, 322, 9579, 20336, 313, 29954, 536, 29891, 29897, 796, 6669, 29891, 29889, 13, 8179, 719, 292, 373, 670, 25000, 526, 670, 6532, 4121, 2200, 423, 2261, 386, 11850, 29892, 670, 4344, 10705, 313, 29933, 265, 2786, 29897, 2261, 386, 11850, 29892, 4699, 313, 29950, 18368, 29897, 2261, 386, 11850, 29892, 15862, 313, 29931, 272, 2733, 29897, 2261, 386, 11850, 29892, 4121, 2200, 423, 313, 18529, 29897, 8507, 10281, 29892, 8075, 313, 29940, 6906, 29897, 2261, 386, 11850, 29892, 322, 7266, 1233, 313, 11626, 275, 29897, 2610, 29880, 493, 29889, 6265, 11991, 29901, 23647, 295, 313, 2744, 386, 2592, 511, 319, 5022, 313, 29940, 23249, 511, 12936, 1416, 801, 313, 29967, 265, 11385, 511, 20983, 29892, 15862, 2330, 313, 5323, 455, 511, 23132, 29892, 18888, 29892, 11571, 29892, 6044, 339, 5570, 313, 18275, 511, 322, 4827, 29889, 7027, 6265, 11991, 29901, 2739, 3857, 29892, 7801, 29926, 10738, 29892, 476, 2486, 29876, 29892, 8612, 8903, 29892, 20212, 29892, 402, 29893, 948, 2147, 29872, 29892, 4755, 29892, 322, 341, 3028, 347, 29889, 13, 29909, 2626, 9020, 2669, 674, 367, 4934, 373, 5468, 29871, 29896, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 472, 435, 473, 3801, 6291, 313, 29896, 29900, 29955, 29900, 29900, 29871, 29955, 29945, 386, 624, 29892, 10015, 359, 2350, 29892, 399, 29902, 467, 5741, 7018, 411, 278, 3942, 674, 367, 472, 29871, 29929, 29901, 29941, 29900, 314, 322, 278, 2669, 674, 367, 472, 29871, 29896, 29900, 29901, 29900, 29900, 314, 411, 20080, 7906, 943, 304, 1101, 29889, 960, 1098, 2548, 278, 6493, 362, 470, 2626, 9020, 2669, 591, 2244, 393, 366, 3113, 367, 3390, 1319, 310, 4045, 322, 6944, 5264, 1320, 19985, 1410, 10652, 1475, 29889, 13, 29956, 13794, 674, 367, 1006, 1127, 472, 14234, 22581, 478, 1308, 550, 19722, 315, 22875, 297, 7761, 6070, 345, 29892, 399, 29902, 472, 263, 2678, 2635, 29889, 13, 1762, 5967, 8133, 3842, 669, 11790, 324, 2063, 304, 278, 3942, 748, 304, 7821, 29889, 8259, 29891, 27104, 5856, 29889, 510, 29889, 3872, 800, 508, 367, 1754, 297, 10705 ]

1,332,858

8,192

CommonCrawl

0

3

's name to Gideons International www.gideons.org. The family would like to thank Dr. Neil Shepler. Casey Family Options Funerals and Cremations Stephen P. Casey, Funeral Director and Owner 3016-75th Street, Kenosha WI 53142 www.CaseyFamilyOptions.com Barbara "Barb" M. Pofahl Barbara "Barb" M. Pofahl, 77, of Kenosha, passed away peacefully, Monday, June 29, 2020 at the Hospice Alliance Hospice House. Please see our webster for a complete obituary. Bruch Funeral Home Visit Barb's www.bruchfuneralhome.net Richard C. Smith Richard C. Smith, age 78 of Somers, WI, passed away on June 30, 2020 at his home. Born in Kenosha, WI on September 22, 1941, he was the son of the late Milton and Violet (Falk) Smith. Richard was a graduate of Bradford High School. Rich was employed as a Maintenance Mechanic with Chrysler. Prior to working at Chrysler, he was employed with Chevrolet Garage for 25 years and operated his own lawn service. He enjoyed spending time with his sons. Rich loved hunting, fishing, cribbage and most of all, his daily trips to play pull tabs with his black lab Sally. Rich is survived by his companion, Diane Gunderson; his children, Jeffrey (Tricia) Smith and Gregory Smith; his grandchildren, Ryan Dauster, Christopher Smith; his sister, Janann (Tom) Botzau; and his former wife Judy Smith. In addition to his parents, Rich was preceded in death by his daughter, Rhonda Smith. Services honoring Rich's life will be held privately. Inurnment will take place in St. George Cemetery. A Celebration of Rich's life will be held on Thursday, July 9, 2020 at 12 p.m. at Tina's Somers Inn, 8013-12th St, Somers, WI 53144. Laura Burke Laura Burke, of Camarillo, California, peacefully passed into heaven on May 14, 2020, at the age of 87. She was born in July of 1932, in Kenosha, Wisconsin, to Giuseppe (Joseph) Turco and Rose (Covelli) Turco, the second of their four children. As a child of the Depression she worked beside her parents to provide for the family, helping to plant crops, care for animals, preserve the harvest, and learned the value of a dollar. She often walked to town to do the family errands. Laura graduated from Mary D. Bradford High School in 1950. She worked at J.J. Newberry's and fondly remembered her days as a "soda jerk" at Mayer Drug in Kenosha. Later, she joined the work force at Great Lakes Naval Base in Illinois. One sunny day, when she was walking down the gravel road to add a letter to the mailbox, the boy next door, Hozie Burke, noticed her, and declared that they would be married one day. Laura told him that was "quite a line", but in October of 1953, they were joined in matrimony at Holy Rosary Catholic Church. They were married 64 years. In 1964 they moved to Oxnard, California, Hozie filling a position at Oxnard Air Force Base and Laura becoming a teller at the Bank of America branch serving the SeaBee base in Port Hueneme. They later relocated to Apple Valley, California. Laura worked for Bank of America for 23 years, becoming a loan officer, a branch manager and serving as a member of the regional staff. During those years she helped countless individuals buy their first homes, start businesses, realize goals, and overcome personal tragedy. She did this with skill, professionalism, grace, and compassion. Laura loved numbers—she actually enjoyed balancing her checkbook! But most of all, she treasured her faith, cherished her friends, and loved her family. Her thoughtfulness, the warmth of

0.027824

-0.687443

-0.935498

-1.741232

[ -0.7857631947848029, 0.8414112148657245 ]

[ -1.201800591907708, -0.17308447194527454 ]

[ -1.5480002123910466, -0.3229957971304447 ]

[ -1.9935650059306493, -1.4888991738895898 ]

1,024

[ 512, 512 ]

[ 29915, 29879, 1024, 304, 402, 680, 787, 4623, 7821, 29889, 29887, 680, 787, 29889, 990, 29889, 450, 3942, 723, 763, 304, 6452, 4942, 29889, 29334, 2296, 20069, 29889, 13, 8259, 29891, 14662, 25186, 13811, 261, 1338, 322, 315, 1745, 800, 13, 7789, 9789, 349, 29889, 11733, 29891, 29892, 13811, 13537, 15944, 322, 438, 23007, 13, 29941, 29900, 29896, 29953, 29899, 29955, 29945, 386, 7103, 29892, 10015, 359, 2350, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 13, 1636, 29889, 8259, 29891, 27104, 5856, 29889, 510, 13, 4297, 13839, 376, 4297, 29890, 29908, 341, 29889, 349, 974, 4494, 13, 4297, 13839, 376, 4297, 29890, 29908, 341, 29889, 349, 974, 4494, 29892, 29871, 29955, 29955, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 29892, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 472, 278, 379, 4705, 625, 29855, 379, 4705, 625, 5619, 29889, 13, 12148, 1074, 1749, 1856, 2475, 363, 263, 4866, 704, 1981, 653, 29889, 13, 29933, 582, 305, 13811, 13537, 8778, 13, 6116, 277, 21826, 29915, 29879, 13, 1636, 29889, 16670, 305, 7692, 13537, 5184, 29889, 1212, 13, 25627, 538, 315, 29889, 7075, 13, 25627, 538, 315, 29889, 7075, 29892, 5046, 29871, 29955, 29947, 310, 6254, 414, 29892, 399, 29902, 29892, 4502, 3448, 373, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 670, 3271, 29889, 13, 29933, 1398, 297, 10015, 359, 2350, 29892, 399, 29902, 373, 3839, 29871, 29906, 29906, 29892, 29871, 29896, 29929, 29946, 29896, 29892, 540, 471, 278, 1487, 310, 278, 5683, 3833, 880, 322, 478, 601, 1026, 313, 29943, 2235, 29897, 7075, 29889, 6123, 471, 263, 10591, 403, 310, 15862, 4006, 5057, 4523, 29889, 13, 25627, 471, 15723, 408, 263, 4241, 841, 749, 27439, 293, 411, 678, 18450, 1358, 29889, 22096, 304, 1985, 472, 678, 18450, 1358, 29892, 540, 471, 15723, 411, 6561, 29894, 307, 1026, 7455, 482, 363, 29871, 29906, 29945, 2440, 322, 19623, 670, 1914, 425, 1233, 2669, 29889, 13, 3868, 27849, 805, 2548, 931, 411, 670, 18025, 29889, 4385, 18012, 29826, 29892, 9427, 292, 29892, 274, 1091, 17807, 322, 1556, 310, 599, 29892, 670, 14218, 3367, 567, 304, 1708, 8206, 18859, 411, 670, 4628, 9775, 317, 635, 29889, 13, 25627, 338, 10503, 2347, 491, 670, 18708, 29892, 360, 16677, 402, 870, 1330, 29936, 670, 4344, 29892, 12208, 8903, 313, 29911, 2200, 423, 29897, 7075, 322, 29094, 7075, 29936, 670, 4595, 11991, 29892, 20916, 7266, 5402, 29892, 18888, 7075, 29936, 670, 9883, 29892, 2627, 812, 313, 21599, 29897, 11273, 29920, 585, 29936, 322, 670, 4642, 6532, 8660, 29891, 7075, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 4385, 471, 9399, 287, 297, 4892, 491, 670, 8750, 29892, 7861, 14287, 7075, 29889, 13, 13779, 4207, 8253, 4385, 29915, 29879, 2834, 674, 367, 4934, 5999, 2486, 29889, 512, 595, 358, 674, 2125, 2058, 297, 624, 29889, 5122, 315, 22875, 29889, 319, 315, 6146, 1182, 362, 310, 4385, 29915, 29879, 2834, 674, 367, 4934, 373, 498, 1295, 3250, 29892, 5468, 29871, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29896, 29906, 282, 29889, 29885, 29889, 472, 323, 1099, 29915, 29879, 6254, 414, 25408, 29892, 29871, 29947, 29900, 29896, 29941, 29899, 29896, 29906, 386, 624, 29892, 6254, 414, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29946, 29889, 13, 5661, 2002, 6640, 446, 13, 5661, 2002, 6640, 446, 29892, 310, 5500, 279, 9093, 29892, 8046, 29892, 10776, 3730, 4502, 964, 18356, 373, 2610, 29871, 29896, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 278, 5046, 310, 29871, 29947, 29955, 29889, 13, 13468, 471, 6345, 297, 5468, 310, 29871, 29896, 29929, 29941, 29906, 29892, 297, 10015, 359, 2350, 29892, 22581, 29892, 304, 18824, 313, 26473, 561, 29897, 5383, 1111, 322, 14008, 313, 29907, 586, 5481, 29897, 5383, 1111, 29892, 278, 1473, 310, 1009, 3023, 4344, 29889, 1094, 263, 2278, 310, 278, 897, 2590, 1183, 3796, 17620, 902, 11825, 304, 3867, 363, 278, 3942, 29892, 19912, 304, 8024, 8182, 567, 29892, 2562, 363, 15006, 29892, 19905, 278, 4023, 10147, 29892, 322, 10972, 278, 995, 310, 263, 11232, 279, 29889, 2296, 4049, 17096, 304, 4726, 304, 437, 278, 3942, 4589, 4167, 29889, 13, 5661, 2002, 23588, 515, 6182, 360, 29889, 15862, 4006, 5057, 4523, 297, 29871, 29896, 29929, 29945, 29900, 29889, 2296, 3796, 472, 435, 29889, 29967, 29889, 1570, 16344, 29915, 29879, 322, 6299, 368, 21832, 902, 3841, 408, 263, 376, 29879, 8887, 432, 5968, 29908, 472, 2610, 261, 360, 11124, 297, 10015, 359, 2350, 29889, 12699, 29892, 1183, 8772, 278, 664, 4889, 472, 7027, 365, 6926, 21590, 7399, 297, 17066, 29889, 13, 6716, 6575, 1460, 2462, 29892, 746, 1183, 471, 22049, 1623, 278, 2646, 955, 6520, 304, 788, 263, 5497, 304, 278, 10524, 1884, 29892, 278, 8023, 2446, 3050, 29892, 379, 2112, 347, 6640, 446, 29892, 10548, 902, 29892, 322, 8052, 393, 896, 723, 367, 8300, 697, 2462, 29889, 21671, 5429, 1075, 393, 471, 376, 339, 568, 263, 1196, 613, 541, 297, 5533, 310, 29871, 29896, 29929, 29945, 29941, 29892, 896, 892, 8772, 297, 1775, 5632, 2592, 472, 17733, 5678, 653, 11865, 6291, 29889, 2688, 892, 8300, 29871, 29953, 29946, 2440, 29889, 13, 797, 29871, 29896, 29929, 29953, 29946, 896, 6153, 304, 9471, 29876, 538, 29892, 8046, 29892, 379, 2112, 347, 27523, 263, 2602, 472, 9471, 29876, 538, 5593, 11004, 7399, 322, 21671, 14171, 263, 2649, 261, 472, 278, 10253, 310, 6813, 5443, 16330, 278, 14070, 3629, 29872, 2967, 297, 3371, 379, 3837, 2004, 29889, 2688, 2678, 337, 28809, 304, 12113, 13939, 29892, 8046, 29889, 21671, 3796, 363, 10253, 310, 6813, 363, 29871, 29906, 29941, 2440, 29892, 14171, 263, 24806, 12139, 29892, 263, 5443, 8455, 322, 16330, 408, 263, 4509, 310, 278, 14014, 13925, 29889, 7133, 1906, 2440, 1183, 9213, 2302, 2222, 15724, 15649, 1009, 937, 17774, 29892, 1369, 5381, 267, 29892, 16289, 14433, 29892, 322, 25688, 7333, 1020, 3192, 29891, 29889, 2296, 1258, 445, 411, 19911, 29892, 10257, 1608, 29892, 17659, 29892, 322, 752, 465, 291, 29889, 13, 5661, 2002, 18012, 3694, 30003, 11360, 2869, 27849, 6411, 19985, 902, 1423, 2909, 29991, 1205, 1556, 310, 599, 29892, 1183, 2578, 294, 2955, 902, 10847, 29892, 14954, 3276, 902, 7875, 29892, 322, 18012, 902, 3942, 29889, 2439, 2714, 1319, 2264, 29892, 278, 14294, 386, 310 ]

1,332,858

9,216

CommonCrawl

0

3

her home, and the hospitality she offered were legendary—the coffee, treats, and conversation were wonderful; there were amazing Italian dinners; and grandchildren and their friends could always count on a full cookie jar and her fabulous milkshakes. Laura is survived by her son, William Burke (Linda) of Camarillo; daughter, Laurie (Charles Vanoni) of Somis; five grandchildren, Matthew Vanoni, Mark (Gwyndolin) Vanoni, Michaela (Michael) Otani, Tierney (Michael) Meyer and Lee Burke; five great-grandchildren; brother, Guy Turco; and sister, Janet (Ewald) Weiss; as well as many much-loved in-laws, nieces and nephews. She was preceded in death by her husband, parents, and sister, Mary Jane Sorensen Due to restrictions imposed by COVID-19 mandates, funeral services and interment will be private. Arrangements are under the direction of Joseph P. Reardon Funeral Home, Ventura, California, and Proko Funeral Home, Kenosha, Wisconsin. Jon Buckingham January 21, 1939—June 25, 2020 Jon E. Buckingham, age 81 of Kenosha passed away peacefully on Thursday, June 25, 2020 at Burlington Memorial Hospital. Loving father of Ann Delaney; Dear grandfather of Jessica, Patrick, David, and Michael; brother of Tom (Mardell) Buckingham; special friend of Michael D. Klopp. A celebration of Jon's life will be held on Monday, July 6, 2020 at 2:00 p.m. at the funeral home. Friends are invited to meet with the family on Monday from 12:00 Noon until the time of the service. Memorial remembrances to Safe Harbor Humane Society, 7811 60th Ave., Kenosha, WI 53142 would be appreciated. Jon's complete obituary will be made available on the funeral home website on Wednesday, July 1, 2020. DRAEGER-LANGENDORF FUNERAL HOME & CREMATORY 4600 COUNTY LINE ROAD (corner of KR & 22nd Avenue) www.draeger-langendorf.com Ada DeBartolo Ada DeBartolo, 83, of Kenosha, passed away peacefully at her home on Monday, June 29, 2020, surrounded by her loving family. Born on April 9, 1937, in Marano Principato, Prov. of Cosenza, Italy, she was the daughter of the late Serafino and Maria (Filippelli) Bosco. In 1955, she came from Italy to Kenosha to make her home. On September 12, 1954, she married Ignazio DeBartolo in Italy. He preceded her in death on January 6, 2009. Ada and Ignazio owned and operated DeBartolo's Deli & Liquor from 1974 until 2000 when they retired. Ada was a member of Our Lady of Mt. Carmel Catholic Church. She greatly enjoyed cooking and entertaining family and friends, knitting blankets with love, baking and playing old maid with her grandchildren, telling stories of Italy while listening to Elvis and her Italian favorites, gardening and planting flowers, traveling all over the world with the love of her life, and her daily phone calls with her siblings. Above all else, she treasured her time spent being surrounded by her family. Surviving Ada are her six adoring children, Frank (Peggy) DeBartolo of Salem, Susan DeBartolo of Pleasant Prairie, Tina (John) Serpe of Pleasant Prairie, Carla (Scott) Lamos of Kenosha, Sandy (Robert) Morrone of Kenosha, and Tony (Katie) DeBartolo of Pleasant Prairie; her ten grandchildren, Nicole (Eddie) Briggs-Mulloy, Michael Briggs, Vincent (Charlotte) Morrone, Vanessa (Michael) Ambrosini, Francesca Ser

0.19471

-1.063922

-1.464304

-1.876503

[ 0.5510400239179873, -0.16161922273293022 ]

[ -0.9797626478253028, -1.1480817344684164 ]

[ -1.4110431970202961, -1.5175653200864354 ]

[ -1.8010636060799359, -1.9519430816386032 ]

1,024

[ 512, 512 ]

[ 902, 3271, 29892, 322, 278, 13457, 537, 1183, 12520, 892, 15983, 653, 30003, 1552, 26935, 29892, 2578, 1446, 29892, 322, 14983, 892, 20695, 29936, 727, 892, 21863, 292, 10545, 270, 16697, 29936, 322, 4595, 11991, 322, 1009, 7875, 1033, 2337, 2302, 373, 263, 2989, 15327, 14631, 322, 902, 10135, 352, 681, 27274, 845, 6926, 29889, 13, 5661, 2002, 338, 10503, 2347, 491, 902, 1487, 29892, 4667, 6640, 446, 313, 29931, 11054, 29897, 310, 5500, 279, 9093, 29936, 8750, 29892, 14019, 347, 313, 5914, 793, 6556, 5271, 29897, 310, 6254, 275, 29936, 5320, 4595, 11991, 29892, 22292, 6556, 5271, 29892, 4485, 313, 29954, 12822, 299, 22878, 29897, 6556, 5271, 29892, 3375, 29874, 3100, 313, 24083, 29897, 8540, 3270, 29892, 29088, 3801, 313, 24083, 29897, 26581, 322, 9371, 6640, 446, 29936, 5320, 2107, 29899, 27857, 11991, 29936, 8099, 29892, 15880, 5383, 1111, 29936, 322, 9883, 29892, 2627, 300, 313, 29923, 18370, 29897, 1334, 790, 29936, 408, 1532, 408, 1784, 1568, 29899, 417, 1490, 297, 29899, 433, 5652, 29892, 4930, 778, 322, 23446, 354, 5652, 29889, 13, 13468, 471, 9399, 287, 297, 4892, 491, 902, 10216, 29892, 11825, 29892, 322, 9883, 29892, 6182, 10447, 17784, 14762, 13, 29928, 434, 304, 25091, 527, 4752, 491, 19937, 29899, 29896, 29929, 9619, 1078, 29892, 2090, 13537, 5786, 322, 1006, 358, 674, 367, 2024, 29889, 13, 16401, 574, 4110, 526, 1090, 278, 5305, 310, 6936, 349, 29889, 830, 20342, 13811, 13537, 8778, 29892, 21141, 2002, 29892, 8046, 29892, 322, 1019, 2901, 13811, 13537, 8778, 29892, 10015, 359, 2350, 29892, 22581, 29889, 13, 29967, 265, 16281, 16094, 13, 29967, 15623, 653, 29871, 29906, 29896, 29892, 29871, 29896, 29929, 29941, 29929, 30003, 29967, 1540, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 13, 29967, 265, 382, 29889, 16281, 16094, 29892, 5046, 29871, 29947, 29896, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 498, 1295, 3250, 29892, 5306, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 472, 6640, 1847, 880, 19722, 15967, 29889, 13, 29931, 21081, 4783, 310, 8081, 5556, 273, 1032, 29936, 360, 799, 4595, 22212, 310, 23010, 983, 29892, 14875, 29892, 4699, 29892, 322, 5765, 29936, 8099, 310, 4335, 313, 29924, 538, 514, 29897, 16281, 16094, 29936, 4266, 5121, 310, 5765, 360, 29889, 476, 417, 407, 29889, 13, 29909, 10894, 362, 310, 9937, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 29889, 11169, 1975, 526, 23610, 304, 5870, 411, 278, 3942, 373, 27822, 515, 29871, 29896, 29906, 29901, 29900, 29900, 1939, 265, 2745, 278, 931, 310, 278, 2669, 29889, 19722, 1083, 1590, 661, 778, 304, 5701, 1725, 3536, 4089, 13863, 1662, 7765, 29892, 29871, 29955, 29947, 29896, 29896, 29871, 29953, 29900, 386, 319, 345, 1696, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 723, 367, 7556, 29889, 9937, 29915, 29879, 4866, 704, 1981, 653, 674, 367, 1754, 3625, 373, 278, 2090, 13537, 3271, 4700, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 29928, 4717, 11787, 1001, 29899, 29931, 19453, 11794, 1955, 29943, 383, 3904, 1001, 1964, 29832, 2303, 669, 315, 1525, 29924, 1299, 18929, 13, 29946, 29953, 29900, 29900, 21122, 29979, 365, 8895, 16641, 3035, 13, 29898, 2616, 1089, 310, 476, 29934, 669, 29871, 29906, 29906, 299, 18874, 29897, 13, 1636, 29889, 19811, 387, 261, 29899, 3893, 21466, 29889, 510, 13, 29909, 1388, 897, 29933, 442, 3543, 13, 29909, 1388, 897, 29933, 442, 3543, 29892, 29871, 29947, 29941, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 472, 902, 3271, 373, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 22047, 491, 902, 12355, 292, 3942, 29889, 13, 29933, 1398, 373, 3786, 29871, 29929, 29892, 29871, 29896, 29929, 29941, 29955, 29892, 297, 1085, 1562, 14771, 29886, 1219, 29892, 9133, 29889, 310, 13526, 5723, 29892, 12730, 29892, 1183, 471, 278, 8750, 310, 278, 5683, 317, 1572, 29888, 1789, 322, 6217, 313, 29943, 2638, 407, 5481, 29897, 10211, 1111, 29889, 512, 29871, 29896, 29929, 29945, 29945, 29892, 1183, 2996, 515, 12730, 304, 10015, 359, 2350, 304, 1207, 902, 3271, 29889, 1551, 3839, 29871, 29896, 29906, 29892, 29871, 29896, 29929, 29945, 29946, 29892, 1183, 8300, 18076, 834, 601, 897, 29933, 442, 3543, 297, 12730, 29889, 940, 9399, 287, 902, 297, 4892, 373, 5490, 29871, 29953, 29892, 29871, 29906, 29900, 29900, 29929, 29889, 13, 29909, 1388, 322, 18076, 834, 601, 15205, 322, 19623, 897, 29933, 442, 3543, 29915, 29879, 360, 5037, 669, 2718, 339, 272, 515, 29871, 29896, 29929, 29955, 29946, 2745, 29871, 29906, 29900, 29900, 29900, 746, 896, 16528, 29889, 13, 29909, 1388, 471, 263, 4509, 310, 8680, 10040, 310, 341, 29873, 29889, 1704, 12873, 11865, 6291, 29889, 2296, 11180, 27849, 7984, 292, 322, 22684, 292, 3942, 322, 7875, 29892, 889, 5367, 9654, 1691, 411, 5360, 29892, 289, 5086, 322, 8743, 2030, 611, 333, 411, 902, 4595, 11991, 29892, 14509, 15874, 310, 12730, 1550, 19866, 304, 1260, 1730, 322, 902, 10545, 7853, 3246, 29892, 16423, 292, 322, 8024, 292, 18281, 29892, 9850, 292, 599, 975, 278, 3186, 411, 278, 5360, 310, 902, 2834, 29892, 322, 902, 14218, 9008, 5717, 411, 902, 27767, 18964, 29889, 319, 29205, 599, 1683, 29892, 1183, 2578, 294, 2955, 902, 931, 10398, 1641, 22047, 491, 902, 3942, 29889, 13, 18498, 29894, 4357, 23255, 526, 902, 4832, 594, 8253, 4344, 29892, 4976, 313, 29925, 387, 1927, 29897, 897, 29933, 442, 3543, 310, 317, 12698, 29892, 25914, 897, 29933, 442, 3543, 310, 19777, 13186, 9002, 24135, 29892, 323, 1099, 313, 11639, 29897, 1816, 412, 310, 19777, 13186, 9002, 24135, 29892, 1704, 433, 313, 4421, 1501, 29897, 12718, 359, 310, 10015, 359, 2350, 29892, 8564, 29891, 313, 9588, 2151, 29897, 3879, 29878, 650, 310, 10015, 359, 2350, 29892, 322, 15293, 313, 29968, 9474, 29897, 897, 29933, 442, 3543, 310, 19777, 13186, 9002, 24135, 29936, 902, 3006, 4595, 11991, 29892, 405, 23249, 313, 29923, 1289, 347, 29897, 13051, 3174, 29899, 29924, 352, 2376, 29892, 5765, 13051, 3174, 29892, 19748, 313, 5914, 8276, 371, 29897, 3879, 29878, 650, 29892, 6556, 9297, 313, 24083, 29897, 15145, 1883, 2172, 29892, 10986, 1113, 1816 ]

1,332,858

10,240

CommonCrawl

0

3

pe, Ignazio (Diamond) DeBartolo, McKenzie Lamos, Luciano, Ava, and Enzo DeBartolo; one great-grandchild, Ignazio Francesco DeBartolo III; brother, Aldo (Connie) Bosco; sister, Iolanda (Mario) Sorrentino; two brothers-in-law, Eugenio "Gino" (Connie) DeBartolo and Orlando Bartello; and three sisters-in-law, Irma Bosco, Ersilia (Domenico) Casalena and Gloria Presta. She was preceded in death by her great-grandson, Benjamin Robert Morrone in infancy; brother, Francesco Bosco; two sisters-in-law, Carmella Ruffolo and Emma Bartello; and brother-in-law, Aldo Presta. The family would like to extend a special Thank You to Dr. Giuseppe Garretto and his staff, and the staff of Hospice Alliance and the staff at Society Assets for the wonderful care that was extended to Ada and her family during her illness. A visitation will be held on Monday, July 6, 2020, at Proko Funeral Home from 4:00 p.m. until 7:00 p.m. For the safety and security of our guests we will require those in attendance to wear a face covering. We thank everyone for their understanding and cooperation during this difficult time. A private Mass of Christian Burial will be celebrated at Our Lady of Mt. Carmel Catholic Church with entombment following at All Saints Mausoleum. Visit Ada's Online Memorial Book at: Stanley M. Widzins Stanley M. Widzins, 80 years old of Kenosha, WI passed away Monday, June 29, 2020, at his home surrounded by his family. He was born September 19, 1939, in Cambridge, NJ the son of the late John and Jane (Anderson) Widzins. He lived in Tomah, WI and Grayslake, IL before settling in Kenosha in 1996. Stan proudly served in the U.S. Army from 1966-1972 before being honorably discharged. On June 25, 1987, Stan married MaryAnn (Tokarz) in Tomah, WI. He went on to work as a civilian in engineering maintenance at Ft. McCoy and Ft. Sheridan before retiring in 1991. Stan was a member of Christian Life Church, Delavan, WI and participated in many mission trips to places like Guatemala, Costa Rica, and Peru, volunteering his time and devotion to others. He was also a chaplain at the Kenosha County Detention Center for several years. Stan was a family man and cherished the time he spent with his grandchildren and great-grandchildren. Survivors include his wife of 33 years, MaryAnn; his children, Michael Widzins, Ken (Laura) Widzins, Daniel (Karla) Widzins, Dawn (Lesley) Fitzgerald, Denny (Marcia) Steele, and Holly (Matt) Dufek; two brothers, Joseph Widzins and John Widzins; 18 grandchildren and 3 great-grandchildren. In addition to his parents, Stanley was preceded in death by a daughter, Jackie Widzins; and a brother, Walt Widzins. Funeral services will be held at a later date. Arrangements were entrusted to Proko Funeral Home. Visit & Sign Stan's Marilyn Emma Ehlen Marilyn Emma Ehlen, 90 years old of Nokomis, FL, passed away Wednesday, June 24, 2020. She was born April 5, 1930 in Kenosha, WI, the daughter of the late Reinhardt and Emma (Barth) Hoffmann. She attended Kenosha schools. On February 1, 1950, she married Jack Ehlen in Kenosha, WI. He preceded her in death in 1982. In 1985, Marilyn moved to Las Vegas, NV, to escape Wisconsin winters. She was employed by the City of Las Vegas until her retirement in 1998. She and

-0.2884

-0.731313

-1.322275

-1.657988

[ -0.4803255741180793, -0.0964740351411767 ]

[ -1.1051066485169831, -0.35751921582017554 ]

[ -1.7356820482694826, -0.9088674739942109 ]

[ -1.712617016959338, -1.6033594656927168 ]

1,024

[ 512, 512 ]

[ 412, 29892, 18076, 834, 601, 313, 29928, 2829, 898, 29897, 897, 29933, 442, 3543, 29892, 24053, 264, 3914, 12718, 359, 29892, 23817, 1562, 29892, 319, 1564, 29892, 322, 1174, 2502, 897, 29933, 442, 3543, 29936, 697, 2107, 29899, 27857, 5145, 29892, 18076, 834, 601, 16922, 897, 29933, 442, 3543, 4786, 29936, 8099, 29892, 18242, 29877, 313, 1168, 2786, 29897, 10211, 1111, 29936, 9883, 29892, 306, 324, 5863, 313, 29924, 2628, 29897, 17784, 7771, 1789, 29936, 1023, 21383, 29899, 262, 29899, 10653, 29892, 22864, 601, 376, 29954, 1789, 29908, 313, 1168, 2786, 29897, 897, 29933, 442, 3543, 322, 1394, 28514, 12245, 3156, 29936, 322, 2211, 9883, 29879, 29899, 262, 29899, 10653, 29892, 6600, 655, 10211, 1111, 29892, 1425, 29879, 11836, 313, 29928, 2770, 1417, 29897, 6960, 284, 2386, 322, 8467, 4108, 1588, 4405, 29889, 13, 13468, 471, 9399, 287, 297, 4892, 491, 902, 2107, 29899, 27857, 1100, 29892, 20212, 4755, 3879, 29878, 650, 297, 3041, 6906, 29936, 8099, 29892, 16922, 10211, 1111, 29936, 1023, 9883, 29879, 29899, 262, 29899, 10653, 29892, 1704, 29885, 3547, 390, 3096, 3543, 322, 26422, 12245, 3156, 29936, 322, 8099, 29899, 262, 29899, 10653, 29892, 18242, 29877, 1588, 4405, 29889, 13, 1576, 3942, 723, 763, 304, 10985, 263, 4266, 3374, 887, 304, 4942, 29889, 18824, 7455, 21161, 322, 670, 13925, 29892, 322, 278, 13925, 310, 379, 4705, 625, 29855, 322, 278, 13925, 472, 7765, 1094, 7224, 363, 278, 20695, 2562, 393, 471, 10410, 304, 23255, 322, 902, 3942, 2645, 902, 4486, 2264, 29889, 13, 29909, 6493, 362, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 1019, 2901, 13811, 13537, 8778, 515, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 2745, 29871, 29955, 29901, 29900, 29900, 282, 29889, 29885, 29889, 1152, 278, 15332, 322, 6993, 310, 1749, 28865, 591, 674, 1996, 1906, 297, 14333, 749, 304, 19531, 263, 3700, 21653, 29889, 1334, 6452, 14332, 363, 1009, 8004, 322, 1302, 16453, 2645, 445, 5189, 931, 29889, 319, 2024, 7360, 310, 6111, 6640, 616, 674, 367, 26301, 472, 8680, 10040, 310, 341, 29873, 29889, 1704, 12873, 11865, 6291, 411, 875, 3424, 358, 1494, 472, 2178, 14342, 1372, 341, 1485, 1772, 398, 29889, 13, 6116, 277, 23255, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 855, 273, 2330, 341, 29889, 399, 333, 29920, 1144, 13, 855, 273, 2330, 341, 29889, 399, 333, 29920, 1144, 29892, 29871, 29947, 29900, 2440, 2030, 310, 10015, 359, 2350, 29892, 399, 29902, 4502, 3448, 27822, 29892, 5306, 29871, 29906, 29929, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 472, 670, 3271, 22047, 491, 670, 3942, 29889, 13, 3868, 471, 6345, 3839, 29871, 29896, 29929, 29892, 29871, 29896, 29929, 29941, 29929, 29892, 297, 12585, 29892, 405, 29967, 278, 1487, 310, 278, 5683, 2259, 322, 10447, 313, 2855, 1330, 29897, 399, 333, 29920, 1144, 29889, 940, 10600, 297, 4335, 801, 29892, 399, 29902, 322, 18956, 29879, 433, 446, 29892, 17674, 1434, 3604, 1847, 297, 10015, 359, 2350, 297, 29871, 29896, 29929, 29929, 29953, 29889, 13, 855, 273, 22314, 368, 6766, 297, 278, 501, 29889, 29903, 29889, 8811, 515, 29871, 29896, 29929, 29953, 29953, 29899, 29896, 29929, 29955, 29906, 1434, 1641, 10657, 2197, 766, 25389, 287, 29889, 1551, 5306, 29871, 29906, 29945, 29892, 29871, 29896, 29929, 29947, 29955, 29892, 7813, 8300, 6182, 2744, 29876, 313, 29911, 554, 11129, 29897, 297, 4335, 801, 29892, 399, 29902, 29889, 940, 3512, 373, 304, 664, 408, 263, 7631, 713, 297, 21639, 25413, 472, 383, 29873, 29889, 4052, 7967, 29891, 322, 383, 29873, 29889, 17375, 29219, 1434, 3240, 8491, 297, 29871, 29896, 29929, 29929, 29896, 29889, 13, 855, 273, 471, 263, 4509, 310, 6111, 4634, 6291, 29892, 5556, 29080, 29892, 399, 29902, 322, 25223, 297, 1784, 10655, 3367, 567, 304, 7600, 763, 2088, 17533, 2883, 29892, 17513, 29750, 29892, 322, 25493, 29892, 27886, 3241, 670, 931, 322, 2906, 8194, 304, 4045, 29889, 940, 471, 884, 263, 10708, 7420, 472, 278, 10015, 359, 2350, 5127, 5953, 2509, 7817, 363, 3196, 2440, 29889, 7813, 471, 263, 3942, 767, 322, 14954, 3276, 278, 931, 540, 10398, 411, 670, 4595, 11991, 322, 2107, 29899, 27857, 11991, 29889, 13, 18498, 24759, 943, 3160, 670, 6532, 310, 29871, 29941, 29941, 2440, 29892, 6182, 2744, 29876, 29936, 670, 4344, 29892, 5765, 399, 333, 29920, 1144, 29892, 10015, 313, 5661, 2002, 29897, 399, 333, 29920, 1144, 29892, 8432, 313, 24115, 433, 29897, 399, 333, 29920, 1144, 29892, 7266, 1233, 313, 24560, 2330, 29897, 22963, 914, 2741, 29892, 3384, 1460, 313, 7083, 1512, 29897, 2443, 6146, 29892, 322, 4168, 368, 313, 29924, 1131, 29897, 360, 1137, 1416, 29936, 1023, 21383, 29892, 6936, 399, 333, 29920, 1144, 322, 2259, 399, 333, 29920, 1144, 29936, 29871, 29896, 29947, 4595, 11991, 322, 29871, 29941, 2107, 29899, 27857, 11991, 29889, 13, 797, 6124, 304, 670, 11825, 29892, 21631, 471, 9399, 287, 297, 4892, 491, 263, 8750, 29892, 5457, 347, 399, 333, 29920, 1144, 29936, 322, 263, 8099, 29892, 399, 1997, 399, 333, 29920, 1144, 29889, 13, 25394, 13537, 5786, 674, 367, 4934, 472, 263, 2678, 2635, 29889, 25681, 574, 4110, 892, 9953, 16656, 304, 1019, 2901, 13811, 13537, 8778, 29889, 13, 6116, 277, 669, 9954, 7813, 29915, 29879, 13, 7083, 309, 948, 26422, 382, 29785, 13, 7083, 309, 948, 26422, 382, 29785, 29892, 29871, 29929, 29900, 2440, 2030, 310, 405, 554, 290, 275, 29892, 383, 29931, 29892, 4502, 3448, 15050, 4515, 3250, 29892, 5306, 29871, 29906, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 2296, 471, 6345, 3786, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29900, 297, 10015, 359, 2350, 29892, 399, 29902, 29892, 278, 8750, 310, 278, 5683, 18334, 25603, 322, 26422, 313, 4297, 386, 29897, 22151, 4403, 29889, 2296, 14283, 10015, 359, 2350, 12462, 29889, 1551, 6339, 29871, 29896, 29892, 29871, 29896, 29929, 29945, 29900, 29892, 1183, 8300, 5457, 382, 29785, 297, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 9399, 287, 902, 297, 4892, 297, 29871, 29896, 29929, 29947, 29906, 29889, 512, 29871, 29896, 29929, 29947, 29945, 29892, 1085, 309, 948, 6153, 304, 7413, 17236, 294, 29892, 405, 29963, 29892, 304, 10169, 22581, 13851, 29879, 29889, 2296, 471, 15723, 491, 278, 4412, 310, 7413, 17236, 294, 2745, 902, 3240, 19211, 297, 29871, 29896, 29929, 29929, 29947, 29889, 2296, 322 ]

1,332,858

11,264

CommonCrawl

0

3

her sister Carol enjoyed many years in Las Vegas, welcoming family and friends into the home they shared. In 2013, Marilyn returned to Wisconsin to be close to her family. In 2016 she moved to Nokomis, FL, with John and Diane. Marilyn is survived by her brother John Hoffmann of Kenosha, WI; her children John (Diane) Ehlen of Nokomis, FL, and Douglas Ehlen of Fullerton, CA; her two granddaughters, Tanya Parent of Kenosha, WI, and Linda Ehlen of Milwaukee, WI; three grandchildren, Branden, Dean & Elizabeth Parent of Kenosha, WI; and many nieces, nephews, cousins and friends. In addition to her parents and her husband, she was preceded in death by eight siblings, Ruth Hoffmann, June Kubert, Hope Cole, Doris Bosman, Audrea VanArsdale, Raymond Hoffmann, Alice Theivagt and Carol LeMay. Memorial remembrances in Marilyn's name can be made to: Tidewell Hospice or the Alzheimer's Association There will be a memorial service for family and friends at a later date Full obituary information will appear in Sunday's newspaper. Visit Ada's Online Memorial Book at: Roger A. Nicholson Roger A. Nicholson, 80, of Kenosha, passed away peacefully, Tuesday, June 30, 2020 at Froedtert So. Kenosha Medical Center Campus. Private Family Services will be held. Visit Roger's Beverly J. DeSeife (Née: Seehafer) Beverly J (Néee: Seehafer) DeSeife, 74, of Marshfield, WI, peacefully passed away at her home June 26, 2020, in Kenosha WI. Beverly was born in Marshfield, WI, to the late Chester & Angeline (Luther) Seehafer on the June 19,1946. She graduated from Marshfield Sr. High class of 1964 and then moved to Kenosha, WI. She married David J. DeSeife of Kenosha, WI, on August 27, 1966. Beverly retired form American Motor Corporation / Chrysler with over 30 years of service. She also attended Gateway Technical Collage while obtaining her associates degree for Interior Design. Beverly was a hard worker who loved gardening to her last day. She loved her dear friends with all her heart. She enjoyed boating, golfing, bowling, softball and riding motorcycles. Beverly is preceded in death by her loving husband, David J DeSeife; parents, Chester & Angeline Seehafer; and one beloved brother, Charles Seehafer. Beverly is survived by two sons, Daniel DeSeife of Kenosha, WI, & Douglas (Elizabeth) DeSeife of Kenosha, WI; her beloved brothers and sisters, Rodney (Patty) Seehafer of Marshfield, WI, Carol (Ed) Schulze of Naples, FL, James (Pat) Seehafer of Marshfield, WI, Dian (Lloyd) Mueller of Marshfield, WI, Bruce (Kris) Seehafer of Marshfield, WI, Gary (Annie) Seehafer of Marshfield, WI, and Alan (Kathy) Seehafer of Marshfield, WI. Also surviving Beverly are her precious grandchildren, Jessica (Kyle) Worcester, Emily (Brandon) Prell, John DeSeife, Randy DeSeife, Leah DeSeife, Destini Elisasson and David, Derek, Nathaniel and Ryan DeSeife. She is further survived by many cousins, nieces, nephews and in-laws to whom she loved dearly. A celebration of Beverly's life will be held on Monday, July 6, 2020, 6:00pm, at Draeger-Langendorf Funeral Home and Crematory, 4600 County Line Road, Mount Pleasant. Visitation will be from 5:00pm until the time of the service. The service will be live streamed via YouTube

-0.050419

-0.904556

-1.274086

-1.684002

[ 0.12096193921237652, -0.22179933689456324 ]

[ -0.8759061901093391, -0.9332063047112501 ]

[ -1.2943761098526196, -1.2537962534464715 ]

[ -1.6605896115942802, -1.7074142764228322 ]

1,024

[ 512, 512 ]

[ 902, 9883, 8562, 27849, 1784, 2440, 297, 7413, 17236, 294, 29892, 5476, 11506, 3942, 322, 7875, 964, 278, 3271, 896, 7258, 29889, 512, 29871, 29906, 29900, 29896, 29941, 29892, 1085, 309, 948, 4133, 304, 22581, 304, 367, 3802, 304, 902, 3942, 29889, 512, 29871, 29906, 29900, 29896, 29953, 1183, 6153, 304, 405, 554, 290, 275, 29892, 383, 29931, 29892, 411, 2259, 322, 360, 16677, 29889, 13, 7083, 309, 948, 338, 10503, 2347, 491, 902, 8099, 2259, 22151, 4403, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 902, 4344, 2259, 313, 29928, 16677, 29897, 382, 29785, 310, 405, 554, 290, 275, 29892, 383, 29931, 29892, 322, 16721, 382, 29785, 310, 14846, 28634, 29892, 12766, 29936, 902, 1023, 4595, 29881, 6334, 2153, 29892, 323, 20912, 22280, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 322, 365, 11054, 382, 29785, 310, 3833, 29893, 585, 23137, 29892, 399, 29902, 29936, 2211, 4595, 11991, 29892, 1771, 7257, 29892, 23263, 669, 13061, 22280, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 274, 681, 1144, 322, 7875, 29889, 512, 6124, 304, 902, 11825, 322, 902, 10216, 29892, 1183, 471, 9399, 287, 297, 4892, 491, 9475, 27767, 18964, 29892, 23130, 22151, 4403, 29892, 5306, 29024, 814, 29892, 7963, 16816, 29892, 9579, 275, 10211, 1171, 29892, 8612, 5638, 6556, 1433, 4928, 744, 29892, 21380, 22151, 4403, 29892, 16308, 450, 440, 21416, 322, 8562, 951, 12703, 29889, 13, 11442, 9020, 1083, 1590, 661, 778, 297, 1085, 309, 948, 29915, 29879, 1024, 508, 367, 1754, 304, 29901, 13, 29911, 680, 5872, 379, 4705, 625, 470, 278, 838, 29920, 27400, 29915, 29879, 7993, 13, 8439, 674, 367, 263, 2626, 9020, 2669, 363, 3942, 322, 7875, 472, 263, 2678, 2635, 13, 13658, 704, 1981, 653, 2472, 674, 2615, 297, 16340, 29915, 29879, 19656, 29889, 13, 6116, 277, 23255, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 29934, 468, 261, 319, 29889, 16371, 324, 1100, 13, 29934, 468, 261, 319, 29889, 16371, 324, 1100, 29892, 29871, 29947, 29900, 29892, 310, 10015, 359, 2350, 29892, 4502, 3448, 10776, 3730, 29892, 323, 1041, 3250, 29892, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 472, 25022, 287, 357, 29873, 1105, 29889, 10015, 359, 2350, 20795, 7817, 7259, 375, 29889, 13, 25207, 14662, 15538, 674, 367, 4934, 29889, 13, 6116, 277, 14159, 29915, 29879, 13, 29933, 1310, 368, 435, 29889, 897, 2008, 1607, 313, 29940, 1318, 29901, 2823, 2350, 571, 29897, 13, 29933, 1310, 368, 435, 313, 29940, 1318, 29872, 29901, 2823, 2350, 571, 29897, 897, 2008, 1607, 29892, 29871, 29955, 29946, 29892, 310, 13216, 2671, 29892, 399, 29902, 29892, 10776, 3730, 4502, 3448, 472, 902, 3271, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 297, 10015, 359, 2350, 399, 29902, 29889, 13, 29933, 1310, 368, 471, 6345, 297, 13216, 2671, 29892, 399, 29902, 29892, 304, 278, 5683, 678, 4156, 669, 3218, 5570, 313, 29931, 14107, 29897, 2823, 2350, 571, 373, 278, 5306, 29871, 29896, 29929, 29892, 29896, 29929, 29946, 29953, 29889, 2296, 23588, 515, 13216, 2671, 26250, 29889, 5057, 770, 310, 29871, 29896, 29929, 29953, 29946, 322, 769, 6153, 304, 10015, 359, 2350, 29892, 399, 29902, 29889, 2296, 8300, 4699, 435, 29889, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 373, 3111, 29871, 29906, 29955, 29892, 29871, 29896, 29929, 29953, 29953, 29889, 350, 1310, 368, 16528, 883, 3082, 16843, 15025, 847, 678, 18450, 1358, 411, 975, 29871, 29941, 29900, 2440, 310, 2669, 29889, 2296, 884, 14283, 22510, 1582, 8364, 936, 1530, 6184, 1550, 4017, 292, 902, 4067, 1078, 7426, 363, 4124, 1611, 12037, 29889, 350, 1310, 368, 471, 263, 2898, 15645, 1058, 18012, 16423, 292, 304, 902, 1833, 2462, 29889, 2296, 18012, 902, 9425, 7875, 411, 599, 902, 5192, 29889, 2296, 27849, 1045, 1218, 29892, 29416, 292, 29892, 12580, 1847, 29892, 4964, 2135, 322, 364, 4821, 10992, 1270, 7799, 29889, 13, 29933, 1310, 368, 338, 9399, 287, 297, 4892, 491, 902, 12355, 292, 10216, 29892, 4699, 435, 897, 2008, 1607, 29936, 11825, 29892, 678, 4156, 669, 3218, 5570, 2823, 2350, 571, 29936, 322, 697, 1339, 8238, 8099, 29892, 5322, 2823, 2350, 571, 29889, 13, 29933, 1310, 368, 338, 10503, 2347, 491, 1023, 18025, 29892, 8432, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29892, 669, 16721, 313, 6489, 466, 9394, 29897, 897, 2008, 1607, 310, 10015, 359, 2350, 29892, 399, 29902, 29936, 902, 1339, 8238, 21383, 322, 9883, 29879, 29892, 7733, 3801, 313, 11457, 1017, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 8562, 313, 3853, 29897, 12988, 911, 310, 8344, 793, 29892, 383, 29931, 29892, 5011, 313, 11457, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 360, 713, 313, 29931, 18966, 29897, 8229, 4539, 310, 13216, 2671, 29892, 399, 29902, 29892, 18885, 313, 29968, 3780, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 23529, 313, 2744, 2786, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29892, 322, 17102, 313, 29968, 493, 29891, 29897, 2823, 2350, 571, 310, 13216, 2671, 29892, 399, 29902, 29889, 3115, 10503, 4357, 350, 1310, 368, 526, 902, 758, 8802, 4595, 11991, 29892, 23010, 983, 313, 29968, 1508, 29897, 19662, 29883, 4156, 29892, 2812, 2354, 313, 12432, 9214, 29897, 4721, 645, 29892, 2259, 897, 2008, 1607, 29892, 390, 13910, 897, 2008, 1607, 29892, 951, 801, 897, 2008, 1607, 29892, 15435, 2172, 21279, 465, 265, 322, 4699, 29892, 360, 20400, 29892, 27650, 709, 322, 20916, 897, 2008, 1607, 29889, 2296, 338, 4340, 10503, 2347, 491, 1784, 274, 681, 1144, 29892, 4930, 778, 29892, 23446, 354, 5652, 322, 297, 29899, 433, 5652, 304, 6029, 1183, 18012, 9425, 368, 29889, 13, 29909, 10894, 362, 310, 350, 1310, 368, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 29871, 29953, 29901, 29900, 29900, 3358, 29892, 472, 16322, 387, 261, 29899, 29931, 574, 21466, 13811, 13537, 8778, 322, 315, 1745, 7606, 29892, 29871, 29946, 29953, 29900, 29900, 5127, 7407, 9321, 29892, 8040, 19777, 13186, 29889, 5741, 7018, 674, 367, 515, 29871, 29945, 29901, 29900, 29900, 3358, 2745, 278, 931, 310, 278, 2669, 29889, 450, 2669, 674, 367, 5735, 4840, 287, 3025, 14711 ]

1,332,858

12,288

CommonCrawl

0

3

. The link to the stream will be available on the funeral home website on the day of the service. Private burial will take place at Sunset Ridge Memorial Park. 4600 COUNTY LINE ROAD, MOUNT PLEASANT, WI 53403 Jon. E. Buckingham, age 81 of Kenosha passed away peacefully on Thursday, June 25, 2020 at Burlington Memorial Hospital. A celebration of Jon's life will be held on Monday, July 6, 2020 at 2:00 p.m. at the funeral home. Friends are invited to meet with the family on Monday from 12:00 Noon until the time of the service. Memorial remembrances to Safe Harbor Humane Society, 7811 60th Ave., Kenosha, WI 53142 would be appreciated. Jon's complete obituary will be made available on the funeral home webster on Wednesday, July 1, 2020. Timothy Pfaff On June 24, 2020, Tim Pfaff / Slim left his body to be in the arms of God, and the loved ones who have passed before him. Born in Kenosha, on December 16, 1971, he was the first-born child of Ralph and Michelle (St. John) Pfaff. He was a loving big brother to Steven and Kyle Pfaff. He was most proud of his two sons, Justin Timothy and Tyler Joseph Pfaff. Tim loved them to the moon and stars. And he was recently introduced to his wonderful new grandson, Kingston Ramsey Pfaff. Tim also leaves behind his sister, Michelle Moon, first best friend, Scott Anderson, and dear friend Jen; uncles Gary, John, and Rick and his auntie Cher and aunt Sharon. He has been blessed with many cousins, aunts, and uncles from both the Pfaff's and St. John's and kept contact with many of them on FB. Slim loved fishing and the Packers. He loved taking his boys camping and having cookouts with his many family and friends. He loved music; it filled his life wherever he was. Tim loved BIG. If he told you he loved you, he meant it. He was going to love you forever. He will be dearly missed by those who loved him back. 5111-60th Street Kenosha, WI 53144 Visit & Sign Tim's Online Memorial Book at: Mario Caira After 96 years, Mario Caira peacefully shed the bonds of this world on Friday, June 26, 202,0 for his life in eternity. A son of the late Gaspere and Raffaela Caira, Mario was born December 8, 1923, in Rende (Calabria) Italy. He was educated in local schools there. Following the war, in January 1947, he married his childhood sweetheart, Amelia Chiappetta in Rende. They shared some 71 wonderful years together before her death in 2018. Together they raised three children. In 1955, Mario and Amelia made their new home in the United States settling in Kenosha. Mario took an entry level position at the American Brass where he advanced to a pipefitter by his retirement, 30 years later. Always a hard worker and provider, Mario took side jobs delivering groceries, landscaping, and painting. After leaving the Brass, Mario started the Kenosha Antenna Services for Kenosha and Racine. He put up 100s of TV antennas and towers before taking his full retirement. Family came first for Mario. He had a keen mind, good sense of humor, and winning personality. He spent many hours in the garden and enjoyed sharing the harvest. Mario also would get away to his "secret" fishing spot. He served in the Italian Army before coming to this country. Mario was immensely proud to take U.S. citizenship in 1962. Mario was a member of St. Anthony's Church. Treasuring his memory are his daughter, Lena (Fred) Schlater; son, Reno Caira, both of Kenosha; and his son, Tony (Terry Hartnell) C

-0.163931

-0.974391

-1.319739

-1.85049

[ -0.5090887581270532, 0.181227658088322 ]

[ -1.194638077582469, -0.7541434465802782 ]

[ -1.532782766238741, -1.1066942739741839 ]

[ -1.8999156762735456, -1.8010636060799359 ]

1,024

[ 512, 512 ]

[ 29889, 450, 1544, 304, 278, 4840, 674, 367, 3625, 373, 278, 2090, 13537, 3271, 4700, 373, 278, 2462, 310, 278, 2669, 29889, 12230, 6866, 616, 674, 2125, 2058, 472, 8991, 842, 390, 5525, 19722, 4815, 29889, 13, 29946, 29953, 29900, 29900, 21122, 29979, 365, 8895, 16641, 3035, 29892, 16999, 10356, 349, 1307, 3289, 13566, 29892, 399, 29902, 29871, 29945, 29941, 29946, 29900, 29941, 13, 29967, 265, 29889, 382, 29889, 16281, 16094, 29892, 5046, 29871, 29947, 29896, 310, 10015, 359, 2350, 4502, 3448, 10776, 3730, 373, 498, 1295, 3250, 29892, 5306, 29871, 29906, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 472, 6640, 1847, 880, 19722, 15967, 29889, 13, 29909, 10894, 362, 310, 9937, 29915, 29879, 2834, 674, 367, 4934, 373, 27822, 29892, 5468, 29871, 29953, 29892, 29871, 29906, 29900, 29906, 29900, 472, 29871, 29906, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 278, 2090, 13537, 3271, 29889, 11169, 1975, 526, 23610, 304, 5870, 411, 278, 3942, 373, 27822, 515, 29871, 29896, 29906, 29901, 29900, 29900, 1939, 265, 2745, 278, 931, 310, 278, 2669, 29889, 19722, 1083, 1590, 661, 778, 304, 5701, 1725, 3536, 4089, 13863, 1662, 7765, 29892, 29871, 29955, 29947, 29896, 29896, 29871, 29953, 29900, 386, 319, 345, 1696, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29906, 723, 367, 7556, 29889, 9937, 29915, 29879, 4866, 704, 1981, 653, 674, 367, 1754, 3625, 373, 278, 2090, 13537, 3271, 1856, 2475, 373, 15050, 4515, 3250, 29892, 5468, 29871, 29896, 29892, 29871, 29906, 29900, 29906, 29900, 29889, 13, 13711, 20336, 10022, 3470, 13, 2951, 5306, 29871, 29906, 29946, 29892, 29871, 29906, 29900, 29906, 29900, 29892, 7870, 10022, 3470, 847, 317, 2576, 2175, 670, 3573, 304, 367, 297, 278, 10188, 310, 4177, 29892, 322, 278, 18012, 6743, 1058, 505, 4502, 1434, 1075, 29889, 13, 29933, 1398, 297, 10015, 359, 2350, 29892, 373, 5846, 29871, 29896, 29953, 29892, 29871, 29896, 29929, 29955, 29896, 29892, 540, 471, 278, 937, 29899, 4939, 2278, 310, 23438, 322, 3375, 1808, 313, 855, 29889, 2259, 29897, 10022, 3470, 29889, 13, 3868, 471, 263, 12355, 292, 4802, 8099, 304, 24703, 322, 476, 1508, 10022, 3470, 29889, 13, 3868, 471, 1556, 22314, 310, 670, 1023, 18025, 29892, 26408, 7870, 20336, 322, 9656, 1358, 6936, 10022, 3470, 29889, 7870, 18012, 963, 304, 278, 18786, 322, 10819, 29889, 1126, 540, 471, 10325, 9129, 304, 670, 20695, 716, 4595, 1100, 29892, 4088, 7352, 8292, 7759, 10022, 3470, 29889, 13, 13711, 884, 11308, 5742, 670, 9883, 29892, 3375, 1808, 17549, 29892, 937, 1900, 5121, 29892, 8075, 17483, 29892, 322, 9425, 5121, 21116, 29936, 443, 7799, 23529, 29892, 2259, 29892, 322, 24218, 322, 670, 263, 1657, 347, 23816, 322, 263, 1657, 1383, 5022, 29889, 13, 3868, 756, 1063, 1999, 11517, 411, 1784, 274, 681, 1144, 29892, 263, 348, 1372, 29892, 322, 443, 7799, 515, 1716, 278, 10022, 3470, 29915, 29879, 322, 624, 29889, 2259, 29915, 29879, 322, 8126, 6958, 411, 1784, 310, 963, 373, 28816, 29889, 13, 29903, 2576, 18012, 9427, 292, 322, 278, 18744, 414, 29889, 940, 18012, 5622, 670, 12544, 4242, 292, 322, 2534, 7984, 17718, 411, 670, 1784, 3942, 322, 7875, 29889, 940, 18012, 4696, 29936, 372, 10423, 670, 2834, 29693, 540, 471, 29889, 13, 13711, 18012, 350, 6259, 29889, 960, 540, 5429, 366, 540, 18012, 366, 29892, 540, 6839, 372, 29889, 940, 471, 2675, 304, 5360, 366, 22296, 29889, 13, 3868, 674, 367, 9425, 368, 13726, 491, 1906, 1058, 18012, 1075, 1250, 29889, 13, 29945, 29896, 29896, 29896, 29899, 29953, 29900, 386, 7103, 10015, 359, 2350, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29946, 29946, 13, 6116, 277, 669, 9954, 7870, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 29924, 2628, 315, 1794, 336, 13, 13555, 29871, 29929, 29953, 2440, 29892, 16262, 315, 1794, 336, 10776, 3730, 28453, 278, 289, 13788, 310, 445, 3186, 373, 28728, 29892, 5306, 29871, 29906, 29953, 29892, 29871, 29906, 29900, 29906, 29892, 29900, 363, 670, 2834, 297, 634, 824, 537, 29889, 13, 29909, 1487, 310, 278, 5683, 402, 4692, 406, 322, 390, 3470, 29874, 3100, 315, 1794, 336, 29892, 16262, 471, 6345, 5846, 29871, 29947, 29892, 29871, 29896, 29929, 29906, 29941, 29892, 297, 390, 3324, 313, 7856, 370, 2849, 29897, 12730, 29889, 940, 471, 27729, 297, 1887, 12462, 727, 29889, 12206, 278, 1370, 29892, 297, 5490, 29871, 29896, 29929, 29946, 29955, 29892, 540, 8300, 670, 2278, 6614, 14225, 23057, 29892, 1913, 18556, 678, 423, 7988, 941, 297, 390, 3324, 29889, 2688, 7258, 777, 29871, 29955, 29896, 20695, 2440, 4208, 1434, 902, 4892, 297, 29871, 29906, 29900, 29896, 29947, 29889, 323, 12966, 896, 10425, 2211, 4344, 29889, 13, 797, 29871, 29896, 29929, 29945, 29945, 29892, 16262, 322, 1913, 18556, 1754, 1009, 716, 3271, 297, 278, 3303, 3900, 3604, 1847, 297, 10015, 359, 2350, 29889, 16262, 3614, 385, 6251, 3233, 2602, 472, 278, 3082, 1771, 465, 988, 540, 12862, 304, 263, 14282, 29888, 5171, 491, 670, 3240, 19211, 29892, 29871, 29941, 29900, 2440, 2678, 29889, 29849, 263, 2898, 15645, 322, 13113, 29892, 16262, 3614, 2625, 17643, 12021, 292, 4071, 2265, 583, 29892, 2982, 1557, 21430, 29892, 322, 20413, 29889, 2860, 10124, 278, 1771, 465, 29892, 16262, 4687, 278, 10015, 359, 2350, 530, 841, 1056, 15538, 363, 10015, 359, 2350, 322, 390, 562, 457, 29889, 940, 1925, 701, 29871, 29896, 29900, 29900, 29879, 310, 5648, 25504, 22911, 322, 304, 17538, 1434, 5622, 670, 2989, 3240, 19211, 29889, 13, 27104, 2996, 937, 363, 16262, 29889, 940, 750, 263, 28430, 3458, 29892, 1781, 4060, 310, 27448, 29892, 322, 15613, 2022, 2877, 29889, 940, 10398, 1784, 6199, 297, 278, 16423, 322, 27849, 19383, 278, 4023, 10147, 29889, 16262, 884, 723, 679, 3448, 304, 670, 376, 19024, 29908, 9427, 292, 9758, 29889, 940, 6766, 297, 278, 10545, 8811, 1434, 6421, 304, 445, 4234, 29889, 16262, 471, 5198, 575, 873, 22314, 304, 2125, 501, 29889, 29903, 29889, 18363, 4034, 297, 29871, 29896, 29929, 29953, 29906, 29889, 13, 29924, 2628, 471, 263, 4509, 310, 624, 29889, 16477, 29915, 29879, 6291, 29889, 13, 29911, 12588, 3864, 670, 3370, 526, 670, 8750, 29892, 365, 2386, 313, 29943, 1127, 29897, 21262, 1008, 29936, 1487, 29892, 7493, 29877, 315, 1794, 336, 29892, 1716, 310, 10015, 359, 2350, 29936, 322, 670, 1487, 29892, 15293, 313, 29911, 261, 719, 12321, 18437, 29897, 315 ]

1,332,858

13,312

CommonCrawl

0

3

aira, of Boca Raton, FL. Mario leaves behind his brothers-in-law, Franchino (Olimpia) Chiappetta of Rende, and Leo (Marikay) Chiappetta of Kenosha. The blessings of a growing family were a joy to Mario. His grandchildren include, Peggy (Rodger) Kormylo and Reno Caira of Kenosha, Amy (Tommy) Cunningham of Atlanta, and Gina DiLeo of Orlando. Great-grandchildren surviving Mario are Cameron (Maddy) Kormylo & Katherine Kormylo, Gianna & Janessa DiLeo, and Joseph & Edison Cunningham. Surviving nieces and nephews include, Beniamino (Tina) Caira, Marisa (Enrico Bosco) Caira, and Gaspere Caira. Grand nieces and nephews include, Olympia, Francesco and Valerio Chiappetta, as well as Francesco (Federica) Petrasso and Paola Giovanna (Francesco Imbrogno) Petrasso; and a great-grandnephew, Peter Imbrogno. Mario was predeceased by his wife, Amelia; his parents; a brother, Ceaser Caira of Rende; and a brother, Aldo Caira of Buenos Aires, Argentina. The family expresses deep appreciation to Claridge House for their diligent care and Genesis Rehab Services for their continuous support and therapy for Mario. Visitation in celebration of the life of Mario Caira will be held Sunday, July 5th, from 1:00 a.m. to 4:00 p.m. at Proko Funeral Home. A Mass of Christian Burial will be held Monday, July 6th, at 10:00 a.m. at St. Anthony of Padua Catholic Church, 2223 – 51st St. Kenosha. Interment will follow at All Saints Cemetery & Mausoleum. Memorials for Masses will be appreciated by the family, in lieu of flowers. Visit Mario's Online Memorial Book at: Verle Roy Swenson Verle Roy Swenson, 98 years old of Camp Lake, WI passed away Saturday, June 27, 2020 at Aurora Medical Center, Kenosha, WI. He was born August 23, 1921 in Camp Lake, WI the son of the late Roy A. and Evelyn Mildred (nèe Orvis) Swenson. Verle served his country proudly in the United States Navy. He was a member of the United States Navy Reserves and was called to active duty on April 4, 1944 during World War II. His sea duty was on the USS Montauk LSV 6, where he was a Machinist Mate 1st Class. When he returned, he married, Dorothy E. Ott on June 11, 1949 in Ebenezer Lutheran Church, West Milwaukee, WI. After returning from their honeymoon, they began to build the house that they would live in for the next 66 years. Verle was then drafted into the United States Navy and sent to Korea for his second tour. He reported for active duty on September 9, 1950 and served on the USS Osprey AMS28 as an Engineman 1st Class. This vessel was a minesweeper in the Korean waters during the war. Verle was a 74-year active member of the Schultz-Hahn American Legion Post #293 in Silver Lake, WI. He was the Past Finance Officer, the Past Post Commander, Past Kenosha County Commander, and Lifetime Member of the Past Commanders of Wisconsin. Verle was also a member of the Naval Minewarfare Association, the Kenosha County Last Man's Club of WWII, Korean War Veterans and a 50-year member of the International Association of Machinists, with several years served as shop steward. He was a member of Peace Evangelical Lutheran Church in Wilmot, WI since 1950, where he sang in the choir and served on the church council. He also served 19 years on the school board of Wilmot Union High School. Verle spent a lot of his time in carpentry. He also enjoyed playing the mandolin, guitar, banjo, and electric organ with various groups at nurs

-0.035609

-0.322602

-1.228434

-1.387446

[ 0.040151088901449666, -0.11136925543153821 ]

[ -0.9511125905243473, 0.3059086735550752 ]

[ -1.5632176585433524, -0.8936500278419052 ]

[ -1.618967687302234, -1.1559237795532207 ]

1,024

[ 512, 512 ]

[ 1794, 336, 29892, 310, 350, 6400, 390, 14114, 29892, 383, 29931, 29889, 16262, 11308, 5742, 670, 21383, 29899, 262, 29899, 10653, 29892, 1352, 305, 1789, 313, 29949, 12552, 423, 29897, 678, 423, 7988, 941, 310, 390, 3324, 29892, 322, 22533, 313, 7083, 638, 388, 29897, 678, 423, 7988, 941, 310, 10015, 359, 2350, 29889, 13, 1576, 17065, 886, 310, 263, 15678, 3942, 892, 263, 15331, 304, 16262, 29889, 3600, 4595, 11991, 3160, 29892, 27281, 1927, 313, 29934, 397, 914, 29897, 476, 555, 29891, 417, 322, 7493, 29877, 315, 1794, 336, 310, 10015, 359, 2350, 29892, 28533, 313, 21599, 1357, 29897, 315, 27389, 3391, 310, 26484, 29892, 322, 402, 1099, 4671, 3226, 29877, 310, 1394, 28514, 29889, 7027, 29899, 27857, 11991, 10503, 4357, 16262, 526, 20939, 265, 313, 29924, 25644, 29897, 476, 555, 29891, 417, 669, 476, 16490, 476, 555, 29891, 417, 29892, 21569, 1056, 669, 2627, 9297, 4671, 3226, 29877, 29892, 322, 6936, 669, 2155, 2285, 315, 27389, 3391, 29889, 6298, 29894, 4357, 4930, 778, 322, 23446, 354, 5652, 3160, 29892, 4111, 2829, 1789, 313, 29911, 1099, 29897, 315, 1794, 336, 29892, 1085, 8069, 313, 2369, 24855, 10211, 1111, 29897, 315, 1794, 336, 29892, 322, 402, 4692, 406, 315, 1794, 336, 29889, 6265, 4930, 778, 322, 23446, 354, 5652, 3160, 29892, 6167, 423, 29892, 16922, 322, 2630, 261, 601, 678, 423, 7988, 941, 29892, 408, 1532, 408, 16922, 313, 29943, 2447, 983, 29897, 5879, 29878, 9979, 322, 2621, 2963, 11429, 9713, 313, 7675, 778, 1111, 1954, 6729, 29887, 1217, 29897, 5879, 29878, 9979, 29936, 322, 263, 2107, 29899, 27857, 484, 29886, 13636, 29892, 5310, 1954, 6729, 29887, 1217, 29889, 13, 29924, 2628, 471, 27978, 346, 1463, 491, 670, 6532, 29892, 1913, 18556, 29936, 670, 11825, 29936, 263, 8099, 29892, 7747, 29440, 315, 1794, 336, 310, 390, 3324, 29936, 322, 263, 8099, 29892, 18242, 29877, 315, 1794, 336, 310, 17882, 16981, 29892, 13798, 29889, 13, 1576, 3942, 4653, 267, 6483, 5108, 362, 304, 15183, 5525, 5619, 363, 1009, 21749, 25692, 2562, 322, 5739, 6656, 830, 7308, 15538, 363, 1009, 9126, 2304, 322, 29220, 27580, 363, 16262, 29889, 13, 6116, 7018, 297, 10894, 362, 310, 278, 2834, 310, 16262, 315, 1794, 336, 674, 367, 4934, 16340, 29892, 5468, 29871, 29945, 386, 29892, 515, 29871, 29896, 29901, 29900, 29900, 263, 29889, 29885, 29889, 304, 29871, 29946, 29901, 29900, 29900, 282, 29889, 29885, 29889, 472, 1019, 2901, 13811, 13537, 8778, 29889, 319, 7360, 310, 6111, 6640, 616, 674, 367, 4934, 27822, 29892, 5468, 29871, 29953, 386, 29892, 472, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 472, 624, 29889, 16477, 310, 18011, 3357, 11865, 6291, 29892, 29871, 29906, 29906, 29906, 29941, 785, 29871, 29945, 29896, 303, 624, 29889, 10015, 359, 2350, 29889, 4124, 358, 674, 1101, 472, 2178, 14342, 1372, 315, 22875, 669, 341, 1485, 1772, 398, 29889, 13, 11442, 9020, 29879, 363, 7360, 267, 674, 367, 7556, 491, 278, 3942, 29892, 297, 13003, 310, 18281, 29889, 13, 6116, 277, 16262, 29915, 29879, 13542, 19722, 6726, 472, 29901, 13, 6565, 280, 15793, 3925, 25151, 13, 6565, 280, 15793, 3925, 25151, 29892, 29871, 29929, 29947, 2440, 2030, 310, 7259, 9459, 29892, 399, 29902, 4502, 3448, 24211, 29892, 5306, 29871, 29906, 29955, 29892, 29871, 29906, 29900, 29906, 29900, 472, 23266, 2207, 20795, 7817, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 940, 471, 6345, 3111, 29871, 29906, 29941, 29892, 29871, 29896, 29929, 29906, 29896, 297, 7259, 9459, 29892, 399, 29902, 278, 1487, 310, 278, 5683, 15793, 319, 29889, 322, 7298, 873, 29876, 341, 789, 1127, 313, 29876, 30000, 29872, 1394, 1730, 29897, 3925, 25151, 29889, 1798, 280, 6766, 670, 4234, 22314, 368, 297, 278, 3303, 3900, 13166, 29889, 940, 471, 263, 4509, 310, 278, 3303, 3900, 13166, 2538, 20098, 322, 471, 2000, 304, 6136, 13360, 373, 3786, 29871, 29946, 29892, 29871, 29896, 29929, 29946, 29946, 2645, 2787, 3362, 1944, 29889, 3600, 7205, 13360, 471, 373, 278, 17676, 4526, 585, 29895, 365, 7597, 29871, 29953, 29892, 988, 540, 471, 263, 17197, 262, 391, 29566, 29871, 29896, 303, 4134, 29889, 1932, 540, 4133, 29892, 540, 8300, 29892, 9579, 20336, 382, 29889, 13476, 373, 5306, 29871, 29896, 29896, 29892, 29871, 29896, 29929, 29946, 29929, 297, 26302, 1600, 3298, 24760, 273, 6291, 29892, 3122, 3833, 29893, 585, 23137, 29892, 399, 29902, 29889, 2860, 7863, 515, 1009, 298, 650, 962, 6150, 29892, 896, 4689, 304, 2048, 278, 3699, 393, 896, 723, 5735, 297, 363, 278, 2446, 29871, 29953, 29953, 2440, 29889, 1798, 280, 471, 769, 18195, 287, 964, 278, 3303, 3900, 13166, 322, 2665, 304, 19109, 363, 670, 1473, 6282, 29889, 940, 8967, 363, 6136, 13360, 373, 3839, 29871, 29929, 29892, 29871, 29896, 29929, 29945, 29900, 322, 6766, 373, 278, 17676, 438, 1028, 8903, 319, 4345, 29906, 29947, 408, 385, 2201, 262, 11422, 29871, 29896, 303, 4134, 29889, 910, 21239, 471, 263, 29086, 705, 11356, 297, 278, 22467, 19922, 2645, 278, 1370, 29889, 1798, 280, 471, 263, 29871, 29955, 29946, 29899, 6360, 6136, 4509, 310, 278, 1102, 499, 29920, 29899, 29950, 5422, 3082, 5682, 291, 4918, 396, 29906, 29929, 29941, 297, 16466, 9459, 29892, 399, 29902, 29889, 940, 471, 278, 19793, 4231, 749, 28288, 29892, 278, 19793, 4918, 27317, 29892, 19793, 10015, 359, 2350, 5127, 27317, 29892, 322, 365, 361, 5410, 19495, 310, 278, 19793, 10516, 414, 310, 22581, 29889, 1798, 280, 471, 884, 263, 4509, 310, 278, 21590, 26833, 4495, 24658, 7993, 29892, 278, 10015, 359, 2350, 5127, 9208, 2315, 29915, 29879, 5977, 310, 399, 29956, 2687, 29892, 22467, 3362, 478, 1308, 550, 322, 263, 29871, 29945, 29900, 29899, 6360, 4509, 310, 278, 4623, 7993, 310, 17197, 262, 2879, 29892, 411, 3196, 2440, 6766, 408, 18296, 1886, 1328, 29889, 13, 3868, 471, 263, 4509, 310, 24819, 21827, 936, 24760, 273, 6291, 297, 4624, 14817, 29892, 399, 29902, 1951, 29871, 29896, 29929, 29945, 29900, 29892, 988, 540, 13625, 297, 278, 3060, 381, 322, 6766, 373, 278, 6586, 18701, 29889, 940, 884, 6766, 29871, 29896, 29929, 2440, 373, 278, 3762, 7613, 310, 4624, 14817, 7761, 5057, 4523, 29889, 13, 6565, 280, 10398, 263, 3287, 310, 670, 931, 297, 1559, 29886, 8269, 29889, 940, 884, 27849, 8743, 278, 9619, 22878, 29892, 11210, 29892, 9892, 2212, 29892, 322, 12646, 2894, 411, 5164, 6471, 472, 302, 1295 ]

1,332,858

14,336

CommonCrawl

0

3

ing homes and many senior citizen get togethers. Verle is survived by his son, Dale (Laura) of Waukesha, WI; his grandchildren, Kelly (Jeremy) Brockwell and Adam Swenson; his great-grandchildren, Henry, Samuel, and Evelyn Brockwell; his brother-in-law, Don Bockman; his sister-in-law, Virginia Swenson; and many nieces, nephews, cousins, and friends. In addition to his parents and wife, Dorothy, he was preceded in death by his brother, Harry Swenson. Visitation will be held from 10:00 a.m. to 11:30 a.m. Friday, July 3, 2020 with a Funeral Service commencing at 11:30 a.m. at Strang Funeral Home, 1055 Main St., Antioch, IL 60002. Interment with Military Honors will immediately follow at Sunset Ridge Memorial Park, Kenosha, WI. For additional information, call 847-395-4000. In lieu of flowers, donations are appreciated to Peace Evangelical Lutheran Church, 11233 306th Avenue, Wilmot, WI 53192 or the Schultz-Hahn American Legion Post #293, Silver Lake, WI in Verle's memory. Please sign the online guestbook for Verle at www.strangfh.com. Joseph P. Cresto Joseph Philip Cresto, age 89, died in peace Sunday, June 21st in Raleigh, NC. Born on November 5, 1930 to Joseph and Margaret Cresto in Joliet, IL. He was a wonderful husband, father, grandfather, great grandfather, uncle and cousin. He is survived by his children; Susan (Nick) Berrong, Sally (Blake) Frodin, Michael, and Joseph (Kim) Cresto; grandchildren Erin (Ryan) McKevett, Reed and Margaret Frodin, Michael, Benjamin and Ava Cresto and great-granddaughter, Nora Maeve McKevett. Joe was preceded in death by his wife Marian, sister Marjorie Lyons and parents. In his later years, he found happiness again with Elizabeth Hund who passed in 2019. Joe will be fondly remembered by family and friends as a kind and caring man who was always the life of the party. He was a proud patriot and U.S. Marine Corps veteran. In lieu of flowers, the family requests a donation to a charity of your choice. Fredericksen remembered as a skilled officer, photographer and 'outstanding human being' As a law enforcement officer handling sensitive crimes, Cindy Fredericksen put away the wors… COLLECTION: Recent obituaries in the Kenosha News (June 24 - June 30, 2020) COLLECTION: Recent obituaries in the Kenosha News (June 17-23, 2020) COLLECTION: Recent obits in the Kenosha News (July 10-15, 2020) Mount Pleasant reaches settlement with couple on their property near Foxconn site UPDATE: A total of 13 KUSD schools switching to virtual learning protocols due to COVID-19 resurgence; more approaching threshold New felony charges filed against Kenosha man Baker Street eatery closes, owners cite staffing shortages for the decision Kenosha couple facing drug, child neglect charges COMING SOON: Get the latest Olympic Updates daily during the 2022 games Receive the latest local crime & courts coverage in your inbox every week. BEECH POINTE - Ad from 2022-01-09 Harbor Market c/o Kenosha Harbor Market - Ad from 2022-01-14 ON THE BORDER - Ad from 2022-01-12 St. Catherine Commons C/O Capri Communities, LLC - Ad from 2022-01-12 ADVOCATE AURORA HEALTH - Ad from 2022-01-12 BERKOTS SUPER FOODS /

-0.676874

-1.277007

-1.71032

-2.063802

[ -0.4912829775500694, -0.8624650188087335 ]

[ -1.2805882494853356, -1.2734257351600966 ]

[ -1.6393048893048803, -1.7813343867263993 ]

[ -1.9155238978830629, -2.2120801084638915 ]

1,024

[ 512, 512 ]

[ 292, 17774, 322, 1784, 16336, 14497, 264, 679, 3996, 621, 414, 29889, 13, 6565, 280, 338, 10503, 2347, 491, 670, 1487, 29892, 360, 744, 313, 5661, 2002, 29897, 310, 399, 585, 10794, 2350, 29892, 399, 29902, 29936, 670, 4595, 11991, 29892, 21872, 313, 29967, 261, 6764, 29897, 4358, 384, 5872, 322, 11783, 3925, 25151, 29936, 670, 2107, 29899, 27857, 11991, 29892, 6498, 29892, 15316, 29892, 322, 7298, 873, 29876, 4358, 384, 5872, 29936, 670, 8099, 29899, 262, 29899, 10653, 29892, 3872, 350, 1698, 1171, 29936, 670, 9883, 29899, 262, 29899, 10653, 29892, 11653, 3925, 25151, 29936, 322, 1784, 4930, 778, 29892, 23446, 354, 5652, 29892, 274, 681, 1144, 29892, 322, 7875, 29889, 512, 6124, 304, 670, 11825, 322, 6532, 29892, 9579, 20336, 29892, 540, 471, 9399, 287, 297, 4892, 491, 670, 8099, 29892, 10686, 3925, 25151, 29889, 13, 6116, 7018, 674, 367, 4934, 515, 29871, 29896, 29900, 29901, 29900, 29900, 263, 29889, 29885, 29889, 304, 29871, 29896, 29896, 29901, 29941, 29900, 263, 29889, 29885, 29889, 28728, 29892, 5468, 29871, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 411, 263, 13811, 13537, 6692, 844, 16750, 472, 29871, 29896, 29896, 29901, 29941, 29900, 263, 29889, 29885, 29889, 472, 3767, 574, 13811, 13537, 8778, 29892, 29871, 29896, 29900, 29945, 29945, 4241, 624, 1696, 5459, 601, 305, 29892, 17674, 29871, 29953, 29900, 29900, 29900, 29906, 29889, 4124, 358, 411, 20080, 7906, 943, 674, 7389, 1101, 472, 8991, 842, 390, 5525, 19722, 4815, 29892, 10015, 359, 2350, 29892, 399, 29902, 29889, 1152, 5684, 2472, 29892, 1246, 29871, 29947, 29946, 29955, 29899, 29941, 29929, 29945, 29899, 29946, 29900, 29900, 29900, 29889, 512, 13003, 310, 18281, 29892, 1016, 800, 526, 7556, 304, 24819, 21827, 936, 24760, 273, 6291, 29892, 29871, 29896, 29896, 29906, 29941, 29941, 29871, 29941, 29900, 29953, 386, 18874, 29892, 4624, 14817, 29892, 399, 29902, 29871, 29945, 29941, 29896, 29929, 29906, 470, 278, 1102, 499, 29920, 29899, 29950, 5422, 3082, 5682, 291, 4918, 396, 29906, 29929, 29941, 29892, 16466, 9459, 29892, 399, 29902, 297, 1798, 280, 29915, 29879, 3370, 29889, 3529, 1804, 278, 7395, 17838, 2909, 363, 1798, 280, 472, 7821, 29889, 710, 574, 29888, 29882, 29889, 510, 29889, 13, 26473, 561, 349, 29889, 6781, 4778, 13, 26473, 561, 14920, 6781, 4778, 29892, 5046, 29871, 29947, 29929, 29892, 6423, 297, 10776, 16340, 29892, 5306, 29871, 29906, 29896, 303, 297, 390, 744, 1141, 29892, 25166, 29889, 19298, 373, 3979, 29871, 29945, 29892, 29871, 29896, 29929, 29941, 29900, 304, 6936, 322, 18364, 6781, 4778, 297, 435, 324, 2035, 29892, 17674, 29889, 940, 471, 263, 20695, 10216, 29892, 4783, 29892, 4595, 22212, 29892, 2107, 4595, 22212, 29892, 22169, 322, 22618, 29889, 940, 338, 10503, 2347, 491, 670, 4344, 29936, 25914, 313, 29940, 860, 29897, 2292, 29373, 29892, 317, 635, 313, 29933, 433, 446, 29897, 383, 5964, 262, 29892, 5765, 29892, 322, 6936, 313, 29968, 326, 29897, 6781, 4778, 29936, 4595, 11991, 1425, 262, 313, 29934, 10094, 29897, 24053, 5750, 1803, 29892, 830, 287, 322, 18364, 383, 5964, 262, 29892, 5765, 29892, 20212, 322, 319, 1564, 6781, 4778, 322, 2107, 29899, 27857, 29881, 6334, 357, 29892, 405, 2207, 3219, 29872, 345, 24053, 5750, 1803, 29889, 11131, 471, 9399, 287, 297, 4892, 491, 670, 6532, 24236, 29892, 9883, 1085, 3418, 347, 8626, 787, 322, 11825, 29889, 512, 670, 2678, 2440, 29892, 540, 1476, 22722, 1449, 411, 13061, 379, 870, 1058, 4502, 297, 29871, 29906, 29900, 29896, 29929, 29889, 13, 29967, 7297, 674, 367, 6299, 368, 21832, 491, 3942, 322, 7875, 408, 263, 2924, 322, 1559, 292, 767, 1058, 471, 2337, 278, 2834, 310, 278, 6263, 29889, 940, 471, 263, 22314, 16967, 327, 322, 501, 29889, 29903, 29889, 15929, 16408, 25808, 273, 29889, 13, 797, 13003, 310, 18281, 29892, 278, 3942, 7274, 263, 1016, 362, 304, 263, 1373, 537, 310, 596, 7348, 29889, 13, 23923, 672, 860, 4881, 21832, 408, 263, 2071, 24455, 12139, 29892, 17739, 261, 322, 525, 449, 11235, 5199, 1641, 29915, 13, 2887, 263, 4307, 24555, 13561, 12139, 11415, 20502, 2181, 1355, 29892, 315, 513, 29891, 19769, 4881, 1925, 3448, 278, 281, 943, 30098, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 1540, 29871, 29906, 29946, 448, 5306, 29871, 29941, 29900, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1981, 4314, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 1540, 29871, 29896, 29955, 29899, 29906, 29941, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 15032, 3281, 2725, 29901, 3599, 296, 704, 1169, 297, 278, 10015, 359, 2350, 10130, 313, 29967, 11850, 29871, 29896, 29900, 29899, 29896, 29945, 29892, 29871, 29906, 29900, 29906, 29900, 29897, 13, 27648, 19777, 13186, 22170, 16493, 411, 7303, 373, 1009, 2875, 2978, 14802, 13082, 3268, 13, 14474, 29901, 319, 3001, 310, 29871, 29896, 29941, 476, 3308, 29928, 12462, 21293, 304, 6901, 6509, 9608, 29879, 2861, 304, 19937, 29899, 29896, 29929, 620, 2007, 663, 29936, 901, 28702, 16897, 13, 4373, 7995, 2592, 21090, 934, 29881, 2750, 10015, 359, 2350, 767, 13, 29933, 5790, 7103, 17545, 708, 4694, 267, 29892, 1914, 414, 274, 568, 13925, 292, 3273, 1179, 363, 278, 10608, 13, 29968, 264, 359, 2350, 7303, 14870, 15721, 29892, 2278, 22851, 21090, 13, 19795, 4214, 7791, 1164, 29901, 3617, 278, 9281, 19025, 5020, 15190, 14218, 2645, 278, 29871, 29906, 29900, 29906, 29906, 8090, 13, 24131, 278, 9281, 1887, 17268, 669, 28033, 23746, 297, 596, 297, 1884, 1432, 4723, 29889, 13, 15349, 29923, 3210, 349, 6992, 4330, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29900, 29929, 13, 21972, 4089, 28794, 274, 29914, 29877, 10015, 359, 2350, 3536, 4089, 28794, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29946, 13, 1164, 6093, 350, 22364, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 855, 29889, 21688, 3468, 315, 29914, 29949, 5915, 374, 20473, 1907, 29892, 365, 12182, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 3035, 29963, 20166, 3040, 319, 29965, 1672, 4717, 17714, 1964, 4690, 448, 2087, 515, 29871, 29906, 29900, 29906, 29906, 29899, 29900, 29896, 29899, 29896, 29906, 13, 13635, 29968, 2891, 29903, 317, 4897, 1001, 18322, 29949, 8452, 847 ]

1,332,858

15,360

CommonCrawl

0

3

\section{Introduction} \label{intro} Let $A_0$ be a self-adjoint operator in a separable Hilbert space $\gH$ and let $C=C^*$ be a trace class operator in $\gH$, $C\in\mathfrak S_1(\gH)$. Recall, that according to the Kato-Rosenblum theorem, cf. \cite{Kat57,Ros57} the absolutely continuous parts $A^{ac}_0$ and ${\wt A}^{ac}$, { in short the $ac$-parts}, of the operators $A_0$ and ${\wt A}=A_0+C$ {are unitarily equivalent. In other words, the { absolutely continuous spectrum}, { in short $ac$-spectrum}, of $A_0$ and its spectral multiplicity { are} stable under { \emph{additive}} trace class perturbations. At the same time, the Weyl-von~Neumann-Kuroda theorem \cite[Theorem 94.2]{AG81}, \cite{Neu35}, \cite{Kur58} shows that the condition $C\in\mathfrak S_1(\gH)$ cannot be replaced by $C\in\mathfrak S_p(\gH)$ with $p\in (1,\infty]$ (where $\mathfrak S_p(\gH)$ denotes the Neumann-Schatten operator ideals). \begin{theorem}[{\cite[Theorem 10.2.1 and Theorem 10.2.3]{Ka76}}]\label{WNth} For any operator $A_0=A^*_0$ in $\gH$ and any $p\in (1,\infty]$ there exists an operator $C= C^*\in \mathfrak S_p(\gH)$ such that the perturbed operator ${\wt A} = A_0 + C$ has purely point spectrum. In particular, $\sigma_{ac}(A_0 + C)=\emptyset.$ \end{theorem} The Kato-Rosenblum theorem was generalized by Birman \cite{Bir63a} and Birman and Krein \cite{BirKrei62} to the case of \emph{non-additive} perturbations. Namely, it was shown that $A^{ac}_0$ and ${\wt A}^{ac}$ still remain unitary equivalent whenever \begin{displaymath} ({\wt A}-i)^{-1}-(A_0-i)^{-1}\in\mathfrak S_1(\gH). \end{displaymath} In particular, this is true if $A_0=A^*_0$ and ${\wt A}={\wt A}^*$ are self-adjoint extensions of a symmetric operator $A$ (in short $A_0, {\wt A}\in {\rm Ext\,}_A$). This rises the following Weyl-von~Neumann problem for extensions: Given $p \in (1,\infty]$ and a self-adjoint extension $A_0$ of $A.$ Does there exist a self-adjoint extension $\wt A$ of $A$ such that $\wt A$ has purely point spectrum and the difference $(\wt A - i)^{-1} - (A_0 - i)^{-1}$ belongs to $\mathfrak S_p(\gotH)$? To the best of our knowledge this problem was not investigated. In the present paper we show that the Weyl-von~Neumann theorem for extensions becomes false in general. We show that under an additional assumption on the symmetric operator $A$ the $ac$-part of a certain extension $A_0=A^*_0$ is unitarily equivalent to the $ac$-part of any extension ${\wt A}={\wt A}^*$ of $A$ provided that their resolvent difference is compact, that is, \begin{equation}\label{0.2} K_{\wt A} := ({\wt A}-i)^{-1}-(A_0-i)^{-1}\in{\mathfrak S}_{\infty}(\gH). \end{equation} The additional assumption on the pair $\{A,A_0\}$ is formulated in terms of the Weyl function of the pair $\{A,A_0\}$. The latter is the main object in the boundary triplet approach to the extension theory developed in the last three decades

0.46749

-0.725493

0.526645

2.501603

[ 0.6113057427939328, 0.3236739027041931 ]

[ -0.825768589832667, -0.6252181887259785 ]

[ 0.7802690489117124, 0.2730208438348586 ]

[ 2.6576850337055076, 2.3455206015151613 ]

1,024

[ 512, 512 ]

[ 320, 2042, 29912, 25898, 29913, 320, 1643, 29912, 23333, 29913, 13, 13, 12024, 29871, 395, 29909, 29918, 29900, 29938, 367, 263, 1583, 29899, 328, 12090, 5455, 297, 263, 2903, 519, 12338, 2151, 2913, 13, 4535, 29887, 29950, 29938, 322, 1235, 395, 29907, 29922, 29907, 6622, 29938, 367, 263, 9637, 770, 5455, 297, 779, 29887, 29950, 1628, 13, 29938, 29907, 29905, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 4935, 3599, 497, 29892, 393, 5034, 304, 278, 13, 29968, 1219, 29899, 29934, 7749, 2204, 398, 9185, 29892, 274, 29888, 29889, 320, 2036, 29912, 29968, 271, 29945, 29955, 29892, 29934, 359, 29945, 29955, 29913, 278, 13312, 13, 20621, 681, 5633, 29871, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 7555, 14554, 319, 2844, 562, 4429, 426, 297, 3273, 278, 13, 29938, 562, 4388, 20895, 1118, 310, 278, 12768, 395, 29909, 29918, 29900, 29938, 322, 7555, 14554, 319, 5369, 29909, 29918, 29900, 29974, 29907, 29938, 426, 598, 13, 348, 3673, 2354, 7126, 29889, 512, 916, 3838, 29892, 278, 426, 13312, 9126, 13, 21494, 5848, 1118, 426, 297, 3273, 395, 562, 4388, 21494, 5848, 1118, 310, 395, 29909, 29918, 29900, 29938, 322, 967, 23161, 13, 18056, 17024, 426, 526, 29913, 13714, 1090, 426, 320, 7278, 29912, 1202, 3321, 930, 9637, 770, 13, 10700, 9265, 800, 29889, 2180, 278, 1021, 931, 29892, 278, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 29899, 29968, 2192, 1388, 13, 14648, 320, 2036, 29961, 28831, 29871, 29929, 29946, 29889, 29906, 3199, 10051, 29947, 29896, 1118, 320, 2036, 29912, 8139, 29884, 29941, 29945, 1118, 320, 2036, 29912, 29968, 332, 29945, 29947, 29913, 29871, 13, 845, 1242, 393, 278, 4195, 13, 29938, 29907, 29905, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 1262, 2609, 367, 8611, 491, 395, 29907, 29905, 262, 29905, 7237, 13, 29903, 29918, 29886, 1194, 29887, 29950, 1262, 411, 395, 29886, 29905, 262, 313, 29896, 2053, 3411, 9341, 313, 3062, 779, 7237, 317, 29918, 29886, 1194, 29887, 29950, 1262, 13, 1145, 4769, 278, 2448, 22553, 29899, 4504, 8606, 5455, 1957, 1338, 467, 13, 29905, 463, 29912, 14648, 4400, 741, 2036, 29961, 28831, 29871, 29896, 29900, 29889, 29906, 29889, 29896, 322, 10244, 29871, 29896, 29900, 29889, 29906, 29889, 29941, 3199, 29968, 29874, 29955, 29953, 930, 10725, 1643, 29912, 16048, 386, 29913, 13, 2831, 738, 5455, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 297, 779, 29887, 29950, 29938, 322, 738, 29871, 395, 29886, 29905, 262, 313, 29896, 2053, 3411, 9341, 13, 12711, 4864, 385, 5455, 395, 29907, 29922, 315, 6622, 29905, 262, 320, 7237, 317, 29918, 29886, 1194, 29887, 29950, 1262, 29871, 1316, 393, 13, 1552, 13499, 28179, 5455, 7555, 14554, 319, 29913, 353, 319, 29918, 29900, 718, 315, 29938, 756, 24837, 1298, 13, 21494, 5848, 29889, 512, 3153, 29892, 779, 3754, 648, 562, 2119, 29909, 29918, 29900, 718, 315, 7950, 26153, 7449, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 1576, 476, 1219, 29899, 29934, 7749, 2204, 398, 9185, 471, 28803, 491, 17853, 1171, 13, 29905, 2036, 29912, 29933, 381, 29953, 29941, 29874, 29913, 322, 17853, 1171, 322, 7706, 262, 320, 2036, 29912, 29933, 381, 29968, 5803, 29953, 29906, 29913, 13, 517, 278, 1206, 310, 320, 7278, 29912, 5464, 29899, 1202, 3321, 29913, 22786, 800, 29889, 13041, 873, 29892, 372, 471, 13, 845, 776, 393, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 7555, 14554, 319, 2844, 562, 1042, 1603, 3933, 5190, 653, 13, 1686, 27445, 10940, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 13670, 14554, 319, 7402, 29875, 21604, 29896, 7402, 29898, 29909, 29918, 29900, 29899, 29875, 21604, 29896, 1012, 262, 29905, 7237, 317, 29918, 29896, 1194, 29887, 29950, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 797, 3153, 29892, 445, 338, 1565, 565, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 322, 7555, 14554, 319, 5369, 741, 14554, 319, 2137, 29394, 13, 598, 1583, 29899, 328, 12090, 17752, 310, 263, 13, 11967, 16414, 5455, 395, 29909, 29938, 313, 262, 3273, 395, 29909, 29918, 29900, 29892, 29871, 2802, 14554, 319, 1012, 262, 2802, 1758, 7338, 5940, 2403, 29909, 18724, 13, 4013, 364, 4637, 278, 1494, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 1108, 363, 13, 24299, 29901, 11221, 29871, 395, 29886, 320, 262, 313, 29896, 2053, 3411, 9341, 322, 263, 1583, 29899, 328, 12090, 13, 29871, 6081, 259, 395, 29909, 29918, 29900, 29938, 310, 395, 29909, 7449, 29871, 5538, 29871, 727, 1863, 13, 263, 1583, 29899, 328, 12090, 6081, 29871, 779, 14554, 319, 29938, 310, 395, 29909, 29938, 1316, 393, 779, 14554, 319, 29938, 756, 13, 29886, 545, 368, 1298, 18272, 322, 278, 4328, 12211, 14554, 319, 448, 13, 29875, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 1042, 14393, 304, 779, 7237, 317, 29918, 29886, 1194, 7085, 29950, 1262, 29973, 1763, 13, 1552, 1900, 310, 1749, 7134, 445, 1108, 471, 451, 7405, 630, 29889, 13, 13, 797, 278, 2198, 5650, 591, 1510, 393, 278, 399, 1032, 29880, 29899, 23696, 30022, 8139, 22553, 9185, 363, 13, 24299, 7415, 2089, 297, 2498, 29889, 1334, 1510, 393, 1090, 385, 13, 1202, 3245, 11833, 373, 278, 18348, 5455, 395, 29909, 29938, 278, 395, 562, 4388, 1595, 310, 263, 13, 14082, 6081, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 29871, 338, 443, 3673, 2354, 7126, 304, 278, 395, 562, 4388, 1595, 310, 738, 13, 17588, 7555, 14554, 319, 5369, 741, 14554, 319, 2137, 29394, 310, 395, 29909, 29938, 4944, 393, 1009, 13, 9778, 794, 4328, 338, 11071, 29892, 393, 338, 29892, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29906, 29913, 13, 29968, 1665, 14554, 319, 29913, 3490, 313, 741, 14554, 319, 7402, 29875, 21604, 29896, 7402, 29898, 29909, 29918, 29900, 29899, 29875, 21604, 29896, 1012, 262, 741, 7237, 13, 29903, 6353, 3411, 4678, 29887, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1576, 5684, 11833, 373, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 338, 883, 7964, 297, 13, 357, 1516, 310, 278, 399, 1032, 29880, 740, 310, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 23699, 29871, 450, 13, 29880, 2620, 338, 278, 1667, 1203, 297, 278, 10452, 21954, 29873, 2948, 304, 278, 13, 17588, 6368, 8906, 297, 278, 1833, 2211, 1602, 3076 ]

1,332,863

0

ArXiv

-1

, see \cite{DM91,DM95,GG91} and references therein. The core of this approach is the following abstract version of Green's formula \begin{equation}\label{0.3} (A^*f,g) - (f,A^*g) = ({\Gamma}_1f,{\Gamma}_0g)_{\cH} - ({\Gamma}_0f,{\Gamma}_1g)_{\cH}, \qquad f,g\in{\rm dom\,}(A^*), \end{equation} where $\cH$ is an auxiliary Hilbert space and $\Gamma_0,\Gamma_1 : {\rm dom\,}(A^*)\rightarrow \cH$ are linear mappings. A triplet $\Pi=\{\cH,\Gamma_0,\Gamma_1\}$ is called a boundary triplet for the operator $A^*$ if \eqref{0.3} holds and the mapping $\Gamma:=\{\Gamma_0,\Gamma_1\}: {\rm dom\,}(A^*)\rightarrow \cH\oplus \cH$ is surjective. With a boundary triplet ${\Pi}$ for $A^*$ one associates in a natural way the Weyl function $M(\cdot)= M_{\Pi}(\cdot)$ (see Definition \ref{Weylfunc}), which is the key object of this approach. It is an operator-valued Nevanlinna function with values in $[\cH]$ (i.e. $R_{\cH}$-function) and its role in the extension theory is similar to that of the classical Weyl function in the spectral theory of Sturm-Liouville operators. In particular, if $A$ is simple, then $M(\cdot)$ determines the pair $\{A,A_0\}$, where $A_0 :=A^*\upharpoonright {\xker\,}{\Gamma}_0$, uniquely, up to unitary equivalence. Moreover, $M(\cdot)$ is regular (holomorphic) precisely on the resolvent set $\varrho(A_0)$ of $A_0$ and the spectral properties of $A_0$ are described in terms of the limits $M(t+i0)$ at the real line (see \cite{BMN02}). One of our main results (Theorem \ref{V.5}) reads now as follows. \begin{theorem}\label{th0.1} Let $\Pi=\{\cH,\Gamma_0,\Gamma_1\}$ be a boundary triplet for $A^*$ { such that} the corresponding Weyl function $M(\cdot)$ has weak limits \begin{equation}\label{0.2A} M(t+i0) :=\,\mbox{\rm w-}\hspace{-2pt} \lim_{y\downarrow 0}M(t+iy)\quad \text{for a.e. }\ t\in{\mathbb R}. \end{equation} If a self-adjoint extension $\wt A$ of $A$ satisfies condition \eqref{0.2}, then the { $ac$-parts} ${\wt A}^{ac}$ and $A^{ac}_0$ of ${\wt A}$ and { $A_0 \,(= A^*\upharpoonright{\xker\,}({\Gamma}_0)$)} are unitarily equivalent. \end{theorem} We apply this result to direct sums $A :=\oplus^{\infty}_{n=1} S_n$ of symmetric operators $S_n$ { with equal and finite deficiency indices $n_\pm(S_n)$}. { Let $S_{0n}$ be a self-adjoint extension of $S_n$ for each $n \in \N$. We show that the $ac$-part of $A_0 :=\oplus^{\infty}_{n=1} S_{0n}$ is unitarily equivalent to the $ac$-part of any other extension $\wt A=\wt A^*\in {\rm Ext\,}_A$ provided that condition \eqref{0.2} is satisfied and the symmetric operators $S_n$ are unitarily equivalent to $S_1$ for any $n \in \N$.} The second part of the paper is concerned with a spectral extremal property of certain self-adjoint extensions of $A$ described by the following definition. \begin{

0.701704

-0.5236

0.737153

2.491197

[ 0.7482732856938088, 0.6551353565218931 ]

[ -0.45600378779221007, -0.5911962456810939 ]

[ 0.7041818181501843, 0.7701240848101754 ]

[ 2.6160631094134614, 2.3663315636611846 ]

1,024

[ 512, 512 ]

[ 29892, 1074, 13, 29905, 2036, 29912, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29892, 26788, 29929, 29896, 29913, 322, 9282, 727, 262, 29889, 13, 13, 1576, 7136, 310, 445, 2948, 338, 278, 1494, 9846, 1873, 310, 13, 24599, 29915, 29879, 7063, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29941, 29913, 13, 313, 29909, 6622, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 6622, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 741, 6642, 2403, 29900, 29887, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 29888, 29892, 741, 6642, 2403, 29896, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 6622, 511, 13, 418, 320, 355, 29912, 2573, 29913, 13, 3062, 779, 29883, 29950, 29938, 29871, 338, 385, 29587, 653, 12338, 2151, 2913, 322, 13, 4535, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 584, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29938, 29871, 526, 5608, 611, 27775, 29889, 29871, 319, 21954, 29873, 13, 4535, 12197, 2013, 741, 29883, 29950, 2053, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 11854, 338, 2000, 263, 10452, 21954, 29873, 29871, 363, 13, 1552, 5455, 395, 29909, 6622, 29938, 565, 320, 4915, 29912, 29900, 29889, 29941, 29913, 8640, 322, 278, 10417, 13, 4535, 6642, 29901, 2013, 741, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29905, 6177, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29905, 17201, 13, 29905, 29883, 29950, 29938, 338, 1190, 25674, 29889, 13, 13, 3047, 263, 10452, 21954, 29873, 7555, 12197, 1042, 363, 395, 29909, 6622, 29938, 697, 4067, 1078, 297, 263, 13, 25047, 982, 278, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 3892, 341, 1665, 12197, 4678, 3822, 1262, 313, 4149, 13, 14683, 320, 999, 29912, 29956, 1032, 29880, 9891, 9594, 607, 338, 278, 1820, 1203, 310, 445, 2948, 29889, 739, 13, 275, 385, 5455, 29899, 4387, 287, 2448, 3703, 1915, 1056, 740, 411, 1819, 297, 395, 7110, 29883, 29950, 9341, 13, 29898, 29875, 29889, 29872, 29889, 395, 29934, 1665, 29883, 29950, 23021, 2220, 29897, 322, 967, 6297, 297, 278, 6081, 6368, 338, 13, 29764, 304, 393, 310, 278, 14499, 399, 1032, 29880, 740, 297, 278, 23161, 13, 14138, 310, 624, 17095, 29899, 23410, 283, 4909, 12768, 29889, 512, 3153, 29892, 565, 395, 29909, 29938, 338, 13, 12857, 29892, 769, 395, 29924, 1194, 3822, 1262, 3683, 1475, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 28538, 988, 13, 29938, 29909, 29918, 29900, 3490, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 3331, 6642, 2403, 29900, 1628, 20498, 873, 29892, 701, 304, 13, 5441, 653, 24796, 29889, 12808, 29892, 395, 29924, 1194, 3822, 1262, 338, 4943, 13, 29898, 5391, 16898, 29897, 17503, 373, 278, 3770, 794, 731, 779, 1707, 4650, 29898, 29909, 29918, 29900, 1262, 310, 13, 29938, 29909, 29918, 29900, 29938, 29871, 322, 278, 23161, 4426, 310, 395, 29909, 29918, 29900, 29938, 526, 5439, 297, 4958, 13, 974, 278, 13071, 395, 29924, 29898, 29873, 29974, 29875, 29900, 1262, 472, 278, 1855, 1196, 313, 4149, 320, 2036, 29912, 29933, 29924, 29940, 29900, 29906, 7690, 13, 13, 6716, 310, 1749, 1667, 2582, 313, 28831, 320, 999, 29912, 29963, 29889, 29945, 1800, 13623, 1286, 408, 13, 23031, 29879, 29889, 13, 29905, 463, 29912, 14648, 1012, 1643, 29912, 386, 29900, 29889, 29896, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 2053, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 11854, 367, 263, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 29938, 29871, 426, 1316, 393, 29913, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 756, 29871, 8062, 13071, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29906, 29909, 29913, 13, 29924, 29898, 29873, 29974, 29875, 29900, 29897, 584, 2013, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 3204, 2936, 29871, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 2144, 3425, 320, 726, 29912, 1454, 263, 29889, 29872, 29889, 17704, 260, 29905, 262, 741, 1995, 390, 1836, 13, 320, 355, 29912, 2573, 29913, 13, 3644, 263, 1583, 29899, 328, 12090, 6081, 779, 14554, 319, 29938, 310, 395, 29909, 29938, 17150, 4195, 13, 29905, 4915, 29912, 29900, 29889, 29906, 1118, 769, 278, 426, 395, 562, 4388, 20895, 29913, 7555, 14554, 319, 2844, 562, 1042, 322, 13, 29938, 29909, 998, 562, 2403, 29900, 29938, 29871, 310, 29871, 7555, 14554, 319, 1042, 322, 426, 395, 29909, 29918, 29900, 7179, 29898, 29922, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 2915, 526, 443, 3673, 2354, 13, 1686, 27445, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 4806, 3394, 445, 1121, 304, 1513, 25470, 395, 29909, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 13, 29903, 29918, 29876, 29938, 310, 18348, 12768, 395, 29903, 29918, 29876, 29938, 426, 411, 5186, 322, 8093, 13, 1753, 293, 13396, 16285, 395, 29876, 3187, 3358, 29898, 29903, 29918, 29876, 1262, 1836, 426, 2803, 395, 29903, 648, 29900, 29876, 1042, 367, 263, 13, 1311, 29899, 328, 12090, 6081, 310, 395, 29903, 29918, 29876, 29938, 363, 1269, 395, 29876, 320, 262, 320, 29940, 1504, 1334, 1510, 29871, 393, 13, 1552, 395, 562, 4388, 1595, 310, 395, 29909, 29918, 29900, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317, 648, 29900, 29876, 1042, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 278, 395, 562, 4388, 1595, 310, 738, 916, 6081, 779, 14554, 13, 29909, 2013, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 29871, 4944, 393, 4195, 320, 4915, 29912, 29900, 29889, 29906, 29913, 338, 13, 29879, 27685, 1000, 322, 278, 18348, 12768, 395, 29903, 29918, 29876, 29938, 526, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29903, 29918, 29896, 29938, 363, 738, 395, 29876, 320, 262, 320, 29940, 1504, 29913, 13, 13, 1576, 1473, 760, 310, 278, 5650, 338, 15041, 411, 29871, 263, 23161, 13, 1062, 1745, 284, 2875, 310, 3058, 1583, 29899, 328, 12090, 17752, 310, 395, 29909, 29938, 13, 2783, 23059, 491, 278, 1494, 5023, 29889, 13, 29905, 463, 29912 ]

1,332,863

1,024

ArXiv

-1

definition}\Label{0.3AA} {\em (i) Let $T_j=T_j^*\in \cC(\gotH_j)$, $j = 1,2$. We say that $T_1$ is a part of $T_2$ if there is an isometry $V$ from $\gotH_1$ into $\gotH_2$ such that $VT_1V^* \subseteq T_2$. (ii) { Let $A_0=A^*_0$ be an extension of $A$. We say that $A_0$ is $ac$-minimal if $A^{ac}_0$ is a part of any self-adjoint extension ${\wt A}$ of $A$.} (iii) Let ${\sigma}_0 :={\sigma}_{ac}(A_0)$. We say that $A_0$ is strictly $ac$-minimal if for any extension $\wt A=\wt A^*$ of $A$ the parts $A^{ac}_0$ and $\wt A^{ac}E_{\wt A}(\sigma_0)$ are unitarily equivalent. } \end{definition} In particular, if $A_0$ is $ac$-minimal, then $\sigma_{ac}({\wt A})\supseteq \sigma_{ac}( A_0)$. Note that an $ac$-minimal extension of $A$ is not unique. For any two $ac$-minimal extensions their $ac$-parts are unitarily equivalent. We show (cf. Theorem \ref{VI.6}) that if $n_{\pm}(S_n)<\infty,$ then the $ac$-part $A^{ac}_0$ of any direct sum extension $A_0 =\oplus^{\infty}_{n=1} S_{0n}$ of $A :=\oplus^{\infty}_{n=1} S_{n}$ is $ac$-minimal. In particular, $\sigma_{ac}({\wt A})\supseteq \sigma_{ac}( A_0)$ for any ${\wt A}={\wt A}^*\in {\rm Ext\,}_A.$ This result looks surprising with respect to Theorem \ref{WNth}. Indeed, in this case $A^{ac}_0$ is still a part of $\wt A^{ac}$ for any ${\wt A}\in {\rm Ext\,}_A$ though the resolvent difference $K_{\wt A}$ (see \eqref{0.2}) is not even compact. In other words, in this case the $ac$-spectrum of $A_0$ (but not its spectral multiplicity) remains stable under (non-additive) compact perturbations $K_{\wt A}$ though both $\sigma_{ac}( A_0)$ and its multiplicity can only increase, whenever} $K_{\wt A}\notin\gotS_{\infty}.$ Moreover, we apply our technique to minimal symmetric non-negative Sturm-Liouville operator $A$ with an unbounded operator potential \begin{eqnarray}\Label{0.4} (Af)(x) = -f''(x) + Tf(x). \end{eqnarray} We show that the Friedrichs extension $A^F$ is $ac$-minimal and under a simple additional assumption is even strictly $ac$-minimal. The paper is organized as follows. In Section 2 we give a short introduction into the theory of ordinary and generalized boundary triplets and the corresponding Weyl functions. In Section 3 we express the spectral multiplicity function of the { $ac$-part $\wt A^{ac}$ of $\wt A= \wt A^*(\in {\rm Ext\,}_A)$} by means of the corresponding Weyl function. In Section 4 we apply this technique to prove Theorem \ref{th0.1} as well as to give a simple proof of the Kato-Rosenblum theorem. In Section 5 direct sums of boundary triplets ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for operators $S_n^*$ adjoint to symmetric operators $S_n$ are investigated. We show that though, in general, ${\Pi} = \oplus^\infty_{n=1} {\Pi}_n$ is not a boundary triplet for the direct sum $A^* :=\oplus^{\infty}_{n=1} S

-0.035866

-0.931416

0.245122

2.158222

[ -0.3296612769282156, 0.2579294821122526 ]

[ -0.9797626478253028, -0.883068704434578 ]

[ 0.37954296690099787, 0.11070141821026537 ]

[ 2.0333561693248154, 2.2830877150770923 ]

1,024

[ 512, 512 ]

[ 16553, 1012, 4775, 29912, 29900, 29889, 29941, 6344, 29913, 13, 741, 331, 13, 29898, 29875, 29897, 13, 12024, 395, 29911, 29918, 29926, 29922, 29911, 29918, 29926, 6622, 29905, 262, 320, 29883, 29907, 1194, 7085, 29950, 29918, 29926, 5767, 395, 29926, 353, 29871, 29896, 29892, 29906, 1504, 1334, 13, 20834, 393, 395, 29911, 29918, 29896, 29938, 338, 263, 760, 310, 29871, 395, 29911, 29918, 29906, 29938, 29871, 565, 727, 338, 385, 338, 7843, 395, 29963, 29938, 13, 3166, 779, 7085, 29950, 29918, 29896, 29938, 964, 779, 7085, 29950, 29918, 29906, 29938, 1316, 393, 395, 29963, 29911, 29918, 29896, 29963, 6622, 320, 11725, 323, 29918, 29906, 1504, 13, 13, 13, 29898, 2236, 29897, 426, 2803, 395, 29909, 29918, 29900, 29922, 29909, 6622, 29918, 29900, 29938, 367, 385, 6081, 310, 395, 29909, 1504, 13, 4806, 1827, 393, 395, 29909, 29918, 29900, 29938, 338, 395, 562, 4388, 1195, 3039, 565, 395, 29909, 998, 562, 2403, 29900, 29938, 338, 263, 760, 310, 738, 13, 1311, 29899, 328, 12090, 6081, 7555, 14554, 319, 1042, 310, 395, 29909, 1504, 29913, 13, 13, 29898, 25609, 29897, 2803, 7555, 3754, 2403, 29900, 3490, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 4935, 1334, 1827, 393, 395, 29909, 29918, 29900, 29938, 338, 18719, 395, 562, 4388, 1195, 3039, 565, 363, 13, 1384, 6081, 779, 14554, 319, 2013, 14554, 319, 6622, 29938, 310, 395, 29909, 29938, 278, 5633, 395, 29909, 998, 562, 2403, 29900, 29938, 322, 779, 14554, 13, 29909, 998, 562, 29913, 29923, 1665, 14554, 319, 4678, 3754, 29918, 29900, 1262, 526, 443, 3673, 2354, 7126, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 797, 3153, 29892, 565, 395, 29909, 29918, 29900, 29938, 338, 395, 562, 4388, 1195, 3039, 29892, 769, 13, 4535, 3754, 648, 562, 2119, 741, 14554, 319, 11606, 2146, 567, 300, 1837, 320, 3754, 648, 562, 2119, 319, 29918, 29900, 4935, 3940, 13, 5747, 385, 395, 562, 4388, 1195, 3039, 6081, 310, 395, 29909, 29938, 338, 451, 5412, 29889, 13, 2831, 738, 1023, 29871, 395, 562, 4388, 1195, 3039, 17752, 1009, 395, 562, 4388, 20895, 526, 13, 348, 3673, 2354, 7126, 29889, 13, 13, 4806, 1510, 313, 6854, 29889, 10244, 320, 999, 29912, 18118, 29889, 29953, 1800, 393, 565, 395, 29876, 1665, 3358, 2119, 29903, 29918, 29876, 29897, 13505, 3411, 8209, 13, 6098, 278, 395, 562, 4388, 1595, 395, 29909, 998, 562, 2403, 29900, 29938, 310, 738, 1513, 2533, 6081, 13, 29938, 29909, 29918, 29900, 17313, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317, 648, 29900, 29876, 1042, 310, 395, 29909, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 13, 29903, 648, 29876, 1042, 338, 395, 562, 4388, 1195, 3039, 29889, 512, 3153, 29892, 13, 4535, 3754, 648, 562, 2119, 741, 14554, 319, 11606, 2146, 567, 300, 1837, 320, 3754, 648, 562, 2119, 319, 29918, 29900, 1262, 363, 738, 7555, 14554, 13, 29909, 5369, 741, 14554, 319, 2137, 17710, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 4013, 1121, 3430, 26800, 411, 3390, 304, 10244, 320, 999, 29912, 16048, 386, 1836, 13, 2568, 12613, 29892, 297, 445, 1206, 395, 29909, 998, 562, 2403, 29900, 29938, 338, 1603, 29871, 263, 760, 310, 779, 14554, 13, 29909, 998, 562, 1042, 363, 738, 7555, 14554, 319, 1012, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 2466, 278, 3770, 794, 13, 29881, 17678, 395, 29968, 1665, 14554, 319, 1042, 313, 4149, 320, 4915, 29912, 29900, 29889, 29906, 1800, 338, 451, 1584, 11071, 29889, 13, 797, 916, 3838, 29892, 297, 445, 1206, 278, 395, 562, 4388, 21494, 5848, 310, 395, 29909, 29918, 29900, 29938, 13, 29898, 4187, 451, 967, 23161, 6674, 17024, 29897, 9242, 13714, 1090, 13, 29898, 5464, 29899, 1202, 3321, 29897, 11071, 22786, 800, 395, 29968, 1665, 14554, 319, 1042, 2466, 13, 20313, 779, 3754, 648, 562, 2119, 319, 29918, 29900, 1262, 322, 967, 6674, 17024, 29871, 508, 871, 7910, 29892, 13, 8256, 1310, 29913, 395, 29968, 1665, 14554, 319, 1012, 29842, 29905, 7085, 29903, 1665, 3411, 1836, 29938, 13, 13, 20761, 957, 29892, 591, 3394, 1749, 11043, 304, 29871, 13114, 18348, 13, 5464, 29899, 22198, 29871, 624, 17095, 29899, 23410, 283, 4909, 5455, 395, 29909, 29938, 411, 385, 443, 29306, 13, 6891, 7037, 13, 29905, 463, 29912, 9441, 1012, 4775, 29912, 29900, 29889, 29946, 29913, 13, 29898, 29909, 29888, 5033, 29916, 29897, 259, 353, 29871, 448, 29888, 4907, 29898, 29916, 29897, 718, 323, 29888, 29898, 29916, 467, 13, 29905, 355, 29912, 9441, 29913, 13, 4806, 1510, 393, 278, 9542, 29879, 6081, 395, 29909, 29985, 29943, 29938, 338, 395, 562, 4388, 1195, 3039, 13, 392, 1090, 263, 2560, 5684, 11833, 338, 1584, 18719, 13, 29938, 562, 4388, 1195, 3039, 29889, 13, 13, 1576, 5650, 338, 19098, 408, 4477, 29889, 512, 9779, 29871, 29906, 591, 2367, 263, 3273, 13, 524, 13210, 964, 278, 6368, 310, 15311, 322, 28803, 10452, 13, 3626, 552, 1372, 322, 29871, 278, 6590, 399, 1032, 29880, 3168, 29889, 512, 9779, 29871, 29941, 591, 13, 17073, 278, 23161, 6674, 17024, 740, 310, 278, 426, 395, 562, 4388, 1595, 13, 4535, 14554, 319, 998, 562, 1042, 310, 29871, 779, 14554, 319, 29922, 320, 14554, 319, 6622, 1194, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1262, 29913, 491, 2794, 310, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 29889, 512, 9779, 29871, 29946, 591, 3394, 445, 11043, 13, 517, 6356, 10244, 320, 999, 29912, 386, 29900, 29889, 29896, 29913, 408, 1532, 408, 304, 2367, 263, 2560, 5296, 310, 13, 1552, 476, 1219, 29899, 29934, 7749, 2204, 398, 9185, 29889, 13, 13, 797, 9779, 29871, 29945, 1513, 25470, 310, 10452, 21954, 1372, 7555, 12197, 2403, 29876, 353, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 29871, 363, 12768, 29871, 395, 29903, 29918, 29876, 6622, 29938, 594, 12090, 304, 13, 11967, 16414, 12768, 395, 29903, 29918, 29876, 29938, 526, 7405, 630, 29889, 29871, 1334, 1510, 393, 2466, 29892, 13, 262, 2498, 29892, 7555, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 2802, 12197, 2403, 29876, 29938, 338, 451, 263, 10452, 13, 3626, 552, 29873, 363, 278, 1513, 2533, 395, 29909, 6622, 584, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 317 ]

1,332,863

2,048

ArXiv

-1

^*_n,$ it is always possible to modify the triplets ${\Pi}_n$ in such a way that a new sequence $\wt {\Pi}_n= \{\cH_n,\wt{\Gamma}_{0n},\wt{\Gamma}_{1n}\}$ of boundary triplets for $S_n^*$ satisfies the following properties: $\wt {\Pi} = \oplus^\infty_{n=1} \wt {\Pi}_n$ forms a boundary triplet for $A^*$ { such that $S_{0n} := S^*_n\upharpoonright {\xker\,}({\Gamma}_{0n}) = S^*_n\upharpoonright {\xker\,}(\wt {\Gamma}_{0n}) =: {\wt S}_{0n},\ n \in \N$. In particular, the corresponding Weyl function $M(\cdot)$ is { block}-diagonal (see Theorem \ref{VI.3}). { Our spectral applications to direct sums are substantially based on this result. In particular, it is used in proving of Theorem \ref{VI.6} mentioned above}. Finally, in Section 6 we apply the technique (and abstract results) to operators \eqref{0.4} with { bounded and} unbounded operator potentials. { In particular, we investigate the $ac$-spectrum of self-adjoint realizations of Schr\"odinger operator \begin{displaymath} \cL = - \left(\frac{\partial^2}{\partial t^2} + \sum^n_{j=1}\frac{\partial^2}{\partial x^2_j}\right) + q(x). \quad (t,x) \in \R_+ \times \R^n, \quad q \in L^\infty(\R^n), \end{displaymath} in $L^2(\R_+\times\R^n)$, $n \ge 1$. For instance, we show that if $q(\cdot)\ge 0$ and} \begin{equation}\label{0.33} \lim_{|x|\to\infty}\int_{|x-y|\le 1}|q(y)|dy = 0, \end{equation} { then the Dirichlet realization $L^D$ is absolutely continuous, strictly $ac$-minimal and ${\sigma}(L^D) = {\sigma}_{ac}(L^D)= [0,\infty).$} {\bf Notations} In the following we consider only separable Hilbert spaces which are denoted by $\mathfrak H$, $\cH$ etc. { The symbols $\cC(\cH_1, \cH_2)$ and $[\mathfrak H_1, \mathfrak H_2]$ stand for the set of closed densely defined { linear} operators and the set of bounded linear operators from $\mathfrak H_1$ to $\mathfrak H_2,$ respectively}. { We set} $\cC(\cH):= \cC(\cH, \cH)$ and $[\mathfrak H] := [\mathfrak H, \mathfrak H]$. { The symbols ${\rm dom\,}(\cdot),$ ${\rm ran\,}(\cdot),$ $\varrho(T)$ and $\sigma(T)$ stand for the domain, the range, the resolvent set and the spectrum of an operator $T\in \cC(\cH),$ respectively}; $T^{ac}$ and $\sigma_{ac}(T)$ stand for the $ac$-part and the $ac$ spectrum of an operator $T=T^*\in \cC(\cH).$ $\mathfrak S_p(\gH),$ $p\in [1,\infty],$ stand for the Schatten-von~Neumann ideals in $\gH$. { Denote by $\cB({\R})$ the Borel $\sigma$-algebra of the line $\R$ and by $\cB_b({\R})$ the algebra of bounded subsets in} $\cB_b(\R)$. The Lebesgue measure of a set ${\delta} \in \cB({\R})$ is denoted by $|{\delta}|$. \section{Preliminaries} \subsection{Operator measures} \begin{definition} {\em Let $\cH$ be a separable Hilbert space. A mapping ${\Sigma}(\cdot):\ \cB

0.039809

-1.318191

0.106897

1.94491

[ 0.3264132535621906, -0.24679591347379062 ]

[ -0.825768589832667, -1.8106143095530123 ]

[ 0.1817161669210249, 0.03207794642335302 ]

[ 2.3247096393691384, 1.5651095210392962 ]

1,024

[ 512, 512 ]

[ 6622, 29918, 29876, 8209, 372, 13, 275, 2337, 1950, 304, 6623, 278, 21954, 1372, 7555, 12197, 2403, 29876, 29938, 297, 1316, 263, 982, 13, 5747, 263, 716, 5665, 779, 14554, 2802, 12197, 2403, 29876, 29922, 320, 741, 29883, 29950, 29918, 29876, 2053, 14554, 741, 6642, 3227, 29900, 29876, 7570, 14554, 741, 6642, 3227, 29896, 29876, 1012, 1042, 13, 974, 10452, 21954, 1372, 363, 395, 29903, 29918, 29876, 6622, 29938, 17150, 278, 1494, 13, 11330, 29901, 779, 14554, 2802, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 14554, 2802, 12197, 2403, 29876, 29938, 7190, 263, 13, 9917, 653, 21954, 29873, 363, 395, 29909, 6622, 29938, 426, 1316, 393, 395, 29903, 648, 29900, 29876, 29913, 3490, 13, 29903, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 1800, 353, 317, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 13, 741, 29916, 3946, 5940, 4678, 14554, 2802, 6642, 3227, 29900, 29876, 1800, 353, 29901, 2802, 14554, 317, 3227, 29900, 29876, 7570, 29871, 302, 320, 262, 320, 29940, 1504, 512, 3153, 29892, 13, 1552, 6590, 399, 1032, 29880, 740, 29871, 395, 29924, 1194, 3822, 1262, 338, 426, 13, 1271, 7402, 6051, 351, 7177, 313, 4149, 29871, 10244, 320, 999, 29912, 18118, 29889, 29941, 7690, 29871, 426, 8680, 23161, 13, 932, 5795, 304, 1513, 25470, 526, 23228, 368, 2729, 373, 445, 13, 2914, 29889, 512, 3153, 29892, 372, 338, 1304, 297, 1326, 292, 310, 10244, 320, 999, 29912, 18118, 29889, 29953, 29913, 13, 358, 28487, 2038, 1836, 13, 13, 12881, 635, 29892, 297, 9779, 29871, 29953, 591, 3394, 278, 29871, 11043, 313, 392, 9846, 13, 9902, 29897, 304, 29871, 12768, 320, 4915, 29912, 29900, 29889, 29946, 29913, 29871, 411, 426, 12635, 322, 29913, 13, 348, 29306, 5455, 7037, 29879, 29889, 426, 512, 3153, 29892, 591, 13, 11569, 5286, 403, 278, 395, 562, 4388, 21494, 5848, 310, 1583, 29899, 328, 12090, 8869, 800, 310, 13, 4504, 29878, 5931, 3689, 261, 5455, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 29883, 29931, 353, 448, 320, 1563, 1194, 1154, 741, 3846, 29985, 29906, 3331, 3846, 260, 29985, 29906, 29913, 718, 13, 29905, 2083, 29985, 29876, 648, 29926, 29922, 29896, 1012, 1154, 741, 3846, 29985, 29906, 3331, 3846, 921, 29985, 29906, 29918, 29926, 1012, 1266, 29897, 718, 3855, 29898, 29916, 467, 320, 3425, 13, 29898, 29873, 29892, 29916, 29897, 320, 262, 320, 29934, 28842, 320, 3706, 320, 29934, 29985, 29876, 29892, 320, 3425, 3855, 320, 262, 365, 3823, 3411, 1194, 29934, 29985, 29876, 511, 13, 418, 320, 355, 29912, 4990, 755, 29913, 13, 262, 395, 29931, 29985, 29906, 1194, 29934, 29918, 3124, 3706, 29905, 29934, 29985, 29876, 5767, 395, 29876, 320, 479, 29871, 29896, 1504, 1152, 2777, 29892, 591, 1510, 393, 565, 13, 29938, 29939, 1194, 3822, 2144, 479, 29871, 29900, 29938, 322, 29913, 13, 1678, 320, 463, 29912, 2573, 1012, 1643, 29912, 29900, 29889, 29941, 29941, 29913, 13, 29905, 2576, 648, 29989, 29916, 4295, 517, 29905, 3411, 1012, 524, 648, 29989, 29916, 29899, 29891, 4295, 280, 29871, 29896, 11079, 29939, 29898, 29891, 10531, 4518, 353, 29871, 29900, 29892, 13, 1678, 320, 355, 29912, 2573, 29913, 13, 29912, 769, 278, 19378, 436, 1026, 1855, 2133, 259, 395, 29931, 29985, 29928, 29938, 338, 13312, 13, 20621, 681, 29892, 29871, 18719, 395, 562, 4388, 1195, 3039, 322, 29871, 7555, 3754, 2119, 29931, 29985, 29928, 29897, 353, 2802, 3754, 3227, 562, 2119, 29931, 29985, 29928, 3892, 13, 29961, 29900, 2053, 3411, 467, 17133, 13, 13, 13, 13, 13, 741, 1635, 2216, 800, 29913, 29871, 512, 278, 1494, 591, 2050, 871, 2903, 519, 13, 29950, 309, 2151, 8162, 607, 526, 27291, 491, 779, 7237, 379, 1628, 779, 29883, 29950, 29938, 2992, 29889, 13, 29912, 450, 15072, 779, 29883, 29907, 1194, 29883, 29950, 29918, 29896, 29892, 320, 29883, 29950, 29918, 29906, 1262, 322, 395, 7110, 7237, 379, 29918, 29896, 29892, 13, 29905, 7237, 379, 29918, 29906, 9341, 2317, 363, 278, 731, 310, 5764, 6245, 873, 3342, 426, 13, 10660, 29913, 12768, 322, 278, 731, 310, 12635, 5608, 12768, 515, 13, 4535, 7237, 379, 29918, 29896, 29938, 304, 779, 7237, 379, 29918, 29906, 8209, 8307, 1836, 13, 29912, 1334, 731, 29913, 779, 29883, 29907, 1194, 29883, 29950, 1125, 29922, 320, 29883, 29907, 1194, 29883, 29950, 29892, 320, 29883, 29950, 1262, 322, 395, 7110, 7237, 379, 29962, 3490, 13, 7110, 7237, 379, 29892, 320, 7237, 379, 22689, 29871, 426, 450, 15072, 7555, 1758, 2432, 5940, 4678, 3822, 511, 29938, 13, 29938, 741, 1758, 6350, 5940, 4678, 3822, 511, 29938, 779, 1707, 4650, 29898, 29911, 1262, 322, 779, 3754, 29898, 29911, 1262, 2317, 363, 278, 5354, 29892, 13, 1552, 3464, 29892, 29871, 278, 3770, 794, 731, 322, 278, 18272, 310, 385, 5455, 13, 29938, 29911, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 511, 29938, 8307, 3400, 395, 29911, 998, 562, 1042, 322, 13, 4535, 3754, 648, 562, 2119, 29911, 1262, 2317, 363, 278, 395, 562, 4388, 1595, 322, 278, 395, 562, 29938, 13, 21494, 5848, 310, 385, 5455, 395, 29911, 29922, 29911, 6622, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 13, 13, 4535, 7237, 317, 29918, 29886, 1194, 29887, 29950, 511, 29938, 29871, 395, 29886, 29905, 262, 518, 29896, 2053, 3411, 1402, 29938, 2317, 363, 278, 13, 4504, 8606, 29899, 23696, 30022, 8139, 22553, 1957, 1338, 297, 779, 29887, 29950, 1504, 13, 29912, 3384, 866, 491, 779, 29883, 29933, 13670, 29934, 8435, 278, 6780, 295, 779, 3754, 4388, 15742, 310, 278, 13, 1220, 779, 29934, 29938, 29871, 322, 29871, 491, 779, 29883, 29933, 29918, 29890, 13670, 29934, 8435, 278, 9623, 310, 12635, 27639, 13, 262, 29913, 779, 29883, 29933, 29918, 29890, 1194, 29934, 4935, 450, 9388, 267, 13000, 5645, 310, 263, 731, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 13670, 29934, 8435, 13, 275, 27291, 491, 11892, 741, 4181, 11079, 1504, 13, 13, 29905, 2042, 29912, 6572, 2576, 262, 4314, 29913, 13, 13, 29905, 7235, 29912, 26486, 15366, 29913, 13, 29905, 463, 29912, 16553, 29913, 13, 741, 331, 13, 12024, 29871, 779, 29883, 29950, 29938, 367, 263, 2903, 519, 12338, 2151, 2913, 29889, 319, 29871, 10417, 13, 29938, 741, 10142, 4678, 3822, 1125, 29905, 29871, 320, 29883, 29933 ]

1,332,863

3,072

ArXiv

-1

_b({\R})\to[\cH]$ is called an operator (operator-valued) measure if \item[\;\;{\rm (i)}] ${\Sigma}(\cdot)$ is ${\delta}$-additive in the strong sense and \item[\;\;{\rm (ii)}] ${\Sigma}({\delta})={\Sigma}({\delta})^*\ge 0$ for ${\delta}\in \cB_b({\R})$. The operator measure ${\Sigma}({\cdot})$ is called bounded if it extends to the Borel algebra $\cB({\R})$ of $\R$, i.e. ${\Sigma}({\R})\in[\cH]$. Otherwise, it is called unbounded. A bounded operator measure ${\Sigma}(\cdot)=E(\cdot)$ is called orthogonal if, in addition the conditions \item[\;\;{\rm (iii)}] $E({\delta}_1)E({\delta}_2)=E({\delta}_1\cap{\delta}_2)$ for ${\delta}_1,{\delta}_2\in \cB({\R})$ and $E({\R})=I_{\cH}$ are satisfied. } \end{definition} Setting in (iii) ${\delta}_1={\delta}_2$, one gets that an orthogonal measure $E(\cdot)$ takes its values in the set of orthogonal projections on $\cH$. Every orthogonal measure $E(\cdot)$ defines an operator $T= T^*= \int_{{\R}}{\lambda} d E({\lambda})$ in $\cH$ with $E(\cdot)$ being its spectral measure. Conversely, by the spectral theorem, every operator $T=T^*$ in $\cH$ admits the above representation with the orthogonal spectral measure $E=:E_T$. By ${\Sigma}^{ac}$, ${\Sigma}^s$, ${\Sigma}^{sc}$ and ${\Sigma}^{pp}$ we denote absolutely continuous, singular, singular continuous and pure point parts of the measure ${\Sigma}$, respectively. The Lebesgue decomposition of ${\Sigma}$ is given by ${\Sigma} = {\Sigma}^{ac} + {\Sigma}^s = {\Sigma}^{ac} + {\Sigma}^{sc} + {\Sigma}^{pp}$. The operator measure ${\Sigma}_1$ is called subordinated to the operator measure ${\Sigma}_2$, in short ${\Sigma}_1 \prec {\Sigma}_2$, if ${\Sigma}_2({\delta}) = 0$ yields ${\Sigma}_1({\delta}) = 0$ for ${\delta} \in \cB_b(\R)$. If the measures ${\Sigma}_1$ and ${\Sigma}_2$ are mutually subordinated, then they are called equivalent, in short ${\Sigma}_1 \thicksim {\Sigma}_2$. Note, that there are always exists a scalar measure $\rho$ defined on $\cB_b(\R)$ such that ${\Sigma} \thicksim \rho$, see \cite[Remark 2.2]{MM03}. In particular, there is always a scalar measure such that ${\Sigma} \prec \rho$. Usually, with the operator-valued measure ${\Sigma}(\cdot)$ one associates a distribution operator-valued function ${\Sigma}(\cdot)$ defined by \begin{equation}\Label{a1} {\Sigma}(t) = \begin{cases} {\Sigma}([0,t)) & t > 0 \\ 0 & t = 0 \\ -{\Sigma}([t,0)) & t < 0 \end{cases} \end{equation} which is called the spectral function of ${\Sigma}$. Clearly, ${\Sigma}(\cdot)$ is strongly left continuous, ${\Sigma}(t-0)= {\Sigma}(t),$ and satisfies ${\Sigma}(t) = {\Sigma}(t)^*, \quad {\Sigma}(s) \le {\Sigma}(t)$, $s \le t$. \begin{definition}[{\cite[Definition 4.5]{MM03}}] {\em Let ${\Sigma}$ be an operator measure in $\cH$ and let $\rho$ be a scalar measure on $\cB(\R)$ such that ${\Sigma} \prec \rho$. Further, let $e=\{e_j\}^{\infty}_{j=1}$ be an orthonormal basis in $\cH$. Let \begin{eqnarray*} {\Sigma}_{ij}(t):=\bigl({\Sigma}(t)e_i,e_j\bigr), \qquad \Psi_{ij}(t):=d

0.072338

-1.201801

0.318673

2.355926

[ 0.16068252665334057, -0.016005603687499512 ]

[ -0.9726001335000639, -1.4310010503153519 ]

[ 0.5266449463732855, 0.11070141821026537 ]

[ 2.4703863743912997, 2.241465790785046 ]

1,024

[ 512, 512 ]

[ 29918, 29890, 13670, 29934, 11606, 517, 7110, 29883, 29950, 9341, 338, 2000, 385, 5455, 13, 29898, 6891, 29899, 4387, 287, 29897, 5645, 565, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 29875, 2915, 29962, 7555, 10142, 4678, 3822, 1262, 338, 7555, 4181, 23021, 1202, 3321, 297, 278, 4549, 13, 1678, 4060, 322, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 2236, 2915, 29962, 7555, 10142, 2119, 741, 4181, 1800, 21854, 10142, 2119, 741, 4181, 1800, 6622, 29905, 479, 29871, 29900, 29938, 363, 7555, 4181, 1012, 262, 13, 29905, 29883, 29933, 29918, 29890, 13670, 29934, 23462, 13, 13, 1576, 5455, 5645, 7555, 10142, 2119, 741, 3822, 8435, 338, 2000, 12635, 565, 372, 13, 1062, 1975, 304, 278, 6780, 295, 9623, 779, 29883, 29933, 13670, 29934, 8435, 310, 779, 29934, 1628, 474, 29889, 29872, 29889, 13, 29938, 741, 10142, 2119, 741, 29934, 11606, 262, 7110, 29883, 29950, 22689, 13466, 29892, 29871, 372, 13, 275, 2000, 443, 29306, 29889, 319, 12635, 5455, 5645, 13, 29938, 741, 10142, 4678, 3822, 3892, 29923, 1194, 3822, 1262, 338, 2000, 28143, 565, 29892, 297, 6124, 278, 5855, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 25609, 2915, 29962, 395, 29923, 13670, 4181, 2403, 29896, 29897, 29923, 13670, 4181, 2403, 29906, 3892, 29923, 13670, 4181, 2403, 29896, 29905, 5030, 741, 4181, 2403, 29906, 1262, 363, 13, 29938, 741, 4181, 2403, 29896, 29892, 741, 4181, 2403, 29906, 29905, 262, 320, 29883, 29933, 13670, 29934, 8435, 322, 13, 29938, 29923, 13670, 29934, 1800, 29922, 29902, 1665, 29883, 29950, 1042, 13, 13, 598, 15787, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29020, 297, 313, 25609, 29897, 7555, 4181, 2403, 29896, 21854, 4181, 2403, 29906, 1628, 697, 4947, 393, 385, 28143, 13, 26658, 395, 29923, 1194, 3822, 1262, 4893, 967, 1819, 297, 278, 731, 310, 28143, 13, 771, 24247, 373, 779, 29883, 29950, 1504, 7569, 28143, 5645, 395, 29923, 1194, 3822, 1262, 13, 1753, 1475, 385, 5455, 395, 29911, 29922, 323, 6622, 29922, 320, 524, 24033, 29934, 12431, 2892, 29913, 29871, 270, 382, 13670, 2892, 8435, 297, 13, 4535, 29883, 29950, 29938, 411, 395, 29923, 1194, 3822, 1262, 1641, 967, 23161, 5645, 29889, 1281, 874, 873, 29892, 491, 13, 1552, 23161, 9185, 29892, 1432, 5455, 395, 29911, 29922, 29911, 6622, 29938, 297, 779, 29883, 29950, 29938, 7336, 1169, 278, 13, 27215, 8954, 411, 278, 28143, 23161, 5645, 13, 29938, 29923, 29922, 29901, 29923, 29918, 29911, 1504, 13, 13, 2059, 7555, 10142, 2844, 562, 4429, 7555, 10142, 2137, 29879, 1628, 7555, 10142, 2844, 1557, 1042, 322, 7555, 10142, 2844, 407, 1042, 29871, 591, 13530, 13, 370, 2929, 11579, 9126, 29892, 13512, 29892, 13512, 9126, 322, 8296, 13, 3149, 5633, 310, 278, 5645, 7555, 10142, 4429, 8307, 29889, 450, 9388, 267, 13000, 13, 311, 510, 3283, 310, 7555, 10142, 1042, 338, 2183, 491, 13, 29938, 741, 10142, 29913, 353, 2802, 10142, 2844, 562, 29913, 718, 2802, 10142, 2137, 29879, 353, 2802, 10142, 2844, 562, 29913, 718, 2802, 10142, 2844, 1557, 29913, 718, 2802, 10142, 2844, 407, 4311, 13, 13, 1576, 5455, 5645, 7555, 10142, 2403, 29896, 29938, 338, 2000, 1014, 4194, 630, 304, 13, 1552, 5455, 5645, 7555, 10142, 2403, 29906, 1628, 297, 3273, 7555, 10142, 2403, 29896, 320, 17990, 2802, 10142, 2403, 29906, 1628, 565, 13, 29938, 741, 10142, 2403, 29906, 13670, 4181, 1800, 353, 29871, 29900, 29938, 17498, 7555, 10142, 2403, 29896, 13670, 4181, 1800, 353, 29871, 29900, 29938, 363, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 4935, 960, 13, 1552, 15366, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 526, 5478, 1474, 1014, 4194, 630, 29892, 769, 13, 19562, 526, 2000, 7126, 29892, 297, 3273, 7555, 10142, 2403, 29896, 320, 27996, 3601, 2802, 10142, 2403, 29906, 1504, 13, 9842, 29892, 393, 29871, 727, 526, 2337, 4864, 263, 17336, 5645, 779, 4650, 29938, 13, 12119, 373, 779, 29883, 29933, 29918, 29890, 1194, 29934, 1262, 1316, 393, 7555, 10142, 29913, 320, 27996, 3601, 320, 4650, 1628, 1074, 13, 29905, 2036, 29961, 7301, 935, 29871, 29906, 29889, 29906, 3199, 7428, 29900, 29941, 1836, 512, 3153, 29892, 727, 338, 2337, 263, 17336, 13, 26658, 1316, 393, 7555, 10142, 29913, 320, 17990, 320, 4650, 1504, 13, 13, 15922, 1474, 29892, 411, 278, 5455, 29899, 4387, 287, 5645, 7555, 10142, 4678, 3822, 1262, 697, 13, 21264, 1078, 263, 4978, 5455, 29899, 4387, 287, 740, 7555, 10142, 4678, 3822, 1262, 13, 12119, 491, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29874, 29896, 29913, 13, 741, 10142, 2119, 29873, 29897, 353, 13, 29905, 463, 29912, 11436, 29913, 13, 741, 10142, 2119, 29961, 29900, 29892, 29873, 876, 669, 260, 1405, 29871, 29900, 2474, 13, 29900, 9651, 669, 260, 353, 29871, 29900, 2474, 13, 29899, 741, 10142, 2119, 29961, 29873, 29892, 29900, 876, 669, 260, 529, 29871, 29900, 13, 29905, 355, 29912, 11436, 29913, 13, 29905, 355, 29912, 2573, 29913, 13, 4716, 338, 2000, 278, 23161, 740, 310, 7555, 10142, 4311, 13, 18759, 368, 29892, 7555, 10142, 4678, 3822, 1262, 338, 13818, 2175, 9126, 29892, 7555, 10142, 2119, 29873, 29899, 29900, 3892, 13, 741, 10142, 2119, 29873, 511, 29938, 322, 17150, 13, 29938, 741, 10142, 2119, 29873, 29897, 353, 2802, 10142, 2119, 29873, 4887, 15966, 320, 3425, 2802, 10142, 2119, 29879, 29897, 320, 280, 2802, 10142, 2119, 29873, 5767, 395, 29879, 320, 280, 260, 1504, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29961, 14683, 29871, 29946, 29889, 29945, 3199, 7428, 29900, 29941, 930, 29962, 13, 741, 331, 13, 12024, 7555, 10142, 1042, 367, 385, 5455, 5645, 297, 13, 4535, 29883, 29950, 29938, 322, 1235, 779, 4650, 29938, 367, 263, 17336, 5645, 373, 779, 29883, 29933, 1194, 29934, 1262, 1316, 393, 13, 29938, 741, 10142, 29913, 320, 17990, 320, 4650, 1504, 8725, 29892, 1235, 395, 29872, 27805, 29872, 29918, 29926, 29905, 6292, 3411, 3227, 29926, 29922, 29896, 1042, 13, 915, 385, 14219, 265, 2759, 8405, 297, 779, 29883, 29950, 1504, 2803, 13, 29905, 463, 29912, 9441, 4044, 13, 741, 10142, 3227, 823, 2119, 29873, 1125, 2013, 3752, 29880, 13670, 10142, 2119, 29873, 29897, 29872, 29918, 29875, 29892, 29872, 29918, 29926, 29905, 3752, 29878, 511, 320, 12014, 13, 29905, 14118, 648, 823, 2119, 29873, 1125, 29922, 29881 ]

1,332,863

4,096

ArXiv

-1

{\Sigma}_{ij}(t)/d\rho,\\ \Psi^e_n(t):=\bigl(\Psi_{ij}(t)\bigr)^n_{i,j=1}, \qquad \Psi^e(t):=\bigl(\Psi_{ij}(t)\bigr)^{\infty}_{i,j=1}. \end{eqnarray*} We call \begin{equation}\label{2.1A} N^e_{{\Sigma}}(t):={\rm rank\,}(\Psi^e(t)) := \sup_{n\ge 1} {\rm rank\,}(\Psi^e_n(t))\;({\rm mod}(\rho)) \end{equation} and \begin{displaymath} N_{\Sigma}(t) := {\rm ess\,}\!\sup_e N^e_{{\Sigma}}(t)\;({\rm mod}(\rho)) \end{displaymath} the multiplicity function and the total multiplicity of ${\Sigma}$, respectively. } \end{definition} By \cite[Proposition 4.6]{MM03} $N^e_{{\Sigma}}(\cdot)$ does not depend on the orthogonal basis $e$. Therefore one always has $N_{{\Sigma}}(t) := N^e_{{\Sigma}}(t)$ and one can omit the index $e$ in \eqref{2.1A}. When applying this definition to the absolutely continuous part ${\Sigma}^{ac}$ of ${\Sigma}$ the scalar measure $\rho^{ac}$ can be chosen to be the Lebesgue measure $|\cdot|$ on $\cB(\R)$. The concept of the multiplicity function allows one to introduce the following definitions. \begin{definition}\label{II.3} {\em Let ${\Sigma}_1$ and ${\Sigma}_2$ be two operator measures. \item[\;\;\rm (i)] The operator measure ${\Sigma}_1$ is called spectrally subordinate to the operator measure ${\Sigma}_2$, in short ${\Sigma}_1\prec\!\!\prec{\Sigma}_2$, if ${\Sigma}_1\prec{\Sigma}_2$ and $N_{{\Sigma}_1}(t)\le N_{{\Sigma}_2}(t)\;(\mbox{{\rm mod}}({\Sigma}_2))$. \item[\;\;\rm (ii)] The operator measures ${\Sigma}_1$ and ${\Sigma}_2$ are called spectrally equivalent, in short ${\Sigma}_1 \thickapprox {\Sigma}_2$, if ${\Sigma}_1 \thicksim {\Sigma}_2$ and $N_{{\Sigma}_1}(t)=N_{{\Sigma}_2}(t)(\mbox{{\rm mod}}({\Sigma}_2))$. } \end{definition} { Crucial for us in the sequel is the following theorem}. \begin{theorem}\Label{II.4a} { Let $T_j$ be self-adjoint operators acting in $\gotH_j$ with corresponding spectral measures $E_{T_j}(\cdot)$, $j =1,2$. Let $\cD \in \cB(\R)$. \item[\;\;\rm (i)] $T_1E_{T_1}(\cD)$ is a part of $T_2E_{T_2}(\cD)$ if and only if $E_{T_1,\cD} \prec\!\!\prec E_{T_2,\cD}$, where $E_{T_j,\cD}({\delta}) := E_{T_j}({\delta}\cap\cD), \ j = 1,2$. \item[\;\;\rm (ii)] The parts $T_1E_{T_1}(\cD)$ and $T_2E_{T_2}(\cD)$ are unitarily equivalent if and only if $E_{T_1,\cD} \thickapprox E_{T_2,\cD}$.} \end{theorem} The proof is immediate from \cite[Theorem 7.5.1]{BS87}. For $\cD = \R$ Theorem \ref{II.4a} gives conditions for $T_1$ to be unitarily equivalent either to a part of $T_2$ or to $T_2$ itself. \subsection{$R$-Functions} Let ${\cH}$ be a separable Hilbert space. We recall that an operator-valued function $F(\cdot)$ with values in $[{\cH}]$ is called to be a Her

-0.177114

-1.148082

0.162694

1.970923

[ -0.17728488545210352, -0.17694246659485385 ]

[ -1.1480817344684164, -1.1480817344684164 ]

[ -0.033864320236637976, 0.35925303869792374 ]

[ 2.0541671314708383, 1.8876794343026537 ]

1,024

[ 512, 512 ]

[ 741, 10142, 3227, 823, 2119, 29873, 6802, 29881, 29905, 4650, 29892, 1966, 13, 29905, 14118, 29985, 29872, 29918, 29876, 29898, 29873, 1125, 2013, 3752, 29880, 1194, 14118, 648, 823, 2119, 29873, 2144, 3752, 29878, 4887, 29876, 648, 29875, 29892, 29926, 29922, 29896, 1118, 320, 12014, 13, 29905, 14118, 29985, 29872, 29898, 29873, 1125, 2013, 3752, 29880, 1194, 14118, 648, 823, 2119, 29873, 2144, 3752, 29878, 21422, 3411, 3227, 29875, 29892, 29926, 29922, 29896, 1836, 13, 29905, 355, 29912, 9441, 4044, 13, 4806, 1246, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29909, 29913, 13, 29940, 29985, 29872, 24033, 10142, 12156, 29873, 1125, 21854, 1758, 7115, 5940, 4678, 14118, 29985, 29872, 29898, 29873, 876, 3490, 320, 12587, 648, 29876, 29905, 479, 29871, 29896, 29913, 2802, 1758, 7115, 5940, 4678, 14118, 29985, 29872, 29918, 29876, 29898, 29873, 876, 23891, 13670, 1758, 878, 4678, 4650, 876, 13, 29905, 355, 29912, 2573, 29913, 13, 392, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29940, 1665, 10142, 2119, 29873, 29897, 3490, 2802, 1758, 3686, 5940, 1012, 9903, 12587, 29918, 29872, 405, 29985, 29872, 24033, 10142, 12156, 29873, 2144, 29936, 13670, 1758, 878, 4678, 4650, 876, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1552, 6674, 17024, 740, 322, 278, 3001, 6674, 17024, 310, 7555, 10142, 4429, 8307, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 2059, 29871, 320, 2036, 29961, 1184, 3283, 29871, 29946, 29889, 29953, 3199, 7428, 29900, 29941, 29913, 395, 29940, 29985, 29872, 24033, 10142, 20828, 3822, 1262, 947, 13, 1333, 8839, 373, 278, 28143, 8405, 395, 29872, 1504, 7857, 697, 2337, 756, 13, 29938, 29940, 24033, 10142, 12156, 29873, 29897, 3490, 405, 29985, 29872, 24033, 10142, 12156, 29873, 1262, 29871, 322, 697, 508, 288, 2415, 278, 2380, 395, 29872, 29938, 297, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29909, 1836, 13, 13, 10401, 29871, 15399, 29871, 445, 5023, 304, 278, 13312, 13, 20621, 681, 760, 7555, 10142, 2844, 562, 1042, 310, 7555, 10142, 1042, 29871, 278, 17336, 5645, 13, 4535, 4650, 998, 562, 1042, 29871, 508, 367, 10434, 29871, 304, 367, 29871, 278, 9388, 267, 13000, 5645, 25984, 3822, 25183, 13, 265, 779, 29883, 29933, 1194, 29934, 4935, 13, 13, 1576, 6964, 310, 278, 6674, 17024, 740, 6511, 697, 304, 14944, 13, 1552, 1494, 15848, 29889, 13, 29905, 463, 29912, 16553, 1012, 1643, 29912, 2687, 29889, 29941, 29913, 13, 741, 331, 13, 12024, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 367, 1023, 5455, 15366, 29889, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 13, 1576, 5455, 5645, 7555, 10142, 2403, 29896, 29938, 338, 2000, 13, 21494, 29878, 635, 1014, 16065, 304, 278, 5455, 5645, 7555, 10142, 2403, 29906, 1628, 297, 3273, 13, 29938, 741, 10142, 2403, 29896, 29905, 17990, 29905, 9903, 9903, 17990, 741, 10142, 2403, 29906, 1628, 565, 7555, 10142, 2403, 29896, 29905, 17990, 741, 10142, 2403, 29906, 29938, 13, 392, 395, 29940, 24033, 10142, 2403, 29896, 2119, 29873, 2144, 280, 405, 24033, 10142, 2403, 29906, 2119, 29873, 2144, 29936, 1194, 8264, 16195, 1758, 878, 12156, 741, 10142, 2403, 29906, 876, 1504, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 13, 1576, 5455, 15366, 7555, 10142, 2403, 29896, 29938, 322, 7555, 10142, 2403, 29906, 29938, 526, 2000, 6683, 29878, 635, 13, 1686, 27445, 29892, 297, 3273, 7555, 10142, 2403, 29896, 320, 27996, 14850, 2802, 10142, 2403, 29906, 1628, 565, 7555, 10142, 2403, 29896, 320, 27996, 3601, 2802, 10142, 2403, 29906, 29938, 322, 13, 29938, 29940, 24033, 10142, 2403, 29896, 2119, 29873, 3892, 29940, 24033, 10142, 2403, 29906, 2119, 29873, 29897, 1194, 8264, 16195, 1758, 878, 12156, 741, 10142, 2403, 29906, 876, 1504, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29912, 11263, 1455, 363, 502, 297, 278, 8617, 295, 338, 278, 1494, 9185, 1836, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 2687, 29889, 29946, 29874, 29913, 13, 29912, 2803, 395, 29911, 29918, 29926, 29938, 367, 1583, 29899, 328, 12090, 12768, 16684, 297, 779, 7085, 29950, 29918, 29926, 29938, 13, 2541, 6590, 23161, 15366, 395, 29923, 648, 29911, 29918, 29926, 4678, 3822, 5767, 395, 29926, 353, 29896, 29892, 29906, 1504, 13, 12024, 779, 29883, 29928, 320, 262, 320, 29883, 29933, 1194, 29934, 4935, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 13, 29938, 29911, 29918, 29896, 29923, 648, 29911, 29918, 29896, 4678, 29883, 29928, 1262, 338, 263, 760, 310, 395, 29911, 29918, 29906, 29923, 648, 29911, 29918, 29906, 4678, 29883, 29928, 1262, 565, 322, 871, 565, 13, 29938, 29923, 648, 29911, 29918, 29896, 2053, 29883, 29928, 29913, 320, 17990, 29905, 9903, 9903, 17990, 29871, 382, 648, 29911, 29918, 29906, 2053, 29883, 29928, 4429, 988, 395, 29923, 648, 29911, 29918, 29926, 2053, 29883, 29928, 2119, 741, 4181, 1800, 3490, 13, 29923, 648, 29911, 29918, 29926, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 511, 320, 432, 353, 29871, 29896, 29892, 29906, 1504, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 13, 1576, 5633, 395, 29911, 29918, 29896, 29923, 648, 29911, 29918, 29896, 4678, 29883, 29928, 1262, 322, 395, 29911, 29918, 29906, 29923, 648, 29911, 29918, 29906, 4678, 29883, 29928, 1262, 526, 443, 3673, 2354, 7126, 13, 361, 322, 871, 565, 395, 29923, 648, 29911, 29918, 29896, 2053, 29883, 29928, 29913, 29871, 320, 27996, 14850, 382, 648, 29911, 29918, 29906, 2053, 29883, 29928, 4311, 29913, 13, 29905, 355, 29912, 14648, 29913, 13, 13, 1576, 5296, 338, 16800, 515, 320, 2036, 29961, 28831, 29871, 29955, 29889, 29945, 29889, 29896, 3199, 9851, 29947, 29955, 1836, 13, 2831, 29871, 779, 29883, 29928, 353, 320, 29934, 29938, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 29913, 4076, 5855, 363, 13, 29938, 29911, 29918, 29896, 29938, 304, 367, 443, 3673, 2354, 7126, 2845, 304, 263, 760, 310, 395, 29911, 29918, 29906, 29938, 29871, 470, 304, 13, 29938, 29911, 29918, 29906, 29938, 3528, 29889, 13, 13, 29905, 7235, 8290, 29934, 4388, 6678, 29879, 29913, 13, 13, 12024, 7555, 29883, 29950, 1042, 367, 263, 2903, 519, 12338, 2151, 2913, 29889, 1334, 17386, 393, 385, 5455, 29899, 4387, 287, 13, 2220, 395, 29943, 1194, 3822, 1262, 411, 1819, 297, 11970, 741, 29883, 29950, 6525, 29938, 338, 2000, 304, 367, 263, 13, 18650 ]

1,332,863

5,120

ArXiv

-1

glotz, Nevanlinna or $R$-function \cite{AG81,Ber68,GG91,KN77}, if it is holomorphic in $\C_+$ and its imaginary part is non-negative, i.e. $\im(F(z)) := (2i)^{-1}\bigl({F(z) - F(z)^*}\bigr) \ge 0, \ z\in \C_+$. In what follows we prefer the notion of R-function. The class of R-functions with values in $[\cH]$ will be denoted by $(R_\cH)$. Any $(R_\cH)$-function $F(\cdot)$ admits an integral representation \begin{equation}\label{1.2} F(z) = C_0 + C_1 z + \int_{-\infty}^{\infty} \left(\frac{1}{t-z}- \frac{t}{1 + t^2}\right) d{\Sigma}_F,\quad z\in \C_+, \end{equation} (see, for instance, \cite{AG81, Ber68, KN77}), where $C_0 = C_0^*, \ C_1\ge 0$ and ${\Sigma}_F$ is an operator-valued Borel measure on $\R$ satisfying $\int_\R (1+t^2)^{-1}d{\Sigma}_F \in [\cH]$. The integral is understood in the strong sense. In contrast to spectral measures of self-adjoint operators the measure ${\Sigma}_F$ is not necessarily orthogonal. However, the operator-valued measure ${\Sigma}_F$ is uniquely determined by the $R$-function $F(\cdot)$. It is called the spectral measure of $F(\cdot)$. The associated spectral function is denoted by ${\Sigma}_F(t)$, $t \in \R$, cf. { \eqref{a1}}. Let us calculate $N_{{\Sigma}^{ac}_F}(t)$, $t \in \R$. For any Hilbert-Schmidt operator ${ D} \in {\mathfrak S}_2(\cH)$ satisfying ${\xker\,}({D}) = {\xker\,}({D}^*) = \{0\}$ let us consider the modified $R_\cH$-function \begin{displaymath} (F^{ D})(z) := { D}^*F(z){ D}, \quad z \in \C_+. \end{displaymath} For $F^D(\cdot)$ the strong limit $F^D(t) := F^D(t+i0) :=\,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+\infty}F^D(t+iy)$ exists for a.e. $t \in \R$. We set \begin{equation}\Label{2.13} d_{F^D}(t):= {\rm dim}({\rm ran\,}(\im(F^D)(t))), \quad \mbox{for a.e.} \quad t \in \R. \end{equation} \begin{proposition}\Label{II.4} Let $F(\cdot)\in (R_\cH),$ \ $D \in {\mathfrak S}_2(\cH)$ and ${\xker\,}(D) = {\xker\,}(D^*) = \{0\}.$ Then $N_{{\Sigma}^{ac}_F}(t) = d_{F^{ D}}(t)$ for a.e. $t \in \R$. \end{proposition} \begin{proof} It follows from \eqref{1.2} that \begin{equation}\label{2.12} \im(F({\lambda} + iy)) = y C_1 +\int^\infty_{-\infty}\frac{y}{(t-{\lambda})^2 +y^2}d{\Sigma}_F, \qquad {\lambda} \in \R. \end{equation} By Berezanskii-Gel'fand-Kostyuchenko theorem \cite{Ber68,BS87} the derivative $\Psi_{D^*{\Sigma}_FD}(t) := \frac{d}{dt}D^*{\Sigma}_F(t)D$ exists for a.e. $t \in \R$ and the representation \begin{displaymath} D^*{\Sigma}^{ac}_F({\delta

0.143219

-1.080933

0.063781

2.298696

[ 0.5346039187700022, -0.2481655889027894 ]

[ -0.6377525887951465, -1.5241137365434572 ]

[ 0.40997785920560914, -0.2824159407242964 ]

[ 2.553630222975392, 2.043761650397827 ]

1,024

[ 512, 512 ]

[ 3820, 327, 29920, 29892, 2448, 3703, 1915, 1056, 470, 395, 29934, 4388, 2220, 13, 29905, 2036, 29912, 10051, 29947, 29896, 29892, 17104, 29953, 29947, 29892, 26788, 29929, 29896, 29892, 29968, 29940, 29955, 29955, 1118, 565, 372, 338, 8753, 16898, 297, 779, 29907, 29918, 24035, 322, 13, 1169, 6382, 3821, 760, 338, 1661, 29899, 22198, 29892, 474, 29889, 29872, 29889, 13, 4535, 326, 29898, 29943, 29898, 29920, 876, 3490, 313, 29906, 29875, 21604, 29896, 1012, 3752, 29880, 3319, 29943, 29898, 29920, 29897, 448, 383, 29898, 29920, 4887, 29930, 1012, 3752, 29878, 29897, 320, 479, 29871, 29900, 29892, 320, 29871, 503, 29905, 262, 13, 29905, 29907, 28842, 1504, 512, 825, 4477, 591, 5821, 278, 17837, 310, 390, 29899, 2220, 29889, 450, 770, 310, 13, 29934, 29899, 12171, 411, 1819, 297, 395, 7110, 29883, 29950, 9341, 674, 367, 27291, 491, 2427, 29934, 3187, 29883, 29950, 4935, 13, 10773, 2427, 29934, 3187, 29883, 29950, 26725, 2220, 395, 29943, 1194, 3822, 1262, 7336, 1169, 385, 10160, 13, 276, 26081, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29896, 29889, 29906, 29913, 13, 29943, 29898, 29920, 29897, 353, 315, 29918, 29900, 718, 315, 29918, 29896, 503, 718, 13, 29905, 524, 648, 2612, 3411, 6292, 3411, 29913, 320, 1563, 1194, 1154, 29912, 29896, 1157, 29873, 29899, 29920, 7402, 320, 1154, 29912, 29873, 1157, 29896, 718, 260, 29985, 29906, 1012, 1266, 29897, 270, 741, 10142, 2403, 29943, 2053, 3425, 503, 29905, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 29898, 4149, 29892, 363, 2777, 29892, 320, 2036, 29912, 10051, 29947, 29896, 29892, 2292, 29953, 29947, 29892, 476, 29940, 29955, 29955, 9594, 29871, 988, 395, 29907, 29918, 29900, 353, 315, 29918, 29900, 6622, 29892, 320, 315, 29918, 29896, 29905, 479, 29871, 29900, 29938, 322, 7555, 10142, 2403, 29943, 29938, 338, 385, 13, 6891, 29899, 4387, 287, 6780, 295, 5645, 373, 779, 29934, 29938, 24064, 779, 524, 3187, 29934, 13, 29898, 29896, 29974, 29873, 29985, 29906, 21604, 29896, 29913, 29881, 741, 10142, 2403, 29943, 320, 262, 12452, 29883, 29950, 22689, 450, 10160, 338, 11098, 297, 278, 13, 1110, 4060, 29889, 13, 13, 797, 12814, 304, 23161, 15366, 310, 1583, 29899, 328, 12090, 12768, 278, 13, 26658, 7555, 10142, 2403, 29943, 29938, 338, 451, 12695, 28143, 29889, 2398, 29892, 278, 13, 6891, 29899, 4387, 287, 5645, 7555, 10142, 2403, 29943, 29938, 338, 20498, 873, 10087, 491, 278, 13, 29938, 29934, 4388, 2220, 395, 29943, 1194, 3822, 4935, 29871, 739, 338, 2000, 278, 23161, 13, 26658, 310, 395, 29943, 1194, 3822, 4935, 450, 6942, 23161, 740, 338, 27291, 13, 1609, 7555, 10142, 2403, 29943, 29898, 29873, 5767, 395, 29873, 320, 262, 320, 29934, 1628, 274, 29888, 29889, 426, 320, 4915, 29912, 29874, 29896, 27243, 13, 13, 12024, 502, 29871, 8147, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 5767, 395, 29873, 320, 262, 320, 29934, 1504, 1152, 738, 13, 29950, 309, 2151, 29899, 4504, 19720, 5455, 6435, 360, 29913, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 13, 29879, 27685, 5414, 7555, 29916, 3946, 5940, 2119, 29912, 29928, 1800, 353, 2802, 29916, 3946, 5940, 2119, 29912, 29928, 2137, 7528, 353, 9991, 29900, 11854, 1235, 502, 2050, 278, 13, 1545, 2164, 395, 29934, 3187, 29883, 29950, 4388, 2220, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29943, 998, 360, 1800, 29898, 29920, 29897, 3490, 426, 360, 2137, 29930, 29943, 29898, 29920, 2597, 360, 1118, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 2831, 395, 29943, 29985, 29928, 1194, 3822, 1262, 278, 4549, 13, 13400, 395, 29943, 29985, 29928, 29898, 29873, 29897, 3490, 383, 29985, 29928, 29898, 29873, 29974, 29875, 29900, 29897, 584, 2013, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 3124, 3411, 29913, 29943, 29985, 29928, 29898, 29873, 29974, 19881, 1262, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29941, 29913, 13, 270, 648, 29943, 29985, 29928, 2119, 29873, 1125, 29922, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29943, 29985, 29928, 5033, 29873, 876, 511, 320, 3425, 320, 8264, 29912, 1454, 263, 29889, 29872, 5003, 29871, 320, 3425, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 2687, 29889, 29946, 29913, 13, 12024, 395, 29943, 1194, 3822, 2144, 262, 313, 29934, 3187, 29883, 29950, 511, 29938, 320, 395, 29928, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 13, 392, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 29905, 1836, 29938, 1987, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 29897, 353, 270, 648, 29943, 998, 360, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 3112, 4477, 515, 320, 4915, 29912, 29896, 29889, 29906, 29913, 393, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29906, 29913, 13, 320, 326, 29898, 29943, 13670, 2892, 29913, 718, 474, 29891, 876, 353, 343, 315, 29918, 29896, 17501, 524, 3823, 3411, 648, 2612, 3411, 1012, 1154, 29912, 29891, 19048, 29873, 29899, 741, 2892, 28813, 29906, 718, 29891, 29985, 29906, 29913, 29881, 741, 10142, 2403, 29943, 29892, 13, 29905, 12014, 2802, 2892, 29913, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 2059, 13143, 29920, 550, 1984, 29875, 29899, 29954, 295, 29915, 29888, 392, 29899, 29968, 520, 29891, 987, 264, 2901, 9185, 320, 2036, 29912, 17104, 29953, 29947, 29892, 9851, 29947, 29955, 29913, 278, 13, 672, 440, 1230, 779, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 29873, 29897, 3490, 320, 1154, 29912, 29881, 1157, 6008, 29913, 29928, 6622, 741, 10142, 2403, 29943, 29898, 29873, 29897, 29928, 29938, 4864, 363, 263, 29889, 29872, 29889, 13, 29938, 29873, 320, 262, 320, 29934, 29938, 322, 278, 8954, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 360, 6622, 741, 10142, 2844, 562, 2403, 29943, 13670, 4181 ]

1,332,863

6,144

ArXiv

-1

})D = \int_{\delta} \Psi_{D^*{\Sigma}_FD}(t) dt, \qquad {\delta} \in \cB_b(\R) \end{displaymath} holds. Applying the Fatou theorem (see \cite{KN77}) to \eqref{2.12} and using \eqref{2.13} we obtain \begin{equation}\Label{2.16} \im((F^D)({\lambda})) = \pi\Psi_{D^*{\Sigma}_FD}({\lambda}) \quad \text{for a.e.}\quad {\lambda} \in \R. \end{equation} By \cite[Corollary 4.7]{MM03} $N_{{\Sigma}^{ac}_F}({\lambda}) = {\rm rank\,}(\Psi_{D^*{\Sigma}_FD}({\lambda})) = {\rm dim}(\overline{{\rm ran\,}(\Psi_{D^*{\Sigma}_FD}({\lambda}))})$ for a.e. ${\lambda} \in \R$. Finally, using \eqref{2.16} we get $N_{{\Sigma}^{ac}_F}({\lambda}) = d_{F^D}({\lambda})$ for a.e. ${\lambda} \in \R$. \end{proof} { Notice that Proposition \ref{II.4} implies that $D_{F^D}(t)$ does not dependent on $D$}. Assuming the existence of the limit $F(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}F(t + iy)$ for a.e. $t \in \R$, we set \begin{displaymath} d_F(t) := {\rm rank\,}(\im(F(t)) = {\rm dim}({\rm ran\,}(\im(F(t)))) \end{displaymath} for a.e. $t\in \R$. In this case Proposition \ref{II.4} can be modified as follows. \begin{corollary}\Label{II.5} Let $F(\cdot)\in (R_\cH)$. If the limit $F(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}F(t + iy)$ exists for a.e. $t \in \R$, then $N_{{\Sigma}^{ac}_F}(t) = d_F(t)$ for a.e. $t \in \R$. \end{corollary} \subsection{Boundary triplets and self-adjoint extensions} In this section we briefly recall the basic facts on boundary triplets and the corresponding Weyl functions, cf. \cite{DM87,DM91,DM95,GG91}. Let $A$ be a densely defined closed symmetric operator in the separable Hilbert space $\gH$ with equal deficiency indices $n_\pm(A)={\rm dim}({\xker\,}(A^*\mp i)) \leq \infty$. \begin{definition}[\cite{GG91}]\Label{t1.9} {\em A triplet $\Pi = \{\cH, \Gamma_0, \Gamma_1\}$, where $\cH$ is an auxiliary Hilbert space and $\Gamma_0,\Gamma_1:\ {\rm dom\,}(A^*)\rightarrow \cH$ are linear mappings, is called an (ordinary) boundary triplet for $A^*$ if the "abstract Green's identity" \begin{equation}\Label{2.10A} (A^*f,g) - (f,A^*g) = ({\Gamma}_1f,{\Gamma}_0g)_{\cH} - ({\Gamma}_0f,{\Gamma}_1g)_{\cH}, \qquad f,g\in{\rm dom\,}(A^*), \end{equation} holds and the mapping ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top: {\rm dom\,}(A^*) \rightarrow \cH \oplus \cH$ is surjective. } \end{definition} \begin{definition}[\cite{GG91}]\Label{def2.2} {\em A closed extension $A'$ of $A$ is called a proper extension, in short $A'\in {\rm Ext\,}_A,$

-0.380339

-1.452489

-0.213303

1.892882

[ -0.3419883557892045, -0.41869017981313505 ]

[ -1.6602015087229958, -1.2447756778591412 ]

[ -0.3293363996939053, -0.09727034587124471 ]

[ 2.012545207178792, 1.773219142499527 ]

1,024

[ 512, 512 ]

[ 1800, 29928, 353, 320, 524, 1665, 4181, 29913, 320, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 29873, 29897, 11636, 29892, 13, 29905, 12014, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 8640, 29889, 2401, 5890, 278, 29871, 383, 271, 283, 9185, 313, 4149, 320, 2036, 29912, 29968, 29940, 29955, 29955, 1800, 304, 320, 4915, 29912, 29906, 29889, 29896, 29906, 29913, 322, 773, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29941, 29913, 591, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29953, 29913, 13, 29905, 326, 3552, 29943, 29985, 29928, 5033, 741, 2892, 20073, 353, 320, 1631, 29905, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 1800, 320, 3425, 320, 726, 29912, 1454, 13, 29874, 29889, 29872, 29889, 1012, 3425, 2802, 2892, 29913, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 2059, 29871, 320, 2036, 29961, 12521, 21982, 29871, 29946, 29889, 29955, 3199, 7428, 29900, 29941, 29913, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 741, 2892, 1800, 353, 13, 741, 1758, 7115, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 20073, 353, 2802, 1758, 3964, 4678, 6875, 16195, 1758, 6350, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2403, 26453, 2119, 741, 2892, 20073, 8435, 363, 263, 29889, 29872, 29889, 13, 29938, 741, 2892, 29913, 320, 262, 320, 29934, 1504, 9788, 29892, 773, 320, 4915, 29912, 29906, 29889, 29896, 29953, 29913, 591, 679, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 741, 2892, 1800, 353, 13, 29881, 648, 29943, 29985, 29928, 2119, 741, 2892, 8435, 363, 263, 29889, 29872, 29889, 7555, 2892, 29913, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29912, 16393, 393, 22206, 320, 999, 29912, 2687, 29889, 29946, 29913, 10469, 393, 395, 29928, 648, 29943, 29985, 29928, 2119, 29873, 1262, 947, 451, 13, 18980, 373, 395, 29928, 29938, 1836, 17090, 13, 1552, 10379, 310, 278, 29871, 4046, 395, 29943, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29943, 29898, 29873, 718, 474, 29891, 1262, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 29871, 591, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29881, 29918, 29943, 29898, 29873, 29897, 3490, 2802, 1758, 7115, 5940, 4678, 326, 29898, 29943, 29898, 29873, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29943, 29898, 29873, 13697, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 29905, 262, 320, 29934, 1504, 512, 445, 1206, 22206, 320, 999, 29912, 2687, 29889, 29946, 29913, 13, 3068, 367, 9120, 408, 4477, 29889, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 2687, 29889, 29945, 29913, 13, 12024, 395, 29943, 1194, 3822, 2144, 262, 313, 29934, 3187, 29883, 29950, 4935, 960, 13, 1552, 4046, 395, 29943, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29943, 29898, 29873, 718, 474, 29891, 1262, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 395, 29940, 24033, 10142, 2844, 562, 2403, 29943, 2119, 29873, 29897, 353, 270, 29918, 29943, 29898, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 13, 29905, 7235, 29912, 17109, 653, 21954, 1372, 322, 1583, 29899, 328, 12090, 17752, 29913, 13, 13, 797, 445, 4004, 591, 23359, 13, 3757, 497, 278, 6996, 17099, 373, 29871, 10452, 21954, 1372, 322, 278, 6590, 13, 29956, 1032, 29880, 3168, 29892, 274, 29888, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29892, 26788, 29929, 29896, 1836, 13, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 278, 13, 25048, 519, 12338, 2151, 2913, 779, 29887, 29950, 29938, 411, 5186, 822, 293, 13396, 16285, 13, 29938, 29876, 3187, 3358, 29898, 29909, 3892, 741, 1758, 3964, 2119, 741, 29916, 3946, 5940, 2119, 29909, 6622, 29905, 1526, 474, 876, 320, 3797, 320, 3411, 1504, 13, 29905, 463, 29912, 16553, 4400, 29905, 2036, 29912, 26788, 29929, 29896, 6525, 29905, 4775, 29912, 29873, 29896, 29889, 29929, 29913, 13, 741, 331, 13, 29909, 21954, 29873, 779, 12197, 353, 320, 741, 29883, 29950, 29892, 320, 6642, 29918, 29900, 29892, 13, 29905, 6642, 29918, 29896, 28538, 988, 779, 29883, 29950, 29938, 338, 385, 29587, 653, 12338, 2151, 2913, 322, 13, 4535, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 3583, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 2144, 5211, 320, 29883, 29950, 29938, 526, 5608, 13, 655, 27775, 29892, 29871, 338, 2000, 385, 313, 24310, 29897, 10452, 21954, 29873, 363, 395, 29909, 6622, 29938, 565, 13, 1552, 376, 16595, 7646, 29915, 29879, 10110, 29908, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29906, 29889, 29896, 29900, 29909, 29913, 13, 29898, 29909, 6622, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 6622, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 741, 6642, 2403, 29900, 29887, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 29888, 29892, 741, 6642, 2403, 29896, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 6622, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 23177, 322, 278, 10417, 7555, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29901, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 13, 29905, 5211, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 29938, 338, 1190, 25674, 29889, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 29905, 463, 29912, 16553, 4400, 29905, 2036, 29912, 26788, 29929, 29896, 6525, 29905, 4775, 29912, 1753, 29906, 29889, 29906, 29913, 13, 741, 331, 13, 29909, 5764, 6081, 395, 29909, 13090, 310, 395, 29909, 29938, 338, 2000, 263, 1571, 6081, 29892, 13, 262, 3273, 395, 29909, 12764, 262, 2802, 1758, 7338, 5940, 2403, 29909, 8209 ]

