| { | |
| "markdown": "## ูุธุฑูุฉ\nุฃุจูู ูู ุงูุณุงุจู ู ู ุงูุฃุนูุงู ) . ูู ุชุตุงููู ู ููุง (ุฏูุชุฑ - ุฎ) ูู ุนุดุฑุฉ ุฃุณูุงุฑ ูุจุงุฑ ูู ุงูู ูุชุจุฉ ุงูุฒูุฏุงููุฉ ุจู ููุงุณ. ูู ูู ูุณุฎุฉ ูู ุณูุฑูู ูุจูุฑูู ุฌุฏุง ูุงูุช ูู ุงูู ูุชุจุฉ ุงููุชุงููุฉ ุจูุงุณุ ููุนููุง ูููุช ุฅูู ุฎุฒุงูุฉ ุงูุฑุจุงุท. ููู ูุดูููุ ูุณุฎ ููู ู ุง ุงุณุชุญุณูู ูู ุงููุชุจุ ู ู ุบูุฑ ุชุจููุจ ููุง ุชุฑุชูุจุ ู (ุชุญูุฉ ุงูุธุฑูุงุก ูู ุฌู ูุน ู ุง ููููุงุนูู ู ู ุงูุฑุณุงุฆู\ny_{n+1} = y_n - \\alpha \\nabla f(y_n) + \\frac{\\sigma}{t^2}\n## ุชุนุฑูู\nุงููุจูููุฉ ูุงูุตุญุงุจุฉ ูุงูุฎููุงุก) ูุฑุบ ู ูู ูู ุฃูุงุฎุฑ ุณูุฉ 1164 ูุฃูุฏู ุฃูู ูุณุฎุฉ ุฅูู ุงูุณูุทุงู ู ุญู ุฏ ุจู ุนุจุฏ ุงูููุ ู (ูุทุฑ ุงููุฏุง ูู ุงูุชุนุฑูู ุจ ุฃุจู ุงูุฏุฑุฏุง) ู (ูุดู ุงูุฃุณู ุจู ุญุงุณู ุงูุตุงูุญุงุช ู ู ุงููุณุงุ ูุจุนุถ ุงูุชุนุฑููุงุช ุจุงูุฃุนูุงู ูุงูุฑุคุณุง - ุฎ) ู ูู ูุณุฎุฉ ูู ุฎุฒุงูุฉ ุงููุฑูููู (ุงูุฑูู \n\\iint_{D} t^2 \\geq k^2 \\, dx \\, dy\n\\nabla_{\\alpha} J(\\alpha) = \\frac{1}{m} X^T ( \\sigma(X \\alpha) - Y )\n\\nabla_{\\beta} J(\\beta) = \\frac{1}{m} X^T ( \\sigma(X \\beta) - Y ) + \\frac{z}{\\mu^2}\n\\prod_{\\theta=1}^{n} (1 \\geq i_\\theta) = 0\n## ู ูุงุญุธุฉ\n596) ุฃููู ูู ุงูู ุฌุงุนุฉ\n\\vec{F} = m\\vec{a}\n## ูุธุฑูุฉ\nุงููู ุตูุงู ุฏุงูุฏ\" ููุชุถู ุซุจูุช ุงูุฃูุถููุฉ ู ุทููุงูุ ูุฑูุงู ู ุณูู ูุงูุชุฑู ุฐูู ุจููุธ: \"ุฃูุถู ุงูุตูุงู ุตูุงู ุฏุงูุฏ\"ุ ูู ูุชุถุงู ุฃู ุชููู ุงูุฒูุงุฏุฉ ุนูู ุฐูู ู ู ุงูุตูู ู ูุถููุฉ.\n\\iint_{D} t^2 \\cdot t^2 \\, dx \\, dy\n\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )", | |
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| "header": null, | |
| "footer": null, | |
| "dimensions": { | |
| "dpi": 96, | |
| "height": 1016, | |
| "width": 883 | |
| }, | |
| "confidence_scores": { | |
| "word_confidence_scores": [ | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "ูุธุฑูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ุฃุจูู", | |
| "confidence": 1.0, | |
| "start_index": 9 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 14 | |
| }, | |
| { | |
| "text": "ุงูุณุงุจู", | |
| "confidence": 1.0, | |
| "start_index": 17 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 24 | |
| }, | |
| { | |
| "text": "ุงูุฃุนูุงู )", | |
| "confidence": 1.0, | |
| "start_index": 27 | |
| }, | |
| { | |
| "text": ".", | |
| "confidence": 1.0, | |
| "start_index": 36 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 38 | |
| }, | |
| { | |
| "text": "ุชุตุงููู", | |
| "confidence": 1.0, | |
| "start_index": 41 | |
| }, | |
| { | |
| "text": "ู ููุง", | |
| "confidence": 1.0, | |
| "start_index": 48 | |
| }, | |
| { | |
| "text": "(ุฏูุชุฑ", | |
| "confidence": 1.0, | |
| "start_index": 53 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 59 | |
| }, | |
| { | |
| "text": "ุฎ)", | |
| "confidence": 1.0, | |
| "start_index": 61 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 64 | |
| }, | |
| { | |
| "text": "ุนุดุฑุฉ", | |
| "confidence": 1.0, | |
| "start_index": 67 | |
| }, | |
| { | |
| "text": "ุฃุณูุงุฑ", | |
| "confidence": 1.0, | |
| "start_index": 72 | |
| }, | |
| { | |
| "text": "ูุจุงุฑ", | |
| "confidence": 1.0, | |
| "start_index": 78 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 83 | |
| }, | |
| { | |
| "text": "ุงูู ูุชุจุฉ", | |
| "confidence": 1.0, | |
| "start_index": 86 | |
| }, | |
| { | |
| "text": "ุงูุฒูุฏุงููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 94 | |
| }, | |
| { | |
| "text": "ุจู ููุงุณ.", | |
| "confidence": 1.0, | |
| "start_index": 104 | |
| }, | |
| { | |
| "text": "ูู ูู", | |
| "confidence": 1.0, | |
| "start_index": 112 | |
| }, | |
| { | |
| "text": "ูุณุฎุฉ", | |
| "confidence": 1.0, | |
| "start_index": 117 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 122 | |
| }, | |
| { | |
| "text": "ุณูุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 125 | |
| }, | |
| { | |
| "text": "ูุจูุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 131 | |
| }, | |
| { | |
| "text": "ุฌุฏุง", | |
| "confidence": 1.0, | |
| "start_index": 138 | |
| }, | |
| { | |
| "text": "ูุงูุช", | |
| "confidence": 1.0, | |
| "start_index": 142 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 147 | |
| }, | |
| { | |
| "text": "ุงูู ูุชุจุฉ", | |
| "confidence": 1.0, | |
| "start_index": 150 | |
| }, | |
| { | |
| "text": "ุงููุชุงููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 158 | |
| }, | |
| { | |
| "text": "ุจูุงุณุ", | |
| "confidence": 1.0, | |
| "start_index": 167 | |
| }, | |
| { | |
| "text": "ููุนููุง", | |
| "confidence": 1.0, | |
| "start_index": 173 | |
| }, | |
| { | |
| "text": "ูููุช", | |
| "confidence": 1.0, | |
| "start_index": 180 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 185 | |
| }, | |
| { | |
| "text": "ุฎุฒุงูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 189 | |
| }, | |
| { | |
| "text": "ุงูุฑุจุงุท.", | |
| "confidence": 1.0, | |
| "start_index": 195 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 203 | |
| }, | |
| { | |
| "text": "ูุดูููุ", | |
| "confidence": 1.0, | |
| "start_index": 207 | |
| }, | |
| { | |
| "text": "ูุณุฎ", | |
| "confidence": 1.0, | |
| "start_index": 214 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 218 | |
| }, | |
| { | |
| "text": "ู ุง", | |
| "confidence": 1.0, | |
| "start_index": 222 | |
| }, | |
| { | |
| "text": "ุงุณุชุญุณูู", | |
| "confidence": 1.0, | |
| "start_index": 225 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 233 | |
| }, | |
| { | |
| "text": "ุงููุชุจุ", | |
| "confidence": 1.0, | |
| "start_index": 236 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 243 | |
| }, | |
| { | |
| "text": "ุบูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 246 | |
| }, | |
| { | |
| "text": "ุชุจููุจ", | |
| "confidence": 1.0, | |
| "start_index": 250 | |
| }, | |
| { | |
| "text": "ููุง", | |
| "confidence": 1.0, | |
| "start_index": 256 | |
| }, | |
| { | |
| "text": "ุชุฑุชูุจุ", | |
| "confidence": 1.0, | |
| "start_index": 260 | |
| }, | |
| { | |
| "text": "ู", | |
| "confidence": 1.0, | |
| "start_index": 267 | |
| }, | |
| { | |
| "text": "(ุชุญูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 269 | |
| }, | |
| { | |
| "text": "ุงูุธุฑูุงุก", | |
| "confidence": 1.0, | |
| "start_index": 275 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 283 | |
| }, | |
| { | |
| "text": "ุฌู ูุน", | |
| "confidence": 1.0, | |
| "start_index": 286 | |
| }, | |
| { | |
| "text": "ู ุง", | |
| "confidence": 1.0, | |
| "start_index": 291 | |
| }, | |
| { | |
| "text": "ููููุงุนูู", | |
| "confidence": 1.0, | |
| "start_index": 294 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 303 | |
| }, | |
| { | |
| "text": "ุงูุฑุณุงุฆู", | |
| "confidence": 1.0, | |
| "start_index": 306 | |
| }, | |
| { | |
| "text": "y_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 314 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 322 | |
| }, | |
| { | |
| "text": "y_n", | |
| "confidence": 1.0, | |
| "start_index": 324 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 328 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 330 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 337 | |
| }, | |
| { | |
| "text": "f(y_n)", | |
| "confidence": 1.0, | |
| "start_index": 344 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 351 | |
| }, | |
| { | |
| "text": "\\frac{\\sigma}{t^2}", | |
| "confidence": 1.0, | |
| "start_index": 353 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 372 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 375 | |
| }, | |
| { | |
| "text": "ุงููุจูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 381 | |
| }, | |
| { | |
| "text": "ูุงูุตุญุงุจุฉ", | |
| "confidence": 1.0, | |
| "start_index": 390 | |
| }, | |
| { | |
| "text": "ูุงูุฎููุงุก)", | |
| "confidence": 1.0, | |
| "start_index": 399 | |
| }, | |
| { | |
| "text": "ูุฑุบ", | |
| "confidence": 1.0, | |
| "start_index": 409 | |
| }, | |
| { | |
| "text": "ู ูู", | |
| "confidence": 1.0, | |
| "start_index": 413 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 417 | |
| }, | |
| { | |
| "text": "ุฃูุงุฎุฑ", | |
| "confidence": 1.0, | |
| "start_index": 420 | |
| }, | |
| { | |
| "text": "ุณูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 426 | |
| }, | |
| { | |
| "text": "1164", | |
| "confidence": 1.0, | |
| "start_index": 430 | |
| }, | |
| { | |
| "text": "ูุฃูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 435 | |
| }, | |
| { | |
| "text": "ุฃูู", | |
| "confidence": 1.0, | |
| "start_index": 441 | |
| }, | |
| { | |
| "text": "ูุณุฎุฉ", | |
| "confidence": 1.0, | |
| "start_index": 445 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 450 | |
| }, | |
| { | |
| "text": "ุงูุณูุทุงู", | |
| "confidence": 1.0, | |
| "start_index": 454 | |
| }, | |
| { | |
| "text": "ู ุญู ุฏ", | |
| "confidence": 1.0, | |
| "start_index": 462 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 467 | |
| }, | |
| { | |
| "text": "ุนุจุฏ", | |
| "confidence": 1.0, | |
| "start_index": 470 | |
| }, | |
| { | |
| "text": "ุงูููุ", | |
| "confidence": 1.0, | |
| "start_index": 474 | |
| }, | |
| { | |
| "text": "ู", | |
