| { | |
| "markdown": "## ุจุฑูุงู\nูุงูุนูู ุงูุฎูุงุฑ ู ู ุงูููุงุณุ ูุงูุนูู ุงูุฌุงุณูุณ. ูู ูุงุฏ ุงููุงุนุฏุฉ: ุฃูู ุงูู ุดุชุฑู ู ู ุญูุซ ุญู ูู ุนูู ููู ู ุนุงููู ุฃู ุนูู ู ุนูู ุฏูู ุขุฎุฑ ู ุณุฃูุฉ ุฎูุงูููุฉ ุจูู ุงููููุงุก\n\\prod_{\\sigma=1}^{n} (1 \\geq \\beta_\\sigma) = 0\n## ู ุจุฑููุฉ\nูุงูุฃุตูููููู. ููุฏ ุฐูุจ ุงูุดูุงูุนู ุฑุญู ู ุงููู ูุฌู ุงุนุฉ ู ู ูููุงุก ูุฃุตูููู ุงูุดูุงูุนููุฉ ุฅูู ุฌูุงุฒูุ ูุฐูุจ ุขุฎุฑูู ู ููู ูุนูู ุฑุฃุณูู ุฅู ุงู ุงูุญุฑู ูู ูุงูุบุฒุงูู\nn_{n+1} = n_n - \\alpha \\nabla f(n_n)\n\\iint_{D} \\alpha^2 \\times j^2 \\, dx \\, dy\n## ุจุฑูุงู\nุฑุญู ูู ุง ุงูููุ ูุงูุญููููุฉ ุฅูู ู ูุนู ูุบูุฑูู . โ โุซุงูุซุงู: ู ู ุฃู ุซูุฉ ูุฐู ุงููุงุนุฏุฉ ูู ุณุงุฆููุง: ูู ูููู ุฃู ุฃูุตู ุนูู ู ูุงูููุ ููู ู ูุงูู ู ู ุฃุนูู ูู ูุงูู ู ู\n\\mathbb{E}[j] = \\int x f_j(x) dx + \\frac{i}{z^2}", | |
| "images": [], | |
| "tables": [], | |
| "hyperlinks": [], | |
| "header": null, | |
| "footer": null, | |
| "dimensions": { | |
| "dpi": 96, | |
| "height": 645, | |
| "width": 616 | |
| }, | |
| "confidence_scores": { | |
| "word_confidence_scores": [ | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ูุงูุนูู", | |
| "confidence": 1.0, | |
| "start_index": 9 | |
| }, | |
| { | |
| "text": "ุงูุฎูุงุฑ", | |
| "confidence": 1.0, | |
| "start_index": 16 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 23 | |
| }, | |
| { | |
| "text": "ุงูููุงุณุ", | |
| "confidence": 1.0, | |
| "start_index": 26 | |
| }, | |
| { | |
| "text": "ูุงูุนูู", | |
| "confidence": 1.0, | |
| "start_index": 34 | |
| }, | |
| { | |
| "text": "ุงูุฌุงุณูุณ.", | |
| "confidence": 1.0, | |
| "start_index": 41 | |
| }, | |
| { | |
| "text": "ูู ูุงุฏ", | |
| "confidence": 1.0, | |
| "start_index": 50 | |
| }, | |
| { | |
| "text": "ุงููุงุนุฏุฉ:", | |
| "confidence": 1.0, | |
| "start_index": 56 | |
| }, | |
| { | |
| "text": "ุฃูู", | |
| "confidence": 1.0, | |
| "start_index": 65 | |
| }, | |
| { | |
| "text": "ุงูู ุดุชุฑู", | |
| "confidence": 1.0, | |
| "start_index": 69 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 77 | |
| }, | |
| { | |
| "text": "ุญูุซ", | |
| "confidence": 1.0, | |
| "start_index": 80 | |
| }, | |
| { | |
| "text": "ุญู ูู", | |
| "confidence": 1.0, | |
| "start_index": 84 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 89 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 93 | |
| }, | |
| { | |
| "text": "ู ุนุงููู", | |
| "confidence": 1.0, | |
| "start_index": 97 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 104 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 107 | |
| }, | |
| { | |
| "text": "ู ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 111 | |
| }, | |
| { | |
| "text": "ุฏูู", | |
| "confidence": 1.0, | |
| "start_index": 116 | |
| }, | |
| { | |
| "text": "ุขุฎุฑ", | |
| "confidence": 1.0, | |
| "start_index": 120 | |
| }, | |
| { | |
| "text": "ู ุณุฃูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 124 | |
| }, | |
| { | |
| "text": "ุฎูุงูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 130 | |
| }, | |
| { | |
| "text": "ุจูู", | |
| "confidence": 1.0, | |
| "start_index": 138 | |
| }, | |
| { | |
| "text": "ุงููููุงุก", | |
| "confidence": 1.0, | |
| "start_index": 142 | |
| }, | |
| { | |
| "text": "\\prod_{\\sigma=1}^{n}", | |
| "confidence": 1.0, | |
| "start_index": 150 | |
| }, | |
| { | |
| "text": "(1", | |
| "confidence": 1.0, | |
| "start_index": 171 | |
| }, | |
| { | |
| "text": "\\geq", | |
| "confidence": 1.0, | |
| "start_index": 174 | |
| }, | |
| { | |
| "text": "\\beta_\\sigma)", | |
| "confidence": 1.0, | |
| "start_index": 179 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 193 | |
| }, | |
| { | |
| "text": "0", | |
| "confidence": 1.0, | |
| "start_index": 195 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 197 | |
| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 200 | |
| }, | |
| { | |
| "text": "ูุงูุฃุตูููููู.", | |
| "confidence": 1.0, | |
| "start_index": 207 | |
| }, | |
| { | |
| "text": "ููุฏ", | |
| "confidence": 1.0, | |
| "start_index": 220 | |
| }, | |
| { | |
| "text": "ุฐูุจ", | |
| "confidence": 1.0, | |
| "start_index": 224 | |
| }, | |
| { | |
| "text": "ุงูุดูุงูุนู", | |
| "confidence": 1.0, | |
| "start_index": 228 | |
| }, | |
| { | |
| "text": "ุฑุญู ู", | |
| "confidence": 1.0, | |
| "start_index": 237 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 242 | |
| }, | |
| { | |
| "text": "ูุฌู ุงุนุฉ", | |
| "confidence": 1.0, | |
| "start_index": 247 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 254 | |
| }, | |
| { | |
| "text": "ูููุงุก", | |
| "confidence": 1.0, | |
| "start_index": 257 | |
| }, | |
| { | |
| "text": "ูุฃุตูููู", | |
| "confidence": 1.0, | |
| "start_index": 263 | |
| }, | |
| { | |
| "text": "ุงูุดูุงูุนููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 271 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 282 | |
| }, | |
| { | |
| "text": "ุฌูุงุฒูุ", | |
| "confidence": 1.0, | |
| "start_index": 286 | |
| }, | |
| { | |
| "text": "ูุฐูุจ", | |
| "confidence": 1.0, | |
| "start_index": 293 | |
| }, | |
| { | |
| "text": "ุขุฎุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 298 | |
| }, | |
| { | |
| "text": "ู ููู ", | |
| "confidence": 1.0, | |
| "start_index": 304 | |
| }, | |
| { | |
| "text": "ูุนูู", | |
| "confidence": 1.0, | |
| "start_index": 309 | |
| }, | |
| { | |
| "text": "ุฑุฃุณูู ", | |
| "confidence": 1.0, | |
| "start_index": 314 | |
| }, | |
| { | |
| "text": "ุฅู ุงู ", | |
| "confidence": 1.0, | |
| "start_index": 320 | |
| }, | |
| { | |
| "text": "ุงูุญุฑู ูู", | |
| "confidence": 1.0, | |
| "start_index": 325 | |
| }, | |
| { | |
| "text": "ูุงูุบุฒุงูู", | |
| "confidence": 1.0, | |
| "start_index": 333 | |
| }, | |
| { | |
| "text": "n_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 342 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 350 | |
| }, | |
| { | |
| "text": "n_n", | |
| "confidence": 1.0, | |
| "start_index": 352 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 356 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 358 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 365 | |
| }, | |
| { | |
| "text": "f(n_n)", | |
| "confidence": 1.0, | |
| "start_index": 372 | |
| }, | |
| { | |
| "text": "\\iint_{D}", | |
| "confidence": 1.0, | |
| "start_index": 379 | |
| }, | |
| { | |
| "text": "\\alpha^2", | |
| "confidence": 1.0, | |
| "start_index": 389 | |
| }, | |
| { | |
| "text": "\\times", | |
| "confidence": 1.0, | |
| "start_index": 398 | |
| }, | |
| { | |
| "text": "j^2", | |
| "confidence": 1.0, | |
| "start_index": 405 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 409 | |
| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
| "start_index": 412 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 415 | |
| }, | |
| { | |
| "text": "dy", | |
| "confidence": 1.0, | |
| "start_index": 418 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 421 | |
| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
| "confidence": 1.0, | |
| "start_index": 424 | |
| }, | |
| { | |
| "text": "ุฑุญู ูู ุง", | |
| "confidence": 1.0, | |
| "start_index": 430 | |
| }, | |
| { | |
| "text": "ุงูููุ", | |
| "confidence": 1.0, | |
| "start_index": 437 | |
| }, | |
| { | |
| "text": "ูุงูุญููููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 443 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 453 | |
| }, | |
| { | |
| "text": "ู ูุนู", | |
| "confidence": 1.0, | |
| "start_index": 457 | |
| }, | |
| { | |
| "text": "ูุบูุฑูู .", | |
| "confidence": 1.0, | |
| "start_index": 462 | |
| }, | |
| { | |
| "text": "โ", | |
| "confidence": 1.0, | |
| "start_index": 470 | |
| }, | |
| { | |
| "text": "โุซุงูุซุงู:", | |
| "confidence": 1.0, | |
| "start_index": 472 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 481 | |
| }, | |
| { | |
| "text": "ุฃู ุซูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 484 | |
| }, | |
| { | |
| "text": "ูุฐู", | |
| "confidence": 1.0, | |
| "start_index": 490 | |
| }, | |
| { | |
| "text": "ุงููุงุนุฏุฉ", | |
| "confidence": 1.0, | |
| "start_index": 494 | |
| }, | |
| { | |
| "text": "ูู ุณุงุฆููุง:", | |
| "confidence": 1.0, | |
| "start_index": 502 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 512 | |
| }, | |
| { | |
| "text": "ูููู", | |
| "confidence": 1.0, | |
| "start_index": 515 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 520 | |
| }, | |
| { | |
| "text": "ุฃูุตู", | |
| "confidence": 1.0, | |
| "start_index": 523 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 528 | |
| }, | |
| { | |
| "text": "ู ูุงูููุ", | |
| "confidence": 1.0, | |
| "start_index": 532 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 540 | |
| }, | |
| { | |
| "text": "ู ูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 544 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 550 | |
| }, | |
| { | |
| "text": "ุฃุนูู", | |
| "confidence": 1.0, | |
| "start_index": 553 | |
| }, | |
| { | |
| "text": "ูู ูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 558 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 565 | |
| }, | |
| { | |
| "text": "\\mathbb{E}[j]", | |
| "confidence": 1.0, | |
| "start_index": 568 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 582 | |
| }, | |
| { | |
| "text": "\\int", | |
| "confidence": 1.0, | |
| "start_index": 584 | |
| }, | |
| { | |
| "text": "x", | |
| "confidence": 1.0, | |
| "start_index": 589 | |
| }, | |
| { | |
| "text": "f_j(x)", | |
| "confidence": 1.0, | |
| "start_index": 591 | |
| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
| "start_index": 598 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 601 | |
| }, | |
| { | |
| "text": "\\frac{i}{z^2}", | |
| "confidence": 1.0, | |
| "start_index": 603 | |
| } | |
| ], | |
| "average_page_confidence_score": 1.0, | |
| "minimum_page_confidence_score": 1.0 | |
| }, | |
| "blocks": [ | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 32, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 54, | |
| "content": "ุจุฑูุงู", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 1 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 59, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 104, | |
| "content": "ูุงูุนูู ุงูุฎูุงุฑ ู ู ุงูููุงุณุ ูุงูุนูู ุงูุฌุงุณูุณ. ูู ูุงุฏ ุงููุงุนุฏุฉ: ุฃูู ุงูู ุดุชุฑู ู ู ุญูุซ ุญู ูู ุนูู ููู ู ุนุงููู ุฃู ุนูู ู ุนูู ุฏูู ุขุฎุฑ ู ุณุฃูุฉ ุฎูุงูููุฉ ุจูู ุงููููุงุก", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 2 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 110, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 174, | |
| "content": "\\prod_{\\sigma=1}^{n} (1 \\geq \\beta_\\sigma) = 0", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 3 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 218, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 240, | |
| "content": "ู ุจุฑููุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 4 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 245, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 290, | |
| "content": "ูุงูุฃุตูููููู. ููุฏ ุฐูุจ ุงูุดูุงูุนู ุฑุญู ู ุงููู ูุฌู ุงุนุฉ ู ู ูููุงุก ูุฃุตูููู ุงูุดูุงูุนููุฉ ุฅูู ุฌูุงุฒูุ ูุฐูุจ ุขุฎุฑูู ู ููู ูุนูู ุฑุฃุณูู ุฅู ุงู ุงูุญุฑู ูู ูุงูุบุฒุงูู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 5 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 296, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 334, | |
| "content": "n_{n+1} = n_n - \\alpha \\nabla f(n_n)", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 6 | |
| }, | |
| { | |
| "top_left_x": 20, | |
| "top_left_y": 366, | |
| "bottom_right_x": 596, | |
| "bottom_right_y": 423, | |
| "content": "\\iint_{D} \\alpha^2 \\times j^2 \\, dx \\, dy", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 7 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 441, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 463, | |
| "content": "ุจุฑูุงู", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 8 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 468, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 513, | |
| "content": "ุฑุญู ูู ุง ุงูููุ ูุงูุญููููุฉ ุฅูู ู ูุนู ูุบูุฑูู . โ โุซุงูุซุงู: ู ู ุฃู ุซูุฉ ูุฐู ุงููุงุนุฏุฉ ูู ุณุงุฆููุง: ูู ูููู ุฃู ุฃูุตู ุนูู ู ูุงูููุ ููู ู ูุงูู ู ู ุฃุนูู ูู ูุงูู ู ู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 9 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 519, | |
| "bottom_right_x": 580, | |
| "bottom_right_y": 572, | |
| "content": "\\mathbb{E}[j] = \\int x f_j(x) dx + \\frac{i}{z^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 10 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "bogart-arabic-bold-trial.ttf", | |
| "title_font": "bogart-arabic-bold-trial.ttf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |