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"probability": 0.9560546875}, {"start": 279.6, "end": 280.72, "word": " إذن", "probability": 0.7237955729166666}, {"start": 280.72, "end": 281.08, "word": " الآن", "probability": 0.794921875}, {"start": 281.08, "end": 281.6, "word": " عندي", "probability": 0.6658935546875}, {"start": 281.6, "end": 282.64, "word": " سميت", "probability": 0.97265625}, {"start": 282.64, "end": 282.8, "word": " اللي", "probability": 0.986572265625}, {"start": 282.8, "end": 283.0, "word": " هي", "probability": 0.865234375}, {"start": 283.0, "end": 283.16, "word": " الـ", "probability": 0.83837890625}, {"start": 283.16, "end": 283.3, "word": " M", "probability": 0.93896484375}, {"start": 283.3, "end": 283.46, "word": " K", "probability": 0.9521484375}, {"start": 283.46, "end": 283.78, "word": " Capital", "probability": 0.97265625}, {"start": 283.78, "end": 283.96, "word": " هي", "probability": 0.81982421875}, {"start": 283.96, "end": 284.12, "word": " الـ", "probability": 0.5655517578125}, {"start": 284.12, "end": 284.56, "word": " Supremum", "probability": 0.6978352864583334}, {"start": 284.56, "end": 285.2, "word": " والـ", "probability": 0.75732421875}, {"start": 285.2, "end": 285.36, "word": " M", "probability": 0.9599609375}, {"start": 285.36, "end": 285.56, "word": " K", "probability": 0.931640625}, {"start": 285.56, "end": 286.02, "word": " Small", "probability": 0.85400390625}, {"start": 286.02, "end": 286.32, "word": " هي", "probability": 0.92578125}, {"start": 286.32, "end": 286.72, "word": " عبارة", "probability": 0.9952392578125}, {"start": 286.72, "end": 286.92, "word": " عن", "probability": 0.99609375}, {"start": 286.92, "end": 287.08, "word": " الـ", "probability": 0.5501708984375}, {"start": 287.08, "end": 287.54, "word": " Infimum", "probability": 0.7508138020833334}, {"start": 287.54, "end": 288.26, "word": " وهلجيت", "probability": 0.732421875}, {"start": 288.26, "end": 289.04, "word": " حنشوف", "probability": 0.823486328125}, {"start": 289.04, "end": 289.74, "word": " إيش", "probability": 0.800537109375}, {"start": 289.74, "end": 290.74, "word": " دواعي", "probability": 0.9639892578125}, {"start": 290.74, "end": 291.24, "word": " هذه", "probability": 0.467041015625}, {"start": 291.24, "end": 291.9, "word": " التسمية", "probability": 0.9913736979166666}, {"start": 291.9, "end": 292.2, "word": " أو", "probability": 0.861328125}, {"start": 292.2, "end": 292.42, "word": " ليش", "probability": 0.9619140625}, {"start": 292.42, "end": 292.84, "word": " سمينا", "probability": 0.9071044921875}, {"start": 292.84, "end": 293.12, "word": " هيك", "probability": 0.950927734375}], "temperature": 1.0}, {"id": 12, "seek": 32102, "start": 294.32, "end": 321.02, "text": "الان بدنا نعرف اللي هو .. بدنا نعرف الآن اللي هو حاجة اسمها lower sum و حاجة اسمها ايش ال upper sum الان لو جيت بعد ما عملت ال partition اللي عندي هذا و جيت أخدت اللي هي", "tokens": [6027, 7649, 47525, 8315, 8717, 3615, 28480, 13672, 1829, 31439, 4386, 47525, 8315, 8717, 3615, 28480, 6024, 48506, 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"probability": 0.86865234375}, {"start": 300.38, "end": 300.76, "word": " نعرف", "probability": 0.9900716145833334}, {"start": 300.76, "end": 301.34, "word": " الآن", "probability": 0.6279296875}, {"start": 301.34, "end": 301.68, "word": " اللي", "probability": 0.960205078125}, {"start": 301.68, "end": 301.92, "word": " هو", "probability": 0.98046875}, {"start": 301.92, "end": 302.3, "word": " حاجة", "probability": 0.9724934895833334}, {"start": 302.3, "end": 302.68, "word": " اسمها", "probability": 0.958984375}, {"start": 302.68, "end": 303.0, "word": " lower", "probability": 0.669921875}, {"start": 303.0, "end": 303.46, "word": " sum", "probability": 0.448486328125}, {"start": 303.46, "end": 304.08, "word": " و", "probability": 0.92822265625}, {"start": 304.08, "end": 304.38, "word": " حاجة", "probability": 0.8515625}, {"start": 304.38, "end": 304.78, "word": " اسمها", "probability": 0.9793294270833334}, {"start": 304.78, "end": 305.28, "word": " ايش", "probability": 0.6162109375}, {"start": 305.28, "end": 305.88, "word": " ال", "probability": 0.9091796875}, {"start": 305.88, "end": 306.26, "word": " upper", "probability": 0.78369140625}, {"start": 306.26, "end": 307.02, "word": " sum", "probability": 0.9521484375}, {"start": 307.02, "end": 308.4, "word": " الان", "probability": 0.750732421875}, {"start": 308.4, "end": 309.34, "word": " لو", "probability": 0.97021484375}, {"start": 309.34, "end": 309.94, "word": " جيت", "probability": 0.993408203125}, {"start": 309.94, "end": 311.9, "word": " بعد", "probability": 0.95068359375}, {"start": 311.9, "end": 312.1, "word": " ما", "probability": 0.9599609375}, {"start": 312.1, "end": 312.42, "word": " عملت", "probability": 0.93359375}, {"start": 312.42, "end": 312.54, "word": " ال", "probability": 0.97119140625}, {"start": 312.54, "end": 312.92, "word": " partition", "probability": 0.8408203125}, {"start": 312.92, "end": 313.22, "word": " اللي", "probability": 0.96533203125}, {"start": 313.22, "end": 313.54, "word": " عندي", "probability": 0.6805419921875}, {"start": 313.54, "end": 314.14, "word": " هذا", "probability": 0.9609375}, {"start": 314.14, "end": 315.46, "word": " و", "probability": 0.76220703125}, {"start": 315.46, "end": 315.84, "word": " جيت", "probability": 0.933837890625}, {"start": 315.84, "end": 318.38, "word": " أخدت", "probability": 0.869140625}, {"start": 318.38, "end": 320.66, "word": " اللي", "probability": 0.9794921875}, {"start": 320.66, "end": 321.02, "word": " هي", "probability": 0.923828125}], "temperature": 1.0}, {"id": 13, "seek": 35699, "start": 328.55, "end": 356.99, "text": "أخدت الـ partition B اللي عندي هذا هذا ال partition B هو عبارة عن X0 X1 X2 اللي عند XN جيت أنا أخدت اللي هو الـ supremum للدالة في هذه المنطقة والتي تكون طبعا هنا شكلها اللي هي سميتها M1 في X1 نقص X0", "tokens": [10721, 9778, 3215, 2655, 2423, 39184, 24808, 363, 13672, 1829, 18871, 16254, 23758, 23758, 2423, 24808, 363, 31439, 6225, 3555, 9640, 3660, 18871, 1783, 15, 1783, 16, 1783, 17, 13672, 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"word": " هذا", "probability": 0.83154296875}, {"start": 331.39, "end": 332.63, "word": " هذا", "probability": 0.34375}, {"start": 332.63, "end": 332.77, "word": " ال", "probability": 0.94921875}, {"start": 332.77, "end": 333.09, "word": " partition", "probability": 0.58056640625}, {"start": 333.09, "end": 333.53, "word": " B", "probability": 0.64892578125}, {"start": 333.53, "end": 333.85, "word": " هو", "probability": 0.86865234375}, {"start": 333.85, "end": 334.23, "word": " عبارة", "probability": 0.9945068359375}, {"start": 334.23, "end": 334.41, "word": " عن", "probability": 0.9892578125}, {"start": 334.41, "end": 335.05, "word": " X0", "probability": 0.46533203125}, {"start": 335.05, "end": 336.51, "word": " X1", "probability": 0.919677734375}, {"start": 336.51, "end": 337.49, "word": " X2", "probability": 0.963623046875}, {"start": 337.49, "end": 337.71, "word": " اللي", "probability": 0.657470703125}, {"start": 337.71, "end": 337.91, "word": " عند", "probability": 0.7841796875}, {"start": 337.91, "end": 338.51, "word": " XN", "probability": 0.6146240234375}, {"start": 338.51, "end": 340.11, "word": " جيت", "probability": 0.713623046875}, {"start": 340.11, "end": 340.27, "word": " أنا", "probability": 0.6103515625}, {"start": 340.27, "end": 341.13, "word": " أخدت", "probability": 0.962646484375}, {"start": 341.13, "end": 341.69, "word": " اللي", "probability": 0.922607421875}, {"start": 341.69, "end": 341.99, "word": " هو", "probability": 0.994140625}, {"start": 341.99, "end": 343.07, "word": " الـ", "probability": 0.548583984375}, {"start": 343.07, "end": 343.59, "word": " supremum", "probability": 0.68603515625}, {"start": 343.59, "end": 344.21, "word": " للدالة", "probability": 0.9068603515625}, {"start": 344.21, "end": 344.37, "word": " في", "probability": 0.9384765625}, {"start": 344.37, "end": 344.59, "word": " هذه", "probability": 0.9248046875}, {"start": 344.59, "end": 345.29, "word": " المنطقة", "probability": 0.9910888671875}, {"start": 345.29, "end": 346.45, "word": " والتي", "probability": 0.5460205078125}, {"start": 346.45, "end": 346.69, "word": " تكون", "probability": 0.643310546875}, {"start": 346.69, "end": 347.07, "word": " طبعا", "probability": 0.9193115234375}, {"start": 347.07, "end": 347.35, "word": " هنا", "probability": 0.50146484375}, {"start": 347.35, "end": 348.55, "word": " شكلها", "probability": 0.9762369791666666}, {"start": 348.55, "end": 350.71, "word": " اللي", "probability": 0.936279296875}, {"start": 350.71, "end": 350.95, "word": " هي", "probability": 0.466064453125}, {"start": 350.95, "end": 351.55, "word": " سميتها", "probability": 0.97900390625}, {"start": 351.55, "end": 352.41, "word": " M1", "probability": 0.933349609375}, {"start": 352.41, "end": 353.37, "word": " في", "probability": 0.52783203125}, {"start": 353.37, "end": 354.65, "word": " X1", "probability": 0.9697265625}, {"start": 354.65, "end": 356.37, "word": " نقص", "probability": 0.6982421875}, {"start": 356.37, "end": 356.99, "word": " X0", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 14, "seek": 38269, "start": 357.87, "end": 382.69, "text": "و جيت ضفت لها برضه ال supremum للدالة في المنطقة هذه اللي هي زائد M2 سميت ال supremum اللي هو M2 في X2-X0 لما نوصلت لآخر واحدة بنفس الأسلوب أخدت اللي هو ال supremum اللي هي ال supremum طبعا M1 عندى", "tokens": [2407, 10874, 36081, 48812, 5172, 2655, 5296, 11296, 4724, 43042, 3224, 2423, 23710, 449, 24976, 3215, 6027, 3660, 8978, 9673, 1863, 9566, 28671, 29538, 13672, 1829, 39896, 30767, 16373, 3215, 376, 17, 8608, 2304, 36081, 2423, 23710, 449, 13672, 1829, 31439, 376, 17, 8978, 1783, 17, 12, 55, 15, 5296, 15042, 8717, 2407, 36520, 2655, 5296, 148, 95, 34740, 36764, 24401, 3660, 44945, 36178, 16247, 3794, 1211, 37746, 5551, 9778, 3215, 2655, 13672, 1829, 31439, 2423, 23710, 449, 13672, 1829, 39896, 2423, 23710, 449, 23032, 3555, 3615, 995, 376, 16, 43242, 7578], "avg_logprob": -0.18968413786221577, "compression_ratio": 1.681081081081081, 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47027, "start": 443.37, "end": 470.27, "text": "الأن similarly بدي آجي أعرف اللي هو ال lower sum إذا ال upper sum بيساوي ال summation ل X K نقص X K minus واحد مضروب في ال M K capital K من عند واحد لعند N هذه اللي بيسميها ال upper sum similarly بدي أعرف مين اللي هو ال lower sum", "tokens": [6027, 33456, 14138, 4724, 16254, 19753, 7435, 1829, 5551, 3615, 28480, 13672, 1829, 31439, 2423, 3126, 2408, 11933, 15730, 2423, 6597, 2408, 4724, 1829, 3794, 995, 45865, 2423, 28811, 5296, 1783, 591, 8717, 4587, 9381, 1783, 591, 3175, 36764, 24401, 3714, 11242, 32887, 3555, 8978, 2423, 376, 591, 4238, 591, 9154, 43242, 36764, 24401, 5296, 3615, 41260, 426, 29538, 13672, 1829, 4724, 1829, 38251, 1829, 11296, 2423, 6597, 2408, 14138, 4724, 16254, 5551, 3615, 28480, 3714, 9957, 13672, 1829, 31439, 2423, 3126, 2408], "avg_logprob": -0.23902530010257447, "compression_ratio": 1.7083333333333333, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 443.37, "end": 443.77, "word": "الأن", 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الدالة اللي بنعملها أو لو وجدلها ال lower sum و ال upper sum الهن واضح أن ال lower sum ال lower sum واضح أنه اللي هو دائما", "tokens": [2407, 12, 87, 74, 12, 16, 39896, 6225, 3555, 9640, 3660, 18871, 12174, 32640, 2423, 24808, 13672, 1829, 18871, 16254, 11933, 15730, 2423, 3126, 2408, 34051, 11331, 49975, 2423, 6597, 2408, 16712, 2304, 2655, 9957, 4724, 995, 34268, 2304, 3215, 9957, 6225, 45340, 25528, 15844, 13672, 1829, 31439, 2423, 24808, 4032, 3615, 23942, 32748, 6027, 3660, 13672, 1829, 44945, 25957, 1211, 11296, 34051, 45164, 49610, 3215, 1211, 11296, 2423, 3126, 2408, 4032, 2423, 6597, 2408, 2423, 3224, 1863, 4032, 46958, 5016, 14739, 2423, 3126, 2408, 2423, 3126, 2408, 4032, 46958, 5016, 14739, 3224, 13672, 1829, 31439, 11778, 16373, 15042], "avg_logprob": -0.20265625342726706, "compression_ratio": 1.979899497487437, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 580.36, "end": 580.54, "word": "و", "probability": 0.580078125}, {"start": 580.54, "end": 582.14, 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599.26, "word": " و", "probability": 0.78076171875}, {"start": 599.26, "end": 599.42, "word": " ال", "probability": 0.72119140625}, {"start": 599.42, "end": 599.8, "word": " upper", "probability": 0.85107421875}, {"start": 599.8, "end": 600.62, "word": " sum", "probability": 0.96923828125}, {"start": 600.62, "end": 601.46, "word": " الهن", "probability": 0.5410970052083334}, {"start": 601.46, "end": 602.38, "word": " واضح", "probability": 0.9580078125}, {"start": 602.38, "end": 602.64, "word": " أن", "probability": 0.50341796875}, {"start": 602.64, "end": 602.86, "word": " ال", "probability": 0.61962890625}, {"start": 602.86, "end": 603.16, "word": " lower", "probability": 0.81201171875}, {"start": 603.16, "end": 603.62, "word": " sum", "probability": 0.9697265625}, {"start": 603.62, "end": 604.4, "word": " ال", "probability": 0.7744140625}, {"start": 604.4, "end": 604.7, "word": " lower", "probability": 0.78515625}, {"start": 604.7, "end": 604.96, "word": " sum", "probability": 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"probability": 0.99267578125}, {"start": 624.84, "end": 625.6, "word": " then", "probability": 0.77294921875}, {"start": 625.6, "end": 626.18, "word": " ال", "probability": 0.73388671875}, {"start": 626.18, "end": 626.54, "word": " lower", "probability": 0.479736328125}, {"start": 626.54, "end": 627.0, "word": " sum", "probability": 0.970703125}, {"start": 627.0, "end": 627.36, "word": " لل", "probability": 0.6923828125}, {"start": 627.36, "end": 627.52, "word": " B", "probability": 0.80322265625}, {"start": 627.52, "end": 627.66, "word": " و", "probability": 0.78369140625}, {"start": 627.66, "end": 627.74, "word": " ال", "probability": 0.37451171875}, {"start": 627.74, "end": 627.98, "word": " F", "probability": 0.9814453125}, {"start": 627.98, "end": 628.42, "word": " أصغر", "probability": 0.9925537109375}, {"start": 628.42, "end": 628.76, "word": " سوى", "probability": 0.473876953125}, {"start": 628.76, "end": 628.88, "word": " ال", "probability": 0.89208984375}, {"start": 628.88, 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الـMK", "probability": 0.8942057291666666}, {"start": 664.7, "end": 665.3, "word": " Small", "probability": 0.85986328125}, {"start": 665.3, "end": 665.9, "word": " وهذا", "probability": 0.787353515625}, {"start": 665.9, "end": 666.22, "word": " الكلام", "probability": 0.8987630208333334}, {"start": 666.22, "end": 666.64, "word": " صحيح", "probability": 0.9891357421875}, {"start": 666.64, "end": 666.8, "word": " على", "probability": 0.91943359375}, {"start": 666.8, "end": 667.08, "word": " كل", "probability": 0.99169921875}, {"start": 667.08, "end": 668.14, "word": " الـSubintervals", "probability": 0.895703125}, {"start": 668.14, "end": 668.5, "word": " يعني", "probability": 0.74853515625}, {"start": 668.5, "end": 669.28, "word": " صحيح", "probability": 0.99169921875}, {"start": 669.28, "end": 669.68, "word": " لكل", "probability": 0.8955078125}, {"start": 669.68, "end": 669.9, "word": " K", "probability": 0.78125}, {"start": 669.9, "end": 670.04, "word": " من", "probability": 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"الأن لو أخدنا الفترة اللي هي A وB و جزّقناها X0 X1 لعند XN", "tokens": [6027, 33456, 45164, 5551, 9778, 3215, 8315, 27188, 2655, 25720, 13672, 1829, 39896, 316, 4032, 33, 4032, 10874, 11622, 11703, 4587, 8315, 11296, 1783, 15, 1783, 16, 5296, 3615, 41260, 1783, 45], "avg_logprob": -0.2921401515151515, "compression_ratio": 1.0555555555555556, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 765.57, "end": 765.95, "word": "الأن", "probability": 0.61376953125}, {"start": 765.95, "end": 766.09, "word": " لو", "probability": 0.89208984375}, {"start": 766.09, "end": 766.73, "word": " أخدنا", "probability": 0.920166015625}, {"start": 766.73, "end": 769.13, "word": " الفترة", "probability": 0.9637044270833334}, {"start": 769.13, "end": 770.39, "word": " اللي", "probability": 0.677734375}, {"start": 770.39, "end": 770.75, "word": " هي", "probability": 0.95263671875}, {"start": 770.75, "end": 771.35, "word": " A", "probability": 0.40771484375}, {"start": 771.35, "end": 773.09, 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"probability": 0.8603515625}, {"start": 875.27, "end": 876.15, "word": " لل", "probability": 0.58984375}, {"start": 876.15, "end": 877.01, "word": " xk", "probability": 0.8056640625}, {"start": 877.01, "end": 877.43, "word": " minus", "probability": 0.97607421875}, {"start": 877.43, "end": 877.89, "word": " xk", "probability": 0.979248046875}, {"start": 877.89, "end": 878.21, "word": " minus", "probability": 0.99462890625}, {"start": 878.21, "end": 878.75, "word": " واحد", "probability": 0.97998046875}, {"start": 878.75, "end": 879.75, "word": " mk", "probability": 0.7744140625}, {"start": 879.75, "end": 880.35, "word": " capital", "probability": 0.85498046875}, {"start": 880.35, "end": 880.89, "word": " k", "probability": 0.607421875}, {"start": 880.89, "end": 881.01, "word": " من", "probability": 0.98779296875}, {"start": 881.01, "end": 881.27, "word": " عند", "probability": 0.990234375}, {"start": 881.27, "end": 881.81, "word": " واحد", "probability": 0.993896484375}, {"start": 881.81, "end": 882.81, "word": " لعند", "probability": 0.9772135416666666}, {"start": 882.81, "end": 883.11, "word": " n", "probability": 0.69189453125}], "temperature": 1.0}, {"id": 34, "seek": 90747, "start": 883.73, "end": 907.47, "text": "وقلنا إن الـ lower للـ B و الـ F دايما أصغر سوى ال upper للـ B و الـ F فده اللي حتى الآن اللي حكيناه الآن نيجي ناخد الملاحظة اللي عندي if Q above is a refinement of B لو قلنا إن Q عبارة عن إيه شمالها؟ refinement of B", "tokens": [2407, 4587, 1211, 8315, 36145, 2423, 39184, 3126, 24976, 39184, 363, 4032, 2423, 39184, 479, 11778, 47302, 15042, 5551, 9381, 17082, 2288, 8608, 2407, 7578, 2423, 6597, 24976, 39184, 363, 4032, 2423, 39184, 479, 6156, 3215, 3224, 13672, 1829, 11331, 49975, 6024, 48506, 13672, 1829, 11331, 4117, 1829, 8315, 3224, 6024, 48506, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 9673, 15040, 5016, 19913, 3660, 13672, 1829, 18871, 16254, 498, 1249, 3673, 307, 257, 1895, 30229, 295, 363, 45164, 12174, 1211, 8315, 36145, 1249, 6225, 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"probability": 0.8216145833333334}, {"start": 888.59, "end": 889.05, "word": " أصغر", "probability": 0.8829345703125}, {"start": 889.05, "end": 889.37, "word": " سوى", "probability": 0.5177001953125}, {"start": 889.37, "end": 889.47, "word": " ال", "probability": 0.57177734375}, {"start": 889.47, "end": 889.79, "word": " upper", "probability": 0.359619140625}, {"start": 889.79, "end": 890.59, "word": " للـ", "probability": 0.7470703125}, {"start": 890.59, "end": 890.91, "word": " B", "probability": 0.6904296875}, {"start": 890.91, "end": 891.41, "word": " و", "probability": 0.93994140625}, {"start": 891.41, "end": 891.49, "word": " الـ", "probability": 0.76318359375}, {"start": 891.49, "end": 891.63, "word": " F", "probability": 0.8896484375}, {"start": 891.63, "end": 891.91, "word": " فده", "probability": 0.6388346354166666}, {"start": 891.91, "end": 892.03, "word": " اللي", "probability": 0.85791015625}, {"start": 892.03, "end": 892.39, "word": " حتى", "probability": 0.944580078125}, {"start": 892.39, "end": 892.85, "word": " الآن", "probability": 0.83056640625}, {"start": 892.85, "end": 893.49, "word": " اللي", "probability": 0.893798828125}, {"start": 893.49, "end": 894.71, "word": " حكيناه", "probability": 0.921484375}, {"start": 894.71, "end": 895.35, "word": " الآن", "probability": 0.6026611328125}, {"start": 895.35, "end": 896.89, "word": " نيجي", "probability": 0.78515625}, {"start": 896.89, "end": 897.27, "word": " ناخد", "probability": 0.9698893229166666}, {"start": 897.27, "end": 897.93, "word": " الملاحظة", "probability": 0.991015625}, {"start": 897.93, "end": 898.03, "word": " اللي", "probability": 0.967041015625}, {"start": 898.03, "end": 898.47, "word": " عندي", "probability": 0.699951171875}, {"start": 898.47, "end": 899.67, "word": " if", "probability": 0.5087890625}, {"start": 899.67, "end": 900.13, "word": " Q", "probability": 0.54150390625}, {"start": 900.13, "end": 900.87, "word": " above", "probability": 0.91162109375}, {"start": 900.87, "end": 901.41, "word": " is", "probability": 0.955078125}, {"start": 901.41, "end": 901.55, "word": " a", "probability": 0.94970703125}, {"start": 901.55, "end": 901.97, "word": " refinement", "probability": 0.880615234375}, {"start": 901.97, "end": 902.29, "word": " of", "probability": 0.984375}, {"start": 902.29, "end": 902.59, "word": " B", "probability": 0.9853515625}, {"start": 902.59, "end": 903.37, "word": " لو", "probability": 0.8916015625}, {"start": 903.37, "end": 903.69, "word": " قلنا", "probability": 0.9557291666666666}, {"start": 903.69, "end": 903.83, "word": " إن", "probability": 0.93408203125}, {"start": 903.83, "end": 904.11, "word": " Q", "probability": 0.6884765625}, {"start": 904.11, "end": 904.51, "word": " عبارة", "probability": 0.983642578125}, {"start": 904.51, "end": 904.65, "word": " عن", "probability": 0.9873046875}, {"start": 904.65, "end": 904.77, "word": " إيه", "probability": 0.7947591145833334}, {"start": 904.77, "end": 905.93, "word": " شمالها؟", "probability": 0.7572265625}, {"start": 905.93, "end": 906.55, "word": " refinement", "probability": 0.733642578125}, {"start": 906.55, "end": 907.23, "word": " of", "probability": 0.9833984375}, {"start": 907.23, "end": 907.47, "word": " B", "probability": 0.98828125}], "temperature": 1.0}, {"id": 35, "seek": 92959, "start": 908.23, "end": 929.59, "text": "refinement معناته اضفت اللي هو نقطة او اكتر من نقطة لنقاط ال partition اللي عندى اذا اي فترة اي فترة اللي هي xk minus واحد لعند xk اللي هو في ال partition بيه هقدر اكتبها على صورة مين", "tokens": [33115, 30229, 20449, 8315, 47395, 1975, 11242, 5172, 2655, 13672, 1829, 31439, 8717, 47432, 3660, 1975, 2407, 1975, 4117, 2655, 2288, 9154, 8717, 47432, 3660, 5296, 1863, 4587, 41193, 2423, 24808, 13672, 1829, 43242, 7578, 1975, 15730, 1975, 1829, 6156, 2655, 25720, 1975, 1829, 6156, 2655, 25720, 13672, 1829, 39896, 2031, 74, 3175, 36764, 24401, 5296, 3615, 41260, 2031, 74, 13672, 1829, 31439, 8978, 2423, 24808, 4724, 1829, 3224, 8032, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 15844, 20328, 13063, 3660, 3714, 9957], "avg_logprob": -0.1834077448362396, "compression_ratio": 1.697674418604651, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 908.23, "end": 908.87, "word": "refinement", "probability": 0.7802734375}, {"start": 908.87, "end": 909.39, "word": " معناته", "probability": 0.77978515625}, {"start": 909.39, "end": 910.03, "word": " اضفت", "probability": 0.647216796875}, {"start": 910.03, "end": 910.37, "word": " اللي", "probability": 0.3516845703125}, {"start": 910.37, "end": 910.75, "word": " هو", "probability": 0.98388671875}, {"start": 910.75, "end": 911.85, "word": " نقطة", "probability": 0.91064453125}, {"start": 911.85, "end": 912.45, "word": " او", "probability": 0.715087890625}, {"start": 912.45, "end": 912.97, "word": " اكتر", "probability": 0.930419921875}, {"start": 912.97, "end": 913.09, "word": " من", "probability": 0.99072265625}, {"start": 913.09, "end": 913.65, "word": " نقطة", "probability": 0.9768880208333334}, {"start": 913.65, "end": 914.57, "word": " لنقاط", "probability": 0.9158935546875}, {"start": 914.57, "end": 914.69, "word": " ال", "probability": 0.93701171875}, {"start": 914.69, "end": 915.05, "word": " partition", "probability": 0.5048828125}, {"start": 915.05, "end": 915.35, "word": " اللي", "probability": 0.94140625}, {"start": 915.35, "end": 915.79, "word": " عندى", "probability": 0.702880859375}, {"start": 915.79, "end": 916.51, "word": " اذا", "probability": 0.83837890625}, {"start": 916.51, "end": 916.87, "word": " اي", "probability": 0.728515625}, {"start": 916.87, "end": 917.41, "word": " فترة", "probability": 0.99267578125}, {"start": 917.41, "end": 918.07, "word": " اي", "probability": 0.758056640625}, {"start": 918.07, "end": 918.67, "word": " فترة", "probability": 0.9899088541666666}, {"start": 918.67, "end": 919.41, "word": " اللي", "probability": 0.883056640625}, {"start": 919.41, "end": 919.73, "word": " هي", "probability": 0.861328125}, {"start": 919.73, "end": 920.81, "word": " xk", "probability": 0.669189453125}, {"start": 920.81, "end": 922.45, "word": " minus", "probability": 0.219482421875}, {"start": 922.45, "end": 923.21, "word": " واحد", "probability": 0.85986328125}, {"start": 923.21, "end": 923.69, "word": " لعند", "probability": 0.9231770833333334}, {"start": 923.69, "end": 924.73, "word": " xk", "probability": 0.871826171875}, {"start": 924.73, "end": 925.53, "word": " اللي", "probability": 0.9150390625}, {"start": 925.53, "end": 925.75, "word": " هو", "probability": 0.97314453125}, {"start": 925.75, "end": 925.91, "word": " في", "probability": 0.84375}, {"start": 925.91, "end": 926.07, "word": " ال", "probability": 0.86181640625}, {"start": 926.07, "end": 926.51, "word": " partition", "probability": 0.8720703125}, {"start": 926.51, "end": 927.55, "word": " بيه", "probability": 0.8486328125}, {"start": 927.55, "end": 928.07, "word": " هقدر", "probability": 0.8850911458333334}, {"start": 928.07, "end": 928.51, "word": " اكتبها", "probability": 0.98671875}, {"start": 928.51, "end": 928.73, "word": " على", "probability": 0.908203125}, {"start": 928.73, "end": 929.17, "word": " صورة", "probability": 0.9332682291666666}, {"start": 929.17, "end": 929.59, "word": " مين", "probability": 0.9111328125}], "temperature": 1.0}, {"id": 36, "seek": 94602, "start": 930.18, "end": 946.02, "text": "اللي هو yj-1 yj اتحاد ال yj yj زاد 1 اتحاد ده ما اصل عند اتحاد yn نقص 1 لعند مين لعند ال yn ماشي الحال طبعا الان هذول عدد الفترات على حسب الإضافة اللي هنا", "tokens": [6027, 20292, 31439, 288, 73, 12, 16, 288, 73, 1975, 2655, 5016, 18513, 2423, 288, 73, 288, 73, 30767, 18513, 502, 1975, 2655, 5016, 18513, 11778, 3224, 19446, 1975, 36520, 43242, 1975, 2655, 5016, 18513, 17861, 8717, 4587, 9381, 502, 5296, 3615, 41260, 3714, 9957, 5296, 3615, 41260, 2423, 17861, 3714, 33599, 1829, 21542, 6027, 23032, 3555, 3615, 995, 2423, 7649, 8032, 8848, 12610, 6225, 3215, 3215, 27188, 2655, 2288, 9307, 15844, 11331, 35457, 33688, 11242, 31845, 3660, 13672, 1829, 34105], "avg_logprob": -0.2551448250689158, "compression_ratio": 1.6688311688311688, "no_speech_prob": 2.086162567138672e-06, "words": [{"start": 930.18, "end": 930.58, "word": "اللي", "probability": 0.597900390625}, {"start": 930.58, "end": 930.88, "word": " هو", "probability": 0.9541015625}, {"start": 930.88, "end": 931.46, "word": " yj", "probability": 0.539306640625}, {"start": 931.46, "end": 932.22, "word": "-1", "probability": 0.653076171875}, {"start": 932.22, "end": 933.14, "word": " yj", "probability": 0.578857421875}, {"start": 933.14, "end": 933.96, "word": " اتحاد", "probability": 0.81829833984375}, {"start": 933.96, "end": 934.06, "word": " ال", "probability": 0.79736328125}, {"start": 934.06, "end": 934.48, "word": " yj", "probability": 0.724365234375}, {"start": 934.48, "end": 934.88, "word": " yj", "probability": 0.5792236328125}, {"start": 934.88, "end": 935.14, "word": " زاد", "probability": 0.259857177734375}, {"start": 935.14, "end": 935.28, "word": " 1", "probability": 0.7314453125}, {"start": 935.28, "end": 935.82, "word": " اتحاد", "probability": 0.98388671875}, {"start": 935.82, "end": 935.98, "word": " ده", "probability": 0.812744140625}, {"start": 935.98, "end": 936.1, "word": " ما", "probability": 0.802734375}, {"start": 936.1, "end": 936.26, "word": " اصل", "probability": 0.484619140625}, {"start": 936.26, "end": 936.5, "word": " عند", "probability": 0.91845703125}, {"start": 936.5, "end": 936.86, "word": " اتحاد", "probability": 0.9896240234375}, {"start": 936.86, "end": 937.18, "word": " yn", "probability": 0.439697265625}, {"start": 937.18, "end": 937.52, "word": " نقص", "probability": 0.7312825520833334}, {"start": 937.52, "end": 937.94, "word": " 1", "probability": 0.6484375}, {"start": 937.94, "end": 938.62, "word": " لعند", "probability": 0.8219401041666666}, {"start": 938.62, "end": 939.14, "word": " مين", "probability": 0.740234375}, {"start": 939.14, "end": 940.0, "word": " لعند", "probability": 0.9005533854166666}, {"start": 940.0, "end": 940.14, "word": " ال", "probability": 0.92919921875}, {"start": 940.14, "end": 940.54, "word": " yn", "probability": 0.6591796875}, {"start": 940.54, "end": 941.16, "word": " ماشي", "probability": 0.8400065104166666}, {"start": 941.16, "end": 941.48, "word": " الحال", "probability": 0.95751953125}, {"start": 941.48, "end": 942.16, "word": " طبعا", "probability": 0.9619140625}, {"start": 942.16, "end": 942.9, "word": " الان", "probability": 0.729248046875}, {"start": 942.9, "end": 943.7, "word": " هذول", "probability": 0.73828125}, {"start": 943.7, "end": 944.04, "word": " عدد", "probability": 0.85595703125}, {"start": 944.04, "end": 944.62, "word": " الفترات", "probability": 0.971923828125}, {"start": 944.62, "end": 944.82, "word": " على", "probability": 0.79736328125}, {"start": 944.82, "end": 945.14, "word": " حسب", "probability": 0.99462890625}, {"start": 945.14, "end": 945.64, "word": " 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"word": " عبارة", "probability": 0.994384765625}, {"start": 1121.7, "end": 1121.86, "word": " عن", "probability": 0.9853515625}, {"start": 1121.86, "end": 1122.16, "word": " remen", "probability": 0.2269287109375}, {"start": 1122.16, "end": 1122.56, "word": " integral", "probability": 0.69580078125}, {"start": 1122.56, "end": 1122.82, "word": " بل", "probability": 0.569091796875}, {"start": 1122.82, "end": 1123.22, "word": " وقيمة", "probability": 0.76171875}, {"start": 1123.22, "end": 1123.34, "word": " ال", "probability": 0.88525390625}, {"start": 1123.34, "end": 1123.6, "word": " remen", "probability": 0.8544921875}, {"start": 1123.6, "end": 1124.08, "word": " integral", "probability": 0.76708984375}, {"start": 1124.08, "end": 1124.68, "word": " هو", "probability": 0.91357421875}, {"start": 1124.68, "end": 1125.12, "word": " عبارة", "probability": 0.99560546875}, {"start": 1125.12, "end": 1125.26, "word": " عن", "probability": 0.9970703125}, {"start": 1125.26, "end": 1125.52, 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"compression_ratio": 1.8059701492537314, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1127.1, "end": 1127.66, "word": "من", "probability": 0.93017578125}, {"start": 1127.66, "end": 1128.06, "word": " اللي", "probability": 0.742431640625}, {"start": 1128.06, "end": 1128.46, "word": " هو", "probability": 0.98583984375}, {"start": 1128.46, "end": 1129.7, "word": " انه", "probability": 0.5838623046875}, {"start": 1129.7, "end": 1130.62, "word": " ناخد", "probability": 0.8792317708333334}, {"start": 1130.62, "end": 1131.52, "word": " نزغر", "probability": 0.72515869140625}, {"start": 1131.52, "end": 1131.68, "word": " اللي", "probability": 0.95654296875}, {"start": 1131.68, "end": 1131.86, "word": " هو", "probability": 0.98583984375}, {"start": 1131.86, "end": 1132.34, "word": " الأبر", "probability": 0.6556396484375}, {"start": 1132.34, "end": 1132.84, "word": " و", "probability": 0.94482421875}, {"start": 1132.84, "end": 1133.4, "word": " نرفع", "probability": 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139694, "start": 1374.62, "end": 1396.94, "text": "لأن هذه أشملها جزء من 100 من هذه كلها فال supremum لل function عالي كبيرة أكبر أو يساوي ال supremum على مين؟ على الصغيرة و similarly للتانية إذا ال MK أكبر أو يساوي MK' Similarly MK أكبر يساوي MKW' لأن هذه عبارة عن ال supremum على الجزء الثاني منها اللي إلى جاي، واضح؟", "tokens": [1211, 33456, 29538, 5551, 8592, 42213, 11296, 10874, 11622, 38207, 9154, 2319, 9154, 29538, 28242, 11296, 6156, 6027, 23710, 449, 24976, 2445, 6225, 6027, 1829, 9122, 3555, 48923, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 2423, 23710, 449, 15844, 3714, 9957, 22807, 15844, 31767, 17082, 48923, 4032, 14138, 24976, 2655, 7649, 10632, 11933, 15730, 2423, 30770, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 30770, 6, 13157, 30770, 5551, 4117, 26890, 7251, 3794, 995, 45865, 30770, 54, 6, 5296, 33456, 29538, 6225, 3555, 9640, 3660, 18871, 2423, 23710, 449, 15844, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 11296, 13672, 1829, 30731, 10874, 47302, 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" الجزء", "probability": 0.9778645833333334}, {"start": 1394.16, "end": 1394.76, "word": " الثاني", "probability": 0.946044921875}, {"start": 1394.76, "end": 1395.22, "word": " منها", "probability": 0.994384765625}, {"start": 1395.22, "end": 1395.62, "word": " اللي", "probability": 0.56488037109375}, {"start": 1395.62, "end": 1395.8, "word": " إلى", "probability": 0.408935546875}, {"start": 1395.8, "end": 1396.4, "word": " جاي،", "probability": 0.7403971354166666}, {"start": 1396.4, "end": 1396.94, "word": " واضح؟", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 57, "seek": 140530, "start": 1397.48, "end": 1405.3, "text": "إذا صار عندي therefore الآن بدأ أصل لحاجة معينة اللي هي mk في xk ناقص xk minus واحد", "tokens": [28814, 15730, 20328, 9640, 18871, 16254, 4412, 6024, 48506, 47525, 10721, 5551, 36520, 5296, 5016, 26108, 3660, 20449, 9957, 3660, 13672, 1829, 39896, 275, 74, 8978, 2031, 74, 8717, 995, 4587, 9381, 2031, 74, 3175, 36764, 24401], "avg_logprob": 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والF", "tokens": [1863, 4587, 9381, 1783, 45, 8717, 4587, 9381, 502, 23758, 8978, 2423, 14407, 4587, 3615, 3714, 9957, 31439, 5551, 9381, 15040, 14111, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 2423, 6597, 2408, 24976, 24808, 3714, 9957, 2423, 363, 6, 31439, 4724, 3794, 995, 45865, 2423, 6597, 2408, 24976, 363, 6, 16070, 37], "avg_logprob": -0.32338169536420275, "compression_ratio": 1.4285714285714286, "no_speech_prob": 1.8477439880371094e-05, "words": [{"start": 1595.51, "end": 1596.15, "word": "نقص", "probability": 0.6288248697916666}, {"start": 1596.15, "end": 1596.69, "word": " XN", "probability": 0.3997802734375}, {"start": 1596.69, "end": 1597.19, "word": " نقص", "probability": 0.8736979166666666}, {"start": 1597.19, "end": 1597.53, "word": " 1", "probability": 0.51220703125}, {"start": 1597.53, "end": 1598.39, "word": " هذا", "probability": 0.56640625}, {"start": 1598.39, "end": 1598.57, "word": " في", "probability": 0.91552734375}, {"start": 1598.57, 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{"start": 1617.95, "end": 1618.33, "word": " partition", "probability": 0.529296875}, {"start": 1618.33, "end": 1619.37, "word": " صار", "probability": 0.931396484375}, {"start": 1619.37, "end": 1619.61, "word": " عند", "probability": 0.96337890625}, {"start": 1619.61, "end": 1619.83, "word": " الـ", "probability": 0.759765625}, {"start": 1619.83, "end": 1620.21, "word": " partition", "probability": 0.96337890625}, {"start": 1620.21, "end": 1620.63, "word": " اللي", "probability": 0.97900390625}, {"start": 1620.63, "end": 1620.93, "word": " هو", "probability": 0.63623046875}, {"start": 1620.93, "end": 1621.35, "word": " الأبر", "probability": 0.874267578125}, {"start": 1621.35, "end": 1621.65, "word": " للـ", "probability": 0.628662109375}, {"start": 1621.65, "end": 1622.01, "word": " partition", "probability": 0.9677734375}, {"start": 1622.01, "end": 1622.91, "word": " الجديد", "probability": 0.9508463541666666}, {"start": 1622.91, "end": 1623.59, "word": " أصغر", "probability": 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"temperature": 1.0}, {"id": 85, "seek": 205146, "start": 2036.56, "end": 2051.46, "text": "Integral هو عبارة عن الـ Supremum للـ Lower Sums و ال .. واضح يا عيسى و ال Upper Integral هو عبارة عن ال Infimum لمن؟ لل Upper Sums متوقع أنه يقول لنا أنه احنا بنقول عنها", "tokens": [40, 9358, 861, 304, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 9141, 2579, 449, 24976, 39184, 25523, 318, 8099, 4032, 2423, 4386, 4032, 46958, 5016, 35186, 6225, 1829, 3794, 7578, 4032, 2423, 36926, 23894, 304, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 11537, 332, 449, 5296, 27842, 22807, 24976, 36926, 318, 8099, 44650, 30543, 3615, 14739, 3224, 7251, 39648, 5296, 8315, 14739, 3224, 1975, 5016, 8315, 44945, 39648, 18871, 11296], "avg_logprob": -0.2860243196288745, "compression_ratio": 1.537037037037037, "no_speech_prob": 8.106231689453125e-06, "words": [{"start": 2036.56, "end": 2037.24, "word": "Integral", "probability": 0.772705078125}, {"start": 2037.24, "end": 2037.4, "word": " هو", "probability": 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remain integrable اذا تساوت ايش اتجهتين ماشي جابيه لبس خلينا نبرهن او نتطلع على هذه اللي أمامنا برضه ملاحظة سهلة الملاحظة بتقولي لو الان جينا", "tokens": [5172, 30543, 31767, 5172, 5016, 3660, 16712, 7649, 10632, 44650, 30543, 3615, 7251, 39648, 8315, 16472, 3224, 6225, 8315, 6024, 48506, 44945, 38251, 1829, 11296, 6222, 16200, 424, 638, 1975, 15730, 6055, 3794, 995, 35473, 1975, 1829, 8592, 1975, 2655, 7435, 3224, 2655, 9957, 3714, 33599, 1829, 10874, 16758, 1829, 3224, 5296, 3555, 3794, 16490, 20292, 8315, 8717, 26890, 3224, 1863, 1975, 2407, 8717, 2655, 9566, 1211, 3615, 15844, 29538, 13672, 1829, 5551, 2304, 10943, 8315, 4724, 43042, 3224, 3714, 15040, 5016, 19913, 3660, 8608, 3224, 37977, 9673, 15040, 5016, 19913, 3660, 39894, 39648, 1829, 45164, 2423, 7649, 10874, 1829, 8315], "avg_logprob": -0.20297180948888555, "compression_ratio": 1.6220095693779903, "no_speech_prob": 3.552436828613281e-05, "words": [{"start": 2051.93, "end": 2052.49, "word": "فوق", "probability": 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هناك واضح أه نيجي لنظرية اللي عندى هذه", "tokens": [2304, 3615, 32887, 5172, 23758, 41850, 37893, 11331, 26108, 3660, 5296, 11622, 27842, 3224, 5551, 9381, 15040, 14111, 6156, 3555, 9381, 13546, 2752, 5551, 9381, 17082, 2288, 8608, 2407, 16606, 5296, 4032, 4724, 5172, 4032, 5296, 4032, 4724, 5172, 5551, 9381, 17082, 2288, 8608, 2407, 16606, 2752, 8978, 2423, 272, 12, 64, 13672, 1829, 4032, 11242, 33753, 3224, 34105, 4117, 34051, 11242, 5016, 9154, 13672, 1829, 3714, 4117, 2655, 37746, 34105, 4117, 4032, 46958, 5016, 5551, 3224, 8717, 1829, 7435, 1829, 5296, 1863, 19913, 2288, 10632, 13672, 1829, 43242, 7578, 29538], "avg_logprob": -0.3147078681251277, "compression_ratio": 1.6666666666666667, "no_speech_prob": 2.7358531951904297e-05, "words": [{"start": 2199.26, "end": 2199.9, "word": "معروف", "probability": 0.8226318359375}, {"start": 2199.9, "end": 2200.06, "word": " هذا", "probability": 0.88427734375}, {"start": 2200.06, "end": 2200.2, "word": " أنا", "probability": 0.19580078125}, 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"end": 2476.66, "text": "الـ U of F هو الـ infimum لكل الـ U, B, T, 2 و F such that B2 element in the set of all partitions نيجي الآن لبعده الـ Definition الان .. الان احنا زغرنا ال other sums و كبرنا ال other sums", "tokens": [6027, 39184, 624, 295, 479, 31439, 2423, 39184, 1536, 332, 449, 5296, 28820, 2423, 39184, 624, 11, 363, 11, 314, 11, 568, 4032, 479, 1270, 300, 363, 17, 4478, 294, 264, 992, 295, 439, 644, 2451, 8717, 1829, 7435, 1829, 6024, 48506, 5296, 3555, 22488, 3224, 2423, 39184, 46245, 849, 2423, 7649, 4386, 2423, 7649, 1975, 5016, 8315, 30767, 17082, 2288, 8315, 2423, 661, 34499, 4032, 9122, 26890, 8315, 2423, 661, 34499], "avg_logprob": -0.3062928082191781, "compression_ratio": 1.4114285714285715, "no_speech_prob": 0.0, "words": [{"start": 2449.0, "end": 2449.34, "word": "الـ", "probability": 0.79541015625}, {"start": 2449.34, "end": 2449.46, "word": " U", "probability": 0.537109375}, {"start": 2449.46, "end": 2449.64, "word": " of", "probability": 0.7021484375}, 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" كبرنا", "probability": 0.9274088541666666}, {"start": 2475.68, "end": 2475.82, "word": " ال", "probability": 0.9140625}, {"start": 2475.82, "end": 2476.08, "word": " other", "probability": 0.64697265625}, {"start": 2476.08, "end": 2476.66, "word": " sums", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 104, "seek": 250386, "start": 2477.6, "end": 2503.86, "text": "يوم مالتجهن مع بعض بنسمي اللي هو الالتقاء هذا أو الرقم اللي التقن فيه هو قيمة الـ Remain Integral للفункشن F على الفترة المذكورة وهذا هو التعريف let I بسوء A و B and let F من I لعند R be a bounded function then F is said to be Remain Integrable on I if L of F", "tokens": [1829, 20498, 3714, 6027, 2655, 7435, 3224, 1863, 20449, 45030, 11242, 44945, 38251, 1829, 13672, 1829, 31439, 2423, 6027, 2655, 4587, 16606, 23758, 34051, 34892, 4587, 2304, 13672, 1829, 16712, 4587, 1863, 8978, 3224, 31439, 12174, 32640, 3660, 2423, 39184, 4080, 491, 23894, 304, 24976, 5172, 26533, 8592, 1863, 479, 15844, 27188, 2655, 25720, 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