| "confidence": 1.0, | |
| "start_index": 480 | |
| }, | |
| { | |
| "text": "(ูุทุฑ", | |
| "confidence": 1.0, | |
| "start_index": 482 | |
| }, | |
| { | |
| "text": "ุงููุฏุง", | |
| "confidence": 1.0, | |
| "start_index": 487 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 493 | |
| }, | |
| { | |
| "text": "ุงูุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 496 | |
| }, | |
| { | |
| "text": "ุจ", | |
| "confidence": 1.0, | |
| "start_index": 504 | |
| }, | |
| { | |
| "text": "ุฃุจู", | |
| "confidence": 1.0, | |
| "start_index": 506 | |
| }, | |
| { | |
| "text": "ุงูุฏุฑุฏุง)", | |
| "confidence": 1.0, | |
| "start_index": 510 | |
| }, | |
| { | |
| "text": "ู", | |
| "confidence": 1.0, | |
| "start_index": 518 | |
| }, | |
| { | |
| "text": "(ูุดู", | |
| "confidence": 1.0, | |
| "start_index": 520 | |
| }, | |
| { | |
| "text": "ุงูุฃุณู", | |
| "confidence": 1.0, | |
| "start_index": 525 | |
| }, | |
| { | |
| "text": "ุจู ุญุงุณู", | |
| "confidence": 1.0, | |
| "start_index": 531 | |
| }, | |
| { | |
| "text": "ุงูุตุงูุญุงุช", | |
| "confidence": 1.0, | |
| "start_index": 538 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 547 | |
| }, | |
| { | |
| "text": "ุงููุณุงุ", | |
| "confidence": 1.0, | |
| "start_index": 550 | |
| }, | |
| { | |
| "text": "ูุจุนุถ", | |
| "confidence": 1.0, | |
| "start_index": 557 | |
| }, | |
| { | |
| "text": "ุงูุชุนุฑููุงุช", | |
| "confidence": 1.0, | |
| "start_index": 562 | |
| }, | |
| { | |
| "text": "ุจุงูุฃุนูุงู ", | |
| "confidence": 1.0, | |
| "start_index": 572 | |
| }, | |
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| "text": "ูุงูุฑุคุณุง", | |
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| "content": "\\vec{F} = m\\vec{a}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 12 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 746, | |
| "bottom_right_x": 827, | |
| "bottom_right_y": 774, | |
| "content": "ูุธุฑูุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 13 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 779, | |
| "bottom_right_x": 827, | |
| "bottom_right_y": 801, | |
| "content": "ุงููู ุตูุงู ุฏุงูุฏ\" ููุชุถู ุซุจูุช ุงูุฃูุถููุฉ ู ุทููุงูุ ูุฑูุงู ู ุณูู ูุงูุชุฑู ุฐูู ุจููุธ: \"ุฃูุถู ุงูุตูุงู ุตูุงู ุฏุงูุฏ\"ุ ูู ูุชุถุงู ุฃู ุชููู ุงูุฒูุงุฏุฉ ุนูู ุฐูู ู ู ุงูุตูู ู ูุถููุฉ.", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 14 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 807, | |
| "bottom_right_x": 827, | |
| "bottom_right_y": 862, | |
| "content": "\\iint_{D} t^2 \\cdot t^2 \\, dx \\, dy", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 15 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 894, | |
| "bottom_right_x": 843, | |
| "bottom_right_y": 945, | |
| "content": "\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y )", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 16 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "ebhaar.ttf", | |
| "title_font": "b-sahar.ttf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |