| { | |
| "markdown": "## ุชุนุฑูู\nุนูู ุฐูู/: (ุจููู ููู ู ููู ุดูููู ู ููููุง ุจููู ููู ู ู ููููุง ุนูู ูููู) ยซ2ยป ุฃู: ู ู ุนู ููุง. ู ยซููยป ุจู ุนูู ุงูุจุงุกุ ุฃู: ูู ูุฏุฑููุง ุนูู ูุงุ ููู ููุธุฑูุง ูู ุญูููุชูุง ููุฏุฑูููุงุ ุฃู ุฅุฏุฑุงู\nj_{n+1} = j_n - \\alpha \\nabla f(j_n)\n## ูุธุฑูุฉ\nุนูู ูู ุจุญุฏูุซูุงุ ุจู ูู ูู ุดู ู ู ุญุฏูุซูุงุ ุจู ูู ุนู ุนูู ูุง ุนู ูู. ูู ู ุฐูู ูููู ุชุนุงูู:\n\\iint_{D} n^2 \\approx \\sigma^2 \\, dx \\, dy\n## ู ูุงุญุธุฉ\n(ุฃูุฌูุนูููุชูู ู ุณููุงููุฉู ุงููุญุงุฌูู) ยซ3ยป ุฃู: ุตุงุญุจ ุณูุงูุฉ ุงูุญุงุฌ. ููุงู ุนุฒ ู ู ูุงุฆู: (ููููุฃูููููู ู ููู\n\\vec{F} = m\\vec{a}\n## ุจุฑูุงู\nููุฑูููุฉู) ยซ4ยป ุฃู: ู ู ุฃูู ูุฑูุฉ (ูููู ุฃูุดูุฏูู ูููููุฉู ู ููู ููุฑูููุชููู ุงูููุชูู ุฃูุฎูุฑูุฌูุชููู) ยซ5ยป ุฃู: ุฃุฎุฑุฌู\nj_{n+1} = j_n - \\alpha \\nabla f(j_n)", | |
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| }, | |
| "confidence_scores": { | |
| "word_confidence_scores": [ | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 9 | |
| }, | |
| { | |
| "text": "ุฐูู/:", | |
| "confidence": 1.0, | |
| "start_index": 13 | |
| }, | |
| { | |
| "text": "(ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 19 | |
| }, | |
| { | |
| "text": "ููู ู", | |
| "confidence": 1.0, | |
| "start_index": 25 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 30 | |
| }, | |
| { | |
| "text": "ุดูููู", | |
| "confidence": 1.0, | |
| "start_index": 34 | |
| }, | |
| { | |
| "text": "ู ููููุง", | |
| "confidence": 1.0, | |
| "start_index": 40 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 47 | |
| }, | |
| { | |
| "text": "ููู ู", | |
| "confidence": 1.0, | |
| "start_index": 52 | |
| }, | |
| { | |
| "text": "ู ููููุง", | |
| "confidence": 1.0, | |
| "start_index": 57 | |
| }, | |
| { | |
| "text": "ุนูู ูููู)", | |
| "confidence": 1.0, | |
| "start_index": 64 | |
| }, | |
| { | |
| "text": "ยซ2ยป", | |
| "confidence": 1.0, | |
| "start_index": 73 | |
| }, | |
| { | |
| "text": "ุฃู:", | |
| "confidence": 1.0, | |
| "start_index": 77 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 81 | |
| }, | |
| { | |
| "text": "ุนู ููุง.", | |
| "confidence": 1.0, | |
| "start_index": 84 | |
| }, | |
| { | |
| "text": "ู", | |
| "confidence": 1.0, | |
| "start_index": 91 | |
| }, | |
| { | |
| "text": "ยซููยป", | |
| "confidence": 1.0, | |
| "start_index": 93 | |
| }, | |
| { | |
| "text": "ุจู ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 98 | |
| }, | |
| { | |
| "text": "ุงูุจุงุกุ", | |
| "confidence": 1.0, | |
| "start_index": 104 | |
| }, | |
| { | |
| "text": "ุฃู:", | |
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| "start_index": 111 | |
| }, | |
| { | |
| "text": "ูู ", | |
| "confidence": 1.0, | |
| "start_index": 115 | |
| }, | |
| { | |
| "text": "ูุฏุฑููุง", | |
| "confidence": 1.0, | |
| "start_index": 118 | |
| }, | |
| { | |
| "text": "ุนูู ูุงุ", | |
| "confidence": 1.0, | |
| "start_index": 125 | |
| }, | |
| { | |
| "text": "ููู ", | |
| "confidence": 1.0, | |
| "start_index": 132 | |
| }, | |
| { | |
| "text": "ููุธุฑูุง", | |
| "confidence": 1.0, | |
| "start_index": 136 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 143 | |
| }, | |
| { | |
| "text": "ุญูููุชูุง", | |
| "confidence": 1.0, | |
| "start_index": 146 | |
| }, | |
| { | |
| "text": "ููุฏุฑูููุงุ", | |
| "confidence": 1.0, | |
| "start_index": 154 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 164 | |
| }, | |
| { | |
| "text": "ุฅุฏุฑุงู", | |
| "confidence": 1.0, | |
| "start_index": 167 | |
| }, | |
| { | |
| "text": "j_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 173 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 181 | |
| }, | |
| { | |
| "text": "j_n", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 187 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 189 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 196 | |
| }, | |
| { | |
| "text": "f(j_n)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 210 | |
| }, | |
| { | |
| "text": "ูุธุฑูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 213 | |
| }, | |
| { | |
| "text": "ุนูู ูู ", | |
| "confidence": 1.0, | |
| "start_index": 219 | |
| }, | |
| { | |
| "text": "ุจุญุฏูุซูุงุ", | |
| "confidence": 1.0, | |
| "start_index": 225 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 234 | |
| }, | |
| { | |
| "text": "ูู ", | |
| "confidence": 1.0, | |
| "start_index": 237 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 240 | |
| }, | |
| { | |
| "text": "ุดู", | |
| "confidence": 1.0, | |
| "start_index": 243 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 246 | |
| }, | |
| { | |
| "text": "ุญุฏูุซูุงุ", | |
| "confidence": 1.0, | |
| "start_index": 249 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 257 | |
| }, | |
| { | |
| "text": "ูู ", | |
| "confidence": 1.0, | |
| "start_index": 260 | |
| }, | |
| { | |
| "text": "ุนู", | |
| "confidence": 1.0, | |
| "start_index": 263 | |
| }, | |
| { | |
| "text": "ุนูู ูุง", | |
| "confidence": 1.0, | |
| "start_index": 266 | |
| }, | |
| { | |
| "text": "ุนู ูู.", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ูู ู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฐูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ูููู", | |
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| { | |
| "text": "ุชุนุงูู:", | |
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| { | |
| "text": "\\iint_{D}", | |
| "confidence": 1.0, | |
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| { | |
| "text": "n^2", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\approx", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\sigma^2", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
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| "text": "dy", | |
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| { | |
| "text": "##", | |
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| { | |
| "text": "ู ูุงุญุธุฉ", | |
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| { | |
| "text": "(ุฃูุฌูุนูููุชูู ู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุณููุงููุฉู", | |
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| }, | |
| { | |
| "text": "ุงููุญุงุฌูู)", | |
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| }, | |
| { | |
| "text": "ยซ3ยป", | |
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| { | |
| "text": "ุฃู:", | |
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| }, | |
| { | |
| "text": "ุตุงุญุจ", | |
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| }, | |
| { | |
| "text": "ุณูุงูุฉ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุงูุญุงุฌ.", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููุงู", | |
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| }, | |
| { | |
| "text": "ุนุฒ", | |
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| { | |
| "text": "ู ู", | |
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| }, | |
| { | |
| "text": "ูุงุฆู:", | |
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| { | |
| "text": "(ููููุฃูููููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ู ููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\vec{F}", | |
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| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| "text": "##", | |
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| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
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| { | |
| "text": "ููุฑูููุฉู)", | |
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| { | |
| "text": "ยซ4ยป", | |
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| }, | |
| { | |
| "text": "ุฃู:", | |
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| "text": "ู ู", | |
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| }, | |
| { | |
| "text": "ุฃูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ูุฑูุฉ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "(ูููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃูุดูุฏูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ูููููุฉู", | |
