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212.05, "end": 212.37, "word": " Alpha", "probability": 0.8662109375}, {"start": 212.37, "end": 212.73, "word": " و", "probability": 0.953125}, {"start": 212.73, "end": 212.97, "word": " Beta", "probability": 0.533203125}], "temperature": 1.0}, {"id": 10, "seek": 24208, "start": 213.52, "end": 242.08, "text": "لأن لو كان في عندي function F is continuous on any interval I containing Phi of J لأن فرضنا أن F دالة على I تحتوي Phi of J عساس إن بعد شوية هعرّق .. هيلزمني اللي هو composition of two functions عشان هيك أنا باخد ال F عبارة عن function من I لعند مين؟ لعند ال R إيش ال I هذه؟ هذه I interval", "tokens": [1211, 33456, 45164, 25961, 8978, 18871, 16254, 2445, 479, 307, 10957, 322, 604, 15035, 286, 19273, 41435, 295, 508, 5296, 33456, 6156, 43042, 8315, 14739, 479, 11778, 6027, 3660, 15844, 286, 6055, 33753, 45865, 41435, 295, 508, 6225, 3794, 32277, 36145, 39182, 13412, 2407, 10632, 8032, 3615, 2288, 11703, 4587, 4386, 39896, 1211, 11622, 2304, 22653, 13672, 1829, 31439, 12686, 295, 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أنه", "probability": 0.6871337890625}, {"start": 1027.22, "end": 1027.44, "word": " فيه", "probability": 0.748291015625}, {"start": 1027.44, "end": 1027.74, "word": " function", "probability": 0.95849609375}, {"start": 1027.74, "end": 1028.1, "word": " ψ", "probability": 0.53582763671875}, {"start": 1028.1, "end": 1028.44, "word": " من", "probability": 0.8173828125}, {"start": 1028.44, "end": 1028.68, "word": " I", "probability": 0.99169921875}, {"start": 1028.68, "end": 1029.08, "word": " لعند", "probability": 0.8326822916666666}, {"start": 1029.08, "end": 1029.5, "word": " R", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 46, "seek": 105394, "start": 1030.06, "end": 1053.94, "text": "بـ a function اللي هو inverse لـ mean اللي هي الـ Phi يعني عندي Phi بشروط النظرية اللي فاتت من J لعند مين لعند R وعندي ب Psi من عند I لعند R ومفترضين أنه بPsi هي ال inverse ل mean للـ Phi يعني Phi composite بPsi", "tokens": [3555, 39184, 257, 2445, 13672, 1829, 31439, 17340, 5296, 39184, 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{"start": 1038.34, "end": 1038.58, "word": " اللي", "probability": 0.9541015625}, {"start": 1038.58, "end": 1039.24, "word": " فاتت", "probability": 0.994140625}, {"start": 1039.24, "end": 1039.88, "word": " من", "probability": 0.9716796875}, {"start": 1039.88, "end": 1040.44, "word": " J", "probability": 0.6552734375}, {"start": 1040.44, "end": 1041.16, "word": " لعند", "probability": 0.9039713541666666}, {"start": 1041.16, "end": 1041.7, "word": " مين", "probability": 0.8203125}, {"start": 1041.7, "end": 1042.26, "word": " لعند", "probability": 0.9500325520833334}, {"start": 1042.26, "end": 1042.66, "word": " R", "probability": 0.9521484375}, {"start": 1042.66, "end": 1044.14, "word": " وعندي", "probability": 0.9490966796875}, {"start": 1044.14, "end": 1044.52, "word": " ب", "probability": 0.91552734375}, {"start": 1044.52, "end": 1044.98, "word": " Psi", "probability": 0.56829833984375}, {"start": 1044.98, "end": 1045.74, "word": " من", "probability": 0.99267578125}, {"start": 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0.953125}], "temperature": 1.0}, {"id": 116, "seek": 273306, "start": 2720.3, "end": 2733.06, "text": "أو الـ Taylor's theorem إذا صح التعبير for integration و Taylor's theorem for differentiations الآن الجزء اللي هو الـ for integration نشوف أشي اللي بقوله", "tokens": [10721, 2407, 2423, 39184, 12060, 311, 20904, 11933, 15730, 20328, 5016, 16712, 3615, 3555, 13546, 337, 10980, 4032, 12060, 311, 20904, 337, 27372, 763, 6024, 48506, 25724, 11622, 38207, 13672, 1829, 31439, 2423, 39184, 337, 10980, 8717, 8592, 38688, 5551, 8592, 1829, 13672, 1829, 4724, 39648, 3224], "avg_logprob": -0.31608072978754836, "compression_ratio": 1.4236111111111112, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2720.3, "end": 2720.6, "word": "أو", "probability": 0.6693115234375}, {"start": 2720.6, "end": 2720.9, "word": " الـ", "probability": 0.4891357421875}, {"start": 2720.9, "end": 2721.92, "word": " Taylor's", "probability": 0.736083984375}, {"start": 2721.92, "end": 2722.32, "word": " theorem", "probability": 0.77490234375}, {"start": 2722.32, "end": 2723.22, "word": " إذا", "probability": 0.555816650390625}, {"start": 2723.22, "end": 2723.56, "word": " صح", "probability": 0.953125}, {"start": 2723.56, "end": 2724.22, "word": " التعبير", "probability": 0.80572509765625}, {"start": 2724.22, "end": 2724.9, "word": " for", "probability": 0.7919921875}, {"start": 2724.9, "end": 2725.64, "word": " integration", "probability": 0.9697265625}, {"start": 2725.64, "end": 2726.56, "word": " و", "probability": 0.66845703125}, {"start": 2726.56, "end": 2727.06, "word": " Taylor's", "probability": 0.930419921875}, {"start": 2727.06, "end": 2727.32, "word": " theorem", "probability": 0.86572265625}, {"start": 2727.32, "end": 2727.6, "word": " for", "probability": 0.97314453125}, {"start": 2727.6, "end": 2728.52, "word": " differentiations", "probability": 0.6678466796875}, {"start": 2728.52, "end": 2729.1, "word": " الآن", "probability": 0.5504150390625}, {"start": 2729.1, "end": 2729.5, "word": " الجزء", "probability": 0.9720052083333334}, {"start": 2729.5, "end": 2729.66, "word": " اللي", "probability": 0.916259765625}, {"start": 2729.66, "end": 2729.82, "word": " هو", "probability": 0.9951171875}, {"start": 2729.82, "end": 2730.16, "word": " الـ", "probability": 0.439208984375}, {"start": 2730.16, "end": 2730.6, "word": " for", "probability": 0.82861328125}, {"start": 2730.6, "end": 2731.8, "word": " integration", "probability": 0.9697265625}, {"start": 2731.8, "end": 2732.28, "word": " نشوف", "probability": 0.87109375}, {"start": 2732.28, "end": 2732.5, "word": " أشي", "probability": 0.7015787760416666}, {"start": 2732.5, "end": 2732.6, "word": " اللي", "probability": 0.99072265625}, {"start": 2732.6, "end": 2733.06, "word": " بقوله", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 117, "seek": 276375, "start": 2735.05, "end": 2763.75, "text": "suppose that the function f and its derivatives f prime of w prime عند fn and fn زائد واحد are كلهم إيه شمالهم continuous يعني نفترض أن الانث derivative الانث زائد واحد derivative is continuous exist وcontinuous نفترض أن الدالة f عبارة عن دالة قابلة للاشتقاق n زائد واحد من المرات وتكون الان زائد واحد كمان نفسها continuous", "tokens": [36622, 541, 300, 264, 2445, 283, 293, 1080, 33733, 283, 5835, 295, 261, 5835, 43242, 283, 77, 293, 283, 77, 30767, 16373, 3215, 36764, 24401, 366, 28242, 16095, 11933, 1829, 3224, 13412, 2304, 6027, 16095, 10957, 37495, 22653, 8717, 5172, 2655, 43042, 14739, 2423, 7649, 12984, 13760, 2423, 7649, 12984, 30767, 16373, 3215, 36764, 24401, 13760, 307, 10957, 2514, 4032, 9000, 259, 12549, 8717, 5172, 2655, 43042, 14739, 32748, 6027, 3660, 283, 6225, 3555, 9640, 3660, 18871, 11778, 6027, 3660, 12174, 16758, 37977, 24976, 33599, 2655, 4587, 995, 4587, 297, 30767, 16373, 3215, 36764, 24401, 9154, 9673, 2288, 9307, 34683, 30544, 2423, 7649, 30767, 16373, 3215, 36764, 24401, 9122, 2304, 7649, 8717, 36178, 11296, 10957], "avg_logprob": -0.2050107698245295, "compression_ratio": 1.9404255319148935, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2735.05, "end": 2735.69, "word": "suppose", "probability": 0.6160888671875}, {"start": 2735.69, "end": 2735.99, "word": " that", "probability": 0.8984375}, {"start": 2735.99, "end": 2736.19, "word": " the", "probability": 0.85302734375}, {"start": 2736.19, "end": 2736.57, "word": " function", "probability": 0.9248046875}, {"start": 2736.57, "end": 2736.87, "word": " f", "probability": 0.488525390625}, {"start": 2736.87, "end": 2737.19, "word": " and", "probability": 0.90869140625}, {"start": 2737.19, "end": 2738.09, "word": " its", "probability": 0.7548828125}, {"start": 2738.09, "end": 2738.63, "word": " derivatives", "probability": 0.9150390625}, {"start": 2738.63, "end": 2738.89, "word": " f", "probability": 0.677734375}, {"start": 2738.89, "end": 2739.21, "word": " prime", "probability": 0.1719970703125}, {"start": 2739.21, "end": 2739.39, "word": " of", "probability": 0.9267578125}, {"start": 2739.39, "end": 2739.61, "word": " w", "probability": 0.7666015625}, {"start": 2739.61, "end": 2739.87, "word": " prime", "probability": 0.8779296875}, {"start": 2739.87, "end": 2740.07, "word": " عند", "probability": 0.498291015625}, {"start": 2740.07, "end": 2740.63, "word": " fn", "probability": 0.609619140625}, {"start": 2740.63, "end": 2741.23, "word": " and", "probability": 0.6904296875}, {"start": 2741.23, "end": 2741.67, "word": " fn", "probability": 0.935546875}, {"start": 2741.67, "end": 2742.01, "word": " زائد", "probability": 0.6698404947916666}, {"start": 2742.01, "end": 2742.41, "word": " واحد", "probability": 0.89208984375}, {"start": 2742.41, "end": 2742.65, "word": " are", "probability": 0.89208984375}, {"start": 2742.65, "end": 2743.03, "word": " كلهم", "probability": 0.774169921875}, {"start": 2743.03, "end": 2743.19, "word": " إيه", "probability": 0.83984375}, {"start": 2743.19, "end": 2743.59, "word": " شمالهم", "probability": 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"word": " continuous", "probability": 0.955078125}, {"start": 2750.43, "end": 2750.81, "word": " exist", "probability": 0.50244140625}, {"start": 2750.81, "end": 2751.57, "word": " وcontinuous", "probability": 0.83416748046875}, {"start": 2751.57, "end": 2752.75, "word": " نفترض", "probability": 0.960205078125}, {"start": 2752.75, "end": 2753.07, "word": " أن", "probability": 0.91455078125}, {"start": 2753.07, "end": 2753.67, "word": " الدالة", "probability": 0.92138671875}, {"start": 2753.67, "end": 2753.89, "word": " f", "probability": 0.6328125}, {"start": 2753.89, "end": 2754.41, "word": " عبارة", "probability": 0.992919921875}, {"start": 2754.41, "end": 2754.75, "word": " عن", "probability": 0.990234375}, {"start": 2754.75, "end": 2755.73, "word": " دالة", "probability": 0.95556640625}, {"start": 2755.73, "end": 2756.25, "word": " قابلة", "probability": 0.9895833333333334}, {"start": 2756.25, "end": 2757.33, "word": " للاشتقاق", "probability": 0.8097330729166666}, {"start": 2757.33, "end": 2757.67, "word": " n", "probability": 0.51025390625}, {"start": 2757.67, "end": 2758.13, "word": " زائد", "probability": 0.9635416666666666}, {"start": 2758.13, "end": 2758.59, "word": " واحد", "probability": 0.98974609375}, {"start": 2758.59, "end": 2758.85, "word": " من", "probability": 0.99365234375}, {"start": 2758.85, "end": 2759.61, "word": " المرات", "probability": 0.9490559895833334}, {"start": 2759.61, "end": 2760.85, "word": " وتكون", "probability": 0.765380859375}, {"start": 2760.85, "end": 2761.27, "word": " الان", "probability": 0.751953125}, {"start": 2761.27, "end": 2761.75, "word": " زائد", "probability": 0.7960611979166666}, {"start": 2761.75, "end": 2762.25, "word": " واحد", "probability": 0.99560546875}, {"start": 2762.25, "end": 2762.71, "word": " كمان", "probability": 0.9462890625}, {"start": 2762.71, "end": 2763.31, "word": " نفسها", "probability": 0.93896484375}, {"start": 2763.31, "end": 2763.75, "word": " continuous", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 118, "seek": 278485, "start": 2764.65, "end": 2784.85, "text": "ماشي على الفترة a و b then بقوللي اللي هو f of b بيساوي f of a زي f prime of v على 1 factorial في b minus a زي f double prime of a على 2 factorial في b minus a تربيع زائد لما أصل عند f n of a على n factorial في b minus a الكولوسن هذا كله إيش معله", "tokens": [2304, 33599, 1829, 15844, 27188, 2655, 25720, 257, 4032, 272, 550, 4724, 39648, 20292, 13672, 1829, 31439, 283, 295, 272, 4724, 1829, 3794, 995, 45865, 283, 295, 257, 30767, 1829, 283, 5835, 295, 371, 15844, 502, 36916, 8978, 272, 3175, 257, 30767, 1829, 283, 3834, 5835, 295, 257, 15844, 568, 36916, 8978, 272, 3175, 257, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 5296, 15042, 5551, 36520, 43242, 283, 297, 295, 257, 15844, 297, 36916, 8978, 272, 3175, 257, 33251, 12610, 41779, 1863, 23758, 28242, 3224, 11933, 1829, 8592, 20449, 43761], "avg_logprob": -0.2901785845284934, "compression_ratio": 1.7591623036649215, 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