{ "markdown": "\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)\n\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )\n## برهان\nوسلم بقتالهم بقوله: {قاتِلُوا الَّذِينَ لا يُؤْمِنُونَ بِاللهِ وَلا بِالْيَوْمِ الْآخِرِ.}. الآية، إلى قوله: {وَهُمْ صاغِرُونَ} (1) وغير ذلك من الآيات، فقتلوا بني قريظة؛ وأجلوا\n\\vec{F} = m\\vec{a}\n## نظرية\nبني النضير. وقيل: معناه: {(حَتّى يَأْتِيَ اللهُ بِأَمْرِهِ)}:قيام الساعة ويجازيهم بأعمالهم. {إِنَّ اللهَ عَلى كُلِّ شَيْءٍ قَدِيرٌ} (109).\n\\vec{F} = m\\vec{a}", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 479, "width": 566 }, "confidence_scores": { "word_confidence_scores": [ { "text": "\\mu_{n+1}", "confidence": 1.0, "start_index": 0 }, { "text": "=", "confidence": 1.0, "start_index": 10 }, { "text": "\\mu_n", "confidence": 1.0, "start_index": 12 }, { "text": "-", "confidence": 1.0, "start_index": 18 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 20 }, { 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"start_index": 117 }, { "text": "بقوله:", "confidence": 1.0, "start_index": 125 }, { "text": "{قاتِلُوا", "confidence": 1.0, "start_index": 132 }, { "text": "الَّذِينَ", "confidence": 1.0, "start_index": 142 }, { "text": "لا", "confidence": 1.0, "start_index": 152 }, { "text": "يُؤْمِنُونَ", "confidence": 1.0, "start_index": 155 }, { "text": "بِاللهِ", "confidence": 1.0, "start_index": 167 }, { "text": "وَلا", "confidence": 1.0, "start_index": 175 }, { "text": "بِالْيَوْمِ", "confidence": 1.0, "start_index": 180 }, { "text": "الْآخِرِ.}.", "confidence": 1.0, "start_index": 192 }, { "text": "الآية،", "confidence": 1.0, "start_index": 204 }, { "text": "إلى", "confidence": 1.0, "start_index": 211 }, { "text": "قوله:", "confidence": 1.0, "start_index": 215 }, { "text": "{وَهُمْ", "confidence": 1.0, "start_index": 221 }, { "text": "صاغِرُونَ}", "confidence": 1.0, "start_index": 229 }, { "text": "(1)", "confidence": 1.0, "start_index": 240 }, { "text": "وغير", "confidence": 1.0, "start_index": 244 }, { "text": "ذلك", "confidence": 1.0, "start_index": 249 }, { "text": "من", "confidence": 1.0, "start_index": 253 }, { "text": "الآيات،", "confidence": 1.0, "start_index": 256 }, { "text": "فقتلوا", "confidence": 1.0, "start_index": 264 }, { "text": "بني", "confidence": 1.0, "start_index": 271 }, { "text": "قريظة؛", "confidence": 1.0, "start_index": 275 }, { "text": "وأجلوا", "confidence": 1.0, "start_index": 282 }, { "text": "\\vec{F}", "confidence": 1.0, "start_index": 289 }, { "text": "=", "confidence": 1.0, "start_index": 297 }, { "text": "m\\vec{a}", "confidence": 1.0, "start_index": 299 }, { "text": "##", "confidence": 1.0, "start_index": 308 }, { "text": "نظرية", "confidence": 1.0, "start_index": 311 }, { "text": "بني", "confidence": 1.0, "start_index": 317 }, { "text": "النضير.", "confidence": 1.0, "start_index": 321 }, { "text": "وقيل:", "confidence": 1.0, "start_index": 329 }, { "text": "معناه:", "confidence": 1.0, "start_index": 335 }, { "text": "{(حَتّى", "confidence": 1.0, "start_index": 342 }, { "text": "يَأْتِيَ", "confidence": 1.0, "start_index": 350 }, { "text": "اللهُ", "confidence": 1.0, "start_index": 359 }, { "text": "بِأَمْرِهِ)}:قيام", "confidence": 1.0, "start_index": 365 }, { "text": "الساعة", "confidence": 1.0, "start_index": 383 }, { "text": "ويجازيهم", "confidence": 1.0, "start_index": 390 }, { "text": "بأعمالهم.", "confidence": 1.0, "start_index": 399 }, { "text": "{إِنَّ", "confidence": 1.0, "start_index": 409 }, { "text": "اللهَ", "confidence": 1.0, "start_index": 416 }, { "text": "عَلى", "confidence": 1.0, "start_index": 422 }, { "text": "كُلِّ", "confidence": 1.0, "start_index": 427 }, { "text": "شَيْءٍ", "confidence": 1.0, "start_index": 433 }, { "text": "قَدِيرٌ}", "confidence": 1.0, "start_index": 440 }, { "text": "(109).", "confidence": 1.0, "start_index": 449 }, { "text": "\\vec{F}", "confidence": 1.0, "start_index": 456 }, { "text": "=", "confidence": 1.0, "start_index": 464 }, { "text": "m\\vec{a}", "confidence": 1.0, "start_index": 466 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 20, "top_left_y": 26, "bottom_right_x": 546, "bottom_right_y": 69, "content": "\\mu_{n+1} = \\mu_n - \\alpha \\nabla f(\\mu_n)", "type": "text", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 20, "top_left_y": 75, "bottom_right_x": 546, "bottom_right_y": 125, "content": "\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )", "type": "text", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 143, "bottom_right_x": 530, "bottom_right_y": 169, "content": "برهان", "type": "title", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 32, "top_left_y": 174, "bottom_right_x": 530, "bottom_right_y": 219, "content": "وسلم بقتالهم بقوله: {قاتِلُوا الَّذِينَ لا يُؤْمِنُونَ بِاللهِ وَلا بِالْيَوْمِ الْآخِرِ.}. الآية، إلى قوله: {وَهُمْ صاغِرُونَ} (1) وغير ذلك من الآيات، فقتلوا بني قريظة؛ وأجلوا", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 32, "top_left_y": 225, "bottom_right_x": 530, "bottom_right_y": 264, "content": "\\vec{F} = m\\vec{a}", "type": "text", "confidence_scores": null, "reading_index": 5 }, { "top_left_x": 32, "top_left_y": 308, "bottom_right_x": 530, "bottom_right_y": 334, "content": "نظرية", "type": "title", "confidence_scores": null, "reading_index": 6 }, { "top_left_x": 32, "top_left_y": 339, "bottom_right_x": 530, "bottom_right_y": 361, "content": "بني النضير. وقيل: معناه: {(حَتّى يَأْتِيَ اللهُ بِأَمْرِهِ)}:قيام الساعة ويجازيهم بأعمالهم. {إِنَّ اللهَ عَلى كُلِّ شَيْءٍ قَدِيرٌ} (109).", "type": "text", "confidence_scores": null, "reading_index": 7 }, { "top_left_x": 32, "top_left_y": 367, "bottom_right_x": 530, "bottom_right_y": 406, "content": "\\vec{F} = m\\vec{a}", "type": "text", "confidence_scores": null, "reading_index": 8 } ], "meta": { "template": "math_proof", "hybrid": null, 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