1,332,863

7,168

ArXiv

-1

if $A\subset A' \subset A^*;$ Two proper extensions $A', A''$ are called disjoint if ${\rm dom\,}( A')\cap {\rm dom\,}( A'') = {\rm dom\,}( A)$ and transversal if in addition ${\rm dom\,}( A') + {\rm dom\,}( A'') = {\rm dom\,}( A^*).$ } \end{definition} Clearly, any self-adjoint extension $\wt A= {\wt A}^*$ is proper, $\wt A\in {\rm Ext\,}_A.$ A boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^*$ exists whenever $n_+(A) = n_-(A)$. Moreover, the relations $n_\pm(A) = {\rm dim}(\cH)$ and ${\xker\,}(\Gamma_0) \cap {\xker\,}(\Gamma_1)={\rm dom\,}(A)$ are valid. Besides, $\Gamma_0, \Gamma_1\in [{\mathfrak H}_+, \cH]$, where ${\mathfrak H}_+$ denotes the Hilbert space { obtained by equipping} ${\rm dom\,}(A^*)$ with the graph norm of $A^*$. With any boundary triplet $\Pi$ one associates two extensions $A_j:=A^*\!\upharpoonright{\xker\,}({\Gamma}_j), \ j\in \{0,1\}$, which are self-adjoint in view of Proposition \ref{prop2.1} below. Conversely, for any extension $A_0=A_0^*\in {\rm Ext\,}_A$ there exists a (non-unique) boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^*$ such that $A_0:=A^*\!\upharpoonright{\xker\,}({\Gamma}_0)$. Using the concept of { boundary triplets} one can parameterize all proper, in particular, self-adjoint extensions of $A$. For this purpose denote by $\widetilde\cC(\cH)$ the set of closed linear relations in $\cH$, that is, the set of (closed) linear subspaces of $\cH\oplus\cH$. The adjoint relation $\Theta^*\in\widetilde\cC(\cH)$ of a linear relation $\Theta$ in $\cH$ is defined by \begin{equation*} \Theta^*= \left\{ \begin{pmatrix} k\\k^\prime \end{pmatrix}: (h^\prime,k)=(h,k^\prime)\,\,\text{for all}\, \begin{pmatrix} h\\h^\prime\end{pmatrix} \in\Theta\right\}. \end{equation*} A linear relation $\Theta$ is called {\it symmetric} if $\Theta\subset\Theta^*$ and self-adjoint if $\Theta=\Theta^*$. The multivalued part ${\rm mul\,}(\Theta)$ of { $\Theta\in \wt\cC(\cH)$ is} ${\rm mul\,}(\Theta) = \{h \in \cH: \{0,h\}\in \Theta\}.$ Setting $\cH_{\infty} :={\rm mul\,}(\Theta)$ and $\cH_{\rm op} :=\cH^{\perp}_{\infty}$ we get $\cH=\cH_{\rm op}\oplus\cH_{\infty}$. This decomposition yields an orthogonal { decomposition} $\Theta=\Theta_{\rm op}\oplus\Theta_{\infty}$ where $\Theta_{\infty}:= \{0\}\oplus{\rm mul\,}(\Theta)$ and $\Theta_{\rm op}:= \{\{f,g\}\in\Theta:\ f\in {\rm dom\,}(\Theta), g\perp{\rm mul\,}(\Theta)\}$. For the definition of the inverse and the resolvent set of a linear relation $\Theta$ we refer to \cite{DS87}. \begin{proposition}\label{prop2.1} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^*.$ Then the mapping \begin{equation}\label{bij} ({\rm Ext\,}_A\ni)\ \widetilde A \to \Gamma {\rm dom\,}(\widetilde A) =\{\{\Gamma_0 f,\Gamma_1f \} : \

0.182597

-1.092572

0.37447

2.345521

[ 0.24149337696426745, 0.12370129007037405 ]

[ -0.9761813906626834, -1.2089631062329467 ]

[ 0.5063550181702113, 0.24258595153024737 ]

[ 2.220654828639023, 2.4703863743912997 ]

1,024

[ 512, 512 ]

[ 565, 395, 29909, 29905, 6484, 319, 29915, 320, 6484, 319, 6622, 29936, 29938, 13, 13, 13985, 1571, 17752, 395, 29909, 742, 319, 4907, 29938, 526, 2000, 766, 12090, 565, 13, 29938, 741, 1758, 2432, 5940, 2119, 319, 1495, 29905, 5030, 2802, 1758, 2432, 5940, 2119, 319, 29915, 1495, 353, 2802, 1758, 2432, 5940, 2119, 319, 1262, 322, 29871, 1301, 874, 284, 565, 297, 13, 1202, 654, 7555, 1758, 2432, 5940, 2119, 319, 1495, 718, 2802, 1758, 2432, 5940, 2119, 319, 29915, 1495, 353, 2802, 1758, 2432, 5940, 2119, 319, 6622, 467, 29938, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 18759, 368, 29892, 738, 29871, 1583, 29899, 328, 12090, 6081, 779, 14554, 319, 29922, 2802, 14554, 319, 2137, 29394, 338, 1571, 29892, 13, 779, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 29909, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 4864, 13, 8256, 1310, 29871, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 4935, 12808, 29892, 278, 5302, 395, 29876, 3187, 3358, 29898, 29909, 29897, 353, 13, 741, 1758, 3964, 4678, 29883, 29950, 1262, 322, 7555, 29916, 3946, 5940, 4678, 6642, 29918, 29900, 29897, 320, 5030, 2802, 29916, 3946, 5940, 4678, 6642, 29918, 29896, 3892, 741, 1758, 2432, 5940, 2119, 29909, 1262, 526, 13, 3084, 29889, 19065, 29892, 779, 6642, 29918, 29900, 29892, 320, 6642, 29918, 29896, 29905, 262, 518, 741, 7237, 379, 2403, 29974, 29892, 320, 29883, 29950, 25473, 13, 3062, 7555, 7237, 379, 2403, 24035, 20169, 278, 12338, 2151, 2913, 426, 7625, 13, 1609, 1592, 17347, 29913, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 411, 278, 3983, 6056, 310, 395, 29909, 6622, 1504, 13, 13, 3047, 738, 10452, 21954, 29873, 779, 12197, 29938, 697, 4067, 1078, 29871, 1023, 17752, 13, 29938, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 511, 320, 432, 29905, 262, 9991, 29900, 29892, 29896, 28538, 607, 526, 13, 1311, 29899, 328, 12090, 297, 1776, 310, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 2400, 29889, 13, 1168, 874, 873, 29892, 363, 738, 6081, 395, 29909, 29918, 29900, 29922, 29909, 29918, 29900, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 727, 4864, 13, 29874, 313, 5464, 29899, 13092, 29897, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 13, 14565, 393, 395, 29909, 29918, 29900, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 13, 13, 15156, 278, 6964, 310, 426, 10452, 21954, 1372, 29913, 697, 508, 3443, 675, 599, 13, 771, 546, 29892, 297, 3153, 29892, 1583, 29899, 328, 12090, 17752, 310, 395, 29909, 1504, 1152, 445, 13, 15503, 4220, 13530, 491, 779, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 278, 731, 29871, 310, 5764, 5608, 13, 2674, 800, 297, 779, 29883, 29950, 1628, 393, 338, 29892, 278, 731, 310, 313, 15603, 29897, 5608, 1014, 22854, 13, 974, 779, 29883, 29950, 29905, 17201, 29905, 29883, 29950, 1504, 450, 594, 12090, 8220, 13, 4535, 17458, 6622, 29905, 262, 29905, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 310, 263, 5608, 8220, 779, 17458, 29938, 297, 13, 4535, 29883, 29950, 29938, 338, 3342, 491, 13, 29905, 463, 29912, 2573, 4044, 13, 29905, 17458, 6622, 29922, 320, 1563, 10045, 13, 29905, 463, 29912, 12571, 29913, 413, 1966, 29895, 3823, 10080, 13, 29905, 355, 29912, 12571, 6177, 313, 29882, 3823, 10080, 29892, 29895, 3892, 29898, 29882, 29892, 29895, 3823, 10080, 2144, 2053, 2053, 726, 29912, 1454, 599, 15379, 13, 29905, 463, 29912, 12571, 29913, 298, 1966, 29882, 3823, 10080, 29905, 355, 29912, 12571, 29913, 13, 29905, 262, 29905, 17458, 29905, 1266, 29905, 1836, 13, 29905, 355, 29912, 2573, 4044, 13, 29909, 5608, 8220, 779, 17458, 29938, 338, 2000, 2802, 277, 18348, 29913, 565, 13, 4535, 17458, 29905, 6484, 29905, 17458, 6622, 29938, 322, 1583, 29899, 328, 12090, 565, 779, 17458, 2013, 17458, 6622, 1504, 13, 13, 1576, 1773, 2561, 6742, 760, 7555, 1758, 15065, 5940, 4678, 17458, 1262, 310, 426, 779, 17458, 29905, 262, 13, 29905, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 338, 29913, 7555, 1758, 15065, 5940, 4678, 17458, 29897, 353, 9991, 29882, 320, 262, 320, 29883, 29950, 29901, 9991, 29900, 29892, 29882, 25848, 262, 13, 29905, 17458, 29905, 1836, 29938, 21605, 779, 29883, 29950, 1665, 3411, 29913, 3490, 741, 1758, 15065, 5940, 4678, 17458, 1262, 322, 779, 29883, 29950, 1665, 1758, 1015, 29913, 13, 29901, 2013, 29883, 29950, 3311, 24598, 6353, 3411, 1042, 591, 679, 779, 29883, 29950, 2013, 29883, 29950, 1665, 1758, 13, 459, 1012, 17201, 29905, 29883, 29950, 1665, 3411, 4311, 910, 26227, 17498, 385, 28143, 13, 29912, 26227, 29913, 13, 4535, 17458, 2013, 17458, 1665, 1758, 1015, 1012, 17201, 29905, 17458, 1665, 3411, 1042, 29871, 988, 13, 4535, 17458, 1665, 3411, 6177, 29922, 9991, 29900, 25848, 17201, 741, 1758, 15065, 5940, 4678, 17458, 1262, 322, 779, 17458, 1665, 1758, 1015, 6177, 29922, 13, 24976, 29912, 29888, 29892, 29887, 25848, 262, 29905, 17458, 3583, 285, 29905, 262, 2802, 1758, 2432, 5940, 4678, 17458, 511, 330, 29905, 24598, 741, 1758, 15065, 5940, 4678, 17458, 2144, 4311, 1152, 13, 1552, 5023, 310, 278, 16402, 322, 278, 3770, 794, 731, 310, 263, 5608, 13, 23445, 779, 17458, 29938, 591, 2737, 304, 320, 2036, 29912, 8452, 29947, 29955, 1836, 13, 29905, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29906, 29889, 29896, 29913, 13, 12024, 29871, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 367, 263, 13, 9917, 653, 21954, 29873, 363, 29871, 395, 29909, 6622, 7449, 29871, 1987, 278, 10417, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 19352, 29913, 13, 13670, 1758, 7338, 5940, 2403, 29909, 29905, 1240, 2144, 320, 10737, 319, 320, 517, 29871, 320, 6642, 2802, 1758, 2432, 5940, 4678, 10737, 319, 29897, 13, 2013, 741, 741, 6642, 29918, 29900, 285, 2053, 6642, 29918, 29896, 29888, 320, 29913, 584, 320, 29871 ]

1,332,863

8,192

ArXiv

-1

f\in {\rm dom\,}(\widetilde A) \} =: \Theta \in \widetilde\cC(\cH) \end{equation} establishes a bijective correspondence between the sets ${\rm Ext\,}_A$ and $\widetilde\cC(\cH)$. We put $A_\Theta :=\widetilde A$ where $\Theta$ is defined by \eqref{bij}. { Moreover, the} following holds: \item[\;\;\rm (i)] $A_\Theta= A_\Theta^*$ if and only if $\Theta= \Theta^*;$ \item[\;\;\rm (ii)] The extensions $A_\Theta$ and $A_0$ are disjoint if and only if $\Theta\in \cC(\cH).$ In this case \eqref{bij} becomes \begin{displaymath} A_\Theta = A^*\!\upharpoonright{\xker\,}({\Gamma}_1- \Theta{\Gamma}_0); \end{displaymath} \item[\;\;\rm (iii)] The extensions $A_\Theta$ and $A_0$ are transversal if and only if $\Theta = \Theta^*\in [\cH].$ \end{proposition} In particular, $A_j:=A^*\!\upharpoonright{\xker\,}({\Gamma}_j) = A_{\Theta_j},\ j\in \{0,1\}$ where ${\Theta}_0:= \{0\} \times \cH$ and ${\Theta}_1 := \cH \times \{0\}$. Hence $A_j= A_j^*$ since ${\Theta}_j = {\Theta}^*_j.$ In the sequel the extension $A_0$ is usually regarded as a reference self-adjoint extension. \subsection{Weyl functions and $\gamma$-fields}\label{weylsec} It is well known that Weyl functions give an important tool in the direct and inverse spectral theory of singular Sturm-Liouville operators. In \cite{DM87,DM91,DM95} the concept of Weyl function was generalized to the case of an arbitrary symmetric operator $A$ with $n_+(A) = n_-(A).$ Following \cite{DM87,DM91,DM95} we recall basic facts on Weyl functions and $\gamma$-fields associated with a boundary triplet $\Pi$. \begin{definition}[{\cite{DM87,DM91}}]\label{Weylfunc} {\em Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^*.$ The functions $\gamma(\cdot): \varrho(A_0)\rightarrow [\cH,\gH]$ and $M(\cdot): \varrho(A_0)\rightarrow [\cH]$ defined by \begin{equation}\label{2.3A} \gamma(z):=\bigl(\Gamma_0\!\upharpoonright\mathfrak N_z\bigr)^{-1} \qquad\text{and}\qquad M(z):=\Gamma_1\gamma(z), \qquad z\in\varrho(A_0), \end{equation} are called the {\em $\gamma$-field} and the {\em Weyl function}, respectively, corresponding to $\Pi.$ } \end{definition} It follows from the identity ${\rm dom\,}(A^*)={\xker\,}(\Gamma_0)\dot + {\mathfrak N}_z$, $z\in\varrho(A_0)$, where $A_0 = A^*\!\upharpoonright{\xker\,}({\Gamma}_0)$, and ${\mathfrak N}_z :={\xker\,}(A^* - z)$, that the $\gamma$-field $\gamma(\cdot)$ is well defined and takes values in $[\cH,\gH]$. Since ${\Gamma}_1 \in [\gH_+, \cH]$, it follows from \eqref{2.3A} that $M(\cdot)$ is well defined too and takes values in $[\cH]$. Moreover, both $\gamma(\cdot)$ and $M(\cdot)$ are holomorphic on $\varrho(A_0)$ and satisfy the following relations (see \cite{DM91}) \begin{equation}\label{2.

0.178488

-0.833826

0.47592

2.407953

[ 0.312716499272203, 0.04426011518844594 ]

[ -1.194638077582469, -0.4730147593146524 ]

[ 0.2831658079363957, 0.6686744437948046 ]

[ 2.2830877150770923, 2.532819260829369 ]

1,024

[ 512, 512 ]

[ 285, 29905, 262, 2802, 1758, 2432, 5940, 4678, 10737, 319, 29897, 320, 29913, 353, 29901, 13, 29905, 17458, 320, 262, 320, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 342, 370, 1674, 267, 29871, 263, 4768, 25674, 3928, 663, 1546, 278, 6166, 7555, 1758, 7338, 5940, 2403, 29909, 29938, 13, 392, 29871, 779, 10737, 29905, 29883, 29907, 1194, 29883, 29950, 4935, 1334, 1925, 395, 29909, 3187, 17458, 584, 2013, 10737, 319, 29938, 988, 13, 4535, 17458, 29938, 338, 3342, 491, 320, 4915, 29912, 19352, 1836, 426, 12808, 29892, 278, 29913, 1494, 8640, 29901, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 395, 29909, 3187, 17458, 29922, 319, 3187, 17458, 6622, 29938, 565, 322, 871, 565, 779, 17458, 29922, 13, 29905, 17458, 6622, 29936, 29938, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 450, 17752, 395, 29909, 3187, 17458, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 13, 2218, 12090, 565, 322, 871, 565, 779, 17458, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 512, 445, 1206, 13, 29905, 4915, 29912, 19352, 29913, 7415, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29909, 3187, 17458, 353, 319, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 29899, 13, 29905, 17458, 741, 6642, 2403, 29900, 416, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 25609, 4638, 450, 17752, 395, 29909, 3187, 17458, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 13, 3286, 874, 284, 565, 322, 871, 565, 779, 17458, 353, 320, 17458, 6622, 29905, 262, 12452, 29883, 29950, 1822, 29938, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 797, 3153, 29892, 13, 29938, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 29897, 353, 319, 1665, 17458, 29918, 29926, 7570, 432, 29905, 262, 13, 10045, 29900, 29892, 29896, 11854, 988, 7555, 17458, 2403, 29900, 9361, 9991, 29900, 18105, 320, 3706, 320, 29883, 29950, 29938, 322, 7555, 17458, 2403, 29896, 3490, 320, 29883, 29950, 320, 3706, 13, 10045, 29900, 23699, 10133, 395, 29909, 29918, 29926, 29922, 319, 29918, 29926, 6622, 29938, 1951, 7555, 17458, 2403, 29926, 13, 29922, 2802, 17458, 2137, 29930, 29918, 29926, 7449, 512, 278, 8617, 295, 278, 6081, 395, 29909, 29918, 29900, 29938, 13, 275, 5491, 17878, 408, 263, 3407, 13, 1311, 29899, 328, 12090, 6081, 29889, 13, 13, 29905, 7235, 29912, 29956, 1032, 29880, 3168, 322, 779, 4283, 4388, 9621, 1012, 1643, 29912, 705, 2904, 3471, 29913, 13, 13, 3112, 338, 1532, 2998, 393, 399, 1032, 29880, 3168, 2367, 385, 4100, 5780, 297, 278, 13, 11851, 322, 16402, 23161, 6368, 310, 13512, 624, 17095, 29899, 23410, 283, 4909, 13, 3372, 4097, 29889, 512, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29913, 278, 6964, 310, 399, 1032, 29880, 740, 13, 11102, 28803, 304, 278, 1206, 310, 385, 11472, 18348, 5455, 395, 29909, 29938, 13, 2541, 29871, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 467, 29938, 12206, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 29913, 591, 17386, 13, 16121, 17099, 373, 399, 1032, 29880, 3168, 322, 779, 4283, 4388, 9621, 6942, 411, 13, 29874, 10452, 21954, 29873, 779, 12197, 1504, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 930, 10725, 1643, 29912, 29956, 1032, 29880, 9891, 29913, 13, 741, 331, 13, 2803, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 10452, 21954, 29873, 29871, 363, 395, 29909, 6622, 7449, 13, 1576, 3168, 779, 4283, 1194, 3822, 1125, 13, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5211, 12452, 29883, 29950, 2053, 29887, 29950, 9341, 322, 29871, 395, 29924, 1194, 3822, 1125, 13, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5211, 29871, 12452, 29883, 29950, 9341, 3342, 491, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29941, 29909, 29913, 13, 29905, 4283, 29898, 29920, 1125, 2013, 3752, 29880, 1194, 6642, 29918, 29900, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 29905, 7237, 405, 29918, 29920, 29905, 3752, 29878, 21604, 29896, 29913, 13, 29905, 12014, 29905, 726, 29912, 392, 1012, 12014, 341, 29898, 29920, 1125, 2013, 6642, 29918, 29896, 29905, 4283, 29898, 29920, 511, 320, 12014, 13, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 418, 320, 355, 29912, 2573, 29913, 13, 598, 2000, 278, 2802, 331, 779, 4283, 4388, 2671, 29913, 322, 278, 2802, 331, 399, 1032, 29880, 740, 1118, 13, 690, 1103, 3598, 29892, 6590, 304, 29871, 779, 12197, 7449, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 3112, 4477, 515, 278, 10110, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 3892, 741, 29916, 3946, 5940, 4678, 6642, 29918, 29900, 2144, 6333, 718, 13, 741, 7237, 405, 2403, 29920, 1628, 395, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 5767, 988, 29871, 395, 29909, 29918, 29900, 353, 13, 29909, 6622, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 322, 7555, 7237, 405, 2403, 29920, 3490, 741, 29916, 3946, 5940, 2119, 29909, 6622, 448, 13, 29920, 5767, 393, 278, 779, 4283, 4388, 2671, 779, 4283, 1194, 3822, 1262, 338, 1532, 3342, 322, 13, 29873, 6926, 1819, 297, 395, 7110, 29883, 29950, 2053, 29887, 29950, 22689, 4001, 7555, 6642, 2403, 29896, 320, 262, 12452, 29887, 29950, 28842, 29892, 320, 29883, 29950, 25473, 372, 13, 23031, 29879, 515, 320, 4915, 29912, 29906, 29889, 29941, 29909, 29913, 393, 29871, 395, 29924, 1194, 3822, 1262, 338, 1532, 3342, 2086, 322, 13, 29873, 6926, 1819, 297, 259, 395, 7110, 29883, 29950, 22689, 12808, 29892, 1716, 779, 4283, 1194, 3822, 1262, 322, 13, 29938, 29924, 1194, 3822, 1262, 526, 8753, 16898, 373, 779, 1707, 4650, 29898, 29909, 29918, 29900, 1262, 322, 15523, 278, 13, 23031, 292, 5302, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 1800, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889 ]

1,332,863

9,216

ArXiv

-1

15} \gamma(z)=\bigl(I+(z-\zeta)(A_0 - z)^{-1}\bigr)\gamma(\zeta), \qquad z, \zeta\in\varrho(A_0), \end{equation} and \begin{equation}\label{mlambda} M(z) - M(\zeta)^*= (z - \bar\zeta)\gamma(\zeta)^*\gamma(z), \qquad z, \zeta\in\varrho(A_0). \end{equation} The last identity yields that $M(\cdot)$ is a $R_{\cH}$-function, that is, $M(\cdot)$ is a $[\cH]$-valued holomorphic function on $\C\backslash \R$ satisfying \begin{displaymath} M(z)=M(\overline z)^*\qquad\text{and}\qquad \frac{{\rm Im\,}(M(z))}{{\rm Im\,}(z)}\geq 0, \qquad z\in\C\backslash\R. \end{displaymath} Moreover, it follows from \eqref{mlambda} that $M(\cdot)$ satisfies $0\in \varrho({\rm Im\,}(M(z))),\ z\in\C\backslash\R$. If $A$ is a simple symmetric operator, then the Weyl function $M(\cdot)$ determines the pair $\{A,A_0\}$ uniquely up to unitary equivalence (see \cite{DM95,KL71}). Therefore $M(\cdot)$ contains (implicitly) full information on spectral properties of $A_0$. We recall that a symmetric operator is said to be {\it simple} if there is no non-trivial subspace which reduces it to a self-adjoint operator. For a fixed $A_0 = A_0^*$ a boundary triplet $\Pi =\{\cH, {\Gamma}_0,{\Gamma}_1\}$ satisfying ${\rm dom\,}(A_0)={\xker\,} (\Gamma_0)$ is not unique. Let $\Pi_j =\{\cH_j, {\Gamma}^j_0,{\Gamma}^j_1\}, \ j\in \{1,2\},$ be two such triplets. Then the corresponding Weyl functions $M_1(\cdot)$ and $M_2(\cdot)$ are related by \begin{equation}\label{2.11} M_2(z) = R^* M_1(z) R + R_0, \end{equation} where $R_0= R^*_0 \in [{\cH}_2]$ and $R \in [{\cH}_2,{\cH}_1]$ is boundedly invertible. According to Proposition \ref{prop2.1} the extensions $A_{{\Theta}}$ and $A_0$ are not disjoint whenever ${\rm mul\,}(\Theta)\not = \{0\}.$ Considering $A_{{\Theta}}$ and $A_0$ as extensions of an intermediate extension $S := A_0\upharpoonright({\rm dom\,}(A_0) \cap {\rm dom\,}(A_{\Theta}))$ we can avoid this inconvenience. \begin{lemma}\Label{III.4} Let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^*$, $M(\cdot)$ the corresponding Weyl function, ${\Theta}= {\Theta}^* \in \wt\cC(\cH)$ and ${\Theta} = \Theta_{op}\oplus \Theta_\infty $ its orthogonal decomposition. Further let $S := A_0\upharpoonright({\rm dom\,}(A_0) \cap {\rm dom\,}(A_{\Theta}))$. Then the triplet $\wh{\Pi} = \{\wh\cH,\wh{\Gamma}_0,\wh{\Gamma}_1\}$, defined by \begin{displaymath} \wh\cH := \cH_{\rm op} = \overline{{\rm dom\,}(\Theta)},\quad \wh{\Gamma}_0 := {\Gamma}_0\upharpoonright{\rm dom\,}( S^*),\quad \wh{\Gamma}_1 := \pi_{\rm op}{\Gamma}_1\upharpoonright{\rm dom\,}(S^*), \end{displaymath} is a

-0.010527

-1.149872

0.032078

2.210249

[ 0.1154832374963815, -0.13653704143939044 ]

[ -1.0191564766141166, -1.2805882494853356 ]

[ 0.09802021308334402, -0.033864320236637976 ]

[ 2.303898677223115, 2.1166000179089077 ]

1,024

[ 512, 512 ]

[ 29896, 29945, 29913, 13, 29905, 4283, 29898, 29920, 7950, 3752, 29880, 29898, 29902, 17108, 29920, 2612, 11327, 5033, 29909, 29918, 29900, 448, 503, 21604, 29896, 1012, 3752, 29878, 2144, 4283, 1194, 11327, 511, 13, 29905, 12014, 503, 29892, 320, 11327, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 392, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 828, 2269, 29913, 13, 29924, 29898, 29920, 29897, 448, 341, 1194, 11327, 4887, 29930, 29922, 313, 29920, 448, 320, 1646, 29905, 11327, 2144, 4283, 1194, 11327, 4887, 17710, 4283, 29898, 29920, 511, 320, 12014, 503, 29892, 13, 29905, 11327, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1576, 1833, 10110, 17498, 393, 395, 29924, 1194, 3822, 1262, 338, 263, 395, 29934, 1665, 29883, 29950, 23021, 2220, 29892, 13, 5747, 338, 29892, 395, 29924, 1194, 3822, 1262, 338, 263, 395, 7110, 29883, 29950, 29962, 4388, 4387, 287, 8753, 16898, 740, 373, 13, 4535, 29907, 29905, 1627, 17057, 320, 29934, 29938, 29871, 24064, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29898, 29920, 3892, 29924, 1194, 6875, 503, 4887, 17710, 12014, 29905, 726, 29912, 392, 1012, 12014, 13, 29905, 1154, 16195, 1758, 1954, 5940, 2119, 29924, 29898, 29920, 876, 1157, 741, 1758, 1954, 5940, 2119, 29920, 11383, 6279, 29871, 29900, 29892, 320, 12014, 503, 29905, 262, 29905, 29907, 29905, 1627, 17057, 29905, 29934, 29889, 13, 320, 355, 29912, 4990, 755, 29913, 13, 20761, 957, 29892, 372, 4477, 515, 320, 4915, 29912, 828, 2269, 29913, 393, 395, 29924, 1194, 3822, 1262, 17150, 13, 29938, 29900, 29905, 262, 320, 1707, 4650, 13670, 1758, 1954, 5940, 2119, 29924, 29898, 29920, 876, 20481, 29871, 503, 29905, 262, 29905, 29907, 29905, 1627, 17057, 29905, 29934, 1504, 13, 13, 13, 3644, 395, 29909, 29938, 338, 263, 2560, 18348, 5455, 29892, 769, 29871, 278, 399, 1032, 29880, 740, 13, 29938, 29924, 1194, 3822, 1262, 3683, 1475, 278, 5101, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 20498, 873, 701, 304, 5190, 653, 13, 1686, 2561, 663, 313, 4149, 320, 2036, 29912, 23560, 29929, 29945, 29892, 29968, 29931, 29955, 29896, 7690, 7857, 395, 29924, 1194, 3822, 1262, 3743, 13, 29898, 6574, 4019, 368, 29897, 29871, 2989, 2472, 373, 23161, 4426, 310, 395, 29909, 29918, 29900, 1504, 13, 4806, 17386, 393, 263, 18348, 5455, 338, 13, 4977, 333, 304, 367, 2802, 277, 2560, 29913, 565, 727, 338, 694, 1661, 29899, 29873, 9473, 1014, 3493, 607, 13, 9313, 778, 372, 304, 263, 1583, 29899, 328, 12090, 5455, 29889, 13, 13, 2831, 263, 4343, 395, 29909, 29918, 29900, 353, 319, 29918, 29900, 6622, 29938, 263, 10452, 21954, 29873, 779, 12197, 17313, 741, 29883, 29950, 29892, 13, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 24064, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 3892, 741, 29916, 3946, 5940, 29913, 3441, 6642, 29918, 29900, 1262, 338, 451, 13, 13092, 29889, 2803, 779, 12197, 29918, 29926, 17313, 741, 29883, 29950, 29918, 29926, 29892, 2802, 6642, 2137, 29926, 29918, 29900, 29892, 741, 6642, 2137, 29926, 29918, 29896, 29905, 1118, 320, 432, 29905, 262, 9991, 29896, 29892, 29906, 29905, 1118, 29938, 13, 915, 1023, 1316, 21954, 1372, 29889, 1987, 278, 6590, 399, 1032, 29880, 3168, 13, 29938, 29924, 29918, 29896, 1194, 3822, 1262, 322, 395, 29924, 29918, 29906, 1194, 3822, 1262, 526, 4475, 491, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29896, 29913, 13, 29924, 29918, 29906, 29898, 29920, 29897, 353, 390, 6622, 341, 29918, 29896, 29898, 29920, 29897, 390, 718, 390, 29918, 29900, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29934, 29918, 29900, 29922, 390, 6622, 29918, 29900, 320, 262, 518, 741, 29883, 29950, 2403, 29906, 9341, 322, 395, 29934, 320, 262, 13, 29961, 741, 29883, 29950, 2403, 29906, 29892, 741, 29883, 29950, 2403, 29896, 9341, 338, 12635, 368, 21292, 1821, 29889, 13, 13, 7504, 3278, 304, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 278, 17752, 13, 29938, 29909, 24033, 17458, 7920, 322, 395, 29909, 29918, 29900, 29938, 526, 451, 766, 12090, 10940, 7555, 1758, 15065, 5940, 4678, 17458, 2144, 1333, 353, 13, 10045, 29900, 29905, 1836, 29938, 10056, 292, 395, 29909, 24033, 17458, 7920, 322, 395, 29909, 29918, 29900, 29938, 408, 17752, 310, 385, 13, 1639, 13847, 6081, 29871, 395, 29903, 3490, 319, 29918, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 13670, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 1665, 17458, 20073, 29938, 591, 508, 4772, 445, 22629, 854, 5597, 29889, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 5287, 29889, 29946, 29913, 13, 12024, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 29938, 29924, 1194, 3822, 1262, 278, 6590, 29871, 399, 1032, 29880, 740, 29892, 259, 7555, 17458, 5369, 2802, 17458, 2137, 29930, 320, 262, 13, 29905, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 322, 7555, 17458, 29913, 353, 320, 17458, 648, 459, 1012, 17201, 320, 17458, 3187, 3411, 13, 29938, 967, 28143, 26227, 29889, 8725, 1235, 29871, 395, 29903, 3490, 319, 29918, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 13670, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 1665, 17458, 20073, 1504, 1987, 278, 21954, 29873, 779, 1332, 741, 12197, 29913, 353, 13, 24976, 1332, 29905, 29883, 29950, 2053, 1332, 741, 6642, 2403, 29900, 2053, 1332, 741, 6642, 2403, 29896, 28538, 3342, 491, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 1332, 29905, 29883, 29950, 3490, 320, 29883, 29950, 1665, 1758, 1015, 29913, 353, 320, 6875, 16195, 1758, 2432, 5940, 4678, 17458, 29897, 7570, 3425, 13, 29905, 1332, 741, 6642, 2403, 29900, 3490, 2802, 6642, 2403, 29900, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 317, 6622, 20481, 3425, 320, 1332, 741, 6642, 2403, 29896, 3490, 13, 29905, 1631, 1665, 1758, 1015, 3331, 6642, 2403, 29896, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29903, 6622, 511, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 275, 263 ]

1,332,863

10,240

ArXiv

-1

boundary triplet for $S^*$, where $\pi_{\rm op}$ is the orthogonal projection from $\cH$ onto $\cH_{\rm op}$, $A_0 = S^*\upharpoonright{\xker\,}(\wh {\Gamma}_0)$ and $A_{\Theta} = S_{{\Theta}_{\rm op}}$. The corresponding Weyl function is \begin{equation}\label{2.13a} \wh M(z) := \pi_{\rm op}M(z)\upharpoonright\cH_{\rm op}, \quad z \in \C_\pm. \end{equation} \end{lemma} The proof can be found in \cite{DHMS00}. Hence without loss of generality we can very often assume that the ``coordinate'' ${\Theta}:={\Gamma}\wt A$ of an extension $\wt A = A_{\Theta}=A_{\Theta}^* \in {\rm Ext\,}_A$ corresponds to the graph of a self-adjoint operator. In what follows, without loss of generality, we always assume that the closed symmetric $A$ is simple and, due to Lemma \ref{III.4}, the ``coordinate'' ${\Theta}$ of {\color{black} the extension $A_{\Theta} = A_{\Theta}^*\in {{\rm Ext\,}}_A$ is the graph of a self-adjoint operator. \subsection{Krein type formula for resolvents and comparability} With any boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^*$ and any proper (not necessarily self-adjoint) extension $A_{\Theta}\in {\rm Ext\,}_A$ it is naturally associated the following (unique) Krein type formula (cf. \cite{DM87,DM91,DM95}) \begin{equation}\label{2.30} (A_\Theta - z)^{-1} - (A_0 - z)^{-1} = \gamma(z) (\Theta - M(z))^{-1} \gamma({\overline z})^*, \quad z\in \varrho(A_0)\cap \varrho(A_\Theta). \end{equation} Formula \eqref{2.30} is a generalization of the known Krein formula for resolvents. We note also, that all objects in \eqref{2.30} are expressed in terms of the boundary triplet $\Pi$ (cf. \cite{DM87,DM91,DM95}). In other words, \eqref{2.30} gives a relation between Krein-type formula for canonical resolvents and the theory of abstract boundary value problems (framework of boundary triplets). The following result is deduced from formula \eqref{2.30} (cf. \cite[Theorem 2]{DM91}). \begin{proposition}\label{prop2.9} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a boundary triplet for $A^*$, $\Theta_i = \Theta_i^* \in \wt\cC(\cH), \ i\in \{1,2\}$. Then for any Schatten-von~Neumann ideal ${\mathfrak S}_p$, $p \in (0,\infty]$, and any $z \in \C\setminus\R$ the following equivalence holds \begin{displaymath} (A_{\Theta_1}-z)^{-1} - (A_{\Theta_2}-z)^{-1}\in{\mathfrak S}_p(\gH) \Longleftrightarrow \bigl(\Theta_1 - z\bigr)^{-1}- \bigl(\Theta_2 - z \bigr)^{-1}\in{\mathfrak S}_p(\cH) \end{displaymath} In particular, $(A_{{\Theta}_1} - z)^{-1} - (A_0 - z)^{-1} \in {\mathfrak S}_p(\gH) \Longleftrightarrow \bigl(\Theta_1 - i\bigr)^{-1} \in {\mathfrak S}_p(\cH)$. If in addition $\Theta_1, \Theta_2\in[\cH]$, then for any $p \in (0, \infty]$ the equivalence holds \begin{displaymath} (A_{\Theta_1}-z)^{-1

0.175407

-0.859791

0.204542

2.376737

[ 0.3784609198641435, -0.027647844833988976 ]

[ -0.9475313333617279, -0.7720497323933754 ]

[ 0.039686669499505826, 0.36939800279946083 ]

[ 2.595252147267438, 2.158221942200954 ]

1,024

[ 512, 512 ]

[ 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 988, 779, 1631, 1665, 1758, 1015, 1042, 338, 278, 13, 2072, 23419, 18246, 515, 779, 29883, 29950, 29938, 11480, 779, 29883, 29950, 1665, 1758, 1015, 4429, 395, 29909, 29918, 29900, 353, 13, 29903, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 4678, 1332, 2802, 6642, 2403, 29900, 1262, 322, 395, 29909, 1665, 17458, 29913, 353, 317, 24033, 17458, 6353, 1758, 1015, 26253, 13, 1576, 6590, 29871, 399, 1032, 29880, 740, 13, 275, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29941, 29874, 29913, 13, 29905, 1332, 341, 29898, 29920, 29897, 3490, 320, 1631, 1665, 1758, 1015, 29913, 29924, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 1665, 1758, 1015, 1118, 320, 3425, 503, 13, 29905, 262, 320, 29907, 3187, 3358, 29889, 320, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 13846, 29913, 13, 1576, 5296, 508, 367, 1476, 297, 320, 2036, 29912, 29928, 29950, 4345, 29900, 29900, 1836, 10133, 1728, 6410, 310, 13, 4738, 2877, 591, 508, 1407, 4049, 5251, 29871, 393, 278, 4954, 29302, 4907, 13, 29938, 741, 17458, 6177, 21854, 6642, 1012, 14554, 319, 29938, 310, 385, 6081, 779, 14554, 319, 353, 319, 1665, 17458, 5369, 29909, 1665, 17458, 2137, 29930, 320, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 16161, 304, 278, 29871, 3983, 310, 263, 1583, 29899, 328, 12090, 5455, 29889, 13, 13, 797, 825, 4477, 29892, 1728, 6410, 310, 2498, 537, 29892, 591, 2337, 13, 465, 2017, 393, 278, 5764, 18348, 395, 29909, 29938, 338, 2560, 322, 29892, 2861, 304, 29871, 11894, 13, 29905, 999, 29912, 5287, 29889, 29946, 1118, 278, 4954, 29302, 4907, 7555, 17458, 1042, 310, 2802, 2780, 29912, 8517, 29913, 278, 29871, 6081, 13, 29938, 29909, 1665, 17458, 29913, 353, 319, 1665, 17458, 2137, 17710, 262, 426, 741, 1758, 7338, 5940, 15609, 29909, 29938, 338, 278, 3983, 310, 263, 1583, 29899, 328, 12090, 13, 6891, 29889, 13, 13, 29905, 7235, 29912, 29968, 276, 262, 1134, 7063, 363, 3770, 794, 29879, 322, 5734, 3097, 29913, 13, 13, 3047, 29871, 738, 29871, 10452, 21954, 29873, 259, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 363, 395, 29909, 6622, 29938, 13, 392, 738, 1571, 313, 1333, 12695, 29871, 1583, 29899, 328, 12090, 29897, 29871, 6081, 395, 29909, 1665, 17458, 1012, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 372, 338, 18180, 29871, 6942, 29871, 278, 1494, 313, 13092, 29897, 7706, 262, 13, 1853, 7063, 313, 6854, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 1800, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29941, 29900, 29913, 13, 29898, 29909, 3187, 17458, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 353, 320, 4283, 29898, 29920, 29897, 3441, 17458, 448, 13, 29924, 29898, 29920, 876, 3426, 29896, 29913, 320, 4283, 13670, 6875, 503, 1800, 6622, 29892, 320, 3425, 503, 29905, 262, 320, 1707, 4650, 29898, 29909, 29918, 29900, 2144, 5030, 13, 29905, 1707, 4650, 29898, 29909, 3187, 17458, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 2500, 2497, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 338, 263, 2498, 2133, 310, 278, 2998, 7706, 262, 13, 689, 2497, 363, 3770, 794, 29879, 29889, 13, 4806, 4443, 884, 29892, 393, 599, 3618, 297, 13, 29905, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 526, 13384, 297, 4958, 310, 278, 10452, 21954, 29873, 779, 12197, 29938, 13, 29898, 6854, 29889, 320, 2036, 29912, 23560, 29947, 29955, 29892, 23560, 29929, 29896, 29892, 23560, 29929, 29945, 7690, 512, 916, 3838, 29892, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 4076, 263, 8220, 13, 14811, 7706, 262, 29899, 1853, 29871, 7063, 363, 24420, 3770, 794, 29879, 29871, 322, 278, 6368, 310, 9846, 13, 9917, 653, 995, 4828, 313, 4468, 310, 10452, 21954, 1372, 467, 13, 13, 1576, 1494, 1121, 338, 21049, 1133, 515, 29871, 7063, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 313, 6854, 29889, 13, 29905, 2036, 29961, 28831, 29871, 29906, 3199, 23560, 29929, 29896, 7690, 13, 29905, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29906, 29889, 29929, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 367, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 4535, 17458, 29918, 29875, 353, 320, 17458, 29918, 29875, 6622, 320, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 511, 320, 474, 29905, 262, 9991, 29896, 29892, 29906, 23699, 29871, 1987, 363, 13, 1384, 1102, 8606, 29899, 23696, 30022, 8139, 22553, 10839, 7555, 7237, 317, 2403, 29886, 1628, 395, 29886, 320, 262, 313, 29900, 2053, 3411, 25473, 322, 738, 395, 29920, 320, 262, 13, 29905, 29907, 29905, 15375, 29905, 29934, 29938, 278, 1494, 24796, 8640, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29918, 29896, 7402, 29920, 21604, 29896, 29913, 448, 313, 29909, 1665, 17458, 29918, 29906, 7402, 29920, 21604, 29896, 1012, 262, 741, 7237, 13, 29903, 2403, 29886, 1194, 29887, 29950, 29897, 13, 29905, 8208, 25874, 28751, 29871, 320, 3752, 29880, 1194, 17458, 29918, 29896, 448, 503, 29905, 3752, 29878, 21604, 29896, 7402, 13, 29905, 3752, 29880, 1194, 17458, 29918, 29906, 448, 503, 320, 3752, 29878, 21604, 29896, 1012, 262, 741, 7237, 317, 2403, 29886, 1194, 29883, 29950, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 797, 3153, 29892, 29871, 2427, 29909, 24033, 17458, 2403, 29896, 29913, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 320, 262, 13, 741, 7237, 317, 2403, 29886, 1194, 29887, 29950, 29897, 320, 8208, 25874, 28751, 320, 3752, 29880, 1194, 17458, 29918, 29896, 448, 474, 29905, 3752, 29878, 21604, 29896, 29913, 320, 262, 2802, 7237, 13, 29903, 2403, 29886, 1194, 29883, 29950, 4935, 13, 13, 3644, 297, 6124, 779, 17458, 29918, 29896, 29892, 320, 17458, 29918, 29906, 29905, 262, 7110, 29883, 29950, 25473, 769, 363, 738, 395, 29886, 320, 262, 13, 29898, 29900, 29892, 320, 3411, 9341, 278, 24796, 8640, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29918, 29896, 7402, 29920, 21604, 29896 ]

1,332,863

11,264

ArXiv

-1

} - (A_{\Theta_2}-z)^{-1}\in{\mathfrak S}_p(\gH) \Longleftrightarrow \Theta_1 - \Theta_2 \in{\mathfrak S}_p(\cH). \end{displaymath} \end{proposition} \subsection{Generalized boundary triplets and proper extensions} In applications the concept of boundary triplets is too restrictive. Here we recall some facts on generalized boundary triplets following \cite{DM95}. \begin{definition}[{\cite[Definition 6.1]{DM95}}]\label{def3.1} {\em { A triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ is called a \emph{generalized boundary triplet for $A^*$} if $\cH$ is an auxiliary Hilbert space and { ${\Gamma}_j: {\rm dom\,}(\Gamma_j) \to\cH$}, $j = 0,1$ are linear mappings such that { ${\rm dom\,}(\Gamma) := {\rm dom\,}({\Gamma}_0) \cap {\rm dom\,}({\Gamma}_1)$ is a core for $A^*$}, ${\Gamma}_0$ is surjective, $A_0:= A^*\upharpoonright{\xker\,}({\Gamma}_0)$ is self-adjoint and the following Green's formula holds} \begin{equation}\label{3.1} (A_*f, g) - (f, A_*g) = ({\Gamma}_1f, {\Gamma}_0 g)_{\cH} - ({\Gamma}_0 f, {\Gamma}_1 g)_{\cH}, \qquad f,g\in{\rm dom\,}(A_*), \end{equation} where $A_*:= A^*\upharpoonright{\rm dom\,}(\Gamma).$ } \end{definition} { By definition, { $A_* := A^*\upharpoonright{\rm dom\,}(\Gamma)$} and $A_* \subseteq A^* = \overline{A_*}$ and $(A_*)^*=A.$} Clearly, every ordinary boundary triplet is a generalized boundary triplet. \begin{lemma}[{\cite[Proposition 6.1]{DM95}}]\label{lem3.2} Let $A$ be a densely defined closed symmetric operator and let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A^*.$ Then the following assertions are true: \item[\;\;{\rm (i)}] ${\mathfrak N}^*_{z}:={\rm dom\,}(A_*)\cap{\N}_{z}$ is dense in $\mathfrak N_{z}$ and ${\rm dom\,}(A_*) ={\rm dom\,}(A_0) + \mathfrak N^*_{z}$; \item[\;\;{\rm (ii)}] $\overline{{\Gamma}_1{\rm dom\,}(A_0)}=\cH$; \item[\;\;{\rm (iii)}] ${\xker\,}({\Gamma}) = {\rm dom\,}(A)$ and ${\overline{{\rm ran\,}({\Gamma})}} = \cH \oplus \cH$. \end{lemma} \begin{lemma}\label{lem3.3} Let $A$ be a densely defined closed symmetric operator and let $\Pi = \{\cH, \Gamma_0, \Gamma_1\}$ be a generalized boundary triplet for $A^*$. Then the mapping ${\Gamma} = \{{\Gamma}_0,{\Gamma}_1\}^\top$ is closable and $\overline{{\Gamma}} \in \cC(\gH_+, \cH)$. \end{lemma} \begin{proof} The Green's formula can be rewritten as $(A_*f,g) - (f,A_*g) = (J{\Gamma} f,{\Gamma} g)$ where ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top$ and $J := \begin{pmatrix} 0 & I\\ -I & 0 \end{pmatrix}$. Let $f_n\in{\rm dom\,}(\Gamma_0)\cap{\rm dom\,}(\Gamma_1)={\rm dom\,}(A_*),$\ $\|f_n\|_{\gH_+}\to 0$ and $\Gamma

-0.246453

-0.990506

0.262242

2.220655

[ -0.4830649249760768, -0.009842064257005092 ]

[ -1.4310010503153519, -0.5500117883109703 ]

[ -0.3065102304654469, 0.8309938694193978 ]

[ 1.8668684721566307, 2.5744411851214153 ]

1,024

[ 512, 512 ]

[ 29913, 448, 13, 29898, 29909, 1665, 17458, 29918, 29906, 7402, 29920, 21604, 29896, 1012, 262, 741, 7237, 317, 2403, 29886, 1194, 29887, 29950, 29897, 320, 8208, 25874, 28751, 13, 29905, 17458, 29918, 29896, 448, 320, 17458, 29918, 29906, 320, 262, 741, 7237, 317, 2403, 29886, 1194, 29883, 29950, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 29905, 7235, 29912, 15263, 1891, 10452, 21954, 1372, 322, 1571, 17752, 29913, 13, 13, 797, 8324, 278, 6964, 310, 10452, 21954, 1372, 338, 2086, 13, 5060, 4146, 573, 29889, 2266, 591, 17386, 777, 17099, 373, 28803, 10452, 13, 3626, 552, 1372, 1494, 320, 2036, 29912, 23560, 29929, 29945, 1836, 13, 29905, 463, 29912, 16553, 4400, 741, 2036, 29961, 14683, 29871, 29953, 29889, 29896, 3199, 23560, 29929, 29945, 930, 10725, 1643, 29912, 1753, 29941, 29889, 29896, 29913, 13, 741, 331, 13, 29912, 319, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 338, 2000, 263, 13, 29905, 7278, 29912, 17492, 1891, 10452, 21954, 29873, 363, 395, 29909, 6622, 17133, 565, 779, 29883, 29950, 29938, 338, 385, 13, 2993, 2638, 653, 12338, 2151, 2913, 322, 426, 7555, 6642, 2403, 29926, 29901, 2802, 1758, 2432, 5940, 4678, 6642, 29918, 29926, 29897, 320, 517, 29905, 29883, 29950, 29938, 1118, 395, 29926, 13, 29922, 29871, 29900, 29892, 29896, 29938, 526, 5608, 13, 655, 27775, 1316, 393, 426, 7555, 1758, 2432, 5940, 4678, 6642, 29897, 3490, 2802, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29900, 29897, 320, 5030, 2802, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29896, 1262, 13, 275, 263, 7136, 363, 395, 29909, 6622, 29938, 1118, 13, 29938, 741, 6642, 2403, 29900, 29938, 338, 1190, 25674, 29892, 395, 29909, 29918, 29900, 9361, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 338, 13, 1311, 29899, 328, 12090, 322, 278, 1494, 7646, 29915, 29879, 7063, 29871, 8640, 29913, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29896, 29913, 13, 29898, 29909, 24563, 29888, 29892, 330, 29897, 448, 313, 29888, 29892, 319, 24563, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 2802, 6642, 2403, 29900, 330, 29897, 1665, 29883, 29950, 29913, 448, 313, 741, 6642, 2403, 29900, 285, 29892, 2802, 6642, 2403, 29896, 13, 29887, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 29909, 24563, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 29871, 395, 29909, 24563, 9361, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 4678, 6642, 467, 29938, 13, 29913, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 29912, 2648, 5023, 29892, 426, 395, 29909, 24563, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 4678, 6642, 1262, 29913, 322, 395, 29909, 24563, 13, 29905, 11725, 319, 6622, 353, 320, 6875, 29912, 29909, 24563, 1042, 322, 2427, 29909, 24563, 4887, 29930, 29922, 29909, 7449, 29913, 29871, 17732, 368, 29892, 29871, 1432, 13, 24310, 10452, 21954, 29873, 338, 263, 28803, 10452, 21954, 29873, 29889, 13, 29905, 463, 29912, 13846, 4400, 741, 2036, 29961, 1184, 3283, 29871, 29953, 29889, 29896, 3199, 23560, 29929, 29945, 930, 10725, 1643, 29912, 2409, 29941, 29889, 29906, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 322, 1235, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29871, 263, 28803, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 7449, 1987, 278, 1494, 4974, 1080, 526, 1565, 29901, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 29875, 2915, 29962, 7555, 7237, 405, 2137, 29930, 648, 29920, 6177, 21854, 1758, 2432, 5940, 2119, 29909, 24563, 2144, 5030, 741, 29940, 3227, 29920, 1042, 338, 13, 1145, 344, 297, 779, 7237, 405, 648, 29920, 1042, 322, 7555, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 353, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 320, 7237, 405, 6622, 648, 29920, 1042, 29936, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 2236, 2915, 29962, 779, 6875, 16195, 6642, 2403, 29896, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 2915, 2013, 29883, 29950, 22073, 13, 13, 29905, 667, 7110, 10436, 29936, 741, 1758, 313, 25609, 2915, 29962, 7555, 29916, 3946, 5940, 2119, 741, 6642, 1800, 353, 2802, 1758, 2432, 5940, 2119, 29909, 1262, 322, 13, 29938, 741, 6875, 16195, 1758, 6350, 5940, 2119, 741, 6642, 1800, 930, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 13846, 1012, 1643, 29912, 2409, 29941, 29889, 29941, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 322, 1235, 13, 4535, 12197, 353, 320, 741, 29883, 29950, 29892, 320, 6642, 29918, 29900, 29892, 320, 6642, 29918, 29896, 11854, 367, 263, 28803, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 1504, 1987, 278, 10417, 7555, 6642, 29913, 353, 9991, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 29905, 10206, 3332, 29938, 13, 275, 4694, 519, 322, 779, 6875, 16195, 6642, 930, 320, 262, 320, 29883, 29907, 1194, 29887, 29950, 28842, 29892, 320, 29883, 29950, 4935, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1576, 7646, 29915, 29879, 7063, 508, 367, 337, 17625, 408, 2427, 29909, 24563, 29888, 29892, 29887, 29897, 448, 313, 29888, 29892, 29909, 24563, 29887, 29897, 353, 13, 29898, 29967, 741, 6642, 29913, 285, 29892, 741, 6642, 29913, 330, 1262, 988, 29871, 7555, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29938, 322, 29871, 395, 29967, 3490, 13, 29905, 463, 29912, 12571, 29913, 13, 29900, 669, 306, 1966, 13, 29899, 29902, 669, 29871, 29900, 13, 29905, 355, 29912, 12571, 4311, 13, 12024, 395, 29888, 29918, 29876, 29905, 262, 741, 1758, 2432, 5940, 4678, 6642, 29918, 29900, 2144, 5030, 741, 1758, 2432, 5940, 4678, 6642, 29918, 29896, 3892, 741, 1758, 2432, 5940, 2119, 29909, 24563, 511, 4535, 13, 4535, 29989, 29888, 29918, 29876, 7893, 1665, 29887, 29950, 28842, 1012, 517, 29871, 29900, 29938, 322, 779, 6642 ]

1,332,863

12,288

ArXiv

-1

f_n=\{\Gamma_0 f_n,\Gamma_1 f_n\}\to\{\varphi, \psi\}$ as $n\to\infty$. Hence \begin{displaymath} 0 = \lim_{n\to\infty}[(A_*f_n, g) - (f_n, A_* g)] = \left(Jf_\infty,{\Gamma} g\right), \quad \mbox{where} \quad f_\infty := \{\varphi, \psi \}^\top. \end{displaymath} Since ${\rm ran\,}({\Gamma})$ is dense in $\cH \oplus \cH$ one has $Jf_\infty = 0$. Thus, $\varphi=\psi=0$ and $\Gamma$ is closable. \end{proof} For any generalized boundary triplet $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ we set $A_j:=A^*\upharpoonright{\xker\,}({\Gamma}_j)$, $j \in \{0,1\}$. The extensions $A_0$ and $A_1$ are disjoint but not necessarily transversal. The latter holds if and only if $\Pi$ is an ordinary boundary triplet. In general, the extension $A_1$ is only essentially self-adjoint. Starting with Definition \ref{def3.1}, one easily extends the definitions of ${\gamma}$-field and Weyl function to the case of a generalized boundary triplet $\Pi$ by analogy with Definition \ref{Weylfunc} (cf. {\cite[Definition 6.2]{DM95}}). \begin{definition} \label{def3.2} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A^*.$ Then the operator valued functions $\gamma(\cdot)$ and $M(\cdot)$ defined by \begin{equation}\label{3.3A} \gamma(z):=\bigl(\Gamma_0\!\upharpoonright\mathfrak N^*_z\bigr)^{-1}:\ \cH\to \mathfrak N_{z} \;\;\text{and}\;\;M(z):=\Gamma_1\gamma(z), \;\;z\in\varrho(A_0), \end{equation} are called the (generalized) {\em $\gamma$-field} and the {\em Weyl function} associated with the generalized boundary triplet $\Pi$, { respectively}. \end{definition} It follows from Lemma \ref{lem3.2}(i) that $\gamma(\cdot)$ takes values in $[\cH, \gH]$, ${\rm ran\,}({\gamma}(z))=\mathfrak N^*_{z} := {\rm dom\,}(A_*) \cap \mathfrak N_z$ and it satisfies the identity similar to that of \eqref{2.15} which shows that ${\gamma}(z)$ is a holomorphic operator valued function on $\varrho(A_0)$. Further, one has ${\rm dom\,} (M(z))= \cH$ since ${\rm ran\,}\gamma(z)\subset {\rm dom\,}({\Gamma}_1),\ z\in\varrho(A_0).$ By \eqref{3.3A} $M(z)$ is closable since $\gamma(z)$ is bounded and ${\Gamma}_1$ is closable, by Lemma \ref{lem3.3}. Hence, by the closed graph theorem $M(\cdot)$ takes values in $[\cH]$. Moreover, it is holomorphic on $\varrho(A_0)$, because so is $\gamma(\cdot)$, and satisfies the relation \eqref{mlambda}. It follows that ${\xker\,}(\im M(z)) =\{0\}, \ z\in \C_+,$ though the stronger condition $0 \in \varrho(\im M(i)) (\Longleftrightarrow {\rm ran\,}({\gamma}(i))=\mathfrak N_{i})$ is satisfied if and only if $\Pi$ is an ordinary boundary triplet (in the sense of Definition \ref{t1.9}). In the sequel we need the following simple but useful statement. \begin{proposition}\label{prop3.1} Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1

0.102471

-1.137338

0.170303

2.137411

[ 0.04289043975944719, 0.16205220208233934 ]

[ -1.1803130489319913, -1.0943628770291247 ]

[ 0.0828027669310384, 0.25780339768255295 ]

[ 2.1374109800549306, 2.1374109800549306 ]

1,024

[ 512, 512 ]

[ 285, 29918, 29876, 2013, 741, 6642, 29918, 29900, 285, 29918, 29876, 2053, 6642, 29918, 29896, 13, 29888, 29918, 29876, 25848, 517, 24976, 6827, 29892, 320, 6134, 11854, 408, 395, 29876, 29905, 517, 29905, 3411, 1504, 10133, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29900, 353, 320, 2576, 648, 29876, 29905, 517, 29905, 3411, 4400, 29898, 29909, 24563, 29888, 29918, 29876, 29892, 330, 29897, 448, 313, 29888, 29918, 29876, 29892, 319, 24563, 330, 4638, 353, 13, 29905, 1563, 29898, 29967, 29888, 3187, 3411, 29892, 741, 6642, 29913, 330, 29905, 1266, 511, 320, 3425, 320, 8264, 29912, 3062, 29913, 320, 3425, 285, 3187, 3411, 3490, 13, 24976, 6827, 29892, 29871, 320, 6134, 320, 10206, 3332, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 7555, 1758, 6350, 5940, 2119, 741, 6642, 8435, 338, 20619, 297, 779, 29883, 29950, 320, 17201, 320, 29883, 29950, 29938, 697, 756, 395, 29967, 29888, 3187, 3411, 353, 29871, 29900, 1504, 13, 1349, 375, 29892, 779, 6827, 2013, 6134, 29922, 29900, 29938, 322, 779, 6642, 29938, 338, 4694, 519, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 2831, 738, 28803, 10452, 21954, 29873, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 591, 13, 842, 395, 29909, 29918, 29926, 9361, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29926, 5767, 395, 29926, 320, 262, 9991, 29900, 29892, 29896, 23699, 450, 13, 24299, 395, 29909, 29918, 29900, 29938, 322, 395, 29909, 29918, 29896, 29938, 526, 766, 12090, 541, 451, 12695, 13, 3286, 874, 284, 29889, 450, 7480, 8640, 565, 322, 871, 565, 779, 12197, 29938, 338, 385, 15311, 13, 9917, 653, 21954, 29873, 29889, 512, 2498, 29892, 278, 6081, 395, 29909, 29918, 29896, 29938, 338, 871, 13674, 13, 1311, 29899, 328, 12090, 29889, 13, 13, 4763, 292, 411, 21940, 320, 999, 29912, 1753, 29941, 29889, 29896, 1118, 29871, 697, 5948, 29871, 4988, 278, 13, 25476, 2187, 310, 7555, 4283, 23021, 2671, 322, 399, 1032, 29880, 740, 13, 517, 278, 1206, 310, 263, 28803, 10452, 21954, 29873, 779, 12197, 29938, 491, 13, 7054, 6933, 411, 21940, 320, 999, 29912, 29956, 1032, 29880, 9891, 29913, 313, 6854, 29889, 2802, 2036, 29961, 14683, 13, 29953, 29889, 29906, 3199, 23560, 29929, 29945, 930, 467, 13, 29905, 463, 29912, 16553, 29913, 320, 1643, 29912, 1753, 29941, 29889, 29906, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29871, 263, 28803, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 7449, 259, 1987, 278, 5455, 659, 6742, 3168, 779, 4283, 1194, 3822, 1262, 13, 392, 395, 29924, 1194, 3822, 1262, 29871, 3342, 491, 13, 320, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29941, 29909, 29913, 13, 29905, 4283, 29898, 29920, 1125, 2013, 3752, 29880, 1194, 6642, 29918, 29900, 29905, 9903, 29884, 561, 279, 1129, 265, 1266, 29905, 7237, 405, 6622, 29918, 29920, 29905, 3752, 29878, 21604, 29896, 29913, 3583, 13, 29905, 29883, 29950, 29905, 517, 320, 7237, 405, 648, 29920, 29913, 320, 10436, 10436, 726, 29912, 392, 1012, 10436, 29936, 29924, 29898, 29920, 1125, 2013, 6642, 29918, 29896, 29905, 4283, 29898, 29920, 511, 13, 29905, 10436, 29936, 29920, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 598, 2000, 278, 313, 17492, 1891, 29897, 2802, 331, 779, 4283, 4388, 2671, 29913, 322, 278, 2802, 331, 13, 29956, 1032, 29880, 740, 29913, 6942, 411, 278, 28803, 13, 9917, 653, 21954, 29873, 779, 12197, 1628, 426, 8307, 1836, 13, 29905, 355, 29912, 16553, 29913, 13, 13, 3112, 4477, 515, 29871, 11894, 320, 999, 29912, 2409, 29941, 29889, 29906, 2119, 29875, 29897, 393, 779, 4283, 1194, 3822, 1262, 4893, 13, 5975, 297, 395, 7110, 29883, 29950, 29892, 320, 29887, 29950, 25473, 7555, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29920, 876, 2013, 7237, 405, 6622, 648, 29920, 29913, 3490, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 13, 29905, 5030, 320, 7237, 405, 29918, 29920, 29938, 322, 372, 17150, 278, 10110, 2788, 304, 393, 310, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29945, 29913, 607, 3697, 393, 7555, 4283, 2119, 29920, 1262, 13, 275, 263, 8753, 16898, 5455, 659, 6742, 740, 373, 13, 4535, 1707, 4650, 29898, 29909, 29918, 29900, 4935, 13, 13, 29943, 332, 721, 29892, 697, 756, 7555, 1758, 2432, 5940, 29913, 313, 29924, 29898, 29920, 876, 29922, 320, 29883, 29950, 29938, 1951, 7555, 1758, 6350, 5940, 1012, 4283, 29898, 29920, 2144, 6484, 13, 741, 1758, 2432, 5940, 2119, 741, 6642, 2403, 29896, 20481, 29871, 503, 29905, 262, 29905, 1707, 4650, 29898, 29909, 29918, 29900, 467, 29938, 2648, 320, 4915, 29912, 29941, 29889, 29941, 29909, 29913, 395, 29924, 29898, 29920, 1262, 13, 275, 4694, 519, 29871, 1951, 779, 4283, 29898, 29920, 1262, 338, 12635, 322, 7555, 6642, 2403, 29896, 29938, 338, 4694, 519, 29892, 13, 1609, 11894, 320, 999, 29912, 2409, 29941, 29889, 29941, 1836, 29871, 10133, 29892, 491, 278, 5764, 3983, 9185, 395, 29924, 1194, 3822, 1262, 13, 29873, 6926, 1819, 297, 395, 7110, 29883, 29950, 22689, 12808, 29892, 372, 338, 8753, 16898, 373, 13, 4535, 1707, 4650, 29898, 29909, 29918, 29900, 5767, 1363, 577, 338, 779, 4283, 1194, 3822, 5767, 322, 17150, 278, 13, 23445, 320, 4915, 29912, 828, 2269, 1836, 13, 3112, 4477, 393, 7555, 29916, 3946, 5940, 4678, 326, 341, 29898, 29920, 876, 353, 10045, 29900, 29905, 1118, 320, 29871, 503, 29905, 262, 320, 29907, 28842, 8209, 2466, 278, 13, 1110, 261, 4195, 395, 29900, 320, 262, 320, 1707, 4650, 1194, 326, 341, 29898, 29875, 876, 3441, 8208, 25874, 28751, 13, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 876, 2013, 7237, 405, 648, 29875, 8435, 338, 15787, 565, 322, 871, 565, 779, 12197, 29938, 13, 275, 385, 15311, 10452, 21954, 29873, 313, 262, 278, 4060, 310, 21940, 13, 29905, 999, 29912, 29873, 29896, 29889, 29929, 7690, 13, 13, 797, 278, 8617, 295, 591, 817, 278, 1494, 2560, 541, 5407, 3229, 29889, 13, 268, 320, 463, 29912, 771, 3283, 1012, 1643, 29912, 7728, 29941, 29889, 29896, 29913, 13, 12024, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896 ]

1,332,863

13,312

ArXiv

-1

\}$ be an ordinary boundary triplet for $A^*$, $M(\cdot)$ the corresponding Weyl function, $B=B^* \in \cC(\cH)$ and $A_B = A^*\upharpoonright {\xker\,}({\Gamma}_1 - B{\Gamma}_0)$. Let ${\Gamma}^B_1 :={\Gamma}_0$ and ${\Gamma}^B_0 := B{\Gamma}_0-{\Gamma}_1$. Then \item[\;\;\rm (i)] $\Pi_B=\{\cH,{\Gamma}^B_0,{\Gamma}^B_1\}$ is a generalized boundary triplet for $A^*$ such that it holds ${\rm dom\,}(A_*) := {\rm dom\,}({\Gamma}) := {\rm dom\,}(A_0) + {\rm dom\,}(A_B) \subseteq {\rm dom\,}(A^*)$, $A^*_* = A$; \item[\;\;\rm (ii)] the corresponding (generalized) Weyl function $M_B(\cdot)$ is \begin{displaymath} M_B(z)=\left(B-M(z)\right)^{-1}, \qquad z\in\C_\pm; \end{displaymath} \item[\;\;\rm (iii)] $\Pi_B$ is an (ordinary) boundary triplet if and only if $B = B^* \in[\cH]$. In this case $M_B(\cdot)$ is an ordinary Weyl function in the sense of Definition \ref{t1.9}. \end{proposition} Note, an analogon of Proposition \ref{prop2.1} does not hold for generalized boundary triplets. Nevertheless, since the corresponding Weyl function determines the pair $\{A,A_0\}$ uniquely, up to unitary equivalence, it is possible to describe the spectral properties of $A_0$ in terms of the (generalized) Weyl function $M(\cdot).$ \section{Weyl function and spectral multiplicity} Throughout of this section $A$ is a densely defined simple closed symmetric operator in $\gH$ with $n_+(A) = n_-(A).$ Let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized} boundary triplet for $A^*$, and { let $M(\cdot)$ be} the corresponding generalized Weyl function. Since $M(\cdot)\in (R_{\cH})$ it admits representation \eqref{1.2}. Since $A$ is densely defined (see \cite{DM95, Ma92b}), one gets $C_1 = 0$, i.e. \begin{displaymath} M(z) = C_0 + \int^\infty_{-\infty} \left(\frac{1}{t-z} - \frac{t}{1+t^2}\right)d{\Sigma}_M. \end{displaymath} \begin{proposition}\Label{IV.6} Let $A$ be a densely defined, simple closed symmetric operator and let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a generalized boundary triplet for $A_* (\subseteq A^*)$, $A^*_* = A$, and { let} $M(\cdot)$ { be} the corresponding Weyl function. If $E_{A_0}$ is the spectral measure of $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$, then ${\Sigma}_M \thickapprox E_{A_0}$ and ${\Sigma}^{ac}_M \thickapprox E^{ac}_{A_0}$. \end{proposition} \begin{proof} Alongside ${\Sigma}_M(\cdot)$ we introduce the bounded operator measure ${\Sigma}^0_M(\cdot),$ \begin{displaymath} {\Sigma}^0_M({\delta}) = \int_{\delta} \frac{1}{1+t^2} \;d{\Sigma}_M, \qquad {\delta} \in \cB_b(\R). \end{displaymath} Clearly, ${\Sigma}^0_M(\cdot) \thickapprox {\Sigma}_M(\cdot)$. According to \cite[formula (2.16)]{ABMN05

0.162052

-1.067503

0.232441

2.459981

[ 0.2332753243902749, 0.0908290797744038 ]

[ -0.9045562474102946, -1.2304506492086633 ]

[ 0.3338906284440811, 0.1309913464133395 ]

[ 2.532819260829369, 2.3871425258072074 ]

1,024

[ 512, 512 ]

[ 11854, 367, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 1628, 395, 29924, 1194, 3822, 1262, 278, 6590, 399, 1032, 29880, 740, 29892, 259, 395, 29933, 29922, 29933, 6622, 320, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 322, 395, 29909, 29918, 29933, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 448, 350, 741, 6642, 2403, 29900, 4935, 2803, 13, 29938, 741, 6642, 2137, 29933, 29918, 29896, 3490, 741, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2137, 29933, 29918, 29900, 3490, 350, 741, 6642, 2403, 29900, 29899, 741, 6642, 2403, 29896, 1504, 1987, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 29875, 4638, 779, 12197, 29918, 29933, 2013, 741, 29883, 29950, 29892, 741, 6642, 2137, 29933, 29918, 29900, 29892, 741, 6642, 2137, 29933, 29918, 29896, 11854, 29871, 338, 263, 13, 17492, 1891, 10452, 21954, 29873, 363, 395, 29909, 6622, 29938, 1316, 393, 372, 8640, 13, 29938, 741, 1758, 2432, 5940, 2119, 29909, 29918, 7528, 3490, 2802, 1758, 2432, 5940, 2119, 741, 6642, 1800, 3490, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29933, 29897, 320, 11725, 13, 741, 1758, 2432, 5940, 2119, 29909, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 22073, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 2236, 4638, 278, 6590, 29871, 313, 17492, 1891, 29897, 399, 1032, 29880, 740, 13, 29938, 29924, 29918, 29933, 1194, 3822, 1262, 338, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29918, 29933, 29898, 29920, 7950, 1563, 29898, 29933, 29899, 29924, 29898, 29920, 2144, 1266, 21604, 29896, 1118, 320, 12014, 503, 29905, 262, 29905, 29907, 3187, 3358, 29936, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 13, 29905, 667, 7110, 10436, 10436, 1758, 313, 25609, 4638, 259, 779, 12197, 29918, 29933, 29938, 338, 385, 313, 24310, 29897, 10452, 21954, 29873, 565, 13, 392, 871, 565, 395, 29933, 353, 350, 6622, 320, 262, 7110, 29883, 29950, 22689, 512, 445, 1206, 395, 29924, 29918, 29933, 1194, 3822, 1262, 338, 385, 15311, 13, 29956, 1032, 29880, 740, 297, 278, 4060, 29871, 310, 21940, 320, 999, 29912, 29873, 29896, 29889, 29929, 1836, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 13, 9842, 29892, 385, 15690, 265, 29871, 310, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 947, 451, 4808, 363, 13, 17492, 1891, 10452, 21954, 1372, 29889, 13, 29940, 1310, 16561, 29892, 1951, 278, 6590, 399, 1032, 29880, 740, 3683, 1475, 278, 13, 18784, 12564, 29909, 29892, 29909, 29918, 29900, 11854, 20498, 873, 29892, 701, 304, 5190, 653, 24796, 29892, 29871, 372, 338, 13, 27338, 304, 8453, 278, 23161, 4426, 310, 395, 29909, 29918, 29900, 29938, 13, 262, 4958, 310, 278, 313, 17492, 1891, 29897, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 467, 29938, 13, 13, 29905, 2042, 29912, 29956, 1032, 29880, 740, 322, 23161, 6674, 17024, 29913, 13, 13, 29911, 1092, 820, 449, 310, 445, 4004, 395, 29909, 29938, 338, 263, 6245, 873, 3342, 13, 12857, 5764, 18348, 5455, 297, 779, 29887, 29950, 29938, 411, 395, 29876, 29918, 17108, 29909, 29897, 353, 302, 29918, 17722, 29909, 467, 29938, 13, 12024, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 28803, 29913, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 392, 29871, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 28803, 399, 1032, 29880, 740, 29889, 13, 23036, 395, 29924, 1194, 3822, 2144, 262, 313, 29934, 1665, 29883, 29950, 8435, 372, 7336, 1169, 8954, 13, 29905, 4915, 29912, 29896, 29889, 29906, 1836, 4001, 13, 395, 29909, 29938, 338, 6245, 873, 3342, 313, 4149, 320, 2036, 29912, 23560, 29929, 29945, 29892, 3219, 29929, 29906, 29890, 9594, 697, 4947, 395, 29907, 29918, 29896, 353, 29871, 29900, 1628, 474, 29889, 29872, 29889, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 29898, 29920, 29897, 353, 315, 29918, 29900, 29871, 718, 320, 524, 3823, 3411, 648, 2612, 3411, 29913, 13, 29905, 1563, 1194, 1154, 29912, 29896, 1157, 29873, 29899, 29920, 29913, 448, 13, 29871, 320, 1154, 29912, 29873, 1157, 29896, 29974, 29873, 29985, 29906, 1012, 1266, 29897, 29881, 741, 10142, 2403, 29924, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 5667, 29889, 29953, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 29892, 2560, 5764, 18348, 5455, 322, 13, 1026, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 28803, 10452, 21954, 29873, 13, 1454, 395, 29909, 24563, 3441, 11725, 319, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 1628, 259, 322, 426, 1235, 29913, 13, 29938, 29924, 1194, 3822, 1262, 426, 367, 29913, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 960, 395, 29923, 648, 29909, 29918, 29900, 1042, 338, 278, 23161, 13, 26658, 310, 395, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 769, 7555, 10142, 2403, 29924, 13, 29905, 27996, 14850, 382, 648, 29909, 29918, 29900, 1042, 322, 7555, 10142, 2844, 562, 2403, 29924, 320, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29900, 4311, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2499, 549, 2975, 7555, 10142, 2403, 29924, 1194, 3822, 1262, 591, 14944, 278, 29871, 12635, 29871, 5455, 5645, 13, 29938, 741, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 511, 29938, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 10142, 2137, 29900, 29918, 29924, 13670, 4181, 1800, 353, 320, 524, 1665, 4181, 29913, 320, 1154, 29912, 29896, 1157, 29896, 29974, 29873, 29985, 29906, 29913, 18175, 29881, 741, 10142, 2403, 29924, 29892, 320, 12014, 13, 741, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 18759, 368, 29892, 7555, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 29897, 320, 27996, 14850, 29871, 2802, 10142, 2403, 29924, 1194, 3822, 4935, 13, 29871, 7579, 304, 320, 2036, 29961, 689, 2497, 313, 29906, 29889, 29896, 29953, 29897, 3199, 2882, 29924, 29940, 29900, 29945 ]

1,332,863

14,336

ArXiv

-1

} one has \begin{equation}\label{2.15A} {\Sigma}^0_M({\delta}) = {\gamma}(i)^*E_{A_0}({\delta}){\gamma}(i), \qquad {\delta} \in \cB(\R), \end{equation} where ${\gamma}(\cdot)$ is the generalized ${\gamma}$-field of ${\Pi}$. Note, that though formula \eqref{2.15A} is proved in \cite{ABMN05} for ordinary boundary triplets, the proof remains valid for generalized boundary triplets. Due to the simplicity of $A$ one has \begin{displaymath} {\rm span\,}\left\{(A_0 - z)^{-1}{\rm ran\,}({\gamma}(i)): \quad z \in \C_+ \cup \C_-\right\} = \gH. \end{displaymath} Hence the subspace $\mathfrak{N}_i := \overline{{\mathfrak N}^*_i},$ where ${\mathfrak N}^*_i := {\rm ran\,}({\gamma}(i))$ is cyclic for $A_0$. Next, let $P_i$ be the orthogonal projection from $\gH$ onto $\mathfrak{N}_i$. We set $\widetilde{{\Sigma}}^0_M(\cdot) := P_iE_{A_0}(\cdot)\upharpoonright{\mathfrak N}_i$. Clearly, $\widetilde{{\Sigma}}^0_M(\cdot)$ is an operator measure. Since the linear manifold ${\mathfrak N}^*_i$ is cyclic for $A_0$, one gets from \cite[Theorem 4.15]{MM03} that the measures $\widetilde{{\Sigma}}^0_M$ and $E_{A_0}$ are spectrally equivalent. Note that ${\Sigma}^0_M(\cdot) = {\gamma}(i)^*\widetilde{{\Sigma}}^0_M(\cdot){\gamma}(i)$. Since ${\rm ran\,}({\gamma}(i))$ is dense in ${\mathfrak N}_i$, the latter yields ${\Sigma}^0_M \thicksim \wt{\Sigma}^0_M$. Let $D\in {\mathfrak S}_2(\cH)$ and ${\xker\,}(D) = {\xker\,}(D^*) = \{0\}$. We set \begin{displaymath} \Psi_{D^*{\Sigma}^0_MD}(t) := \frac{dD^*{\Sigma}^0_M(t)D}{d\rho(t)} \quad \mbox{and} \quad \Psi_{\wt D^*\wt {\Sigma}^0_M\wt D}(t) := \frac{d\widetilde{D}^*\widetilde{{\Sigma}}^0_M(t)\widetilde{D}}{d\rho(t)} \end{displaymath} where $\rho$ is a scalar measure such that $\widetilde{{\Sigma}}^0_M \thicksim \rho$ and $\widetilde{D} := {\gamma}(i)D: \cH \longrightarrow {\mathfrak N}_i$. We note that ${\xker\,}(\widetilde{D}) = {\xker\,}(\widetilde{D}^*) = \{0\}$. By \cite[Corollary 4.7]{MM03} we have \begin{displaymath} N_{{\Sigma}^0_M}(t) = {\rm rank\,}(\Psi_{D^*{\Sigma}^0_MD}(t)) \quad \mbox{and} \quad N_{\wt {\Sigma}^0_M}(t) = {\rm rank\,}(\Psi_{\wt D^*\wt {\Sigma}^0_M\wt D}(t)) \end{displaymath} for a.e. $t \in \R$ (${\rm mod}(\rho)$). Since $\Psi_{D^*{\Sigma}^0_MD}(t) = \Psi_{\wt D^*\wt {\Sigma}^0_M\wt D}(t)$ for a.e. $t \in \R$ (${\rm mod}(\rho)$) we get $N_{{\Sigma}^0_M}(t) = N_{\widetilde{{\Sigma}}^0_M}(t)$ for a.e. $t \in \R$ (${\rm mod}(\rho)$). Hence $\widetilde{{\Sigma}}^0_M$ and ${\Sigma}^0_M$ are spectrally equivalent. Since $\wt{\Sigma}^0_M$ and $E_{A_0}$ are spectrally equivalent the measures ${{\

-0.153658

-1.438164

-0.27988

2.127005

[ 0.13876771978936042, -0.44608368839311024 ]

[ -1.130175448655319, -1.7461516806258623 ]

[ 0.016860500271047407, -0.5766198996688716 ]

[ 2.241465790785046, 2.012545207178792 ]

1,024

[ 512, 512 ]

[ 29913, 697, 756, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29906, 29889, 29896, 29945, 29909, 29913, 2802, 10142, 2137, 29900, 29918, 29924, 13670, 4181, 1800, 353, 2802, 4283, 2119, 29875, 4887, 29930, 29923, 648, 29909, 29918, 29900, 2119, 741, 4181, 1800, 741, 4283, 2119, 29875, 511, 13, 29905, 12014, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 1194, 29934, 511, 320, 355, 29912, 2573, 29913, 13, 3062, 7555, 4283, 4678, 3822, 1262, 338, 278, 28803, 7555, 4283, 23021, 2671, 310, 13, 29938, 741, 12197, 4311, 3940, 29892, 393, 2466, 7063, 320, 4915, 29912, 29906, 29889, 29896, 29945, 29909, 29913, 13, 275, 11827, 297, 320, 2036, 29912, 2882, 29924, 29940, 29900, 29945, 29913, 363, 15311, 10452, 21954, 1372, 29892, 278, 5296, 9242, 2854, 13, 1454, 28803, 10452, 21954, 1372, 29889, 16809, 304, 278, 23205, 310, 395, 29909, 29938, 13, 650, 756, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 1758, 10638, 5940, 1012, 1563, 29905, 8001, 29909, 29918, 29900, 448, 503, 21604, 29896, 3331, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 22164, 320, 3425, 503, 320, 262, 320, 29907, 28842, 320, 5231, 13, 29905, 29907, 29918, 2612, 1266, 18105, 353, 320, 29887, 29950, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29950, 663, 278, 1014, 3493, 779, 7237, 29912, 29940, 2403, 29875, 3490, 13, 29905, 6875, 16195, 7237, 405, 2137, 29930, 29918, 29875, 1118, 29938, 988, 7555, 7237, 405, 2137, 29930, 29918, 29875, 3490, 13, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 23846, 338, 5094, 28746, 363, 395, 29909, 29918, 29900, 1504, 8084, 29892, 1235, 395, 29925, 29918, 29875, 29938, 367, 278, 13, 2072, 23419, 18246, 515, 779, 29887, 29950, 29938, 11480, 779, 7237, 29912, 29940, 2403, 29875, 1504, 13, 4806, 731, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 29897, 3490, 13, 29925, 29918, 29875, 29923, 648, 29909, 29918, 29900, 4678, 3822, 2144, 29884, 561, 279, 1129, 265, 1266, 741, 7237, 405, 2403, 29875, 1504, 13, 13, 18759, 368, 29892, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 1262, 338, 385, 5455, 5645, 29889, 13, 23036, 278, 5608, 25941, 7555, 7237, 405, 2137, 29930, 29918, 29875, 29938, 338, 5094, 28746, 13, 1454, 395, 29909, 29918, 29900, 1628, 697, 4947, 515, 320, 2036, 29961, 28831, 29871, 29946, 29889, 29896, 29945, 3199, 7428, 29900, 29941, 29913, 393, 278, 13, 1004, 25414, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 13, 13, 9842, 393, 7555, 10142, 2137, 29900, 29918, 29924, 1194, 3822, 29897, 353, 13, 741, 4283, 2119, 29875, 4887, 17710, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 1194, 3822, 21964, 4283, 2119, 29875, 4935, 4001, 13, 29938, 741, 1758, 6350, 5940, 2119, 741, 4283, 2119, 29875, 23846, 338, 20619, 297, 7555, 7237, 405, 2403, 29875, 1628, 278, 7480, 13, 17498, 7555, 10142, 2137, 29900, 29918, 29924, 320, 27996, 3601, 320, 14554, 741, 10142, 2137, 29900, 29918, 29924, 1504, 2803, 395, 29928, 29905, 262, 13, 741, 7237, 317, 2403, 29906, 1194, 29883, 29950, 1262, 322, 29871, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 13, 10045, 29900, 23699, 1334, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 29897, 3490, 320, 1154, 29912, 29881, 29928, 6622, 741, 10142, 2137, 29900, 29918, 29924, 29898, 29873, 29897, 29928, 1157, 29881, 29905, 4650, 29898, 29873, 2915, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29905, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 29897, 3490, 13, 29905, 1154, 29912, 29881, 29905, 10737, 29912, 29928, 2137, 17710, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29898, 29873, 2144, 10737, 29912, 29928, 7585, 29881, 29905, 4650, 29898, 29873, 2915, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 779, 4650, 29938, 338, 263, 17336, 5645, 1316, 13, 5747, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29871, 320, 27996, 3601, 320, 4650, 29938, 322, 13, 4535, 10737, 29912, 29928, 29913, 3490, 2802, 4283, 2119, 29875, 29897, 29928, 29901, 320, 29883, 29950, 320, 24225, 13, 741, 7237, 405, 2403, 29875, 1504, 1334, 4443, 393, 7555, 29916, 3946, 5940, 4678, 10737, 29912, 29928, 1800, 353, 13, 741, 29916, 3946, 5940, 4678, 10737, 29912, 29928, 2137, 7528, 353, 9991, 29900, 23699, 2648, 29871, 320, 2036, 29961, 12521, 21982, 13, 29946, 29889, 29955, 3199, 7428, 29900, 29941, 29913, 591, 505, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29940, 24033, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 2802, 1758, 7115, 5940, 4678, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 876, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29940, 1665, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 2802, 1758, 7115, 5940, 4678, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 876, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 3255, 741, 1758, 878, 4678, 4650, 1262, 467, 4001, 779, 14118, 648, 29928, 6622, 741, 10142, 2137, 29900, 29918, 5773, 2119, 29873, 29897, 353, 13, 29905, 14118, 1665, 14554, 360, 6622, 29905, 14554, 2802, 10142, 2137, 29900, 29918, 29924, 29905, 14554, 360, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 13, 1566, 741, 1758, 878, 4678, 4650, 1262, 29897, 591, 679, 395, 29940, 24033, 10142, 2137, 29900, 29918, 29924, 2119, 29873, 29897, 353, 13, 29940, 1665, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 3255, 741, 1758, 878, 4678, 4650, 1262, 467, 13, 29950, 663, 779, 10737, 16195, 10142, 24251, 29900, 29918, 29924, 29938, 322, 7555, 10142, 2137, 29900, 29918, 29924, 29938, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 4001, 779, 14554, 741, 10142, 2137, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 278, 15366, 6435, 741 ]

1,332,863

15,360

ArXiv

-1

Sigma}}^0_M$ and $E_{A_0}$ are spectrally equivalent. This proves the first statement. The second statement follows from the equality ${\Sigma}^{0,ac}_M({\delta}) = {\gamma}(i)^*E^{ac}_{A_0}({\delta}){\gamma}(i),$\ ${\delta} \in \mathcal \cB(\R)$ where ${\Sigma}^{0,ac}_M$ is the absolutely continuous part of ${\Sigma}^0_M$. \end{proof} The proof of Proposition \ref{IV.6} leads to the following computing procedure for $N_{{\Sigma}^{ac}_M}(t)$: choosing $D \in {\mathfrak S}_2(\cH) $ { such that} ${\xker\,}(D) = {\xker\,}(D^*) = \{0\}$ we introduce the sandwiched Weyl function $M^D(\cdot)$, \begin{displaymath} (M^D)(z) := D^*M(z)D, \quad z \in \C_+. \end{displaymath} It turns out that the limit $(M^D)(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M^D(t+iy)$ exists for a.e. $t \in \R$. We define in accordance with \eqref{2.13a} the function $d_{M^D}(\cdot): \R \to \N\cup\{\infty\}$, \begin{displaymath} d_{M^D}(t) := {\rm rank\,}(\im(M^D(t))) = {\rm dim}({\rm ran\,}(\im(M^D(t)))) \end{displaymath} which is well-defined for a.e. $t \in \R$. For a measurable non-negative function $\xi: \R \longrightarrow \R_+$ defined for a.e. $t \in \R$ we introduce its support ${\rm supp\,}(\xi) := \{t \in \R: \ \xi(t)>0\}$. By ${\rm cl}_{ac}(\cdot)$ we denote the absolutely continuous closure of a Borel set of $\R$., cf. Appendix. \begin{proposition}\Label{III.8} Let $A$ be as in Proposition \ref{IV.6}, { let} ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ { be} a generalized boundary triplet for $A_* (\subseteq A^*)$, $A^*_* = A$, and { let} $M(\cdot)$ { be} the corresponding Weyl function. Further, let $E_{A_0}(\cdot)$ be the spectral measure of $A_0 = A_*\upharpoonright{\xker\,}({\Gamma}_0)= A_0^*.$ If $D \in \gotS_2(\cH)$ { and} satisfies ${\xker\,}( D) = {\xker\,}(D^*) = \{0\}$, then $N_{E^{ac}_{A_0}}(t) = d_{M^D}(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_{M^D}))$. If, in addition, the limit $M(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ exists for a.e. $t \in \R$, then $N_{E^{ac}_{A_0}}(t) = d_M(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_M))$. \end{proposition} \begin{proof} The relation $N_{E^{ac}_{A_0}}(t) = d_{M^D}(t)$ follows from Theorem \ref{II.4} and Theorem \ref{IV.6}. Further, let $\{g_k\}^N_{k=1}$, $1 \le N \le \infty$, be a total set in $\cH$. We set $h_k := Dg_k$. One easily verifies that $\{h_n\}^N_{n=1}$

0.017209

-1.253729

0.110701

2.022951

[ 0.07439297462641867, -0.03997492369497782 ]

[ -1.3522133927377242, -1.1552442487936552 ]

[ 0.08533900795642267, 0.13606382846410806 ]

[ 1.8252465478645845, 2.220654828639023 ]

1,024

[ 512, 512 ]

[ 10142, 24251, 29900, 29918, 29924, 29938, 322, 395, 29923, 648, 29909, 29918, 29900, 1042, 526, 6683, 29878, 635, 13, 1686, 27445, 29889, 910, 29871, 28281, 29871, 278, 937, 3229, 29889, 13, 13, 1576, 29871, 1473, 3229, 4477, 515, 278, 17193, 13, 29938, 741, 10142, 2844, 29900, 29892, 562, 2403, 29924, 13670, 4181, 1800, 353, 2802, 4283, 2119, 29875, 4887, 29930, 29923, 998, 562, 3227, 29909, 29918, 29900, 2119, 741, 4181, 1800, 741, 4283, 2119, 29875, 511, 4535, 29871, 7555, 4181, 29913, 13, 29905, 262, 320, 1942, 320, 29883, 29933, 1194, 29934, 1262, 988, 7555, 10142, 2844, 29900, 29892, 562, 2403, 29924, 29938, 338, 278, 13312, 13, 20621, 681, 760, 310, 7555, 10142, 2137, 29900, 29918, 29924, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 1576, 5296, 310, 22206, 320, 999, 29912, 5667, 29889, 29953, 29913, 11981, 304, 278, 1494, 13, 12097, 292, 8792, 363, 395, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 1262, 29901, 23906, 13, 29938, 29928, 320, 262, 2802, 7237, 317, 2403, 29906, 1194, 29883, 29950, 29897, 395, 426, 1316, 393, 29913, 13, 29938, 741, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 11854, 591, 14944, 13, 1552, 11982, 16416, 287, 399, 1032, 29880, 740, 395, 29924, 29985, 29928, 1194, 3822, 5767, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29924, 29985, 29928, 5033, 29920, 29897, 3490, 360, 6622, 29924, 29898, 29920, 29897, 29928, 29892, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3112, 12169, 714, 393, 278, 4046, 2427, 29924, 29985, 29928, 5033, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29985, 29928, 29898, 29873, 29974, 19881, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 1334, 4529, 13, 262, 15017, 749, 411, 320, 4915, 29912, 29906, 29889, 29896, 29941, 29874, 29913, 278, 740, 13, 29938, 29881, 648, 29924, 29985, 29928, 4678, 3822, 1125, 320, 29934, 320, 517, 320, 29940, 29905, 5231, 24976, 3411, 28538, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 3490, 2802, 1758, 7115, 5940, 4678, 326, 29898, 29924, 29985, 29928, 29898, 29873, 4961, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29985, 29928, 29898, 29873, 13697, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 4716, 338, 1532, 29899, 12119, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 13, 13, 2831, 263, 7540, 21115, 1661, 29899, 22198, 740, 779, 5389, 29901, 320, 29934, 320, 24225, 13, 29905, 29934, 29918, 24035, 3342, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 591, 14944, 967, 2304, 13, 29938, 741, 1758, 1462, 5940, 4678, 5389, 29897, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 320, 29871, 320, 5389, 29898, 29873, 15410, 29900, 23699, 2648, 7555, 1758, 1067, 3227, 562, 4678, 3822, 1262, 13, 29871, 591, 13530, 278, 13312, 9126, 18424, 310, 263, 6780, 295, 731, 310, 13, 29871, 779, 29934, 1504, 29892, 274, 29888, 29889, 22871, 861, 29889, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 5287, 29889, 29947, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 22206, 320, 999, 29912, 5667, 29889, 29953, 1118, 426, 1235, 29913, 7555, 12197, 29913, 353, 13, 24976, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 426, 367, 29913, 263, 28803, 10452, 21954, 29873, 363, 13, 29938, 29909, 24563, 3441, 11725, 319, 6622, 5767, 395, 29909, 6622, 24563, 353, 319, 1628, 29871, 322, 426, 1235, 29913, 395, 29924, 1194, 3822, 1262, 13, 29912, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 8725, 29892, 1235, 13, 29938, 29923, 648, 29909, 29918, 29900, 4678, 3822, 1262, 367, 278, 23161, 5645, 310, 395, 29909, 29918, 29900, 353, 13, 29909, 29918, 17710, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 3892, 319, 29918, 29900, 6622, 7449, 960, 395, 29928, 320, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 13, 29912, 322, 29913, 17150, 7555, 29916, 3946, 5940, 2119, 360, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 353, 9991, 29900, 28538, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 1504, 13, 13, 3644, 29892, 297, 6124, 29892, 278, 4046, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 4864, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 395, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 29918, 29924, 29898, 29873, 1262, 363, 263, 29889, 29872, 29889, 13, 29938, 29873, 320, 262, 320, 29934, 29938, 322, 7555, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 29918, 29924, 876, 1504, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1576, 8220, 395, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29900, 12156, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 4477, 13, 3166, 10244, 320, 999, 29912, 2687, 29889, 29946, 29913, 322, 10244, 320, 999, 29912, 5667, 29889, 29953, 1836, 8725, 29892, 1235, 13, 4535, 29912, 29887, 29918, 29895, 29905, 2137, 29940, 648, 29895, 29922, 29896, 4429, 395, 29896, 320, 280, 405, 320, 280, 320, 3411, 1628, 367, 263, 3001, 731, 297, 779, 29883, 29950, 1504, 13, 4806, 731, 395, 29882, 29918, 29895, 3490, 360, 29887, 29918, 29895, 1504, 3118, 5948, 1147, 11057, 393, 13, 4535, 29912, 29882, 29918, 29876, 29905, 2137, 29940, 648, 29876, 29922, 29896, 1042 ]

1,332,863

16,384

ArXiv

-1

is a total set. We set $M_{h_n}(z) := (M(z)h_n,h_n)$, $z \in \C_+$. Clearly, $M_{h_n}(z)$ is $R$-function for {\color{black} every} $n \in \{ 1,2,\ldots,N\}$ and \begin{displaymath} M_{h_n}(t) := \lim_{y\to+0}M_{h_n}(t+iy) = (M(t)h_n,h_n) \end{displaymath} exists for a.e. $t \in \R$. Set \begin{displaymath} {\Omega}_{ac}(M_{h_n}) := \{t \in \R: \; 0 < \im(M_{h_n}(t)) < \infty\}. \end{displaymath} Combining \cite[Proposition 4.1]{BMN02} with Lemma \ref{III.7} we obtain \begin{equation}\Label{3.23} {\sigma}_{ac}(A_0) = \overline{\bigcup^N_{k=1}{\rm cl}_{ac}({\Omega}_{ac}(M_{h_n}))} = {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right). \end{equation} If $t \in {\rm supp\,}(d_{M^D})$, then $\im((M^D)(t)) \not= 0$. Hence $t \in {\Omega}_{ac}(M_{h_n})$ for some $n \in \{ 1,2,\dots,N\}.$ Therefore ${\rm supp\,}(d_{M^D}) \subseteq \bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})$ which yields \begin{equation}\Label{3.24} {\rm cl}_{ac}({\rm supp\,}(d_{M^D})) \subseteq {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right). \end{equation} Conversely, if $t \in {\Omega}_{ac}(M_{h_n}) \cap \cE_{M^D}$, where $\cE_{M^D} := \{t \in \R: \; \exists\;(M^D)(t)\}$, for some $n$, then $0 < d_{M^ D}(t)$. Hence ${\Omega}_{ac}(M_{h_n}) \cap \cE_{M^D} \subseteq {\rm supp\,}(d_{M^D})$ which yields $\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n}) \cap \;\cE_{M^D} \subseteq {\rm supp\,}(d_{M^D})$. Hence \begin{equation*} {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n}) \cap \; \cE_M\right) = {\rm cl}_{ac}\left(\bigcup^N_{k=1}{\Omega}_{ac}(M_{h_n})\right) \subseteq {\rm cl}_{ac}({\rm supp\,}(d_{M^D})) \end{equation*} Combining this equality with \eqref{3.23} and \eqref{3.24} we obtain ${\sigma}_{ac}(A_0) = {\rm cl}_{ac}({\rm supp\,}(d_{M^D}))$. \end{proof} \begin{corollary}\Label{IV.9} Let $A$ be as in Proposition \ref{III.8}, { let }$\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ { be} an ordinary boundary triplet for $A^*$ and { let} $M(\cdot)$ { be} the corresponding Weyl function. Further, let $B= B^* \in \cC(\cH)$, $A_B = A^*\upharpoonright {\xker\,}({\Gamma}_1 - B{\Gamma}_0)$ and $E_{A_B}(\cdot)$ the spectral measure of $A_B$. If $D\in \gotS_2(\cH)$ { and satisfies } ${\xker\,}(

-0.394036

-1.688852

-0.363893

1.825247

[ -0.32144322435422307, -0.4666288198280917 ]

[ -1.5169512222182184, -1.8607519098296845 ]

[ -0.28748842277506487, -0.4402969445544671 ]

[ 1.773219142499527, 1.8772739532296423 ]

1,024

[ 512, 512 ]

[ 338, 263, 3001, 731, 29889, 1334, 731, 395, 29924, 648, 29882, 29918, 29876, 2119, 29920, 29897, 3490, 13, 29898, 29924, 29898, 29920, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 5767, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 17732, 368, 29892, 395, 29924, 648, 29882, 29918, 29876, 2119, 29920, 1262, 338, 13, 29938, 29934, 4388, 2220, 363, 2802, 2780, 29912, 8517, 29913, 1432, 29913, 395, 29876, 320, 262, 9991, 29871, 29896, 29892, 29906, 2053, 7796, 29892, 29940, 11854, 29871, 322, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29924, 648, 29882, 29918, 29876, 2119, 29873, 29897, 3490, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 648, 29882, 29918, 29876, 2119, 29873, 29974, 19881, 29897, 353, 313, 29924, 29898, 29873, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 29897, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 9933, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 3789, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 18175, 29871, 29900, 529, 320, 326, 29898, 29924, 648, 29882, 29918, 29876, 2119, 29873, 876, 529, 13, 29905, 3411, 29905, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 1523, 2109, 292, 29871, 320, 2036, 29961, 1184, 3283, 29871, 29946, 29889, 29896, 3199, 29933, 29924, 29940, 29900, 29906, 29913, 411, 11894, 320, 999, 29912, 5287, 29889, 29955, 29913, 591, 13, 711, 2408, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29906, 29941, 29913, 13, 741, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 13, 29905, 6875, 741, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 1758, 1067, 3227, 562, 2119, 741, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 20073, 29913, 353, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 467, 13, 320, 355, 29912, 2573, 29913, 13, 3644, 395, 29873, 320, 262, 2802, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 27394, 769, 779, 326, 3552, 29924, 29985, 29928, 5033, 29873, 876, 320, 1333, 29922, 29871, 29900, 1504, 10133, 13, 29938, 29873, 320, 262, 2802, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 8435, 363, 777, 29871, 395, 29876, 320, 262, 9991, 29871, 29896, 29892, 29906, 2053, 7778, 29892, 29940, 29905, 1836, 29938, 13, 8439, 1079, 7555, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 1800, 320, 11725, 13, 29905, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 8435, 607, 17498, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29906, 29946, 29913, 13, 741, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 320, 11725, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1168, 874, 873, 29892, 565, 395, 29873, 320, 262, 2802, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 29883, 29923, 648, 29924, 29985, 29928, 4429, 13, 3062, 779, 29883, 29923, 648, 29924, 29985, 29928, 29913, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 18175, 13, 29905, 9933, 23891, 29898, 29924, 29985, 29928, 5033, 29873, 2144, 4429, 363, 777, 395, 29876, 1628, 769, 395, 29900, 529, 270, 648, 29924, 29985, 13, 29928, 2119, 29873, 4935, 10133, 7555, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 29883, 29923, 648, 29924, 29985, 29928, 29913, 320, 11725, 13, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 8435, 607, 17498, 13, 4535, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 320, 10436, 29883, 29923, 648, 29924, 29985, 29928, 29913, 13, 29905, 11725, 2802, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 23462, 10133, 13, 29905, 463, 29912, 2573, 4044, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 1800, 320, 5030, 18175, 13, 29905, 29883, 29923, 29918, 29924, 29905, 1266, 29897, 353, 13, 741, 1758, 1067, 3227, 562, 1012, 1563, 1194, 3752, 5231, 29985, 29940, 648, 29895, 29922, 29896, 3331, 5981, 3227, 562, 2119, 29924, 648, 29882, 29918, 29876, 11606, 1266, 29897, 320, 11725, 13, 741, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 13, 268, 320, 355, 29912, 2573, 4044, 13, 1523, 2109, 292, 445, 17193, 411, 29871, 320, 4915, 29912, 29941, 29889, 29906, 29941, 29913, 322, 320, 4915, 29912, 29941, 29889, 29906, 29946, 29913, 591, 13, 711, 2408, 7555, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29985, 29928, 20073, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 5667, 29889, 29929, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 22206, 320, 999, 29912, 5287, 29889, 29947, 1118, 29871, 426, 1235, 13, 1042, 29905, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 426, 29871, 367, 29913, 385, 15311, 10452, 21954, 29873, 13, 1454, 395, 29909, 6622, 29938, 322, 426, 1235, 29913, 395, 29924, 1194, 3822, 1262, 426, 367, 29913, 278, 6590, 13, 29956, 1032, 29880, 740, 29889, 8725, 29892, 1235, 395, 29933, 29922, 350, 6622, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 5767, 395, 29909, 29918, 29933, 353, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 448, 350, 741, 6642, 2403, 29900, 1262, 322, 395, 29923, 648, 29909, 29918, 29933, 4678, 3822, 1262, 278, 13, 21494, 1705, 5645, 310, 395, 29909, 29918, 29933, 1504, 29871, 960, 395, 29928, 29905, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 426, 322, 13, 29879, 27685, 583, 500, 7555, 29916, 3946, 5940, 2119 ]

1,332,863

17,408

ArXiv

-1

D) = {\xker\,}( D^*) = \{0\}$, then $N_{E^{ac}_{A_B}}(t) = d_{M_B^D}(t)$ for a.e. $t\in \R$ and ${\sigma}_{ac}(A_B) = {\rm cl}_{ac}({\rm supp\,}(d_{M_B^D}))$. If, in addition, the limit $M_B(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}M_B(t + iy)$ exists for a.e. $t \in \R$, then $N_{E^{ac}_{A_B}}(t) = d_{M_B}(t)$ for a.e. $t \in \R$ and ${\sigma}_{ac}(A_B) = {\rm cl}_{ac}({\rm supp\,}(d_{M_B}))$. \end{corollary} \begin{proof} By Proposition \ref{prop3.1} ${\Pi}_B = \{\cH,{\Gamma}^B_0,{\Gamma}^B_1\}$ is a generalized boundary triplet for $A_* := A^*\upharpoonright{\rm dom\,}(A_*)$, ${\rm dom\,}(A_*)= {\rm dom\,}(A_0) + {\rm dom\,}(A_B)$, and $M_B(z) = (B - M(z))^{-1}$, $z \in \C_+$, the corresponding generalized Weyl function. Clearly, $A_B = A_*\upharpoonright{\xker\,}({\Gamma}^B_0)$. It remains to apply Proposition \ref{III.8}. \end{proof} This leads to the following theorem. \begin{theorem}\Label{IV.10} { Let $A$ be a densely defined closed symmetric operator, let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be an ordinary boundary triplet for $A^*$ and let $M(\cdot)$ be the corresponding Weyl function. Further, let $A_B := A^*\upharpoonright{\xker\,}({\Gamma}_1-B{\Gamma}_0)$, $B = B^* \in \cC(\cH)$, and $E_{A_B}(\cdot)$ the spectral measure of $A_B$. Let $D \in \gotS_2(\cH)$} { and } ${\xker\,}(D) = {\xker\,}(D^*) = \{0\}$. Then \item[{\rm\;\;(i)}] { $A_0E^{ac}_{A_0}(\cD)$ is a part of $A_BE^{ac}_{A_B}(\cD)$} if and only if $d_{M^{ D}}(t) \le d_{M_B^{ D}}(t)$ for a.e. $t \in \cD.$ \item[{\rm\;\;(ii)}] $A_0E^{ac}_{A_0}(\cD)$ and $A_BE^{ac}_{A_B}(\cD)$ are unitarily equivalent if and only if $d_{M^D}(t) = d_{M_B^D}(t)$ for a.e. $t \in \cD.$ \end{theorem} \begin{proof} Without loss of generality we assume that $A$ is simple since the self-adjoint part of $A$ is contained as a direct summand in any self-adjoint extension of $A$. We to show that ${\Sigma}^{ac}_M({\delta}) = 0$ for some ${\delta} \in \cB_b(\R)$ if and only if $d_{M^D}(t) = 0$ for a.e $t \in {\delta}$. By the Berezanskii-Gel'fand-Kostyuchenko theorem \cite{Ber68,BS87} the derivative $\Psi_{{ D}^*{\Sigma}_M{ D}}(t) :=\frac{d}{dt}{ D}^*{\Sigma}(t){D}$ exists and the relation \begin{displaymath} {D}^*{\Sigma}^{ac}_M({\delta}\cap\cD){ D} = \int_{{\delta}\cap\cD}

-0.345199

-1.491882

-0.344237

2.199844

[ -0.15665414930280971, -0.5337429158490309 ]

[ -1.4381635646405908, -1.5456012795191738 ]

[ -0.27353909713545144, -0.41493453430062444 ]

[ 2.241465790785046, 2.158221942200954 ]

1,024

[ 512, 512 ]

[ 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 360, 6622, 29897, 353, 9991, 29900, 28538, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 29905, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29933, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29918, 29933, 29985, 29928, 20073, 1504, 13, 13, 3644, 29892, 297, 6124, 29892, 278, 4046, 395, 29924, 29918, 29933, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29918, 29933, 29898, 29873, 13, 29974, 474, 29891, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 13, 29938, 29940, 648, 29923, 998, 562, 3227, 29909, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 13, 29938, 741, 3754, 3227, 562, 2119, 29909, 29918, 29933, 29897, 353, 2802, 1758, 1067, 3227, 562, 2119, 741, 1758, 1462, 5940, 2119, 29881, 648, 29924, 29918, 29933, 20073, 1504, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 22206, 320, 999, 29912, 7728, 29941, 29889, 29896, 29913, 29871, 7555, 12197, 2403, 29933, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2137, 29933, 29918, 29900, 29892, 741, 6642, 2137, 29933, 29918, 29896, 11854, 338, 13, 29874, 28803, 10452, 21954, 29873, 363, 395, 29909, 24563, 29871, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29909, 24563, 5767, 7555, 1758, 2432, 5940, 2119, 29909, 24563, 3892, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 718, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29933, 5767, 13, 392, 29871, 395, 29924, 29918, 29933, 29898, 29920, 29897, 353, 313, 29933, 448, 341, 29898, 29920, 876, 3426, 29896, 4429, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 278, 6590, 13, 17492, 1891, 399, 1032, 29880, 740, 29889, 17732, 368, 29892, 395, 29909, 29918, 29933, 353, 13, 29909, 29918, 17710, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2137, 29933, 29918, 29900, 4935, 739, 9242, 304, 3394, 13, 1184, 3283, 320, 999, 29912, 5287, 29889, 29947, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 4013, 11981, 304, 278, 1494, 9185, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 5667, 29889, 29896, 29900, 29913, 13, 29912, 2803, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 29892, 1235, 13, 29938, 741, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 322, 1235, 395, 29924, 1194, 3822, 1262, 367, 278, 6590, 399, 1032, 29880, 740, 29889, 13, 29943, 332, 721, 29892, 1235, 395, 29909, 29918, 29933, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 29899, 29933, 741, 6642, 2403, 29900, 5767, 395, 29933, 353, 13, 29933, 6622, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 5767, 322, 395, 29923, 648, 29909, 29918, 29933, 4678, 3822, 1262, 278, 23161, 5645, 310, 13, 29938, 29909, 29918, 29933, 1504, 2803, 395, 29928, 320, 262, 320, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 1262, 29913, 426, 322, 500, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29928, 6622, 29897, 13, 29922, 9991, 29900, 23699, 1987, 13, 13, 29905, 667, 29961, 741, 1758, 29905, 10436, 29936, 29898, 29875, 2915, 29962, 426, 395, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 13, 29874, 760, 310, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 29913, 565, 322, 871, 565, 13, 259, 395, 29881, 648, 29924, 998, 360, 12156, 29873, 29897, 320, 280, 270, 648, 29924, 29918, 29933, 998, 360, 12156, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 7449, 13, 13, 13, 29905, 667, 29961, 741, 1758, 29905, 10436, 29936, 29898, 2236, 2915, 29962, 395, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 13, 392, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 29871, 526, 443, 3673, 2354, 7126, 565, 322, 871, 565, 13, 29938, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 29985, 29928, 2119, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 7449, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 3047, 449, 6410, 310, 2498, 537, 591, 5251, 393, 395, 29909, 29938, 338, 2560, 13, 16076, 278, 1583, 29899, 328, 12090, 760, 310, 395, 29909, 29938, 338, 11122, 408, 263, 1513, 13, 2083, 29885, 392, 297, 738, 1583, 29899, 328, 12090, 6081, 310, 395, 29909, 1504, 1334, 304, 1510, 13, 5747, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1800, 353, 29871, 29900, 29938, 363, 777, 7555, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 1194, 29934, 1262, 565, 322, 13, 6194, 565, 395, 29881, 648, 29924, 29985, 29928, 2119, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 395, 29873, 320, 262, 2802, 4181, 4311, 2648, 278, 13, 29933, 406, 29920, 550, 1984, 29875, 29899, 29954, 295, 29915, 29888, 392, 29899, 29968, 520, 29891, 987, 264, 2901, 9185, 320, 2036, 29912, 17104, 29953, 29947, 29892, 9851, 29947, 29955, 29913, 13, 1552, 16291, 779, 14118, 648, 29912, 360, 2137, 29930, 741, 10142, 2403, 29924, 29912, 360, 12156, 29873, 29897, 584, 2013, 1154, 29912, 29881, 1157, 6008, 1157, 13, 29928, 2137, 29930, 741, 10142, 2119, 29873, 2597, 29928, 1042, 4864, 322, 278, 8220, 13, 29905, 463, 29912, 4990, 755, 29913, 426, 29928, 2137, 29930, 741, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 2597, 360, 29913, 353, 320, 524, 24033, 4181, 1012, 5030, 29905, 29883, 29928, 29913 ]

1,332,863

18,432

ArXiv

-1

\Psi_{{ D}^*{\Sigma}_M{D}}(t) dt, \quad {\delta} \in \cB_b, \end{displaymath} holds. One has ${\Sigma}^{ac}_M({\delta}) = 0$ if and only if $\Psi_{ D^*{\Sigma}_MD}(t) = 0$ for a.e. $t \in {\delta}$. Since $d_{M^{ D}}(t) = {\rm dim}({\rm ran\,}(\Psi_{{D}^*{\Sigma}_M{ D}}(t)))$ for a.e. $t \in \R$ we find that ${\Sigma}^{ac}_M({\delta}\cap\cD) = 0$ if and only if $d_{M^{ D}}(t) = 0$\ for a.e. $t \in {\delta}\cap\cD$. Similarly we prove that ${\Sigma}^{ac}_{M_B}({\delta}\cap\cD) = 0$ if and only if $d_{{ D}^*{M_B}{ D}}(t) = 0$ for a.e. $t \in {\delta}\cap\cD$. (i) Since by assumption $d_{M^{D}}(t) \le d_{M_B^{ D}}(t)$ for a.e. $t \in \cD,$ one gets by the considerations above that ${\Sigma}^{ac}_M({\delta}\cap\cD) \prec {\Sigma}^{ac}_{M_B}({\delta}\cap\cD)$. By Theorem \ref{II.4} we have $N_{{\Sigma}^{ac}_M}(t) = d_{M^{D}}(t)$ and $N_{{\Sigma}^{ac}_{M_B}}(t) = d_{M_B^{D}}(t)$ for a.e $t \in \R$. Hence $N_{{\Sigma}^{ac}_M}(t) \le N_{{\Sigma}^{ac}_{M_B}}(t)$ for a.e. $t \in \cD$ which proves that the restricted measures ${\Sigma}^{ac}_M(\cdot\cap\cD)$ is spectrally subordinated to ${\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$, cf. Definition \ref{II.3}(i). Since ${\Sigma}^{ac}_M \thickapprox E^{ac}_{A_0}$ and ${\Sigma}^{ac}_{M_B} \thickapprox E^{ac}_{A_B},$ by Theorem \ref{IV.6}, we get that $E^{ac}_{A_0}(\cdot\cap\cD)$ is spectrally subordinated to $E^{ac}_{A_B}(\cdot\cap\cD)$. Applying Theorem \ref{II.4a}(i) we complete the proof. (ii) If $d_{M^{ D}}(t) = d_{{ D}^*{M_B}{ D}}(t)$ for a.e. $t \in \cD,$ then ${\Sigma}^{ac}_M(\cdot\cap\cD) \thicksim {\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$. By Theorem \ref{II.4}, $N_{{\Sigma}^{ac}_M}(t) = d_{M^D}(t)$ and $N_{{\Sigma}^{ac}_{M_B}}(t) = d_{M^D_B}(t)$ for a.e $t \in \R$ which implies that the operator measures ${\Sigma}^{ac}_M(\cdot\cap\cD)$ and ${\Sigma}^{ac}_{M_B}(\cdot\cap\cD)$ are spectrally equivalent, cf. Definition \ref{II.3}(ii). By Theorem \ref{IV.6}, $E^{ac}_{A_0}(\cdot\cap\cD)$ and $E^{ac}_{A_B}(\cdot\cap\cD)$ are spectrally equivalent. Applying Theorem \ref{II.4a}(ii) we prove that the absolutely continuous parts $A_0E^{ac}_{A_0}(\cD)$ and $A_BE^{ac}_{A_B}(\cD)$ are unitarily equivalent. \end{proof} Theorem \ref{IV.10} reduces the problem of unitary equivalence of $ac$-parts of certain self-adjoint extensions of $A$ to investigation of the functions $d_{M^{D}}(\cdot)$ and $d_{M_B^{D

-0.416721

-1.674527

-0.218693

1.960518

[ -0.6789285113228996, -0.15451403144499917 ]

[ -1.8106143095530123, -1.538438765193935 ]

[ -0.46692747532100193, 0.029541705397968753 ]

[ 1.8460575100106076, 2.0749780936168616 ]

1,024

[ 512, 512 ]

[ 320, 14118, 648, 29912, 13, 29928, 2137, 29930, 741, 10142, 2403, 29924, 29912, 29928, 12156, 29873, 29897, 11636, 29892, 320, 3425, 2802, 4181, 29913, 320, 262, 320, 29883, 29933, 29918, 29890, 29892, 13, 320, 355, 29912, 4990, 755, 29913, 13, 23177, 29889, 3118, 756, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1800, 353, 29871, 29900, 29938, 565, 322, 871, 565, 779, 14118, 648, 13, 29928, 6622, 741, 10142, 2403, 5773, 2119, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 4311, 4001, 395, 29881, 648, 29924, 998, 13, 29928, 12156, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 14118, 648, 29912, 29928, 2137, 29930, 741, 10142, 2403, 29924, 29912, 360, 12156, 29873, 876, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 13, 705, 1284, 393, 7555, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 353, 29871, 29900, 29938, 565, 322, 871, 565, 395, 29881, 648, 29924, 998, 13, 29928, 12156, 29873, 29897, 353, 29871, 29900, 4535, 29871, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 1012, 5030, 29905, 29883, 29928, 1504, 20175, 591, 6356, 393, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 353, 29871, 29900, 29938, 565, 322, 871, 565, 395, 29881, 648, 29912, 360, 2137, 19740, 29924, 29918, 29933, 1157, 13, 29928, 12156, 29873, 29897, 353, 29871, 29900, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 1012, 5030, 29905, 29883, 29928, 1504, 13, 13, 29898, 29875, 29897, 4001, 491, 11833, 395, 29881, 648, 29924, 998, 29928, 12156, 29873, 29897, 320, 280, 270, 648, 29924, 29918, 29933, 998, 360, 12156, 29873, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 8209, 29871, 697, 4947, 491, 278, 2050, 800, 2038, 393, 13, 29938, 741, 10142, 2844, 562, 2403, 29924, 13670, 4181, 1012, 5030, 29905, 29883, 29928, 29897, 320, 17990, 2802, 10142, 2844, 562, 3227, 29924, 29918, 29933, 2119, 741, 4181, 1012, 5030, 29905, 29883, 29928, 4935, 2648, 13, 28831, 320, 999, 29912, 2687, 29889, 29946, 29913, 591, 505, 395, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 353, 270, 648, 29924, 998, 29928, 12156, 29873, 1262, 322, 13, 29938, 29940, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 29897, 353, 270, 648, 29924, 29918, 29933, 998, 29928, 12156, 29873, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 1504, 10133, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 320, 280, 405, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29883, 29928, 29938, 13, 4716, 28281, 393, 278, 22078, 15366, 13, 29938, 741, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 338, 6683, 29878, 635, 1014, 4194, 630, 304, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 5767, 274, 29888, 29889, 21940, 320, 999, 29912, 2687, 29889, 29941, 2119, 29875, 467, 13, 23036, 7555, 10142, 2844, 562, 2403, 29924, 320, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29900, 1042, 322, 7555, 10142, 2844, 562, 3227, 29924, 29918, 29933, 29913, 13, 29905, 27996, 14850, 382, 998, 562, 3227, 29909, 29918, 29933, 1118, 29938, 491, 10244, 320, 999, 29912, 5667, 29889, 29953, 1118, 591, 679, 393, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 338, 6683, 29878, 635, 1014, 4194, 630, 304, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 4935, 2401, 5890, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 2119, 29875, 29897, 591, 13, 8835, 278, 5296, 29889, 13, 13, 29898, 2236, 29897, 960, 395, 29881, 648, 29924, 998, 360, 12156, 29873, 29897, 353, 270, 648, 29912, 360, 2137, 19740, 29924, 29918, 29933, 1157, 360, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29883, 29928, 8209, 769, 7555, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 29897, 320, 27996, 3601, 13, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 4935, 2648, 10244, 320, 999, 29912, 2687, 29889, 29946, 1118, 13, 29938, 29940, 24033, 10142, 2844, 562, 2403, 29924, 2119, 29873, 29897, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 1262, 322, 395, 29940, 24033, 10142, 2844, 562, 3227, 29924, 29918, 29933, 12156, 29873, 29897, 13, 29922, 270, 648, 29924, 29985, 29928, 29918, 29933, 2119, 29873, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 29938, 607, 10469, 393, 13, 1552, 5455, 15366, 7555, 10142, 2844, 562, 2403, 29924, 1194, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 322, 13, 29938, 741, 10142, 2844, 562, 3227, 29924, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 526, 6683, 29878, 635, 7126, 29892, 274, 29888, 29889, 13, 14683, 320, 999, 29912, 2687, 29889, 29941, 2119, 2236, 467, 2648, 10244, 320, 999, 29912, 5667, 29889, 29953, 1118, 13, 29938, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 322, 395, 29923, 998, 562, 3227, 29909, 29918, 29933, 4678, 3822, 29905, 5030, 29905, 29883, 29928, 1262, 526, 13, 21494, 29878, 635, 7126, 29889, 29871, 2401, 5890, 10244, 320, 999, 29912, 2687, 29889, 29946, 29874, 2119, 2236, 29897, 13, 705, 6356, 393, 278, 13312, 9126, 5633, 13, 29938, 29909, 29918, 29900, 29923, 998, 562, 3227, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 322, 395, 29909, 29918, 15349, 998, 562, 3227, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 526, 443, 3673, 2354, 13, 1686, 27445, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 28831, 320, 999, 29912, 5667, 29889, 29896, 29900, 29913, 26830, 278, 1108, 310, 5190, 653, 13, 1686, 2561, 663, 310, 395, 562, 4388, 20895, 29871, 310, 3058, 1583, 29899, 328, 12090, 17752, 310, 13, 29938, 29909, 29938, 304, 22522, 310, 278, 3168, 395, 29881, 648, 29924, 998, 29928, 20828, 3822, 1262, 322, 13, 29938, 29881, 648, 29924, 29918, 29933, 998, 29928 ]

1,332,863

19,456

ArXiv

-1

}}(\cdot).$ \begin{corollary} Let $A$ be as in Theorem \ref{IV.10}. { If the self-adjoint extensions { $\wt A$ and $\wt A'$ of $A$ are $ac$-minimal, then their $ac$-parts are unitarily equivalent.}} \end{corollary} \section{Unitary equivalence} \subsection{Preliminaries} In what follows we assume that $A$ is a densely defined simple closed symmetric operator in $\gotH$. By $A_0$ we denote a self-adjoint extension of $A$ which is fixed. Alongside $A_0$ we consider $\wt A = \wt A^*\in {\rm Ext\,}_A$. Usually we assume that \begin{equation}\Label{5.0} (\wt A - i)^{-1} - (A_0 - i)^{-1} \in \gotS_\infty(\gotH). \end{equation} It is known (see \cite{DM91} that there exists a boundary triplet ${\Pi} := \{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^*$ such that $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$. Of course, the boundary triplet ${\Pi}$ is not uniquely determined by the assumption $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$. { If $\Pi_1$ and $\Pi_2$ are two such boundary triplets of $A^*$, then their Weyl functions $M_1(\cdot)$ and $M_2(\cdot)$ are related by \eqref{2.11} (cf. \cite{DM91})}. { Fix a boundary triplet ${\Pi} := \{\cH,{\Gamma}_0,{\Gamma}_1\}$ for $A^*$ such that $A_0 = A^*{\xker\,}({\Gamma}_0)$. By Proposition \ref{prop2.1} there is a linear relation ${\Theta}= {\Theta}^* \in \wt\cC(\cH)$ such that $\wt A = A_{\Theta}$. In general, ${\Theta}$ is not the graph of an operator, ${\Theta} \not \in \cC(\cH)$. However, let us assume that ${\Theta}$ is the graph an operator $B$. By Proposition} \ref{prop2.9} { we get} that $(B - i)^{-1} \in \gotS_\infty(\gotH)$, that means, that $B$ is a self-adjoint operator with discrete spectrum. Hence, $\varrho(B)\cap \R \not = \emptyset.$ In what follows we assume without loss of generality that $0 \in \varrho(B).$ According to the polar decomposition { we have} $B^{-1} = DJD$ where \begin{equation}\label{4.2A} D := |B|^{-1/2} = D^* \in \gotS_\infty(\gotH) \quad \mbox{and} \quad J := {\rm sign}(B) = J^* = J^{-1}. \end{equation} Clearly, $D \in \gotS_\infty(\cH)$, ${\xker\,}(D) = \{0\}$, and $D$ commutes with $J$. We set \begin{equation}\label{4.2} G(z) := J - M^D(z), \quad z \in \C_+, \end{equation} { $M^D(z) := DM(z)D$, $z \in \C_+$, as usually}. Obviously, ${ M^D(z)}$ and $-G(z)$ are $R$-functions. We have ${\xker\,}(G(z)) = \{0\}$ for every $z \in \C_+$. Indeed, if $G(z)f = 0$, then $Jf = DM(z)Df.$ Hence, $\im(M(z)Df,Df) = \im(Jf,f) = 0$ which yields $Df = 0$ or $f = 0$. Since $J$ is a Fredholm operator satisfying ${\xker\,}(J) = {\xker\,}(J^*) = \{0\}$ we find by \

-0.199564

-1.345051

0.052368

2.012545

[ -0.26254718090727636, -0.13657984379654664 ]

[ -1.4310010503153519, -1.259100706509619 ]

[ 0.18678864897179345, -0.08205289971893909 ]

[ 1.9084903964486768, 2.1166000179089077 ]

1,024

[ 512, 512 ]

[ 20828, 3822, 467, 29938, 13, 29905, 463, 29912, 2616, 21982, 29913, 13, 12024, 395, 29909, 29938, 367, 408, 297, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 1836, 426, 960, 278, 1583, 29899, 328, 12090, 13, 24299, 426, 779, 14554, 319, 29938, 322, 779, 14554, 319, 13090, 310, 395, 29909, 29938, 526, 395, 562, 4388, 1195, 3039, 29892, 13, 6098, 1009, 395, 562, 4388, 20895, 526, 443, 3673, 2354, 7126, 29889, 930, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 13, 13, 29905, 2042, 29912, 8325, 653, 24796, 29913, 13, 13, 29905, 7235, 29912, 6572, 2576, 262, 4314, 29913, 13, 13, 13, 797, 825, 29871, 4477, 591, 5251, 393, 395, 29909, 29938, 338, 263, 6245, 873, 3342, 13, 12857, 5764, 18348, 5455, 297, 779, 7085, 29950, 1504, 2648, 395, 29909, 29918, 29900, 29938, 591, 13530, 263, 13, 1583, 29899, 328, 12090, 6081, 310, 395, 29909, 29938, 607, 338, 4343, 29889, 13, 2499, 549, 2975, 395, 29909, 29918, 29900, 29938, 591, 2050, 29871, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1504, 13, 15922, 1474, 591, 5251, 393, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29900, 29913, 13, 1194, 14554, 319, 448, 474, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 3112, 338, 2998, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 29913, 393, 727, 4864, 263, 10452, 13, 3626, 552, 29873, 7555, 12197, 29913, 3490, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 395, 29909, 6622, 29938, 1316, 393, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 4587, 3236, 29892, 278, 10452, 21954, 29873, 13, 29938, 741, 12197, 1042, 338, 451, 20498, 873, 10087, 491, 278, 11833, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 426, 960, 13, 4535, 12197, 29918, 29896, 29938, 322, 779, 12197, 29918, 29906, 29938, 526, 1023, 1316, 10452, 21954, 1372, 310, 395, 29909, 6622, 1628, 769, 13, 1552, 381, 399, 1032, 29880, 3168, 395, 29924, 29918, 29896, 1194, 3822, 1262, 322, 395, 29924, 29918, 29906, 1194, 3822, 1262, 526, 4475, 491, 320, 4915, 29912, 29906, 29889, 29896, 29896, 29913, 313, 6854, 29889, 13, 29905, 2036, 29912, 23560, 29929, 29896, 1800, 1836, 13, 13, 29912, 24778, 29871, 263, 10452, 21954, 29873, 7555, 12197, 29913, 3490, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 363, 13, 29938, 29909, 6622, 29938, 1316, 393, 395, 29909, 29918, 29900, 353, 319, 6622, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 29871, 2648, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 727, 338, 263, 5608, 8220, 13, 29938, 741, 17458, 5369, 2802, 17458, 2137, 29930, 320, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 1262, 1316, 393, 779, 14554, 319, 353, 319, 1665, 17458, 4311, 13, 797, 2498, 29892, 29871, 7555, 17458, 1042, 338, 451, 278, 3983, 310, 385, 5455, 29892, 13, 29938, 741, 17458, 29913, 320, 1333, 320, 262, 320, 29883, 29907, 1194, 29883, 29950, 4935, 2398, 29892, 1235, 502, 5251, 393, 7555, 17458, 1042, 338, 13, 1552, 3983, 385, 5455, 395, 29933, 1504, 13, 2059, 22206, 29913, 320, 999, 29912, 7728, 29906, 29889, 29929, 29913, 426, 591, 679, 29913, 393, 2427, 29933, 448, 474, 21604, 29896, 29913, 320, 262, 13, 29905, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 5767, 393, 2794, 29892, 393, 395, 29933, 29938, 338, 263, 1583, 29899, 328, 12090, 13, 6891, 411, 19554, 18272, 29889, 10133, 29892, 779, 1707, 4650, 29898, 29933, 2144, 5030, 320, 29934, 13, 29905, 1333, 353, 320, 26153, 7449, 29871, 512, 825, 4477, 591, 5251, 1728, 6410, 310, 13, 4738, 2877, 393, 395, 29900, 320, 262, 320, 1707, 4650, 29898, 29933, 467, 29938, 7579, 304, 278, 16755, 13, 311, 510, 3283, 426, 591, 505, 29913, 395, 29933, 3426, 29896, 29913, 353, 23366, 29928, 29938, 988, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29906, 29909, 29913, 360, 3490, 891, 29933, 29989, 3426, 29896, 29914, 29906, 29913, 353, 360, 6622, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 29897, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 435, 3490, 2802, 1758, 1804, 2119, 29933, 29897, 353, 435, 6622, 353, 435, 3426, 29896, 1836, 320, 355, 29912, 2573, 29913, 13, 18759, 368, 29892, 395, 29928, 320, 262, 320, 7085, 29903, 3187, 3411, 1194, 29883, 29950, 5767, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 9991, 29900, 28538, 13, 392, 259, 395, 29928, 29938, 844, 2667, 411, 395, 29967, 1504, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29906, 29913, 13, 29954, 29898, 29920, 29897, 3490, 435, 448, 341, 29985, 29928, 29898, 29920, 511, 320, 3425, 503, 320, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 27692, 29898, 29920, 29897, 29928, 1628, 29871, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 408, 5491, 1836, 25735, 29892, 13, 5303, 341, 29985, 29928, 29898, 29920, 15604, 322, 15727, 29954, 29898, 29920, 1262, 526, 395, 29934, 4388, 12171, 29889, 1334, 505, 7555, 29916, 3946, 5940, 2119, 29954, 29898, 29920, 876, 13, 29922, 9991, 29900, 11854, 363, 1432, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 14598, 29892, 565, 395, 29954, 29898, 29920, 29897, 29888, 353, 29871, 29900, 1628, 769, 395, 29967, 29888, 13, 29922, 27692, 29898, 29920, 29897, 29928, 29888, 7449, 10133, 29892, 779, 326, 29898, 29924, 29898, 29920, 29897, 29928, 29888, 29892, 29928, 29888, 29897, 353, 320, 326, 29898, 29967, 29888, 29892, 29888, 29897, 353, 29871, 29900, 29938, 607, 17498, 13, 29938, 29928, 29888, 353, 29871, 29900, 29938, 470, 395, 29888, 353, 29871, 29900, 1504, 4001, 395, 29967, 29938, 338, 263, 12001, 13376, 5455, 24064, 13, 29938, 741, 29916, 3946, 5940, 2119, 29967, 29897, 353, 2802, 29916, 3946, 5940, 2119, 29967, 6622, 29897, 353, 9991, 29900, 11854, 591, 1284, 491, 320 ]

1,332,863

20,480

ArXiv

-1

cite[Theorem 5.26]{Ka76} that $G(z)$ is boundedly invertible for $z \in \C_+$. We set $T(z) := G(z)^{-1}$, $z \in \cC_+$ { and note that $T(\cdot)$ is a Nevanlinna function because so is $M^D(\cdot).$} Moreover, $T(z) - J = T(z)M^D(z)J\in \gotS_\infty(\gotH)$ for $z \in \C_+$. \subsection{Trace class perturbations: Rosenblum-Kato theorem} Here we apply the Weyl function technique in order to obtain a simple and quite different proof of the classical Rosenblum-Kato theorem. In fact, we prove a generalization of the Rosenblum-Kato theorem due to Birman and Krein \cite{BirKrei62} which includes non-additive (trace class) perturbations. Our proof demonstrates the main idea of the proof of more general { results} contained in the next subsection. \begin{theorem}\Label{V.1} Let $A_0$ and $\wt A$ be self-adjoint operators in $\gH$ satisfying \begin{equation}\label{4.3} (\wt A - i)^{-1} - (A_0 - i)^{-1} \in \gotS_1(\gotH). \end{equation} Then the absolutely continuous parts $\wt A^{ac}$ and $A^{ac}_0$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{theorem} \begin{proof} To include the operators $\wt A^{ac}$ and $A^{ac}_0$ in the framework of extension theory we set \begin{displaymath} A:= { A_0}\upharpoonright {\rm dom\,}(A),\quad {\rm dom\,}(A)=\{f\in {\rm dom\,}({\wt A})\cap {\rm dom\,}(A_0):\ A_0f = {\wt A}f\}. \end{displaymath} { Obviously, we have $A := \wt A\upharpoonright{\rm dom\,}(A)$}. Clearly, $A$ is a closed symmetric operator in $\gH$ with equal deficiency indices and $A_0,\wt A\in {\rm Ext\,}_A$. { First we assume that $A$ is densely defined}. Let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a (ordinary) boundary triplet for $A^*,$ such that $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$, and { $M(\cdot)$ } the corresponding Weyl function. { By definition $\wt A = \wt A^*\in {\rm Ext\,}_A$ and $\wt A$ and $A_0$ are disjoint, that is, ${\rm dom\,}(A) = {\rm dom\,}(A_0) \cap {\rm dom\,}(\wt A)$. Hence, by Proposition \ref{prop2.1}(ii), there exists an operator $B = B^*\in \cC(\cH)$ such that $\wt A = A_B.$} It follows from \eqref{2.30} and \eqref{4.3} that $M_B(z) := (B - M(z))^{-1} \in \gotS_1(\cH)$ for $z \in \C_+$. In accordance with \cite[Lemma 2.4]{BirEnt67}, see also \cite{Yaf92}, the limits $M_B(t) := \lim_{y\to+0}M_B(t + iy)$ exist in $\gotS_2(\cH)$, for a.e $t \in \R$. By Theorem \ref{IV.10} it is { it suffices} to calculate the multiplicity function $d_{M_B}(t) := {\rm rank\,}(M_B(t)) = {\rm dim}({\rm ran\,}(\im(M_B(t))))$. { It follows from \eqref{4.2A} and \eqref{

0.315456

-0.866058

0.308528

2.303899

[ 0.381200270722141, 0.24971142953826003 ]

[ -0.609102531494191, -1.1230129343300803 ]

[ 0.49113757201790575, 0.125918864362571 ]

[ 2.3871425258072074, 2.220654828639023 ]

1,024

[ 512, 512 ]

[ 2036, 29961, 28831, 29871, 29945, 29889, 29906, 29953, 3199, 29968, 29874, 29955, 29953, 29913, 13, 5747, 395, 29954, 29898, 29920, 1262, 338, 12635, 368, 21292, 1821, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 1334, 731, 395, 29911, 29898, 29920, 29897, 13, 9361, 402, 29898, 29920, 21604, 29896, 4429, 395, 29920, 320, 262, 320, 29883, 29907, 29918, 24035, 426, 322, 4443, 393, 395, 29911, 1194, 3822, 1262, 338, 29871, 263, 13, 8139, 3703, 1915, 1056, 740, 1363, 577, 338, 29871, 395, 29924, 29985, 29928, 1194, 3822, 467, 17133, 12808, 29892, 29871, 395, 29911, 29898, 29920, 29897, 13, 29899, 435, 353, 323, 29898, 29920, 29897, 29924, 29985, 29928, 29898, 29920, 29897, 29967, 29905, 262, 320, 7085, 29903, 3187, 3411, 1194, 7085, 29950, 1262, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 13, 13, 29905, 7235, 29912, 11591, 770, 22786, 800, 29901, 28929, 2204, 398, 29899, 29968, 1219, 9185, 29913, 13, 13, 10605, 591, 3394, 278, 399, 1032, 29880, 740, 11043, 297, 1797, 304, 13, 711, 2408, 263, 2560, 322, 3755, 1422, 5296, 310, 278, 14499, 13, 29934, 7749, 2204, 398, 29899, 29968, 1219, 9185, 29889, 13, 797, 2114, 29892, 591, 6356, 263, 2498, 2133, 310, 278, 28929, 2204, 398, 29899, 29968, 1219, 9185, 13, 29123, 304, 17853, 1171, 322, 7706, 262, 320, 2036, 29912, 29933, 381, 29968, 5803, 29953, 29906, 29913, 607, 7805, 13, 5464, 29899, 1202, 3321, 313, 15003, 770, 29897, 22786, 800, 29889, 8680, 5296, 9004, 1078, 13, 1552, 1667, 2969, 310, 278, 5296, 310, 901, 2498, 426, 2582, 29913, 11122, 297, 278, 13, 4622, 1014, 2042, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 29963, 29889, 29896, 29913, 13, 12024, 29871, 395, 29909, 29918, 29900, 29938, 322, 779, 14554, 319, 29938, 29871, 367, 29871, 1583, 29899, 328, 12090, 12768, 297, 779, 29887, 29950, 29938, 13, 29879, 27685, 5414, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29941, 29913, 13, 1194, 14554, 319, 448, 474, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 7085, 29950, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 11760, 278, 13312, 9126, 5633, 779, 14554, 319, 998, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 13, 974, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 1628, 8307, 29892, 29871, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 1762, 3160, 278, 12768, 779, 14554, 319, 998, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 297, 278, 13, 4468, 310, 6081, 6368, 591, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29909, 9361, 426, 319, 29918, 29900, 1012, 29884, 561, 279, 1129, 265, 1266, 2802, 1758, 2432, 5940, 2119, 29909, 20481, 3425, 29871, 2802, 1758, 2432, 5940, 2119, 29909, 7950, 29912, 29888, 29905, 262, 2802, 1758, 2432, 5940, 2119, 741, 14554, 319, 11606, 5030, 13, 741, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 1125, 29905, 29871, 319, 29918, 29900, 29888, 353, 2802, 14554, 319, 29913, 29888, 29905, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29912, 25735, 29892, 591, 505, 395, 29909, 3490, 320, 14554, 319, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 1758, 2432, 5940, 2119, 29909, 1262, 1836, 13, 18759, 368, 29892, 395, 29909, 29938, 338, 263, 5764, 18348, 5455, 297, 779, 29887, 29950, 29938, 411, 13, 11745, 822, 293, 13396, 16285, 322, 29871, 395, 29909, 29918, 29900, 2053, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 1504, 13, 13, 29912, 29871, 3824, 591, 5251, 393, 395, 29909, 29938, 338, 6245, 873, 3342, 1836, 2803, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 263, 313, 24310, 29897, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 8209, 29871, 1316, 393, 395, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 5767, 322, 13, 29912, 29871, 395, 29924, 1194, 3822, 1262, 500, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 426, 2648, 13, 16553, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 13, 392, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 29938, 526, 766, 12090, 29892, 393, 338, 29892, 7555, 1758, 2432, 5940, 2119, 29909, 29897, 353, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 13, 29905, 5030, 2802, 1758, 2432, 5940, 4678, 14554, 319, 4935, 10133, 29892, 491, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 2119, 2236, 511, 727, 13, 9933, 29871, 385, 5455, 395, 29933, 353, 350, 6622, 29905, 262, 320, 29883, 29907, 1194, 29883, 29950, 1262, 1316, 393, 779, 14554, 319, 353, 319, 29918, 29933, 7449, 29913, 13, 13, 13, 3112, 4477, 515, 29871, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 322, 320, 4915, 29912, 29946, 29889, 29941, 29913, 393, 395, 29924, 29918, 29933, 29898, 29920, 29897, 3490, 313, 29933, 448, 13, 29924, 29898, 29920, 876, 3426, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 1262, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 29871, 512, 15017, 749, 411, 13, 29905, 2036, 29961, 29931, 331, 655, 29871, 29906, 29889, 29946, 3199, 29933, 381, 5292, 29953, 29955, 1118, 1074, 884, 320, 2036, 29912, 29979, 2142, 29929, 29906, 1118, 29871, 278, 13071, 13, 29938, 29924, 29918, 29933, 29898, 29873, 29897, 3490, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29918, 29933, 29898, 29873, 718, 474, 29891, 1262, 1863, 297, 779, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 5767, 29871, 363, 13, 29874, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 1504, 2648, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 29913, 372, 338, 426, 372, 9378, 1575, 29913, 13, 517, 8147, 278, 6674, 17024, 740, 395, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 3490, 13, 741, 1758, 7115, 5940, 2119, 29924, 29918, 29933, 29898, 29873, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29918, 29933, 29898, 29873, 13697, 1504, 13, 13, 29912, 739, 4477, 515, 29871, 320, 4915, 29912, 29946, 29889, 29906, 29909, 29913, 322, 320, 4915, 29912 ]

1,332,863

21,504

ArXiv

-1

4.2} that} \begin{eqnarray} \lefteqn{ T(z) = G(z)^{-1} = \bigl(J - M^D(z)\bigr)^{-1} = \bigl(J - D M(z)D \bigr)^{-1} }\\ & & = D^{-1}\bigl(D^{-1}JD^{-1}-M(z)\bigr)^{-1}D^{-1} =|B|^{1/2}\bigl(B-M(z)\bigr)^{-1} |B|^{1/2}, \;\; z \in \C_+. \nonumber \end{eqnarray} { Combining this relation with \eqref{4.2A} yields} \begin{displaymath} M_B(z) := (B - M(z))^{-1} = DT(z)D, \qquad z \in \C_+. \end{displaymath} In turn, this equality implies \begin{equation}\label{4.5} \im(M_B(z)) = DT(z)^*\im({ M^D(z)})T(z)D, \qquad z \in \C_+. \end{equation} { Moreover, since ${ M^D(z)} \in \gotS_1(\cH)$ and $T(z) - J \in \gotS_1$ for $z \in \C_+$, by \cite[Lemma 2.4]{BirEnt67} (see also \cite{Yaf92})}, { for a.e $t \in \R$ and $y\to 0$ there exist the limits $M^D(t)$ and $T(t)$ in $\gotS_2(\cH)$-norm of the Nevanlinna operator functions ${ M^D((t+iy))}$ and $T(t+iy)$, respectively.} Therefore passing to the limit in \eqref{4.5} as $y\to 0$ we get \begin{equation}\Label{5.3} \im(M_B(t)) = {D}T(t)^*\im({ M^D(t)})T(t){D}\quad \text{for a.e.}\quad t \in \R. \end{equation} Therefore we find \begin{eqnarray}\Label{5.3a} \lefteqn{ d_{M_B}(t) = {\rm dim}({\rm ran\,}(\im(M_B(t)))) }\\ & & = {\rm dim}({\rm ran\,}(\sqrt{\im(M_B(t))}\,)) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}T(t)D)). \nonumber \end{eqnarray} Since $(J - { M^D(t)})T(t) = T(t)(J - { M^D(t)}) = I$ for a.e. $t \in \R,$ we find ${\rm ran\,}(T(t)) = \cH$ for a.e. $t \in \R$. Combining this relation with $\overline {{\rm ran\,}(D)} = \cH$ and \eqref{5.3a} we obtain \begin{equation}\Label{5.3b} d_{M_B}(t) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}\,)) = {\rm dim}({\rm ran\,}(\im({ M^D(t)}))) = d_{M^D}(t) \end{equation} for a.e. $t \in \R$. { Applying} Theorem \ref{IV.10}(ii) we complete this part of the proof. { If $A$ is not densely defined} { one can repeat the above reasonings applying only} the boundary triplet technique for non-densely defined symmetric operators developed in \cite{DM95, Ma92b}. It turns out that the proof above can easily be carried over to this case. \end{proof} In the following corollary we show that in proving of unitary equivalence of $A_0$ and $\wt A\in {\rm Ext\,}_A$ it suffices to { restrict the

-0.142701

-1.42742

0.019397

2.074978

[ -0.00573303797000881, -0.27966812376976086 ]

[ -1.3020757924610522, -1.5527637938444128 ]

[ -0.01864687408433236, 0.057440356677195714 ]

[ 2.1790329043469767, 1.9709232828867462 ]

1,024

[ 512, 512 ]

[ 29946, 29889, 29906, 29913, 393, 29913, 13, 29905, 463, 29912, 9441, 29913, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29911, 29898, 29920, 29897, 353, 402, 29898, 29920, 21604, 29896, 29913, 353, 320, 3752, 29880, 29898, 29967, 448, 341, 29985, 29928, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 353, 320, 3752, 29880, 29898, 29967, 448, 360, 341, 29898, 29920, 29897, 29928, 320, 3752, 29878, 21604, 29896, 29913, 500, 1966, 13, 29987, 669, 353, 360, 3426, 29896, 1012, 3752, 29880, 29898, 29928, 3426, 29896, 29913, 29967, 29928, 3426, 29896, 7402, 29924, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 29928, 3426, 29896, 29913, 13, 29922, 29989, 29933, 29989, 998, 29896, 29914, 29906, 1012, 3752, 29880, 29898, 29933, 29899, 29924, 29898, 29920, 2144, 3752, 29878, 21604, 29896, 29913, 891, 29933, 29989, 998, 29896, 29914, 29906, 1118, 29871, 320, 10436, 29936, 13, 29871, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 13621, 13, 29905, 355, 29912, 9441, 29913, 13, 29912, 422, 2109, 292, 445, 8220, 411, 29871, 320, 4915, 29912, 29946, 29889, 29906, 29909, 29913, 17498, 29913, 13, 29871, 320, 463, 29912, 4990, 755, 29913, 13, 29924, 29918, 29933, 29898, 29920, 29897, 3490, 313, 29933, 448, 341, 29898, 29920, 876, 3426, 29896, 29913, 353, 360, 29911, 29898, 29920, 29897, 29928, 29892, 320, 12014, 13, 29871, 503, 320, 262, 320, 29907, 28842, 29889, 13, 29871, 320, 355, 29912, 4990, 755, 29913, 13, 797, 2507, 29892, 29871, 445, 17193, 10469, 13, 418, 320, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29945, 29913, 13, 29905, 326, 29898, 29924, 29918, 29933, 29898, 29920, 876, 353, 360, 29911, 29898, 29920, 4887, 17710, 326, 3319, 341, 29985, 29928, 29898, 29920, 26972, 29911, 29898, 29920, 29897, 29928, 29892, 320, 12014, 503, 320, 262, 13, 29905, 29907, 28842, 29889, 13, 418, 320, 355, 29912, 2573, 29913, 13, 29912, 12808, 29892, 1951, 6435, 341, 29985, 29928, 29898, 29920, 2915, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 1262, 322, 395, 29911, 29898, 29920, 29897, 13, 29899, 435, 320, 262, 320, 7085, 29903, 29918, 29896, 29938, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 491, 320, 2036, 29961, 29931, 331, 655, 29871, 29906, 29889, 29946, 3199, 29933, 381, 5292, 29953, 29955, 29913, 13, 29898, 4149, 884, 320, 2036, 29912, 29979, 2142, 29929, 29906, 1800, 1118, 426, 29871, 363, 263, 29889, 29872, 395, 29873, 320, 262, 320, 29934, 29938, 322, 395, 29891, 29905, 517, 29871, 29900, 29938, 13, 12711, 1863, 278, 13071, 395, 29924, 29985, 29928, 29898, 29873, 1262, 322, 395, 29911, 29898, 29873, 1262, 297, 779, 7085, 29903, 29918, 29906, 1194, 29883, 29950, 26725, 12324, 13, 974, 278, 29871, 2448, 3703, 1915, 1056, 5455, 3168, 6435, 341, 29985, 29928, 3552, 29873, 29974, 19881, 876, 1042, 322, 13, 29938, 29911, 29898, 29873, 29974, 19881, 5767, 8307, 5003, 13, 8439, 1079, 6819, 304, 278, 4046, 297, 320, 4915, 29912, 29946, 29889, 29945, 29913, 408, 395, 29891, 29905, 517, 29871, 29900, 29938, 591, 679, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29941, 29913, 13, 29905, 326, 29898, 29924, 29918, 29933, 29898, 29873, 876, 353, 426, 29928, 29913, 29911, 29898, 29873, 4887, 17710, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 2597, 29928, 1012, 3425, 320, 726, 29912, 1454, 13, 29874, 29889, 29872, 29889, 1012, 3425, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 7857, 591, 1284, 13, 29905, 463, 29912, 9441, 1012, 4775, 29912, 29945, 29889, 29941, 29874, 29913, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29918, 29933, 29898, 29873, 13697, 29871, 500, 1966, 13, 29987, 669, 29871, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29918, 29933, 29898, 29873, 876, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 29913, 29911, 29898, 29873, 29897, 29928, 8106, 320, 13621, 320, 355, 29912, 9441, 29913, 13, 4001, 2427, 29967, 448, 13, 29912, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 29897, 353, 323, 29898, 29873, 5033, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 353, 306, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 8209, 591, 1284, 13, 29938, 741, 1758, 6350, 5940, 2119, 29911, 29898, 29873, 876, 353, 320, 29883, 29950, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 422, 2109, 292, 445, 8220, 13, 2541, 29871, 779, 6875, 426, 741, 1758, 6350, 5940, 2119, 29928, 2915, 353, 320, 29883, 29950, 29938, 322, 29871, 320, 4915, 29912, 29945, 29889, 29941, 29874, 29913, 29871, 591, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29941, 29890, 29913, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 3319, 341, 29985, 29928, 29898, 29873, 2915, 4961, 353, 270, 648, 29924, 29985, 29928, 2119, 29873, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 426, 2401, 5890, 29913, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 591, 13, 8835, 445, 760, 310, 278, 5296, 29889, 13, 13, 29912, 960, 395, 29909, 29938, 338, 451, 6245, 873, 3342, 29913, 426, 697, 508, 12312, 278, 13, 27215, 2769, 886, 29871, 15399, 871, 29913, 29871, 278, 10452, 21954, 29873, 11043, 13, 1454, 1661, 29899, 21518, 873, 3342, 18348, 12768, 8906, 297, 13, 29905, 2036, 29912, 23560, 29929, 29945, 29892, 3219, 29929, 29906, 29890, 1836, 739, 12169, 714, 393, 278, 5296, 2038, 508, 29871, 5948, 13, 915, 8988, 975, 304, 445, 1206, 29889, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 797, 278, 1494, 29871, 1034, 21982, 591, 1510, 393, 297, 29871, 1326, 292, 310, 13, 5441, 653, 24796, 310, 29871, 395, 29909, 29918, 29900, 29938, 322, 779, 14554, 319, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 372, 9378, 1575, 304, 13, 29912, 9250, 278 ]

1,332,863

22,528

ArXiv

-1

consideration to disjoint extensions}. \begin{corollary}\Label{V.1A} Let $A$ be a densely defined closed symmetric operator in $\gH,$ { let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be} an ordinary boundary triplet for $A^*$, and { let $M(\cdot)$ be} the corresponding Weyl function. Let also $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$ and $\cD \in \cB(\R)$. \item[\rm\;\;(i)] If $A^{ac}_0E_{A_0}(\cD)$ is a part { of} ${\wt A}^{ac} E_{\wt A}(\cD)$ for any extension $\wt A = {\wt A}^*\in {\rm Ext\,}_A$ disjoint with $A_0,$ then $A^{ac}_0E_{A_0}(\cD)$ is a part { of} $\wt A^{ac}E_{\wt A}(\cD)$ for any extension $\wt A = \wt A^*\in {\rm Ext\,}_A.$ \item[\rm\;\;(ii)] If $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $\wt A^{ac} E_{\wt A}(\cD)$ for any extension $\wt A = \wt A^*\in {\rm Ext\,}_A$ disjoint with $A_0$, then $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to the absolutely continuous part $\wt A^{ac}E_{\wt A}(\cD)$ of any extension $\wt A = \wt A^*\in {\rm Ext\,}_A.$ \end{corollary} \begin{proof} By Proposition \ref{prop2.1} an extension $\wt A\in {\rm Ext\,}_A$ which is not disjoint with $A_0$ admits a representation $\wt A_{\Theta}$ with ${\Theta}= {\Theta}^*\in \wt\cC(\cH) \setminus \cC(\cH).$ { However}, ${\Theta}$ admits a decomposition $\cH = \cH_{\rm op} \oplus \cH_\infty,$ \ ${\Theta} = {\Theta}_{\rm op} \oplus {\Theta}_{\infty}$ where ${\Theta}_{\rm op}$ is the graph of the operator $B_{\rm op}= B_{\rm op}^*\in \cC(\cH_{\rm op})$ (cf. Section 2). Denoting by $\pi_{\rm op}$ the orthogonal projection from $\cH$ onto $\cH_{\rm op}$ and $M_{\rm op}(z) := \pi_{\rm op}M(z)\upharpoonright\cH_{\rm op}$, we get $({\Theta} - M(z))^{-1} = (B_{\rm op} - M_{\rm op}(z))^{-1}\pi_{\rm op}.$ Therefore formula \eqref{2.30} takes the form \begin{displaymath} (A_{\Theta} - z)^{-1} - (A_0 - z)^{-1} = {\gamma}(z)(B_{\rm op} - M_{\rm op}(z))^{-1}\pi_{\rm op}{\gamma}(\overline{z})^*, \quad z \in \C_\pm. \end{displaymath} Choose an operator $B_\infty = B_\infty^* \in \cC(\cH_\infty)$ such that $(B_\infty - i)^{-1} \in \gotS_1(\cH_\infty)$ and put $B = B_{\rm op} \oplus B_\infty.$ It follows from Proposition \ref{prop2.9} that \begin{displaymath} (A_{\Theta} - z)^{-1} - ({ A_B} - z)^{-1} \in \gotS_1(\gotH), \end{displaymath} since $(B_\infty - i)^{-1} \in \gotS_1(\cH_\infty).$ By Theorem \ref{V.1} the absolutely continuous parts $A^{ac}_{\Theta}$ and $A^{ac}_B$ of $A_{\Theta}$ and $A_B$, respectively, are unitarily equivalent. (i) Since by assumption $A^{ac}_0E_{A_0}(\cD)$ is

-0.100412

-1.287751

0.133528

2.376737

[ -0.21769031060756697, 0.016866606608470735 ]

[ -1.194638077582469, -1.3808634500386798 ]

[ 0.34910807459638665, -0.08205289971893909 ]

[ 2.303898677223115, 2.449575412245277 ]

1,024

[ 512, 512 ]

[ 19220, 304, 766, 12090, 17752, 1836, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 29963, 29889, 29896, 29909, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 779, 29887, 29950, 8209, 13, 29912, 1235, 779, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29913, 29871, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 1628, 322, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 2803, 884, 13, 29938, 29909, 29918, 29900, 3490, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 322, 29871, 779, 29883, 29928, 320, 262, 320, 29883, 29933, 1194, 29934, 4935, 13, 13, 29905, 667, 7110, 1758, 29905, 10436, 29936, 29898, 29875, 4638, 960, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 760, 426, 310, 29913, 13, 29938, 741, 14554, 319, 2844, 562, 29913, 382, 1665, 14554, 319, 4678, 29883, 29928, 1262, 363, 738, 6081, 779, 14554, 319, 353, 2802, 14554, 13, 29909, 2137, 17710, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 766, 12090, 411, 395, 29909, 29918, 29900, 8209, 13, 6098, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 760, 426, 310, 29913, 779, 14554, 319, 998, 562, 29913, 29923, 1665, 14554, 13, 29909, 4678, 29883, 29928, 1262, 363, 738, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 13, 29905, 667, 7110, 1758, 29905, 10436, 29936, 29898, 2236, 4638, 960, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 29871, 779, 14554, 319, 998, 562, 29913, 382, 1665, 14554, 319, 4678, 29883, 29928, 1262, 13, 1454, 738, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 29938, 766, 12090, 411, 13, 29938, 29909, 29918, 29900, 1628, 769, 29871, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 278, 13312, 9126, 760, 29871, 779, 14554, 319, 998, 562, 29913, 29923, 1665, 14554, 13, 29909, 4678, 29883, 29928, 1262, 310, 738, 29871, 6081, 779, 14554, 319, 353, 320, 14554, 319, 6622, 29905, 262, 2802, 1758, 7338, 5940, 2403, 29909, 7449, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 22206, 320, 999, 29912, 7728, 29906, 29889, 29896, 29913, 385, 6081, 29871, 779, 14554, 319, 29905, 262, 13, 741, 1758, 7338, 5940, 2403, 29909, 29938, 607, 338, 451, 766, 12090, 411, 395, 29909, 29918, 29900, 29938, 7336, 1169, 263, 8954, 13, 4535, 14554, 319, 1665, 17458, 1042, 411, 29871, 7555, 17458, 5369, 2802, 17458, 2137, 17710, 262, 320, 14554, 29905, 29883, 29907, 1194, 29883, 29950, 29897, 320, 15375, 320, 29883, 29907, 1194, 29883, 29950, 467, 29938, 13, 29912, 2398, 1118, 7555, 17458, 1042, 29871, 7336, 1169, 263, 26227, 779, 29883, 29950, 353, 320, 29883, 29950, 1665, 1758, 1015, 29913, 320, 17201, 13, 29905, 29883, 29950, 3187, 3411, 8209, 320, 7555, 17458, 29913, 353, 2802, 17458, 6353, 1758, 1015, 29913, 320, 17201, 2802, 17458, 6353, 3411, 1042, 988, 13, 29938, 741, 17458, 6353, 1758, 1015, 1042, 338, 278, 3983, 310, 278, 5455, 395, 29933, 1665, 1758, 1015, 5369, 350, 1665, 1758, 13, 459, 2137, 17710, 262, 320, 29883, 29907, 1194, 29883, 29950, 1665, 1758, 1015, 8435, 313, 6854, 29889, 9779, 29871, 29906, 467, 3384, 11427, 491, 779, 1631, 1665, 1758, 13, 459, 1042, 278, 28143, 18246, 515, 779, 29883, 29950, 29938, 11480, 779, 29883, 29950, 1665, 1758, 1015, 1042, 322, 13, 29938, 29924, 1665, 1758, 1015, 2119, 29920, 29897, 3490, 320, 1631, 1665, 1758, 1015, 29913, 29924, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 1665, 1758, 1015, 4429, 591, 13, 657, 2427, 741, 17458, 29913, 448, 341, 29898, 29920, 876, 3426, 29896, 29913, 353, 313, 29933, 1665, 1758, 1015, 29913, 448, 341, 1665, 1758, 1015, 2119, 29920, 876, 3426, 29896, 1012, 1631, 1665, 1758, 13, 459, 1836, 29938, 7857, 7063, 320, 4915, 29912, 29906, 29889, 29941, 29900, 29913, 4893, 278, 883, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 29909, 1665, 17458, 29913, 448, 503, 21604, 29896, 29913, 448, 313, 29909, 29918, 29900, 448, 503, 21604, 29896, 29913, 353, 2802, 4283, 2119, 29920, 5033, 29933, 1665, 1758, 1015, 29913, 448, 13, 29924, 1665, 1758, 1015, 2119, 29920, 876, 3426, 29896, 1012, 1631, 1665, 1758, 1015, 3331, 4283, 4678, 6875, 29912, 29920, 1800, 6622, 29892, 320, 3425, 503, 320, 262, 13, 29905, 29907, 3187, 3358, 29889, 320, 355, 29912, 4990, 755, 29913, 13, 15954, 852, 385, 5455, 395, 29933, 3187, 3411, 353, 350, 3187, 3411, 6622, 320, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 3187, 3411, 1262, 1316, 393, 2427, 29933, 3187, 3411, 448, 474, 21604, 29896, 29913, 320, 262, 13, 29905, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 3187, 3411, 1262, 322, 1925, 395, 29933, 353, 350, 1665, 1758, 1015, 29913, 320, 17201, 350, 3187, 3411, 7449, 739, 13, 23031, 29879, 515, 22206, 320, 999, 29912, 7728, 29906, 29889, 29929, 29913, 393, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 1665, 17458, 29913, 448, 503, 21604, 29896, 29913, 448, 21313, 319, 29918, 29933, 29913, 448, 503, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 7085, 29950, 511, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 16076, 29871, 2427, 29933, 3187, 3411, 448, 474, 21604, 29896, 29913, 320, 262, 320, 7085, 29903, 29918, 29896, 1194, 29883, 29950, 3187, 3411, 467, 29938, 13, 2059, 10244, 320, 999, 29912, 29963, 29889, 29896, 29913, 278, 13312, 9126, 5633, 395, 29909, 998, 562, 6353, 17458, 1042, 13, 392, 395, 29909, 998, 562, 2403, 29933, 29938, 310, 29871, 395, 29909, 1665, 17458, 1042, 322, 395, 29909, 29918, 29933, 1628, 8307, 29892, 526, 13, 348, 3673, 2354, 7126, 29889, 13, 13, 29898, 29875, 29897, 4001, 491, 11833, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338 ]

1,332,863

23,552

ArXiv

-1

a part of $A^{ac}_B E_{A_B}(\cD)$ and $A^{ac}_B$ is unitarily equivalent to $A_{\Theta}^{ac}$ we get that $A^{ac}_0E_{A_0}(\cD)$ is a part of $A^{ac}_{\Theta} E_{A_{\Theta}}(\cD)$. (ii) Since, by assumption, $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $A^{ac}_BE_{A_B}(\cD)$ and $A^{ac}_B$ is unitarily equivalent to $A_{\Theta}$, we get that $A^{ac}_0E_{A_0}(\cD)$ is unitarily equivalent to $A^{ac}_{\Theta} E_{A_{\Theta}}(\cD)$. \end{proof} \subsection{Compact non-additive perturbations} Here we generalize the Rosenblum-Kato theorem for the case of compact perturbations. To this end we assume that the maximal normal function \begin{displaymath} m^+(t) := \sup_{0<y\le 1}\|M(t+iy)\| \end{displaymath} is finite for a.e. $t \in \R$. This is the case if and only if the normal limits $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t + iy)$ exist and are bounded operators for a.e. $t \in \R$. Indeed, let $D = D^*$ be a Hilbert-Schmidt operator such that ${\xker\,}(D) = \{0\}$ and let $M^D(z) := DM(z)D$, $z \in \C_+$. Since the limit $M^D(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}M^D(t + iy)$ exists and is a bounded operator for a.e. $t \in \R$, see \cite{BirEnt67, Yaf92}, we find that \begin{displaymath} \lim_{y\to+0}(M(t+iy)Df,Dg) = ({ M^D(t)}f,g), \quad f,g \in \cH, \quad \text{for a.e.} \quad t \in \R. \end{displaymath} Hence the limit $\lim_{y\to+0}(M(t+iy)h,k)$ exists for a.e. $t \in \R$ and $h,k \in {\rm ran\,}(D)$ which yields the existence of $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ for a.e. $t \in \R$. The converse statement is obvious. Now we are ready to prove the main result of this section. \begin{theorem}\Label{V.5} Let $A$ be a densely defined, closed symmetric operator in $\gH$, { let $\Pi=\{\cH,{\Gamma}_0,{\Gamma}_1\}$ be} an ordinary boundary triplet for $A^*$, and { let $M(\cdot)$ be} the corresponding Weyl function. Let $\wt A$ be a self-adjoint extension of $A$ and $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0)$. If the maximal normal function $m^+(t)$ is finite for a.e. $t \in \R$ and condition \eqref{5.0} is satisfied, then the absolutely continuous parts $\wt A^{ac}$ and $A^{ac}_0$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{theorem} \begin{proof} We divide the proof into several steps. (i) { First we assume that the extensions $\wt A$ and $A_0$ are disjoint, that is} $\wt A = A_B$ where $B = B^*\in \cC(\cH).$ We { define} the operator $D\in \gotS_{\infty}(\cH)$ in accordance with \eqref{4.

-0.432387

-1.663783

-0.230582

1.898085

[ -0.7939812473587955, -0.07079262084744993 ]

[ -1.7819642522520567, -1.5456012795191738 ]

[ -0.5820094118478132, 0.12084638231180245 ]

[ 1.8252465478645845, 1.9709232828867462 ]

1,024

[ 512, 512 ]

[ 263, 760, 13, 974, 395, 29909, 998, 562, 2403, 29933, 382, 648, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 322, 395, 29909, 998, 562, 2403, 29933, 29938, 338, 443, 3673, 2354, 7126, 13, 517, 395, 29909, 1665, 17458, 2844, 562, 1042, 591, 679, 393, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 263, 13, 1595, 310, 395, 29909, 998, 562, 6353, 17458, 29913, 382, 648, 29909, 1665, 17458, 20828, 29883, 29928, 4935, 13, 13, 29898, 2236, 29897, 4001, 29892, 491, 11833, 29892, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29909, 998, 562, 2403, 15349, 648, 29909, 29918, 29933, 4678, 29883, 29928, 1262, 322, 395, 29909, 998, 562, 2403, 29933, 29938, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 395, 29909, 1665, 17458, 4429, 591, 679, 393, 395, 29909, 998, 562, 2403, 29900, 29923, 648, 29909, 29918, 29900, 4678, 29883, 29928, 1262, 338, 13, 348, 3673, 2354, 7126, 304, 395, 29909, 998, 562, 6353, 17458, 29913, 382, 648, 29909, 1665, 17458, 20828, 29883, 29928, 4935, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29905, 7235, 29912, 6843, 627, 1661, 29899, 1202, 3321, 22786, 800, 29913, 13, 13, 10605, 29871, 591, 29871, 2498, 675, 278, 28929, 2204, 398, 29899, 29968, 1219, 9185, 363, 278, 1206, 310, 13, 2388, 627, 22786, 800, 29889, 1763, 445, 1095, 591, 5251, 393, 278, 23183, 13, 8945, 740, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29885, 14747, 29898, 29873, 29897, 3490, 320, 12587, 648, 29900, 29966, 29891, 29905, 280, 29871, 29896, 1012, 29989, 29924, 29898, 29873, 29974, 19881, 2144, 29989, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 275, 8093, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 910, 338, 278, 1206, 565, 322, 871, 565, 278, 13, 8945, 13071, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 718, 474, 29891, 1262, 1863, 322, 526, 13, 29306, 12768, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 14598, 29892, 1235, 29871, 395, 29928, 353, 360, 6622, 29938, 367, 263, 13, 29950, 309, 2151, 29899, 4504, 19720, 5455, 1316, 393, 7555, 29916, 3946, 5940, 2119, 29928, 29897, 353, 9991, 29900, 11854, 322, 13, 1026, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 27692, 29898, 29920, 29897, 29928, 1628, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 4001, 278, 4046, 13, 29938, 29924, 29985, 29928, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29985, 29928, 29898, 29873, 718, 474, 29891, 1262, 4864, 322, 338, 263, 12635, 13, 6891, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 1074, 320, 2036, 29912, 29933, 381, 5292, 29953, 29955, 29892, 612, 2142, 29929, 29906, 1118, 591, 1284, 13, 5747, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29924, 29898, 29873, 29974, 19881, 29897, 29928, 29888, 29892, 29928, 29887, 29897, 353, 21313, 341, 29985, 29928, 29898, 29873, 2915, 29888, 29892, 29887, 511, 320, 3425, 285, 29892, 29887, 320, 262, 320, 29883, 29950, 29892, 13, 29905, 3425, 320, 726, 29912, 1454, 263, 29889, 29872, 5003, 320, 3425, 29871, 260, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29950, 663, 278, 4046, 779, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29924, 29898, 29873, 29974, 19881, 29897, 29882, 29892, 29895, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29934, 29938, 322, 395, 29882, 29892, 29895, 320, 262, 2802, 1758, 6350, 5940, 2119, 29928, 1262, 607, 17498, 278, 10379, 310, 395, 29924, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 450, 378, 3901, 3229, 13, 275, 6924, 29889, 13, 13, 10454, 591, 526, 7960, 29871, 304, 6356, 278, 1667, 1121, 310, 445, 4004, 29889, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 29963, 29889, 29945, 29913, 13, 12024, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 29892, 5764, 18348, 5455, 297, 779, 29887, 29950, 1628, 13, 29912, 1235, 13, 4535, 12197, 2013, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 367, 29913, 385, 15311, 10452, 21954, 29873, 363, 395, 29909, 6622, 1628, 13, 392, 29871, 426, 1235, 395, 29924, 1194, 3822, 1262, 367, 29913, 278, 6590, 399, 1032, 29880, 740, 29889, 2803, 779, 14554, 319, 29938, 367, 263, 13, 1311, 29899, 328, 12090, 6081, 310, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 960, 278, 23183, 4226, 740, 13, 29938, 29885, 14747, 29898, 29873, 1262, 338, 8093, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 29938, 322, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 13, 275, 15787, 29892, 769, 278, 13312, 9126, 5633, 779, 14554, 319, 998, 562, 1042, 13, 392, 395, 29909, 998, 562, 2403, 29900, 29938, 310, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 1628, 8307, 29892, 29871, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 4806, 16429, 278, 5296, 964, 3196, 6576, 29889, 13, 13, 29898, 29875, 29897, 426, 3824, 591, 5251, 393, 29871, 278, 17752, 779, 14554, 319, 29938, 322, 395, 29909, 29918, 29900, 29938, 13, 598, 766, 12090, 29892, 393, 338, 29913, 29871, 779, 14554, 319, 353, 319, 29918, 29933, 29938, 29871, 988, 395, 29933, 353, 350, 6622, 29905, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 467, 29938, 1334, 426, 4529, 29913, 278, 5455, 395, 29928, 29905, 262, 13, 29905, 7085, 29903, 1665, 3411, 4678, 29883, 29950, 1262, 297, 15017, 749, 411, 320, 4915, 29912, 29946, 29889 ]

1,332,863

24,576

ArXiv

-1

2A}, $D := |B|^{-1/2},$ and investigate the function $M^D(z) := M^D(z):= DM(z)D$, $z \in \C_+$. Let $ M^D(t) := DM(t)D.$ Since the (weak) limit $M(t) := \,\mbox{\rm w-}\hspace{-2pt} \lim_{y\to+0}M(t+iy)$ exists for a.e. $t \in \R,$ by \cite[Lemma 6.1.4]{Yaf92}, the following limit exists \begin{equation}\label{4.9} \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0} \|{ M^D(}t+iy) - { M^D(t)}\| = 0 \qquad\text {for a.e.} \quad t \in \R. \end{equation} Let ${\delta}_a := \{t \in \R: \|M(t)\| \le a\}$. Since $D = D^*$ is a { a non-negative } compact operator, it admits the spectral decomposition \begin{displaymath} D = \sum_{l \in \N} \mu_lQ_l \end{displaymath} where $\{\mu_l\}^\infty_{l=1}$, is the { decreasing } sequence of eigenvalues of $D$, $\{Q_l\}_{l \in \N}$ the corresponding sequence of eigenprojections, ${\rm dim}\{Q_l\}<\infty.$ Since $\mu_l\to 0$ as $l\to \infty,$ there exists a number $l_a\in \N$ such that $\mu_{l_a}< 1/\sqrt {2a}$. We put $\cH_1 := \bigoplus^\infty_{l=l_a+1}Q_l\cH$ and $\cH_2 := \bigoplus^{l_a}_{l=1}Q_l\cH.$ Clearly, $\cH = \cH_1 \oplus \cH_2$ and ${\rm dim}(\cH_2) <\infty.$ Moreover, the operator $D$ admits the following decomposition $D = D_1 \oplus D_2$ where \begin{displaymath} D_1 := \sum^\infty_{l = l_a + 1}\mu_lQ_l \quad \text{and}\quad D_2 := \sum^{l_a}_{l=1}\mu_lQ_l. \end{displaymath} Since $\mu_{l_a}< 1/\sqrt {2a},$ we have $\|D_1\|< 1/\sqrt {2a}.$ Hence \begin{equation}\Label{5.5} \|D_1M(t)D_1\| < 1/2, \qquad t \in {\delta}_a. \end{equation} Denote by $P_1$ and $P_2$ the orthogonal projections from $\cH$ onto $\cH_1$ and $\cH_2$, respectively. Note that $P_1J = JP_1$ and $P_2J = JP_2$. (ii) Our next aim is to show that the operator function $G(z) := J - { M^D(z)}$ is invertible in $\C_+$ and { that $T(z) := G(z)^{-1}$ has the limits $T(t) := \,\mbox{\rm s-}\hspace{-2pt} \lim_{y\to+0}T(t+iy)$ for a.e. $t \in {\delta}_a$}. For this purpose we consider the decompositions \begin{displaymath} { M^D(z)} := \bigg(D_iM(z)D_j\bigg)_{i,j=1}^2 := \begin{pmatrix} M^D_{11}(z) & M^D_{12}(z)\\ M^D_{21}(z) & M^D_{22}(z) \end{pmatrix}: \begin{array}{c} \cH_1\\ \oplus \\ \cH_2 \end{array}

-0.339249

-1.169569

-0.271003

2.085384

[ -0.3337703032152119, -0.344727706647202 ]

[ -1.3808634500386798, -0.9582751048495861 ]

[ -0.3204595561050604, -0.2215461561150739 ]

[ 2.0749780936168616, 2.0957890557628844 ]

1,024

[ 512, 512 ]

[ 29906, 29909, 1118, 29871, 395, 29928, 3490, 13, 29989, 29933, 29989, 3426, 29896, 29914, 29906, 1118, 29938, 322, 23033, 278, 740, 395, 29924, 29985, 29928, 29898, 29920, 29897, 3490, 341, 29985, 29928, 29898, 29920, 1125, 29922, 13, 23560, 29898, 29920, 29897, 29928, 1628, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 2803, 395, 341, 29985, 29928, 29898, 29873, 29897, 3490, 27692, 29898, 29873, 29897, 29928, 7449, 4001, 278, 313, 25129, 29897, 13, 13400, 395, 29924, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 281, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29924, 29898, 29873, 29974, 19881, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 8209, 13, 1609, 320, 2036, 29961, 29931, 331, 655, 29871, 29953, 29889, 29896, 29889, 29946, 3199, 29979, 2142, 29929, 29906, 1118, 278, 1494, 4046, 4864, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29929, 29913, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 29898, 29913, 29873, 29974, 19881, 29897, 448, 426, 341, 29985, 29928, 29898, 29873, 11383, 29989, 353, 29871, 29900, 320, 12014, 29905, 726, 426, 1454, 263, 29889, 29872, 5003, 320, 3425, 13, 29873, 320, 262, 320, 29934, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 12024, 7555, 4181, 2403, 29874, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 12926, 29924, 29898, 29873, 2144, 29989, 320, 280, 263, 23699, 4001, 395, 29928, 353, 360, 6622, 29938, 338, 263, 13, 29912, 263, 1661, 29899, 22198, 500, 29871, 11071, 5455, 29892, 372, 29871, 7336, 1169, 278, 23161, 13, 311, 510, 3283, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29928, 353, 320, 2083, 648, 29880, 320, 262, 320, 29940, 29913, 320, 2589, 29918, 29880, 29984, 29918, 29880, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 779, 741, 2589, 29918, 29880, 29905, 10206, 3411, 648, 29880, 29922, 29896, 4429, 29871, 338, 278, 426, 9263, 5832, 500, 13, 16506, 310, 25973, 310, 395, 29928, 1628, 12564, 29984, 29918, 29880, 29905, 3227, 29880, 320, 262, 320, 29940, 1042, 29871, 278, 13, 2616, 3636, 292, 5665, 310, 7388, 771, 24247, 29892, 7555, 1758, 3964, 1012, 29912, 29984, 29918, 29880, 18105, 13505, 3411, 7449, 13, 13, 23036, 29871, 779, 2589, 29918, 29880, 29905, 517, 29871, 29900, 29938, 408, 395, 29880, 29905, 517, 320, 3411, 8209, 727, 4864, 263, 1353, 13, 29938, 29880, 29918, 29874, 29905, 262, 320, 29940, 29938, 1316, 393, 259, 779, 2589, 648, 29880, 29918, 29874, 29913, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 4311, 1334, 1925, 779, 29883, 29950, 29918, 29896, 13, 9361, 320, 3752, 17201, 3823, 3411, 648, 29880, 29922, 29880, 29918, 29874, 29974, 29896, 29913, 29984, 29918, 29880, 29905, 29883, 29950, 29938, 322, 29871, 779, 29883, 29950, 29918, 29906, 3490, 13, 29905, 3752, 17201, 998, 29880, 29918, 29874, 3227, 29880, 29922, 29896, 29913, 29984, 29918, 29880, 29905, 29883, 29950, 7449, 259, 17732, 368, 29892, 29871, 779, 29883, 29950, 353, 320, 29883, 29950, 29918, 29896, 320, 17201, 13, 29905, 29883, 29950, 29918, 29906, 29938, 322, 29871, 7555, 1758, 3964, 4678, 29883, 29950, 29918, 29906, 29897, 529, 29905, 3411, 7449, 12808, 29892, 278, 5455, 395, 29928, 29938, 7336, 1169, 13, 1552, 1494, 26227, 395, 29928, 353, 360, 29918, 29896, 320, 17201, 360, 29918, 29906, 29938, 988, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29928, 29918, 29896, 3490, 320, 2083, 3823, 3411, 648, 29880, 353, 301, 29918, 29874, 718, 29871, 29896, 1012, 2589, 29918, 29880, 29984, 29918, 29880, 320, 3425, 13, 29905, 726, 29912, 392, 1012, 3425, 29871, 360, 29918, 29906, 3490, 320, 2083, 998, 29880, 29918, 29874, 3227, 29880, 29922, 29896, 1012, 2589, 29918, 29880, 29984, 29918, 29880, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 779, 2589, 648, 29880, 29918, 29874, 29913, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 1118, 29938, 591, 505, 29871, 779, 29989, 29928, 29918, 29896, 7893, 29966, 29871, 29896, 7998, 3676, 426, 29906, 29874, 1836, 29938, 13, 29950, 663, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29945, 29913, 13, 7893, 29928, 29918, 29896, 29924, 29898, 29873, 29897, 29928, 29918, 29896, 7893, 529, 29871, 29896, 29914, 29906, 29892, 320, 12014, 260, 320, 262, 13, 741, 4181, 2403, 29874, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29315, 866, 491, 395, 29925, 29918, 29896, 29938, 322, 395, 29925, 29918, 29906, 29938, 278, 28143, 410, 24247, 515, 779, 29883, 29950, 29938, 13, 10268, 779, 29883, 29950, 29918, 29896, 29938, 322, 779, 29883, 29950, 29918, 29906, 1628, 8307, 29889, 3940, 393, 395, 29925, 29918, 29896, 29967, 353, 435, 29925, 29918, 29896, 29938, 13, 392, 395, 29925, 29918, 29906, 29967, 353, 435, 29925, 29918, 29906, 1504, 13, 13, 29898, 2236, 29897, 8680, 2446, 12242, 338, 304, 1510, 393, 278, 5455, 740, 395, 29954, 29898, 29920, 29897, 3490, 435, 13, 29899, 426, 341, 29985, 29928, 29898, 29920, 15604, 338, 21292, 1821, 297, 779, 29907, 29918, 24035, 29871, 322, 426, 393, 395, 29911, 29898, 29920, 29897, 3490, 13, 29954, 29898, 29920, 21604, 29896, 1042, 29871, 756, 278, 13071, 395, 29911, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 269, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 29974, 19881, 1262, 363, 13, 29874, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 29938, 1836, 1152, 445, 6437, 591, 2050, 278, 13, 311, 22410, 2187, 13, 29905, 463, 29912, 4990, 755, 29913, 426, 341, 29985, 29928, 29898, 29920, 2915, 3490, 320, 17633, 29898, 29928, 29918, 29875, 29924, 29898, 29920, 29897, 29928, 29918, 29926, 29905, 17633, 20439, 29875, 29892, 29926, 29922, 29896, 2137, 29906, 3490, 13, 29905, 463, 29912, 12571, 29913, 13, 29924, 29985, 29928, 648, 29896, 29896, 2119, 29920, 29897, 669, 341, 29985, 29928, 648, 29896, 29906, 2119, 29920, 18775, 13, 29924, 29985, 29928, 648, 29906, 29896, 2119, 29920, 29897, 669, 341, 29985, 29928, 648, 29906, 29906, 2119, 29920, 29897, 13, 29905, 355, 29912, 12571, 6177, 13, 29905, 463, 29912, 2378, 1157, 29883, 29913, 13, 29905, 29883, 29950, 29918, 29896, 1966, 13, 29905, 17201, 2474, 13, 29905, 29883, 29950, 29918, 29906, 13, 29905, 355, 29912, 2378, 29913 ]

1,332,863

25,600

ArXiv

-1

\longrightarrow \begin{array}{c} \cH_1\\ \oplus \\ \cH_2 \end{array}, \end{displaymath} $z \in \C_+$, and \begin{displaymath} G(z) = J - { M^D(z)} = \begin{pmatrix} J_1 - M^D_{11}(z) & -M^D_{12}(z)\\ -M^D_{21}(z) & J_2 - M^D_{22}(z) \end{pmatrix}, \qquad z \in \C_+, \end{displaymath} where $J_1 := JP_1$ and $J_2 := JP_2$. { ${\rm (ii)_1}$} Let us prove that ${\xker\,}(J_1 - { M^D_{11}}(z)) = \{0\}$ for $z \in \C_+$. Indeed, from $0= J_1g - { M^D_{11}}(z)g = J_1g - D_1M(z)D_1g $ one gets that $0 = \im({ M^D_{11}}(z)g,g) = (\im(M(z)D_1g,D_1g)$. Hence $0 = D_1g = Dg$ which yields $g = 0$. Since $0\in \varrho(J_1)$ and ${ M^D_{11}}(\cdot)\in{\gotS}_\infty,$ we obtain that the operator $J_1 - { M^D_{11}}(z) = J_1({ I_1} - J_1{ M^D_{11}}(z))$ is boundedly invertible for every $z \in \C_+$. Since ${ M^D_{11}}(z)$ is a $R_{\cH_1}$-function, we get that ${ \Xi}(z):= (J_1 - { M^D_{11}(z)})^{-1}$, $z \in \C_+$, is a $R_{\cH_1}$-function too. { ${\rm (ii)_2}$} We show that for a.e. $t \in {\delta}_a$, $a>0$, the limit ${ \Xi}(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}{ \Xi}(t + iy)$ exists in the operator norm and the following representation holds \begin{equation}\Label{5.6} { \Xi}(t) = (J_1 - { M^D_{11}}(t))^{-1}. \end{equation} First we note that $J_1 - { M^D_{11}}(z) = J_1(I_1 - J_1{ M^D_{11}}(z)$. Using \eqref{5.5} we get $\|J_1{ M^D_{11}}(t)\| <1$ for $t \in {\delta}_a$. Hence the inverse operator $(I_1 - J_1{ M^D_{11}}(t))^{-1}$ exists for $t \in {\delta}_a$. Using $(J_1 - { M^D_{11}}(t))^{-1} = (I_1 - J_1{ M^D_{11}}(t))^{-1}J_1$ we find that the inverse operator $(J_1 - { M^D_{11}}(t))^{-1}$ exist for $t \in {\delta}_a$. Since ${ M^D_{11}}(z)$ has limits ${ M^D_{11}}(t)$ for a.e. $t \in \R$ one gets that $J_1{ M^D_{11}}(t) = \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}J_1{ M^D_{11}}(t + iy)$ for a.e. $t \in \R$. Fix any such $t_0\in {\delta}_a.$ Then due to estimate \eqref{5.5} there exists $\eta =\eta(t_0)$ such that $\sup_{y \in (0,\eta)}\|J_1{ M^D_{11}}(t_0 + iy)\| \le 1/2$. Therefore, the family

-0.401569

-1.631551

-0.305559

1.94491

[ -0.4447140129641115, -0.3584244609371896 ]

[ -1.710339108999668, -1.5527637938444128 ]

[ -0.41239829327524014, -0.19871998688661546 ]

[ 1.9709232828867462, 1.9188958775216884 ]

1,024

[ 512, 512 ]

[ 13, 29905, 24225, 13, 29905, 463, 29912, 2378, 1157, 29883, 29913, 13, 29905, 29883, 29950, 29918, 29896, 1966, 13, 29905, 17201, 2474, 13, 29905, 29883, 29950, 29918, 29906, 13, 29905, 355, 29912, 2378, 1118, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29938, 29920, 320, 262, 320, 29907, 28842, 1628, 322, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29954, 29898, 29920, 29897, 353, 435, 448, 426, 341, 29985, 29928, 29898, 29920, 2915, 353, 13, 29905, 463, 29912, 12571, 29913, 13, 29967, 29918, 29896, 448, 341, 29985, 29928, 648, 29896, 29896, 2119, 29920, 29897, 29871, 669, 448, 29924, 29985, 29928, 648, 29896, 29906, 2119, 29920, 18775, 13, 29899, 29924, 29985, 29928, 648, 29906, 29896, 2119, 29920, 29897, 669, 435, 29918, 29906, 448, 341, 29985, 29928, 648, 29906, 29906, 2119, 29920, 29897, 13, 29905, 355, 29912, 12571, 1118, 320, 12014, 503, 320, 262, 320, 29907, 28842, 29892, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 3062, 395, 29967, 29918, 29896, 3490, 435, 29925, 29918, 29896, 29938, 322, 395, 29967, 29918, 29906, 3490, 435, 29925, 29918, 29906, 1504, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29896, 1042, 29913, 2803, 502, 6356, 393, 29871, 7555, 29916, 3946, 5940, 2119, 29967, 29918, 29896, 448, 426, 13, 29924, 29985, 29928, 648, 29896, 29896, 12156, 29920, 876, 353, 9991, 29900, 11854, 363, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 14598, 29892, 515, 395, 29900, 29922, 435, 29918, 29896, 29887, 448, 13, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 29887, 353, 435, 29918, 29896, 29887, 448, 360, 29918, 29896, 29924, 29898, 29920, 29897, 29928, 29918, 29896, 29887, 395, 697, 4947, 393, 395, 29900, 353, 13, 29905, 326, 3319, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 29887, 29892, 29887, 29897, 353, 3441, 326, 29898, 29924, 29898, 29920, 29897, 29928, 29918, 29896, 29887, 29892, 29928, 29918, 29896, 29887, 4935, 10133, 395, 29900, 353, 360, 29918, 29896, 29887, 13, 29922, 360, 29887, 29938, 607, 17498, 29871, 395, 29887, 353, 29871, 29900, 1504, 4001, 395, 29900, 29905, 262, 320, 1707, 4650, 29898, 29967, 29918, 29896, 1262, 322, 6435, 13, 29924, 29985, 29928, 648, 29896, 29896, 20828, 3822, 2144, 262, 741, 7085, 29903, 12806, 3411, 8209, 29871, 591, 4017, 393, 278, 5455, 13, 29938, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 353, 435, 29918, 29896, 3319, 306, 29918, 29896, 29913, 448, 29871, 435, 29918, 29896, 29912, 13, 29924, 29985, 29928, 648, 29896, 29896, 12156, 29920, 23846, 338, 12635, 368, 21292, 1821, 363, 1432, 395, 29920, 320, 262, 320, 29907, 28842, 1504, 13, 23036, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 1262, 338, 263, 395, 29934, 1665, 29883, 29950, 29918, 29896, 23021, 2220, 29892, 591, 679, 29871, 393, 13, 5303, 320, 29990, 29875, 2119, 29920, 1125, 29922, 313, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 2119, 29920, 26972, 3426, 29896, 4429, 395, 29920, 320, 262, 320, 29907, 28842, 1628, 13, 275, 263, 395, 29934, 1665, 29883, 29950, 29918, 29896, 23021, 2220, 2086, 29889, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29906, 1042, 29913, 1334, 1510, 393, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1628, 395, 29874, 29958, 29900, 1628, 278, 4046, 13, 5303, 320, 29990, 29875, 2119, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 1157, 320, 29990, 29875, 2119, 29873, 718, 474, 29891, 1262, 4864, 297, 278, 5455, 6056, 13, 392, 278, 1494, 8954, 8640, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29953, 29913, 13, 29912, 320, 29990, 29875, 2119, 29873, 29897, 353, 313, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1836, 320, 355, 29912, 2573, 29913, 13, 6730, 591, 4443, 393, 395, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 29897, 353, 435, 29918, 29896, 29898, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 4935, 5293, 320, 4915, 29912, 29945, 29889, 29945, 29913, 591, 679, 779, 29989, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 2144, 29989, 529, 29896, 29938, 363, 13, 29938, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 10133, 278, 16402, 5455, 2427, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 4864, 363, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 5293, 2427, 29967, 29918, 29896, 448, 13, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 29913, 353, 313, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 29913, 29967, 29918, 29896, 29938, 591, 1284, 393, 278, 13, 262, 3901, 5455, 2427, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 1863, 363, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 23036, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 1262, 756, 13071, 6435, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 1262, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 13, 29905, 29934, 29938, 697, 4947, 393, 395, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29897, 353, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 718, 474, 29891, 1262, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 24778, 29871, 738, 1316, 395, 29873, 29918, 29900, 29905, 262, 2802, 4181, 2403, 29874, 7449, 1987, 2861, 304, 13, 342, 6490, 320, 4915, 29912, 29945, 29889, 29945, 29913, 727, 4864, 779, 1187, 17313, 1187, 29898, 29873, 29918, 29900, 1262, 1316, 393, 13, 4535, 12587, 648, 29891, 320, 262, 313, 29900, 2053, 1187, 11383, 29989, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 2144, 29989, 320, 280, 29871, 29896, 29914, 29906, 1504, 7857, 29892, 13, 1552, 3942 ]

1,332,863

26,624

ArXiv

-1

$\{\|(I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1}\|\}_{y \in (0,\eta)}$ is uniformly bounded for any fixed $t_0 \in {\delta}_a.$ Using this fact and \eqref{4.9} we can pass to the limit as $y \to 0$ in the identity \begin{eqnarray*} \lefteqn{ (I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1} - (I_1 - J_1{ M^D_{11}}(t_0))^{-1} }\\ & & \hspace{-5mm} =(I_1 - J_1{ M^D_{11}}(t_0 + iy))^{-1} (J_1{ M^D_{11}}(t_0 + iy)) - J_1{ M^D_{11}}(t_0))(I_1 - J_1{ M^D_{11}}(t_0))^{-1}. \end{eqnarray*} We obtain $\,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}((I_1 - J_1{ M^D_{11}}(t + iy))^{-1} = (I_1 - J_1{ M^D_{11}}(t))^{-1}$ for a.e. $t \in {\delta}_a$ which yields the existence of ${ \Xi}(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}{ \Xi}(t + iy)$ and proves representation \eqref{5.6}. { ${\rm (ii)_3}$} Next we set \begin{displaymath} {\Delta}(z) := { M^D_{22}}(z) + { M^D_{21}}(z)(J_1 - { M^D_{11}}(z))^{-1}{ M^D_{12}}(z), \quad z \in \C_+. \end{displaymath} and show that the function $T_2(\cdot) := (J_2 - {\Delta}(\cdot))^{-1}$ is $R_{\cH_2}$-function. Clearly, ${\Delta}(\cdot)$ is holomorphic in $\C_+$ and it acts in a finite dimensional Hilbert space $\cH_2$. Since $\det(J_2 - {\Delta}(\cdot))$ is also holomorphic in $\C_+,$ the determinant $\det(J_2 - {\Delta}(\cdot))$ has only a discrete set of zeros in $\C_+$. Hence the inverse operator $T_2(\cdot) := (J_2 - {\Delta}(\cdot))^{-1}$ exists for $z\in \Omega \subset\C_+$ where $\C_+ \setminus\Omega$ is at most countable discrete set, that is, $T_2(\cdot)$ is meromorphic in $\C_+$. As we just mentioned the inverse operator $(J_2 - {\Delta}(z))^{-1}$ exists for $z \in \Omega \subset \C_+$. Choose any $z \in \Omega.$ Then, by the { Frobenius} formula, \begin{equation}\Label{5.7} T(z) := (J - { M^D(z)})^{-1} = \begin{pmatrix} T_1(z) & { \Xi}(z){ M^D_{12}}(z)T_2(z)\\ T_2(z){ M^D_{21}}(z){ \Xi}(z) & T_2(z) \end{pmatrix} \end{equation} where \begin{equation}\Label{5.7A} T_1(z) := { \Xi}(z) + { \Xi}(z){ M^D_{12}}(z)T_2(z){ M^D_{21}}(z){ \Xi}(z). \end{equation} Hence \begin{displaymath} T_2(z) = P_2T(z)\upharpoonright\cH_2, \qquad z\in \Omega. \end{displaymath} Since $T(\cdot)$ is a $R

-0.23006

-1.509789

-0.2393

2.074978

[ -0.3337703032152119, -0.12635008043621215 ]

[ -1.7962892809025344, -1.2232881348834246 ]

[ -0.4903877048058064, 0.011788018220278867 ]

[ 1.9709232828867462, 2.1790329043469767 ]

1,024

[ 512, 512 ]

[ 779, 741, 29989, 29898, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 1012, 4295, 3227, 29891, 320, 262, 13, 29898, 29900, 2053, 1187, 15604, 338, 26018, 12635, 363, 738, 4343, 395, 29873, 29918, 29900, 320, 262, 2802, 4181, 2403, 29874, 7449, 13, 15156, 445, 2114, 322, 320, 4915, 29912, 29946, 29889, 29929, 29913, 259, 591, 508, 1209, 304, 278, 4046, 408, 395, 29891, 13, 29905, 517, 29871, 29900, 29938, 297, 278, 10110, 13, 29905, 463, 29912, 9441, 4044, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29898, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 29913, 448, 13, 29898, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 3426, 29896, 29913, 29871, 500, 1966, 13, 29987, 669, 29871, 320, 14158, 8499, 29945, 4317, 29913, 13, 7607, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 3426, 29896, 29913, 13, 29898, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 718, 474, 29891, 876, 448, 29871, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 29898, 29902, 29918, 29896, 448, 13, 29967, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 29918, 29900, 876, 3426, 29896, 1836, 13, 29905, 355, 29912, 9441, 4044, 13, 4806, 4017, 29871, 779, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 2119, 29898, 29902, 29918, 29896, 29871, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 718, 474, 29891, 876, 3426, 29896, 29913, 13, 29922, 313, 29902, 29918, 29896, 448, 435, 29918, 29896, 29912, 341, 29985, 29928, 648, 29896, 29896, 12156, 29873, 876, 3426, 29896, 1042, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 29938, 607, 13, 29891, 969, 29879, 278, 10379, 310, 6435, 320, 29990, 29875, 2119, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 1157, 320, 29990, 29875, 2119, 29873, 718, 474, 29891, 1262, 322, 13, 771, 1960, 8954, 320, 4915, 29912, 29945, 29889, 29953, 1836, 13, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29941, 1042, 29913, 8084, 591, 29871, 731, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 741, 5268, 2119, 29920, 29897, 3490, 426, 341, 29985, 29928, 648, 29906, 29906, 12156, 29920, 29897, 718, 13, 29912, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 5033, 29967, 29918, 29896, 448, 426, 341, 29985, 29928, 648, 29896, 29896, 12156, 29920, 876, 3426, 29896, 1157, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 511, 320, 3425, 13, 29920, 320, 262, 320, 29907, 28842, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 392, 29871, 1510, 393, 278, 740, 395, 29911, 29918, 29906, 1194, 3822, 29897, 3490, 313, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 876, 3426, 29896, 1042, 338, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29889, 13, 13, 18759, 368, 29892, 29871, 7555, 5268, 4678, 3822, 1262, 338, 8753, 16898, 297, 779, 29907, 29918, 24035, 322, 372, 14741, 297, 263, 13, 18925, 22112, 12338, 2151, 2913, 779, 29883, 29950, 29918, 29906, 1504, 4001, 779, 4801, 29898, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 23846, 338, 884, 8753, 16898, 297, 779, 29907, 28842, 8209, 278, 11806, 424, 13, 4535, 4801, 29898, 29967, 29918, 29906, 448, 2802, 5268, 4678, 3822, 23846, 756, 871, 263, 19554, 731, 310, 24786, 297, 13, 4535, 29907, 28842, 1504, 10133, 278, 16402, 5455, 395, 29911, 29918, 29906, 1194, 3822, 29897, 3490, 313, 29967, 29918, 29906, 448, 13, 741, 5268, 4678, 3822, 876, 3426, 29896, 1042, 4864, 363, 29871, 395, 29920, 29905, 262, 320, 5981, 320, 6484, 29905, 29907, 29918, 24035, 13, 3062, 779, 29907, 28842, 320, 15375, 29905, 5981, 29938, 29871, 338, 472, 1556, 2302, 519, 19554, 731, 29892, 13, 5747, 338, 29892, 395, 29911, 29918, 29906, 1194, 3822, 1262, 338, 2778, 16898, 297, 779, 29907, 28842, 1504, 13, 13, 2887, 591, 925, 29871, 5276, 278, 16402, 5455, 2427, 29967, 29918, 29906, 448, 2802, 5268, 2119, 29920, 876, 3426, 29896, 1042, 13, 9933, 363, 259, 395, 29920, 320, 262, 320, 5981, 320, 6484, 320, 29907, 28842, 1504, 29871, 14542, 852, 738, 29871, 395, 29920, 320, 262, 13, 29905, 5981, 7449, 1987, 29892, 491, 278, 426, 25022, 1785, 2482, 29913, 7063, 29892, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29955, 29913, 13, 29911, 29898, 29920, 29897, 3490, 313, 29967, 448, 426, 341, 29985, 29928, 29898, 29920, 26972, 3426, 29896, 29913, 353, 13, 29905, 463, 29912, 12571, 29913, 13, 29911, 29918, 29896, 29898, 29920, 29897, 669, 426, 320, 29990, 29875, 2119, 29920, 2597, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 29897, 29911, 29918, 29906, 29898, 29920, 18775, 13, 29911, 29918, 29906, 29898, 29920, 2597, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 2597, 320, 29990, 29875, 2119, 29920, 29897, 669, 323, 29918, 29906, 29898, 29920, 29897, 13, 29905, 355, 29912, 12571, 29913, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29955, 29909, 29913, 13, 323, 29918, 29896, 29898, 29920, 29897, 3490, 426, 320, 29990, 29875, 2119, 29920, 29897, 718, 13, 29912, 320, 29990, 29875, 2119, 29920, 2597, 341, 29985, 29928, 648, 29896, 29906, 12156, 29920, 29897, 29911, 29918, 29906, 29898, 29920, 2597, 341, 29985, 29928, 648, 29906, 29896, 12156, 29920, 2597, 320, 29990, 29875, 2119, 29920, 467, 13, 539, 320, 355, 29912, 2573, 29913, 13, 29950, 663, 13, 1678, 320, 463, 29912, 4990, 755, 29913, 13, 29911, 29918, 29906, 29898, 29920, 29897, 353, 349, 29918, 29906, 29911, 29898, 29920, 2144, 29884, 561, 279, 1129, 265, 1266, 29905, 29883, 29950, 29918, 29906, 29892, 320, 12014, 503, 29905, 262, 320, 5981, 29889, 13, 268, 320, 355, 29912, 4990, 755, 29913, 13, 23036, 395, 29911, 1194, 3822, 1262, 338, 263, 395, 29934 ]

1,332,863

27,648

ArXiv

-1

_{\cH}$-function, we get that $\im {(T_2(z))}>0$ for $z\in \Omega.$ Since in addition $T_2(\cdot)$ is meromorphic in $\C_+$, we conclude that it is holomorphic. Thus, $T_2(\cdot) = (J_2 - {\Delta}(\cdot))^{-1}$ is $R_{\cH_2}$-function, too. { ${\rm (ii)_4}$} In this step we show that for any $a > 0$ the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exists in the operator norm for a.e. $t \in {\delta}_a$. Since $T_2(\cdot)$ is the matrix $R_{\cH_2}$-function, the limit $T_2(t) = \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T_2(t+iy)$ exists for { a.e.} $t \in \R$. Besides, \eqref{4.9} yields \begin{displaymath} \lim_{y\to+0} \|{ M^D_{12}}(t+iy) - { M^D_{12}}(t)\| = 0 \quad \text{and} \quad \lim_{y\to+0} \|{ M^D_{21}}(t+iy) - { M^D_{21}}(t)\| = 0 \end{displaymath} for { a.e.} $t \in \R$. { Combining} these relations with \eqref{5.6} and \eqref{5.7A} { yields} the existence of the limit $T_1(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T_1(t+iy)$ for a.e $t \in {\delta}_a$. Finally, combining all these relations with the block-matrix representation \eqref{5.7} we complete the proof of { (ii)}. { ${\rm (iii)}$} { Using the results of (ii) we are now going to complete the proof of the theorem}. We set ${\delta}_n := \{t \in \R:\ m^+(t) \le n\}$ { and } note that $\bigcup_{n \in \N}{\delta}_n$ differs from $\R$ by a set of Lebesgue measure zero. By step { (ii)} the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exists for a.e. $t \in \bigcup_{n \in \N}{\delta}_n$ in the operator norm. Hence the limit $T(t) := \,\mbox{\rm o-}\hspace{-2pt} \lim_{y\to+0}T(t + iy)$ exist for { a.e.} $t \in \R$. Combining this fact with \eqref{4.9} we can pass to the limit in the identity $(J - { M^D(}t+iy))T(t +iy) = I$ { as $y\to 0.$} We get \begin{equation}\label{4.13} (J - { M^D(t)})T(t) = T(t)(J - { M^D(t)}) = I \qquad \text{ for a.e.} \quad t \in \R \end{equation} The rest of the proof is similar to that of Theorem \ref{V.1}. First we assume that $\wt A$ is disjoint with $A_0$, hence, it admits a representation $\wt A = A_B$ with $B\in \cC(\cH)$. Therefore, setting $M_B(\cdot) := (B-M(\cdot))^{-1}$ and assuming without loss of generality that $0 \in \varrho(B)$ we arrive at the representation \eqref{5.3} with $D=|B|^{-1/2}$ for a.e. $t \in \R$. Moreover, \eqref{4.13} yields ${\rm ran\,}(T(t)) = \cH

0.009676

-1.362957

-0.018647

1.830449

[ -0.015320765973000134, 0.03467238718545462 ]

[ -1.4166760216648742, -1.309238306786291 ]

[ -0.06176297151586494, 0.024469223347200215 ]

[ 1.9293013585947, 1.7315972182074808 ]

1,024

[ 512, 512 ]

[ 1665, 29883, 29950, 23021, 2220, 29892, 591, 679, 393, 779, 326, 13, 8001, 29911, 29918, 29906, 29898, 29920, 876, 17428, 29900, 29938, 363, 395, 29920, 29905, 262, 320, 5981, 7449, 4001, 297, 6124, 395, 29911, 29918, 29906, 1194, 3822, 1262, 29871, 338, 13, 1050, 16898, 297, 779, 29907, 28842, 1628, 591, 17668, 29871, 393, 372, 338, 8753, 16898, 29889, 6549, 29892, 13, 395, 29911, 29918, 29906, 1194, 3822, 29897, 353, 313, 29967, 29918, 29906, 448, 2802, 5268, 4678, 3822, 876, 3426, 29896, 1042, 338, 29871, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29892, 13, 2086, 29889, 13, 13, 29912, 7555, 1758, 313, 2236, 20344, 29946, 1042, 29913, 512, 445, 4331, 591, 1510, 393, 363, 738, 29871, 395, 29874, 1405, 29871, 29900, 29938, 278, 13, 13400, 395, 29911, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 4864, 297, 278, 5455, 13, 12324, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 23036, 395, 29911, 29918, 29906, 1194, 3822, 1262, 338, 278, 4636, 395, 29934, 1665, 29883, 29950, 29918, 29906, 23021, 2220, 29892, 278, 13, 13400, 395, 29911, 29918, 29906, 29898, 29873, 29897, 353, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29918, 29906, 29898, 29873, 29974, 19881, 1262, 4864, 363, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 13, 29905, 29934, 1504, 19065, 29892, 320, 4915, 29912, 29946, 29889, 29929, 29913, 17498, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 648, 29896, 29906, 12156, 29873, 29974, 19881, 29897, 448, 426, 341, 29985, 29928, 648, 29896, 29906, 12156, 29873, 2144, 29989, 13, 29922, 29871, 29900, 320, 3425, 320, 726, 29912, 392, 29913, 320, 3425, 29871, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 12926, 29912, 341, 29985, 29928, 648, 29906, 29896, 12156, 29873, 29974, 19881, 29897, 13, 29899, 426, 341, 29985, 29928, 648, 29906, 29896, 12156, 29873, 2144, 29989, 353, 29871, 29900, 320, 355, 29912, 4990, 755, 29913, 13, 1454, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 320, 29934, 1504, 426, 422, 2109, 292, 29913, 29871, 1438, 5302, 411, 13, 29905, 4915, 29912, 29945, 29889, 29953, 29913, 322, 320, 4915, 29912, 29945, 29889, 29955, 29909, 29913, 426, 29871, 17498, 29913, 278, 10379, 310, 278, 13, 13400, 395, 29911, 29918, 29896, 29898, 29873, 29897, 3490, 320, 2053, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29918, 29896, 29898, 29873, 29974, 19881, 1262, 363, 263, 29889, 29872, 395, 29873, 320, 262, 2802, 4181, 2403, 29874, 1504, 13, 12881, 635, 29892, 29299, 599, 1438, 5302, 411, 29871, 278, 2908, 29899, 5344, 13, 276, 26081, 320, 4915, 29912, 29945, 29889, 29955, 29913, 591, 4866, 278, 5296, 310, 426, 313, 2236, 29512, 13, 13, 29912, 7555, 1758, 313, 25609, 15604, 29913, 426, 5293, 278, 2582, 310, 313, 2236, 29897, 591, 526, 1286, 2675, 13, 29871, 304, 4866, 278, 5296, 310, 278, 9185, 1836, 1334, 731, 13, 29938, 741, 4181, 2403, 29876, 3490, 9991, 29873, 320, 262, 320, 29934, 3583, 286, 14747, 29898, 29873, 29897, 320, 280, 302, 11854, 426, 322, 500, 4443, 393, 13, 4535, 3752, 5231, 648, 29876, 320, 262, 320, 29940, 3331, 4181, 2403, 29876, 29938, 2923, 414, 515, 779, 29934, 29938, 491, 263, 731, 310, 9388, 267, 13000, 13, 26658, 5225, 29889, 2648, 4331, 426, 313, 2236, 2915, 29871, 278, 4046, 395, 29911, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 4864, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 3752, 5231, 648, 29876, 320, 262, 13, 29905, 29940, 3331, 4181, 2403, 29876, 29938, 297, 278, 5455, 6056, 29889, 10133, 278, 4046, 395, 29911, 29898, 29873, 29897, 3490, 13, 15013, 8264, 741, 1758, 288, 29899, 1012, 14158, 8499, 29906, 415, 29913, 320, 2576, 648, 29891, 29905, 517, 29974, 29900, 29913, 29911, 29898, 29873, 718, 474, 29891, 1262, 1863, 363, 426, 263, 29889, 29872, 5003, 395, 29873, 320, 262, 320, 29934, 1504, 13, 1523, 2109, 292, 445, 2114, 411, 29871, 320, 4915, 29912, 29946, 29889, 29929, 29913, 591, 508, 1209, 304, 278, 4046, 297, 13, 1552, 10110, 2427, 29967, 448, 426, 341, 29985, 29928, 29898, 29913, 29873, 29974, 19881, 876, 29911, 29898, 29873, 718, 19881, 29897, 353, 306, 29938, 426, 29871, 408, 395, 29891, 29905, 517, 13, 29900, 7449, 29913, 1334, 679, 13, 320, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29896, 29941, 29913, 13, 29898, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 29911, 29898, 29873, 29897, 353, 323, 29898, 29873, 5033, 29967, 448, 426, 341, 29985, 29928, 29898, 29873, 26972, 353, 306, 320, 12014, 320, 726, 29912, 363, 263, 29889, 29872, 5003, 320, 3425, 13, 29873, 320, 262, 320, 29934, 13, 4706, 320, 355, 29912, 2573, 29913, 13, 1576, 1791, 310, 278, 5296, 338, 2788, 304, 393, 310, 10244, 13, 29905, 999, 29912, 29963, 29889, 29896, 1836, 3824, 591, 5251, 393, 779, 14554, 319, 29938, 338, 766, 12090, 411, 395, 29909, 29918, 29900, 1628, 13, 29882, 663, 29892, 372, 7336, 1169, 263, 8954, 259, 779, 14554, 319, 353, 319, 29918, 29933, 29938, 411, 395, 29933, 29905, 262, 13, 29905, 29883, 29907, 1194, 29883, 29950, 4935, 7857, 29892, 4444, 29871, 395, 29924, 29918, 29933, 1194, 3822, 29897, 3490, 313, 29933, 29899, 29924, 1194, 3822, 876, 3426, 29896, 1042, 13, 392, 10241, 29871, 1728, 6410, 310, 2498, 537, 393, 395, 29900, 320, 262, 320, 1707, 4650, 29898, 29933, 1262, 13, 705, 18331, 472, 278, 8954, 320, 4915, 29912, 29945, 29889, 29941, 29913, 411, 395, 29928, 29922, 29989, 29933, 29989, 3426, 29896, 29914, 29906, 1042, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 12808, 29892, 320, 4915, 29912, 29946, 29889, 29896, 29941, 29913, 17498, 7555, 1758, 6350, 5940, 2119, 29911, 29898, 29873, 876, 353, 13, 29905, 29883, 29950 ]

1,332,863

28,672

ArXiv

-1

$ for a.e. $t \in \R$. Therefore arguing as in \eqref{5.3a} and \eqref{5.3b} we obtain \begin{eqnarray*} \lefteqn{ d_{M_B}(t) = {\rm dim}({\rm ran\,}(\sqrt{\im({ M^D(t)})}\,)) = {\rm dim}({\rm ran\,}(\sqrt{\im(M(t))}D\,)) }\\ & & = {\rm dim}({\rm ran\,}(\sqrt{\im(M(t))}\,)) = {\rm dim}({\rm ran\,}(\im(M(t)))) = d_M(t) \end{eqnarray*} for a.e. $t \in \R$. Applying Theorem \ref{IV.10}(ii) we complete the proof. { Finally, we apply Corollary \ref{V.1A} to extend the proof for extensions $\wt A$ not disjoint with $A_0.$} \end{proof} \begin{remark} {\em { The result as well as the proof remains valid} if $A$ is { non-densely} defined. In this case { it suffices to use} the boundary triplet technique for non-densely defined operators developed in \cite{DM95,Ma92b}, cf. proof of Theorem \ref{V.1}. However, the assumptions on the Weyl function are indispensable. } \end{remark} { The following result is immediate from Theorem \ref{IV.10}(ii) and Theorem \ref{V.5}.} \begin{corollary}\Label{V.6} Let the assumptions of Theorem \ref{V.5} be satisfied and let \begin{equation} \cF := \{t \in \R: m^+(t) < \infty\}. \end{equation} If condition \eqref{5.0} holds, then the parts $\wt A^{ac} E_{\wt A^{ac}}(\cF)$ and $A^{ac}_0 E_{A^{ac}_0}(\cF)$ of $\wt A$ and $A_0$, respectively, are unitarily equivalent. \end{corollary} \begin{remark}\Label{V.7} {\em { Let us} define the invariant maximal normal function \begin{equation}\label{4.12A}\hspace{-1.45mm} \gotm^+(t) := \sup_{y\in(0,1]} \left\|{\im(M(i))}^{-1/2}\left(M(t+iy) - \re(M(i))\right){\im(M(i))}^{-1/2} \right\|, \end{equation} for $t \in \R$. For Weyl functions one easily proves that $m^+(t)$ is finite if and only if $\gotm^+(t)$ is finite. \item[\;\;(i)] The quantity $\gotm^+(t)$ has the advantage that it is invariant: Let $A$ be a densely defined closed symmetric operator, ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ a boundary triplet for $A^*,$ and $M(\cdot)$ the corresponding Weyl function. Further, let $\wt{\Pi} = \{\wt\cH,\wt{\Gamma}_0,\wt{\Gamma}_1\}$ be another boundary triplet for $A^*$ with the Weyl function $\wt{M}(\cdot)$ and let $A_0 := A^*\upharpoonright{\xker\,}({\Gamma}_0) = A^*\upharpoonright{\xker\,}(\wt{\Gamma}_0)$. In this case $M(\cdot)$ and $\wt M(\cdot)$ are related by \eqref{2.11} However, $\wt \gotm^+(t) = \gotm^+(t)$ for $t \in \R$, where $\gotm^+(t)$ is obtained { by} replacing in \eqref{4.12A} $M(\cdot)$ by $\wt M(\cdot)$. \item[\;\;(ii)] Further, if the Weyl function $M(\cdot)$ satisfies $M(i) = i$, then $m^+(t) = \got

-0.032977

-1.294913

0.184252

1.804436

[ 0.08672005348740752, -0.15267353008728207 ]

[ -1.309238306786291, -1.2805882494853356 ]

[ 0.26794836178409004, 0.1005564541087283 ]

[ 2.1166000179089077, 1.4922711535282154 ]

1,024

[ 512, 512 ]

[ 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 7857, 1852, 26420, 408, 297, 320, 4915, 29912, 29945, 29889, 29941, 29874, 29913, 322, 13, 29905, 4915, 29912, 29945, 29889, 29941, 29890, 29913, 591, 4017, 13, 29905, 463, 29912, 9441, 4044, 13, 29905, 280, 11927, 29939, 29876, 29912, 13, 29881, 648, 29924, 29918, 29933, 2119, 29873, 29897, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 3319, 341, 29985, 29928, 29898, 29873, 26972, 15379, 876, 353, 13, 741, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29898, 29873, 876, 29913, 29928, 5940, 876, 500, 1966, 13, 29987, 669, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 3676, 741, 326, 29898, 29924, 29898, 29873, 876, 15379, 876, 353, 2802, 1758, 3964, 2119, 741, 1758, 6350, 5940, 4678, 326, 29898, 29924, 29898, 29873, 13697, 353, 13, 29881, 29918, 29924, 29898, 29873, 29897, 320, 355, 29912, 9441, 4044, 13, 1454, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1504, 2401, 5890, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 591, 4866, 278, 13, 8017, 29889, 13, 13, 29912, 29871, 9788, 29892, 29871, 591, 3394, 29871, 2994, 21982, 320, 999, 29912, 29963, 29889, 29896, 29909, 29913, 304, 10985, 278, 13, 8017, 363, 17752, 779, 14554, 319, 29938, 451, 766, 12090, 411, 395, 29909, 29918, 29900, 7449, 29913, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 331, 13, 13, 29912, 29871, 450, 1121, 408, 1532, 408, 278, 5296, 9242, 2854, 29913, 565, 395, 29909, 29938, 338, 13, 29912, 1661, 29899, 21518, 873, 29913, 3342, 29889, 512, 445, 1206, 426, 29871, 372, 9378, 1575, 304, 13, 1509, 29913, 278, 10452, 21954, 29873, 11043, 363, 1661, 29899, 21518, 873, 3342, 13, 3372, 4097, 8906, 297, 320, 2036, 29912, 23560, 29929, 29945, 29892, 21870, 29929, 29906, 29890, 1118, 274, 29888, 29889, 5296, 310, 10244, 13, 29905, 999, 29912, 29963, 29889, 29896, 1836, 2398, 29892, 278, 20813, 373, 278, 399, 1032, 29880, 740, 526, 13, 513, 11936, 575, 519, 29889, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 13, 29912, 450, 1494, 1121, 13, 275, 16800, 515, 10244, 320, 999, 29912, 5667, 29889, 29896, 29900, 2119, 2236, 29897, 322, 10244, 320, 999, 29912, 29963, 29889, 29945, 1836, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 4775, 29912, 29963, 29889, 29953, 29913, 13, 12024, 278, 20813, 310, 10244, 320, 999, 29912, 29963, 29889, 29945, 29913, 367, 15787, 322, 1235, 13, 29905, 463, 29912, 2573, 29913, 13, 29905, 29883, 29943, 3490, 9991, 29873, 320, 262, 320, 29934, 29901, 286, 14747, 29898, 29873, 29897, 529, 320, 3411, 29905, 1836, 13, 29905, 355, 29912, 2573, 29913, 13, 3644, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 8640, 29892, 769, 278, 5633, 779, 14554, 319, 998, 562, 29913, 382, 1665, 14554, 13, 29909, 998, 562, 20828, 29883, 29943, 1262, 322, 395, 29909, 998, 562, 2403, 29900, 382, 648, 29909, 998, 562, 2403, 29900, 4678, 29883, 29943, 1262, 310, 779, 14554, 319, 29938, 322, 13, 29938, 29909, 29918, 29900, 1628, 8307, 29892, 526, 443, 3673, 2354, 7126, 29889, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 26294, 1012, 4775, 29912, 29963, 29889, 29955, 29913, 13, 741, 331, 13, 29912, 2803, 502, 29913, 4529, 29871, 278, 22619, 23183, 4226, 740, 13, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29946, 29889, 29896, 29906, 29909, 1012, 14158, 8499, 29896, 29889, 29946, 29945, 4317, 29913, 13, 29905, 7085, 29885, 14747, 29898, 29873, 29897, 3490, 320, 12587, 648, 29891, 29905, 262, 29898, 29900, 29892, 29896, 12258, 13, 29905, 1563, 7893, 741, 326, 29898, 29924, 29898, 29875, 876, 19579, 29896, 29914, 29906, 1012, 1563, 29898, 29924, 29898, 29873, 29974, 19881, 29897, 448, 13, 29905, 276, 29898, 29924, 29898, 29875, 28986, 1266, 21964, 326, 29898, 29924, 29898, 29875, 876, 19579, 29896, 29914, 29906, 29913, 13, 29905, 1266, 7893, 29892, 13, 29905, 355, 29912, 2573, 29913, 13, 1454, 395, 29873, 320, 262, 320, 29934, 1504, 1152, 399, 1032, 29880, 3168, 697, 5948, 28281, 393, 13, 29938, 29885, 14747, 29898, 29873, 1262, 338, 8093, 565, 322, 871, 565, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 8093, 29889, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 29875, 4638, 450, 14728, 779, 7085, 29885, 14747, 29898, 29873, 1262, 756, 278, 10631, 393, 372, 338, 13, 262, 19365, 29901, 2803, 395, 29909, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 29892, 13, 29938, 741, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 8209, 322, 13, 29938, 29924, 1194, 3822, 1262, 278, 6590, 29871, 399, 1032, 29880, 740, 29889, 8725, 29892, 1235, 779, 14554, 741, 12197, 29913, 13, 29922, 320, 741, 14554, 29905, 29883, 29950, 2053, 14554, 741, 6642, 2403, 29900, 2053, 14554, 741, 6642, 2403, 29896, 11854, 367, 1790, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 411, 278, 399, 1032, 29880, 740, 779, 14554, 29912, 29924, 4678, 3822, 1262, 322, 1235, 395, 29909, 29918, 29900, 3490, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 29897, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 4678, 14554, 741, 6642, 2403, 29900, 4935, 13, 797, 445, 1206, 395, 29924, 1194, 3822, 1262, 322, 779, 14554, 341, 1194, 3822, 1262, 526, 4475, 491, 13, 29905, 4915, 29912, 29906, 29889, 29896, 29896, 29913, 2398, 29892, 779, 14554, 320, 7085, 29885, 14747, 29898, 29873, 29897, 353, 320, 7085, 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 13, 29905, 29934, 1628, 988, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 7625, 426, 491, 29913, 15270, 297, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 395, 29924, 1194, 3822, 1262, 491, 779, 14554, 341, 1194, 3822, 4935, 13, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 2236, 4638, 8725, 29892, 29871, 565, 278, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 13, 29879, 27685, 583, 395, 29924, 29898, 29875, 29897, 353, 474, 1628, 769, 395, 29885, 14747, 29898, 29873, 29897, 353, 320, 7085 ]

1,332,863

29,696

ArXiv

-1

m^+(t)$ for $t \in \R$. \item[\;\;(iii)] Let $\pi$ be an orthogonal projection onto a subspace $\wh\cH$ { of $\cH$}. If $\gotm^+(t)$ is finite, then the invariant maximal normal function $\wh \gotm^+(t)$, obtained from \eqref{4.12A} replacing $M(\cdot)$ by $\wh M(\cdot) := \pi M(\cdot)\upharpoonright \wh\cH$, is also finite and satisfies $\wh \gotm^+(t) \le \gotm^+(t)$ for $t \in \R$. } \end{remark} \section{Direct sums of symmetric operators} \subsection{Boundary triplets for direct sums} Let ${ S_n}$ be a closed densely defined symmetric { operators} in $\gotH_n,$ \ $n_+({ S_n})=n_-( S_n),$ and { let ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ be} a boundary triplet for $S_n^*,\ n\in \N.$ Let \begin{equation}\Label{6.5a} A := \bigoplus^\infty_{n=1}{ S_n}, \quad {\rm dom\,}(A) := \bigoplus^\infty_{n=1}{\rm dom\,}({ S_n}). \end{equation} Clearly, $A$ is a closed densely defined symmetric operator in the Hilbert space $\gotH := \bigoplus^\infty_{n=1}\gotH_n$ with $n_\pm(A)= \infty.$ Consider the direct sum ${\Pi}:=\oplus_{n=1}^{\infty} {\Pi}_n=: \{\cH,{\Gamma}_{0},{\Gamma}_{1}\}$ of (ordinary) boundary triplets defined by \begin{equation}\Label{6.5} \cH := \bigoplus^\infty_{n=1}\cH_n, \quad {\Gamma}_0 := \bigoplus^\infty_{n=1}{\Gamma}_{0n} \quad \mbox{and} \quad {\Gamma}_1 := \bigoplus^\infty_{n=1}{\Gamma}_{1n}. \end{equation} { Clearly,} \begin{equation}\Label{6.5b} A^* = \bigoplus^\infty_{n=1}{ S}^*_n, \quad {\rm dom\,}(A^*) = \bigoplus^\infty_{n=1}{\rm dom\,}({ S}^*_n). \end{equation} { We note that the Green's identity} \begin{displaymath} ( S_n^*f_n, g_n) - (f_n, S_n^*g_n) = ({\Gamma}_{1n}f_n,{\Gamma}_{0n}g_n)_{\cH_n} - ({\Gamma}_{0n}f_n, {\Gamma}_{1n}g_n)_{\cH_n}, \end{displaymath} { $f_n, g_n \in {\rm dom\,}( S_n^*)$, holds for every $S^*_n$, $n \in \N$. This yields the} Green's identity \eqref{3.1} for $A_*:= A^*\upharpoonright {\rm dom\,} ({\Gamma})$, ${\rm dom\,} ({\Gamma}) := {\rm dom\,} ({\Gamma}_0) \cap {\rm dom\,} ({\Gamma}_1) \subseteq {\rm dom\,} (A^*)$, that is, for $f=\oplus_{n=1}^{\infty}f_n$, $g = \oplus_{n=1}^\infty g_n \in {\rm dom\,} ({\Gamma})$ we have \begin{equation}\label{3.1AA} (A_*f, g) - (f, A_*g) = ({\Gamma}_1f, {\Gamma}_0 g)_{\cH} - ({\Gamma}_0 f, {\Gamma}_1 g)_{\cH}, \qquad f,g\in{\rm dom\,}({\Gamma}), \end{equation} where $A^*$ and ${\Gamma}_j$ are defined by \eqref{6.5b} and \eqref{6.5}, respectively

-0.404309

-1.373701

-0.22218

1.846058

[ -0.42279920610013133, -0.3858179695171648 ]

[ -1.3880259643639186, -1.3593759070629632 ]

[ -0.11756027407431886, -0.3268001586685211 ]

[ 1.7628136614265153, 1.9293013585947 ]

1,024

[ 512, 512 ]

[ 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 320, 29934, 1504, 13, 13, 13, 29905, 667, 7110, 10436, 29936, 29898, 25609, 4638, 2803, 779, 1631, 29938, 367, 385, 28143, 18246, 11480, 263, 1014, 3493, 13, 4535, 1332, 29905, 29883, 29950, 29938, 426, 310, 779, 29883, 29950, 29938, 1836, 960, 779, 7085, 29885, 14747, 29898, 29873, 1262, 338, 8093, 29892, 769, 278, 13, 262, 19365, 23183, 4226, 740, 779, 1332, 320, 7085, 29885, 14747, 29898, 29873, 5767, 29871, 7625, 515, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 15270, 395, 29924, 1194, 3822, 1262, 491, 779, 1332, 341, 1194, 3822, 29897, 3490, 320, 1631, 13, 29924, 1194, 3822, 2144, 29884, 561, 279, 1129, 265, 1266, 320, 1332, 29905, 29883, 29950, 1628, 338, 884, 8093, 322, 17150, 779, 1332, 13, 29905, 7085, 29885, 14747, 29898, 29873, 29897, 320, 280, 320, 7085, 29885, 14747, 29898, 29873, 1262, 363, 395, 29873, 320, 262, 320, 29934, 1504, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 29905, 2042, 29912, 17392, 25470, 310, 18348, 12768, 29913, 13, 13, 29905, 7235, 29912, 17109, 653, 21954, 1372, 363, 1513, 25470, 29913, 13, 13, 12024, 6435, 317, 29918, 29876, 1042, 367, 263, 5764, 6245, 873, 3342, 18348, 426, 13, 3372, 4097, 29913, 297, 779, 7085, 29950, 29918, 29876, 8209, 320, 395, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 17722, 317, 29918, 29876, 511, 29938, 322, 426, 1235, 13, 29938, 741, 12197, 2403, 29876, 353, 320, 741, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 29871, 367, 29913, 263, 10452, 21954, 29873, 363, 13, 29938, 29903, 29918, 29876, 6622, 2053, 302, 29905, 262, 320, 29940, 7449, 2803, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29874, 29913, 13, 29909, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 29918, 29876, 1118, 320, 3425, 2802, 1758, 2432, 5940, 2119, 29909, 29897, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 7690, 13, 29905, 355, 29912, 2573, 29913, 13, 18759, 368, 29892, 395, 29909, 29938, 338, 263, 5764, 6245, 873, 3342, 18348, 5455, 29871, 297, 13, 1552, 12338, 2151, 2913, 29871, 779, 7085, 29950, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 7085, 29950, 29918, 29876, 29938, 411, 13, 29938, 29876, 3187, 3358, 29898, 29909, 3892, 320, 3411, 7449, 10056, 278, 1513, 2533, 13, 29938, 741, 12197, 6177, 2013, 17201, 648, 29876, 29922, 29896, 6292, 3411, 29913, 2802, 12197, 2403, 29876, 29922, 29901, 320, 741, 29883, 29950, 29892, 741, 6642, 3227, 29900, 1118, 741, 6642, 3227, 29896, 1012, 1042, 310, 13, 29898, 24310, 29897, 10452, 21954, 1372, 3342, 491, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29913, 13, 29905, 29883, 29950, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 29883, 29950, 29918, 29876, 29892, 320, 3425, 2802, 6642, 2403, 29900, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 3227, 29900, 29876, 29913, 320, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 2802, 6642, 2403, 29896, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 3227, 29896, 29876, 1836, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 17732, 368, 29892, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29945, 29890, 29913, 13, 29909, 6622, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 2137, 29930, 29918, 29876, 29892, 320, 3425, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 353, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 317, 2137, 29930, 29918, 29876, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 1334, 4443, 393, 278, 7646, 29915, 29879, 10110, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 317, 29918, 29876, 6622, 29888, 29918, 29876, 29892, 330, 29918, 29876, 29897, 448, 313, 29888, 29918, 29876, 29892, 29871, 317, 29918, 29876, 6622, 29887, 29918, 29876, 29897, 353, 13, 13670, 6642, 3227, 29896, 29876, 29913, 29888, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 29913, 29887, 29918, 29876, 29897, 1665, 29883, 29950, 29918, 29876, 29913, 448, 313, 741, 6642, 3227, 29900, 29876, 29913, 29888, 29918, 29876, 29892, 13, 741, 6642, 3227, 29896, 29876, 29913, 29887, 29918, 29876, 29897, 1665, 29883, 29950, 29918, 29876, 1118, 320, 355, 29912, 4990, 755, 29913, 13, 29912, 395, 29888, 29918, 29876, 29892, 330, 29918, 29876, 320, 262, 2802, 1758, 2432, 5940, 2119, 317, 29918, 29876, 6622, 5767, 8640, 363, 1432, 395, 29903, 6622, 29918, 29876, 1628, 395, 29876, 320, 262, 13, 29905, 29940, 1504, 910, 17498, 278, 29913, 7646, 29915, 29879, 10110, 320, 4915, 29912, 29941, 29889, 29896, 29913, 363, 395, 29909, 24563, 9361, 13, 29909, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 2802, 1758, 2432, 5940, 29913, 313, 741, 6642, 27394, 7555, 1758, 2432, 5940, 29913, 313, 741, 6642, 1800, 3490, 2802, 1758, 2432, 5940, 29913, 313, 741, 6642, 2403, 29900, 29897, 320, 5030, 13, 741, 1758, 2432, 5940, 29913, 313, 741, 6642, 2403, 29896, 29897, 320, 11725, 2802, 1758, 2432, 5940, 29913, 313, 29909, 6622, 5767, 393, 338, 29892, 363, 13, 29938, 29888, 2013, 17201, 648, 29876, 29922, 29896, 6292, 3411, 29913, 29888, 29918, 29876, 1628, 395, 29887, 353, 320, 17201, 648, 29876, 29922, 29896, 10206, 3411, 330, 29918, 29876, 320, 262, 13, 741, 1758, 2432, 5940, 29913, 313, 741, 6642, 8435, 591, 505, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29896, 6344, 29913, 13, 29898, 29909, 24563, 29888, 29892, 330, 29897, 448, 313, 29888, 29892, 319, 24563, 29887, 29897, 353, 313, 741, 6642, 2403, 29896, 29888, 29892, 2802, 6642, 2403, 29900, 330, 29897, 1665, 29883, 29950, 29913, 448, 13, 13670, 6642, 2403, 29900, 285, 29892, 2802, 6642, 2403, 29896, 330, 29897, 1665, 29883, 29950, 1118, 320, 12014, 285, 29892, 29887, 29905, 262, 741, 1758, 2432, 5940, 2119, 741, 6642, 9594, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29909, 6622, 29938, 322, 7555, 6642, 2403, 29926, 29938, 526, 3342, 491, 320, 4915, 29912, 29953, 29889, 29945, 29890, 29913, 322, 13, 29905, 4915, 29912, 29953, 29889, 29945, 1118, 8307 ]

1,332,863

30,720

ArXiv

-1

. However, the Green's identity \eqref{3.1AA} cannot be extended to ${\rm dom\,}(A^*)$ in general, since ${\rm dom\,}({\Gamma})$ is smaller than ${\rm dom\,}(A^*)$ generically. It might even happen that ${\Gamma}_j$ are not bounded as mappings from ${\rm dom\,}(A^*)$ equipped with the graph norm into $\cH.$ Counterexamples for the direct sum $\Pi=\oplus^\infty_{n=1} \Pi_n$, which { does not form} a boundary triplet, { firstly} appeared in \cite{Koch79}). In this section we show that it is always possible to modify the boundary triplets ${\Pi}_n$ in such a way that a new sequence $\wt {\Pi}_n= \{\cH_n,\wt{\Gamma}_{0},\wt{\Gamma}_{1}\}$ of boundary triplets for ${ S^*_n}$ satisfies the following properties: $\wt {\Pi} = { \oplus^\infty_{n=1}} \wt {\Pi}_n$ { forms} a boundary triplet for $A^*$ and the following relations { hold} \begin{equation}\Label{5.5A} { \wt S_{0n}} := { S^*_n}\upharpoonright {\xker\,}(\wt{\Gamma}_{0n}) = { S^*_n}\upharpoonright {\xker\,}({\Gamma}_{0n}) =: { S_{0n}}, \quad n\in \N. \end{equation} Hence $\wt A_{0} := { \oplus^\infty_{n=1} \wt S_{0n}} = { \oplus^\infty_{n=1}S_{0n}} =: A_0.$ { We note that the} existence of a boundary triplet ${\Pi}'= \{\cH, {\Gamma}'_{0}, {\Gamma}'_{1}\}$ for $A^*$ satisfying ${\xker\,}({\Gamma}'_{0})= {\rm dom\,}(A_0) $ is known (see \cite{GG91, DM91}). However, we emphasize that in applications we need a special form \eqref{6.5} of a boundary triplet for $A^*$ because it leads to the block-diagonal form of the corresponding Weyl function (cf. Sections 5.2, 5.3 below). We start with a simple technical lemma. \begin{lemma}\Label{VI.1} Let $S$ be a densely defined closed symmetric operator with equal deficiency indices, ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ a boundary triplet for $S^*$, and $M(\cdot)$ the corresponding Weyl function. Then there exists a boundary triplet $\wt{{\Pi}} = \{\cH,\wt{{\Gamma}}_0,\wt{{\Gamma}}_1\}$ for $S^*$ such that ${\xker\,}(\wt{{\Gamma}}_0) = {\xker\,}({\Gamma}_0)$ and the corresponding Weyl function $\wt{M}(\cdot)$ satisfies $\wt{M}(i) = i$. \end{lemma} \begin{proof} Let $M(i) = Q + iR^2$ where $Q := \re(M(i)),\ R := \sqrt{\im(M(i))}$. We set \begin{equation}\label{3.8} \wt{{\Gamma}}_0 := R{\Gamma}_0 \quad \mbox{and} \quad \wt{{\Gamma}}_1 := R^{-1}({\Gamma}_1 - Q{\Gamma}_0). \end{equation} A straightforward computation shows that $\wt{{\Pi}} : = \{\cH,\wt{{\Gamma}}_0,\wt{{\Gamma}}_1\}$ is a boundary triplet for $A^*$. Clearly, ${\xker\,}(\wt{{\Gamma}}_0) = {\xker\,}({\Gamma}_0)$. The Weyl function $\wt{M}(\cdot)$ of $\wt{{\Pi}}$ is given by $\wt{M}(\cdot) = R^{-1}(M(\cdot) - Q)R^{-1}$ which yields $\wt{M}(i) = i$. \end{proof} If $S$ is a densely defined closed symmetric operator in $\gotH$, then by the first v. Neumann

0.522277

-0.71654

0.529181

2.43917

[ 0.29080169240822284, 0.7537519874098038 ]

[ -0.9153000188981529, -0.5177804738473953 ]

[ 0.1664987207687193, 0.8918636540286202 ]

[ 2.1374109800549306, 2.7409288822896 ]

1,024

[ 512, 512 ]

[ 29889, 2398, 29892, 278, 7646, 29915, 29879, 10110, 13, 29905, 4915, 29912, 29941, 29889, 29896, 6344, 29913, 2609, 367, 10410, 304, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 297, 2498, 29892, 1951, 13, 29938, 741, 1758, 2432, 5940, 2119, 741, 6642, 8435, 338, 7968, 1135, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 1176, 1711, 29889, 739, 1795, 1584, 13, 29882, 19934, 393, 7555, 6642, 2403, 29926, 29938, 526, 451, 12635, 408, 611, 27775, 515, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 13, 1686, 16242, 411, 278, 3983, 6056, 964, 779, 29883, 29950, 7449, 315, 5336, 19057, 363, 278, 13, 11851, 2533, 779, 12197, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 12197, 29918, 29876, 1628, 29871, 607, 426, 13, 13221, 451, 883, 29913, 263, 10452, 21954, 29873, 29892, 426, 937, 368, 29913, 7470, 297, 13, 29905, 2036, 29912, 29968, 2878, 29955, 29929, 7690, 13, 13, 797, 445, 4004, 591, 1510, 393, 372, 338, 2337, 1950, 304, 6623, 278, 13, 9917, 653, 21954, 1372, 7555, 12197, 2403, 29876, 29938, 297, 1316, 263, 982, 393, 263, 29871, 716, 5665, 779, 14554, 13, 741, 12197, 2403, 29876, 29922, 320, 741, 29883, 29950, 29918, 29876, 2053, 14554, 741, 6642, 3227, 29900, 7570, 14554, 741, 6642, 3227, 29896, 1012, 1042, 310, 10452, 21954, 1372, 363, 13, 5303, 317, 6622, 29918, 29876, 1042, 17150, 278, 1494, 4426, 29901, 29871, 779, 14554, 2802, 12197, 29913, 353, 13, 29912, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 930, 320, 14554, 2802, 12197, 2403, 29876, 29938, 426, 7190, 29913, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 29938, 322, 278, 1494, 5302, 426, 4808, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29945, 29889, 29945, 29909, 29913, 13, 29912, 320, 14554, 317, 648, 29900, 29876, 930, 3490, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 13, 741, 29916, 3946, 5940, 4678, 14554, 741, 6642, 3227, 29900, 29876, 1800, 353, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 2802, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 1800, 353, 29901, 13, 29912, 317, 648, 29900, 29876, 11656, 320, 3425, 302, 29905, 262, 320, 29940, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29950, 663, 779, 14554, 319, 648, 29900, 29913, 3490, 426, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 14554, 317, 648, 29900, 29876, 930, 353, 426, 13, 29905, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29903, 648, 29900, 29876, 930, 353, 29901, 319, 29918, 29900, 7449, 426, 1334, 4443, 393, 278, 29913, 13, 735, 11416, 310, 263, 10452, 21954, 29873, 7555, 12197, 10162, 29922, 320, 741, 29883, 29950, 29892, 2802, 6642, 10162, 648, 29900, 1118, 13, 741, 6642, 10162, 648, 29896, 1012, 1042, 363, 395, 29909, 6622, 29938, 24064, 7555, 29916, 3946, 5940, 2119, 741, 6642, 10162, 648, 29900, 1800, 29922, 2802, 1758, 2432, 5940, 2119, 29909, 29918, 29900, 29897, 395, 338, 13, 5203, 313, 4149, 320, 2036, 29912, 26788, 29929, 29896, 29892, 27692, 29929, 29896, 7690, 2398, 29892, 591, 19310, 675, 393, 297, 13, 932, 5795, 591, 817, 263, 4266, 883, 320, 4915, 29912, 29953, 29889, 29945, 29913, 310, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29909, 6622, 29938, 1363, 372, 11981, 304, 278, 2908, 29899, 6051, 351, 7177, 883, 310, 13, 1552, 6590, 399, 1032, 29880, 740, 313, 6854, 29889, 922, 1953, 29871, 29945, 29889, 29906, 29892, 29871, 29945, 29889, 29941, 2400, 467, 13, 13, 4806, 1369, 411, 263, 2560, 16905, 10383, 29889, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 18118, 29889, 29896, 29913, 13, 12024, 395, 29903, 29938, 367, 263, 6245, 873, 3342, 5764, 18348, 5455, 411, 5186, 13, 1753, 293, 13396, 16285, 29892, 29871, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 29871, 263, 10452, 13, 3626, 552, 29873, 363, 395, 29903, 6622, 1628, 29871, 322, 395, 29924, 1194, 3822, 1262, 278, 6590, 399, 1032, 29880, 13, 2220, 29889, 1987, 727, 4864, 29871, 263, 10452, 21954, 29873, 779, 14554, 16195, 12197, 930, 353, 13, 24976, 29883, 29950, 2053, 14554, 16195, 6642, 15609, 29900, 2053, 14554, 16195, 6642, 15609, 29896, 11854, 363, 395, 29903, 6622, 29938, 1316, 393, 13, 29938, 741, 29916, 3946, 5940, 4678, 14554, 16195, 6642, 15609, 29900, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 1262, 322, 29871, 278, 6590, 399, 1032, 29880, 13, 2220, 779, 14554, 29912, 29924, 4678, 3822, 1262, 17150, 29871, 779, 14554, 29912, 29924, 2119, 29875, 29897, 353, 474, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 12024, 395, 29924, 29898, 29875, 29897, 353, 660, 718, 474, 29934, 29985, 29906, 29938, 988, 395, 29984, 3490, 320, 276, 29898, 29924, 29898, 29875, 8243, 29905, 390, 3490, 13, 29905, 3676, 741, 326, 29898, 29924, 29898, 29875, 876, 4311, 1334, 731, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29941, 29889, 29947, 29913, 13, 29905, 14554, 16195, 6642, 15609, 29900, 3490, 390, 741, 6642, 2403, 29900, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 29905, 14554, 16195, 6642, 15609, 29896, 3490, 390, 3426, 29896, 2119, 741, 6642, 2403, 29896, 448, 660, 741, 6642, 2403, 29900, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 29909, 20837, 16287, 3697, 393, 779, 14554, 16195, 12197, 930, 584, 353, 13, 24976, 29883, 29950, 2053, 14554, 16195, 6642, 15609, 29900, 2053, 14554, 16195, 6642, 15609, 29896, 11854, 338, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1504, 13, 18759, 368, 29892, 7555, 29916, 3946, 5940, 4678, 14554, 16195, 6642, 15609, 29900, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 450, 399, 1032, 29880, 740, 13, 4535, 14554, 29912, 29924, 4678, 3822, 1262, 310, 779, 14554, 16195, 12197, 7920, 338, 2183, 491, 779, 14554, 29912, 29924, 4678, 3822, 29897, 353, 13, 29934, 3426, 29896, 2119, 29924, 1194, 3822, 29897, 448, 660, 29897, 29934, 3426, 29896, 1042, 607, 17498, 779, 14554, 29912, 29924, 2119, 29875, 29897, 353, 474, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 3644, 395, 29903, 29938, 338, 263, 6245, 873, 3342, 5764, 18348, 5455, 297, 779, 7085, 29950, 1628, 13, 6098, 491, 278, 937, 325, 29889, 2448, 22553 ]

1,332,863

31,744

ArXiv

-1

formula the direct decomposition ${\rm dom\,}(S^*) = {\rm dom\,}(S) \stackrel{.}{+} \gotN_i \stackrel{.}{+} \gotN_{-i}$ holds where $\gotN_{\pm i} := {\xker\,}(S^*\mp i)$. Equipping ${\rm dom\,}(S^*)$ with the inner product \begin{equation}\Label{3.8b} (f,g)_+ := (S^*f, S^*g) + (f,g), \quad f,g \in {\rm dom\,}(S^*), \end{equation} one obtains a Hilbert space denoted by $\gotH_+$. The first v. Neumann formula leads to the following orthogonal decomposition \begin{displaymath} \gotH_+ = {\rm dom\,}(S) \oplus \gotN_i \oplus \gotN_{-i}. \end{displaymath} \begin{lemma}\Label{VI.2} Let $S$ be as in Lemma \ref{VI.1}, let ${\Pi} = \{\cH,{\Gamma}_0,{\Gamma}_1\}$ be a (ordinary) boundary triplet for $S^*$, and $M(\cdot)$ the corresponding Weyl function. If $M(i) = i$, then the operator ${\Gamma}: \gotH_+ \longrightarrow \cH \oplus \cH$, ${\Gamma}:=(\Gamma_0,\Gamma_1)^\top$ is a contraction. Moreover, ${\Gamma}$ isometrically maps $\gotN := \gotN_i\oplus \gotN_{-i}$ onto $\cH$. \end{lemma} \begin{proof} We show that \begin{equation}\Label{6.4} \|{\Gamma}(f + f_i + f_{-i})\|^2_{\cH \oplus \cH} = \|f_i + f_{-i}\|^2_+ \end{equation} where $f \stackrel{.}{+} f_i \stackrel{.}{+} f_{-i} \in {\rm dom\,}(S) \stackrel{.}{+} \gotN_i \stackrel{.}{+} \gotN_{-i} = {\rm dom\,}(S^*)$. Indeed, { since ${\rm dom\,}(S) = {\xker\,}({\Gamma}_0) \cap {\xker\,}({\Gamma}_1)$, we find} \begin{displaymath} \|{\Gamma}(f + f_i + f_{-i})\|^2_{\cH \oplus \cH} = \|{\Gamma}_0(f_i + f_{-i})\|^2_\cH + \|{\Gamma}_1(f_i + f_{-i})\|^2_\cH. \end{displaymath} Clearly, \begin{equation}\Label{6.4A} \|{\Gamma}_j(f_i + f_{-i})\|^2_\cH = \|{\Gamma}_jf_i\|^2 + 2\re(({\Gamma}_jf_i,{\Gamma}_jf_{-i})) +\ \|{\Gamma}_jf_{-i}\|^2, \quad j\in \{0,1\}. \end{equation} Using ${\Gamma}_1f_i = M(i){\Gamma}_0f_i = i{\Gamma}_0f_i$ and ${\Gamma}_1f_{-i} = M(-i){\Gamma}_0f_{-i} = -i{\Gamma}_0f_{-i}$ we obtain \begin{equation}\Label{6.4B} \|{\Gamma}_1(f_i + f_{-i})\|^2_\cH = ({\Gamma}_0f_i,{\Gamma}_0f_i) - 2\re(({\Gamma}_0f_i,{\Gamma}_0f_{-i})) + ({\Gamma}_0f_{-i},{\Gamma}_0f_{-i}) \end{equation} Taking a sum of \eqref{6.4A} and \eqref{6.4B} we get \begin{equation}\Label{6.4BC} \|{\Gamma}_0(f_i + f_{-i})\|^2_\cH + \|{\Gamma}_1(f_i + f_{-i})\|^2_\cH = 2\|{\Gamma}_0f_i\|^2_\cH + 2\|{\Gamma

0.084537

-1.094363

0.185521

2.428764

[ 0.3291526044201881, -0.16007833787530662 ]

[ -0.7720497323933754, -1.4166760216648742 ]

[ 0.5520073566271282, -0.18096629970892558 ]

[ 2.4703863743912997, 2.3871425258072074 ]

1,024

[ 512, 512 ]

[ 7063, 278, 1513, 26227, 13, 29938, 741, 1758, 2432, 5940, 2119, 29903, 6622, 29897, 353, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 13, 29905, 7085, 29940, 22631, 29875, 1042, 29871, 8640, 988, 779, 7085, 29940, 1665, 3358, 474, 29913, 3490, 2802, 29916, 3946, 5940, 2119, 29903, 6622, 29905, 1526, 474, 4935, 13, 6108, 17347, 29871, 7555, 1758, 2432, 5940, 2119, 29903, 6622, 1262, 411, 278, 6426, 29871, 3234, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29941, 29889, 29947, 29890, 29913, 13, 29898, 29888, 29892, 29887, 20344, 29974, 3490, 313, 29903, 6622, 29888, 29892, 317, 6622, 29887, 29897, 718, 313, 29888, 29892, 29887, 511, 320, 3425, 285, 29892, 29887, 320, 262, 2802, 1758, 2432, 5940, 2119, 29903, 6622, 511, 13, 29905, 355, 29912, 2573, 29913, 13, 650, 4017, 29879, 263, 12338, 2151, 2913, 27291, 491, 779, 7085, 29950, 28842, 1504, 13, 1576, 937, 325, 29889, 2448, 22553, 7063, 11981, 304, 278, 1494, 13, 2072, 23419, 26227, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 7085, 29950, 28842, 353, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 320, 17201, 320, 7085, 29940, 29918, 29875, 320, 17201, 320, 7085, 29940, 22631, 29875, 1836, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 13846, 1012, 4775, 29912, 18118, 29889, 29906, 29913, 13, 12024, 395, 29903, 29938, 367, 408, 297, 11894, 320, 999, 29912, 18118, 29889, 29896, 1118, 1235, 7555, 12197, 29913, 353, 320, 741, 29883, 29950, 29892, 741, 6642, 2403, 29900, 29892, 741, 6642, 2403, 29896, 11854, 13, 915, 263, 313, 24310, 29897, 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 322, 395, 29924, 1194, 3822, 1262, 278, 13, 2616, 3636, 292, 29871, 399, 1032, 29880, 740, 29889, 29871, 960, 395, 29924, 29898, 29875, 29897, 353, 474, 1628, 769, 278, 5455, 13, 29938, 741, 6642, 6177, 320, 7085, 29950, 28842, 320, 24225, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1628, 13, 29938, 741, 6642, 6177, 29922, 1194, 6642, 29918, 29900, 2053, 6642, 29918, 29896, 29897, 3823, 3332, 29938, 29871, 338, 263, 6761, 428, 29889, 12808, 29892, 7555, 6642, 1042, 13, 275, 3297, 29878, 1711, 11053, 779, 7085, 29940, 3490, 320, 7085, 29940, 29918, 29875, 29905, 17201, 320, 7085, 29940, 22631, 29875, 1042, 11480, 779, 29883, 29950, 1504, 13, 29905, 355, 29912, 13846, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 4806, 1510, 393, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29913, 13, 7893, 741, 6642, 2119, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 1665, 29883, 29950, 320, 17201, 320, 29883, 29950, 29913, 353, 12926, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29888, 320, 1429, 2674, 26139, 1157, 29974, 29913, 285, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 285, 22631, 29875, 29913, 320, 262, 2802, 1758, 2432, 5940, 2119, 29903, 29897, 13, 29905, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 22631, 29875, 29913, 353, 2802, 1758, 2432, 5940, 2119, 29903, 6622, 4935, 13, 2568, 12613, 29892, 426, 1951, 7555, 1758, 2432, 5940, 2119, 29903, 29897, 353, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 29897, 320, 5030, 2802, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29896, 5767, 591, 13, 2886, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 7893, 741, 6642, 2119, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 1665, 29883, 29950, 320, 17201, 320, 29883, 29950, 29913, 353, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 29889, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 18759, 368, 29892, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29909, 29913, 12926, 741, 6642, 2403, 29926, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 12926, 741, 6642, 2403, 29926, 29888, 29918, 29875, 7893, 29985, 29906, 29871, 718, 13, 29906, 29905, 276, 3552, 741, 6642, 2403, 29926, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29926, 29888, 22631, 29875, 20073, 17501, 29871, 12926, 741, 6642, 2403, 29926, 29888, 22631, 29875, 1012, 15333, 29906, 29892, 320, 3425, 432, 29905, 262, 13, 10045, 29900, 29892, 29896, 29905, 1836, 320, 355, 29912, 2573, 29913, 13, 15156, 7555, 6642, 2403, 29896, 29888, 29918, 29875, 353, 341, 29898, 29875, 21964, 6642, 2403, 29900, 29888, 29918, 29875, 353, 474, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29938, 322, 7555, 6642, 2403, 29896, 29888, 22631, 29875, 29913, 353, 341, 6278, 29875, 21964, 6642, 2403, 29900, 29888, 22631, 29875, 29913, 353, 448, 29875, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1042, 13, 705, 4017, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29933, 29913, 13, 7893, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 13670, 6642, 2403, 29900, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29897, 448, 29871, 29906, 29905, 276, 3552, 741, 6642, 2403, 29900, 29888, 29918, 29875, 29892, 741, 6642, 2403, 29900, 29888, 22631, 29875, 20073, 718, 313, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1118, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1800, 13, 29905, 355, 29912, 2573, 29913, 13, 29911, 5086, 263, 2533, 310, 320, 4915, 29912, 29953, 29889, 29946, 29909, 29913, 322, 320, 4915, 29912, 29953, 29889, 29946, 29933, 29913, 591, 679, 13, 268, 320, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 5371, 29913, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 29906, 7893, 741, 6642, 2403, 29900, 29888, 29918, 29875, 7893, 29985, 29906, 3187, 29883, 29950, 718, 29871, 29906, 7893, 741, 6642 ]

1,332,863

32,768

ArXiv

-1

}_0f_{-i}\|^2_\cH. \end{equation} Combining equalities ${\Gamma}_1f_{\pm i}= \pm i {\Gamma}_0f_{\pm i}$ with Green's identity \eqref{2.10A} we obtain $\|{\Gamma}_0f_i\|_\cH = \|f_i\|$ and $\|{\Gamma}_0f_{-i}\|_\cH = \|f_{-i}\|$. { Therefore \eqref{6.4BC} takes the form} \begin{equation}\Label{6.4C} \|{\Gamma}_0(f_i + f_{-i})\|^2_\cH + \|{\Gamma}_1(f_i + f_{-i})\|^2_\cH = 2\|f_i\|^2 + 2\|f_{-i}\|^2. \end{equation} A straightforward computation shows $\|f_i + f_{-i}\|^2_+ = 2\|f_i\|^2 + 2\|f_{-i}\|^2$ which together with \eqref{6.4C} proves \eqref{6.4}. Since $\|f_i + f_{-i}\|^2_+ \le \|f\|^2_+ + \|f_i + f_{-i}\|^2_+ = \|f + f_i + f_{-i}\|^2_+$, we get from \eqref{6.4} that ${\Gamma}$ is a contraction. Obviously, ${\Gamma}$ is an isometry from $\gotN$ into $\cH \oplus \cH$. Since ${\Pi}$ is a boundary triplet for $S^*$, ${\rm ran\,}({\Gamma}) = \cH \oplus \cH.$ { Hence} ${\Gamma}$ is an isometry from $\gotN$ onto $\cH \oplus \cH$. \end{proof} Passing to direct sum \eqref{6.5a}, we equip ${\rm dom\,}(A^*_n)$ and ${\rm dom\,}(A^*)$ with the graph's norms and obtain the Hilbert spaces $\gotH_{+n}$ and $\gotH_+$, respectively. Clearly, the corresponding inner products $(f,g)_{+n}$ and $(f,g)_+$ are defined by \eqref{3.8b} with $S$ replaced by ${ S_n}$ and $A$, respectively. Obviously, $\gotH_+ = \bigoplus^\infty_{n=1} \gotH_{+n}.$ \begin{theorem}\Label{VI.3} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^*_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let $A$ and $A_0$ be given by \eqref{6.5a} and \begin{equation}\Label{6.8} A_0 := \bigoplus^\infty_{n=1}{ S_{0n}}, \end{equation} respectively. Then there exist boundary triplets ${\Pi}_n := \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for ${ S^*_n}$ such that ${ S_{0n}} = { S^*_n}\upharpoonright{\xker\,}({\Gamma}_{0n})$, $n \in \N$, and the direct sum ${ {\Pi} = \oplus^\infty_{n=1} {\Pi}_n}$ defined by \eqref{6.5} forms an ordinary boundary triplet for $A^*$ satisfying $A_0 = A^*\upharpoonright{\xker\,}({\Gamma}_0)$. Moreover, the corresponding Weyl function $M(\cdot)$ and the ${\gamma}$-field ${\gamma}(\cdot)$ are { given by} \begin{equation}\Label{6.7} M(z) = \bigoplus^\infty_{n=1}M_n(z) \quad \mbox{and} \quad {\gamma}(z) = \bigoplus^\infty_{n=1}{\gamma}_n(z) \end{equation} where $M_n(\cdot)$ and ${\gamma}_n(\cdot

-0.016519

-1.405932

0.021933

2.199844

[ 0.17163993008533066, -0.20467839403207874 ]

[ -1.5169512222182184, -1.2949132781358133 ]

[ 0.024469223347200215, 0.019396741296431676 ]

[ 2.1374109800549306, 2.262276752931069 ]

1,024

[ 512, 512 ]

[ 2403, 29900, 29888, 22631, 29875, 1012, 15333, 29906, 3187, 29883, 29950, 29889, 13, 539, 320, 355, 29912, 2573, 29913, 13, 1523, 2109, 292, 5186, 1907, 7555, 6642, 2403, 29896, 29888, 1665, 3358, 474, 5369, 320, 3358, 474, 2802, 6642, 2403, 29900, 29888, 1665, 3358, 474, 1042, 411, 13, 24599, 29915, 29879, 29871, 10110, 320, 4915, 29912, 29906, 29889, 29896, 29900, 29909, 29913, 29871, 591, 4017, 779, 29989, 741, 6642, 2403, 29900, 29888, 29918, 29875, 7893, 3187, 29883, 29950, 353, 13, 7893, 29888, 29918, 29875, 7893, 29938, 322, 779, 29989, 741, 6642, 2403, 29900, 29888, 22631, 29875, 1012, 29989, 3187, 29883, 29950, 353, 12926, 29888, 22631, 29875, 1012, 29989, 1504, 426, 7857, 13, 29905, 4915, 29912, 29953, 29889, 29946, 5371, 29913, 4893, 278, 883, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29946, 29907, 29913, 13, 7893, 741, 6642, 2403, 29900, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 718, 12926, 741, 6642, 2403, 29896, 29898, 29888, 29918, 29875, 718, 285, 22631, 29875, 1800, 7893, 29985, 29906, 3187, 29883, 29950, 353, 13, 29906, 7893, 29888, 29918, 29875, 7893, 29985, 29906, 718, 29871, 29906, 7893, 29888, 22631, 29875, 1012, 15333, 29906, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29909, 20837, 16287, 3697, 13, 4535, 29989, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 353, 29871, 29906, 7893, 29888, 29918, 29875, 7893, 29985, 29906, 718, 29871, 29906, 7893, 29888, 22631, 29875, 1012, 15333, 29906, 29938, 13, 4716, 4208, 411, 320, 4915, 29912, 29953, 29889, 29946, 29907, 29913, 28281, 320, 4915, 29912, 29953, 29889, 29946, 1836, 13, 23036, 779, 29989, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 320, 280, 12926, 29888, 7893, 29985, 29906, 28842, 718, 12926, 29888, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 353, 13, 7893, 29888, 718, 285, 29918, 29875, 718, 285, 22631, 29875, 1012, 15333, 29906, 28842, 1628, 591, 679, 515, 320, 4915, 29912, 29953, 29889, 29946, 29913, 393, 7555, 6642, 1042, 338, 263, 6761, 428, 29889, 13, 13, 6039, 16604, 29892, 7555, 6642, 1042, 338, 385, 338, 7843, 515, 779, 7085, 29940, 29938, 964, 779, 29883, 29950, 320, 17201, 13, 29905, 29883, 29950, 1504, 4001, 7555, 12197, 1042, 338, 263, 10452, 21954, 29873, 363, 395, 29903, 6622, 1628, 13, 7555, 1758, 6350, 5940, 2119, 741, 6642, 1800, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 7449, 426, 10133, 29913, 7555, 6642, 1042, 13, 275, 385, 338, 7843, 515, 779, 7085, 29940, 29938, 11480, 779, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 7129, 292, 304, 29871, 1513, 2533, 320, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 591, 29871, 7462, 29871, 7555, 1758, 2432, 5940, 2119, 29909, 6622, 29918, 29876, 1262, 322, 13, 29938, 741, 1758, 2432, 5940, 2119, 29909, 6622, 1262, 411, 278, 3983, 29915, 29879, 6056, 29879, 322, 4017, 278, 12338, 2151, 8162, 13, 4535, 7085, 29950, 648, 29974, 29876, 1042, 322, 779, 7085, 29950, 28842, 1628, 8307, 29889, 17732, 368, 29892, 278, 13, 2616, 3636, 292, 6426, 9316, 2427, 29888, 29892, 29887, 20439, 29974, 29876, 1042, 13, 392, 2427, 29888, 29892, 29887, 20344, 24035, 526, 3342, 491, 320, 4915, 29912, 29941, 29889, 29947, 29890, 29913, 411, 395, 29903, 29938, 8611, 491, 13, 5303, 317, 29918, 29876, 1042, 322, 395, 29909, 1628, 8307, 29889, 25735, 29892, 779, 7085, 29950, 28842, 353, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 320, 7085, 29950, 648, 29974, 29876, 1836, 29938, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 18118, 29889, 29941, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 13, 15603, 18348, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 13, 29903, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 8725, 29892, 1235, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 29938, 367, 13, 29887, 5428, 491, 320, 4915, 29912, 29953, 29889, 29945, 29874, 29913, 322, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29947, 29913, 13, 29909, 29918, 29900, 3490, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1157, 317, 648, 29900, 29876, 11656, 13, 29905, 355, 29912, 2573, 29913, 13, 690, 1103, 3598, 29889, 1987, 727, 1863, 10452, 21954, 1372, 7555, 12197, 2403, 29876, 3490, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 363, 6435, 317, 6622, 29918, 29876, 1042, 1316, 393, 6435, 13, 29903, 648, 29900, 29876, 930, 353, 426, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 395, 29876, 320, 262, 320, 29940, 1628, 13, 392, 278, 1513, 2533, 6435, 2802, 12197, 29913, 353, 320, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 2802, 12197, 2403, 29876, 1042, 13, 12119, 491, 320, 4915, 29912, 29953, 29889, 29945, 29913, 7190, 385, 15311, 10452, 21954, 29873, 363, 13, 29938, 29909, 6622, 29938, 24064, 395, 29909, 29918, 29900, 353, 319, 6622, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 2403, 29900, 4935, 12808, 29892, 13, 1552, 6590, 29871, 399, 1032, 29880, 740, 395, 29924, 1194, 3822, 1262, 322, 278, 7555, 4283, 23021, 2671, 13, 29938, 741, 4283, 4678, 3822, 1262, 526, 426, 2183, 491, 29913, 13, 29905, 463, 29912, 2573, 1012, 4775, 29912, 29953, 29889, 29955, 29913, 13, 29924, 29898, 29920, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29924, 29918, 29876, 29898, 29920, 29897, 13, 29905, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 13, 741, 4283, 2119, 29920, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 4283, 2403, 29876, 29898, 29920, 29897, 13, 29905, 355, 29912, 2573, 29913, 13, 3062, 395, 29924, 29918, 29876, 1194, 3822, 1262, 322, 7555, 4283, 2403, 29876, 1194, 3822 ]

1,332,863

33,792

ArXiv

-1

)$ are the Weyl functions and the ${\gamma}$-field corresponding to ${\Pi}_n, \ n\in \N$. In addition, the condition { $M(i) = iI$} { holds}. \end{theorem} \begin{proof} For every ${ S_{0n}} = { S^*_{0n}}\in {\rm Ext\,} { S_n}$ there exists a boundary triplet ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ for $S_n^*$ such that ${ S_{0n}} := A^*_n\upharpoonright{\xker\,}({\Gamma}_{0n})$ (see \cite{DM91}). By Lemma \ref{VI.1} we can assume without loss of generality that the corresponding Weyl function $M_{n}(\cdot)$ satisfies $M_n(i) = i$. By Lemma \ref{VI.2} the mapping ${\Gamma}^n:=(\Gamma_{0n},\Gamma_{1n})^\top: \gotH_{+n} \longrightarrow \cH_n \oplus \cH_n$, is contractive { for each} $n\in \N$. Hence $\|{\Gamma}_j\| = \sup_{n}\|{\Gamma}_{jn}\|\le 1, j\in \{0,1\}$, where ${\Gamma}_0$ and ${\Gamma}_1$ are defined by \eqref{6.5}. It follows that the mappings ${\Gamma}_0$ and ${\Gamma}_1$ are well-defined on ${\rm dom\,}({\Gamma}) = {\rm dom\,}(A^*) = \bigoplus^\infty_{n=1}{\rm dom\,}({ S^*_n})$. Thus, { the Green's} identity \eqref{3.1AA} holds for all $f,g \in {\rm dom\,}(A^*).$ Further, we set $\gotN_{\pm in} := {\xker\,}({ S^*_n} \mp i)$,\ $\gotN_n := \gotN_{in} \stackrel{.}{+} \gotN_{-in}$, $\gotN_{\pm i} := {\xker\,}(A^* \mp i)$ and $\gotN := \gotN_i \stackrel{.}{+} \gotN_{-i}.$ By Lemma \ref{VI.2} the restriction ${\Gamma}^n\upharpoonright\gotN_n$ is an isometry from $\gotN_n,$ regarded as a subspace of $\gotH_{+n},$ onto $\cH_n \oplus \cH_n$. Since $\gotN$ regarded as a subspace of $\gotH_+$ admits the representation $\gotN = \bigoplus^\infty_{n=1}\gotN_n$, the restriction ${\Gamma}\upharpoonright\gotN$, ${\Gamma} := \bigoplus^\infty_{n=1}{\Gamma}^n$, isometrically maps $\gotN$ onto $\cH \oplus \cH$. Hence ${\rm ran\,}({\Gamma}) = \cH \oplus \cH$. Equalities \eqref{6.7} are immediate from Definition \ref{Weylfunc}. \end{proof} \begin{remark} {\rm Kochubei \cite{Koch79} proved that $\Pi=\oplus^{\infty}_{n=1}\Pi_n$ forms a boundary triplet whenever any pair $\{{ S_n},{ S_{0n}}\},$\ ${ S_{0n}} := S^*_n\upharpoonright{\xker\,}({\Gamma}_{0n})$, ${n\in\N}$, is unitarily equivalent to { $\{S_1,S_{01}\}$}. } \end{remark} Recall, that for any non-negative symmetric operator { $A$} the set of its non-negative self-adjoint extensions { ${\rm Ext\,}_A(0,\infty)$} is non-empty (see \cite{AG81, Ka76}). The set ${\rm Ext\,}_A(0,\infty)$ contains the Friedrichs (the biggest) extension $A^F$ and the Krein (the smallest) extension $A^K$. These extensions are uniquely determined by the following extremal property in the class ${\rm Ext

-0.051275

-1.081828

-0.075712

2.168627

[ -0.2591229923347795, 0.1565735003663443 ]

[ -1.1230129343300803, -1.0406440195898332 ]

[ -0.09727034587124471, -0.05415424843971213 ]

[ 2.0541671314708383, 2.2830877150770923 ]

1,024

[ 512, 512 ]

[ 1262, 526, 278, 399, 1032, 29880, 3168, 322, 13, 1552, 7555, 4283, 23021, 2671, 6590, 304, 7555, 12197, 2403, 29876, 29892, 320, 302, 29905, 262, 320, 29940, 1504, 512, 6124, 29892, 13, 1552, 4195, 426, 395, 29924, 29898, 29875, 29897, 353, 474, 29902, 17133, 29871, 426, 8640, 1836, 13, 29905, 355, 29912, 14648, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2831, 1432, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 29913, 426, 317, 29918, 29876, 1042, 13, 12711, 4864, 263, 10452, 21954, 29873, 7555, 12197, 2403, 29876, 353, 13, 24976, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 363, 395, 29903, 29918, 29876, 6622, 29938, 1316, 393, 6435, 317, 648, 29900, 29876, 930, 13, 9361, 319, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 8435, 313, 4149, 320, 2036, 29912, 23560, 29929, 29896, 7690, 2648, 11894, 13, 29905, 999, 29912, 18118, 29889, 29896, 29913, 591, 508, 5251, 1728, 6410, 310, 2498, 537, 393, 278, 13, 2616, 3636, 292, 399, 1032, 29880, 740, 395, 29924, 648, 29876, 4678, 3822, 1262, 17150, 395, 29924, 29918, 29876, 29898, 29875, 29897, 353, 474, 1504, 13, 2059, 11894, 320, 999, 29912, 18118, 29889, 29906, 29913, 278, 10417, 13, 29938, 741, 6642, 2137, 29876, 9361, 1194, 6642, 648, 29900, 29876, 7570, 6642, 648, 29896, 29876, 1800, 3823, 3332, 29901, 320, 7085, 29950, 648, 29974, 29876, 29913, 320, 24225, 13, 29905, 29883, 29950, 29918, 29876, 320, 17201, 320, 29883, 29950, 29918, 29876, 1628, 338, 8078, 573, 426, 363, 1269, 29913, 395, 29876, 29905, 262, 320, 29940, 1504, 13, 29950, 663, 779, 29989, 741, 6642, 2403, 29926, 7893, 353, 320, 12587, 648, 29876, 1012, 29989, 741, 6642, 3227, 29926, 29876, 1012, 4295, 280, 29871, 29896, 29892, 29871, 432, 29905, 262, 9991, 29900, 29892, 29896, 28538, 13, 3062, 7555, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2403, 29896, 29938, 526, 3342, 491, 320, 4915, 29912, 29953, 29889, 29945, 1836, 739, 4477, 13, 5747, 278, 611, 27775, 7555, 6642, 2403, 29900, 29938, 322, 7555, 6642, 2403, 29896, 29938, 526, 1532, 29899, 12119, 373, 13, 29938, 741, 1758, 2432, 5940, 2119, 741, 6642, 1800, 353, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 29897, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 1758, 2432, 5940, 2119, 29912, 13, 29903, 6622, 29918, 29876, 23462, 6549, 29892, 426, 278, 7646, 29915, 29879, 29913, 10110, 320, 4915, 29912, 29941, 29889, 29896, 6344, 29913, 8640, 13, 1454, 599, 395, 29888, 29892, 29887, 320, 262, 2802, 1758, 2432, 5940, 2119, 29909, 6622, 467, 29938, 13, 13, 29943, 332, 721, 29892, 591, 731, 779, 7085, 29940, 1665, 3358, 297, 29913, 3490, 2802, 29916, 3946, 5940, 2119, 29912, 317, 6622, 29918, 29876, 29913, 320, 1526, 474, 1262, 2053, 29871, 779, 7085, 29940, 29918, 29876, 13, 9361, 320, 7085, 29940, 648, 262, 29913, 320, 1429, 2674, 26139, 1157, 29974, 29913, 320, 7085, 29940, 22631, 262, 4429, 779, 7085, 29940, 1665, 3358, 474, 29913, 3490, 13, 741, 29916, 3946, 5940, 2119, 29909, 6622, 320, 1526, 474, 1262, 322, 779, 7085, 29940, 3490, 320, 7085, 29940, 29918, 29875, 320, 1429, 2674, 26139, 1157, 29974, 29913, 13, 29905, 7085, 29940, 22631, 29875, 1836, 29938, 29871, 2648, 11894, 320, 999, 29912, 18118, 29889, 29906, 29913, 29871, 278, 24345, 13, 29938, 741, 6642, 2137, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 29905, 7085, 29940, 29918, 29876, 29938, 338, 385, 338, 7843, 515, 779, 7085, 29940, 29918, 29876, 8209, 13, 1727, 25600, 408, 263, 1014, 3493, 310, 779, 7085, 29950, 648, 29974, 29876, 1118, 29938, 11480, 779, 29883, 29950, 29918, 29876, 320, 17201, 320, 29883, 29950, 29918, 29876, 1504, 13, 23036, 779, 7085, 29940, 29938, 17878, 408, 263, 1014, 3493, 310, 779, 7085, 29950, 29918, 24035, 7336, 1169, 278, 13, 276, 26081, 779, 7085, 29940, 353, 320, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 1012, 7085, 29940, 29918, 29876, 1628, 278, 13, 5060, 19902, 7555, 6642, 1012, 29884, 561, 279, 1129, 265, 1266, 29905, 7085, 29940, 1628, 7555, 6642, 29913, 3490, 13, 29905, 3752, 17201, 3823, 3411, 648, 29876, 29922, 29896, 3331, 6642, 2137, 29876, 1628, 338, 3297, 29878, 1711, 11053, 779, 7085, 29940, 29938, 11480, 779, 29883, 29950, 13, 29905, 17201, 320, 29883, 29950, 1504, 10133, 7555, 1758, 6350, 5940, 2119, 741, 6642, 1800, 353, 320, 29883, 29950, 320, 17201, 320, 29883, 29950, 1504, 11243, 284, 1907, 13, 29905, 4915, 29912, 29953, 29889, 29955, 29913, 526, 16800, 515, 29871, 21940, 320, 999, 29912, 29956, 1032, 29880, 9891, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 1758, 13, 29968, 2878, 4003, 29875, 320, 2036, 29912, 29968, 2878, 29955, 29929, 29913, 11827, 393, 13, 4535, 12197, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 1012, 12197, 29918, 29876, 29938, 7190, 263, 10452, 21954, 29873, 10940, 13, 1384, 29871, 5101, 779, 6224, 317, 29918, 29876, 29087, 317, 648, 29900, 29876, 4229, 1118, 4535, 6435, 317, 648, 29900, 29876, 930, 3490, 13, 29903, 6622, 29918, 29876, 29905, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 6435, 29876, 29905, 262, 29905, 29940, 4429, 338, 443, 3673, 2354, 13, 1686, 27445, 304, 426, 12564, 29903, 29918, 29896, 29892, 29903, 648, 29900, 29896, 1012, 1042, 1836, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 13, 4789, 497, 29892, 393, 363, 738, 1661, 29899, 22198, 18348, 5455, 426, 395, 29909, 17133, 13, 1552, 731, 310, 967, 1661, 29899, 22198, 1583, 29899, 328, 12090, 17752, 426, 13, 29938, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1262, 29913, 338, 1661, 29899, 6310, 313, 4149, 320, 2036, 29912, 10051, 29947, 29896, 29892, 13680, 29955, 29953, 7690, 450, 731, 13, 29938, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1262, 3743, 278, 9542, 29879, 313, 1552, 24842, 29897, 6081, 13, 29938, 29909, 29985, 29943, 29938, 322, 278, 7706, 262, 313, 1552, 19087, 29897, 6081, 395, 29909, 29985, 29968, 1504, 4525, 13, 24299, 526, 20498, 873, 10087, 491, 278, 1494, 9413, 284, 13, 6799, 297, 278, 770, 7555, 1758, 7338 ]

1,332,863

34,816

ArXiv

-1

\,}_A(0,\infty):$ \begin{displaymath} (A^F + x)^{-1}\le(\wt A+x)^{-1}\le(A^K + x)^{-1},\quad x>0,\quad \wt A\in{\rm Ext\,}_A(0,\infty). \end{displaymath} \begin{corollary}\label{cor5.5} Assume conditions of Theorem \ref{VI.3}. Let $S_n\ge 0$, $n\in{\N},$ and let $S^F_n$ and $S^K_n$ be the { Friedrichs} and the { Krein} extensions of $S_n$, respectively. Then \begin{equation}\label{5.14} A^F=\oplus^\infty_{n=1}S_n^F \qquad \text{and}\qquad A^K=\oplus^\infty_{n=1} S^K_n. \end{equation} \end{corollary} \begin{proof} Let us prove the second of relations \eqref{5.14}. The first one is proved similarly. By Theorem \ref{VI.3} there exists { a} boundary triplet $\Pi_n=\{\cH_n,\Gamma_{0n},\Gamma_{1n}\}$ for $S^*_n$ such that $S^K_n = S_{0n}$ and $\Pi=\oplus^{\infty}_{n=1}\Pi_n$ is a boundary triplet for $A^*$. Fix any $x_2\in\R_+$ and put $C_2:=\|M(-x_2)\|$. Then any $h=\oplus^{\infty}_{n=1} h_n \in \cH$ can be decomposed by $h=h^{(1)}\oplus h^{(2)}$ with $h^{(1)}\in\oplus^p_{n=1} \cH_n$ { and} $h^{(2)}\in\oplus^{\infty}_{n=p+1}\cH_n$ {such that $\|h^{(2)}\| < C^{-1/2}_2$}. Hence $|(M(-x_2)h^{(2)},h^{(2)})| < 1$. { Due to the monotonicity of $M(\cdot)$ we get} \begin{displaymath} \bigg(M(-x)h^{(2)},h^{(2)}\bigg)>\bigg(M(-x_2)h^{(2)},h^{(2)}\bigg)>-1,\qquad x\in (0, x_2). \end{displaymath} Since $S_{0n} = S^K_n$, the Weyl function $M_n(\cdot)$ satisfies \begin{equation}\label{5.16} \lim_{{ x\downarrow 0}}\bigg(M_n(-x)g_n, g_n\bigg)=+\infty, \qquad g_n\in\cH_n\setminus\{0\}, \end{equation} { cf. \cite[Proposition 4]{DM91}}. Since $M(\cdot)= \oplus^\infty_{n=1} M_n(\cdot)$ { is block-diagonal}, cf. \eqref{6.7}, we get from \eqref{5.16} that for any $N>0$ there exists $x_1>0$ such that \begin{equation}\label{5.17} \bigg(M(-x)h^{(1)},h^{(1)}\bigg)=\sum^p_{n=1}\bigg(M_n(-x)h_n,h_n\bigg)> N \quad \text{for}\quad x\in (0, x_1). \end{equation} Combining \eqref{5.16} with \eqref{5.17} and using the diagonal form of $M(\cdot)$, we get \begin{displaymath} (M(-x)h,h) = (M(-x)h^{(1)}, h^{(1)}) + (M(-x)h^{(2)},h^{(2)}) > N-1 \end{displaymath} for $0<x\le\min(x_1,x_2)$. Thus, $\lim_{{x\downarrow 0}}(M(-x)h,h) = + \infty$ for $h\in \cH\setminus\{0\}.$

-0.544015

-1.495464

-0.360722

1.752408

[ -0.45293206553810406, -0.6350988975949392 ]

[ -1.3737009357134409, -1.6172264227715627 ]

[ -0.26719849457199074, -0.4542462701940806 ]

[ 1.9605178018137346, 1.5442985588932732 ]

1,024

[ 512, 512 ]

[ 5940, 2403, 29909, 29898, 29900, 2053, 3411, 1125, 29938, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29898, 29909, 29985, 29943, 718, 921, 21604, 29896, 1012, 280, 1194, 14554, 319, 29974, 29916, 21604, 29896, 1012, 280, 29898, 29909, 29985, 29968, 718, 921, 21604, 29896, 7570, 3425, 921, 29958, 29900, 2053, 3425, 13, 29905, 14554, 319, 29905, 262, 741, 1758, 7338, 5940, 2403, 29909, 29898, 29900, 2053, 3411, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 29905, 463, 29912, 2616, 21982, 1012, 1643, 29912, 2616, 29945, 29889, 29945, 29913, 13, 7900, 2017, 5855, 310, 10244, 320, 999, 29912, 18118, 29889, 29941, 1836, 2803, 395, 29903, 29918, 29876, 29905, 479, 29871, 29900, 1628, 13, 29938, 29876, 29905, 262, 741, 29940, 1118, 29938, 322, 1235, 395, 29903, 29985, 29943, 29918, 29876, 29938, 322, 395, 29903, 29985, 29968, 29918, 29876, 29938, 367, 278, 426, 9542, 29879, 29913, 322, 13, 1552, 426, 7706, 262, 29913, 29871, 17752, 310, 395, 29903, 29918, 29876, 1628, 8307, 29889, 1987, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29946, 29913, 13, 29909, 29985, 29943, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 29903, 29918, 29876, 29985, 29943, 13, 29905, 12014, 320, 726, 29912, 392, 1012, 12014, 13, 29909, 29985, 29968, 2013, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 317, 29985, 29968, 29918, 29876, 29889, 13, 29905, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 2616, 21982, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 12024, 502, 6356, 278, 1473, 310, 5302, 320, 4915, 29912, 29945, 29889, 29896, 29946, 1836, 450, 937, 697, 13, 275, 11827, 22829, 29889, 29871, 2648, 10244, 320, 999, 29912, 18118, 29889, 29941, 29913, 727, 4864, 426, 263, 29913, 13, 9917, 653, 21954, 29873, 779, 12197, 29918, 29876, 2013, 741, 29883, 29950, 29918, 29876, 2053, 6642, 648, 29900, 29876, 7570, 6642, 648, 29896, 29876, 1012, 1042, 363, 13, 29938, 29903, 6622, 29918, 29876, 29938, 1316, 393, 395, 29903, 29985, 29968, 29918, 29876, 353, 317, 648, 29900, 29876, 1042, 322, 13, 4535, 12197, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 1012, 12197, 29918, 29876, 29938, 338, 263, 10452, 21954, 29873, 363, 395, 29909, 6622, 1504, 13, 13, 29943, 861, 738, 395, 29916, 29918, 29906, 29905, 262, 29905, 29934, 29918, 24035, 322, 1925, 395, 29907, 29918, 29906, 29901, 2013, 29989, 29924, 6278, 29916, 29918, 29906, 2144, 29989, 1504, 1987, 738, 13, 29938, 29882, 2013, 17201, 3311, 3411, 3227, 29876, 29922, 29896, 29913, 298, 29918, 29876, 320, 262, 320, 29883, 29950, 29938, 508, 367, 17753, 4752, 491, 13, 29938, 29882, 29922, 29882, 7650, 29896, 11383, 17201, 298, 7650, 29906, 15604, 411, 395, 29882, 7650, 29896, 11383, 262, 29905, 17201, 29985, 29886, 648, 29876, 29922, 29896, 29913, 320, 29883, 29950, 29918, 29876, 29938, 426, 13, 392, 29913, 395, 29882, 7650, 29906, 11383, 262, 29905, 17201, 3311, 3411, 3227, 29876, 29922, 29886, 29974, 29896, 1012, 29883, 29950, 29918, 29876, 29938, 426, 14565, 393, 13, 4535, 29989, 29882, 7650, 29906, 11383, 29989, 529, 315, 3426, 29896, 29914, 29906, 2403, 29906, 29938, 1836, 10133, 11892, 29898, 29924, 6278, 29916, 29918, 29906, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 26972, 29989, 529, 13, 29896, 1504, 426, 29871, 16809, 304, 278, 21196, 8927, 537, 310, 395, 29924, 1194, 3822, 1262, 591, 679, 29913, 13, 29905, 463, 29912, 4990, 755, 29913, 13, 29905, 17633, 29898, 29924, 6278, 29916, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 11383, 17633, 29897, 14247, 17633, 29898, 29924, 6278, 29916, 29918, 29906, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 11383, 17633, 15410, 29899, 29896, 2053, 12014, 13, 29916, 29905, 262, 313, 29900, 29892, 921, 29918, 29906, 467, 13, 29905, 355, 29912, 4990, 755, 29913, 13, 23036, 395, 29903, 648, 29900, 29876, 29913, 353, 317, 29985, 29968, 29918, 29876, 1628, 278, 399, 1032, 29880, 740, 395, 29924, 29918, 29876, 1194, 3822, 1262, 17150, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29953, 29913, 13, 29905, 2576, 648, 29912, 921, 29905, 3204, 2936, 29871, 29900, 4229, 17633, 29898, 29924, 29918, 29876, 6278, 29916, 29897, 29887, 29918, 29876, 29892, 330, 29918, 29876, 29905, 17633, 3892, 3124, 3411, 29892, 320, 12014, 13, 29887, 29918, 29876, 29905, 262, 29905, 29883, 29950, 29918, 29876, 29905, 15375, 10045, 29900, 29905, 1118, 13, 29905, 355, 29912, 2573, 29913, 13, 29912, 274, 29888, 29889, 320, 2036, 29961, 1184, 3283, 29871, 29946, 3199, 23560, 29929, 29896, 27243, 4001, 395, 29924, 1194, 3822, 3892, 13, 29905, 17201, 3823, 3411, 648, 29876, 29922, 29896, 29913, 341, 29918, 29876, 1194, 3822, 1262, 426, 338, 2908, 29899, 6051, 351, 7177, 1118, 274, 29888, 29889, 13, 29905, 4915, 29912, 29953, 29889, 29955, 1118, 591, 679, 515, 320, 4915, 29912, 29945, 29889, 29896, 29953, 29913, 393, 363, 738, 395, 29940, 29958, 29900, 29938, 727, 13, 9933, 395, 29916, 29918, 29896, 29958, 29900, 29938, 1316, 393, 13, 29905, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29955, 29913, 13, 29905, 17633, 29898, 29924, 6278, 29916, 29897, 29882, 7650, 29896, 19230, 29882, 7650, 29896, 11383, 17633, 7950, 2083, 29985, 29886, 648, 29876, 29922, 29896, 1012, 17633, 29898, 29924, 29918, 29876, 6278, 29916, 29897, 29882, 29918, 29876, 29892, 29882, 29918, 29876, 29905, 17633, 15410, 13, 29940, 320, 3425, 320, 726, 29912, 1454, 1012, 3425, 921, 29905, 262, 313, 29900, 29892, 921, 29918, 29896, 467, 13, 29905, 355, 29912, 2573, 29913, 13, 1523, 2109, 292, 320, 4915, 29912, 29945, 29889, 29896, 29953, 29913, 411, 320, 4915, 29912, 29945, 29889, 29896, 29955, 29913, 322, 773, 278, 19640, 13, 689, 310, 395, 29924, 1194, 3822, 5767, 591, 679, 13, 29905, 463, 29912, 4990, 755, 29913, 313, 29924, 6278, 29916, 29897, 29882, 29892, 29882, 29897, 353, 313, 29924, 6278, 29916, 29897, 29882, 7650, 29896, 19230, 298, 7650, 29896, 26972, 718, 313, 29924, 6278, 29916, 29897, 29882, 7650, 29906, 19230, 29882, 7650, 29906, 26972, 13, 29958, 405, 29899, 29896, 320, 355, 29912, 4990, 755, 29913, 13, 1454, 395, 29900, 29966, 29916, 29905, 280, 29905, 1195, 29898, 29916, 29918, 29896, 29892, 29916, 29918, 29906, 4935, 6549, 29892, 779, 2576, 648, 29912, 29916, 29905, 3204, 2936, 29871, 29900, 12156, 29924, 6278, 29916, 29897, 29882, 29892, 29882, 29897, 13, 29922, 718, 320, 3411, 29938, 363, 395, 29882, 29905, 262, 320, 29883, 29950, 29905, 15375, 10045, 29900, 29905, 1836, 29938 ]

1,332,863

35,840

ArXiv

-1

Applying \cite[Proposition 4]{DM91} we {prove the second relation of} \eqref{5.14}. \end{proof} \begin{remark} {\em Another proof can be obtained by using characterization of $A^F$ and $A^K$ by means of the respective quadratic forms. } \end{remark} \subsection{Summands with arbitrary equal deficiency indices} Here we apply Theorem \ref{V.5} to direct sums of symmetric operators \eqref{6.5a}, allowing summands ${ S_n}$ to have arbitrary (finite or infinite) equal deficiency indices. We start with a simple general proposition. \begin{proposition}\Label{VI.5b} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^*_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let $A$ and $A_0$ be given by \eqref{6.5a} and \eqref{6.8}, respectively. If $\wt A$ is a self-adjoint extension of $A$ such that condition \eqref{5.0} is satisfied, then \begin{equation}\label{5.13} {\sigma}_{ac}(A_{0}) = \overline{\bigcup {\sigma}_{ac}({ S_{0n}})} \subseteq {\sigma}(\wt A) \quad \mbox{and} \quad {\sigma}_{ac}(\wt A) \subseteq \overline{\bigcup {\sigma}({ S_{0n}})} = {\sigma}(A_{0}). \end{equation} \end{proposition} \begin{proof} By the Weyl theorem, condition \eqref{5.0} yields ${\sigma}_{\rm ess}(\wt A) = {\sigma}_{\rm ess}(A_0)$. Hence \begin{displaymath} \overline{\bigcup {\sigma}_{ac}({ S_{0n}})} = {\sigma}_{ac}(A_0) \subseteq {\sigma}_{\rm ess}(A_0) = {\sigma}_{\rm ess}(\wt A) \subseteq {\sigma}(\wt A) \end{displaymath} and \begin{displaymath} {\sigma}_{ac}(\wt A) \subseteq {\sigma}_{\rm ess}(\wt A) = {\sigma}_{\rm ess}(A_0) \subseteq {\sigma}(A_0) = \overline{\bigcup {\sigma}({ S_{0n}})}. \end{displaymath} \end{proof} Our further considerations are substantially based on Theorem \ref{VI.3}. \begin{theorem}\Label{VI.4} Let $\{{ S_n}\}^\infty_{n=1}$ be a sequence of densely defined closed symmetric operators, ${\rm dom\,}({ S_n})\subset \gotH_n$, $n_+({ S_n})=n_-({ S_n})$, and let ${ S_{0n}} = { S^*_{0n}}\in {\rm Ext\,}_{{ S_n}}$. Further, let ${\Pi}_n = \{\cH_n,{\Gamma}_{0n},{\Gamma}_{1n}\}$ be an ordinary boundary triplet for ${ S^*_n}$ such that ${ S_{0n}} = { S^*_n}\upharpoonright{\xker\,}({\Gamma}_{0n})$, $n \in \N$, and let $M_n(\cdot)$ be the corresponding Weyl function. Moreover, let $\gotm^+_n(t)$, $n \in \N$, be the { invariant maximal normal function} obtained from \eqref{4.12A} by replacing $M(\cdot)$ by $M_n(\cdot)$. If $\sup_{n\in\N}\gotm^+_n(t) < +\infty$ for a.e. $t \in \R$, then for any self-adjoint extension $\wt{A}$ of $A$ defined by \eqref{6.5a}, which satisfies { the} condition \eqref{5.0}, the absolutely continuous parts $\wt{A}^{ac}$ and $A^{ac}_0$ are

-0.441975

-1.389817

-0.108366

1.721192

[ -0.21049951460532348, -0.6734498096069045 ]

[ -1.1552442487936552, -1.6243889370968014 ]

[ 0.22229602332717321, -0.43902882404177496 ]

[ 1.700380774988446, 1.7420026992804922 ]

1,024

[ 512, 512 ]

[ 29871, 2401, 5890, 13, 29905, 2036, 29961, 1184, 3283, 29871, 29946, 3199, 23560, 29929, 29896, 29913, 591, 426, 771, 345, 278, 1473, 8220, 310, 29913, 13, 29905, 4915, 29912, 29945, 29889, 29896, 29946, 1836, 13, 29905, 355, 29912, 8017, 29913, 13, 29905, 463, 29912, 26294, 29913, 13, 741, 331, 13, 2744, 1228, 5296, 508, 367, 7625, 491, 773, 2931, 2133, 310, 395, 29909, 29985, 29943, 29938, 13, 392, 395, 29909, 29985, 29968, 29938, 491, 2794, 310, 278, 18067, 25904, 7190, 29889, 13, 29913, 13, 29905, 355, 29912, 26294, 29913, 13, 13, 29905, 7235, 29912, 11139, 29885, 4167, 411, 11472, 5186, 822, 293, 13396, 16285, 29913, 13, 13, 10605, 591, 3394, 10244, 320, 999, 29912, 29963, 29889, 29945, 29913, 304, 1513, 25470, 310, 18348, 13, 3372, 4097, 320, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 14372, 22792, 4167, 6435, 317, 29918, 29876, 1042, 304, 505, 11472, 13, 29898, 18925, 470, 10362, 29897, 5186, 822, 293, 13396, 16285, 29889, 1334, 1369, 411, 263, 13, 12857, 2498, 26619, 29889, 13, 29905, 463, 29912, 771, 3283, 1012, 4775, 29912, 18118, 29889, 29945, 29890, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 5764, 13, 11967, 16414, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 13, 29943, 332, 721, 29892, 1235, 395, 29909, 29938, 322, 395, 29909, 29918, 29900, 29938, 367, 2183, 491, 320, 4915, 29912, 29953, 29889, 29945, 29874, 29913, 322, 13, 29905, 4915, 29912, 29953, 29889, 29947, 1118, 8307, 29889, 960, 779, 14554, 319, 29938, 338, 263, 1583, 29899, 328, 12090, 6081, 13, 974, 395, 29909, 29938, 1316, 393, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 338, 15787, 29892, 769, 13, 1678, 320, 463, 29912, 2573, 1012, 1643, 29912, 29945, 29889, 29896, 29941, 29913, 13, 741, 3754, 3227, 562, 2119, 29909, 648, 29900, 1800, 353, 320, 6875, 741, 3752, 5231, 2802, 3754, 3227, 562, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 320, 11725, 13, 741, 3754, 4678, 14554, 319, 29897, 320, 3425, 320, 8264, 29912, 392, 29913, 320, 3425, 2802, 3754, 3227, 562, 4678, 14554, 319, 29897, 320, 11725, 13, 29905, 6875, 741, 3752, 5231, 2802, 3754, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 353, 2802, 3754, 2119, 29909, 648, 29900, 7690, 13, 418, 320, 355, 29912, 2573, 29913, 13, 29905, 355, 29912, 771, 3283, 29913, 13, 29905, 463, 29912, 8017, 29913, 13, 2059, 278, 399, 1032, 29880, 9185, 29892, 4195, 320, 4915, 29912, 29945, 29889, 29900, 29913, 17498, 29871, 7555, 3754, 6353, 1758, 3686, 4678, 14554, 13, 29909, 29897, 353, 2802, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 4935, 10133, 13, 29905, 463, 29912, 4990, 755, 29913, 320, 6875, 741, 3752, 5231, 2802, 3754, 3227, 562, 2119, 29912, 317, 648, 29900, 29876, 930, 2915, 353, 2802, 3754, 3227, 562, 2119, 29909, 29918, 29900, 29897, 320, 11725, 13, 741, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 29897, 353, 2802, 3754, 6353, 1758, 3686, 4678, 14554, 319, 29897, 320, 11725, 2802, 3754, 4678, 14554, 319, 29897, 320, 355, 29912, 4990, 755, 29913, 13, 392, 13, 29905, 463, 29912, 4990, 755, 29913, 2802, 3754, 3227, 562, 4678, 14554, 319, 29897, 320, 11725, 2802, 3754, 6353, 1758, 3686, 4678, 14554, 319, 29897, 353, 2802, 3754, 6353, 1758, 3686, 2119, 29909, 29918, 29900, 29897, 13, 29905, 11725, 2802, 3754, 2119, 29909, 29918, 29900, 29897, 353, 320, 6875, 741, 3752, 5231, 2802, 3754, 2119, 29912, 317, 648, 29900, 29876, 24289, 1836, 320, 355, 29912, 4990, 755, 29913, 13, 29905, 355, 29912, 8017, 29913, 13, 13, 29949, 332, 4340, 2050, 800, 526, 23228, 368, 2729, 373, 10244, 13, 29905, 999, 29912, 18118, 29889, 29941, 1836, 13, 29905, 463, 29912, 14648, 1012, 4775, 29912, 18118, 29889, 29946, 29913, 13, 12024, 779, 6224, 317, 29918, 29876, 1012, 10206, 3411, 648, 29876, 29922, 29896, 1042, 367, 263, 5665, 310, 6245, 873, 3342, 5764, 13, 11967, 16414, 12768, 29892, 7555, 1758, 2432, 5940, 2119, 29912, 317, 29918, 29876, 11606, 6484, 320, 7085, 29950, 29918, 29876, 1628, 13, 29938, 29876, 28842, 3319, 317, 29918, 29876, 1800, 29922, 29876, 29918, 29899, 3319, 317, 29918, 29876, 27394, 322, 1235, 6435, 317, 648, 29900, 29876, 930, 353, 426, 317, 6622, 648, 29900, 29876, 4229, 262, 2802, 1758, 7338, 5940, 3227, 29912, 317, 29918, 29876, 26253, 13, 29943, 332, 721, 29892, 1235, 7555, 12197, 2403, 29876, 353, 320, 741, 29883, 29950, 29918, 29876, 29892, 741, 6642, 3227, 29900, 29876, 1118, 741, 6642, 3227, 29896, 29876, 1012, 1042, 367, 385, 15311, 13, 9917, 653, 21954, 29873, 363, 6435, 317, 6622, 29918, 29876, 1042, 29871, 1316, 393, 6435, 317, 648, 29900, 29876, 930, 353, 13, 29912, 317, 6622, 29918, 29876, 1012, 29884, 561, 279, 1129, 265, 1266, 741, 29916, 3946, 5940, 2119, 741, 6642, 3227, 29900, 29876, 27394, 395, 29876, 320, 262, 320, 29940, 1628, 322, 1235, 13, 29938, 29924, 29918, 29876, 1194, 3822, 1262, 367, 278, 6590, 399, 1032, 29880, 740, 29889, 12808, 29892, 1235, 13, 4535, 7085, 29885, 14747, 29918, 29876, 29898, 29873, 5767, 395, 29876, 320, 262, 320, 29940, 1628, 367, 278, 426, 22619, 23183, 4226, 740, 29913, 7625, 515, 13, 29905, 4915, 29912, 29946, 29889, 29896, 29906, 29909, 29913, 491, 15270, 395, 29924, 1194, 3822, 1262, 491, 395, 29924, 29918, 29876, 1194, 3822, 4935, 960, 13, 4535, 12587, 648, 29876, 29905, 262, 29905, 29940, 1012, 7085, 29885, 14747, 29918, 29876, 29898, 29873, 29897, 529, 17501, 3411, 29938, 363, 263, 29889, 29872, 29889, 395, 29873, 320, 262, 320, 29934, 1628, 769, 13, 1454, 738, 29871, 1583, 29899, 328, 12090, 6081, 779, 14554, 29912, 29909, 1042, 310, 395, 29909, 29938, 3342, 491, 13, 29905, 4915, 29912, 29953, 29889, 29945, 29874, 1118, 607, 17150, 426, 278, 29913, 4195, 320, 4915, 29912, 29945, 29889, 29900, 1118, 278, 13, 370, 2929, 11579, 9126, 5633, 779, 14554, 29912, 29909, 2844, 562, 1042, 322, 395, 29909, 998, 562, 2403, 29900, 29938, 526 ]

1,332,863

36,864

ArXiv

-1