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33, "seek": 78629, "start": 765.97, "end": 786.29, "text": "ولا واحد فيهم يعتمد على الثاني مش vector space هذا وال dimension له نتج عن basis وال basis شروطها ان يكونوا كل العناصر اللي في ال business are linearly independent يبقى هذه المعادلة لها N من الحلول", "tokens": [12610, 995, 36764, 24401, 8978, 16095, 7251, 34268, 2304, 3215, 15844, 6024, 104, 7649, 1829, 37893, 8062, 1901, 23758, 16070, 10139, 46740, 8717, 2655, 7435, 18871, 5143, 16070, 5143, 13412, 32887, 9566, 11296, 16472, 7251, 30544, 14407, 28242, 18863, 1863, 33546, 2288, 13672, 1829, 8978, 2423, 1606, 366, 43586, 6695, 7251, 3555, 4587, 7578, 29538, 9673, 3615, 18513, 37977, 5296, 11296, 426, 9154, 21542, 1211, 12610], "avg_logprob": -0.19811100568344345, "compression_ratio": 1.4558823529411764, "no_speech_prob": 0.0, "words": [{"start": 765.97, "end": 766.73, "word": "ولا", "probability": 0.3892822265625}, {"start": 766.73, "end": 767.35, "word": " واحد", "probability": 0.943115234375}, {"start": 767.35, "end": 767.67, 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هنا قبل أن نمسح", "tokens": [2407, 28820, 29538, 21542, 1211, 12610, 366, 43586, 6695, 4032, 22488, 3215, 11296, 7251, 3794, 995, 45865, 426, 23032, 1829, 3555, 12174, 36150, 14739, 8717, 44510, 10721, 16247, 2304, 12984, 37977, 8978, 11331, 3215, 39894, 3794, 10721, 1211, 36632, 8608, 33604, 6027, 34105, 12174, 36150, 14739, 8717, 2304, 3794, 5016], "avg_logprob": -0.2031250035061556, "compression_ratio": 1.297872340425532, "no_speech_prob": 0.0, "words": [{"start": 786.57, "end": 787.37, "word": "وكل", "probability": 0.74462890625}, {"start": 787.37, "end": 787.89, "word": " هذه", "probability": 0.96240234375}, {"start": 787.89, "end": 788.51, "word": " الحلول", "probability": 0.9895833333333334}, {"start": 788.51, "end": 788.93, "word": " are", "probability": 0.09552001953125}, {"start": 788.93, "end": 789.67, "word": " linearly", "probability": 0.96533203125}, {"start": 789.67, "end": 791.05, "word": " independent", "probability": 0.88818359375}, {"start": 791.05, "end": 792.41, 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"end": 849.9, "word": " y1", "probability": 0.43475341796875}, {"start": 849.9, "end": 850.68, "word": " و", "probability": 0.513671875}, {"start": 850.68, "end": 850.8, "word": " ال", "probability": 0.87451171875}, {"start": 850.8, "end": 851.48, "word": " y2", "probability": 0.975341796875}, {"start": 851.48, "end": 852.36, "word": " و", "probability": 0.951171875}, {"start": 852.36, "end": 852.56, "word": " ال", "probability": 0.97412109375}, {"start": 852.56, "end": 853.34, "word": " yn", "probability": 0.78515625}, {"start": 853.34, "end": 855.08, "word": " are", "probability": 0.70751953125}, {"start": 855.08, "end": 856.9, "word": " linearly", "probability": 0.94287109375}, {"start": 856.9, "end": 858.22, "word": " independent", "probability": 0.95068359375}, {"start": 858.22, "end": 860.88, "word": " solutions", "probability": 0.916015625}], "temperature": 1.0}, {"id": 37, "seek": 89073, "start": 864.89, "end": 890.73, "text": "of L of Y equal to zero then that's it Y1 Y2 YN شكل اللي عندنا هذا form a basis form a basis", "tokens": [2670, 441, 295, 398, 2681, 281, 4018, 550, 300, 311, 309, 398, 16, 398, 17, 398, 45, 13412, 28820, 13672, 1829, 43242, 8315, 23758, 1254, 257, 5143, 1254, 257, 5143], "avg_logprob": -0.3692036194186057, "compression_ratio": 1.07, "no_speech_prob": 0.0, "words": [{"start": 864.89, "end": 865.51, "word": "of", "probability": 0.12286376953125}, {"start": 865.51, "end": 866.85, "word": " L", "probability": 0.50732421875}, {"start": 866.85, "end": 867.33, "word": " of", "probability": 0.81298828125}, {"start": 867.33, "end": 867.77, "word": " Y", "probability": 0.97216796875}, {"start": 867.77, "end": 869.03, "word": " equal", "probability": 0.41357421875}, {"start": 869.03, "end": 869.55, "word": " to", "probability": 0.974609375}, {"start": 869.55, "end": 870.07, "word": " zero", "probability": 0.59619140625}, {"start": 870.07, "end": 872.21, "word": " then", "probability": 0.57470703125}, {"start": 872.21, "end": 872.65, "word": " that's", "probability": 0.720703125}, {"start": 872.65, "end": 875.13, "word": " it", "probability": 0.9580078125}, {"start": 875.13, "end": 877.83, "word": " Y1", "probability": 0.59912109375}, {"start": 877.83, "end": 879.45, "word": " Y2", "probability": 0.819580078125}, {"start": 879.45, "end": 881.49, "word": " YN", "probability": 0.7333984375}, {"start": 881.49, "end": 883.37, "word": " شكل", "probability": 0.6881103515625}, {"start": 883.37, "end": 883.55, "word": " اللي", "probability": 0.943603515625}, {"start": 883.55, "end": 883.91, "word": " عندنا", "probability": 0.902587890625}, {"start": 883.91, "end": 884.37, "word": " هذا", "probability": 0.84765625}, {"start": 884.37, "end": 885.99, "word": " form", "probability": 0.69482421875}, {"start": 885.99, "end": 886.39, "word": " a", "probability": 0.70849609375}, {"start": 886.39, "end": 886.81, "word": " basis", "probability": 0.440185546875}, {"start": 886.81, "end": 888.93, "word": " form", "probability": 0.70166015625}, {"start": 888.93, "end": 890.21, "word": " a", "probability": 0.96728515625}, {"start": 890.21, "end": 890.73, "word": " basis", "probability": 0.86767578125}], "temperature": 1.0}, {"id": 38, "seek": 91749, "start": 893.43, "end": 917.49, "text": "أصبح مؤسسة لكرنل لـ L و من هنا اي حل", "tokens": [10721, 9381, 3555, 5016, 3714, 33604, 3794, 3794, 3660, 5296, 4117, 2288, 1863, 1211, 5296, 39184, 441, 4032, 9154, 34105, 1975, 1829, 11331, 1211], "avg_logprob": -1.035, "compression_ratio": 0.9253731343283582, "no_speech_prob": 0.0, "words": [{"start": 893.43, "end": 894.49, "word": "أصبح", "probability": 0.2493743896484375}, {"start": 894.49, "end": 895.43, "word": " مؤسسة", "probability": 0.647998046875}, {"start": 895.43, "end": 901.09, "word": " لكرنل", "probability": 0.539886474609375}, {"start": 901.09, "end": 903.35, "word": " لـ", "probability": 0.27557373046875}, {"start": 903.35, "end": 905.69, "word": " L", "probability": 0.576171875}, {"start": 905.69, "end": 907.87, "word": " و", "probability": 0.2471923828125}, {"start": 907.87, "end": 908.43, "word": " من", "probability": 0.27783203125}, {"start": 908.43, "end": 908.43, "word": " هنا", "probability": 0.537109375}, {"start": 908.43, "end": 917.21, "word": " اي", "probability": 0.52056884765625}, {"start": 917.21, "end": 917.49, "word": " حل", "probability": 0.56207275390625}], "temperature": 1.0}, {"id": 39, "seek": 95174, "start": 922.72, "end": 951.74, "text": "and hence any solution of L of Y equal to zero has the form بياخد الشكل التالي Y تساو C1 Y1 C2 Y2 زائد CN YN this solution", "tokens": [474, 16678, 604, 3827, 295, 441, 295, 398, 2681, 281, 4018, 575, 264, 1254, 4724, 1829, 47283, 3215, 25124, 28820, 16712, 6027, 1829, 398, 6055, 3794, 995, 2407, 383, 16, 398, 16, 383, 17, 398, 17, 30767, 16373, 3215, 383, 45, 398, 45, 341, 3827], "avg_logprob": -0.3597146661385246, "compression_ratio": 1.106060606060606, "no_speech_prob": 0.0, "words": [{"start": 922.72, "end": 923.06, "word": "and", 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"end": 933.16, "word": " form", "probability": 0.93359375}, {"start": 933.16, "end": 937.48, "word": " بياخد", "probability": 0.72784423828125}, {"start": 937.48, "end": 937.98, "word": " الشكل", "probability": 0.822998046875}, {"start": 937.98, "end": 938.84, "word": " التالي", "probability": 0.9464518229166666}, {"start": 938.84, "end": 939.94, "word": " Y", "probability": 0.7041015625}, {"start": 939.94, "end": 940.7, "word": " تساو", "probability": 0.717529296875}, {"start": 940.7, "end": 941.7, "word": " C1", "probability": 0.6715087890625}, {"start": 941.7, "end": 943.0, "word": " Y1", "probability": 0.7646484375}, {"start": 943.0, "end": 944.34, "word": " C2", "probability": 0.90478515625}, {"start": 944.34, "end": 945.7, "word": " Y2", "probability": 0.93603515625}, {"start": 945.7, "end": 946.8, "word": " زائد", "probability": 0.6438802083333334}, {"start": 946.8, "end": 947.78, "word": " CN", "probability": 0.4893798828125}, {"start": 947.78, "end": 949.5, "word": " YN", 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x يساوي صين ال X form a basis for the space of solutions space of solutions of", "tokens": [69, 17, 295, 2031, 7251, 3794, 995, 45865, 20328, 9957, 2423, 1783, 1254, 257, 5143, 337, 264, 1901, 295, 6547, 1901, 295, 6547, 295], "avg_logprob": -0.335625, "compression_ratio": 1.175, "no_speech_prob": 0.0, "words": [{"start": 1016.43, "end": 1017.55, "word": "f2", "probability": 0.48834228515625}, {"start": 1017.55, "end": 1018.71, "word": " of", "probability": 0.463623046875}, {"start": 1018.71, "end": 1019.39, "word": " x", "probability": 0.92919921875}, {"start": 1019.39, "end": 1020.81, "word": " يساوي", "probability": 0.74822998046875}, {"start": 1020.81, "end": 1021.47, "word": " صين", "probability": 0.733154296875}, {"start": 1021.47, "end": 1021.71, "word": " ال", "probability": 0.82861328125}, {"start": 1021.71, "end": 1022.27, "word": " X", "probability": 0.337646484375}, {"start": 1022.27, "end": 1024.61, "word": " form", "probability": 0.5517578125}, {"start": 1024.61, "end": 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زائد y تساوي Zero نمرأ بيه Find a solution Of the initial value problem", "tokens": [2278, 15756, 5367, 288, 3834, 5835, 30767, 16373, 3215, 288, 6055, 3794, 995, 45865, 17182, 8717, 29973, 10721, 4724, 1829, 3224, 11809, 257, 3827, 2720, 264, 5883, 2158, 1154], "avg_logprob": -0.5364583492279053, "compression_ratio": 1.0406504065040652, "no_speech_prob": 0.0, "words": [{"start": 1047.46, "end": 1048.04, "word": "The", "probability": 0.040679931640625}, {"start": 1048.04, "end": 1050.58, "word": " differential", "probability": 0.755859375}, {"start": 1050.58, "end": 1052.82, "word": " equation", "probability": 0.96484375}, {"start": 1052.82, "end": 1054.38, "word": " y", "probability": 0.390625}, {"start": 1054.38, "end": 1054.78, "word": " double", "probability": 0.1883544921875}, {"start": 1054.78, "end": 1055.64, "word": " prime", "probability": 0.8720703125}, {"start": 1055.64, "end": 1057.08, "word": " زائد", "probability": 0.659423828125}, {"start": 1057.08, "end": 1057.58, 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