{ "markdown": "j_{n+1} = j_n - \\alpha \\nabla f(j_n) + \\frac{t}{\\lambda^2}\n## تعريف\nبك من وَعْثاء السفر … \" الحديث، وفي غير \"المسند\": عن يزيد، أنا عاصم، وثَبّتني فيه شعبة. وقال أبو داود في \"سننه\" عقب حديث الحكم بن حَزْن: ثَبَّتني في\n\\beta_{n+1} = \\beta_n - \\alpha \\nabla f(\\beta_n)\n\\sum_{\\sigma=0}^{\\infty} \\frac{\\alpha^\\sigma}{\\sigma!} = e^{\\alpha}", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 357, "width": 663 }, "confidence_scores": { "word_confidence_scores": [ { "text": "j_{n+1}", "confidence": 1.0, "start_index": 0 }, { "text": "=", "confidence": 1.0, "start_index": 8 }, { "text": "j_n", "confidence": 1.0, "start_index": 10 }, { "text": "-", "confidence": 1.0, "start_index": 14 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 16 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 23 }, { "text": "f(j_n)", "confidence": 1.0, "start_index": 30 }, { "text": "+", "confidence": 1.0, "start_index": 37 }, { "text": "\\frac{t}{\\lambda^2}", "confidence": 1.0, "start_index": 39 }, { "text": "##", "confidence": 1.0, "start_index": 59 }, { "text": "تعريف", "confidence": 1.0, "start_index": 62 }, { "text": "بك", "confidence": 1.0, "start_index": 68 }, { "text": "من", "confidence": 1.0, "start_index": 71 }, { "text": "وَعْثاء", "confidence": 1.0, "start_index": 74 }, { "text": "السفر", "confidence": 1.0, "start_index": 82 }, { "text": "…", "confidence": 1.0, "start_index": 88 }, { "text": "\"", "confidence": 1.0, "start_index": 90 }, { "text": "الحديث،", "confidence": 1.0, "start_index": 92 }, { "text": "وفي", "confidence": 1.0, "start_index": 100 }, { "text": "غير", "confidence": 1.0, "start_index": 104 }, { "text": "\"المسند\":", "confidence": 1.0, "start_index": 108 }, { "text": "عن", "confidence": 1.0, "start_index": 118 }, { "text": "يزيد،", "confidence": 1.0, "start_index": 121 }, { "text": "أنا", "confidence": 1.0, "start_index": 127 }, { "text": "عاصم،", "confidence": 1.0, "start_index": 131 }, { "text": "وثَبّتني", "confidence": 1.0, "start_index": 137 }, { "text": "فيه", "confidence": 1.0, "start_index": 146 }, { "text": "شعبة.", "confidence": 1.0, "start_index": 150 }, { "text": "وقال", "confidence": 1.0, "start_index": 156 }, { "text": "أبو", "confidence": 1.0, "start_index": 161 }, { "text": "داود", "confidence": 1.0, "start_index": 165 }, { "text": "في", "confidence": 1.0, "start_index": 170 }, { "text": "\"سننه\"", "confidence": 1.0, "start_index": 173 }, { "text": "عقب", "confidence": 1.0, "start_index": 180 }, { "text": "حديث", "confidence": 1.0, "start_index": 184 }, { "text": "الحكم", "confidence": 1.0, "start_index": 189 }, { "text": "بن", "confidence": 1.0, "start_index": 195 }, { "text": "حَزْن:", "confidence": 1.0, "start_index": 198 }, { "text": "ثَبَّتني", "confidence": 1.0, "start_index": 205 }, { "text": "في", "confidence": 1.0, "start_index": 214 }, { "text": "\\beta_{n+1}", "confidence": 1.0, "start_index": 217 }, { "text": "=", "confidence": 1.0, "start_index": 229 }, { "text": "\\beta_n", "confidence": 1.0, "start_index": 231 }, { "text": "-", "confidence": 1.0, "start_index": 239 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 241 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 248 }, { "text": "f(\\beta_n)", "confidence": 1.0, "start_index": 255 }, { "text": "\\sum_{\\sigma=0}^{\\infty}", "confidence": 1.0, "start_index": 266 }, { "text": "\\frac{\\alpha^\\sigma}{\\sigma!}", "confidence": 1.0, "start_index": 291 }, { "text": "=", "confidence": 1.0, "start_index": 321 }, { "text": "e^{\\alpha}", "confidence": 1.0, "start_index": 323 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 20, "top_left_y": 26, "bottom_right_x": 643, "bottom_right_y": 78, "content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n) + \\frac{t}{\\lambda^2}", "type": "text", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 32, "top_left_y": 96, "bottom_right_x": 627, "bottom_right_y": 115, "content": "تعريف", "type": "title", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 120, "bottom_right_x": 627, "bottom_right_y": 165, "content": "بك من وَعْثاء السفر … \" الحديث، وفي غير \"المسند\": عن يزيد، أنا عاصم، وثَبّتني فيه شعبة. وقال أبو داود في \"سننه\" عقب حديث الحكم بن حَزْن: ثَبَّتني في", "type": "text", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 32, "top_left_y": 171, "bottom_right_x": 627, "bottom_right_y": 209, "content": "\\beta_{n+1} = \\beta_n - \\alpha \\nabla f(\\beta_n)", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 20, "top_left_y": 241, "bottom_right_x": 643, "bottom_right_y": 311, "content": "\\sum_{\\sigma=0}^{\\infty} \\frac{\\alpha^\\sigma}{\\sigma!} = e^{\\alpha}", "type": "text", "confidence_scores": null, "reading_index": 5 } ], "meta": { "template": "math_proof", "hybrid": null, "page_font": "all-exp02-suleiman-patina.otf", "title_font": "al-mwaheb4.ttf", "language": "ar", "script": "arabic", "direction": "rtl", "augmentation": null } }