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https://e2e.ti.com/support/data-converters/f/73/t/882363	[ "If you have a related question, please click the \"Ask a related question\" button in the top right corner. The newly created question will be automatically linked to this question.\n\n• TI Thinks Resolved\n\n# ADS4129: How to calculate the filter's capacitance of the ADS4129's input\n\nHello!\n\nHow to calculate the filter's capacitance of the ADS4129's input!", null, "Thanks\n\n• User,\n\nYou should be able to figure this out using Figures 114 and 115 in the data sheet. These show the resistance value of Rin and the capacitance value of Cin over frequency.\n\nRegards,\n\nJim\n\n• In reply to jim s:\n\nHello！\n\nIn the input frequency is 250 MHZ, the input capacitance is about 3.6 PF, the input resistance is about 500 Ω，Can you tell me the relationship between the capacitance of r-c-r and the maximum input frequency？\n\nThanks\n\nUser,\n\nThe r-c-r is a 250MHz low pass filter. If your IF is going to be above this frequency, remove these parts from the EVM.\n\nRegards,\n\nJim\n\n• In reply to jim s:\n\nHello，\n\nI want to set the frequency 50MHz ,How should I calculate?\n\nThanks!" ]	[ null, "https://e2e.ti.com/resized-image/__size/2460x0/__key/communityserver-discussions-components-files/73/ADS4129.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90148795,"math_prob":0.8554414,"size":3018,"snap":"2020-10-2020-16","text_gpt3_token_len":652,"char_repetition_ratio":0.1217651,"word_repetition_ratio":0.035714287,"special_character_ratio":0.21570577,"punctuation_ratio":0.1130137,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97330844,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-07T14:38:16Z\",\"WARC-Record-ID\":\"<urn:uuid:f32f3a75-151c-4229-a8c6-63ead296dffa>\",\"Content-Length\":\"91542\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4f620eaf-5241-4e6a-bd55-ff9adca2c8ad>\",\"WARC-Concurrent-To\":\"<urn:uuid:902c742b-880b-4af2-92af-bea3fc192176>\",\"WARC-IP-Address\":\"104.95.177.102\",\"WARC-Target-URI\":\"https://e2e.ti.com/support/data-converters/f/73/t/882363\",\"WARC-Payload-Digest\":\"sha1:AAK5ZZRUIKXDL52XUNG26ANATCGFMWFU\",\"WARC-Block-Digest\":\"sha1:HMCNCKCICSC2XP4SLOBPMEQXYEF6H6WH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371799447.70_warc_CC-MAIN-20200407121105-20200407151605-00105.warc.gz\"}"}
https://deepai.org/publication/modeling-symmetric-positive-definite-matrices-with-an-application-to-functional-brain-connectivity	[ "", null, "", null, "", null, "", null, "Modeling Symmetric Positive Definite Matrices with An Application to Functional Brain Connectivity\n\nIn neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements of distributed neuron areas. An effective statistical model for functional connectivity and its changes over time is critical for better understanding the mechanisms of brain and various neurological diseases. To this end, we propose a matrix-log mean model with an additive heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. The heterogeneity of error terms is introduced specifically to capture the curved nature of the manifold. We then propose to use the local scan statistics to detect change patterns in the functional connectivity. Theoretically, we show that our procedure can recover all change points consistently. Simulation studies and an application to the Human Connectome Project lend further support to the proposed methodology.\n\nAuthors\n\n04/26/2019\n\nDiscovering Common Change-Point Patterns in Functional Connectivity Across Subjects\n\nThis paper studies change-points in human brain functional connectivity ...\n04/10/2019\n\nAnalyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matrices\n\nHuman brain functional connectivity (FC) is often measured as the simila...\n09/13/2020\n\nFunctional random effects modeling of brain shape and connectivity\n\nWe present a statistical framework that jointly models brain shape and f...\n01/26/2017\n\nRiemannian-geometry-based modeling and clustering of network-wide non-stationary time series: The brain-network case\n\nThis paper advocates Riemannian multi-manifold modeling in the context o...\n11/02/2018\n\nBayesian Hierarchical Modeling on Covariance Valued Data\n\nAnalysis of structural and functional connectivity (FC) of human brains ...\n01/28/2020\n\nWISDoM: a framework for the Analysis of Wishart distributed matrices\n\nWISDoM (Wishart Distributed Matrices) is a new framework for the charact...\n08/08/2020\n\nk-means on a log-Cholesky Manifold, with Unsupervised Classification of Radar Products\n\nWe state theoretical properties for k-means clustering of Symmetric Posi...\nThis week in AI\n\nGet the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.\n\n1 Introduction\n\nUnderstanding the functional brain connectivity is critical for understanding the fundamental mechanisms of brain, how it works, and various neurological diseases. It has attracted great interest recently. For instance, the Human Connectome Project investigates the structural and functional connectivity in order to diagnose cognitive abilities of individual subjects. Functional connectivity can be defined as temporary statistical dependence between spatially remote neurophysiological events (Friston, 2011), and has been observed to be dynamic in nature, even in the resting state (Hutchison et al., 2013). In practice, neuroscientist often characterize the dynamic functional connectivity by a series of symmetric positive definite (SPD) covariance matrices between functional measurements of neuronal activities across different regions in human brain. Establishing appropriate dynamic models is critical for understanding fundamental mechanisms of brain networks and has attracted much attention in neuroscience recently (Xu and Lindquist, 2015; Hutchison et al., 2013).\n\nHowever, little has been done in the statistics community for investigating dynamic changes of functional connectivity over time. The non-Euclidean structure of covariances has introduced significant challenges to the development of proper statistical models and their analysis. Indeed, all SPD matrices form a nonlinear Riemannian manifold, which is referred to as the SPD manifold. Motivated by the SPD manifold structure under the Log-Euclidean metric (Arsigny et al., 2007), we use the matrix logarithm to embed the SPD matrices into a Hilbert space – an Euclidean space up to a symmetric structure, to be concrete. We then model the transformed random SPD matrix using a mean model with an additive heterogeneous noise. The heterogeneous error depends on the tangent space of the mean SPD matrix and thus takes the curved structure of the SPD manifold into account. Our work refines the previous work by Chiu et al. (1996), whose model does not respect the original manifold structure.\n\nBuilt on this statistical model, we then propose to use a form of local scan statistics to detect multiple change patterns that are present in the functional brain connectivity over time. To the best of our knowledge, ours is the first work on the study of change point detection for SPD manifold-valued data. Although the proposed method is primarily motivated by discovering change patterns in fMRI, it has the potential to be applied to many other applications, such as diffusion tensor imaging\n\n(Dryden et al., 2009) and longitudinal data analysis (Daniels and Pourahmadi, 2002).\n\n1.1 Related Literature\n\nChange point detection with at most a single change point has been widely studied in the literature. When the distributions of the data are assumed to be known, score- or likelihood-based procedures can be applied (James et al., 1987). Bayesian and nonparametric approaches have also been proposed, see Carlstein et al. (1994) for a review. More recently, Chen and Zhang (2015)\n\nproposed a graph based approach for nonparametric change point detection. When there are multiple change points, the problem becomes much more complicated. Some popular approaches include the exhaustive search with Schwarz criterion\n\n(Yao, 1988), the circularly binary segmentation (Olshen et al., 2004) and the fused lasso method (Tibshirani and Wang, 2007). In genomics, these techniques have been exploited to study DNA copy number variations, see Olshen et al. (2004); Zhang and Siegmund (2007); Tibshirani and Wang (2007) among others. However, none of the above methods deals with Riemannian data.\n\nThere have been a few works on Riemannian data analysis in the statistics literature. For example, Schwartzman (2006)\n\nproposed several test statistics for comparing the means of two populations of symmetric positive definite matrices.\n\nZhu et al. (2009) developed a semiparametric regression model for symmetric definite positive matrices with Euclidean covariates. Later, Yuan et al. (2012) studied the local polynomial regression in the same setting. Steinke and Hein (2009) consider nonparametric regression between general Riemannian manifolds. Petersen and Müller (2017) developed a novel Fréchet regression approach for complex random objects with euclidean covariates. We believe our work will be a valuable addition to the literature.\n\n2 Geometric Interpretation\n\nWe briefly introduce , the Riemannian manifold consisting of all symmetric positive definite matrices, while we refer readers to the appendix for more details. A Riemannian manifold is a smooth manifold endowed with an inner product on the tangent space at each point , such that varies with smoothly. We consider the Log-Euclidean metric for the symmetric positive definite matrix manifold due to its computational tractability (Arsigny et al., 2007). Other metrics include the naive Frobenius metric which does not account for the curved nature of symmetric positive definite matrices and the affine invariant metric which is more difficult to compute (Terras, 2012).\n\nFor a manifold , we use to denote the tangent space at the base point . It can be shown that the tangent space at the identify matrix is the space of symmetric matrices, denoted by . For the Log-Euclidean metric, the inner product between on\n\nat the identity matrix\n\nis defined as . To define the inner product at a general point, we utilize the concept of differential maps. For a smooth transformation between two manifolds, its differential at , denoted by\n\n, is a linear map sending a tangent vector\n\nto a tangent vector . See Figure 1 for a graphical illustration. When both and are Euclidean submanifolds, the differential is the usual notion of differential of the function at , given by a Jacobian matrix. With this formalism, we consider the smooth map , where is the matrix logarithm, the inverse map of the matrix exponential. The matrix exponential of a matrix is defined as . The Riemannian metric at a general point is then defined as , where is a linear operator (Arsigny et al., 2007). The Riemannian exponential map under this metric is given by , where is the matrix exponential. Riemannian exponential maps are closely related to the intrinsic properties of a manifold, such as the geodesics and the Gauss curvature (Lee, 1997).", null, "Figure 1: Illustration of smooth map between manifolds and its differential.\n\n3 Methodology\n\n3.1 A Heterogeneous Matrix-log Mean Model\n\nSuppose we have collected a sequence of matrix-valued observations . We propose the following matrix-log mean model for investigating the mean changes of the data sequence\n\n logYi=logμi+log′μiεi, (1)\n\nwhere is the mean matrix, and is a mean-zero error term in . Here is a linear operator acting on . The noise term has mean zero, but the corresponding covariance depends on . Hence model (1) has a heterogeneous noise component.\n\nInterestingly, the heterogeneity of the noise terms makes use of the Riemannian manifold structure introduced in Section 2. Without using the geometric structure, one could simply apply the matrix logarithm first and then model the random SPD matrices ’s as\n\n logYi=logμi+ξi,\n\nwhere ’s are identically distributed random elements. This naive model, first introduced by Chiu et al. (1996)\n\n, misses the curved structure in the SPD manifold, and thus is less efficient for estimation and inference. Different from theirs, we introduce the location-dependent transformations\n\nin model (1) to respect the original manifold structure, because it turns this model into a geodesic/intrinsic mean model. To appreciate this, we take matrix exponential on both sides and find that\n\n Yi=exp(logμi+log′μiεi)=Expμiεi.\n\nIt can shown that is the minimizer to the following optimization program\n\n μi=\\argminS∈Sym+⋆(m)\\EEg2(S,Yi),\n\nwhere is the geodesic distance between and in Therefore, model (1) serves as an exact counterpart of the Euclidean mean model , where minimizes over .\n\nWe emphasize that the idea of using a matrix logarithm to model SPD matrices was first explored by Leonard and Hsu (1992) and Chiu et al. (1996)\n\n. However, their approach does not take the manifold structure into account. From the modeling perspective, our key contribution is that we establish a parametric model for SPD matrices that respects the original manifold structure.\n\nModel (1) provides a natural way to investigate change-point detection problems for SPD manifold-valued data. For this purpose, we further assume that there exist and such that if and otherwise. Elements in are called change points. Our goal is to detect based on the data sequence .\n\n3.2 Computational Details\n\nComputationally, it is more convenient to work with a basis of the space which is a dimensional Hilbert space under the Frobenius inner product. The Frobenius inner product between and is defined as . Let be an orthonormal basis of under this inner product. Then, for any , we can write with , and identify it with its coefficient vector , denoted by .\n\nIn this paper, we adopt the basis constructed in the following. Let be the matrix of zeros except the and entries, which are set to if , and otherwise. Since , we consider basis matrices ’s with . It can be checked that and if or , where denotes the Frobenius norm. Let , and then form an orthonormal basis for . We use this basis in our computation. Note that the results presented in the paper are identical for all bases.\n\nTo compute the matrix logarithm for\n\n, we first find a unitary matrix\n\nsuch that for a diagonal matrix . The matrices and\n\ncan be computed by eigendecomposition or singular value decomposition (SVD). Then\n\nwith .\n\nTo compute the matrix representation of the linear differential operator for a given symmetric positive definite matrix with respect to the basis , we first note that (Arsigny et al., 2007). Therefore, once we have the matrix representation of the linear operator with respect to the basis , then will be the matrix representation of , noting that the non-singularity of everywhere implies the invertibility of . If is the coefficient vector (viewed as a column vector) of with respect to a chosen basis, then it is seen that the is given by the matrix concatenated by column vectors . Therefore, the problem boils down to the computation of\n\n exp′logμϕj=∞∑k=11k!k−1∑ℓ=0(logμ)k−ℓ−1⋅ϕj⋅(logμ)ℓ.\n\nNumerically, the above series is truncated at a sufficiently large . Note that when , we have specially .\n\n3.3 A Local Scan Procedure\n\nRoughly speaking, an ideal statistic for detecting change patterns, or change points, at a position should directly relate to the possibility that is a change point. The statistic at the position we proposed is a locally weighted average of the transformed ’s near :\n\n G(x,h)=n∑i=1wi(h)−−−→logYi,\n\nwhere if , if , and otherwise. We remind the readers that denotes the coefficient vector of the matrix with respect to a basis . The defined above is constructed based on data points within a local window of size around the point . The intuition is that, if there is no change point within the window , then has mean zero and is close to zero. Otherwise, if is large, then is likely to be a change point. In particular, points that locally maximize have a high chance of being a change point. We say that is a local maximizer if for all . The set of local maximizers is denoted by . Suppose , where is the number of elements in . For a given threshold , we then estimate by , and is estimated by the cardinality of .\n\nHowever, the above procedure for estimating depends on the unknown parameter . In practice, we propose a data-driven alternative based on the -fold cross validation to select the number of change points. Suppose that are change points, which divided all time points into segments. Within each segment, time points are randomly split into partitions. The sample mean of a segment is estimated by using data from any partitions within that segment, and the validation error is evaluated on the rest one partition. The cross validation error of the segment is defined to be the sum of validation errors from the partitions, while the total cross-validation error is the sum of cross-validation errors across all segments. Formally, the total cross-validation error is defined as\n\n CV(k)=k+1∑q=1K∑p=1∑i∈Pq,p(ˆlogμq,p−−−−→logYi)T(ˆlogμq,p−−−−→logYi),\n\nwhere is the th partition of the th segment, and . Here denotes the time points in the th segment but not in the partition and the cardinality of the set . The integer that minimizes is chosen as an estimate of . We then estimate the locations of change points using the proposed scan statistics.\n\n4 Asymptotic Theory\n\nA random vector is called a subgaussian vector with parameter if , and for all ,\n\n E[exp(aT(ξ−ν))]≤exp(∥a∥2σ2/2).\n\nWe say that a random element in is subgaussian if its coefficient vector with respect to the orthonormal basis is subgaussian. One can easily check that this definition is independent of the choice of the orthonormal basis of . Below we shall assume is subgaussian with parameter . This might depend on and thus the linear operator and its matrix representation . For example, one might conceive of i.i.d. subgaussian random elements and applying to , where different transformations result in different distributions of\n\n. Although subgaussianity is well preserved by linear transformations, the subgaussian parameter might differ after transformation. For example, one can show that, if\n\nis subgaussian with a parameter , then is subgaussian, but with a parameter . In this case, might quantify the magnitude, measured by , of the transformation .\n\nTo derive the sure coverage property of the proposed procedure, we define , , and , where we conventionally denote and . We need the following assumption. The quantities , , and satisfy that . Here, characterizes the variability of ’s over all time points. The quantity characterizes the strength of the weakest signal of change points, while indicates the separability of change points. Intuitively, when and are small, no method would succeed in recovering all change points. Recall that denotes the dimension of the space . It is seen that detection of change points becomes harder for higher dimensional matrices, i.e., a larger , since stronger signal (larger ) or better separation of change points (larger ) is required to make the inequality in the above assumption hold.\n\nNow we establish the sure coverage property of the proposed procedure, that is, the union of the intervals selected by our procedure recovers all change points with probability going to\n\n. An nonasymptotic probability bound is also derived, with explicit dependence on the sample size . We use to denote that for all . We are ready to state the main theorem of this paper, whose proof is deferred to the appendix. Suppose that Assumption 4 holds. If and , then\n\n Pr(^J =J,J⊂ˆJ±h)→1, as n→∞.\n\nWe emphasize here that the dimension does not need to be assumed to be fixed and could potentially diverge to infinity as long as Assumption 4 holds.\n\n5 Simulation Studies\n\nIn this section, we examine the empirical performance of our method. We generate data according to model (1). In the first example, we consider different combinations of such that , , , respectively. When , we set , and . When , we set for , where , , , , , and . For the symmetric random noise, we first sample the coefficient vector from distribution , then combine it with the basis to generate the noise . Our second example is concerned with a larger by setting that , , , .\n\nChoosing the optimal bandwidth is usually a difficult task for change point problems, see, for example, Niu and Zhang (2012) for a detailed discussion. Intuitively, when there is only one change point in the interval , the larger is, the more powerful the scan statistic is. But when the bandwidth gets too large, the interval might contain multiple change points. Therefore we need to choose bandwidth carefully. In our simulations, we found that the performance of the procedure is relatively robust to the choice of the bandwidth as long as the bandwidth is not too large, and works relatively well in our case. We use the proposed cross validation technique to select the number of change points. We run 100 repetitions of Monte Carlo studies. For each run, we calculate the estimated number of change points and the locations of the change points. We report the frequencies of the three cases: , and , the mean of the number of change points detected, and the sure coverage probability for each of the change point. We also compare two methods that are frequently used in practice. The first one vectorizes the response without considering any manifold structure, which results in a -dimensional vector. We denote this method as “Vector”. The other one also adopts the vectorization idea, but additionally takes the symmetric information into account, yielding a -dimensional vector. We use “Symmetric” to denote this method. The results are summarized in Tables 1 and 2.\n\nAs indicated by the results, our proposed method performs better than the comparison methods in terms of the percentage of correctively recovering the number of change points, in all cases. Additionally, when , all the methods presented here can detect the second change point very well. But for the first one, our method achieves a higher sure coverage probability. When , our method achieves a higher sure coverage probability for all the change points. These results suggest the importance of considering the geometric structure of the Riemannian data, at least, in change point detection problems.\n\n6 An Application to the Human Connectome Project\n\nWe apply the proposed methodology to the social cognition task related fMRI data from Human Connectome Project Dataset, which includes behavioral and 3T MR imaging data from 970 healthy adult participants collected from 2012 to spring 2015. We focus on the 850 subjects out of the 970 which have the social cognition task related fMRI data. Participants were presented with short video clips (20 seconds) of objects (squares, circles, triangles) that either interacted in some way, or moved randomly on the screen (Castelli et al., 2000; Wheatley et al., 2007). There were 5 video blocks (2 Mental and 3 Random in one run, 3 Mental and 2 Random in the other run) in the task run.\n\nWe use the “Desikan-Killiany” atlas (Desikan et al., 2006) to divide the brain into 68 regions of interest. Figure 2(a) shows the “Desikan-Killiany” parcellation of the cortical surface in the left and right hemisphere. We pick eight possible regions that are related to the social task, that are the left and right part of superior temporal, inferior parietal, temporal pole and precuneus (Green et al., 2015). These eight regions of interest are highlighted in yellow in Figure 2(b). For each subject, the fMRI data are recorded on 274 evenly spaced time points, one per 0.72 seconds. We use a moving local window of size 100 to calculate the cross covariance between these eight regions, which results in 175 cross covariance matrices with dimensions . We then apply the proposed method to detect change points in this sequence of cross covariance matrices with bandwidth set to be .\n\nWe apply the method to all the subjects, and report the locations of change points detected for each subject. In Table 3, we have summarized the count and percentage of the number of change points detected for all the subjects. The mean number of change points detected among all the subjects is . This result matches the physiology well since there are 5 video blocks in the task design, with changes at the time points , , and respectively. To further validate the proposed methodology, we pick up all those subjects with four change points, and calculate the mean locations respectively. The means are , , , , which are fairly close to the task block changes. A more interesting observation is that the lags (4.6s, 2.0s, 1.7s and -1.5s) are becoming shorter and shorter: the last time point even precedes the designed time point. This, to our understanding, witnesses the powerfulness of human brains for learning the change patterns.", null, "Figure 2: Panel (a): the “Desikan-Killiany” parcellation of the cortical surface in left and right hemisphere. Panel (b): the eight regions of interest.\n\n7 Discussion\n\nIn this paper we propose an additive matrix-log mean model with a heterogeneous noise for modeling random symmetric positive definite matrices that lie in a Riemannian manifold. The heterogeneous noise part takes account the manifold structure of the original symmetric positive definite matrices. Built upon this model, we then propose a scan statistic to perform multiple change point detection. Theoretical studies and numerical examples lend further support to our proposed methodology.\n\nOur proposed methodology replies on the assumption that the collected samples ’s are independent. Independence is an ideal assumption that may be violated in some settings. However, this assumption allows us to conduct theoretical analysis, which also produce results that could be useful when the assumption is violated. We will pursue the change-point detection problems under dependence for Riemannian data in future work.\n\nReferences\n\n• Arsigny et al. (2007) Arsigny, V., Fillard, P., Pennec, X. and Ayache, N. (2007). Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM Journal of Matrix Analysis and Applications 29 328–347.\n• Carlstein et al. (1994) Carlstein, E. G., Müller, H.-G. and Siegmund, D. (1994). Change-point problems. Institute of Mathematical Statistics.\n• Castelli et al. (2000) Castelli, F., Happé, F., Frith, U. and Frith, C. (2000). Movement and mind: a functional imaging study of perception and interpretation of complex intentional movement patterns. NeuroImage 12 314–325.\n• Chen and Zhang (2015) Chen, H. and Zhang, N. (2015). Graph-based change-point detection. The Annals of Statistics 43 139–176.\n• Chiu et al. (1996) Chiu, T. Y., Leonard, T. and Tsui, K.-W. (1996). The matrix-logarithmic covariance model. Journal of the American Statistical Association 91 198–210.\n• Daniels and Pourahmadi (2002) Daniels, M. J. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data. Biometrika 89 553–566.\n• Desikan et al. (2006) Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P. and Hyman, B. T. (2006). An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31 968–980.\n• Dryden et al. (2009) Dryden, I. L., Koloydenko, A. and Zhou, D. (2009). Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. The Annals of Applied Statistics 3 1102–1123.\n• Fletcher (2013) Fletcher, P. T. (2013). Geodesic regression and the theory of least squares on Riemannian manifolds.\n\nInternational Journal of Computer Vision\n\n105 171–185.\n• Friston (2011) Friston, K. J. (2011). Functional and effective connectivity: a review. Brain Connectivity 1 13–36.\n• Green et al. (2015) Green, M. F., Horan, W. P. and Lee, J. (2015). Social cognition in schizophrenia. Nature Reviews. Neuroscience 16 620–631.\n• Hsu et al. (2012) Hsu, D., Kakade, S. and Zhang, T. (2012). A tail inequality for quadratic forms of subgaussian random vectors. Electronic Communications in Probability 17 1–6.\n• Hutchison et al. (2013) Hutchison, R. M., Womelsdorf, T., Allen, E. A., Bandettini, P. A., Calhoun, V. D., Corbetta, M., Della Penna, S., Duyn, J. H., Glover, G. H. and Gonzalez-Castillo, J. (2013). Dynamic functional connectivity: promise, issues, and interpretations. NeuroImage 80 360–378.\n• James et al. (1987) James, B., James, K. L. and Siegmund, D. (1987). Tests for a change-point. Biometrika 74 71–83.\n• Lee (1997) Lee, J. M. (1997). Riemannian Manifolds: An Introduction to Curvature. Springer-Verlag, New York.\n• Leonard and Hsu (1992) Leonard, T. and Hsu, J. S. (1992). Bayesian inference for a covariance matrix. The Annals of Statistics 1669–1696.\n• Niu and Zhang (2012) Niu, Y. S. and Zhang, H. (2012). The screening and ranking algorithm to detect DNA copy number variations. The Annals of Applied Statistics 6 1306–1326.\n• Olshen et al. (2004) Olshen, A. B., Venkatraman, E., Lucito, R. and Wigler, M. (2004). Circular binary segmentation for the analysis of array-based dna copy number data. Biostatistics 5 557–572.\n• Petersen and Müller (2017) Petersen, A. and Müller, H.-G. (2017). Fréchet regression for random objects with Euclidean predictors. The Annals of Statistics to appear.\n• Schwartzman (2006) Schwartzman, A. (2006). Random ellipsoids and false discovery rates: Statistics for diffusion tensor imaging data. Ph.D. thesis, Stanford University.\n• Steinke and Hein (2009) Steinke, F. and Hein, M. (2009). Non-parametric regression between manifolds. In Advances in Neural Information Processing Systems.\n• Terras (2012) Terras, A. (2012). Harmonic analysis on symmetric spaces and applications II. Springer Science & Business Media.\n• Tibshirani and Wang (2007) Tibshirani, R. and Wang, P. (2007). Spatial smoothing and hot spot detection for cgh data using the fused lasso. Biostatistics 9 18–29.\n• Wheatley et al. (2007) Wheatley, T., Milleville, S. C. and Martin, A. (2007). Understanding animate agents: distinct roles for the social network and mirror system. Psychological Science 18 469–474.\n• Xu and Lindquist (2015) Xu, Y. and Lindquist, M. A. (2015). Dynamic connectivity detection: an algorithm for determining functional connectivity change points in fmri data. Frontiers in Neuroscience 9.\n• Yao (1988) Yao, Y.-C. (1988). Estimating the number of change-points via Schwarz’ criterion. Statistics & Probability Letters 6 181–189.\n• Yuan et al. (2012) Yuan, Y., Zhu, H., Lin, W. and Marron, J. S. (2012). Local polynomial regression for symmetric positive definite matrices. Journal of the Royal Statistical Society: Series B 74 697–719.\n• Zhang and Siegmund (2007) Zhang, N. R. and Siegmund, D. O. (2007). A modified bayes information criterion with applications to the analysis of comparative genomic hybridization data. Biometrics 63 22–32.\n• Zhu et al. (2009) Zhu, H., Chen, Y., Ibrahim, J. G., Li, Y., Hall, C. and Lin, W. (2009). Intrinsic regression models for positive-definite matrices with applications to diffusion tensor imaging. Journal of the American Statistical Association 104 1203–1212.\n\nAppendix S.1 Preliminary\n\nIn this section, we further discuss the smooth and Riemannian manifold. For a comprehensive treatment on these subjects, readers are referred to the introductory book by Lee (1997).\n\nA smooth manifold is a differentiable manifold with all transition maps being -differentiable. Associated with each point on the manifold , there exists a linear space called the tangent space at the base point\n\n. Each element in the tangent space is called a tangent vector. For a manifold that is a submanifold of a Euclidean space, the tangent space at a point can be geometrically visualized as the hyperplane tangent to that point, while tangent vectors are visualized as Euclidean vectors tangent to the manifold at that point; see Figure\n\nS.3 for an illustration. It is emphasized that tangent vectors at different base points are different, despite that the vectors might point to the same direction. Thus, a tangent vector always implicitly comes with a base point. For Euclidean submanifolds, a tangent vector at a point can also be algebraically interpreted as a directional derivative at , such that for all with denoting the collection of real-valued smooth functions defined on the manifold . Observe that is a derivation at , which satisfies the Leibniz rule,\n\n Dv(fg)=g(x)(Dvf)+f(x)(Dvg),\n\nfor any and , where denotes the pointwise product of functions. This allows one to generalize the concept of tangent vector as directional derivative to non-Euclidean manifolds, by defining tangent vectors at as derivations at , and tangent space at as the space of derivations at . A convenient way to perceive the derivation represented by a tangent vector is to treat as a linear functional that maps into .\n\nFor a smooth transformation that maps points on a manifold to points on the manifold , its differential at , denoted by , is a linear map sending a tangent vector to a tangent vector , such that the derivation corresponding to the tangent vector at the point is depicted by\n\n Dφ′x(v):C∞(M)→R,s.t.∀f∈C∞(M):Dφ′x(v)f=Dv(f∘φ),\n\nwhere denotes the composition of functions. When both and are Euclidean submanifolds, the differential is the usual notion of differential of the function at , given by a Jacobian matrix. Specially, when is an interval of the real line, the tangent space at each is the whole real line . In this case, is often called a (parameterized) smooth curve on , and is denoted by which is the derivative of the curve at time . Here, to properly decode the notation , recall that is a map sending a tangent vector of a manifold to a tangent vector of another manifold, and for the special manifold , the real number can be viewed as a tangent vector at . Geometrically and intuitively, is a vector tangent to the curve at time , as illustrated in Figure S.3.\n\nA Riemannian manifold is a smooth manifold endowed with an inner product on the tangent space at each point , such that varies with smoothly. The collection of such inner products is often called the Riemannian metric tensor, or simply Riemannian metric. One can show that, the metric tensor induces a distance function that turns the manifold into a metric space. A geodesic is a smooth curve on the manifold such that for any sufficiently small segment, the segment is the unique smooth curve with the minimal length among all smooth curves connecting the two endpoints of the segment. Every smooth curve on the manifold can be parameterized by a smooth map from an interval in to the manifold. For any , there exists a unique geodesic such that and . Then the exponential map at , denoted by , is defined by . For example, one can verify that for the unit circle , for and , the defining geodesic for the Riemannian exponential map is , as and . Thus, . A graphical illustration of the Exp map is given in Figure S.3.", null, "Figure S.3: Geometric illustration of tangent vector, tangent space, curve and exponential map. γ(t) with γ(0)=x and γ(1)=q is a smooth curve on M. v is a tangent vector at x and also tangent to the curve γ at t=0, i.e. v=γ′(0). If in addition γ(t) is a geodesic, then q=γ(1)=Expx(v).\n\nFor the Log-Euclidean metric, at the identity matrix , it is defined as for , the Frobenius inner product on . In order to define metric at other points, the following group structure is considered. Define , where and are the matrix exponential and logarithm respectively. The operation turns into a group. Now we define the left-translation operator for . As shown in Arsigny et al. (2007), is a smooth map from to itself. Thus, its differential at is a linear map that sends tangent vectors at to tangent vectors at . For instance, the linear operator maps tangent vectors at to tangent vectors at the identity. Given this property, we can “translate” the metric at the identity matrix to all points by the left-translation operator . More specifically, the Log-Euclidean metric at any is defined by for all , where the last identity is due to (Arsigny et al., 2007). The Riemannian exponential map under this metric is given by .\n\nAppendix S.2 Proofs\n\nLet , and , where denotes the collection of flat points, i.e., if and only if for all . Then holds under the event .\n\nProof of Lemma s.2.\n\nThe proof can be found in Lemma 3 of Niu and Zhang (2012). ∎\n\nProof of Theorem 4.\n\nWe first note the following facts about subgaussian random vectors that will be used in the sequel.\n\n• If are independent and subgaussian with parameters , respectively, then is a subgaussian random vector with parameters and .\n\n• If is a subgaussian random vector with a parameter and is a matrix, then is a subgaussian random vector with parameters and .\n\nA point is called a -flat point (or simply flat point if is clear from the context) if for all . For a flat point , has mean zero and also is a subgaussian random vector with parameters and . Here, we recall that is subgaussian with the parameter . For a change-point , similarly, is subgaussian with parameter .\n\nLet and . For a flat point , we first observe that\n\n Pr{∥G(x,h)∥22>an}≤e−tn=1nlogn\n\naccording to Theorem 1 of Hsu et al. (2012). According to Assumption 1 and the choice of and , we have and thus\n\n Pr{∥G(x,h)∥22>ρ}≤Pr{∥G(x,h)∥22>an}≤1nlogn.\n\nSimilarly, from Assumption 1 we deduce that and . Thus, for a change point ,\n\n Pr{∥G(τ,h)∥2<√ρ} ≤Pr{∥G(τ,h)∥2<∥δτ∥2−√an} ≤Pr{\|∥G(τ,h)∥2−∥δτ∥2\|>√an} ≤Pr{∥G(τ,h)−δτ∥22>an} ≤1nlogn,\n\nor equivalently,\n\n Pr{∥G(τ,h)∥22<ρ}≤1nlogn.\n\nNext, we bound the probabilities of events defined in Lemma S.2.\n\n Pr{En(h,ρ)} ≥1−Pr[{An(h,ρ)}c]−Pr[{Bn(h,ρ)}c]. (S.2)\n\nNow, note that\n\n Pr[{An(h,ρ)}c] =Pr{∃x∈F:∥G(x,h)∥22>ρ}≤∑x∈FPr{∥G(x,h)∥22>ρ} ≤∑x∈F1nlogn≤n(1nlogn)=1logn. (S.3)\n\nSimilarly,\n\n Pr[{Bn(h,ρ)}c] =Pr{∃τ∈J:∥G(τ,h)∥22<ρ}≤∑τ∈JPr{∥G(τ,h)∥22<ρ} ≤∑τ∈J1nlogn≤nnlogn=1logn. (S.4)\n\nCombining (S.2), (S.3) and (S.4), we conclude that\n\n Pr{En(h,ρ)}≥1−2logn→1. (S.5)\n\nFinally, the theorem follows from Lemma S.2. ∎" ]	[ null, "https://deepai.org/static/images/logo.png", null, "https://deepai.org/static/images/twitter-icon-blue-circle.svg", null, "https://deepai.org/static/images/linkedin-icon-blue-circle.svg", null, "https://deepai.org/static/images/discord-icon-blue-circle.svg", null, "https://deepai.org/publication/None", null, "https://deepai.org/publication/None", null, "https://deepai.org/publication/None", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8764119,"math_prob":0.96304417,"size":33492,"snap":"2022-05-2022-21","text_gpt3_token_len":8019,"char_repetition_ratio":0.1367654,"word_repetition_ratio":0.051338065,"special_character_ratio":0.25244835,"punctuation_ratio":0.16726512,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9956634,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-22T08:09:04Z\",\"WARC-Record-ID\":\"<urn:uuid:d29cf38c-c517-4ac1-8b1e-e854ef67f8fa>\",\"Content-Length\":\"996256\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a4c1bd2b-b9e7-46f9-b368-6f68df2c75be>\",\"WARC-Concurrent-To\":\"<urn:uuid:3a8e1c9d-0d8a-46d2-ba92-4bb16664c4c4>\",\"WARC-IP-Address\":\"44.235.123.242\",\"WARC-Target-URI\":\"https://deepai.org/publication/modeling-symmetric-positive-definite-matrices-with-an-application-to-functional-brain-connectivity\",\"WARC-Payload-Digest\":\"sha1:YXHNMEOU5EES42M3Y6FEGS5OC6O3VX3J\",\"WARC-Block-Digest\":\"sha1:KXDFCH4JWJZEG3ZL5OIWFIKRQ4SQJCPP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303779.65_warc_CC-MAIN-20220122073422-20220122103422-00068.warc.gz\"}"}
https://pslab.io/blog/pslab-communication-function-calls/	[ "# PSLab Communication Function Calls\n\nInterfacing with the hardware of PSLab, fetching the data and plotting it is very simple and straight forward. Various sensors can be connected to PSLab and data can be fetched with a simple python code as shown in the following example…\n\n```>>> from PSL import sciencelab\n>>> I = sciencelab.connect() # Initializing: Returns None if device isn't found. The initialization process connects to tty device and loads calibration values.```\n```# An example function that measures voltage present at the specified analog input\n>>> print I.get_average_voltage('CH1')```\n```# An example to capture and plot data\n>>> I.set_gain('CH1', 3) # set input CH1 to +/-4V range\n>>> I.set_sine1(1000) # generate 1kHz sine wave on output W1\n>>> x,y = I.capture1('CH1', 1000, 10) # digitize CH1 1000 times, with 10 usec interval\n>>> plot(x,y)\n>>> show()\n```\n```# An example function to get data from magnetometer sensor connected to PSLab\n>>> from PSL.SENSORS import HMC5883L #A 3-axis magnetometer >>> M = HMC5883L.connect() >>> Gx,Gy,Gz = M.getRaw() ```\n\nThe module sciencelab.py contains all the functions required for communicating with PSLab hardware. It also contains some utility functions. The class ScienceLab() contains methods that can be used to interact with the PSLab.\n\nAfter initiating this class, all the features built into the device can be accessed using various function calls.\n\nCapture1 : for capturing one trace\n\n`capture1(ch, ns, tg)`\n\nArguments\n\n• ch : Channel to select as input. [‘CH1′..’CH3′,’SEN’]\n• ns : Number of samples to fetch. Maximum 10000\n• tg : Time gap between samples in microseconds\n`#Example >>> x,y = I.capture1('CH1', 1000, 10) # digitize CH1 1000 times, with 10 usec interval`\n\nReturns : Arrays X(timestamps),Y(Corresponding Voltage values)\n\nCapture2 : for capturing two traces\n\n`capture2(ns, tg, TraceOneRemap='CH1')`\n\nArguments\n\n• ns : Number of samples to fetch. Maximum 5000\n• tg : Time gap between samples in microseconds\n• TraceOneRemap : Choose the analogue input for channel 1 (Like MIC OR SEN). It is connected to CH1 by default. Channel 2 always reads CH2.\n```#Example\n>>> x,y1,y2 = I.capture2(1600,1.75,'CH1') # digitize CH1 and CH2, 1600 times, with 1.75 usec interval```\n\nReturns: Arrays X(timestamps),Y1(Voltage at CH1),Y2(Voltage at CH2)\n\nCapture4 : for capturing four taces\n\n`capture4(ns, tg, TraceOneRemap='CH1')`\n\nArguments\n\n• ns: Number of samples to fetch. Maximum 2500\n• tg : Time gap between samples in microseconds. Minimum 1.75uS\n• TraceOneRemap : Choose the analogue input for channel 1 (Like MIC OR SEN). It is connected to CH1 by default. Channel 2 always reads CH2, channel 3 always reads CH3 and MIC is channel 4 (CH4)\n```#Example\n>>> x,y1,y2,y3,y4 = I.capture4(800,1.75) # digitize CH1-CH4, 800 times, with 1.75 usec interval```\n\nReturns: Arrays X(timestamps),Y1(Voltage at CH1),Y2(Voltage at CH2),Y3(Voltage at CH3),Y4(Voltage at CH4)\n\nCapture_multiple : for capturing multiple traces\n\n`capture_multiple(samples, tg, args)`\n\nArguments\n\n• samples: Number of samples to fetch. Maximum 10000/(total specified channels)\n• tg : Time gap between samples in microseconds.\n• args : channel names\n```# Example\n>>> from pylab import \n>>> I=interface.Interface()\n>>> x,y1,y2,y3,y4 = I.capture_multiple(800,1.75,'CH1','CH2','MIC','SEN')\n>>> plot(x,y1)\n>>> plot(x,y2)\n>>> plot(x,y3)\n>>> plot(x,y4)\n>>> show()```\n\nReturns: Arrays X(timestamps),Y1,Y2 …\n\nCapture_fullspeed : fetches oscilloscope traces from a single oscilloscope channel at a maximum speed of 2MSPS\n\n`capture_fullspeed(chan, amples, tg, args)`\n\nArguments\n\n• chan: channel name ‘CH1’ / ‘CH2’ … ‘SEN’\n• tg : Time gap between samples in microseconds. minimum 0.5uS\n• args : specify if SQR1 must be toggled right before capturing. ‘SET_LOW’ will set it to 0V, ‘SET_HIGH’ will set it to 5V. if no arguments are specified, a regular capture will be executed.\n```# Example\n>>> from pylab import \n>>> I=interface.Interface()\n>>> x,y = I.capture_fullspeed('CH1',2000,1)\n>>> plot(x,y)\n>>> show()```\n\nReturns: timestamp array ,voltage_value array\n\nSet_gain : Set the gain of selected PGA\n\n`set_gain(channel, gain)`\n\nArguments\n\n• channel: ‘CH1’ , ‘CH2’\n• gain : (0-7) -> (1x,2x,4x,5x,8x,10x,16x,32x)\n\nNote: The gain value applied to a channel will result in better resolution for small amplitude signals.\n\n```# Example\n>>> I.set_gain('CH1',7) #gain set to 32x on CH1\n```\n\nGet_average_voltage : Return the voltage on the selected channel\n`get_average_voltage(channel_name, kwargs)`\nArguments\n\n• channel_name: ‘CH1’,’CH2’,’CH3’, ‘MIC’,’IN1’,’SEN’\n• kwargs : Samples to average can be specified. eg. samples=100 will average a hundred readings\n```# Example\n>>> print I.get_average_voltage('CH4')\n1.002```\n\nGet_freq : Frequency measurement on IDx. Measures time taken for 16 rising edges of input signal. returns the frequency in Hertz\n\n`get_average_voltage(channel='Fin', timeout=0.1)`\nArguments\n\n• channel : The input to measure frequency from. ‘ID1’ , ‘ID2’, ‘ID3’, ‘ID4’, ‘Fin’\n• timeout : This is a blocking call which will wait for one full wavelength before returning the calculated frequency. Use the timeout option if you’re unsure of the input signal. returns 0 if timed out\n```# Example\n>>> I.sqr1(4000,25)\n>>> print I.get_freq('ID1')\n4000.0```\n\nReturn float: frequency\n\nGet_states : Gets the state of the digital inputs. returns dictionary with keys ‘ID1’,’ID2’,’ID3’,’ID4’\n`get_states()`\n```#Example\n>>> print get_states()\n{'ID1': True, 'ID2': True, 'ID3': True, 'ID4': False}\n```\n\nGet_state : Returns the logic level on the specified input (ID1,ID2,ID3, or ID4)\n`get_state(input_id)`\nArguments\n\n• input_id : The input channel ‘ID1’ -> state of ID1 ‘ID4’ -> state of ID4\n```#Example\n>>> print I.get_state(I.ID1)\nFalse\n```\n\nSet_state : Set the logic level on digital outputs SQR1,SQR2,SQR3,SQR4\n`set_state(kwargs)`\nArguments\n\n• kwargs : SQR1,SQR2,SQR3,SQR4 states(0 or 1)\n```#Example\n>>> I.set_state(SQR1=1, SQR2=0) #sets SQR1 HIGH, SQR2 LOw, but leave SQR3,SQR4 untouched.\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6409448,"math_prob":0.8928871,"size":5896,"snap":"2020-10-2020-16","text_gpt3_token_len":1718,"char_repetition_ratio":0.11744738,"word_repetition_ratio":0.14752252,"special_character_ratio":0.3156377,"punctuation_ratio":0.19858782,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97259873,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-25T09:52:58Z\",\"WARC-Record-ID\":\"<urn:uuid:3cc87679-a2e0-4cc9-8559-09fad1b54706>\",\"Content-Length\":\"142599\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d3285f4f-6da2-469c-83f4-e24925ba7ceb>\",\"WARC-Concurrent-To\":\"<urn:uuid:4f4a3543-9046-420a-8d7e-38916a9f4a66>\",\"WARC-IP-Address\":\"104.18.33.23\",\"WARC-Target-URI\":\"https://pslab.io/blog/pslab-communication-function-calls/\",\"WARC-Payload-Digest\":\"sha1:7FOWRHIRIC257PRC5SZZHFN5M67TVF2C\",\"WARC-Block-Digest\":\"sha1:YTXGH3RFXV3X6DXGFMCEM7UYIKFVXONN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875146064.76_warc_CC-MAIN-20200225080028-20200225110028-00477.warc.gz\"}"}
https://quabr.com/72069131/what-does-the-confusion-matrix-line-of-code-do	[ "# What does the confusion_matrix line of code do?\n\n``````from sklearn.pipeline import Pipeline\nmodel = Pipeline([('vectorizer',tvec),('classifier',clf2)])\nmodel.fit(IV_train, DV_train)\nfrom sklearn.metrics import confusion_matrix\npredictions = model.predict(IV_test)\nconfusion_matrix(predictions, DV_test)\n``````\n\nI want to know what the confusion matrix line in the code does." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7007121,"math_prob":0.92562896,"size":17129,"snap":"2022-40-2023-06","text_gpt3_token_len":4343,"char_repetition_ratio":0.10306569,"word_repetition_ratio":0.057983942,"special_character_ratio":0.2731041,"punctuation_ratio":0.18310301,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99319637,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-26T07:16:18Z\",\"WARC-Record-ID\":\"<urn:uuid:f2e02723-883f-4c4f-bd45-0c72637c930d>\",\"Content-Length\":\"42540\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:86bf44c6-f983-4226-9660-88587679d3ea>\",\"WARC-Concurrent-To\":\"<urn:uuid:777190e1-c935-416a-8cde-e7ec78131618>\",\"WARC-IP-Address\":\"5.9.10.113\",\"WARC-Target-URI\":\"https://quabr.com/72069131/what-does-the-confusion-matrix-line-of-code-do\",\"WARC-Payload-Digest\":\"sha1:S5NGKCVHSJFWP7I6UIZZKMA3EYAWJXWM\",\"WARC-Block-Digest\":\"sha1:KNGKLFBUWY6FTDQQ26OC7FAFTEEXKS47\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030334802.16_warc_CC-MAIN-20220926051040-20220926081040-00617.warc.gz\"}"}
https://mathoverflow.net/questions/35812/bounds-on-remainder-term-of-power-series-of-elementary-functions	[ "# Bounds on remainder term of power series of elementary functions\n\nThis is mainly a question about the remainder term of power series for elementary functions.\n\nI'm very interested in aspects of calculating or computing elementary operations and functions, by which I mean:\n\n• trigonometric: $\\sin$, $\\cos$, $\\tan$\n• inverse trig.: $\\sin^{-1}$, $\\cos^{-1}$, $\\tan^{-1}$\n• log and exponential: $\\ln$, $\\exp$\n• hyperbolic: $\\sinh$, $\\cosh$, $\\tanh$\n• inverse hyp.: $\\sinh^{-1}$, $\\cosh^{-1}$, $\\tanh^{-1}$\n• powers, reciprocation, $\\sqrt{\\ \\ \\ }$\n\nperhaps also:\n\n• gamma function: $\\Gamma$\n• and a few other important functions\n\nThere are many contexts (of calculation). For example:\n\n• real versus complex arguments\n• known, fixed precision versus variable precision\n• numerical versus symbolic\n\nThere are many approaches and techniques available too. For example:\n\n• power series expansions and polynomial approximations\n• use of relationships between the functions\n• use of periodic or similar properties to shrink the domain\n• lookup tables and interpolation\n• CORDIC (used within some hand calculators I believe)\n• exact methods\n• interval or other error-tracking methods\n\nSome good references to certain aspects include:\n\nThe main gap in my knowledge is in finding bounds for the error or remainder term in partial power series expansions of certain of the above functions. Some are fairly simple to determine, whilst others seem to be awkward.\n\nAny pointers on this matter would be much appreciated.\n\nLikewise for any further references on any other aspects of or techniques for calculating elementary functions.\n\n• Two things: 1. you might be interested in this book: personales.unican.es/segurajj/book ; and 2. don't just confine yourself to implementing things with only power series, they are almost always only effective within a restricted range of arguments (unless your functions of interest satisfy useful reduction formulae). As might be already obvious to you, the easiest bound for the truncation error of a power series is the first neglected term. – J. M. isn't a mathematician Aug 17 '10 at 1:27\n• You've listed a huge load of references, but not said in detail exactly why these are not enough to solve your problems. I think a detailed question would be helpful; can you give a particular power series for which you cannot determine a good estimate for the remainder, by any of the standard methods you've listed? – Zen Harper Aug 17 '10 at 1:32\n• First of all, thanks to all for the comments and answers; all good and all appreciated. – Rhubbarb Aug 17 '10 at 23:13\n• @J. Mangaldan (2) are there any particular methods beyond power series and the few others I mentioned above that you would particularly recommend I consider? Do you have a reference for the use of the first neglected term as a bound on the remainder? What are the conditions for that to hold? Thanks again. – Rhubbarb Aug 17 '10 at 23:18\n• @Zen Harper: My question was vague partly intentionally (I am very pleased with the responses), and partly as I'm only an amateur mathematician. As a particular case: the terms of the expansion of sin are simple because the sequence of derivatives remains simple. On the other hand, the terms of the expansion of tan seem to become very unwieldy; the closed form is superficially simple, but involves the Bernoulli numbers, which are somewhat erratic. I expect I'm missing something quite simple. In saying that, I wasn't fishing for a specific solution so much as some leads. Thanks again. – Rhubbarb Aug 17 '10 at 23:50\n\nThese bounds you are looking for can be obtained from majorant series. What you seek is implemented in the Dynamic Dictionary of Mathematical Functions; Bruno Salvy gave a very nice talk on this topic at CICM 2010 in early July.\n\nFor the guaranteed numerics aspect, the expert is Marc Mezzarobba, a PhD student of Bruno's. On that page, see the links to NumGfun (software, presentation and paper) for all the details you would ever want on the topic.\n\nfinding bounds for the error or remainder term in partial power series expansions\n\nI think you want the Euler-Maclaurin Summation formula. That bounds the remainder terms, although it would require knowing the closed form of the integral representation of the function you are calculating.\n\n$\\sum_{n=a}^b f(n) \\sim \\int_a^b f(x)\\,dx + \\frac{f(a)+f(b)}{2} + \\sum_{k=1}^\\infty \\,\\frac{B_{2k}}{(2k)!}\\left(f^{(2k-1)}(b)-f^{(2k-1)}(a)\\right)$\n\nThe paper by Apostol \"Elementary view of Euler-Maclaurin\" AMM vol 106 (1999) pp. 409-418 is very accessible.\n\nThe following papers/books may also be helpful\n\n1. R.P. Boas \"Estimating Remainders.\" Math. Mag. 51, pp 83-89, (1978)\n2. http://www.tricki.org/article/Estimating_sums\n3. Bridger and Frampton Bounding Power Series Remainders Math. Mag. 71 (1998), pp. 204-207\n4. Sofo. Computational Techniques for the Summation of Series\n5. Ross. Methods of Summation\n6. Davis. Summation of Series." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8300641,"math_prob":0.912709,"size":1737,"snap":"2021-21-2021-25","text_gpt3_token_len":380,"char_repetition_ratio":0.10905944,"word_repetition_ratio":0.0,"special_character_ratio":0.23373632,"punctuation_ratio":0.13571429,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9910571,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-07T12:51:14Z\",\"WARC-Record-ID\":\"<urn:uuid:175931f5-a26c-48c7-a3fc-caabbc6fb172>\",\"Content-Length\":\"151330\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0da32618-b838-46a6-bdfd-7ad0ee7aab10>\",\"WARC-Concurrent-To\":\"<urn:uuid:0d8fa12d-cdb4-476d-9e94-c96edca5bfc7>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/35812/bounds-on-remainder-term-of-power-series-of-elementary-functions\",\"WARC-Payload-Digest\":\"sha1:USOPSG3A2HUBO4RPQD25VSPIPVWLUIWV\",\"WARC-Block-Digest\":\"sha1:GFXUY3MTXM3M76FH7S2KRAMZQVC3YPPZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988793.99_warc_CC-MAIN-20210507120655-20210507150655-00341.warc.gz\"}"}
https://www.hpmuseum.org/forum/archive/index.php?thread-4353.html	[ "# HP Forums\n\nFull Version: How do I use AFiles in an App?\nYou're currently viewing a stripped down version of our content. View the full version with proper formatting.\nThe following code works if you paste it into a copy of the Function App\nHere's the App:\nCode:\n``` //Variables... t;rh; hi;hi2;tmp; // Subroutine... HeatIndex(); EXPORT HeatIndex1() BEGIN END; VIEW \"Start HeatIndex\",START() BEGIN t:=AVars(\"t\");rh:=AVars(\"rh\"); STARTVIEW(-1,1); WHILE GETKEY<>4 DO REPEAT tmp:=INPUT({{t,,{60,20,1}}, {rh,,{60,20,2}}, {hi,,{60,20,4}}, {hi2,,{60,20,5}} }, \"Heat Index Input and Output\", {\"Temperature, Deg F : \", \"Relative Humidity, % : \", \"Heat Index, Deg F :\", \"Heat Index, Deg F :\" }, {\" Air Temperature (80 to 104 °F)\", \" Relative Humidity (40 to 100 %)\", \" Heat Index from www.weatherimages.org\", \" Heat Index from www.4wx.com\" }, {t,rh,hi,hi2}, {t,rh,hi,hi2}); AVars(\"t\"):=t;AVars(\"rh\"):=rh; IF tmp==0 THEN STARTVIEW(-4,1); MSGBOX(\"End of Program\"); RETURN; END; UNTIL t>=80. AND t<=104. AND rh>=40. AND rh<=100.; HeatIndex(); END; // While STARTVIEW(-4,1); MSGBOX(\"End of Program\"); END; HeatIndex() BEGIN // This is the 16 element equation used to convert // dry bulb temperature (T) and relative humidity (RH) // into the Heat Index. This equation works at // dry bulb temperatures of 70°F and higher. // The symbol \"^\" means \"raised to the power of\". // Source: http://www.weatherimages.org/data/heatindex.html // Where: // hi = Heat Index // t = Temperature (° F) // rh = Relative Humidity (%) tmp:=16.923; tmp:=tmp+1.8521210^(-1)t; tmp:=tmp+5.37941rh; tmp:=tmp-1.0025410^(-1)trh; tmp:=tmp+9.4169510^(-3)t^2; tmp:=tmp+7.2889810^(-3)rh^2; tmp:=tmp+3.4537210^(-4)t^2rh; tmp:=tmp-8.1497110^(-4)trh^2; tmp:=tmp+1.0210210^(-5)t^2rh^2; tmp:=tmp-3.864610^(-5)t^3; tmp:=tmp+2.9158310^(-5)rh^3; tmp:=tmp+1.4272110^(-6)t^3rh; tmp:=tmp+1.9748310^(-7)trh^3; tmp:=tmp-2.1842910^(-8)t^3rh^2; tmp:=tmp+8.4329610^(-10)t^2rh^3; hi:=tmp-4.8197510^(-11)t^3rh^3; hi:=ROUND(hi,0); // Source: http://www.4wx.com/wxcalc/formulas/heatIndex.php tmp:=-42.379; tmp:=tmp+2.04901523t; tmp:=tmp+10.14333127rh; tmp:=tmp-.22475541trh; tmp:=tmp-6.8378310^(-3)t^2; tmp:=tmp-5.48171710^(-2)rh^2; tmp:=tmp+1.2287410^(-3)t^2rh; tmp:=tmp+8.528210^(-4)trh^2; hi2:=tmp-1.9910^(-6)t^2*rh^2; hi2:=ROUND(hi2,0); END;```\nI want to take the subroutine HeatIndex(), and move it to the AFiles folder of this app. For me, the explanation in the AFiles help section of the emulator is inadequate. I need help in how to structure the code in order to run this App with the subroutine HeatIndex() in the AFiles folder. Thanks for any help you can provide.\nrcf\nWhat exactly do you want to do? each app has its own \"script\" place, the \"Afiles\" is (I believe) for external resources (in this moment probably text or images), not for script objects, like 'libraries'\nHello,\n\nApplication files are for data, not programs.\n\nYou can store 2 type of things in files using AFiles:Math \"Objects\" (anything that you can place in a variable) using AFiles(\"name\"):= var (or directly object), and graphics (storing G0-G9).\n\nYou can not store a program in a file, sorry. At this point in time, your program still has to be one single unit of source code.\n\nCyrille" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.53487074,"math_prob":0.9309476,"size":2548,"snap":"2021-43-2021-49","text_gpt3_token_len":1006,"char_repetition_ratio":0.15998428,"word_repetition_ratio":0.0,"special_character_ratio":0.47017267,"punctuation_ratio":0.27982953,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9899158,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-09T05:10:25Z\",\"WARC-Record-ID\":\"<urn:uuid:c813a467-b4d0-44d5-ab03-9bdd56427e3c>\",\"Content-Length\":\"9282\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:58aa9280-5038-48d8-a6c3-a7cea0de99b4>\",\"WARC-Concurrent-To\":\"<urn:uuid:84ae3738-6d58-40e0-b039-73ff5b0bd1fa>\",\"WARC-IP-Address\":\"209.197.117.170\",\"WARC-Target-URI\":\"https://www.hpmuseum.org/forum/archive/index.php?thread-4353.html\",\"WARC-Payload-Digest\":\"sha1:4RJ7NVFHZOAAATPYC47W2QUW3SHF2MIQ\",\"WARC-Block-Digest\":\"sha1:NKJ4LIUGXFR5GXGFDO267UNDC63AE4EL\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363659.21_warc_CC-MAIN-20211209030858-20211209060858-00079.warc.gz\"}"}
https://www.semanticscholar.org/paper/Counterexample-to-the-Laptev--Safronov-conjecture-Bogli-Cuenin/e586bd3d4a0f89bd5ede565401c696b2a0593701	[ "• Corpus ID: 237491585\n\nCounterexample to the Laptev--Safronov conjecture\n\n@inproceedings{Bogli2021CounterexampleTT,\ntitle={Counterexample to the Laptev--Safronov conjecture},\nauthor={Sabine Bogli and Jean-Claude Cuenin},\nyear={2021}\n}\n• Published 13 September 2021\n• Mathematics, Physics\nWe prove that the Laptev–Safronov conjecture (Comm. Math. Phys. 2009) is false in the range that is not covered by Frank’s positive result (Bull. Lond. Math. Soc. 2011). The simple counterexample is adaptable to a large class of Schrödinger type operators, for which we also prove new sharp upper bounds.\n3 Citations\nRandom Schr\\\"odinger operators with complex decaying potentials\n• Mathematics, Physics\n• 2022\nWe prove that the eigenvalues of a continuum random Schrödinger operator −∆+Vω of Anderson type, with complex decaying potential, can be bounded (with high probability) in terms of an L norm of the\nLieb-Thirring and Jensen sums for non-self-adjoint Schr\\\"odinger operators on the half-line\n• Mathematics, Physics\n• 2021\nWe prove upper and lower bounds for sums of eigenvalues of Lieb–Thirring type for non-self-adjoint Schrödinger operators on the half-line. The upper bounds are established for general classes of\nImproved Lieb-Thirring type inequalities for non-selfadjoint Schr\\\"odinger operators\np > 1, if d = 2, p ≥ d2 , if d ≥ 3. Here σd(−∆+V ) denotes the set of discrete eigenvalues, outside the essential spectrum σe(−∆ + V ) = [0,∞). The inequality (1) cannot be true for complex-valued V" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7634595,"math_prob":0.69246805,"size":4418,"snap":"2022-05-2022-21","text_gpt3_token_len":1114,"char_repetition_ratio":0.16130494,"word_repetition_ratio":0.019138755,"special_character_ratio":0.21299231,"punctuation_ratio":0.08085106,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97017765,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-22T03:27:52Z\",\"WARC-Record-ID\":\"<urn:uuid:7459610d-5b98-4d28-a9fc-0596f9843450>\",\"Content-Length\":\"261814\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c5bb4136-4306-48df-92b7-68e06ffd879b>\",\"WARC-Concurrent-To\":\"<urn:uuid:a8bf7343-3dcf-4b2e-9584-507bd6e10a6e>\",\"WARC-IP-Address\":\"99.86.231.114\",\"WARC-Target-URI\":\"https://www.semanticscholar.org/paper/Counterexample-to-the-Laptev--Safronov-conjecture-Bogli-Cuenin/e586bd3d4a0f89bd5ede565401c696b2a0593701\",\"WARC-Payload-Digest\":\"sha1:FP2I3X2YRI6RTB576XY6MT27I4V5XFHJ\",\"WARC-Block-Digest\":\"sha1:47NRABGW3YE6IBQGZ3UZMBZZBJRWXYKW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303729.69_warc_CC-MAIN-20220122012907-20220122042907-00648.warc.gz\"}"}
http://blog.phytools.org/2013/02/on-shape-of-trees-with-random-taxa.html	[ "## Tuesday, February 26, 2013\n\n### On the shape of trees with random taxa addition or subtraction\n\nSince I have a new function for add tips at random to a tree; and it is even easier to write a function to drop tips randomly from the tree - i.e., here it is:\ndrop.random<-function(tree,n=1)\ntree<-drop.tip(tree,tip=sample(tree\\$tip.label)[1:n])\nI thought it might be fun to look at the effects of adding or subtracting tips at random from the tree. We already know that random missing taxa tends to create trees with longer than expected terminal edges - seemingly a slow-down in the rate of lineage diversification through time.\n\nThis is not very scientific, but first let's look at the LTT and Pybus & Harvey's (2000) γ for a single tree that we initiate with 100 species and then add to randomly using add.random in increments of 10. Here's our code (minus creating the video):\nrequire(phytools)\ntree<-pbtree(n=100,scale=1)\nmas<-900\nfor(i in 1:(mas/10+1)){\nx<-ltt(tree,plot=FALSE)\nplot(x\\$times[2:length(x\\$times)],x\\$ltt[2:length(x\\$ltt)], xlab=\"time\",ylab=\"lineages\",log=\"y\",type=\"l\",xlim=c(0,1), ylim=c(2,max(x\\$ltt)))\nlines(c(0,1),c(2,max(x\\$ltt)),lty=2)\ntext(x=0,y=max(x\\$ltt),paste(\"N = \",length(tree\\$tip), \"\\n\",\"gamma = \",round(x\\$gamma,3),sep=\"\"),adj=c(0,1))\n}\n\nAnd here's the result:\n\nOK, next, let's do the opposite - start with 1000 taxa and drop taxa random. First the code:\ndrop.random<-function(tree,n=1) tree<-drop.tip(tree,tip=sample(tree\\$tip.label)[1:n])\nrequire(phytools)\ntree<-pbtree(n=1000,scale=1)\nmenos<-900\nfor(i in 1:(menos/10+1)){\nx<-ltt(tree,plot=FALSE)\nplot(x\\$times[2:length(x\\$times)],x\\$ltt[2:length(x\\$ltt)],xlab=\"time\", ylab=\"lineages\",log=\"y\",type=\"l\",xlim=c(0,1), ylim=c(2,max(x\\$ltt)))\nlines(c(0,1),c(2,max(x\\$ltt)),lty=2)\ntext(x=0,y=max(x\\$ltt),paste(\"N = \",length(tree\\$tip), \"\\n\",\"gamma = \",round(x\\$gamma,3),sep=\"\"),adj=c(0,1))\ntree<-drop.random(tree,n=10)\n}\n\nAnd the video:\n\nAdding taxa at random, at least by our algorithm, does not seem to affect tree shape all that much; but subtracting random tips, as we expected, makes γ turn progressively more and more negative.\n\nTo see if this is idiosyncratic to the specific trees we started with, why don't we replicate the entire process (i.e., 900% addition or subtraction) in a single step for, say, 30 random pure-birth trees. Here's what that looks like. First, adding tips randomly:\nXX<-matrix(NA,31,2,dimnames=list(NULL,c(\"gamma100\",\"gamma1000\")))\nrequire(phytools)\nfor(i in 1:31){\ntree<-pbtree(n=100)\nXX[i,1]<-ltt(tree,plot=F)\\$gamma\nXX[i,2]<-ltt(tree,plot=F)\\$gamma\n}\ncolMeans(XX)\nZZ<-hist(XX[,2]-XX[,1],plot=F,breaks=-9.5:0.5)\nbarplot(ZZ\\$density,names=ZZ\\$mids,space=0,main=expression(gamma-gamma))\n\nAnd the results:\n> colMeans(XX)\ngamma100 gamma1000\n0.3568899 -1.9163830\nAnd if we do the same thing dropping tips, here are the results:\n> colMeans(YY)\ngamma100 gamma1000\n-6.1072618 0.2275565\nSo, on the face of it, it seems as though adding taxa randomly (from 100 to 1000 species in the tree) or dropping taxa (from 1000 to 100) both result in a decrease in γ - however the scale of decrease is highly asymmetrical, with random subtraction resulting in a much greater decrease in γ.\n\nAt the start of this little experiment I wasn't sure if random addition of taxa would increase or decrease γ, and in the end it seems to decrease γ but sometimes only a little.\n\n1.", null, "I think the basis of what you're doing depends on the definition of 'at random'. In a previous post, you describe that you're adding tips as if the probability of an extra tip at any point along any edge increased with time. It isn't exactly clear, but I assume you let the probability increase linearly as branches approach the most terminal tips. This wouldn't be true under any birth/birth-death model; it's much more unlikely for a random tip to be attached further back in time than just a linearly decreasing probability. Just think of the exponential curve of a non-log-scaled LTT...\n\nIf I remember Nee et al. rightly, the probability of an additional random tip should be the same as the probability of having a branching time of time t, as that's just the probability of having a lineage which survived for duration t.\n\nI think if you weighted tip addition in this way, relative to values of the birth and death rates, it would produce trees with no distortion of the estimated gamma parameter.\n\n2.", null, "Actually, looking at your code, perhaps I misinterpreted your previous post about random new tips and cumsum. Now it looks like you're using it to pick an edge at random, with longer edges weighted to have a higher chance of getting chosen relative to their length? That's basically letting edges to go anywhere with uniform probability across the tree, something which would be unexpected under Yule/birth-death.\n\n1.", null, "David - Yes, this is how the function works; and I agree that this should result in trees that are not Yule-like. - Liam\n\nNote: due to the very large amount of spam, all comments are now automatically submitted for moderation." ]	[ null, "http://www.blogger.com/img/blogger_logo_round_35.png", null, "http://www.blogger.com/img/blogger_logo_round_35.png", null, "http://1.bp.blogspot.com/-w4ciG1TNTEA/YqI7UnbegBI/AAAAAAAAD9M/HHbrjTYWzPYI682eJrTcSKxC27pLmYIeQCK4BGAYYCw/s35/E7D41F40-D327-11EC-8FFF-0A541DCB2E73.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7426017,"math_prob":0.98681635,"size":5577,"snap":"2022-27-2022-33","text_gpt3_token_len":1751,"char_repetition_ratio":0.112686165,"word_repetition_ratio":0.12238325,"special_character_ratio":0.31845078,"punctuation_ratio":0.18174963,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.998848,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-30T13:16:30Z\",\"WARC-Record-ID\":\"<urn:uuid:4c59404d-61df-467c-96d4-22307e5303dd>\",\"Content-Length\":\"108178\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4dd126c8-3a99-4d12-9b22-59d63881bd91>\",\"WARC-Concurrent-To\":\"<urn:uuid:d29440ce-26df-4d61-b1cd-5d4f0dd50a95>\",\"WARC-IP-Address\":\"142.250.188.211\",\"WARC-Target-URI\":\"http://blog.phytools.org/2013/02/on-shape-of-trees-with-random-taxa.html\",\"WARC-Payload-Digest\":\"sha1:GNSH2RAR2J5XG2FLUWDC76YY4J3FJEWK\",\"WARC-Block-Digest\":\"sha1:VGAT7LOZ3BMG6YVQ7AIBE3OGQNJNNKYI\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103821173.44_warc_CC-MAIN-20220630122857-20220630152857-00330.warc.gz\"}"}
https://codedocs.xyz/gammasoft71/xtd_drawing/classxtd_1_1drawing_1_1point.html	[ "", null, "xtd.drawing - Reference Guide 0.1.0 Modern c++17 library providing access to GDI+ basic graphics functionality. More advanced functionality is provided in the drawing 2D, imaging, and text.\nxtd::drawing::point Class Reference\n\nRepresents an ordered pair of integer x- and y-coordinates that defines a point in a two-dimensional plane. More...\n\n#include <point.h>\n\n## Public Member Functions\n\npoint ()=default\nInitializes a new instance of the point class. More...\n\npoint (int32_t dw)\nnitializes a new instance of the point class using coordinates specified by an integer value. More...\n\npoint (int32_t x, int32_t y)\nInitializes a new instance of the point class with the specified coordinates. More...\n\npoint (const size &sz)\nInitializes a new instance of the point class from a size. More...\n\nbool is_empty () const\nGets a value indicating whether this point is empty. More...\n\nvoid offset (int dx, int dy)\nTranslates this point by the specified amount. More...\n\nvoid offset (const point &p)\nTranslates this point by the specified point. More...\n\nstd::string to_string () const\nConverts this point to a human-readable string. More...\n\nint32_t x () const\nGets the x-coordinate of this point. More...\n\nvoid x (int32_t x)\nSets the x-coordinate of this point. More...\n\nint32_t y () const\nGets the y-coordinate of this point. More...\n\nvoid y (int32_t y)\nSets the y-coordinate of this point. More...\n\n## Static Public Member Functions\n\nstatic point add (const point &pt, const size &sz)\nAdds the specified size to the specified point. More...\n\nstatic point ceiling (const point_f &value)\nConverts the specified point_f to a point by rounding the values of the point_f to the next higher integer values. More...\n\nstatic point round (const point_f &value)\nConverts the specified point_f to a point object by rounding the point_f values to the nearest integer. More...\n\nstatic point subtract (const point &pt, const size &sz)\nReturns the result of subtracting specified Size from the specified point. More...\n\nstatic point truncate (const point_f &value)\nConverts the specified point_f to a point by truncating the values of the point_f. More...\n\n## Static Public Attributes\n\nstatic const point empty\nRepresents a point that has x and y values set to zero. More...\n\n## Detailed Description\n\nRepresents an ordered pair of integer x- and y-coordinates that defines a point in a two-dimensional plane.\n\nRemarks\nTo convert a point to a point_f, use Implicit cast operator.\nExamples\nvoid create_points_and_sizes(paint_event_args& e) {\n// Create the starting point.\npoint start_point = subtract_button.size();\n// Use the addition operator to get the end point.\npoint end_point = start_point + size(140, 150);\n// Draw a line between the points.\ne.graphics().draw_line(system_pens::highlight, start_point, end_point);\n// Convert the starting point to a size and compare it to the subtractButton size.\nsize button_size(start_point);\nif (button_size == subtract_button.size()) {\n// If the sizes are equal, tell the user.\ne.graphics().draw_string(\"The sizes are equal.\", font(this->font, font_style.italic), brushes::indigo, 10.0F, 65.0F);\n}\n}\n\n## § point() [1/4]\n\n xtd::drawing::point::point ( )\ndefault\n\nInitializes a new instance of the point class.\n\nRemarks\nx and y values are set to zero.\n\n## § point() [2/4]\n\n xtd::drawing::point::point ( int32_t dw )\ninlineexplicit\n\nnitializes a new instance of the point class using coordinates specified by an integer value.\n\nParameters\n dx A 32-bit integer that specifies the coordinates for the new point.\nRemarks\nThe low-order 16 bits of the dw parameter specify the horizontal x-coordinate and the higher 16 bits specify the vertical y-coordinate for the new point.\nExamples\nThe following code example demonstrates how to use the point and size. size constructors and the xtd::drawing::content_alignment enumeration. To run this example, paste this code into a Windows Form (xtd::forms) that contains a label named label1, and call the initialize_label1 method in the form's constructor.\nvoid initialize_label1() {\n// Set a border.\nlabel1.border_style = border_style::fixed_single;\n// Set the size, constructing a size from two integers.\nlabel1.size(drawing::size(100, 50));\n// Set the location, constructing a point from a 32-bit integer\nlabel1.location(point(0x280028));\n// Set and align the text on the lower-right side of the label.\nlabel1.text_align = content_alignment::bottom_right;\nlabel1.text = \"Bottom Right Alignment\";\n}\n\n## § point() [3/4]\n\n xtd::drawing::point::point ( int32_t x, int32_t y )\ninline\n\nInitializes a new instance of the point class with the specified coordinates.\n\nParameters\n x The horizontal position of the point. y The vertical position of the point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## § point() [4/4]\n\n xtd::drawing::point::point ( const size & sz )\n\nInitializes a new instance of the point class from a size.\n\nParameters\n sz A size that specifies the coordinates for the new point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## Member Function Documentation\n\n static point xtd::drawing::point::add ( const point & pt, const size & sz )\nstatic\n\nAdds the specified size to the specified point.\n\nParameters\nReturns\nThe point that is the result of the addition operation.\nRemarks\nThe add adds the width and height of the specified size to the y and y values of the specified point.\nExamples\nThe following example shows how to use the add method. To run this example, paste it into a Windows Form (xtd::formsà. Handle the form's paint event and call the add_point method from the paint event-handling method, passing e as paint_event_args.\npoint point1(10, 10);\ne.graphics().draw_line(pens::red, point1, point2);\n}\n\n## § ceiling()\n\n static point xtd::drawing::point::ceiling ( const point_f & value )\nstatic\n\nConverts the specified point_f to a point by rounding the values of the point_f to the next higher integer values.\n\nParameters\n value The point_f to convert.\nReturns\nThe point this method converts to.\n\n## § is_empty()\n\n bool xtd::drawing::point::is_empty ( ) const\ninline\n\nGets a value indicating whether this point is empty.\n\nReturns\ntrue if both X and Y are 0; otherwise, false.\n\n## § offset() [1/2]\n\n void xtd::drawing::point::offset ( int dx, int dy )\ninline\n\nTranslates this point by the specified amount.\n\nParameters\n dx The amount to offset the x-coordinate. dy The amount to offset the y-coordinate.\n\n## § offset() [2/2]\n\n void xtd::drawing::point::offset ( const point & p )\ninline\n\nTranslates this point by the specified point.\n\nParameters\n p The point used offset this point.\nRemarks\nThis method adjusts the x and y values of this point to the sum of the x and y values of this point and p.\nExamples\nThe following example shows how to use the Offset method. To run this example, paste it into a Windows Form. Handle the form's Paint event and call the Offsetpoint method from the Paint event-handling method, passing e as PaintEventArgs.\nvoid offset_point(paint_event_args& e) {\npoint point1(10, 10);\npoint1.offset(50, 0);\npoint point2(250, 10);\ne.eraphics().draw_line(pens::red, point1, point2);\n}\n\n## § round()\n\n static point xtd::drawing::point::round ( const point_f & value )\nstatic\n\nConverts the specified point_f to a point object by rounding the point_f values to the nearest integer.\n\nParameters\n value The point_f to convert.\nReturns\nThe point this method converts to.\n\n## § subtract()\n\n static point xtd::drawing::point::subtract ( const point & pt, const size & sz )\nstatic\n\nReturns the result of subtracting specified Size from the specified point.\n\nParameters\n pt The point to be subtracted from. sz The size to subtract from the point.\nReturns\nThe point that is the result of the subtraction operation.\nRemarks\nThe subtract subtracts the width and height of the specified size from the x and y values of the specified point.\n\n## § to_string()\n\n std::string xtd::drawing::point::to_string ( ) const\ninline\n\nConverts this point to a human-readable string.\n\nReturns\nA string that represents this point.\n\n## § truncate()\n\n static point xtd::drawing::point::truncate ( const point_f & value )\nstatic\n\nConverts the specified point_f to a point by truncating the values of the point_f.\n\nParameters\n value The point_f to convert.\nReturns\nThe point this method converts to.\n\n## § x() [1/2]\n\n int32_t xtd::drawing::point::x ( ) const\ninline\n\nGets the x-coordinate of this point.\n\nReturns\nThe x-coordinate of this point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## § x() [2/2]\n\n void xtd::drawing::point::x ( int32_t x )\ninline\n\nSets the x-coordinate of this point.\n\nParameters\n x The x-coordinate of this point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## § y() [1/2]\n\n int32_t xtd::drawing::point::y ( ) const\ninline\n\nGets the y-coordinate of this point.\n\nReturns\nThe y-coordinate of this point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## § y() [2/2]\n\n void xtd::drawing::point::y ( int32_t y )\ninline\n\nSets the y-coordinate of this point.\n\nParameters\n y The x-coordinate of this point.\nExamples\nThe following code example demonstrates how to use the Equality operator and how to construct a point from a size or two integers. It also demonstrates how to use the x and y properties. This example is designed to be used with Windows Forms (xtd.forms). Paste the code into a form that contains a button named button1, and associate the button1_click method with the button's click event.\nvoid button1_Click(const control& sender, const event_args& e) {\n// Construct a new point with integers.\npoint point1(100, 100);\n// Create a Graphics object.\ngraphics form_graphics = this->create_graphics();\n// Construct another point, this time using a Size.\npoint point2(size(100, 100));\n// Call the equality operator to see if the points are equal, and if so print out their x and y values.\nif (point1 == point2) {\nform_graphics.draw_string(strings::format(\"point1.x: {}, point2.x: {}, point1.y: {}, point2.y {}\", point1.x(), point2.x(), point1.y(), point2.y()), this->font(), brushes::black, point_f(10, 70));\n}\n}\n\n## § empty\n\n const point xtd::drawing::point::empty\nstatic\n\nRepresents a point that has x and y values set to zero.\n\nThe documentation for this class was generated from the following file:" ]	[ null, "https://codedocs.xyz/gammasoft71/xtd_drawing/drawing_doxygen.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.64658237,"math_prob":0.9918708,"size":11640,"snap":"2020-34-2020-40","text_gpt3_token_len":3002,"char_repetition_ratio":0.15091096,"word_repetition_ratio":0.60426927,"special_character_ratio":0.3064433,"punctuation_ratio":0.23351158,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.992361,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-19T17:58:10Z\",\"WARC-Record-ID\":\"<urn:uuid:d9108dae-b85c-4d61-9437-df0a858ade4e>\",\"Content-Length\":\"58863\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c247acc-5826-4776-9eec-f2b082767aca>\",\"WARC-Concurrent-To\":\"<urn:uuid:efbe9e37-2d92-44a9-854e-838b7690a73c>\",\"WARC-IP-Address\":\"207.38.86.13\",\"WARC-Target-URI\":\"https://codedocs.xyz/gammasoft71/xtd_drawing/classxtd_1_1drawing_1_1point.html\",\"WARC-Payload-Digest\":\"sha1:5ATEOLGFPWICX2NER67VSW6L44LYHKDC\",\"WARC-Block-Digest\":\"sha1:742IZLGBM2LKUHP5B3J4WUCB74BKVBAW\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400192783.34_warc_CC-MAIN-20200919173334-20200919203334-00767.warc.gz\"}"}
https://gsebsolutions.in/gseb-solutions-class-9-maths-chapter-7-ex-7-1/	[ "# GSEB Solutions Class 9 Maths Chapter 7 Triangles Ex 7.1\n\nGujarat Board GSEB Solutions Class 9 Maths Chapter 7 Triangles Ex 7.1 Textbook Questions and Answers.\n\n## Gujarat Board Textbook Solutions Class 9 Maths Chapter 7 Triangles Ex 7.1\n\nQuestion 1.\nIn quadrilateral ABCD, AC = AD, and AB bisect ∠A (see in figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?\nSolution:\nGiven: Quadrilateral ABCD in which AB is the bisector of ∠A and AC = AD.", null, "To show:\nΔABC ≅ ΔABD\nProof: In ΔABC and ΔABD,\n(AB is the bisector of ∠A)\nAB = AB (Common)\n∴ ΔABC ≅ ΔABD (by SAS Congruency)\nHence BC = BD (by CPCT)\n\nc\n\nQuestion 2.\n∠DAB = ∠CBA (see figure). Prove that\n1. ΔABD ≅ ΔBAC\n2. BD = AC\n3. ∠ABD = ∠BAC", null, "Solution:\nGiven: ABCD is a quadrilateral in which\nAD = BC and ∠DAB = ∠CBA.\n1. In ΔABD and ΔBAC,\n∠DAB = ∠CBA (given)\nAB = AB (common)\n∴ ΔABD ≅ ΔBAC (by SAS congruency)\n\n2. ΔABD ≅ ΔBAC (proved above)\n∴ BD = AC (byCPCT)\n\n3. ΔABD ≅ ΔBAC (proved above)\n∴ ∠ABD = ∠BAC (by CPCT)", null, "Question 3.\nAD and BC are equal perpendiculars to a line segment AB (see fig). Show that CD bisects AB.", null, "Solution:\nGiven: AD and BC are perpendiculars on AB\nTo Prove: CD bisects AB.\ni.e., OA = OD\nProof: In ΔAOD and ΔBOC,\nAD \|\| BC (If alternate interior angles are equal then lines are parallel)\n∴ ∠ADO = ∠OCB (Alternate interior angle)\nHence ΔAOD ≅ ΔBOC (by ASA congruency)\nTherefore, OA = OB (by CPCT)\n∴ CD bisects AB.", null, "Question 4.\nl and m are two parallel lines intersected by another pair of parallel lines p and q (see in figure). Show that\nΔABC ≅ ΔCDA\nSolution:\nGiven: l \|\| m and both are intersected by another pair of parallel lines p and q\nTo Prove: ΔABC ≅ ΔCDA", null, "Proof: Since AB \|\| CD\n∠1 = ∠2 (Alternate interior angles\n∠3 = ∠4 (Alternate interior angles)\nand AC = AC (common)\nΔABC ≅ ΔADC (by ASA congruency)\n\nQuestion 5.\nLine l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see figure). Show that\n(i) ΔAPB ≅ ΔAQB\n(ii) BP = BQ or B is equidistant from the arms of ∠A.", null, "Solution:\nGiven: l is the bisector of ∠A, i.e., ∠BAP = ∠BAQ.\nBP and BQ are perpendiculars from B to arms of ∠A.\n\n(i) In ΔAPB and ΔAQB\n∠BPA = ∠BQA (each 90°)\n∠BAP = ∠BAQ (l is the angle bisector of ∠A)\nand AB = AB (Common)\nHence ΔAPB ≅ ΔAQB (By AAS congruency)\n\n(ii) Since ΔAPB ≅ ΔAQB\n∴ BP = BP (By CPCT)", null, "Question 6.\nIn figure,AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.", null, "Solution:\nGiven: In figure AC = AE.\nTo show: BC = DE\nAdding ∠DAC on both sides, we get\n∠BAD + ∠DAC = ∠EAC + ∠DAC\n⇒ ∠BAC = ∠DAE\nAC = AE (given)\n∴ ΔBAC ≅ ΔDAE (By SAS congruency)\nHence BC = DE (By CPCT)", null, "Question 7.\nAB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (see figure). Show that.", null, "Solution:\nProof: (i) In ΔDAP and ΔEBP,\nor ∠DAP = ∠PBE\nAP = PB (P is the mid≅points)\n∠EPA = ∠DPB (given)\nAdding ∠DPE on both sides, we get\n∠EPA + ∠DPE = ∠DPB + ∠DPE\n∠DPA = ∠EPB\n∴ ΔDAP ≅ ΔEBP (By ASA congruency)\n\n(ii) ΔDAP ≅ ΔEBP\n∴ AD = BE (by CPCT)\n\nQuestion 8.\nIn right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see figure). Show that:", null, "1. ∠AMC ≅ ΔBMD\n2. ∠DBC is a right angle.\n3. ΔDBC ≅ ΔACB\n4. CM = $$\\frac {1}{2}$$AB\nSolution:\nProof:\n1. In ΔAMC and ΔBMD,\nAM = BM (M is the mid-point of AB)\n∠AMC = ∠BMD (Vertically opposite angle)\nCM = DM (given)\nHence, ΔAMC ≅ ΔBMD (by SAS congruency)\nAC = BD (by CPCT)", null, "2. ΔAMC ≅ ΔBMD (Proved in part i)\n∴ ∠ACM = ∠BDM (by CPCT)\n(Alternate interior angles)\nHence AC \|\| BD (If alternate interior angles are equal then lines are parallel)\n∴ ∠ACB + ∠DBC = 180°\n(Sum of consecutive interior angles is equal to 180°\n∴ ∠DBC = 180°≅ 90°\n⇒ ∠DBC = 90°\nHence ∠DBC is a right angle.\n\n3. Now in ΔACB and ΔDBC,\n∠ACB = ∠DBC (each 900)\nBC = CB (common)\nAC = BD (Proved in part i)\nHence ΔACB ≅ ΔDBC (by SAS congruency)\n\n4. ΔDBC ≅ ΔACB (Proved in part iii)\nDC = AB (by CPCT)\n⇒ 2CM = AB (DM = CM)\nCM = $$\\frac {1}{2}$$ AB" ]	[ null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-1-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-2-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/07/GSEB-Solutions.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-3-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/07/GSEB-Solutions.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-4-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-5-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/07/GSEB-Solutions.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-6-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/07/GSEB-Solutions.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-7-2.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/09/GSEB-Solutions-Class-9-Maths-Chapter-7-Triangles-Ex-7.1-8-1.png", null, "https://gsebsolutions.in/wp-content/uploads/2020/07/GSEB-Solutions.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8950647,"math_prob":0.9946024,"size":4250,"snap":"2022-27-2022-33","text_gpt3_token_len":1682,"char_repetition_ratio":0.109985866,"word_repetition_ratio":0.090808414,"special_character_ratio":0.31105882,"punctuation_ratio":0.11419069,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99933434,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"im_url_duplicate_count":[null,2,null,2,null,null,null,2,null,null,null,2,null,2,null,null,null,2,null,null,null,2,null,2,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-19T18:09:49Z\",\"WARC-Record-ID\":\"<urn:uuid:ce00e86b-18d8-4939-8f0e-7dd44704b5a8>\",\"Content-Length\":\"133978\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:be5a8b76-53b0-4be5-830d-8081f3003cad>\",\"WARC-Concurrent-To\":\"<urn:uuid:1030b62d-e917-4bc7-8e69-10c2dce0c6d5>\",\"WARC-IP-Address\":\"45.79.123.175\",\"WARC-Target-URI\":\"https://gsebsolutions.in/gseb-solutions-class-9-maths-chapter-7-ex-7-1/\",\"WARC-Payload-Digest\":\"sha1:5ON6KX52HNBWD7IVMQO7F35KJY7QWQQ5\",\"WARC-Block-Digest\":\"sha1:J2M4YQGXLVM4B4S34NTC32UDGNJZ2BQK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882573744.90_warc_CC-MAIN-20220819161440-20220819191440-00787.warc.gz\"}"}
https://simblob.blogspot.com/2015/03/hex-grids-code-generation.html?widgetType=BlogArchive&widgetId=BlogArchive1&action=toggle&dir=open&toggle=MONTHLY-1512115200000&toggleopen=MONTHLY-1425196800000	[ "In the last post I described how I had expected to generate lots of algorithm variants, but ended up discovering a better approach. The new system is different from the system I used when I wrote the hex grid guide. It's simpler and more modular, and I have ideas for making it even simpler. If I am able to simplify enough, I may not need to generate algorithms dynamically. In any case, the final step is to convert the algorithms in abstract format into a specific programming language.\n\nTransforming the algorithms into code was easier than figuring out how to structure the algorithms, but it was also more tedious. For expressions, it's pretty straightforward. A syntax tree like `Add(Name(\"x\"), Int(3))` turns into `x+3` in Python/C/Java/JS or `(+ x 3)` in Racket/Scheme/Lisp/Clojure. For statements, it's pretty straightforward too, but there are a few more differences between languages, including indentation and placement of braces. For declarations, languages start differing more, with functions, structs, classes, methods, modules, namespaces, etc. I wanted to generate code that uses each language's canonical style, including naming conventions and comments. I'll show some examples, using the distance function:\n\n```Function(\"cube_distance\", Int, [Param(\"a\", Cube), Param(\"b\", Cube)],\nReturn(\nInt(\nDivide(\nSubtract(Field(\"a\", \"x\"), Field(\"b\", \"x\"))),\nCall(\"abs\",\nSubtract(Field(\"a\", \"y\"), Field(\"b\", \"y\")))),\nCall(\"abs\",\nSubtract(Field(\"a\", \"z\"), Field(\"b\", \"z\")))\n),\nInt(2)\n)\n)\n)\n)\n```\nPython\nPython uses `/` for float division and `//` for integer division. My syntax tree does not. Instead, when I see a pattern `Call(Int, Divide(a, b))` I want to output `a//b` instead of `int(a/b)`. This shows up in the distance function:\n```def cube_distance(a, b):\nreturn (abs(a.x - b.x) + abs(a.y - b.y) + abs(a.z - b.z)) // 2\n```\n\nPython doesn't need a separate class to hold int and float coordinates, so `FractionalCube` should be merged into `Cube`.\n\nC++\nC++ uses `/` for float division and `/` for integer division, but it depends on the types of the operands. My syntax tree doesn't track the types of the subexpressions, so I don't know which I'll get. As a result, I end up with an unneccessary `int()` in the distance function:\n```int cube_distance(Cube a, Cube b)\n{\nreturn int((abs(a.x - b.x) + abs(a.y - b.y) + abs(a.z - b.z)) / 2);\n}\n```\nRacket\nDivision is tricky here too. Racket uses `quotient` instead of `/` when the result is going to be an integer. Like Python's output, I can look for `Call(Int, Divide(a, b))` and output `(quotient a b)` instead of `(truncate (/ a b))`. Racket also supports multi-argument addition, so I could convert `(+ (+ a b) c)` into `(+ a b c)`. Here's the distance function in Racket:\n```(define (cube-distance a b)\n(quotient\n(+ (abs (- (cube-x a) (cube-x b)))\n(abs (- (cube-y a) (cube-y b)))\n(abs (- (cube-z a) (cube-z b))))\n2))\n```\n\nThe naming convention is `cube-distance` instead of `cube_distance`.\n\nC#, Java\nDeclarations are different here. Instead of top-level functions, I need to make everything into a method. For now, I'm using static methods, but it might make sense to use instance methods for some of the algorithms. Here's what distance looks like in C#:\n```public class Cube\n{\n...\nstatic public int Distance(Cube a, Cube b)\n{\nreturn (int)((Math.Abs(a.x - b.x) + Math.Abs(a.y - b.y) + Math.Abs(a.z - b.z)) / 2);\n}\n}\n```\n\nInstead of `cube_distance`, I should use `Cube.Distance` in C# and `Cube.distance` in Java.\n\nThe differences between languages got larger as I moved to bigger functions. The sequence and record data types translate easily: C++ arrays/structs, Python lists/records, C# arrays/classes, Racket vectors/structs. But some algorithms use sets and maps, and it's less clear what types to use there. For Racket and Haskell, I want to use a more functional style, but for C++ and Python, I use an imperative style. In the end:\n\n• I didn't implement the more complex algorithms. They're harder, and I decided I should prioritize getting the simple ones working across many languages and many grid types. If I had known this from the beginning, I would've used a simpler proto-algorithm approach.\n• I didn't implement the more complex approach of adapting code for each grid type. Instead, I used the simpler approach of having each grid type convert to Cube coordinates, and then use the cube algorithms. If I had known this from the beginning, I would've written the algorithms by hand instead of writing a proto-algorithm to algorithm conversion step.\n• I didn't implement all the grid types. Instead of all the variants of Cube, Axial, and Offset, I only implemented one Cube variant, one Axial variant, and two Offset variants. If I had known this from the beginning, I would've written a simpler system.\n• The code for Axial coordinates is mostly different from the code for Offset coordinates. I was expecting more code to be shared. This made think that I probably shouldn't treat these two the same.\n• I now realize that my choice of Cube/Axial isn't great. Instead of q=x, r=z I should have picked q=x, r=y! I could have switched the y and z axes on the cube diagram. If I merge Cube and Axial I'll make this change then.\n• I wrote the proto-algorithms expecting that I'd output functional style (Racket, Haskell), object-oriented style (C#, Java, Haxe), and module style (C++, Python, Javascript). Looking back, I probably should have used object-oriented style everywhere. The style differences somewhat complicated things.\n• I also wrote the proto-algorithms expecting that I'd use them on the page itself, and also convert them to code for a downloadable library. That complicated things. I should have focused on downloadable libraries.\n• The code generator for Racket mostly works but it wasn't a purely functional style (because my \"proto-algorithms\" are imperative). I had planned to make the standard algorithms work in a purely functional style but some of the more complex algorithms will probably be too much work to justify a separate version. Looking back, I shouldn't have spent time trying to figure out a functional style for Racket; it wasn't worth spending time on a different style for just one language.\n• I didn't implement variants in code style, such as indentation and brace placement. When I started the project it seemed like it would be cool, but it just doesn't seem important anymore.\n• I didn't implement a \"pro\" version of the code that would use small arrays with 2 or 3 elements instead of named fields. Thinking of them as arrays or matrices would also potentially allow SIMD or GPU instructions. Pointy vs flat variants become an index swizzle. Converting hex to pixel and pixel to hex become matrix multiplies.\n\nIt's been a fun project, and as usual there are so many more things I want to do with this, but there are so many other things I want to do too, so I want to wrap this up.\n\n• Should I switch to the simpler system that merges Axial and Cube together? This will require a major update to the hex grid guide. It would make my advice much simpler. Instead of \"use Cube for calculations and Axial for storage\" I could say \"use Axial everywhere\". However, I'm worried that it will annoy anyone who's using the current hex grid page, because the new system will be incompatible.\n• Should I treat pointy vs flat as an x/y switch or as a 90° rotation? I am leaning towards x/y switch. I will also have to switch q/r to keep q being \"columns\" and r being \"rows\".\n\nWhat's my next step? Testing. I have unit tests for the generated code, and they all pass, but I want to test the code in a real project. What real project do I have? The hex grid page itself. I'm going to replace the hand-written hex grid code for the page with the generated code. This will give me confidence that I have the right design and set of algorithms.\n\nWhat are other things I need to do before I publish? Add comments to the generated code, implement more outputs (Javascript, Typescript, Java, Objective C, Racket), add an option for overloaded operators (+ and ==) in languages where that's standard style, and figure out instance vs class methods.\n\nThat's it for now. My blog posts aren't polished but I hope they give you a \"behind the scenes\" view of the stuff that goes through my head and the things I try while working on these projects. I also find that trying to write down what I'm doing helps me work out the design and details, and this series of posts was no exception. By \"thinking out loud\" I've been able to resolve some of the issues I had been trying to figure out. I hope to have the rest of the code generator finished in a few weeks.\n\nLabels: , , ,\n\nCraig wrote at March 30, 2015 7:25 AM\n\nI am enjoying your posts. Good luck!\n\nUnknown wrote at April 11, 2015 8:28 AM\n\nHi,\n\nI have recently started developing a game using a hexgrid and the problem of converting mouse coordinates to a grid location has hassled me for 2 days now.\n\nI tried working with code examples from your website unfortunately to no success (I am working with c++ and none of the information I needed was in c++).\n\nI finally worked it out today and I thought I would share my code with you in hope that you may be able to help provide other people with good solutions.\n\nI am aware the following code is quiet sloppy but all my testing has shown it works.\n\nMy grid layout is “odd-q” vertical layout and the following code only works for that grid type.\n\nNote: sf::Vector2i is from the SFML library and refers to an class that holds an x and y int.\n\nsf::Vector2i HexagonGrid::PixelToHexgrid(double x, double y) {\n\ndouble h = (hex_radius2)0.86; //So currently I have worked out height is 86% of the radius, dodgy? I don't know..\n\nint xgrid = floor(x/w); //What column is it roughly in?\nint splitx = xgridw; //Bring this back to a pixel coordinate, but it's now rounded to the column\n\nif ((int)floor(x/w) & 1) //Is it an odd column?\n{\ny-=h/2; //Shift the y value upward to compensate for the odd column\n}\n\ndouble yp = ((int)y % (int)h)/h; //Percentage of way down y row 0-1 (0% to 100%)\ndouble zigzag = abs((yp2)-1); //Convert yp into a range of 0-2 then -1 to 1 and finally abs it so we get a wrapped result of 0 - 0.5 - 1 (same as 0)\n\nsplitx += zigzag*(w/3); //Multiply the zigzag by 1/4 of the pentagon, or with the current w, 1/3 is 1/4\n\nif ((((int)x % (int)w)/w)<0.33) //Is the point on the join between cells\n{\nif (splitx > x) //Is the current point in the zigzag (join) larger than the pixel x?\n{\nif (xgrid & 1) //Was the old result a odd column?\ny+=h/2; //Remove the shift from earlier\nelse\ny-=h/2; //Add a shift because it is now odd\nxgrid-=1; //Push left one because this isn't really in the next column\n}\n}\n\nint ygrid = floor(y/h);\n\nreturn sf::Vector2i(xgrid, ygrid);\n}\n\nKeep up the good work :) and thanks for the ideas on how to tackle this problem\n\nBecareful not to let pretty diagrams draw away from the information, I found a few times your interactive diagram was absolutely amazing but the information with it was mostly just confusing and involved jumping to other parts of the page to find out what a function was\n\nAmit wrote at April 11, 2015 8:51 AM\n\nThanks Chris! The algorithms (including pixel to hex) should work with any language but I'm also working on some code samples in various languages, including C++." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9233375,"math_prob":0.7487082,"size":11196,"snap":"2021-04-2021-17","text_gpt3_token_len":2730,"char_repetition_ratio":0.10096498,"word_repetition_ratio":0.024767801,"special_character_ratio":0.25187567,"punctuation_ratio":0.124726474,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97754407,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-26T03:41:28Z\",\"WARC-Record-ID\":\"<urn:uuid:1dfc2c8f-0b41-4a65-9209-776cb1bea36f>\",\"Content-Length\":\"114166\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:856588c8-40a8-4481-85b2-32970776440e>\",\"WARC-Concurrent-To\":\"<urn:uuid:eb1ffff2-5b0c-4c11-ac0c-5458996e3ca7>\",\"WARC-IP-Address\":\"142.250.73.193\",\"WARC-Target-URI\":\"https://simblob.blogspot.com/2015/03/hex-grids-code-generation.html?widgetType=BlogArchive&widgetId=BlogArchive1&action=toggle&dir=open&toggle=MONTHLY-1512115200000&toggleopen=MONTHLY-1425196800000\",\"WARC-Payload-Digest\":\"sha1:5DDU7TI4A3QB6DQHTGV5Y2NTTP4QS4XS\",\"WARC-Block-Digest\":\"sha1:L24ZCTOBMVN3YZ62ZVZHQF6NRO2BEH6U\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610704795033.65_warc_CC-MAIN-20210126011645-20210126041645-00542.warc.gz\"}"}
https://www.ituring.com.cn/article/507355	[ "``````var container = [];\ncontainer.push(\"a\");\ncontainer.push(\"b\");\ncontainer.push(\"c\"); // [\"a\", \"b\", \"c\"]\n\nvar idx = container.indexOf(\"z\"); // -1\ncontainer.splice(idx, 1); // [\"c\"]\n``````\n\n``````container.splice(idx < 0 ? -Infinite : idx, 1); // [\"a\"]\n``````\n\n``````container.splice(idx < 0 ? Infinite : idx, 1); // []\n``````\n\n22.1.3.26Array.prototype.splice ( start, deleteCount, ...items ) ...\n\n1. If relativeStart < 0, let actualStart be max((len + relativeStart), 0); else let actualStart be min(relativeStart, len).\n\nPS: 在 ES6 中我们可以愉快的使用 Set ，而无需再使用数组进行模拟啦！" ]	[ null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.74111694,"math_prob":0.9866727,"size":745,"snap":"2020-24-2020-29","text_gpt3_token_len":364,"char_repetition_ratio":0.14979757,"word_repetition_ratio":0.0,"special_character_ratio":0.32214764,"punctuation_ratio":0.3034483,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9691578,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-13T10:24:27Z\",\"WARC-Record-ID\":\"<urn:uuid:88af13a2-e2c9-4e02-9192-269bca4ee4e0>\",\"Content-Length\":\"34522\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8654ef47-35a8-4194-b015-5214051360ed>\",\"WARC-Concurrent-To\":\"<urn:uuid:4dc7486d-1092-488f-afaa-e31055290ad3>\",\"WARC-IP-Address\":\"123.56.144.65\",\"WARC-Target-URI\":\"https://www.ituring.com.cn/article/507355\",\"WARC-Payload-Digest\":\"sha1:SZI4M34DIV6OB2AELFE7V76ZWXYMVB57\",\"WARC-Block-Digest\":\"sha1:BQQ7SM2UFNALN3GVKCAS6G5WYY3HCMZQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657143365.88_warc_CC-MAIN-20200713100145-20200713130145-00212.warc.gz\"}"}
http://pyretis.org/current/examples/examples-retis-1d.html	[ "# RETIS in a 1D potential¶\n\nIn this example, you will explore a rare event with the Replica Exchange Transition Interface Sampling (RETIS) algorithm.\n\nWe will consider a simple 1D potential where a particle is moving. The potential is given by", null, "where", null, "is the position. By plotting this potential, we see that we have two states (at", null, "and", null, ") separated by a barrier (at", null, "):", null, "Fig. 22 The potential energy as a function of the position. We have two stable states (at x = -1 and x = 1) separated by a barrier (at x = 0). In addition, three paths are shown. One is reactive while the two others are not able to escape the state at x = -1. Using the RETIS method, we can generate such paths which gives information about the reaction rate and the mechanism. The vertical dotted lines show two RETIS interfaces.\n\nUsing the RETIS algorithm, we will compute the rate constant for the transition between the two states. This particular problem has been considered before by van Erp and we will here try to reproduce these results.\n\n## Creating the PyRETIS input file¶\n\nWe will now create the input file for PyRETIS. We will do this section by section in order to explain the different keywords and settings. The full input file is given at the end of this section.\n\n### Setting up the simulation task¶\n\nThe first thing we will define is the type of simulation we will run. This is done by creating a simulation section.\n\nHere, we are going to do a retis simulation and we will do 20000 steps . Since we will be running a path sampling simulation, we will also need to specify the positions of the interfaces we will be using.\n\nRetis 1D example\n================\n\nSimulation\n----------\ntask = retis\nsteps = 20000\ninterfaces = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0]\n\n\n### Setting up the system¶\n\nWe will now set up the system we are going to consider. Here, we will actually define several PyRETIS input sections:\n\n• The system section which defines the units, dimensions and temperature we are considering:\n\nSystem\n------\nunits = reduced\ndimensions = 1\ntemperature = 0.07\n\n• The box section, but since we are here just considering a single particle in a 1D potential, we will simply use a 1D box without periodic boundaries:\n\nBox\n---\nperiodic = [False]\n\n• The particles section which add particles to the system and defines the initial state:\n\nParticles\n---------\nposition = {'file': 'initial.xyz'}\nvelocity = {'generate': 'maxwell',\n'momentum': False,\n'seed': 0}\nmass = {'Ar': 1.0}\nname = ['Ar']\ntype = \n\n\nIn this case, we will read the initial configuration from a file initial.xyz and velocities are generated from a Maxwell distribution. Further, we specify the mass, particle type and we label the particle as Ar. Note that this does not mean that we are simulating Argon, it is just a label used in the output of trajectories.\n\n• The force field and potential sections which setup up the 1D double well potential:\n\nForcefield settings\n-------------------\ndescription = 1D double well\n\nPotential\n---------\nclass = DoubleWell\na = 1.0\nb = 2.0\nc = 0.0\n\n\n### Selecting the engine¶\n\nHere, we will make use of a stochastic Langevin engine. We set it up by setting the time step, the friction parameter and whether we are in the high friction limit. The seed given is a seed for the random number generator used by the integrator.\n\nEngine\n------\nclass = Langevin\ntimestep = 0.002\ngamma = 0.3\nhigh_friction = False\nseed = 0\n\n\n### TIS specific settings¶\n\nThe TIS settings control how the TIS algorithm is carried out. Here we set that 50 % of the TIS moves should be shooting moves (keyword freq) and we limit all paths to a maximum length of 20 000 steps. Further, we select aimless shooting and we tell PyRETIS to not set the momentum to zero and to not rescale the energy after drawing new random velocities. We also set allowmaxlength = False which means that for shooting, we determine stochastically the length of new paths based on the length of the path we are shooting from. The given seed is a seed for the random number generator used by the TIS algorithm.\n\nTIS settings\n------------\nfreq = 0.5\nmaxlength = 20000\naimless = True\nallowmaxlength = False\nzero_momentum = False\nrescale_energy = False\nsigma_v = -1\nseed = 0\n\n\n### RETIS specific settings¶\n\nThe RETIS section controls the RETIS algorithm. Here we request that 50 % of the RETIS moves should be swapping moves, while the remaining 50 % will be TIS moves. We further say that we do not do relative shooting and that we attempt to swap several ensembles at the same time. In case an ensemble is not participating in the swap, a null move (that is just accepting the last accepted path again) is carried out.\n\nRETIS settings\n--------------\nswapfreq = 0.5\nrelative_shoots = None\nnullmoves = True\nswapsimul = True\n\n\n### Initial path settings¶\n\nThese settings determine how we find the initial path(s). Here, we ask PyRETIS to generate these using the kick method.\n\nInitial-path settings\n---------------------\nmethod = kick\nkick-from = initial\n\n\n### Selecting the order parameter¶\n\nFor this system, we simply define the order parameter as the position of the single particle we are simulating.\n\nOrderparameter\n--------------\nclass = Position\ndim = x\nindex = 0\nperiodic = False\n\n\n### Modifying the output¶\n\nIn the Output section, we here set the frequency by which PyRETIS will write out information about the trajectories, energies and order parameters.\n\nOutput\n------\ntrajectory-file = 100\nenergy-file = 100\norder-file = 100\n\n\nRetis 1D example\n================\n\nSimulation\n----------\ntask = retis\nsteps = 20000\ninterfaces = [-0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, 1.0]\n\nSystem\n------\nunits = reduced\ndimensions = 1\ntemperature = 0.07\n\nBox\n---\nperiodic = [False]\n\nEngine\n------\nclass = Langevin\ntimestep = 0.002\ngamma = 0.3\nhigh_friction = False\nseed = 0\n\nTIS settings\n------------\nfreq = 0.5\nmaxlength = 20000\naimless = True\nallowmaxlength = False\nzero_momentum = False\nrescale_energy = False\nsigma_v = -1\nseed = 0\n\nRETIS settings\n--------------\nswapfreq = 0.5\nrelative_shoots = None\nnullmoves = True\nswapsimul = True\n\nInitial-path settings\n---------------------\nmethod = kick\nkick-from = initial\n\nParticles\n---------\nposition = {'file': 'initial.xyz'}\nvelocity = {'generate': 'maxwell',\n'momentum': False,\n'seed': 0}\nmass = {'Ar': 1.0}\nname = ['Ar']\ntype = \n\nForcefield settings\n-------------------\ndescription = 1D double well\n\nPotential\n---------\nclass = DoubleWell\na = 1.0\nb = 2.0\nc = 0.0\n\nOrderparameter\n--------------\nclass = Position\ndim = x\nindex = 0\nperiodic = False\n\nOutput\n------\ntrajectory-file = 100\nenergy-file = 100\norder-file = 100\n\n\n## Running the RETIS simulation¶\n\nWe will now run the RETIS simulation. Create a new directory and place the input file (let’s call it retis.rst) here. Also, download the initial configuration initial.xyz and place it in the same folder. The simulation can then be executed using:\n\npyretisrun -i retis.rst -p\n\n\nThe -p option will display a progress bar for your simulation.\n\n## Analysing the results¶\n\nWhen the simulation has finished, we can analyse the results. PyRETIS will create a file, out.rst, which you can use for the analysis. This is a copy of the input retis.rst with some additional settings for the analysis:\n\nAnalysis settings\n-----------------\nmaxordermsd = -1\nngrid = 1001\nreport = ['latex', 'rst', 'html']\nmaxblock = 1000\ntxt-output = 'txt.gz'\nblockskip = 1\nplot = {'output': 'png', 'plotter': 'mpl', 'style': 'pyretis'}\nbins = 100\nskipcross = 1000\n\n\nFor a description of these keywords, we refer to the analysis section.\n\nThe analysis itself is performed using:\n\npyretisanalyse -i out.rst\n\n\nThis will produce a new folder, report which contains the results from the analysis. If you have latex installed, you can generate a pdf using the file retis_report.tex within the report folder. An example result for the crossing probability is shown below.", null, "Fig. 23 Sample output from the analysis. This figure shows the crossing probabilities for the individual ensembles and the overall crossing probability.\n\n## Improving the statistics¶\n\nWe can improve the statistics by running a longer simulation. Modify the number of steps, from 20000 to 1000000 and re-run the simulation and the analysis. Below we show an example for the crossing probability after performing the additional steps", null, "Fig. 24 Sample output from the analysis. This figure shows the crossing probabilities for the individual ensembles and the overall crossing probability after running 1000000 steps." ]	[ null, "http://pyretis.org/current/_images/math/35fc4d2774f38b69ac8afe2a65b0b307ac26a3ad.png", null, "http://pyretis.org/current/_images/math/888f7c323ac0341871e867220ae2d76467d74d6e.png", null, "http://pyretis.org/current/_images/math/627dd8ffb57945e8ded86de9ceb1fef4fb3cd983.png", null, "http://pyretis.org/current/_images/math/23ec360a99998552bf72f9d9020b82cecb309848.png", null, "http://pyretis.org/current/_images/math/c34170440d4046a9b3e1ef2635a2f5d6a529a421.png", null, "http://pyretis.org/current/_images/1dpot.png", null, "http://pyretis.org/current/_images/probability-20000.png", null, "http://pyretis.org/current/_images/probability-1M.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.76788616,"math_prob":0.9813563,"size":7901,"snap":"2021-21-2021-25","text_gpt3_token_len":2043,"char_repetition_ratio":0.14207926,"word_repetition_ratio":0.21815409,"special_character_ratio":0.2907227,"punctuation_ratio":0.1261324,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9912466,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,6,null,null,null,9,null,9,null,9,null,9,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-14T04:53:49Z\",\"WARC-Record-ID\":\"<urn:uuid:2173e7b2-437d-477a-bfb7-0965b7976530>\",\"Content-Length\":\"31151\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2cf2c4d8-90d5-42cb-bcf1-c165a60704ad>\",\"WARC-Concurrent-To\":\"<urn:uuid:675d7032-1825-4d7b-bc16-6606d24c5228>\",\"WARC-IP-Address\":\"46.249.47.169\",\"WARC-Target-URI\":\"http://pyretis.org/current/examples/examples-retis-1d.html\",\"WARC-Payload-Digest\":\"sha1:5FDP7GWISDJR4GEODUIQAYDG3VCXCVQP\",\"WARC-Block-Digest\":\"sha1:IUP6NTMKNTG7PRNU4USJTFQN6V6UFXZB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487611445.13_warc_CC-MAIN-20210614043833-20210614073833-00008.warc.gz\"}"}
https://zbmath.org/?q=an%3A0738.11025	[ "zbMATH — the first resource for mathematics\n\nOn Stirling functions of the second kind. (English) Zbl 0738.11025\nThe authors prove several results for Stirling functions defined by $$S(\\alpha,k)=(1/k!)\\Delta^ kx^ \\alpha\|_{x=0},$$ $$\\alpha\\geq 0$$; $$k\\in{\\mathbb{N}}_ 0$$, viewed as function of $$\\alpha$$, where $$\\Delta$$ is the forward difference operator. Among the results obtained are proofs of the continuity and differentiability of $$S$$, recurrence relations, real integral representations, a representation in terms of the Weyl derivative of fractional order $$\\alpha$$, and connections with the Bernoulli, Stirling, and Bernstein polynomials and with Bernoulli numbers of fractional order.\n\nMSC:\n 11B73 Bell and Stirling numbers 11B68 Bernoulli and Euler numbers and polynomials\nFull Text:\nReferences:\n Abramowitz, Handbook of Mathematical Functions (1965) Andrica, Bernstein’s polynomials for powers via shifting operator, Anal. Numer. Théor. Approx. 16: pp 93– (1987) · Zbl 0645.41016 Butzer, One-Dimensional Theory I (1971) Butzer, Lecture Notes in Math. 457, in: Fractional Calculus and Its Applications pp 116– (1975) Butzer, Factorial functions and Stirling numbers of fractional orders, Resultate Math. 16 pp 16:– (1989) · Zbl 0707.05002 Comtet, Advanced Combinatorics (1974) Doetsch, Einführung in Theorie und Anwendung der Laplace-Transformation (1958) Erdélyi, Tables of Integral Transforms II (1954) Gould, The Lagrange interpolation formula and Stirling numbers, Proc. Amer. Math. Soc. 11: pp 421– (1960) · Zbl 0102.04904 Gould, Note on recurrence relations for Stirling numbers, Publ. Inst. Math. 20: pp 115– (1966) · Zbl 0145.01403 Graham, Concrete Mathematics (1989) Hansen, A Table of Series and Products (1975) Hsu, Note on an asymptotic expansion of the nth difference of zero, Ann. Math. Stat. 19: pp 273– (1948) · Zbl 0035.15702 Jordan, Calculus of Finite Differences (1950) · Zbl 0041.05401 Kimball, The application of Bernoulli polynomials of negative order to differencing, Amer. J. Math. 55: pp 399– (1933) · Zbl 0007.21101 Luke, Mathematical Functions and Their Approximations (1975) Miller, Lecture Notes in Math. 457, in: Fractional Calculus and Its Applications pp 80– (1975) Moser, Stirling numbers of the second kind, Duke Math. J. 25: pp 29– (1958) · Zbl 0079.09102 Nielsen, Die Gammafunktion (1965) Nörlund, Vorlesung über Differenzenrechnung (1954) Oldham, The Fractional Calculus (1974) · Zbl 0206.46601 Rota, Finite Operator Calculus (1975) Schoenberg, CBMS 12, in: Cardinal Spline Interpolation (1973) Schumaker, Spline Functions: Basic Theory (1981) Srivastava, A Treatise on Generating Functions (1984) · Zbl 0535.33001 Westphal, Ein Kalkül für gebrochene Potenzen infinitesimaler Erzeuger von Halbgruppen und Gruppen von Operatoren; Teil I: Halbgruppenerzeuger, Comp. Math. 22: pp 67– (1970) · Zbl 0194.15401 Westphal, An approach to fractional powers of operators via fractional differences, Proc. London Math. Soc. 29 (3) pp 557– (1974) · Zbl 0294.47030 Westphal, Linear Operators and Approximation pp 23– (1974)\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6292013,"math_prob":0.8949268,"size":4059,"snap":"2022-05-2022-21","text_gpt3_token_len":1220,"char_repetition_ratio":0.12996301,"word_repetition_ratio":0.034662046,"special_character_ratio":0.32668144,"punctuation_ratio":0.20158103,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9913718,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-19T23:26:29Z\",\"WARC-Record-ID\":\"<urn:uuid:4b121f36-5763-4b29-a22a-353ece2cd794>\",\"Content-Length\":\"55614\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1ab6ffbc-4715-4b26-9aec-a1ea29b7d22d>\",\"WARC-Concurrent-To\":\"<urn:uuid:0b2323ab-0558-477c-88ed-9ed38c541915>\",\"WARC-IP-Address\":\"141.66.194.2\",\"WARC-Target-URI\":\"https://zbmath.org/?q=an%3A0738.11025\",\"WARC-Payload-Digest\":\"sha1:E44LSJ5T46G7O4377722EYUZE2WAFS4Z\",\"WARC-Block-Digest\":\"sha1:PQDR5O2FEZEIYGYQV467ZM4NRHQU6U2R\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320301592.29_warc_CC-MAIN-20220119215632-20220120005632-00085.warc.gz\"}"}
https://accessmedicine.mhmedical.com/content.aspx?bookid=2724&sectionid=227194691	[ "## KEY CONCEPTS\n\nKEY CONCEPTS\n\n•", null, "Special statistical tests are needed when more than two groups are studied or when a group is measured on several variables.\n\n•", null, "Analysis of variance, or ANOVA, is a statistical method that divides the variance in an observation into the variance among groups and the rest of the variance, called the within-group or error variance.\n\n•", null, "The F test used to compare two variances in Chapter 6 is used to compare the variance among groups to the error.\n\n•", null, "An example of the way ANOVA is calculated from the definitional formulas is helpful in understanding the logic behind the test.\n\n•", null, "The terms used in ANOVA are important, but the details of the computations are given for illustration only, and computer programs are used for all ANOVA procedures.\n\n•", null, "One-way ANOVA is the appropriate method when more than two groups are studied on one variable.\n\n•", null, "As with the t test, certain assumptions must be made to use ANOVA, and equal variances is one of the most important.\n\n•", null, "Making many comparisons among groups increases the chances of a type I error, that a difference is concluded when there is none.\n\n•", null, "Investigators can decide ahead of time what specific comparisons they want to make.\n\n•", null, "The Bonferroni procedure is a common way to compensate for making many comparisons among groups; it works by reducing the size of α for each comparison, essentially increasing the difference needed to be significant.\n\n•", null, "Some multiple comparison methods, called post hoc, are done only if the ANOVA results are statistically significant.\n\n•", null, "Tukey's test is one of the most highly recommended post hoc tests for comparing mean differences.\n\n•", null, "The Scheffé post hoc procedure is the most conservative (requiring a larger difference to be significant), but it is also the most versatile.\n\n•", null, "The Newman–Kuels post hoc procedure is used frequently in basic science research.\n\n•", null, "Dunnett's procedure is the test of choice if the only comparisons being made are between the mean in a control group and the means in other groups.\n\n•", null, "Two-way ANOVA analyzes two factors instead of just one, as in one-way ANOVA. It also permits the analysis of the interaction between two factors.\n\n•", null, "ANOVA designs involving more than two factors are possible, generally called factorial designs.\n\n•", null, "Confounding variables can be accommodated by the ANOVA randomized block design.\n\n•", null, "Repeated-measures ANOVA is a common procedure in medical research; it is analogous to the paired t test with more than two groups and is also called the split-plot design.\n\n•", null, "Nonparametric ANOVA methods include Kruskal-Wallis for one-way designs and Friedman two-way ANOVA for repeated measures. These methods are analogous to the Wilcoxon procedures and are used when the assumptions for ANOVA are not met.\n\n•", null, "The chi-square test can be used to compare more than two proportions and to determine if there is an association between two factors, each of which can have two or more levels. It is a simple extension of the chi-square test we discussed in Chapter 6.\n\n•", null, "As with research questions ...\n\n### Pop-up div Successfully Displayed\n\nThis div only appears when the trigger link is hovered over. 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https://formulas.tutorvista.com/chemistry/molar-mass-formula.html	[ "To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)", null, "Top\n\n# Molar Mass Formula\n\nThe molar mass of a species is the mass in grams of 1 mole (6.023x1023) of that species, i mole of atoms, 1 mole of molecules or 1 mole of formula units. So it is necessary to calculate the molecular or formula mass of each compound to get its molar mass.\n\nMolar mass is the mass (in grams) of one mole of a substance.Using the atomic mass of an element and multiplying it by the conversion factor grams per mole (g/mol), you can calculate the molar mass of that element.\n\nMolecular Mass equals the sum of the atomic masses of all atoms in the molecule. The unit of molecular mass is the amu.\n\nMolar Mass is an amount of the compound equal to its molecular mass in grams. The unit of molar mass is the gram.\n\nTwo important facts to remember:\n1. One mole of an element is 6.023x1023 atoms of that element.\n2. One mole of an element is an amount of that element equal to its molar mass (an amount equal to its atomic mass in grams).", null, "I mole of any element is an amount equal to its atomic mass in grams, its molar mass.\n\n Related Calculators Calculating Molar Mass of a Gas Chemistry Molar Mass Calculator formula mass calculator Calculate Molarity\n\n## Molar Mass Problems\n\nBack to Top\nSolved problems based on molar mass and molecular mass are given below.\n\n### Solved Examples\n\nQuestion 1: Find the molar mass of Ca3(PO4)2?\nSolution:\n\nDetermining the formula mass of calcium phosphate Ca3(PO4)2, which has 3 calcium ions, Ca2+, and 2 phosphate ions PO42-, starts by counting the atoms of each element in the formula 3Ca, 2P and 8O and ends by adding the atomic masses of the 13 atoms.\n\nThe formula of Ca3(PO4)2 = 3Ca + 2P + 8O\n\n(3Ca x 40.08amu) + (2P x 30.97amu) + (8O x 16.00amu) = 310.18amu\n\nThe formula mass of Ca3(PO4)2 = 310.18amu\n\nThe molar mass of Ca3(PO4)2 = 310.18g\n\n1 mole of Ca3(PO4)2 = 310.18g of Ca3(PO4)2 = 6.023 x 1023 formula units\n\nQuestion 2: Find the molar mass of MgSO4.7H2O?\nSolution:\n\nHydrates are also ionic compounds that contain a definite amount of water in the crystalline solid.\nThe hydrate of magnesium sulfate. MgSO4.7H2O has 1 Mg2- ion, 1 SO42- ion and 7 molecules of water in the formula unit.\nSeven moles of water are present for each 1 mole of MgSO4.\nThere are 27 atoms in the formula unit: 1Mg, 1S, 11O and 14H.\nThe formula mass of MgSO4.7H2O is\nThe formula of MgSO4.7H2O = 1Mg + 1S + 11O + 14H\n\n(1Mg x 24.31amu) + (1S x 32.07amu) + (11O x 16.00amu) + (14H x 1.008amu) = 246.49amu\n\nThe molar mass of MgSO4.7H2O = 246.49g\n\n1 mole of MgSO4.7H2O = 246.49g of MgSO4.7H2O = 6.022 x 1023 formula units.\n\n More topics in Molar Mass Formula Gram Formula Mass Mass Percent Formula Molar Volume Formula Percent by Volume Formula Percent by Weight Formula Percent Increase Formula Percent Decrease Formula Percentage Yield Formula\n*AP and SAT are registered trademarks of the College Board." ]	[ null, "https://image.tutorvista.com/seonew/images/searchbutton.png", null, "https://images.tutorvista.com/cms/formulaimages/44/molar-mass.JPG", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.699716,"math_prob":0.9986266,"size":361,"snap":"2019-13-2019-22","text_gpt3_token_len":72,"char_repetition_ratio":0.26890758,"word_repetition_ratio":0.0,"special_character_ratio":0.17174515,"punctuation_ratio":0.0,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998341,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-26T20:39:09Z\",\"WARC-Record-ID\":\"<urn:uuid:f1be3ea0-2410-4280-8a53-2bfce1ff990b>\",\"Content-Length\":\"42868\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2565de5f-151a-4a19-8295-11fa9e83e8ff>\",\"WARC-Concurrent-To\":\"<urn:uuid:a3bf2080-e88d-444e-aa69-876f7da10c39>\",\"WARC-IP-Address\":\"74.86.236.83\",\"WARC-Target-URI\":\"https://formulas.tutorvista.com/chemistry/molar-mass-formula.html\",\"WARC-Payload-Digest\":\"sha1:7WHCT3R4HZNFMW2LCRUZK5BQCEDKUKRU\",\"WARC-Block-Digest\":\"sha1:WFDLIRABCDWUH5DVFF2PJ3NP36YABQ7Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232259452.84_warc_CC-MAIN-20190526185417-20190526211417-00235.warc.gz\"}"}
https://physics.stackexchange.com/questions/32707/how-do-we-distinguish-between-virtual-particle-exchange-and-particle-decay/32748	[ "How do we distinguish between virtual particle exchange and particle decay?\n\nThe difference between virtual particles and unstable particles is discussed at length in this question (namely, virtual particles correspond to internal lines in Feynman diagrams and are not associated with any measurable physical state). So what is going in the case of, say, Higgs production at the LHC, where the Higgs does not live long enough to reach the detector? What are the calculational and experimental differences between producing a Higgs via quark fusion, which then decays into a pair of leptons (for example) and quark-quark to lepton-lepton scattering, proceeding via Higgs exchange?\n\n(To put it another way, we'll see an increase in lepton-lepton production from virtual Higgs exchange, but how is this distinct from seeing particles produced from the decay of an unstable Higgs?)\n\n• The Higgs is always virtual because it is unstable. This was a debate in the 1960s, about whether unstable particles count as particles because they are always virtual. It's ultimately a convention, and people settled on a sensible definition that every independent propagating field in the Lagrangian is a particle. – Ron Maimon Jul 24 '12 at 2:15\n• So would you like to comment on the Arnold Neumaier's answer from that question I linked, in which he clearly distinguishes between the two? – James Jul 24 '12 at 12:52\n• Arnold Neumaier's answer is describing the signature of a new particle on the scattering, it's an additional two fermion-two fermion scattering with a nonlocal vertex. The Higs is still virtual in the answer. – Ron Maimon Jul 24 '12 at 13:12\n• I think that may be referring to his answer here. I meant his answer here: physics.stackexchange.com/questions/4349/… – James Jul 24 '12 at 21:59\n• That answer you link to is mathematically probably ok (I didn't read it carefully), but physically incorrect. It is known since Schwinger and Feynman that the diagrams have an interpretation as a particle process. It is difficult, but possible, to give this heuristic picture a better mathematical grounding, but regardless, it is correct that you can do Feynman graphs as sum over space-time paths, without any modification of the formalism. The answer is unfortunate. – Ron Maimon Jul 25 '12 at 3:33\n\nDecaying particles are described by complex energies, the imaginary part of which encodes life-time information. They are observable; in case of very short-lived particles such as the Higgs in the form of resonances, http://en.wikipedia.org/wiki/Resonance_(particle_physics) , i.e., a peak in the production rate of products of Higgs decays. The decay itself would be visible only at much better time resolution, i.e., far higher energies.\n\nIn contrast, virtual particles have real energies with 4-momentum violating the equation $p^2=(mc)^2$. They are unobservable.\n\nA much more detailed answer can be found at https://physics.stackexchange.com/a/22064/7924\n\n• Virtual Higgs exchange is the computational procedure by which (in a perturbative setting) the peak in the cross-section of dilepton production is predicted. (A lattice gauge theory has no virtual particle concept but could predict the peak, too, at least in principle. This proves that virtual particles are tied to the computational procedure.) - On the other hand, Higgs decay is how Nature actually does it. – Arnold Neumaier Jul 24 '12 at 13:23\n• @ArnoldNeumaier: That's ridiculous. You can't distinguish \"decay\" from virtual exchange--- what if the Higgs decays at a spacelike separation from its production? Virtual particles are not a calculation procedure. – Ron Maimon Jul 24 '12 at 21:58\n• @RonMaimon: If a Higgs decays at some distance from where it was created, it is a real particle with complex energy, not a virtual particle. Virtual particles have no existence outside of perturbation theory. – Arnold Neumaier Jul 25 '12 at 10:07\n• @ArnoldNeumaier: This is completely incorrect. You can have strong virtual photon exchange between a lepton and a quark in a proton which is nonlocal in space, corresponding to a long-range interaction. The Higgs is no different. Your interpretation is an anti-Feynman anti-Schwinger disease that has been going on since 1945, it's got to stop. The idea that the particle thing only works at perturbations is wrong. – Ron Maimon Jul 25 '12 at 16:48\n• @RonMaimon: Feynman diagrams (hence virtual particles) mean something only in perturbation theory. Not even nonperturbative functional integrals feature virtual particles. On the other hand, perturbation theory of a system of classical anharmonic oscillators features virtual particles, though nobody claims their physical existence. – Arnold Neumaier Jul 25 '12 at 17:20\n\nThe standard model predicts that the Higgs boson has a lifetime on the order of $10^{-22}$ seconds. That means that if the Higgs were moving close to the speed of light, it could move something like $34\\gamma$ times the diameter of a proton (on average) before it decays. $\\gamma$ is the time dilation factor from special relativity which is $$\\gamma = \\sqrt{\\frac{1}{1-\\frac{v^2}{c^2}}}$$ So, theoretically, if we could precisely aim two quarks at each other with sufficient precision and measure the vertex of the two outgoing leptons with sufficient precision, we could actually measure how far the Higgs traveled (on average) before it decayed. Note that this, like all radioactive decays, follows an exponential fall off with respect to time, so it could travel significantly longer than $34\\gamma$ proton diameters, but the probability of this rapidly approaches zero.\n\nNow, this distance of $34\\gamma$ proton diameters is far to small to actually be measured at the LHC or any other proposed accelerator. But this lifetime is measurable by measuring the width of the \"bump\" that the Higgs creates in the cross sections that can be measured at accelerators.\n\nThis bump in the cross section and this \"significant\" distance between the vertices will only occur when the total energy center of mass energy of the two incoming quarks is close to the Higgs mass (of 125 GeV - this is called an \"on shell\" Higgs production). You are correct - when the incoming quarks have a mass that is significantly different that 125 GeV (\"off shell\"), the Higgs will still contribute to the cross section for two quarks to create two leptons via a virtual Higgs exchange, but in this cases the incoming quark and outgoing lepton vertices will be VERY close to each other - nothing like $34\\gamma$ proton diameters apart you get for on-shell Higgs production. I am only guessing, but I bet the vertices would be much less than 1 proton diameter apart for these far \"off shell\" lepton production processes.\n\nOf course, as you change the energy of the collision from far off shell to exactly on shell, the distance between the two vertices will continuously change from near zero to the average of $34\\gamma$ proton diameters, but there is no particular point where you can say there is uniquely a \"real\" Higgs in this case versus a \"virtual\" Higgs in that case. However, there is still a dramatic difference between the exactly on-shell versus far off-shell results.\n\n• If you boost the higgs, you time dilate its decay rate. – Jerry Schirmer Jul 24 '12 at 14:46\n• @JerrySchirmer, Thanks! I modified the answer to include that effect. – FrankH Jul 24 '12 at 16:38" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9301846,"math_prob":0.85121405,"size":2449,"snap":"2019-43-2019-47","text_gpt3_token_len":541,"char_repetition_ratio":0.114519425,"word_repetition_ratio":0.0,"special_character_ratio":0.21804819,"punctuation_ratio":0.06013363,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97785413,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-19T06:59:42Z\",\"WARC-Record-ID\":\"<urn:uuid:c15c1f36-070d-4926-87ff-2c83b1e98a90>\",\"Content-Length\":\"167278\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:05d187de-11b6-4ff8-982b-8d9e85d47b68>\",\"WARC-Concurrent-To\":\"<urn:uuid:7a002961-c6b8-4661-b4d3-b7576c65bc60>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://physics.stackexchange.com/questions/32707/how-do-we-distinguish-between-virtual-particle-exchange-and-particle-decay/32748\",\"WARC-Payload-Digest\":\"sha1:74NWOPRZUCNJIC4TLY3E6UYBVXRKUVXY\",\"WARC-Block-Digest\":\"sha1:ULRHIHNOH5YDY6V5OVDKTRC2O2IXDAKY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986692126.27_warc_CC-MAIN-20191019063516-20191019091016-00428.warc.gz\"}"}
https://courses.lumenlearning.com/wm-prealgebra/chapter/solving-applications-with-percent/	[ "## Solving Applications With Percent\n\n### Learning Outcomes\n\n• Calculate the tip for a meal given a percent\n• Find total recommended amount of fiber and sodium given percent and amount\n• Calculate percent calories from fat given total calories and calories from fat\n\nMany applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we’ll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.\n\nWe will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.\n\n### Solve an application\n\n1. Identify what you are asked to find and choose a variable to represent it.\n2. Write a sentence that gives the information to find it.\n3. Translate the sentence into an equation.\n4. Solve the equation using good algebra techniques.\n5. Check the answer in the problem and make sure it makes sense.\n6. Write a complete sentence that answers the question.\n\nNow that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we’ll solve involve everyday situations, you can rely on your own experience.\n\n### example\n\nDezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was $\\text{\\68.50}$. They want to leave an $\\text{18%}$ tip. If the tip will be $\\text{18%}$ of the total bill, how much should the tip be?\n\nSolution\n\n What are you asked to find? the amount of the tip Choose a variable to represent it. Let $t=$ amount of tip. Write a sentence that give the information to find it. The tip is 18% of the total bill. Translate the sentence into an equation.", null, "Multiply. $t=12.33$ Check. Is this answer reasonable? If we approximate the bill to $\\text{\\70}$ and the percent to $20\\text{%}$, we would have a tip of $\\text{\\14}$. So a tip of $\\text{\\12.33}$ seems reasonable. Write a complete sentence that answers the question. The couple should leave a tip of $\\text{\\12.33}$.\n\n### try it\n\nIn the next video we show another example of finding how much tip to give based on percent.\n\n### example\n\nThe label on Masao’s breakfast cereal said that one serving of cereal provides $85$ milligrams (mg) of potassium, which is $\\text{2%}$ of the recommended daily amount. What is the total recommended daily amount of potassium?", null, "### example\n\nMitzi received some gourmet brownies as a gift. The wrapper said each brownie was $480$ calories, and had $240$ calories of fat. What percent of the total calories in each brownie comes from fat?\n\n### try it\n\nThe following video show another example of how to solve an application that involves percent." ]	[ null, "https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/277/2017/04/24221939/CNX_BMath_Figure_06_02_009_img-01.png", null, "https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/277/2017/04/24221942/CNX_BMath_Figure_06_02_002.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9133086,"math_prob":0.9856578,"size":3005,"snap":"2021-43-2021-49","text_gpt3_token_len":702,"char_repetition_ratio":0.1482839,"word_repetition_ratio":0.016806724,"special_character_ratio":0.23693843,"punctuation_ratio":0.094736844,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958471,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,3,null,7,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-27T04:39:23Z\",\"WARC-Record-ID\":\"<urn:uuid:4730dedd-06a0-45ee-8880-f94975f9e0ca>\",\"Content-Length\":\"37828\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:60bff751-b276-4cd3-a176-9bb60bed9cf3>\",\"WARC-Concurrent-To\":\"<urn:uuid:71a54946-edcb-4127-9151-b6eb51c8812b>\",\"WARC-IP-Address\":\"23.185.0.1\",\"WARC-Target-URI\":\"https://courses.lumenlearning.com/wm-prealgebra/chapter/solving-applications-with-percent/\",\"WARC-Payload-Digest\":\"sha1:L7BCAWZ3WMQAFAIR66DFKWZJP33QZV57\",\"WARC-Block-Digest\":\"sha1:2E2SXIMULZ2KEIENBC3534AFI5VRBJHM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588053.38_warc_CC-MAIN-20211027022823-20211027052823-00292.warc.gz\"}"}
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https://www.lfhacks.com/tech/python-flatten-sub-sequence/	[ "# Python 展开多层嵌套的列表", null, "## 背景\n\n``````[1, 'a', ['b', ['c'], [ ], [3, 4]]]\n``````\n\n``````1, a, b, c, 3, 4\n``````\n\n## 未知嵌套层数\n\n``````def 展开（任意序列）\n``````\n\n``````def 展开（任意序列）:\n对于任意序列里的每一项:\n如果仍然是序列:\n给出（yield）展开（这个序列）里的每一项\n否则：\n给出（yield）这一项\n``````\n\n``````def flatten(sequence):\nfor item in sequence:\nif type(item) is list:\nfor subitem in flatten(item):\nyield subitem\nelse:\nyield item\na = [1, 'a', ['b', ['c'], [ ], [3, 4]]]\nfor x in flatten(a):\nprint x,\n``````\n\n## 用列表解析实现\n\n``````flatten = lambda x: [subitem for item in x for subitem in flatten(item)] \\\nif type(x) is list else [x]\na = [1, 'a', ['b', ['c'], [ ], [3, 4]]]\nfor x in flatten(a):\nprint x,\n``````\n\n``````1 a b c 3 4\n``````\n\n## 用 reduce 实现\n\nfrom functools import reduce\n\n``````reduce(lambda x,y:x+y,[[1,2],[3,4]])\n``````\n\n``````[1, 2, 3, 4]\n``````", null, "" ]	[ null, "https://www.lfhacks.com/image/poster/579.jpg", null, "https://www.lfhacks.com/image/common/cc-by.png", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.8490819,"math_prob":0.99028367,"size":1106,"snap":"2021-43-2021-49","text_gpt3_token_len":690,"char_repetition_ratio":0.11524501,"word_repetition_ratio":0.1891892,"special_character_ratio":0.32188064,"punctuation_ratio":0.19742489,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9816496,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T23:38:28Z\",\"WARC-Record-ID\":\"<urn:uuid:58027cd2-51c8-446b-a88a-4ffe401686e2>\",\"Content-Length\":\"13287\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2e4977f4-1046-44e7-9fd8-1929d92726ec>\",\"WARC-Concurrent-To\":\"<urn:uuid:a3cc3fa6-b488-4322-866d-8741bca36d19>\",\"WARC-IP-Address\":\"118.123.21.94\",\"WARC-Target-URI\":\"https://www.lfhacks.com/tech/python-flatten-sub-sequence/\",\"WARC-Payload-Digest\":\"sha1:6YG4BT3R23TFNNAB6VXMWXPUCC752HBY\",\"WARC-Block-Digest\":\"sha1:CWIJJYYXPATMDMGIAIKYSUHY6YGMCITS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585045.2_warc_CC-MAIN-20211016231019-20211017021019-00437.warc.gz\"}"}
https://codereview.stackexchange.com/questions/61899/cron-job-that-runs-a-few-checks-across-different-tables-in-database	[ "# Cron job that runs a few checks across different tables in database\n\nI have been working on a cronjob that runs a few checks across different tables in my database.\n\nThe issue is that although it works, I feel like I am doing something horribly wrong in terms of the standards set out by others and also in the future for any adjustments I make.\n\nThe code below DOES work perfectly, but a foreach in a foreach seems horrible. Is there any way to tidy up what I am doing, or would it be acceptable code by a good standard?\n\n// CRON JOB - Add notification if a build has been updated\nrequire(\"../../commonlive.php\");\nrequire '../../functions/database-functions.php';\n// select all users, and run a foreach\n$query = \"SELECT * FROM users\";$query_params = array();\ntry {\n$stmt =$db->prepare($query);$result = $stmt->execute($query_params);\n}\ncatch(PDOException $ex) { die(\"Failed to run query: \" .$ex->getMessage());\n}\n$rows =$stmt->fetchAll();\n// for each user, check its user ID against the build tracking and then see when the build was updated last\nforeach($rows as$row){\n$id =$row['id'];\n//echo \"user id: $id, \"; // check the build_tracking table for a row that matches the user id$query = \" SELECT * FROM build_tracking WHERE user_id = :user_id\";\n$query_params = array(':user_id' =>$id);\ntry {\n$stmt =$db->prepare($query);$result = $stmt->execute($query_params);\n$rows =$stmt->fetchAll();\nforeach ($rows as$row) {\n\n$build_id =$row['build_id'];\n$user_id =$row['user_id'];\n$view_time =$row['view_time'];\n\n//echo \"build id track: $build_id\"; // check the build_tracking table for a row that matches the user id and build id.$query = \" SELECT * FROM blogs WHERE id = :build_id AND frontpage = 1\";\n$query_params = array(':build_id' =>$build_id);\ntry {\n$stmt =$db->prepare($query);$result = $stmt->execute($query_params);\n$rows =$stmt->fetchAll();\nforeach ($rows as$row) {\n$build_id =$row['id'];\n$buildOwnerID =$row['userid'];\n$lastupdated =$row['lastupdated'];\n\n$stmt =$db->prepare(\"SELECT * FROM followers WHERE userid = $user_id AND blogid =$build_id\");\n$stmt->execute();$stmt->setFetchMode(PDO::FETCH_ASSOC);\n$countfollow =$stmt->rowCount();\n\nif ($view_time <$lastupdated && $countfollow > 0) {$userTo = $id;$userFrom = $buildOwnerID;$type = 'buildUpdate';\n$date = time();$postID = 1;\n$buildID =$build_id;\n$commentID = 1; // see if a notif already exists with the user id and build id$query = \"SELECT * FROM notifications WHERE user_to = :userTo AND buildID = :buildID AND type = :type AND status != 3\";\n$query_params = array(':userTo' =>$userTo, ':buildID' => $buildID, ':type' =>$type);\ntry {\n$stmt =$db->prepare($query);$result = $stmt->execute($query_params);\n$checkForExistOfNotif =$stmt->rowCount();\n}\ncatch(PDOException $ex) { die(\"Failed to run query: \" .$ex->getMessage());\n}\nif (!$checkForExistOfNotif) { //echo \"adding,$build_id\";\naddNotification($userTo,$userFrom, $type,$date, $postID,$buildID, $commentID); } } } } catch(PDOException$ex) { die();\n}\n}\n}\ncatch(PDOException $ex) { die(); } } • you need to work on your formatting, the indentation is terrible, I almost couldn't find the first foreach – Malachi Sep 3 '14 at 22:10 • sorry, its perfect in sublime (using 2 spaces instead of tab) but SO always messes it up. – Lovelock Sep 3 '14 at 22:12 • Using foreach($rows as $row): is pretty unusual when you're not exiting out of the PHP block to insert HTML. – Kid Diamond Sep 3 '14 at 22:12 • should be using foreach($rows as $row){ //code } right? – Lovelock Sep 3 '14 at 22:13 • @user2921557, no one has answered so you can fix the formatting, I assume you already have good formatting, so please fix it quickly – Malachi Sep 3 '14 at 22:17 ## 2 Answers Things that strike me as odd are that you have nested PDOExceptions and in the catch blocks all you do is die. If that is the case, why bother nesting them? Just have one try at the top and one catch at the bottom. You are running this as a cronjob, so if it fails with die(), how does that help anyone trying to debug what went wrong? At least pass some sort of indication as to what the error was. I would also split your code into functions, each function should do 1 thing, then you can easily read what the top level code is doing I am not going to re-write all your code, but here is an example of what it could start to look like if you split it into functions. It becomes a lot more readable (maintainable) even with no comments. try {$users = select_all_users();\n\nforeach ($users as$user) {\n$builds = select_builds_by_user($user['id']);\n\nforeach ($builds as$build) {\n$build_id =$build['build_id'];\n$user_id =$build['user_id'];\n$view_time =$build['view_time'];\n\n\nThe reason I didn't bother to re-write it all, is because I am pretty sure you could merge 3 or more of those SQL statements and using joins to fetch the data in one query, rather then the foreach, foreach, foreach going on.\n\nFor example you start off by selecting all users and then looping though them checking to see if builds exist. (I have no idea what your database structure is, so I can only offer guesses here) but this SQL selects all builds for users in one go.\n\n SELECT *\nFROM build_tracking\n\n\nHope this gives you some of ideas of things to work on\n\nYou can clean up deeply nested situations like this by breaking the nested logic into functions.\n\nforeach($rows as$row) {\n// Do something\nprocessBuilds($row['buildId']); } function processBuilds($buildId) {\n// Do stuff\nforeach($buildRows as$buildRow) {\nprocessBlogs($buildRow['blogId']); } } function processBlogs($blogId) {\n// Do stuff\nforeach($blogRows as$blogRow) {\n// Do more stuff\n}\n}\n\n\nDepending on the size of the application, it may make sense to take this one step further and take advantage of object-oriented programming." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.68293554,"math_prob":0.7562444,"size":3159,"snap":"2020-24-2020-29","text_gpt3_token_len":850,"char_repetition_ratio":0.12488114,"word_repetition_ratio":0.18526316,"special_character_ratio":0.32668567,"punctuation_ratio":0.18819188,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9767402,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-12T11:56:17Z\",\"WARC-Record-ID\":\"<urn:uuid:8faf3d64-d79b-44f7-acf9-8eebf1c42b06>\",\"Content-Length\":\"162512\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7795eaf-884a-4476-bd52-10c4ad8c4601>\",\"WARC-Concurrent-To\":\"<urn:uuid:447572ea-8146-493e-84d5-81ab3da7f1e7>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://codereview.stackexchange.com/questions/61899/cron-job-that-runs-a-few-checks-across-different-tables-in-database\",\"WARC-Payload-Digest\":\"sha1:QJHE4UQMD6I3NDR243AUN5F4PL37FUMB\",\"WARC-Block-Digest\":\"sha1:FEU3QIKSJXDQJNPFBF4KR4JPIPXASRVH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593657138718.61_warc_CC-MAIN-20200712113546-20200712143546-00252.warc.gz\"}"}
https://hackage.haskell.org/package/hmatrix-0.20.0.0/docs/src/Internal.ST.html	[ "```{-# LANGUAGE Rank2Types #-}\n{-# LANGUAGE BangPatterns #-}\n{-# LANGUAGE ViewPatterns #-}\n\n-----------------------------------------------------------------------------\n-- \|\n-- Module : Internal.ST\n-- Copyright : (c) Alberto Ruiz 2008\n-- License : BSD3\n-- Maintainer : Alberto Ruiz\n-- Stability : provisional\n--\n-- In-place manipulation inside the ST monad.\n-- See @examples/inplace.hs@ in the repository.\n--\n-----------------------------------------------------------------------------\n\nmodule Internal.ST (\nST, runST,\n-- * Mutable Vectors\nSTVector, newVector, thawVector, freezeVector, runSTVector,\nreadVector, writeVector, modifyVector, liftSTVector,\n-- * Mutable Matrices\nSTMatrix, newMatrix, thawMatrix, freezeMatrix, runSTMatrix,\nreadMatrix, writeMatrix, modifyMatrix, liftSTMatrix,\nmutable, extractMatrix, setMatrix, rowOper, RowOper(..), RowRange(..), ColRange(..), gemmm, Slice(..),\n-- * Unsafe functions\nnewUndefinedVector,\nunsafeReadVector, unsafeWriteVector,\nunsafeThawVector, unsafeFreezeVector,\nnewUndefinedMatrix,\nunsafeReadMatrix, unsafeWriteMatrix,\nunsafeThawMatrix, unsafeFreezeMatrix\n) where\n\nimport Internal.Vector\nimport Internal.Matrix\nimport Internal.Vectorized\nimport Control.Monad.ST(ST, runST)\nimport Foreign.Storable(Storable, peekElemOff, pokeElemOff)\nimport Control.Monad.ST.Unsafe(unsafeIOToST)\n\n{-# INLINE ioReadV #-}\nioReadV :: Storable t => Vector t -> Int -> IO t\nioReadV v k = unsafeWith v \\$ \\s -> peekElemOff s k\n\n{-# INLINE ioWriteV #-}\nioWriteV :: Storable t => Vector t -> Int -> t -> IO ()\nioWriteV v k x = unsafeWith v \\$ \\s -> pokeElemOff s k x\n\nnewtype STVector s t = STVector (Vector t)\n\nthawVector :: Storable t => Vector t -> ST s (STVector s t)\nthawVector = unsafeIOToST . fmap STVector . cloneVector\n\nunsafeThawVector :: Storable t => Vector t -> ST s (STVector s t)\nunsafeThawVector = unsafeIOToST . return . STVector\n\nrunSTVector :: Storable t => (forall s . ST s (STVector s t)) -> Vector t\nrunSTVector st = runST (st >>= unsafeFreezeVector)\n\n{-# INLINE unsafeReadVector #-}\nunsafeReadVector :: Storable t => STVector s t -> Int -> ST s t\nunsafeReadVector (STVector x) = unsafeIOToST . ioReadV x\n\n{-# INLINE unsafeWriteVector #-}\nunsafeWriteVector :: Storable t => STVector s t -> Int -> t -> ST s ()\nunsafeWriteVector (STVector x) k = unsafeIOToST . ioWriteV x k\n\n{-# INLINE modifyVector #-}\nmodifyVector :: (Storable t) => STVector s t -> Int -> (t -> t) -> ST s ()\nmodifyVector x k f = readVector x k >>= return . f >>= unsafeWriteVector x k\n\nliftSTVector :: (Storable t) => (Vector t -> a) -> STVector s t -> ST s a\nliftSTVector f (STVector x) = unsafeIOToST . fmap f . cloneVector \\$ x\n\nfreezeVector :: (Storable t) => STVector s t -> ST s (Vector t)\nfreezeVector v = liftSTVector id v\n\nunsafeFreezeVector :: (Storable t) => STVector s t -> ST s (Vector t)\nunsafeFreezeVector (STVector x) = unsafeIOToST . return \\$ x\n\n{-# INLINE safeIndexV #-}\nsafeIndexV :: Storable t2\n=> (STVector s t2 -> Int -> t) -> STVector t1 t2 -> Int -> t\nsafeIndexV f (STVector v) k\n\| k < 0 \|\| k>= dim v = error \\$ \"out of range error in vector (dim=\"\n++show (dim v)++\", pos=\"++show k++\")\"\n\| otherwise = f (STVector v) k\n\n{-# INLINE readVector #-}\nreadVector :: Storable t => STVector s t -> Int -> ST s t\nreadVector = safeIndexV unsafeReadVector\n\n{-# INLINE writeVector #-}\nwriteVector :: Storable t => STVector s t -> Int -> t -> ST s ()\nwriteVector = safeIndexV unsafeWriteVector\n\nnewUndefinedVector :: Storable t => Int -> ST s (STVector s t)\nnewUndefinedVector = unsafeIOToST . fmap STVector . createVector\n\n{-# INLINE newVector #-}\nnewVector :: Storable t => t -> Int -> ST s (STVector s t)\nnewVector x n = do\nv <- newUndefinedVector n\nlet go (-1) = return v\ngo !k = unsafeWriteVector v k x >> go (k-1 :: Int)\ngo (n-1)\n\n-------------------------------------------------------------------------\n\n{-# INLINE ioReadM #-}\nioReadM :: Storable t => Matrix t -> Int -> Int -> IO t\nioReadM m r c = ioReadV (xdat m) (r * xRow m + c * xCol m)\n\n{-# INLINE ioWriteM #-}\nioWriteM :: Storable t => Matrix t -> Int -> Int -> t -> IO ()\nioWriteM m r c val = ioWriteV (xdat m) (r * xRow m + c * xCol m) val\n\nnewtype STMatrix s t = STMatrix (Matrix t)\n\nthawMatrix :: Element t => Matrix t -> ST s (STMatrix s t)\nthawMatrix = unsafeIOToST . fmap STMatrix . cloneMatrix\n\nunsafeThawMatrix :: Storable t => Matrix t -> ST s (STMatrix s t)\nunsafeThawMatrix = unsafeIOToST . return . STMatrix\n\nrunSTMatrix :: Storable t => (forall s . ST s (STMatrix s t)) -> Matrix t\nrunSTMatrix st = runST (st >>= unsafeFreezeMatrix)\n\n{-# INLINE unsafeReadMatrix #-}\nunsafeReadMatrix :: Storable t => STMatrix s t -> Int -> Int -> ST s t\nunsafeReadMatrix (STMatrix x) r = unsafeIOToST . ioReadM x r\n\n{-# INLINE unsafeWriteMatrix #-}\nunsafeWriteMatrix :: Storable t => STMatrix s t -> Int -> Int -> t -> ST s ()\nunsafeWriteMatrix (STMatrix x) r c = unsafeIOToST . ioWriteM x r c\n\n{-# INLINE modifyMatrix #-}\nmodifyMatrix :: (Storable t) => STMatrix s t -> Int -> Int -> (t -> t) -> ST s ()\nmodifyMatrix x r c f = readMatrix x r c >>= return . f >>= unsafeWriteMatrix x r c\n\nliftSTMatrix :: (Element t) => (Matrix t -> a) -> STMatrix s t -> ST s a\nliftSTMatrix f (STMatrix x) = unsafeIOToST . fmap f . cloneMatrix \\$ x\n\nunsafeFreezeMatrix :: (Storable t) => STMatrix s t -> ST s (Matrix t)\nunsafeFreezeMatrix (STMatrix x) = unsafeIOToST . return \\$ x\n\nfreezeMatrix :: (Element t) => STMatrix s t -> ST s (Matrix t)\nfreezeMatrix m = liftSTMatrix id m\n\ncloneMatrix :: Element t => Matrix t -> IO (Matrix t)\ncloneMatrix m = copy (orderOf m) m\n\n{-# INLINE safeIndexM #-}\nsafeIndexM :: (STMatrix s t2 -> Int -> Int -> t)\n-> STMatrix t1 t2 -> Int -> Int -> t\nsafeIndexM f (STMatrix m) r c\n\| r<0 \|\| r>=rows m \|\|\nc<0 \|\| c>=cols m = error \\$ \"out of range error in matrix (size=\"\n++show (rows m,cols m)++\", pos=\"++show (r,c)++\")\"\n\| otherwise = f (STMatrix m) r c\n\n{-# INLINE readMatrix #-}\nreadMatrix :: Storable t => STMatrix s t -> Int -> Int -> ST s t\nreadMatrix = safeIndexM unsafeReadMatrix\n\n{-# INLINE writeMatrix #-}\nwriteMatrix :: Storable t => STMatrix s t -> Int -> Int -> t -> ST s ()\nwriteMatrix = safeIndexM unsafeWriteMatrix\n\nsetMatrix :: Element t => STMatrix s t -> Int -> Int -> Matrix t -> ST s ()\nsetMatrix (STMatrix x) i j m = unsafeIOToST \\$ setRect i j m x\n\nnewUndefinedMatrix :: Storable t => MatrixOrder -> Int -> Int -> ST s (STMatrix s t)\nnewUndefinedMatrix ord r c = unsafeIOToST \\$ fmap STMatrix \\$ createMatrix ord r c\n\n{-# NOINLINE newMatrix #-}\nnewMatrix :: Storable t => t -> Int -> Int -> ST s (STMatrix s t)\nnewMatrix v r c = unsafeThawMatrix \\$ reshape c \\$ runSTVector \\$ newVector v (r*c)\n\n--------------------------------------------------------------------------------\n\ndata ColRange = AllCols\n\| ColRange Int Int\n\| Col Int\n\| FromCol Int\n\ngetColRange :: Int -> ColRange -> (Int, Int)\ngetColRange c AllCols = (0,c-1)\ngetColRange c (ColRange a b) = (a `mod` c, b `mod` c)\ngetColRange c (Col a) = (a `mod` c, a `mod` c)\ngetColRange c (FromCol a) = (a `mod` c, c-1)\n\ndata RowRange = AllRows\n\| RowRange Int Int\n\| Row Int\n\| FromRow Int\n\ngetRowRange :: Int -> RowRange -> (Int, Int)\ngetRowRange r AllRows = (0,r-1)\ngetRowRange r (RowRange a b) = (a `mod` r, b `mod` r)\ngetRowRange r (Row a) = (a `mod` r, a `mod` r)\ngetRowRange r (FromRow a) = (a `mod` r, r-1)\n\ndata RowOper t = AXPY t Int Int ColRange\n\| SCAL t RowRange ColRange\n\| SWAP Int Int ColRange\n\nrowOper :: (Num t, Element t) => RowOper t -> STMatrix s t -> ST s ()\n\nrowOper (AXPY x i1 i2 r) (STMatrix m) = unsafeIOToST \\$ rowOp 0 x i1' i2' j1 j2 m\nwhere\n(j1,j2) = getColRange (cols m) r\ni1' = i1 `mod` (rows m)\ni2' = i2 `mod` (rows m)\n\nrowOper (SCAL x rr rc) (STMatrix m) = unsafeIOToST \\$ rowOp 1 x i1 i2 j1 j2 m\nwhere\n(i1,i2) = getRowRange (rows m) rr\n(j1,j2) = getColRange (cols m) rc\n\nrowOper (SWAP i1 i2 r) (STMatrix m) = unsafeIOToST \\$ rowOp 2 0 i1' i2' j1 j2 m\nwhere\n(j1,j2) = getColRange (cols m) r\ni1' = i1 `mod` (rows m)\ni2' = i2 `mod` (rows m)\n\nextractMatrix :: Element a => STMatrix t a -> RowRange -> ColRange -> ST s (Matrix a)\nextractMatrix (STMatrix m) rr rc = unsafeIOToST (extractR (orderOf m) m 0 (idxs[i1,i2]) 0 (idxs[j1,j2]))\nwhere\n(i1,i2) = getRowRange (rows m) rr\n(j1,j2) = getColRange (cols m) rc\n\n-- \| r0 c0 height width\ndata Slice s t = Slice (STMatrix s t) Int Int Int Int\n\nslice :: Element a => Slice t a -> Matrix a\nslice (Slice (STMatrix m) r0 c0 nr nc) = subMatrix (r0,c0) (nr,nc) m\n\ngemmm :: Element t => t -> Slice s t -> t -> Slice s t -> Slice s t -> ST s ()\ngemmm beta (slice->r) alpha (slice->a) (slice->b) = res\nwhere\nres = unsafeIOToST (gemm v a b r)\nv = fromList [alpha,beta]\n\nmutable :: Element t => (forall s . (Int, Int) -> STMatrix s t -> ST s u) -> Matrix t -> (Matrix t,u)\nmutable f a = runST \\$ do\nx <- thawMatrix a\ninfo <- f (rows a, cols a) x\nr <- unsafeFreezeMatrix x\nreturn (r,info)\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.50937366,"math_prob":0.9875644,"size":8100,"snap":"2021-21-2021-25","text_gpt3_token_len":2623,"char_repetition_ratio":0.25185278,"word_repetition_ratio":0.2783235,"special_character_ratio":0.33814815,"punctuation_ratio":0.14347513,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99739414,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-24T13:21:42Z\",\"WARC-Record-ID\":\"<urn:uuid:2060419f-1324-4516-96c5-73dba04f8c2e>\",\"Content-Length\":\"149574\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8b8065ac-c699-40d8-b582-4f05de79814b>\",\"WARC-Concurrent-To\":\"<urn:uuid:fe1b5492-a206-4f54-8d5f-9ddb67ad8127>\",\"WARC-IP-Address\":\"151.101.248.68\",\"WARC-Target-URI\":\"https://hackage.haskell.org/package/hmatrix-0.20.0.0/docs/src/Internal.ST.html\",\"WARC-Payload-Digest\":\"sha1:YAA6CWLQV34BT4IW5R4UULGWTDSY3I7T\",\"WARC-Block-Digest\":\"sha1:W5EIBA3NW7O5WAPKRHPOTH6LGY6P4LK7\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488553635.87_warc_CC-MAIN-20210624110458-20210624140458-00617.warc.gz\"}"}
https://www.ipl.org/essay/Logistic-Regression-Analysis-FCDJ8MSGZVG	[ "", null, "# Logistic Regression Analysis\n\n720 Words3 Pages\nRegression analysis is one of the most useful and the most frequently used statistical methods .regression analysis is a form of predictive modeling technique which investigates the relationship between a dependent and one or more predictor variables. Among the different regression models, logistic regression plays a particular role. However , the basic concept of the linear regression model is quantifying the effect of several explanatory variables on one dependent continuous variable. For situations where the dependent variable is qualitative, however, other methods have been developed. One of the method is logistic regression model, which specifically covers the case of binary or dichotomous response. The statistical analysis of dichotomous outcome variable is frequently interpreted with the use of logistic regression methods. The multiple logistic regression…show more content…\nCramer (2003) discussed an overview of the development of the logistic regression model. He identifies three sources that had a profound impact on the model: applied mathematics, experimental statistics, and economic theory. Agresti (2002) also provided details of the development on logistic regression in different areas. He states, “Sir David R. Cox introduced many statisticians to logistic regression through his 1958 article and 1970 book, The Analysis of Binary Data.” However, logistic regression is widely used as a popular model for the analysis of binary data with the areas of applications including physical, biomedical, and behavioral sciences. For example, Cornfield (1962) presented the preliminary results from the Framingham Study. The purpose of the study was to find the roles of risk factors of cholesterol levels (low versus high values) and blood pressure (low versus high values) in the development of coronary heart disease (yes or no) in the population of the" ]	[ null, "https://assets.ipl.org/1.17/images/icons/burger.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92817354,"math_prob":0.85104674,"size":1885,"snap":"2021-04-2021-17","text_gpt3_token_len":345,"char_repetition_ratio":0.15789473,"word_repetition_ratio":0.0,"special_character_ratio":0.18355438,"punctuation_ratio":0.09120521,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99044394,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-23T02:45:01Z\",\"WARC-Record-ID\":\"<urn:uuid:697ed484-ac0c-496a-92d0-3bf8d8d45925>\",\"Content-Length\":\"22561\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a2a09036-51c2-4836-8edb-2523c5b675b5>\",\"WARC-Concurrent-To\":\"<urn:uuid:6f89c876-51f5-4721-a0f7-cdbd8ede07f7>\",\"WARC-IP-Address\":\"99.84.176.123\",\"WARC-Target-URI\":\"https://www.ipl.org/essay/Logistic-Regression-Analysis-FCDJ8MSGZVG\",\"WARC-Payload-Digest\":\"sha1:DEOPENO73U3SMR52OK2TWEHM3YKE3RIH\",\"WARC-Block-Digest\":\"sha1:TXWARLT2LGJRAY7VNAGB5MW6QSFQDF7Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618039626288.96_warc_CC-MAIN-20210423011010-20210423041010-00506.warc.gz\"}"}
https://alienexpanse.com/index.php?threads/muzyka.25/page-101	[ "Muzyka\n\nDiscussion in 'Arts, Sports, & Entertainment' started by Toroid, Jul 18, 2016.\n\n•", null, "Like x 1\n•", null, "Thanks x 1\n1.\n•", null, "Like x 2\n2.\n•", null, "Like x 2\n3.\n•", null, "Thanks x 1\n•", null, "Like x 2\n4.\n•", null, "Thanks x 1\n5.\n•", null, "Thanks x 1\n6.\n•", null, "Thanks x 1\n7.\n•", null, "Thanks x 1\n8.\n•", null, "Thanks x 1\n9.\n•", null, "Thanks x 1\n10.\n•", null, "Like x 1\n•", null, "Thanks x 1\n11.\n•", null, "Like x 1\n•", null, "Thanks x 1\n•", null, "Thanks x 1\n•", null, "Like x 1\n12.\n•", null, "Thanks x 1\n13.\n•", null, "Thanks x 1\n14.\n•", null, "Thanks x 1\n15.\n\n16. Glory to the King" ]	[ null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/default/xenforo/clear.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null, "https://alienexpanse.com/styles/dark/ratings/thankyou.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.64695287,"math_prob":0.93202955,"size":269,"snap":"2019-26-2019-30","text_gpt3_token_len":95,"char_repetition_ratio":0.21132076,"word_repetition_ratio":0.0,"special_character_ratio":0.25650558,"punctuation_ratio":0.29032257,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9648999,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-18T17:43:28Z\",\"WARC-Record-ID\":\"<urn:uuid:3ae1da83-8b0a-4af1-adb6-daf097da8cb4>\",\"Content-Length\":\"89653\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:69d19ca8-cc66-4dd8-85d6-bf941c670a9b>\",\"WARC-Concurrent-To\":\"<urn:uuid:74ac0fb1-f5a7-4029-bebf-5436f0cc654b>\",\"WARC-IP-Address\":\"160.153.71.38\",\"WARC-Target-URI\":\"https://alienexpanse.com/index.php?threads/muzyka.25/page-101\",\"WARC-Payload-Digest\":\"sha1:ESO5QFZXXD2DC3UHWXTBNSEEJCQLISZK\",\"WARC-Block-Digest\":\"sha1:GIKRCJD3NRODFRW3A3P2GWCX7HRNKAAD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998808.17_warc_CC-MAIN-20190618163443-20190618185443-00415.warc.gz\"}"}
https://paperswithcode.com/paper/quaternion-gradient-and-hessian	[ "13 Jun 2014 · , ·\n\nThe optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions often require the calculation of the gradient and Hessian, however, real functions of quaternion variables are essentially non-analytic... To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized HR (GHR) calculus, thus making possible efficient derivation of optimization algorithms directly in the quaternion field, rather than transforming the problem to the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the proposed quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are elaborated, and the results illuminate the usefulness of the GHR calculus in greatly simplifying the derivation of the quaternion least mean squares, and in quaternion least square and Newton algorithm. The proposed gradient and Hessian are also shown to enable the same generic forms as the corresponding real- and complex-valued algorithms, further illustrating the advantages in algorithm design and evaluation. read more\n\nPDF Abstract\n\n# Code Add Remove Mark official\n\nNo code implementations yet. Submit your code now\n\n# Datasets\n\nAdd Datasets introduced or used in this paper\n\n# Results from the Paper Add Remove\n\nSubmit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.896667,"math_prob":0.9274491,"size":1411,"snap":"2021-43-2021-49","text_gpt3_token_len":247,"char_repetition_ratio":0.17128642,"word_repetition_ratio":0.0,"special_character_ratio":0.16371368,"punctuation_ratio":0.10043668,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9794242,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T12:34:18Z\",\"WARC-Record-ID\":\"<urn:uuid:abff5054-d468-4850-90bc-1989466ffedd>\",\"Content-Length\":\"90925\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1adbf091-3e19-4d11-be87-e7966d96af74>\",\"WARC-Concurrent-To\":\"<urn:uuid:b39976ee-68bc-402a-b3ec-7d30b16a5ace>\",\"WARC-IP-Address\":\"172.67.73.69\",\"WARC-Target-URI\":\"https://paperswithcode.com/paper/quaternion-gradient-and-hessian\",\"WARC-Payload-Digest\":\"sha1:QOMIVRRYWJ63RGX2BGYJNOVK2NKLTCPU\",\"WARC-Block-Digest\":\"sha1:DNS3LCWYA5774XRHJWM7TSPBPIAH3BWR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323584567.81_warc_CC-MAIN-20211016105157-20211016135157-00208.warc.gz\"}"}
https://republicofsouthossetia.org/question/simplify-the-following-epression-using-pemdas-24-6-3-5-8-9-16373655-85/	[ "## Simplify the following expression using PEMDAS: 24 + 6/358-9\n\nQuestion\n\nSimplify the following expression using PEMDAS: 24 + 6/358-9\n\nin progress 0\n2 weeks 2021-09-07T21:10:54+00:00 1 Answer 0\n\n95\n\nStep-by-step explanation:\n\n24+(6\n/3)\n(5)(8)−9\n\n=24+(2)(5)(8)−9\n\n=24+(10)(8)−9\n\n=24+80−9\n\n=104−9\n\n=95" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5075644,"math_prob":0.91386527,"size":351,"snap":"2021-31-2021-39","text_gpt3_token_len":163,"char_repetition_ratio":0.112391934,"word_repetition_ratio":0.23809524,"special_character_ratio":0.55270654,"punctuation_ratio":0.11494253,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.983988,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T02:47:13Z\",\"WARC-Record-ID\":\"<urn:uuid:8fa43e27-9de3-42b5-b0ac-ada4bfccdb33>\",\"Content-Length\":\"68109\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e22630b8-5b3f-484f-8bdf-09eaa524e012>\",\"WARC-Concurrent-To\":\"<urn:uuid:8c1aaa7c-a983-42a5-b05d-1ec00fe8ab95>\",\"WARC-IP-Address\":\"198.252.99.154\",\"WARC-Target-URI\":\"https://republicofsouthossetia.org/question/simplify-the-following-epression-using-pemdas-24-6-3-5-8-9-16373655-85/\",\"WARC-Payload-Digest\":\"sha1:2UMEDO4Q6ZGMEXKVPI2SSMFM5WOTLK5F\",\"WARC-Block-Digest\":\"sha1:M4BHZWCEXGT762F6FEVN43BT5TK3YPWO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056974.30_warc_CC-MAIN-20210920010331-20210920040331-00491.warc.gz\"}"}
https://answers.everydaycalculation.com/compare-fractions/10-20-and-40-84	[ "Solutions by everydaycalculation.com\n\n## Compare 10/20 and 40/84\n\n10/20 is greater than 40/84\n\n#### Steps for comparing fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 20 and 84 is 420\n\nNext, find the equivalent fraction of both fractional numbers with denominator 420\n2. For the 1st fraction, since 20 × 21 = 420,\n10/20 = 10 × 21/20 × 21 = 210/420\n3. Likewise, for the 2nd fraction, since 84 × 5 = 420,\n40/84 = 40 × 5/84 × 5 = 200/420\n4. Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction\n5. 210/420 > 200/420 or 10/20 > 40/84\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.86956036,"math_prob":0.96974945,"size":820,"snap":"2021-31-2021-39","text_gpt3_token_len":278,"char_repetition_ratio":0.19240196,"word_repetition_ratio":0.0,"special_character_ratio":0.43292683,"punctuation_ratio":0.064327486,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9956261,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-20T08:41:25Z\",\"WARC-Record-ID\":\"<urn:uuid:6d43fdbf-6cb6-494c-9a6e-1506df64be5b>\",\"Content-Length\":\"7377\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3bf18f19-d727-4420-96e9-b01b2006d132>\",\"WARC-Concurrent-To\":\"<urn:uuid:25072046-f223-4bb9-8daa-3539023275b2>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/compare-fractions/10-20-and-40-84\",\"WARC-Payload-Digest\":\"sha1:RD4BSM7OHDDOLZEE4SI2XIEDQFNACH2I\",\"WARC-Block-Digest\":\"sha1:XCXMQOAJ23LVEO4J63AIJRGQVFTJKOME\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057033.33_warc_CC-MAIN-20210920070754-20210920100754-00035.warc.gz\"}"}
http://www.apicsllc.com/apics/Ie_ias97/Ie_ias97.htm	[ "APPLIED INDUSTRIAL CONTROL SOLUTIONS LLC", null, "PAPER No. 4\n\nThe Effect of Speed Loop Bandwidths and Line-speed on System Natural Frequencies in Multi-Span Strip Processing Systems\n\n1997 IEEE IAS Annual Meeting\n\nBrian Thomas Boulter\nApplied Industrial Control Solutions LLC\n4597 E Sprague Rd.\nIndependence, OH, USA 44131\n\nAbstract - Web Handling and Strip Processing systems (SPS’s) are composed of multiple tension zones. These zones are separated by driven rolls such as bridles whose speed is regulated by a closed loop controller. Given that the typical tension regulator regulates tension by trimming the reference to a closed speed loop controller, the designer of the tension regulator cannot ignore the effects of closing the speed loop, and line speed, on the strip processing system natural frequencies. These natural frequencies are typically computed as the eigenvalues of an equivalent translational cascaded spring-mass system. This paper discusses these effects.\n\nI. INTRODUCTION\n\nMost frequency domain analysis of strip processing systems (SPS's) involves obtaining the transfer functions from an input variable of interest to an output variable of interest. The most common transfer functions used in this type of analysis are those that provide the analyst with spectral information about system variables that directly affect product quality, such as strip strain (or tension) and roller velocity. For example, the transfer function from shaft torque to tension feedback, or from shaft torque to speed feedback are of interest to both the control system engineer and the O.E.M. The control system engineer is interested in these transfer functions because he is responsible for designing the speed and tension regulators and these variables are controlled through the shaft torque produced by the motor. The O.E.M., because he is interested in ensuring the control system vendor satisfies performance guarantees on speed and tension regulation that directly affect the quality of the final product.\n\nSystem eigenvalues (or natural frequencies) are defined as the roots of the characteristic polynomial of a system of linear time-invariant (LTI) differential equations. In a linear analysis of the SPS the denominator of all SPS transfer functions will be composed of poles whose location in the s-plane are equivalent to the system eigenvalues. Often the analyst assumes the SPS can be modeled analogous to a mass-spring system where the roll inertias (Ji) and the strip springs (Ei*Ai /Li) are analogous with the translational masses (Mi) and springs (ki). The transfer functions from torque (ti) to speed (wi) and tension (Tj) are assumed to be analogous to the transfer functions from a disturbance force (fi) acting on the mass (Mi) to the translational speed of the mass (Vi) and the force in the spring {ki(xi-xi-1)}. This approach does not lump the closed speed loop regulators into the plant model. In a more practical sense, the eigenvalues resulting from such an analysis can be defined as the poles of the transfer function from any motor torque ti to any tension feedback Tj, or speed feedback wi, in a SPS where all the speed regulators are operating open loop.", null, "Figure 1. A Typical Mass-Spring SPS Representation\n\nFigure 1 shows the rotational system and the equivalent mass-spring translational system from which the eigenvalues of such an analysis are typically obtained. It is composed of an entry section fed by a winder that unwinds unprocessed strip, a process section where proprietary strip processing is performed, and a delivery section that winds the processed strip into rolls.\n\nFigure 2. Is a single line diagram of a typical SPS including the drives and speed loops. The entire system may be divided into 'n' tension zones that are separated by 'n+1' driven rolls. The unwinder (payoff reel), winder (tension reel) and driven rolls (bridles, calenders etc.) are in turn driven by a power source (Current/Torque Minor Loop - CMLi). The reference to the CMLi is proportional to a desired torque (ti) and comes from a speed regulator (a PI regulator - SPIi) that regulates speed to match a desired speed reference wri.", null, "Figure 2. A Typical SPS Including Drives and Speed Loops.\n\nGiven that tension regulation in strip processing systems is performed by an outer tension major loop that cascades into a speed minor loop, the eigenvalues of SPS’s that are obtained without the inclusion of the closed speed loops are not useful to the control system engineer responsible for the design of SPS tension regulators. Rather, the design of a single-input, single-output (SISO) tension regulator for the 'ith' section in Figure 2. will require an approximation of the transfer function from the speed reference (wri) to the tension feedback (Ti or Ti+1). This transfer function, which includes the closed speed loop, represents the plant the tension regulator is controlling. The tension regulator may use the tension feedback Ti (i.e. drawing material to control the tension in the 'ith' section) or Ti+1 (feeding material to control tension in the 'i+1' section) to regulate the tension around a desired setpoint.\n\nThere are exceptions to the cascaded architecture. Specifically, in winders, a direct reference to the CML from either a tension or current regulator may be used. However for the sake of brevity only the cascaded architecture will be discussed in this paper.\n\nObtaining a transfer function from wri to Ti is a fairly simple task if there are only two masses and one strip section (e.g. an unwinder and a winder directly coupled by the strip). Approximate transfer functions for this application are derived in , . However the coupling of additional sections into the system makes the derivation of an analytically exact transfer function unwieldy and, as sections are added, beyond the capabilities of even the most sophisticated symbolic math programs.\n\nWhile the approach taken in this paper is one based on linear system theory, the author avoided presenting cumbersome sets of transfer functions and their derivations. This was done with the knowledge that, in the analysis of an actual strip process application, there exists a profusion of non-linear contributions that render exact linear transfer functions more or less inaccurate, depending on the application. The approach taken in this paper is one that describes the expected behavior of the transfer functions in terms of the effect of speed loop bandwidths, and line speed, on the system eigenvalues. The expected behavior is expressed as a series of observations phrased in terms of closed speed loop bandwidths, line speed time constants, and natural frequencies.\n\nII. ANALYSIS\n\n1. Nomenclature\n\n JMOTOR motor inertia [kg m^2] JLOAD, reflected roll (load) inertia [kg m^2] JI JMOTOR + JLOAD [kg m^2] Vi i’th roll surface velocity [m/min] wi i'th motor rotational velocity feedback [rpm] wri i'th motor rotational velocity reference [rpm] qi i'th motor shaft position [rad] w(CML)i i'th CML bandwidth [rad/sec] wS,i i'th speed loop PI lead freq. [rad/sec] wCO,i i'th speed loop crossover [rad/sec] KSi i'th speed loop PI prop. gain KSHAFT spring constant of the drive shaft [kg m^2/rad] Ri i’th roll radius [m] Di i’th roll diameter [m] GRI i’th roll gear ratio Li i’th tension zone length [m] Ti i’th tension zone tension [kgf] ti i’th roll reflected shaft torque [kgf m] tMAX i’th motor maximum torque [kgf m] iI instantaneous CML current [A]. iMAX maximum CML current. [A] E modulus of elasticity [kgf/mm^2] A cross sectional area [mm^2] S Laplace operator LS maximum line speed [m/min] LSI operating line speed [m/min]", null, "i’th per-normal inertia (see Eq. 4) KI strip-spring constant (see Eq. 8) tV strip-span velocity time-constant (see Eq. 9) Wi span natural frequency [rad/sec] (see Eq. 12)", null, "torque loop gain [kgf m/A]", null, "i'th motor gear-in speed [rpm]\n\nB. Plant Representation\n\nThe strip tension equation (1) is a commonly used equation (, , ) describing the dynamics associated with the conveyance of strip through tension zones. It is based on the principle of conservation of mass in a mass-flow system and is derived in ,.", null, "; (1)\n\nwhere:", null, "(2)\n\nThe motor/load torque equation is given as:", null, "; (3)\n\nIn Figure 3. an s-domain block diagram of equations (1-3) is presented. It includes the hooks that allow coupling multiple sections together, it does not include any damping terms. Note that a rigorous representation of equations (1-3) requires the integrators in Figure 3 to be preset to their respective initial conditions.\n\nFor a given operating line velocity LSi, an approximate linear representation of equations (1-3) can be obtained , . A block diagram of the linearized model is shown in Figure 4.", null, "Figure 3. Block Diagram of a Strip Tension Zone", null, "Figure 4. Linearized Block Diagram of a Strip Tension Zone\n\nA linear s-domain block diagram approximation of the plant (Figure 5), as seen by a cascaded tension loop regulator, can be obtained by closing a speed loop around the speed feedback wi in Figure 4.", null, "Figure 5. Plant Model Including the Speed Loop\n\nCascading n sections of the model in Figures 4 & 5 provides a plant model from which an investigation of the effects of speed loop bandwidths on system eigenvalues can be conducted.\n\nC. Some Usefull Quantities\n\nTo simplify the analysis of the multi-span strip processing system the following set of quantities are most useful.\n\nPer-Normal Inertia\n\nLet the per-normal inertia of a system be defined as the time it takes [sec] to accelerate the motor and load inertia to the application gear-in speed (Si) with maximum motor torque (tMAX) It is defined as:", null, "(4)\n\nSpeed Loop Bandwidth\n\nThe bandwidth of a closed speed loop is limited to the frequency at which the magnitude of the speed feedback in response to a sinusoidal input is attenuated 3[db] from the setpoint magnitude. It is also approximated as the crossover of the open speed loop Bode plot. For the speed loop shown in Figure 5. it can be shown that the open loop crossover and hence the approximate bandwidth of the speed loop is:", null, "(5)\n\nIn any drive system the bandwidth of the speed loop will be constrained by the mechanical integrity of the drive train. As a general rule the bandwidth must be an order of magnitude lower than the lowest torsional frequency in the drive train. This constraint can typically be satisfied by:", null, "(6)\n\nIn addition, to avoid torque jitter in the motor shaft, the per-normal controller proportional gain should be limited to 60. For industrial motors, this constraint can be accommodated by limiting the bandwidth to:", null, "(7)\n\nStrip Spring Constant\n\nLet the strip spring constant be equal to:", null, "(8)\n\nStrip-Span Velocity Time-Constant\n\nLet the strip-span velocity time constant be equal to:", null, "(9)\n\nNormal Eigenvalues\n\nThe simple mass-spring system (Figure 1) can be defined in rotational terms as a set of differential equations expressed in the Laplace domain (10):", null, "(10)\n\nLet the normal eigenvalues be defined as the roots of the determinant of A.", null, "(11)\n\nSpan Natural Frequency:\n\nLet the span natural frequency be a measure of the frequency at which the strip span spring (Ki) and attached inertia (Ji) would exchange energy if the strip spring was terminated at an infinitely large mass.", null, "(12)\n\nD. Observations\n\nFollowing is a series of observations that are intended to provide the reader with an intuitive understanding of the effect of speed loop bandwidths and line speeds on SPS system eigenvalues (or transfer function poles).\n\nAnalysis of a 9 section - 10 inertia SPS provides supporting bode plots for each observation. The SPS is comprised of sections structured the same as shown in Figures 4 and 5. Each Observation is followed by a brief discussion, and a plant description for the particular set of Bode plots presented. The plant description is in terms of the quantities described in section 2.3.\n\nThe short discussion is provided to clarify the observation in terms of the stated effect on the poles of the transfer functions (or the system eigenvalues) from speed reference wri to tension feedback Ti and speed feedback wi. The discussions are intended to be of practical use to the control system engineer responsible for the design of SPS tension regulators.\n\nIn addition, it is assumed that the bandwidth of each CML is high enough that in the frequency range of interest it behaves as a linear gain element. Its dynamics can, therefore, be ignored.\n\nObservation No.1\n\nAs additional driven sections are added to a SPS the magnitude of all existing eigenvalues will decrease.\n\nDiscussion: Consider a multi-span SPS without speed regulators, the denominator of the transfer function from any ti to any tension feedback Ti will be composed of poles that can be factored into real poles or complex pole pairs. If a section is added to the SPS the magnitudes of all the existing poles and complex pole pairs in the transfer function from any ti to any tension feedback Ti will decrease.\n\nThis implies that the longer a SPS process line is, the lower the eigenvalues will become. A good way to visualize this is to create a purely symmetric SPS and observe the effect of adding symmetric sections to the SPS on the Bode plot of the transfer function from a torque tn/2+1/2 to a tension feedback Tn/2+1/2 in a SPS with ‘n’ sections. A symmetric SPS is one that has been designed so that the strip span natural frequencies are all approximately the same. Similarly, a symmetric SPS will have sections with very similar per-normal inertias. Figure 6 is a collage of 3 Bode magnitude plots of the transfer function of tn/2+1/2 to a tension feedback Tn/2+1/2. The number of sections varies from five to nine in increments of two.\n\nPlant Description", null, "In Figure 6, the solid line is from the analysis of the 9 section SPS, the dotted line: the 7 section SPS, and the dashed line: the 5 section SPS. It is clear that as symmetrical sections are added the magnitude of the eigenvalues decreases.\n\nFrom the perspective of the tension regulator designer, the problematic plant poles in long SPS’s are significantly lower than the strip span natural frequencies calculated using (12). It is important to keep this perspective in mind when commisioning the tension regulators. In the authors experience the dominant problematic natural frequencies in SPS’s are typically lower than those calculated using linear analysis techniques.", null, "Figure 6. Observation 1. Bode Magnitude Plot of tn/2+1/2 to Tn/2+1/2 for n=5,7, and 9 Section SPS’s\n\nObservation No.2\n\n2.a) If", null, "the eigenvalues of a SPS system that includes the closed speed loops are approximately equal to eig(A).\n\nDiscussion: If the magnitude of all the SPS normal eigenvalues are much greater than the bandwidth of all of the speed loops, the poles of the transfer function from any wri to any closed speed feedback wi or any tension feedback Ti will be approximately the same as the poles in the transfer function from any torque ti to any to any speed feedback wi or any tension feedback Ti in a SPS with no speed loops.\n\n2.b) If", null, "the eigenvalues of a SPS system that includes the closed speed loops are approximately equal to", null, "Discussion: If the bandwidths of all the speed loops are significantly higher than the magnitude of the maximum normal eigenvalue, the denominator of the transfer function from any speed reference wri to any speed feedback wi or any tension feedback Ti will approximately consist of a pole at zero and two real poles at", null, "and", null, "2.c) The damping of all normal eigenvalues with magnitudes greater than the speed loop bandwidth for a given tension zone will increase as the ratio of the eigenvalue magnitude to the speed loop bandwidth decreases.\n\nDiscussion: Speed loops produce a damping effect on natural frequencies. The closer the natural frequency is to the speed loop crossover the more pronounced this damping effect will become.\n\nTo demonstrate the effects described in Observation No.2 a collage of 10 Bode plots (Figure 7.) of the transfer function from wr5 to T5 for the example SPS is presented. The per-normal inertias, speed loop crossovers and span natural frequencies for all 9 sections are identical in each plot. This results in a highly symmetrical plant. The 10 plots are obtained from an analysis performed with 10 logarithmically spaced span natural frequencies that vary from 6 to 600 [rad/sec]. For each plot the natural frequency of all 9 tension zones is identical.\n\nPlant Description", null, "Some additional observations from Figure 6:\n\n1. The low frequency gain of the transfer function does not change significantly until the eigenvalues are low enough for the speed loop to provide damping. For a system that is highly symmetrical, the gain changes linearly with Wi when Observation 2.b is satisfied.\n2. The speed loop PI lead frequency wSi provides the observed lead break frequency at 2 [rad/sec]. wSi effectively cancels the lower pole of the real pole pair that results when Observation 2.b is satisfied.", null, "Figure 7. Observation 2. Bode Plot of wr5 to T5\n\nObservation No.3\n\nDominant speed loop damping effects result from the immediate speed regulator and the speed regulators acting on the preceding and following sections.\n\nDiscussion: Damping of the normal eigenvalues for a given tension zone is dominated by the bandwidth of the speed loop driving that section, the second most dominant factors are the speed loop bandwidths of the sections preceding and following the given tension zone.\n\nTo demonstrate this observation, consider a process line that is composed of two sets of high bandwidth speed regulators separated by a single low bandwidth speed regulator. Poor damping of the system eigenvalues will be observed around the section driven by the low bandwidth regulator. Figures 8,9,10 represent the transfer functions from wr3 to T3, wr4 to T4, wr5 to T5, respectively. The SPS has 10 [rad/sec] speed loop regulator bandwidths for sections 1,2,4-10. The bandwidth of Section 3 is set at 0.1 [rad/sec]. Note that there is little difference between Figure 10 and Figure 7. This indicates that the drive in section 4 provides section 5 with considerable isolation from section 3. As in Figure 7 Figures 8,9,10 are composed of a collage of 10 Bode plots resulting from an analysis of the SPS with 10 logarithmically spaced Wi’s that vary from 6 to 600 [rad/sec].\n\nPlant Description", null, "", null, "Figure 8. Observation 3. Bode Plot of wr3 to T3", null, "Figure 9. Observation 3. Bode Plot of wr4 to T4", null, "Figure 10. Observation 3. Bode Plot of wr5 to T5\n\nObservation No.4\n\nDamping of the normal eigenvalues will increase with line speed.\n\nDiscussion: The damping of the normal eigenvalues is worst case at stall. When the strip begins moving there is a damping effect that is the result of the bulk flow of the material through the tension zone. As a result of the lack of damping at stall, it is not uncommon for drive system vendors to operate tension regulators as proportional only controllers at stall, switching to a PI configuration at a pre-determined strip line speed.\n\nTo demonstrate this a plant with a fixed a set of WI’s equal to 600 [rad/sec] is analyzed with a set of 10 logarithmically spaced velocity time constants tv varying from 10 to 0.01 [sec] (Figure 11).\n\nPlant Description", null, "", null, "Figure 11. Observation 4. Bode Plot of wr5 to T5\n\nObservation No.5\n\nThe pure integration in the transfer function from wri to Ti at stall appears as a real pole that gravitates from the origin of the s-plane towards a value of -1/tV as bulk movement of the strip occurs. The higher the damping of the eigenvalues the better the approximation of -1/tV as the pole location.\n\nDiscussion: At stall, a pure integration is observed in the transfer function from wri to Ti. The moment the bulk movement of the strip begins, the integration becomes a real pole. For most systems this pole is very low in frequency and does not significantly alter the low frequency gain of the plant. When the damping of the normal eigenvalues is such that Observation 2.b is satisfied, the pole location can be approximated as -1/tV.\n\nThis phenomena can be problematic in certain tension regulation schemes. For example, assume a proportional tension regulator is used in a SPS with an extremely high top line speed of 3000 [m/min] and a length between driven sections of 10 [m]. In addition, assume that the speed regulators have ample bandwidth and satisfy Observation 2.b. The transfer function from wri to Ti in a system with such a line speed will result in a pole at 5 [rad/sec]. A significant loss in low frequency gain can be expected and a steady state error in the closed tension loop will be observed. To demonstrate this a plant with a fixed a set of Wi’s equal to 10 [rad/sec] is analyzed with a set of 10 logarithmically spaced velocity time constants varying from 10 to 0.01 [sec] (Figure 12).\n\nThe movement of this pole can also result in a type of low frequency instability in PI tension regulators. If the designed crossover of the tension loop is less than 1/tV, the loop will tend to \"die\" and loose its ability to regulate tension as the speed of the line increases past a certain threshold speed. The exact speed at which this will occur will vary depending on the speed loop bandwidth, the associated eigenvalue damping, and the phase margin built into the tension loop. This instability is not a true instability in the classical sense of the word, it is rather an observed drifting or wandering of the tension that can be attributed to a combination of integral action in the regulator, low tension loop bandwidth, and system noise.\n\nPlant Description", null, "", null, "Figure 12. Observation 5. Bode Plot of wr5 to T5\n\nIII. CONCLUSIONS\n\nIt is clear from the above discussion that the designer of cascaded tension regulators for multi-span strip processing systems should consider the effect of the speed loop bandwidths on the s-plane location of the SPS eigenvalues when designing tension regulators. Based on the above discussion several conclusions can be drawn:\n\nA. The higher the bandwidth of the SPS speed regulators the greater the damping of problematic SPS natural frequencies.\n\nB. If possible, the O.E.M. process design team should strive to create symmetric systems (similar Wi’s in all the sections and per-normal inertias that are approximately equal). This enables consistent damping of SPS eigenvalues with section speed regulators that have identical bandwidths.\n\nC. The per-normal inertias (and by implication the motor horsepowers) and the torsional stiffness of the drive shafts should be selected such that the speed regulators can be tuned for wCO’s that will provide adequate damping of the expected SPS eigenvalues. This significantly improves the performance of the tension regulators.\n\nD. O.E.M.’s should be aware that compensation as a function of line speed may be required in tension loops as line speeds increase and the span lengths decrease.\n\nE. If an LTI linear system analysis is used to determine the SPS eigenvalues it can be considered a worst case analysis if the eigenvalues are computed to determine the minimum bandwidth of the speed regulators required to satisfy Observation 2.b. The actual eigenvalues of the system will always be less than or equal to these analytically derived values.\n\nA. Tuning The Tension Regulator\n\nAs a note of interest, the tuning of a tension regulator for a SPS with speed loop bandwidths that satisfy Observation 2.b for all the product that is processed through the system becomes a fairly simple task. The lead and lag frequencies of a lead/lag compensator and a PI regulator lead are tuned as shown below:", null, "Briefly, the PI lead frequency of the PI controller should be set to 1/5 the desired tension loop crossover. The tension loop crossover should be less than or equal to the speed loop crossover. The lead/lag lead frequency is set to approximately cancel the damped pole from the plant at 0.7 times the speed loop crossover. Recall that the pole at 0.35 times the speed loop crossover is approximately canceled by the transmission zero from the speed PI regulator (i.e. the speed loop PI lead frequency). The lag of the lead/lag compensator is then placed at 10 times the lead/lag lead frequency to ensure that only a minimum of phase margin is lost in the tension regulator. The gain can then be adjusted on-site so that the step response of each tension regulator satisfies a time to peak measure that reflects the desired tension loop bandwidth. Equation (13) can be used to make this determination.", null, "(13)\n\nReferences\n\n Boulter, B.T., \"A Novel Approach for On-Line Self-Tuning Strip Tension Regulation\", Proceedings of the 4th IEEE International Conference on Control Applications, pp 91-98, September 1995.\n\n Boulter, B.T. Fox, H.W.,\"Advanced Dynamic Simulation\", Reliance Electric Systems Engineering Training Course EO108 1995.\n\n Carter, W.C., \"Reducing Transient Strains in Elastic Processes\" , Control Engineering Mar. 1965. pp. 84-87.\n\n Fox, S.J., Lilley, D.G., \"Computer Simulation Of Web Dynamics\", Proceedings of the 1st IWHC International Web Handling Conference Tab 20. Oklahoma State University, March 1991.\n\n Lin, K., \"WTS 6.0, A Computer-Based Analysis Program For Multi-Span Web Transport Systems\", Oklahoma State University 1994.\n\n Wolferman, W., \"Tension Control of Webs - A Review of the Problems and Solutions in the Present and Future\", Tab 15, Proceedings of the 3rd IWHC International Web Handling Conference, Oklahoma State University June 1995." ]	[ null, "http://www.apicsllc.com/apics/Images/Papers.jpg", null, "http://www.apicsllc.com/apics/Ie_ias97/Image423.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image424.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image386.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image425.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image426.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image427.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image428.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image429.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image392.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image393.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image394.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image430.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image431.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image397.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image398.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image399.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image400.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image401.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image402.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image403.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image404.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image432.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image433.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image434.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image435.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image436.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image437.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image438.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image439.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image440.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image441.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image442.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image443.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image444.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image445.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image446.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image447.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image448.gif", null, "http://www.apicsllc.com/apics/Ie_ias97/Image449.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.87896025,"math_prob":0.92122775,"size":25517,"snap":"2021-04-2021-17","text_gpt3_token_len":5656,"char_repetition_ratio":0.17500882,"word_repetition_ratio":0.055032928,"special_character_ratio":0.21326959,"punctuation_ratio":0.08278775,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98083436,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80],"im_url_duplicate_count":[null,null,null,5,null,5,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-16T12:34:39Z\",\"WARC-Record-ID\":\"<urn:uuid:f5e818e0-5932-4b08-9279-a1dc18a9825c>\",\"Content-Length\":\"41716\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3c644c72-8d26-490b-b128-c2f06a0fa85f>\",\"WARC-Concurrent-To\":\"<urn:uuid:d24525ee-eaca-4535-9442-597f92161132>\",\"WARC-IP-Address\":\"185.184.68.93\",\"WARC-Target-URI\":\"http://www.apicsllc.com/apics/Ie_ias97/Ie_ias97.htm\",\"WARC-Payload-Digest\":\"sha1:JAOJPGTINYZC3HI2P6ZZ42HX3J3NNGNX\",\"WARC-Block-Digest\":\"sha1:RVZL6FI75EHICZSVBHWGQLIBBKTR2PWB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703506640.22_warc_CC-MAIN-20210116104719-20210116134719-00194.warc.gz\"}"}
http://download.ecopath.org/trac/Ecopath/wiki/EwEugBasicEstimates?action=diff&version=2	[ "# Changes between Version 1 and Version 2 of EwEugBasicEstimates\n\nIgnore:\nTimestamp:\n2010-02-05 17:09:39 (10 years ago)\nComment:\n\n--\n\nUnmodified\nAdded\nRemoved\nModified\n• ## EwEugBasicEstimates\n\n v1 == 7.3 Basic estimates == Once you have entered sufficient input parameters you can proceed to estimate the parameters of Ecopath by selecting Basic estimates under the Parameterization node in the Navigator window. The missing parameters will be estimated so that mass balance is achieved. Both input (black font) and calculated (blue font) parameters are displayed on the Basic estimates form. Notes on most of the parameters below have already been provided in the notes on [[Basic input.htm\|Basic parameters]], but we repeat them here as a reminder. ==== Trophic level ==== '''Trophic level''' Lindeman (1942) introduced the concept of trophic levels. In Ecopath, the trophic levels are not necessarily integers (1, 2, 3...) as proposed by Lindeman, but can be fractional (e.g., 1.3, 2.7, etc.) as suggested by Odum and Heald (1975). A routine assigns definitional trophic levels (TL) of 1 to producers and detritus and a trophic level of 1 + [the weighted average of the preys' trophic level] to consumers. The trophic level is a dimensionless index. ==== Habitat area (fraction) ==== '''Habitat area (fraction)''' The fraction of the total area in which the group occurs, that is, the fraction of the total area to which the biomass in habitat area pertains. Default is that the habitat area is 1, i.e. that the group occurs in the total area. ==== Biomass in habitat area ==== '''Biomass in habitat area''' The average biomass per unit area in the habitat area where the group occurs. It is assumed that an average value can be used to represent the biomass of each group. Appropriate units should be used, (e.g., t/km²) for the biomasses. Entry of biomasses is optional for living groups but biomass(es) should be entered for the detritus group(s). However, if biomasses are unknown for all living groups and there are no exports from any of the groups, it is necessary to enter at least one biomass estimate, preferably of a top predator. Biomasses should be entered relative to the habitat area where the group occurs. An example: assume a species for instance has a biomass of 1 t/km² in its habitat area, and the habitat area is 100 km², while the total area in your model is 1000 km². You should then enter a habitat area of 0.1 and a biomass in habitat area of 1 t/km² as the biomass for the group in your model. ==== Biomass ==== '''Biomass''' This is the Biomass in habitat area x Habitat area. ==== Production/biomass ==== '''Production/biomass''' Enter the Production/Biomass (''P/B'') ratio for each group using consistent units, e.g., per year. The ''P/B'' ratio is equivalent to the instantaneous rate of total mortality (Z) used by fisheries biologists (Allen 1971). Entry of ''P/B'' ratios is optional. ''P/B'' = Z = F + M2 + NM + BA + M0. For more details, see [[Production.htm\|Production]]. For more details, see [wiki:EwEugProduction Production]. ==== Consumption/biomass ==== '''Consumption/biomass''' Consumption/biomass (''Q/B'') ratios are entered using the same units as for ''''P/B''''. Entry of consumption/biomass ratios is optional. For more details, see [[Consumption.htm\|Consumption]]. Consumption/biomass (''Q/B'') ratios are entered using the same units as for 'P/B'. Entry of consumption/biomass ratios is optional. For more details, see [wiki:EwEugConsumption Consumption]. The ''Q/B'' input box will be blocked (blue colour) for primary producers. If your model unit is carbon, you can however, click the blue input box, and enter a Q/B value, which will be used to calculate respiration for the group. ==== Ecotrophic efficiency ==== '''Ecotrophic efficiency''' The ecotrophic efficiency (''EE'') is the fraction of the production that is used in the system, i.e. either passed up the food web, used for biomass accumulation, migration or export. Ecotrophic efficiency is difficult to measure directly. It varies between 0 and 1 and can be expected to approach 1 for groups with considerable predation pressure. The part of the production that is not included in the ''EE'' is often called ‘[[Other mortality.htm\|other mortality]]’. ''EE'' is dimensionless, and the entry of'' EE'' values is optional." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.836774,"math_prob":0.8813466,"size":4577,"snap":"2019-35-2019-39","text_gpt3_token_len":1217,"char_repetition_ratio":0.14454406,"word_repetition_ratio":0.0465718,"special_character_ratio":0.29691938,"punctuation_ratio":0.11148649,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95648915,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-19T16:49:10Z\",\"WARC-Record-ID\":\"<urn:uuid:ab57f170-0bd1-4d16-b2a6-6a6e8a8fc28c>\",\"Content-Length\":\"28677\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e97de49e-186d-49e6-b0fd-3ea2ff44cb9f>\",\"WARC-Concurrent-To\":\"<urn:uuid:900d43bd-7058-4f42-9c83-089fc912ef7a>\",\"WARC-IP-Address\":\"137.82.155.96\",\"WARC-Target-URI\":\"http://download.ecopath.org/trac/Ecopath/wiki/EwEugBasicEstimates?action=diff&version=2\",\"WARC-Payload-Digest\":\"sha1:WOLRYLPQWRZVMQ3B7U2FM7OVJFL5HHGI\",\"WARC-Block-Digest\":\"sha1:WJBMDG7XJU53QLWHPDIEBYWQLTDPSF7D\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027314852.37_warc_CC-MAIN-20190819160107-20190819182107-00295.warc.gz\"}"}
https://ch.mathworks.com/matlabcentral/cody/problems/304-bottles-of-beer/solutions/104666	[ "Cody\n\n# Problem 304. Bottles of beer\n\nSolution 104666\n\nSubmitted on 28 Jun 2012 by Noah\n• Size: 10\n• This is the leading solution.\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\n%% x = 99; y_correct = 98; assert(isequal(bottles_of_beer(x),y_correct))\n\n2 Pass\n%% x = 9; y_correct = 8; assert(isequal(bottles_of_beer(x),y_correct))\n\n3 Pass\n%% x = 1; y_correct = 0; assert(isequal(bottles_of_beer(x),y_correct))" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.51233256,"math_prob":0.9790295,"size":467,"snap":"2019-51-2020-05","text_gpt3_token_len":154,"char_repetition_ratio":0.16198704,"word_repetition_ratio":0.0,"special_character_ratio":0.3490364,"punctuation_ratio":0.14634146,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9768289,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-10T05:01:55Z\",\"WARC-Record-ID\":\"<urn:uuid:612178a6-2618-4bb1-98ad-1a0b46f9d867>\",\"Content-Length\":\"73199\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7b81dc56-c4e9-4c13-b195-2a1b47d792c2>\",\"WARC-Concurrent-To\":\"<urn:uuid:1991a270-4f00-431f-a4eb-e6a2ecde984c>\",\"WARC-IP-Address\":\"104.110.193.39\",\"WARC-Target-URI\":\"https://ch.mathworks.com/matlabcentral/cody/problems/304-bottles-of-beer/solutions/104666\",\"WARC-Payload-Digest\":\"sha1:NDQ5QOY4GOC3C4UWIHV2CDQOOEX6WZ4S\",\"WARC-Block-Digest\":\"sha1:72SP2KYIXGKQRETCBIRNUZMVULAODR5H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540525821.56_warc_CC-MAIN-20191210041836-20191210065836-00548.warc.gz\"}"}
https://math.stackexchange.com/questions/1508102/showing-8th-cyclotomic-polynomial-is-irreducible	[ "# Showing 8th cyclotomic polynomial is irreducible\n\nI'm reviewing my notes, and I'm not fully understanding an argument that the 8th cyclotomic polynomial is irreducible in $\\mathbb{Q}[x]$. Here's the online of the argument\n\n$\\Phi_8(x)=\\dfrac{x^8-1}{\\Phi_1(x)\\Phi_2(x)\\Phi_4(x)}=\\dfrac{x^8-1}{x^4-1}=x^4+1$.\n\nThis can be factored into: $(x-\\zeta_8)(x-\\zeta_8^3)(x-\\zeta_8^5)(x-\\zeta_8^7)$ where $\\zeta$ is a primitive root of unity. The next part of the argument is what I'm not seeing.\n\n$(x-\\zeta_8)(x-\\zeta_8^3)(x-\\zeta_8^5)(x-\\zeta_8^7)=(x^2-(\\zeta_8 +\\overline{\\zeta_8})x+1)(x^2-(\\zeta_8^3+\\overline{\\zeta_8^3})x+1)=(x^2-\\sqrt{2}x+1)(x^2+\\sqrt{2}x+1)$\n\nSince $\\sqrt{2} \\notin \\mathbb{Q}$, the polynomial isn't reducible in $\\mathbb{Q}$.\n\nAny clarification is greatly appreciated. Thanks\n\nLet $F$ be the real subfield of $\\mathbb{Q}(\\zeta_8)$. By grouping the roots into conjugate pairs, it's clear that the stated factorization is the prime factorization of $\\Phi_8(x)$ over $F$.\n\nThe prime factorization of $\\Phi_8(x)$ over $F$ is a refinement of its prime factorization over $\\mathbb{Q}$ — i.e. the prime factorization over $F$ come from taking the prime factorization over $\\mathbb{Q}$ and then factoring each factor over $F$.\n\nThus, the only possibilities for the prime factorization over $\\mathbb{Q}$ are either the displayed factorization or that it is irreducible... and the displayed factorization is clearly not defined over $\\mathbb{Q}$.\n\nActually, $F$ is itself a Galois extension of $\\mathbb{Q}$, so the prime factorization over $\\mathbb{Q}$ can be obtained by grouping the conjugate factors and multiplying them together, once again showing irreducibility.\n\nIf the polynomial is reducible, then either it can be factored as a product of degree $1$ and degree $3$ polynomials or it can be factored as a product of two degree $2$ polynomials.\n\nThe former case cannot hold because there is no rational root for this polynomial. For the latter you already have the factorization, but the factors do not belong to $\\mathbb{Q}[x]$. Hence even this factorization doesn't work. Thus irreducible.\n\nAnother argument is to apply Eisenstein's criterion with $f(x)=x^4+1$ for $$f(x+1)=(x+1)^4+1=x^4+4x^3+6x^2+4x^2+2.$$ Hence $\\Phi_8(x)=x^4+1$ is irreducible over $\\mathbb{Q}$. The other factorisation you gave is not over $\\mathbb{Q}$; this would rather work with $$x^4+4=(x^2-2x+2)(x^2+2x+2).$$" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.66984797,"math_prob":0.99987197,"size":733,"snap":"2020-24-2020-29","text_gpt3_token_len":310,"char_repetition_ratio":0.1659808,"word_repetition_ratio":0.0,"special_character_ratio":0.39563438,"punctuation_ratio":0.059210528,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999535,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-27T11:37:30Z\",\"WARC-Record-ID\":\"<urn:uuid:23761d0a-3d9f-4f4b-85b2-82d5454b87d2>\",\"Content-Length\":\"153892\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aca8bffd-0a6c-423a-bf01-6804a5d2e455>\",\"WARC-Concurrent-To\":\"<urn:uuid:4bcf2182-630c-4119-9bb3-b134777783cd>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://math.stackexchange.com/questions/1508102/showing-8th-cyclotomic-polynomial-is-irreducible\",\"WARC-Payload-Digest\":\"sha1:U7ABATS7LXJB3CT523WT2PAGJ36V2AYW\",\"WARC-Block-Digest\":\"sha1:YFCTZKSA7JPX4N3EB7N2JALDP2IFKX6O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347394074.44_warc_CC-MAIN-20200527110649-20200527140649-00583.warc.gz\"}"}
https://wvsheep.org/western-australia/change-in-quantity-supplied-example.php	[ "# In supplied change example quantity\n\n## Essay Economics Supply and Demand\n\nChange in supply and Increase/decrease in quantity supplied. what is the difference between a change in demand and change in quantity supplied is exactly refers to the an example of a change in a demand determinant, 8/11/2011 · this site might help you. re: supply vs. quantity supplied? i am having trouble with completely grasping these two concepts. i know that a change in supply).\n\n3. Microeconomic Laws of Demand and Supply. price will lead to a movement along a stable supply curve and result in a change in the quantity supplied. For example Price changes cause changes in quantity supplied represented by movements along the supply curve. For example, at a price of \\$5.00,\n\nWhen price changes, quantity supplied will change. That is a movement along the same supply curve. When factors other than price changes, supply curve will shift. Review of Demand and Supply. Supply vs Quantity Supplied: and quantity supplied and to eliminate shortages and surpluses via changes in prices. Example 1:\n\nThe quantity supplied changes according to the change in price, What Are Examples of Elastic and Inelastic Goods? Difference between Supply and Quantity Supplied; Supply vs Quantity Supplied \"Supply\" and 6.A change in the supply is characterized as a “shift,” while a change in the quantity supplied is marked by an\n\nAn introduction to the price elasticity of demand. how much the quantity demanded changes when given a contemplated change in price. For example, 3/07/2007 · What is the difference between a \"change in demand\" and a \"change in quantity demanded\"? Between a \"change in supply\" and a \"change in quantity supplied\"?\n\nSupply and demand: Supply and demand, calculated as the ratio of the percentage change in quantity supplied or demanded to the percentage change in price. For conventional economics the market by way of the operation of supply and demand answer Examples of inferior goods in Change in quantity supplied verses\n\n14/10/2018 · The vertical line represents price and the horizontal line is quantity supplied. While the previous example provides a basic reason for a change in Supply and demand shifts cause changes in equilibrium price and quantity. events affect equilibrium price and quantity, the quantity supplied of movies at\n\nDefinition of change in supply: A situation that occurs when the producers of a particular good or service change the quantity available for For example, print An example of considering a change in quantity demanded is shown in the graph While a change in quantity demanded will generally be the result of a change in", null, "What Is the Difference Between Supply and Quantity\n\nDifference between change in quantity supplied and change. movements along the curve occur only if there is a change in quantity supplied caused by a an example would be the change in the supply of cookies caused by a, ... example: supply schedule. price a change in quantity supplied for a given price level. if the change causes an increase in the quantity supplied at each price); advertisements: a change in supply occurs when the conditions facing suppliers alter. in such a situation, a different quantity will be offered for sale at each price., target (example) • for finding revenue you should find the income statement for your firm. the income statement (example below) is where you will find revenues.\n\nUnderstanding a Change in Supply vs. a Change in Quantity\n\nDifference between change in quantity supplied and change. home » uncategorized » change in supply/demand vs.change in quantity demanded/supplied in the quantity demanded/supplied. a change in demand example if some, quantity supplied of a good: definition & overview. you can then plot the change in quantity supplied based upon quantity supplied of a good: definition).", null, "What is change in supply? definition and meaning\n\nChange in supply and Increase/decrease in quantity supplied. need to define change in quantity supplied? economic term change in quantity supplied definition. to find out what is change in quantity supplied, see this explanation., review of demand and supply. supply vs quantity supplied: and quantity supplied and to eliminate shortages and surpluses via changes in prices. example 1:).", null, "Changes in Quantity Supplied vs Shift in Supply Example\n\nChanges in Quantity Supplied vs Shift in Supply Example. movements along the curve occur only if there is a change in quantity supplied caused by a an example would be the change in the supply of cookies caused by a, movements along the curve occur only if there is a change in quantity supplied caused by a an example would be the change in the supply of cookies caused by a).", null, "Change in Supply vs. Change in Quantity Supplied Sample\n\nChange in Supply/Demand vs.Change in Quantity eDisc. review of demand and supply. supply vs quantity supplied: and quantity supplied and to eliminate shortages and surpluses via changes in prices. example 1:, what is quantity supplied? the way that supply changes by changes in the price of goods and services is the 1 what does quantity supplied mean? 2 example;).\n\n14/10/2018 · The vertical line represents price and the horizontal line is quantity supplied. While the previous example provides a basic reason for a change in The major difference between demand and quantity demanded is Demand is Key Differences Between Demand and Quantity he refers to the change in quantity\n\nAn introduction to the price elasticity of demand. how much the quantity demanded changes when given a contemplated change in price. For example, A change in quantity supplied is the change in the quantity a company is willing to supply when there has been a change in the price of the good For example\n\nWe will write a custom essay sample on. Elasticity: Supply and Demand and Price be affected by the price change. For example, and the quantity supplied The change in price, which induces a change in quantity demanded (and supplied) is the means of eliminating the instability and restoring equilibrium.\n\n11/05/2008 · A supply curve illustrates how much the quantity supplied changes when the price what will happen if the changes in quantity demanded versus quantity Get an answer for 'Differentiate between a ‘change in quantity supplied’ and a ‘change in supply.’' and find homework help for other Business questions at eNotes\n\nChapter 3 - Demand and Supply - Sample Questions A decrease in the price of juice causes no change in the quantity of juice demanded. 13) 2. 14) 3.2 Shifts in Demand and Supply for Goods and 3.2 Shifts in Demand and Supply for Goods and Services causes a change in quantity supplied or a movement\n\nWhat is the difference between a change in demand and Change in quantity supplied is exactly refers to the An example of a change in a demand determinant Quantity supplied is the quantity of a product which producers are willing to supply at a given price while change in supply refers to the overall shift in supply", null, "Definition of change in quantity supplied definition at" ]	[ null, "https://wvsheep.org/pictures/6426f2378fa87f003c70e3c0851eff18.jpg", null, "https://wvsheep.org/pictures/change-in-quantity-supplied-example.png", null, "https://wvsheep.org/pictures/change-in-quantity-supplied-example-2.jpg", null, "https://wvsheep.org/pictures/5fdfb57081ec0fe2a2a6d49719b7e817.png", null, "https://wvsheep.org/pictures/eb143abe5fc907209d67211aa621b0ce.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9030595,"math_prob":0.84342253,"size":6646,"snap":"2020-45-2020-50","text_gpt3_token_len":1310,"char_repetition_ratio":0.30442637,"word_repetition_ratio":0.25227687,"special_character_ratio":0.19936804,"punctuation_ratio":0.08695652,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9799772,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-04T05:03:23Z\",\"WARC-Record-ID\":\"<urn:uuid:51e09398-2659-4a0e-8fe6-ca1cfc4fe5c7>\",\"Content-Length\":\"24471\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54dea457-0131-4aab-bf5e-20fc8dc07347>\",\"WARC-Concurrent-To\":\"<urn:uuid:7471902a-c502-423e-9409-b0b4c0ca2cd3>\",\"WARC-IP-Address\":\"95.179.164.82\",\"WARC-Target-URI\":\"https://wvsheep.org/western-australia/change-in-quantity-supplied-example.php\",\"WARC-Payload-Digest\":\"sha1:U2MKU5A57YNNKYKQ5GAY5VPAMOTPQW2N\",\"WARC-Block-Digest\":\"sha1:O4ZOY7OUIQOJYWNC2JYOVDKBRHLTYZK4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141733122.72_warc_CC-MAIN-20201204040803-20201204070803-00357.warc.gz\"}"}
https://normaserveert.nl/677/5JpPT.html	[ "# Products", null, "### How Much Do I Need? QUIKRETE: Cement and Concrete Products\n\nYou can use this concrete calculator to help you determine the number of bags of QUIKRETE® Concrete Mix, Mortar Mix, or Fast-Setting Concrete you will need for the following projects. (All calculations are rounded up to the next highest whole bag).\n\nget price\nHand Mixing Technical Data Machine Mixing At Home PouringFinishing Concrete", null, "### How To Calculate Cement, Sand,Aggregate Quantity In 1\n\nAug 03, 2018Density of Cement is 1440/m 3 = 0.28 x 1440 = 403.2 kg We know each bag of cement is 50 kg For Numbers of Bags = 403.2/50 = 8 Bags We Know in one bag of cement = 1.226 CFT For Calculate in CFT (Cubic Feet) = 8 x 1.225 = 9.8 Cubic Feet CALCULATION FOR SAND QUANTITY; Consider volume of concrete = 1m 3\n\nget price", null, "### Quikrete 80 lb. Concrete Mix-110180 The Home Depot\n\nOverviewReviewsQuikrete 80 lb. Concrete Mix can be used for building or repairing foundation walls, sidewalks, curbs, steps and ramps and for setting posts. This mix designed for pouring concrete 2 in. thick or more. Quikrete 80 lb. Concrete Mix consists of a uniformly blended, properly proportioned mixture of gravel, sand and Portland cement.", null, "### Concrete Calculator Estimate Cement, Sand, Gravel\n\nExample calculation Estimate the quantity of cement, sand and stone aggregate required for 1 cubic meter of 1:2:4 concrete mix. Ans. Materials required are 7 nos. of 50 kg bag of cement, 0.42 m 3 of sand and 0.83 m 3 of stone aggregate.\n\nget price", null, "### Volume of One bag Cement in Cubic Feet LT Learning\n\nVolume of One bag Cement in Cubic Feet in Hindi. Ek Bag Cement ki Volume, Cubic Feet me 1.226 Cubic Feet (CFT) hoti hain. Ab apke man me ye sawal jarur ayega ki ‘Kaise’? To ghabraiye mat. Hum yaha pe bahut hi asan tarike se apko batayenge How to Calculate the Volume of one 50 KG Cement bag in Cubic Fe et.\n\nget price", null, "### How Many Bags of Concrete do I Need Housesumo\n\nFeb 26, 2018An 80-pound bag yields approximately 0.60 cubic feet of concrete. 60-pound bags yield 0.45 cubic feet and 40-pound bags just 0.30 cubic feet. The actual yield is approximate because the amount of water added to the mix may vary. 60 to 80 pounds is a lot of weight to lift, carry and handle.\n\nget price", null, "### Concrete Calculator Estimate Concrete for a Slab or Footing\n\nConcrete, which is a mix of water, aggregate, and cement, is most commonly sold by the cubic yard, but is also available in pre-mixed bags. One cubic yard is equal to the volume of a cube with edges that are one yard (three feet) in length.\n\nget price\nEstimating How Much Concrete You NeedOur calculator can estimate the yards of concrete needed by entering the project dimensions in imperial or metric measurements, including inches, f...Estimating The Cost to Install ConcreteThe average cost to install a concrete slab is \\$6 \\$16 per square foot. In addition to the cost of the concrete itself, there are also labor costs...Preparing to Pour ConcreteMuch of the work to pour concrete is done before the truck even arrives at the project. The site must be measured and laid out. Forms must be insta...Tips For Ordering ConcreteCall your concrete supplier and tell them about your project and what the project is. Ask them to advise you on the proper mix given your applicati...", null, "### Quikrete 60 lb. Concrete Mix-110160 The Home Depot\n\nOverviewReviewsQuikrete 60 lb. Concrete Mix is ideal for both structural and non structural applications over 2 in. thick. This ready to use product contains a blend of Portland cement, sand, gravel, and other approved ingredients. Quikrete 60 lb. Concrete Mix is perfect for projects requiring a quality, general use concrete mix.", null, "### Concrete Calculator\n\nSlabs, Square Footings, or Walls. Length (l) Width (w) Thickness or Height (h) Quantity.", null, "### Concrete Calculator How Much Concrete Do I Need? The\n\nApr 23, 2018100 x .33 = 33 cubic feet; 33 x .037 = 1.22 cubic yards; Essentially you are solving for volume and then converting to cubic yards. For concrete, the formula for volume is as follows: length x width x thickness. To determine how many bags of concrete you will need, divide the total cubic yards needed by the yield.\n\nget price", null, "### Quikrete 60 lb. Concrete Mix-110160 The Home Depot\n\nQuikrete 60 lb. Concrete Mix is ideal for both structural and non structural applications over 2 in. thick. This ready to use product contains a blend of Portland cement, sand, gravel, and other approved ingredients. Quikrete 60 lb. Concrete Mix is perfect for projects requiring a quality, general use concrete mix.\n\nget price\n4.5/5(1.7K)", null, "### How much cement sandaggregate required for M20 concrete\n\nHance 8 bags cement = 19 cft sand For 1 bag of cement = 19/8= 2.375 cft sand. Hance 8 bags of cement = 37 cft aggregate For 1 bag of cement = 37/8 = 4.625 cft aggregate Ans. :- 2.375 cft sand4.625 cft aggregate are required per 50 kg of cement bag for m20 grade of concrete. You Can Follow me on Facebook and Subscribe our Youtube Channel. You\n\nget price", null, "### How many cement bags in m25 concrete Civil Sir\n\nHow much cement sand and aggregate required for m25 concrete. 1) quantity of cement in m25 concrete. 11.088 no (554.4 kg) of cement bags are used in m25 grade of 1m3 concrete. 2) volume of sand in cft for m25 concrete. 1m3 = 35.32 cft. Volume =( 1/4) × 1.54×35.32. Sand volume = 13.6 cft\n\nget price", null, "### Calculate Bags of Concrete Mix Round + Square Footing\n\nPre-Mix Concrete Bag Calculator Calculated at 133.3 lb per ft³ Allow extra for waste Cubic Feet 100# Bags 80# Bags 75# Bags 60# Bags 50# Bags 40# Bags 25# Bags 20# Bags 10# Bags @ \\$ per bag\n\nget price", null, "### How to Calculate Quantities of Cement, Sand and Aggregate\n\nOne bag of cement and other ingredients can produce = 400/2400 = 0.167 Cum of concrete (1:2:4) 01 bag cement yield = 0.167 cum concrete with a proportion of 1:2:4 01 cum of concrete will require Cement required = 1(m3/bag)/0.167 (m3) = 5.98 Bags ~ 6 Bags —————–OK Sand required = 115(Kgs)/0.167(m3) = 688 (Kgs/m3) or 14.98 cft\n\nget price", null, "### CONCRETE VOLUME cubic feet per 60lb bag\n\nProcessing\n\nget price", null, "### How Much Concrete Do I Need? Sakrete\n\nIf you take the example above of 1.6 cubic feet, the calculation would be : 1.6 ÷ .6. = 2.7 bags If you happen to be enthralled with math calculations I provide the following information on how to calculate the yield that I said was .6 cubic feet for an 80 lb bag. The first thing you need to know is the “density” of the concrete.\n\nget price", null, "### Concrete Calculator Square Footage Area\n\nOur concrete calculator provides you an easy way to calculate concrete volume and estimated cost of concrete slabs, footers, walls, columns, steps, stairs, curbs and gutters in cubic feet, cubic yards, and cubic meters and inches. It makes your construction project planning and budgeting more accurate.\n\nget price", null, "### An Easy Way to Build Retaining Walls: Leave the Concrete\n\nOct 19, 2018This is method is ignorant of how cement works. I just listened to an audiobook called \"Stuff Matters\" by Mark Miadownik, about the material science behind all the common materials that make our modern world—, concrete, steel, etc. and in it, the author explained that concrete doesn't dry when it hardens; it actually cures in a reaction with water such that it\n\nget price", null, "### Concrete Calculator How Much Concrete Do I Need? The\n\nApr 23, 2018100 x .33 = 33 cubic feet; 33 x .037 = 1.22 cubic yards; Essentially you are solving for volume and then converting to cubic yards. For concrete, the formula for volume is as follows: length x width x thickness. To determine how many bags of concrete you will need, divide the total cubic yards needed by the yield.\n\nget price", null, "### M25 Concrete Grade Cement Sand Aggregate and Water Qnty\n\nM25 Concrete Grade Cement Sand Aggregate and Water Qnty All Units Covered KG, Bags, CFT, CUM In this video we will learn, How to Calculate Cement Sand\n\nget price", null, "### 2020 Concrete Prices Concrete Truck Delivery Costs (Per\n\nPre-mixed concrete costs \\$4.49 to \\$5.57 per 50-pound bag of light-weight and fast-setting concrete mix and is available at most home improvement stores. Pre-mixed concrete comes in two varieties; a \"no-mix\" bag which requires the addition of water, and another which requires renting a concrete mixer to cure the cement.\n\nget price", null, "### CONCRETE VOLUME cubic feet per 80lb bag\n\nJul 24, 2020The approximate volume of concrete produced from a 80 pound bag is 0.6 ft³. To compute how many 80 lb bags of concrete is needed for a total volume, CLICK HERE.. Choose your volume units (e.g. cubic feet) Enter the volume (V) The calculator returns the number of 80 lb bags needed to mix that much concrete.\n\nget price", null, "### How Many Cubic Feet Is One Bag of Cement?\n\nApr 07, 2020An 80-pound bag of concrete makes 0.6 cubic feet. A cubic foot of any material is enough to fill a box that is 1 foot wide, 1 foot tall and 1 foot long.\n\nget price", null, "### How much cement sandaggregate required for M20 concrete\n\nHance 8 bags cement = 19 cft sand For 1 bag of cement = 19/8= 2.375 cft sand. Hance 8 bags of cement = 37 cft aggregate For 1 bag of cement = 37/8 = 4.625 cft aggregate Ans. :- 2.375 cft sand4.625 cft aggregate are required per 50 kg of cement bag for m20 grade of concrete. You Can Follow me on Facebook and Subscribe our Youtube Channel. You\n\nget price", null, "### How many cement bags in m25 concrete Civil Sir\n\nHow much cement sand and aggregate required for m25 concrete. 1) quantity of cement in m25 concrete. 11.088 no (554.4 kg) of cement bags are used in m25 grade of 1m3 concrete. 2) volume of sand in cft for m25 concrete. 1m3 = 35.32 cft. Volume =( 1/4) × 1.54×35.32. Sand volume = 13.6 cft\n\nget price", null, "### Cement Bags In Cft Of Concrete\n\nCement Bags In Cft Of Concrete. How much cement needed for 100 cft roof concrete 2020-2-3example calculation estimate the quantity of cement sand and stone aggregate required for 1 cubic meter of 124 concrete mix ans materials required are 7 nos of 50 kg bag of cement 042 m 3 of sand and 083 m 3 of stone.\n\nget price", null, "### cement bags in 1cft of concrete\n\nHow Much CFT in 1 Bag Cement. Calculating the quantity of CFT in a bag of cement All we know is that a bag of cement is equal to 50 kg,The most important type of cement is used as a component in the production of masonry mortar and concrete, which is a combination of cement and aggregate to form a solid building material. 【】\n\nget price", null, "### M25 Concrete Grade Cement Sand Aggregate and Water Qnty\n\nOct 25, 2019M25 Concrete Grade Cement Sand Aggregate and Water Qnty All Units Covered KG, Bags, CFT, CUM In this video we will learn, How to Calculate Cement Sand\n\nget price", null, "### How to Calculate How Much Quikrete to Use Home Guides\n\nDec 14, 2018Quikrete's Concrete Mix yield's about .15 cubic feet for every 20 pounds of mix, so a 40-pound bag yields .30 cubic feet, 60 pounds of concrete mix yields .45 cubic feet and an 80-pound bag yields\n\nget price", null, "### Concrete Calculator for Deck Footings Decks\n\nOne 60-lb bag of concrete gives you .45 cubic feet of concrete when mixed with 2.5 quarts of water. In order to have enough concrete for 1 cubic yard (27 cubic feet), you’ll require 2.2 bags of 60-lb concrete. Since bags are only sold in whole (not half, or quarter) quantities, you’ll need to purchase three (3) 60-lb. bags for one cubic yard.\n\nget price", null, "### 2020 Concrete Prices Concrete Truck Delivery Costs (Per\n\nPre-mixed concrete costs \\$4.49 to \\$5.57 per 50-pound bag of light-weight and fast-setting concrete mix and is available at most home improvement stores. Pre-mixed concrete comes in two varieties; a \"no-mix\" bag which requires the addition of water, and another which requires renting a concrete mixer to cure the cement.\n\nget price", null, "### How Much Concrete Do I Need? Sakrete\n\nIf you take the example above of 1.6 cubic feet, the calculation would be : 1.6 ÷ .6. = 2.7 bags If you happen to be enthralled with math calculations I provide the following information on how to calculate the yield that I said was .6 cubic feet for an 80 lb bag. The first thing you need to know is the “density” of the concrete.\n\nget price", null, "### An Easy Way to Build Retaining Walls: Leave the Concrete\n\nOct 19, 2018This is method is ignorant of how cement works. I just listened to an audiobook called \"Stuff Matters\" by Mark Miadownik, about the material science behind all the common materials that make our modern world—, concrete, steel, etc. and in it, the author explained that concrete doesn't dry when it hardens; it actually cures in a reaction with water such that it\n\nget price", null, "### How many bags of portland cement is needed to mix 1 cubic\n\nOne cubic meter of concrete is equal to 1.308 cubic yards of concrete. If there are 5 1/2 bags of cement in 1 cubic yard of concrete, there would be 7.2 bags in 1 cubic meter of concrete.\n\nget price", null, "### How To Calculate Cement Bags In 1 Cubic Meter?\n\nDec 21, 2016∴ No. of cement bags required in 1 cubic meter = 0.2171/0.0347 = 6.25 bags. Note: You can use the same formula for calculating cement for other nominal mixes.\n\nget price", null, "### Quantities of Materials Per Cubic Meter of Concrete Mix\n\nsimilarly, for M20 or 20MPa concrete, refer above table with mix ratio of 1:1.5:3, you will find, 395 kg of cement or 7.9 bags of cement, 0.414 cubic meter of sand (FA) and 0.828 cubic meter of stone (CA). I hope this clears the doubt.\n\nget price", null, "### How do I calculate volume of 50 Kg cement bag? we civil\n\nSep 21, 2018Volume of cement bag in cubic feet (CFT) since, 1 m³ = 35.3147 cubic feet = 28.80 No. of bags ∴ Volume of one cement bag = 35.3147/28.80 = 1.226 CFT (cubic feet) Volume of cement bag in Litres. since, 1 m³ = 10³ liters. Volume of one cement bag = 0.0347 m³ = 0.034722 x 10³ = 34.4722 litres ∴ Volume of one cement bag = 34.4722 litres\n\nget price" ]	[ null, "https://normaserveert.nl/pics/276.jpg", null, "https://normaserveert.nl/pics/269.jpg", null, "https://normaserveert.nl/pics/456.jpg", null, "https://normaserveert.nl/pics/406.jpg", null, "https://normaserveert.nl/pics/83.jpg", null, "https://normaserveert.nl/pics/324.jpg", null, "https://normaserveert.nl/pics/421.jpg", null, "https://normaserveert.nl/pics/365.jpg", null, "https://normaserveert.nl/pics/425.jpg", null, "https://normaserveert.nl/pics/237.jpg", null, "https://normaserveert.nl/pics/169.jpg", null, "https://normaserveert.nl/pics/198.jpg", null, "https://normaserveert.nl/pics/437.jpg", null, "https://normaserveert.nl/pics/165.jpg", null, "https://normaserveert.nl/pics/307.jpg", null, "https://normaserveert.nl/pics/184.jpg", null, "https://normaserveert.nl/pics/86.jpg", null, "https://normaserveert.nl/pics/304.jpg", null, "https://normaserveert.nl/pics/343.jpg", null, "https://normaserveert.nl/pics/397.jpg", null, "https://normaserveert.nl/pics/454.jpg", null, "https://normaserveert.nl/pics/97.jpg", null, "https://normaserveert.nl/pics/486.jpg", null, "https://normaserveert.nl/pics/264.jpg", null, "https://normaserveert.nl/pics/52.jpg", null, "https://normaserveert.nl/pics/122.jpg", null, "https://normaserveert.nl/pics/447.jpg", null, "https://normaserveert.nl/pics/401.jpg", null, "https://normaserveert.nl/pics/280.jpg", null, "https://normaserveert.nl/pics/343.jpg", null, "https://normaserveert.nl/pics/8.jpg", null, "https://normaserveert.nl/pics/502.jpg", null, "https://normaserveert.nl/pics/232.jpg", null, "https://normaserveert.nl/pics/324.jpg", null, "https://normaserveert.nl/pics/413.jpg", null, "https://normaserveert.nl/pics/285.jpg", null, "https://normaserveert.nl/pics/57.jpg", null, "https://normaserveert.nl/pics/312.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8654831,"math_prob":0.9683834,"size":10222,"snap":"2020-34-2020-40","text_gpt3_token_len":2748,"char_repetition_ratio":0.18545704,"word_repetition_ratio":0.53176343,"special_character_ratio":0.27939737,"punctuation_ratio":0.121282525,"nsfw_num_words":2,"has_unicode_error":false,"math_prob_llama3":0.95740336,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76],"im_url_duplicate_count":[null,3,null,2,null,1,null,2,null,2,null,4,null,5,null,1,null,1,null,1,null,2,null,4,null,4,null,4,null,4,null,2,null,1,null,1,null,3,null,3,null,4,null,3,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,3,null,2,null,2,null,2,null,4,null,1,null,2,null,2,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T10:39:56Z\",\"WARC-Record-ID\":\"<urn:uuid:a2419e7c-db75-4291-a5ce-6593cfc5dd79>\",\"Content-Length\":\"27941\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fd58487b-c6ce-4f5e-971a-0ae7bb13b966>\",\"WARC-Concurrent-To\":\"<urn:uuid:6ce95b7e-f012-45fb-afd3-d29fb14fe7d1>\",\"WARC-IP-Address\":\"104.24.111.7\",\"WARC-Target-URI\":\"https://normaserveert.nl/677/5JpPT.html\",\"WARC-Payload-Digest\":\"sha1:EY7TWDLYEGJWFGIIWOJJ7Z7IOW7OVINU\",\"WARC-Block-Digest\":\"sha1:KSO7VLYK2UFN5PARH5X4VF2HKWPJZBEP\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400197946.27_warc_CC-MAIN-20200920094130-20200920124130-00099.warc.gz\"}"}
https://community.powerbi.com/t5/Desktop/Adding-Values-Between-Hours/m-p/1913465	[ "cancel\nShowing results for\nDid you mean:", null, "New Member\n\nHello, I have data with the date/time that a sale occurred, and I need to make a table that gathers sales for all days of a certain time interval.\nFor example:\n10/10/2020 09:15 = \\$50\n11/10/2020 09:40 = \\$150\n12/10/2020 09:50 = \\$50\n10/13/2020 10:09 = \\$350\n\nIn the break:\n- 9:00 am to 10:00 am sold in total = \\$250\n- 10:00 am to 11:00 am sold in total = \\$350\n\n1 ACCEPTED SOLUTION", null, "", null, "Super User IV\n\n@Felipe_Nery , You can create a time table with buckets and use that. First split date and time from datetime in power query or DAX.\n\nIn DAX\n\nDate = [datetime].date\nor\nDate = date(year([datetime]),month([datetime]),day([datetime]))\n\nDateTime.Date([datetime])\n\nTime = [datetime].Time\nor\nTime = Time(hour([datetime]),minute([datetime]),second([datetime]))\n\nCreate a time table join with time and use that\n\nhttps://kohera.be/power-bi/how-to-create-a-time-table-in-power-bi-in-a-few-simple-steps/\n\ntime([Hour],0,0) & \" - \" time([Hour]+1,0,0)\n\nsort this on hour if needed\n\nProud to be a Super User!\n\n2 REPLIES 2", null, "", null, "Super User IV\n\n@Felipe_Nery , You can create a time table with buckets and use that. First split date and time from datetime in power query or DAX.\n\nIn DAX\n\nDate = [datetime].date\nor\nDate = date(year([datetime]),month([datetime]),day([datetime]))\n\nDateTime.Date([datetime])\n\nTime = [datetime].Time\nor\nTime = Time(hour([datetime]),minute([datetime]),second([datetime]))\n\nCreate a time table join with time and use that\n\nhttps://kohera.be/power-bi/how-to-create-a-time-table-in-power-bi-in-a-few-simple-steps/\n\ntime([Hour],0,0) & \" - \" time([Hour]+1,0,0)\n\nsort this on hour if needed\n\nProud to be a Super User!", null, "New Member\n\nThank you, I spent days trying. I am Brazilian, and here I didn't find any tutorial about it.", null, "Announcements", null, "#### Welcome to the User Group Public Preview", null, "", null, "" ]	[ null, "https://community.powerbi.com/t5/image/serverpage/avatar-name/modern/avatar-theme/candy/avatar-collection/architecture/avatar-display-size/message/version/2", null, "https://community.powerbi.com/t5/image/serverpage/image-id/353527iCC3523D17BAF3A41/image-dimensions/40x40/image-coordinates/254%2C65%2C2712%2C2523/constrain-image/false", null, "https://community.powerbi.com/html/@5EBC40BFAC84B488C3F19C8B51062A41/rank_icons/[email protected]", null, "https://community.powerbi.com/t5/image/serverpage/image-id/353527iCC3523D17BAF3A41/image-dimensions/40x40/image-coordinates/254%2C65%2C2712%2C2523/constrain-image/false", null, "https://community.powerbi.com/html/@5EBC40BFAC84B488C3F19C8B51062A41/rank_icons/[email protected]", null, "https://community.powerbi.com/t5/image/serverpage/avatar-name/modern/avatar-theme/candy/avatar-collection/architecture/avatar-display-size/message/version/2", null, "https://community.powerbi.com/skins/images/005554E35FAA3084895ACF9A273B7509/responsive_peak/images/icon_anonymous_message.png", null, "https://powerusers.microsoft.com/t5/image/serverpage/image-id/244725iCBB4B71CF6F296A5/image-size/large", null, "https://community.powerbi.com/t5/image/serverpage/image-id/549294i1E9CF37F91B2F549/image-size/large/is-moderation-mode/true", null, "https://community.powerbi.com/html/assets/spinner-slide.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79088724,"math_prob":0.96743727,"size":2200,"snap":"2021-31-2021-39","text_gpt3_token_len":625,"char_repetition_ratio":0.143898,"word_repetition_ratio":0.49324325,"special_character_ratio":0.315,"punctuation_ratio":0.13829787,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97747177,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-24T05:51:21Z\",\"WARC-Record-ID\":\"<urn:uuid:1899fd32-e52c-460e-876f-0ca8ca6ee3c8>\",\"Content-Length\":\"447451\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:913cfd1c-f1bf-4ab4-8041-b5731782545f>\",\"WARC-Concurrent-To\":\"<urn:uuid:ef9cc229-6df8-43eb-9782-9d05498c1a19>\",\"WARC-IP-Address\":\"104.106.176.212\",\"WARC-Target-URI\":\"https://community.powerbi.com/t5/Desktop/Adding-Values-Between-Hours/m-p/1913465\",\"WARC-Payload-Digest\":\"sha1:OSTM3NKP5T5RB4H2JUBQ62XN5QYRF4U5\",\"WARC-Block-Digest\":\"sha1:TLTX76UNCY7EACVUASJBNT5FD7RFMYSK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046150129.50_warc_CC-MAIN-20210724032221-20210724062221-00570.warc.gz\"}"}
https://biz-y.com/molarity-and-molarity-calculator-affects/	[ "", null, "# Molarity and Molarity Calculator-How it Affects you\n\nA molarity calculator is a useful tool for scientist which is used for the calculation of several scientific chemical equations. It is used to calculate the following:\n\n• The mass a compound is requires to have to prepare a solution that has a known concentration and known volume.\n• The volume a solution is required to have to enable it to dissolve a compound with known mass to acquire the desired concentration\n• The concentration a solution has from a compound with a known mass in a specific volume.\n\nWhen calculating the molarity of a solution, the formula used is\n\nMolar Mass= Concentration x Volume x Molecular Weight\n\nThe mass is in grams, the concentration of the solution is in moles per liter, the volume is in liters and the molecular weight is in grams per moles.\n\nTo understand how to solve the equation, you must understand the terms used accurately. This article would define the meaning of each term used in the formula.\n\nMolar Mass\n\nThe molar mass of a compound is said to be the mass that a sample of that particular compound is divided by the amount of substance that can be found in that sample which is usually measured in moles. The mass is not a molecular property of that substance rather, it is just an average of the compound.\n\nHow to calculate", null, "To get the molar mass of an element, all you have to do is divide the moles by gram. When given a question involving the molar mass, you would be given a value in moles which you would divide against the mass( in grams) of an element.\n\nThe concentration of a solution\n\nThe concentration of a solution is simply the amount of solute that can be found in a specific quantity of solution. The concentration is most times represented by molarity which is said to be the number of moles in a solute in 1L of a solution.\n\nHow to calculate\n\nThe formula for calculating the concentration of a solution is C=m/v. Where c is concentration, m is the mass of the dissolved solute and v is the volume of the solution. All you need to have is the values of the mass and the volume and you get your answer easily.\n\nVolume\n\nSimply put, the volume is a total of all the volume of a solute in 1 litre.\n\nHow to calculate\n\nTo calculate the volume of a solution, the formula is V= M/C\n\nWhere m is the mass and c is the concentration of the solution. When asked to find the volume of a solution, you would be given the mass and concentration or you would be given values that would help you find either the concentration or the mass which would make the division easier.", null, "Molecular weight\n\nThe molecular weight is defined as the sum of the atomic weights of atoms found in a molecule. It is usually used to find the stoichiometry which occurs in chemical reactions. The best way to calculate it precisely is by using a molarity calculator. With it, you can never go wrong." ]	[ null, "https://biz-y.com/wp-content/uploads/2019/12/1-1.png", null, "https://biz-y.com/wp-content/uploads/2019/12/2-1.png", null, "https://biz-y.com/wp-content/uploads/2019/12/3-1.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9593677,"math_prob":0.99494874,"size":2805,"snap":"2022-40-2023-06","text_gpt3_token_len":597,"char_repetition_ratio":0.17707962,"word_repetition_ratio":0.023346303,"special_character_ratio":0.20106952,"punctuation_ratio":0.06329114,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99959975,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,3,null,4,null,4,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T07:32:03Z\",\"WARC-Record-ID\":\"<urn:uuid:16b4489e-6678-4abd-a953-fb4782db8b12>\",\"Content-Length\":\"120293\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:30d6f14c-282f-4d29-b901-7ff2f0ddc994>\",\"WARC-Concurrent-To\":\"<urn:uuid:3ea5c945-a7a7-4c7d-9990-ade4aa6ddaa6>\",\"WARC-IP-Address\":\"66.42.64.112\",\"WARC-Target-URI\":\"https://biz-y.com/molarity-and-molarity-calculator-affects/\",\"WARC-Payload-Digest\":\"sha1:3BJFFZEE62SSYBS25DAKE7QAGA724N34\",\"WARC-Block-Digest\":\"sha1:2QKGRHHBV6VC4YPCBFYZ7C5CKUSN5MF4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337480.10_warc_CC-MAIN-20221004054641-20221004084641-00741.warc.gz\"}"}
https://www.nagwa.com/en/videos/849105840262/	[ "# Video: Finding a Decimal between Two Given Decimals and Converting It to a Fraction and a Percentage\n\nWhich of the following expresses a decimal between 0.35 and 0.95, its fraction in simplest form, and its percentage form? [A] 0.4, 2/5, 40%. [B] 0.4, 40/100, 40%. [C] 0.4, 2/5, 35%. [D] 0.45, 40/100, 35%. [E] 0.45, 2/5, 4%.\n\n02:12\n\n### Video Transcript\n\nWhich of the following expresses a decimal between 0.35 and 0.95, its fraction in simplest form, and its percentage form?\n\nLet’s firstly consider the two different decimals that we have, 0.4 and 0.45. Both of these do indeed lie between 0.35 and 0.95. In order to convert a decimal into a percentage, we multiply by 100. 0.4 multiplied by 100 is equal to 40, and 0.45 multiplied by 100 is equal to 45. Our digits moved two places to the left. This means that we can immediately rule out options (C), (D), and (E), as their decimals and percentages do not match.\n\nBoth option (A) and option (B) have the decimal 0.4 and the percentage 40 percent. This means that we have an equivalent percentage form. Our next step is to work out which of the fractions is written in simplest form. The word “percent” means out of 100. So 40 percent can be written as 40 out of or over 100. This suggests that option (B) might be the correct answer.\n\nHowever, 40 over 100 is not in its simplest form, as both the numerator and denominator are divisible by 20. 40 divided by 20 is equal to two, and 100 divided by 20 is equal to five. This means that the decimal 0.4 and the percentage 40 percent written as a fraction in simplest form is two-fifths or two over five. The correct answer was option (A) 0.4, two-fifths, and 40 percent." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9485157,"math_prob":0.99669427,"size":1330,"snap":"2020-45-2020-50","text_gpt3_token_len":365,"char_repetition_ratio":0.13273002,"word_repetition_ratio":0.05785124,"special_character_ratio":0.28421053,"punctuation_ratio":0.13621262,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99927515,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-21T22:35:24Z\",\"WARC-Record-ID\":\"<urn:uuid:7fff2c77-88e1-48fa-b5cf-1f86dc1f7124>\",\"Content-Length\":\"27115\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0106e6f3-a973-46dd-854a-2c87400736c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:a09b8248-fca4-4047-b5f7-948c37c64371>\",\"WARC-IP-Address\":\"34.196.176.227\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/videos/849105840262/\",\"WARC-Payload-Digest\":\"sha1:L622BOPOCJYP3TV7RENEKOM7JF5PSXS4\",\"WARC-Block-Digest\":\"sha1:QYMTWXO5QIDZ734SLY5C3RNKKNSZM26J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107878633.8_warc_CC-MAIN-20201021205955-20201021235955-00630.warc.gz\"}"}
https://es.mathworks.com/matlabcentral/answers/423159-number-of-times-two-numbers-appear-together?s_tid=prof_contriblnk	[ "# Number of times two numbers appear together\n\n2 views (last 30 days)\ndan berkowitz on 10 Oct 2018\nEdited: Stephen23 on 10 Oct 2018\nHi,\nI have an array A = [1 3 2 4 3 4 3 2 1 1 3 2 4 3 3 2].\nHow can I count the number of time the number 2 occurs after 1, the number of times the number 3 occurs after 1, and the number of times the number 4 occurs after 1?\nAny help would be appreciated.\nThanks,\nDB\n\nStephen23 on 10 Oct 2018\nEdited: Stephen23 on 10 Oct 2018\n>> A = [1,3,2,4,3,4,3,2,1,1,3,2,4,3,3,2];\nMethod one: basic indexing and nnz:\n>> nnz(A(1:end-1)==1 & A(2:end)==2)\nans = 0\n>> nnz(A(1:end-1)==1 & A(2:end)==3)\nans = 2\n>> nnz(A(1:end-1)==1 & A(2:end)==4)\nans = 0\nMethod two: strfind:\n>> nnz(strfind(char(A),char([1,2])))\nans = 0\n>> nnz(strfind(char(A),char([1,3])))\nans = 2\n>> nnz(strfind(char(A),char([1,4])))\nans = 0" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6946499,"math_prob":0.9997348,"size":979,"snap":"2022-27-2022-33","text_gpt3_token_len":363,"char_repetition_ratio":0.14461538,"word_repetition_ratio":0.035714287,"special_character_ratio":0.40858018,"punctuation_ratio":0.16535433,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99015355,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-04T06:52:03Z\",\"WARC-Record-ID\":\"<urn:uuid:8815fb16-7f26-4694-a077-74cc9a381762>\",\"Content-Length\":\"111819\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d3d9c185-8b18-4686-8bee-70dcef43ae4e>\",\"WARC-Concurrent-To\":\"<urn:uuid:36395d0b-4509-4565-bf3e-cc26e9bf1410>\",\"WARC-IP-Address\":\"23.35.66.81\",\"WARC-Target-URI\":\"https://es.mathworks.com/matlabcentral/answers/423159-number-of-times-two-numbers-appear-together?s_tid=prof_contriblnk\",\"WARC-Payload-Digest\":\"sha1:ITXIRJARK2ZZS7GLRRICP2HMWJTBZK4E\",\"WARC-Block-Digest\":\"sha1:DOEDW7QDFNP65JB5ZQGPZIP2BUARWUHK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104354651.73_warc_CC-MAIN-20220704050055-20220704080055-00632.warc.gz\"}"}
http://accord-framework.net/docs/html/M_Accord_Statistics_Tools_Center_2.htm	[ " Tools.Center Method (Double[], Double, Double[])", null, "", null, "", null, "Centers an observation, subtracting the empirical mean from each element in the observation vector.\n\nNamespace: Accord.Statistics\nAssembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0", null, "Syntax\n```public static double[] Center(\nthis double[] values,\ndouble mean,\ndouble[] result = null\n)```\n\n#### Parameters\n\nvalues\nType: SystemDouble\nAn array of double precision floating-point numbers.\nmean\nType: SystemDouble\nThe mean of the values, if already known.\nresult (Optional)\nType: SystemDouble\nThe destination array where the result of this operation should be stored.\n\nType: Double\n\n#### Usage Note\n\nIn Visual Basic and C#, you can call this method as an instance method on any object of type . When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).", null, "See Also" ]	[ null, "http://accord-framework.net/docs/icons/TocOpen.gif", null, "http://accord-framework.net/docs/icons/TocClose.gif", null, "http://accord-framework.net/docs/icons/logo.png", null, "http://accord-framework.net/docs/icons/SectionExpanded.png", null, "http://accord-framework.net/docs/icons/SectionExpanded.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.5961624,"math_prob":0.5662098,"size":1122,"snap":"2023-40-2023-50","text_gpt3_token_len":250,"char_repetition_ratio":0.12343471,"word_repetition_ratio":0.0,"special_character_ratio":0.21746881,"punctuation_ratio":0.16062176,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9729919,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-29T20:53:22Z\",\"WARC-Record-ID\":\"<urn:uuid:e99e3fec-cab9-43ca-9f84-e2ad1ca66ccc>\",\"Content-Length\":\"15385\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cfaea4b5-cf1a-46d6-89a5-2fab681f3ed5>\",\"WARC-Concurrent-To\":\"<urn:uuid:d6327c4b-f07c-4ba5-bd3f-fd8a52690bba>\",\"WARC-IP-Address\":\"192.30.252.153\",\"WARC-Target-URI\":\"http://accord-framework.net/docs/html/M_Accord_Statistics_Tools_Center_2.htm\",\"WARC-Payload-Digest\":\"sha1:OKKJI35BHT3RIG3AFF5LLVHSACQR3WSF\",\"WARC-Block-Digest\":\"sha1:2MHAHMC4TAZFC5IVPXUGNL2CRAFX64WN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510528.86_warc_CC-MAIN-20230929190403-20230929220403-00768.warc.gz\"}"}
https://www.easycalculation.com/physics/classical-physics/tangential-velocity-calculator.php	[ "# Tangential Velocity Calculator\n\nThe given below online tangential velocity calculator is an online tool which helps you to determine the velocity of the turning wheel or any circular object. If you know the value of the radius of an object, you can easily calculate the tangential speed with our online tool.\n\n## Calculate Tangential Speed\n\nm/s\n\nThe given below online tangential velocity calculator is an online tool which helps you to determine the velocity of the turning wheel or any circular object. If you know the value of the radius of an object, you can easily calculate the tangential speed with our online tool.\n\nCode to add this calci to your website", null, "", null, "#### Formula:\n\nVt = r ω Where, Vt = Tangential Velocity (meter per second) r = Radius (m) ω = Angular Velocity ( 20 * π )\n\nTangential Velocity: Tangential velocity (speed) is a velocity measured at any point that is tangent to a turning wheel. In detail, when an object is moving along in a circular path at a distance from its center, then its velocity at any point would be directed tangentially. This is called as tangential velocity.\n\nTangential Velocity Formula: The tangential velocity formula defines the relationship between the Radius (r) and Angular velocity (ω) of an object.\n\nOur online tangential velocity calculator would help you to calculate tangential speed by providing the value of radius.\n\n### Example:\n\nAn object has a radius of 5 m. What is its tangential speed?\n\n#### Solution:\n\nVt = r ω\n= 5 x (20 x 3.14)\n= 314.20 m/s" ]	[ null, "https://www.easycalculation.com/images/embed-plus.gif", null, "https://www.easycalculation.com/images/embed-minus.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.90907204,"math_prob":0.98764485,"size":1238,"snap":"2021-21-2021-25","text_gpt3_token_len":267,"char_repetition_ratio":0.20907618,"word_repetition_ratio":0.41904762,"special_character_ratio":0.20678514,"punctuation_ratio":0.08154506,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999532,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-21T04:27:24Z\",\"WARC-Record-ID\":\"<urn:uuid:0755c8e6-f45c-46a0-8742-6e2c13afdee2>\",\"Content-Length\":\"25480\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:295549a6-05b1-4529-b5d8-b1a0bcb4252e>\",\"WARC-Concurrent-To\":\"<urn:uuid:1c14b86c-344f-4b24-be5a-4cc6a9f326a6>\",\"WARC-IP-Address\":\"50.116.14.108\",\"WARC-Target-URI\":\"https://www.easycalculation.com/physics/classical-physics/tangential-velocity-calculator.php\",\"WARC-Payload-Digest\":\"sha1:JVOERVOYDIP73TMPX3NJ3OIICAWD3IF5\",\"WARC-Block-Digest\":\"sha1:RQXYTF4SLMF2D5Z7ZRLRQEG2H4RV7RDT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623488262046.80_warc_CC-MAIN-20210621025359-20210621055359-00474.warc.gz\"}"}
https://xianblog.wordpress.com/2020/11/19/on-completeness/	[ "## on completeness\n\nAnother X validated question that proved a bit of a challenge, enough for my returning to its resolution on consecutive days. The question was about the completeness of the natural sufficient statistic associated with a sample from the shifted exponential distribution", null, "$f(x;\\theta) = \\frac{1}{\\theta^2}\\exp\\{-\\theta^{-2}(x-\\theta)\\}\\mathbb{I}_{x>\\theta}$\n\n[weirdly called negative exponential in the question] meaning the (minimal) sufficient statistic is made of the first order statistic and of the sample sum (or average), or equivalently", null, "$T=(X_{(1)},\\sum_{i=2}^n \\{X_{(i)}-X_{(1)}\\})$\n\nFinding the joint distribution of T is rather straightforward as the first component is a drifted Exponential again and the second a Gamma variate with n-2 degrees of freedom and the scale θ². (Devroye’s Bible can be invoked since the Gamma distribution follows from his section on Exponential spacings, p.211.) While the derivation of a function with constant expectation is straightforward for the alternate exponential distribution", null, "$f(x;\\theta) = \\frac{1}{\\theta}\\exp\\{-\\theta^{-1}(x-\\theta)\\}\\mathbb{I}_{x>\\theta}$\n\nsince the ratio of the components of T has a fixed distribution, it proved harder for the current case as I was seeking a parameter free transform. When attempting to explain the difficulty on my office board, I realised I was seeking the wrong property since an expectation was enough. Removing the dependence on θ was simpler and led to", null, "$\\mathbb E_\\theta\\left[\\frac{X_{(1)}}{Y}-\\frac{\\Gamma(n-2)}{\\Gamma(n-3/2)}Y^\\frac{-1}{2}\\right]=\\frac{\\Gamma(n-2)}{n\\Gamma(n-1)}$\n\nbut one version of a transform with fixed expectation. This also led me to wonder at the range of possible functions of θ one could use as scale and still retrieve incompleteness of T. Any power of θ should work but what about exp(θ²) or sin²(θ³), i.e. functions for which there exists no unbiased estimator..?\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed." ]	[ null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null, "https://s0.wp.com/latex.php", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9488324,"math_prob":0.99004537,"size":1569,"snap":"2021-04-2021-17","text_gpt3_token_len":312,"char_repetition_ratio":0.118849844,"word_repetition_ratio":0.0,"special_character_ratio":0.18801785,"punctuation_ratio":0.067857146,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999374,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-17T09:46:21Z\",\"WARC-Record-ID\":\"<urn:uuid:1c2b379a-636f-49e4-8cdf-463eaf4e13b4>\",\"Content-Length\":\"48865\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e68f0cf9-d138-4521-ad0b-f136a1ef3b2f>\",\"WARC-Concurrent-To\":\"<urn:uuid:6bf35d2b-662b-4df7-a2b9-9708fb2b3454>\",\"WARC-IP-Address\":\"192.0.78.12\",\"WARC-Target-URI\":\"https://xianblog.wordpress.com/2020/11/19/on-completeness/\",\"WARC-Payload-Digest\":\"sha1:7EEIXW2ESNXKE2EP42VOBTIFDZAVJY7F\",\"WARC-Block-Digest\":\"sha1:AHAIILGBHXK5EC4VBP4O4JCBWXLC3KMQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703511903.11_warc_CC-MAIN-20210117081748-20210117111748-00667.warc.gz\"}"}