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| }, | |
| { | |
| "text": "ู ููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููุฑูููุชููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุงูููุชูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃูุฎูุฑูุฌูุชููู)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ยซ5ยป", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃู:", | |
| "confidence": 1.0, | |
| "start_index": 567 | |
| }, | |
| { | |
| "text": "ุฃุฎุฑุฌู", | |
| "confidence": 1.0, | |
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| { | |
| "text": "j_{n+1}", | |
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| { | |
| "text": "=", | |
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| { | |
| "text": "j_n", | |
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| { | |
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| }, | |
| { | |
| "text": "\\alpha", | |
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| { | |
| "text": "\\nabla", | |
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| }, | |
| { | |
| "text": "f(j_n)", | |
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| }, | |
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| "content": "ุชุนุฑูู", | |
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| "content": "ุนูู ุฐูู/: (ุจููู ููู ู ููู ุดูููู ู ููููุง ุจููู ููู ู ู ููููุง ุนูู ูููู) ยซ2ยป ุฃู: ู ู ุนู ููุง. ู ยซููยป ุจู ุนูู ุงูุจุงุกุ ุฃู: ูู ูุฏุฑููุง ุนูู ูุงุ ููู ููุธุฑูุง ูู ุญูููุชูุง ููุฏุฑูููุงุ ุฃู ุฅุฏุฑุงู", | |
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| "content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n)", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 3 | |
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| "content": "ูุธุฑูุฉ", | |
| "type": "title", | |
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| "top_left_x": 32, | |
| "top_left_y": 219, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 241, | |
| "content": "ุนูู ูู ุจุญุฏูุซูุงุ ุจู ูู ูู ุดู ู ู ุญุฏูุซูุงุ ุจู ูู ุนู ุนูู ูุง ุนู ูู. ูู ู ุฐูู ูููู ุชุนุงูู:", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 5 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 247, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 302, | |
| "content": "\\iint_{D} n^2 \\approx \\sigma^2 \\, dx \\, dy", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 6 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 346, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 368, | |
| "content": "ู ูุงุญุธุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 7 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 373, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 395, | |
| "content": "(ุฃูุฌูุนูููุชูู ู ุณููุงููุฉู ุงููุญุงุฌูู) ยซ3ยป ุฃู: ุตุงุญุจ ุณูุงูุฉ ุงูุญุงุฌ. ููุงู ุนุฒ ู ู ูุงุฆู: (ููููุฃูููููู ู ููู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 8 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 401, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 440, | |
| "content": "\\vec{F} = m\\vec{a}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 9 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 484, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 506, | |
| "content": "ุจุฑูุงู", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 10 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 511, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 534, | |
| "content": "ููุฑูููุฉู) ยซ4ยป ุฃู: ู ู ุฃูู ูุฑูุฉ (ูููู ุฃูุดูุฏูู ูููููุฉู ู ููู ููุฑูููุชููู ุงูููุชูู ุฃูุฎูุฑูุฌูุชููู) ยซ5ยป ุฃู: ุฃุฎุฑุฌู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 11 | |
| }, | |
| { | |
| "top_left_x": 32, | |
| "top_left_y": 540, | |
| "bottom_right_x": 571, | |
| "bottom_right_y": 578, | |
| "content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n)", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 12 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "b-tooba.ttf", | |
| "title_font": "a-ketab-araby-italic.ttf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |