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| "markdown": "## ู ูุงุญุธุฉ\nูููุคู ูู ุฑุฌูู ู ููู \"ุ ุฃู: ู ู ุงูููู ุ ูุนูู: ุตุงุญุจ ุงูุจูุช ุฃููู ุจุงูุฅู ุงู ุฉ ู ู ุฃุถูุงูู. * * * 802 - ููุงู ุฃููุณู ุฑุถู ุงููู ุนูู: ุฅููู ุงููููุจููู ุตูู ุงููู ุนููู ูุณูู ุงุณูุชูุฎููููู ุงุจู ุฃูู ูู ู ูููุชููู ู ููุคูู ูู\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ุชุนุฑูู\nุงููููุงุณู ูููููู ุฃูุนูู ูู. \"ูุงู ุฃูุณ: ุฅู ุงููุจู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ุงุณุชุฎูู ุงุจู ุฃู ู ูุชูู \"ุ ุฃู: ุฃูุงู ู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ู ูุงู ู ููุณู ูู ุงูู ุณุฌุฏ ูู ุงูู ุฏููุฉ ุญูู ุฎุฑุฌ ุฅูู ุงูุบุฒู. \"ูุคู ูู ุงููุงุณ ููู ุฃุนู ู\": ููุฏ ุฌุงุก ูู ุจุนุถ ุงูุฑูุงูุงุช: ุฃูููู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ุงุณุชุฎููู ูู ุซูุงุซ ุนุดุฑุฉ ุบุฒูุฉ ู ู ุบุฒูุงุชูุ ููุฐุง ูุฏู ุนูู\nz_{n+1} = z_n - \\alpha \\nabla f(z_n) + \\frac{t}{z^2}\n\\int_{2}^{N} \\ln(\\mu) \\, d\\mu = \\beta^2 \\approx C\n## ู ูุงุญุธุฉ\nุฌูุงุฒ ุฅู ุงู ุฉ ุงูุฃุนู ูุ ูุงููุฑุงูุฉ ุฅูู ุง ูู ุฅุฐุง ูุงู ูู ุงูููู ุณููู ู ุฃุนูู ู ูู ุฃู ู ุณุงูู ูู ุนูู ูุง. * * *\n\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n) + \\frac{y}{\\theta^2}\n## ูุธุฑูุฉ\nุงููุนูุชููููููุ ุซูููุง ู ูุญูู ููุฏู ุจููู ุฃูุญูู ูุฏู ุจููู ุฃูููุณู ุงููููุฑูุดููููุ ุซูููุง ุฃูุจูู ุนูุงุตูู ูุ ุซูููุง ุนูุจููุงุฏู ุจููู ู ูููุตููุฑูุ ุนููู ุนูููุฑูู ูุฉูุ ุนููู ุงุจููู ุนูุจููุงุณูุ ุฑุถู ุงููู ุนููู ุง ููุงูู: ููุงูู ุฑูุณูููู ุงูููููู ุตูู ุงููู ุนููู ูุณูู : ยซุฎูููุฑู ู ูุง ุชูุฏูุงููููุชูู ู\n\\prod_{k=1}^{n} (1 \\times \\mu_k) = 0\n\\vec{F} = m\\vec{a} + \\frac{\\sigma}{z^2}\n## ุชุนุฑูู\nุจููู ุงูุณููุนููุทู ููุงููููุฏููุฏู ููุงููุญูุฌูุงู ูุฉู ููุงููู ูุดูููยป ููุฐูุง ุญูุฏููุซู ุตูุญููุญู ุงููุฅูุณูููุงุฏู ููููู ู ููุฎูุฑููุฌูุงูู \" 7472 - ุนุจุงุฏ ุจู ู ูุตูุฑ ุถุนููู\n\\sum_{\\beta=0}^{100} \\frac{t^\\beta}{\\beta!} = e^{t}", | |
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| { | |
| "text": "##", | |
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| }, | |
| { | |
| "text": "ู ูุงุญุธุฉ", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "ูููุคู ูู ", | |
| "confidence": 1.0, | |
| "start_index": 10 | |
| }, | |
| { | |
| "text": "ุฑุฌูู", | |
| "confidence": 1.0, | |
| "start_index": 18 | |
| }, | |
| { | |
| "text": "ู ููู \"ุ", | |
| "confidence": 1.0, | |
| "start_index": 23 | |
| }, | |
| { | |
| "text": "ุฃู:", | |
| "confidence": 1.0, | |
| "start_index": 30 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 34 | |
| }, | |
| { | |
| "text": "ุงูููู ุ", | |
| "confidence": 1.0, | |
| "start_index": 37 | |
| }, | |
| { | |
| "text": "ูุนูู:", | |
| "confidence": 1.0, | |
| "start_index": 44 | |
| }, | |
| { | |
| "text": "ุตุงุญุจ", | |
| "confidence": 1.0, | |
| "start_index": 50 | |
| }, | |
| { | |
| "text": "ุงูุจูุช", | |
| "confidence": 1.0, | |
| "start_index": 55 | |
| }, | |
| { | |
| "text": "ุฃููู", | |
| "confidence": 1.0, | |
| "start_index": 61 | |
| }, | |
| { | |
| "text": "ุจุงูุฅู ุงู ุฉ", | |
| "confidence": 1.0, | |
| "start_index": 66 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 75 | |
| }, | |
| { | |
| "text": "ุฃุถูุงูู.", | |
| "confidence": 1.0, | |
| "start_index": 78 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 86 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 88 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 90 | |
| }, | |
| { | |
| "text": "802", | |
| "confidence": 1.0, | |
| "start_index": 92 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 96 | |
| }, | |
| { | |
| "text": "ููุงู", | |
| "confidence": 1.0, | |
| "start_index": 98 | |
| }, | |
| { | |
| "text": "ุฃููุณู", | |
| "confidence": 1.0, | |
| "start_index": 103 | |
| }, | |
| { | |
| "text": "ุฑุถู", | |
| "confidence": 1.0, | |
| "start_index": 109 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 113 | |
| }, | |
| { | |
| "text": "ุนูู:", | |
| "confidence": 1.0, | |
| "start_index": 118 | |
| }, | |
| { | |
| "text": "ุฅููู", | |
| "confidence": 1.0, | |
| "start_index": 123 | |
| }, | |
| { | |
| "text": "ุงููููุจููู", | |
| "confidence": 1.0, | |
| "start_index": 128 | |
| }, | |
| { | |
| "text": "ุตูู", | |
| "confidence": 1.0, | |
| "start_index": 138 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 142 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 147 | |
| }, | |
| { | |
| "text": "ูุณูู ", | |
| "confidence": 1.0, | |
| "start_index": 152 | |
| }, | |
| { | |
| "text": "ุงุณูุชูุฎููููู", | |
| "confidence": 1.0, | |
| "start_index": 157 | |
| }, | |
| { | |
| "text": "ุงุจู", | |
| "confidence": 1.0, | |
| "start_index": 169 | |
| }, | |
| { | |
| "text": "ุฃูู ูู", | |
| "confidence": 1.0, | |
| "start_index": 173 | |
| }, | |
| { | |
| "text": "ู ูููุชููู ู", | |
| "confidence": 1.0, | |
| "start_index": 179 | |
| }, | |
| { | |
| "text": "ููุคูู ูู", | |
| "confidence": 1.0, | |
| "start_index": 189 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 206 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 216 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
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| { | |
| "text": "##", | |
| "confidence": 1.0, | |
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| "text": "ุชุนุฑูู", | |
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| { | |
| "text": "ุงููููุงุณู", | |
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| { | |
| "text": "ูููููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃูุนูู ูู.", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\"ูุงู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃูุณ:", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ุฅู", | |
| "confidence": 1.0, | |
| "start_index": 275 | |
| }, | |
| { | |
| "text": "ุงููุจู", | |
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| { | |
| "text": "ุงูุตูุงุฉ", | |
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| }, | |
| { | |
| "text": "ูุงูุณูุงู ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุงุณุชุฎูู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุงุจู", | |
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| }, | |
| { | |
| "text": "ุฃู ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ู ูุชูู \"ุ", | |
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| { | |
| "text": "ุฃู:", | |
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| { | |
| "text": "ุฃูุงู ู", | |
| "confidence": 1.0, | |
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| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 336 | |
| }, | |
| { | |
| "text": "ุงูุตูุงุฉ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ูุงูุณูุงู ", | |
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| { | |
| "text": "ู ูุงู ู", | |
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| "text": "ููุณู", | |
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| { | |
| "text": "ูู", | |
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| { | |
| "text": "ุงูู ุณุฌุฏ", | |
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| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ุงูู ุฏููุฉ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุญูู", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ุฎุฑุฌ", | |
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| "text": "ุฅูู", | |
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| }, | |
| { | |
| "text": "ุงูุบุฒู.", | |
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| { | |
| "text": "\"ูุคู ูู", | |
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| { | |
| "text": "ุงููุงุณ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุฃุนู ู\":", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ููุฏ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ุฌุงุก", | |
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| { | |
| "text": "ูู", | |
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| "text": "ุจุนุถ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "ุงูุฑูุงูุงุช:", | |
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| { | |
| "text": "ุฃูููู", | |
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| "text": "ุนููู", | |
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| { | |
| "text": "ุงูุตูุงุฉ", | |
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| { | |
| "text": "ูุงูุณูุงู ", | |
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| }, | |
| { | |
| "text": "ุงุณุชุฎููู", | |
| "confidence": 1.0, | |
| "start_index": 482 | |
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| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 490 | |
| }, | |
| { | |
| "text": "ุซูุงุซ", | |
| "confidence": 1.0, | |
| "start_index": 493 | |
| }, | |
| { | |
| "text": "ุนุดุฑุฉ", | |
| "confidence": 1.0, | |
| "start_index": 498 | |
| }, | |
| { | |
| "text": "ุบุฒูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 503 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 508 | |
| }, | |
| { | |
| "text": "ุบุฒูุงุชูุ", | |
| "confidence": 1.0, | |
| "start_index": 511 | |
| }, | |
| { | |
| "text": "ููุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 519 | |
| }, | |
| { | |
| "text": "ูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 524 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 528 | |
| }, | |
| { | |
| "text": "z_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 532 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 540 | |
| }, | |
| { | |
| "text": "z_n", | |
| "confidence": 1.0, | |
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| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 546 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 555 | |
| }, | |
| { | |
| "text": "f(z_n)", | |
| "confidence": 1.0, | |
| "start_index": 562 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 569 | |
| }, | |
| { | |
| "text": "\\frac{t}{z^2}", | |
| "confidence": 1.0, | |
| "start_index": 571 | |
| }, | |
| { | |
| "text": "\\int_{2}^{N}", | |
| "confidence": 1.0, | |
| "start_index": 585 | |
| }, | |
| { | |
| "text": "\\ln(\\mu)", | |
| "confidence": 1.0, | |
| "start_index": 598 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 607 | |
| }, | |
| { | |
| "text": "d\\mu", | |
| "confidence": 1.0, | |
| "start_index": 610 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 615 | |
| }, | |
| { | |
| "text": "\\beta^2", | |
| "confidence": 1.0, | |
| "start_index": 617 | |
| }, | |
| { | |
| "text": "\\approx", | |
| "confidence": 1.0, | |
| "start_index": 625 | |
| }, | |
| { | |
| "text": "C", | |
| "confidence": 1.0, | |
| "start_index": 633 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 635 | |
| }, | |
| { | |
| "text": "ู ูุงุญุธุฉ", | |
| "confidence": 1.0, | |
| "start_index": 638 | |
| }, | |
| { | |
| "text": "ุฌูุงุฒ", | |
| "confidence": 1.0, | |
| "start_index": 645 | |
| }, | |
| { | |
| "text": "ุฅู ุงู ุฉ", | |
| "confidence": 1.0, | |
| "start_index": 650 | |
| }, | |
| { | |
| "text": "ุงูุฃุนู ูุ", | |
| "confidence": 1.0, | |
| "start_index": 656 | |
| }, | |
| { | |
| "text": "ูุงููุฑุงูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 664 | |
| }, | |
| { | |
| "text": "ุฅูู ุง", | |
| "confidence": 1.0, | |
| "start_index": 673 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 678 | |
| }, | |
| { | |
| "text": "ุฅุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 681 | |
| }, | |
| { | |
| "text": "ูุงู", | |
| "confidence": 1.0, | |
| "start_index": 685 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 689 | |
| }, | |
| { | |
| "text": "ุงูููู ", | |
| "confidence": 1.0, | |
| "start_index": 692 | |
| }, | |
| { | |
| "text": "ุณููู ู", | |
| "confidence": 1.0, | |
| "start_index": 698 | |
| }, | |
| { | |
| "text": "ุฃุนูู ", | |
| "confidence": 1.0, | |
| "start_index": 704 | |
| }, | |
| { | |
| "text": "ู ูู", | |
| "confidence": 1.0, | |
| "start_index": 709 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 713 | |
| }, | |
| { | |
| "text": "ู ุณุงูู", | |
| "confidence": 1.0, | |
| "start_index": 716 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 722 | |
| }, | |
| { | |
| "text": "ุนูู ูุง.", | |
| "confidence": 1.0, | |
| "start_index": 725 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 732 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 734 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 736 | |
| }, | |
| { | |
| "text": "\\theta_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 738 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 751 | |
| }, | |
| { | |
| "text": "\\theta_n", | |
| "confidence": 1.0, | |
| "start_index": 753 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 762 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 764 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 771 | |
| }, | |
| { | |
| "text": "f(\\theta_n)", | |
| "confidence": 1.0, | |
| "start_index": 778 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 790 | |
| }, | |
| { | |
| "text": "\\frac{y}{\\theta^2}", | |
| "confidence": 1.0, | |
| "start_index": 792 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 811 | |
| }, | |
| { | |
| "text": "ูุธุฑูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 814 | |
| }, | |
| { | |
| "text": "ุงููุนูุชููููููุ", | |
| "confidence": 1.0, | |
| "start_index": 820 | |
| }, | |
| { | |
| "text": "ุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 834 | |
| }, | |
| { | |
| "text": "ู ูุญูู ููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 840 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 850 | |
| }, | |
| { | |
| "text": "ุฃูุญูู ูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 855 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 864 | |
| }, | |
| { | |
| "text": "ุฃูููุณู", | |
| "confidence": 1.0, | |
| "start_index": 869 | |
| }, | |
| { | |
| "text": "ุงููููุฑูุดููููุ", | |
| "confidence": 1.0, | |
| "start_index": 876 | |
| }, | |
| { | |
| "text": "ุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 890 | |
| }, | |
| { | |
| "text": "ุฃูุจูู", | |
| "confidence": 1.0, | |
| "start_index": 896 | |
| }, | |
| { | |
| "text": "ุนูุงุตูู ูุ", | |
| "confidence": 1.0, | |
| "start_index": 902 | |
| }, | |
| { | |
| "text": "ุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 911 | |
| }, | |
| { | |
| "text": "ุนูุจููุงุฏู", | |
| "confidence": 1.0, | |
| "start_index": 917 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 926 | |
| }, | |
| { | |
| "text": "ู ูููุตููุฑูุ", | |
| "confidence": 1.0, | |
| "start_index": 931 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 942 | |
| }, | |
| { | |
| "text": "ุนูููุฑูู ูุฉูุ", | |
| "confidence": 1.0, | |
| "start_index": 947 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 959 | |
| }, | |
| { | |
| "text": "ุงุจููู", | |
| "confidence": 1.0, | |
| "start_index": 964 | |
| }, | |
| { | |
| "text": "ุนูุจููุงุณูุ", | |
| "confidence": 1.0, | |
| "start_index": 970 | |
| }, | |
| { | |
| "text": "ุฑุถู", | |
| "confidence": 1.0, | |
| "start_index": 980 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 984 | |
| }, | |
| { | |
| "text": "ุนููู ุง", | |
| "confidence": 1.0, | |
| "start_index": 989 | |
| }, | |
| { | |
| "text": "ููุงูู:", | |
| "confidence": 1.0, | |
| "start_index": 995 | |
| }, | |
| { | |
| "text": "ููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 1002 | |
| }, | |
| { | |
| "text": "ุฑูุณูููู", | |
| "confidence": 1.0, | |
| "start_index": 1008 | |
| }, | |
| { | |
| "text": "ุงูููููู", | |
| "confidence": 1.0, | |
| "start_index": 1016 | |
| }, | |
| { | |
| "text": "ุตูู", | |
| "confidence": 1.0, | |
| "start_index": 1024 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 1028 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 1033 | |
| }, | |
| { | |
| "text": "ูุณูู :", | |
| "confidence": 1.0, | |
| "start_index": 1038 | |
| }, | |
| { | |
| "text": "ยซุฎูููุฑู", | |
| "confidence": 1.0, | |
| "start_index": 1044 | |
| }, | |
| { | |
| "text": "ู ูุง", | |
| "confidence": 1.0, | |
| "start_index": 1052 | |
| }, | |
| { | |
| "text": "ุชูุฏูุงููููุชูู ู", | |
| "confidence": 1.0, | |
| "start_index": 1056 | |
| }, | |
| { | |
| "text": "\\prod_{k=1}^{n}", | |
| "confidence": 1.0, | |
| "start_index": 1070 | |
| }, | |
| { | |
| "text": "(1", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\times", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\mu_k)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "0", | |
| "confidence": 1.0, | |
| "start_index": 1105 | |
| }, | |
| { | |
| "text": "\\vec{F}", | |
| "confidence": 1.0, | |
| "start_index": 1107 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "m\\vec{a}", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\frac{\\sigma}{z^2}", | |
| "confidence": 1.0, | |
| "start_index": 1128 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 1147 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 1150 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 1156 | |
| }, | |
| { | |
| "text": "ุงูุณููุนููุทู", | |
| "confidence": 1.0, | |
| "start_index": 1161 | |
| }, | |
| { | |
| "text": "ููุงููููุฏููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 1172 | |
| }, | |
| { | |
| "text": "ููุงููุญูุฌูุงู ูุฉู", | |
| "confidence": 1.0, | |
| "start_index": 1185 | |
| }, | |
| { | |
| "text": "ููุงููู ูุดูููยป", | |
| "confidence": 1.0, | |
| "start_index": 1200 | |
| }, | |
| { | |
| "text": "ููุฐูุง", | |
| "confidence": 1.0, | |
| "start_index": 1213 | |
| }, | |
| { | |
| "text": "ุญูุฏููุซู", | |
| "confidence": 1.0, | |
| "start_index": 1219 | |
| }, | |
| { | |
| "text": "ุตูุญููุญู", | |
| "confidence": 1.0, | |
| "start_index": 1227 | |
| }, | |
| { | |
| "text": "ุงููุฅูุณูููุงุฏู", | |
| "confidence": 1.0, | |
| "start_index": 1235 | |
| }, | |
| { | |
| "text": "ููููู ู", | |
| "confidence": 1.0, | |
| "start_index": 1248 | |
| }, | |
| { | |
| "text": "ููุฎูุฑููุฌูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 1255 | |
| }, | |
| { | |
| "text": "\"", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "7472", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1275 | |
| }, | |
| { | |
| "text": "ุนุจุงุฏ", | |
| "confidence": 1.0, | |
| "start_index": 1277 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 1282 | |
| }, | |
| { | |
| "text": "ู ูุตูุฑ", | |
| "confidence": 1.0, | |
| "start_index": 1285 | |
| }, | |
| { | |
| "text": "ุถุนููู", | |
| "confidence": 1.0, | |
| "start_index": 1291 | |
| }, | |
| { | |
| "text": "\\sum_{\\beta=0}^{100}", | |
| "confidence": 1.0, | |
| "start_index": 1297 | |
| }, | |
| { | |
| "text": "\\frac{t^\\beta}{\\beta!}", | |
| "confidence": 1.0, | |
| "start_index": 1318 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "e^{t}", | |
| "confidence": 1.0, | |
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| "content": "ู ูุงุญุธุฉ", | |
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| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
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| "content": "ุงููููุงุณู ูููููู ุฃูุนูู ูู. \"ูุงู ุฃูุณ: ุฅู ุงููุจู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ุงุณุชุฎูู ุงุจู ุฃู ู ูุชูู \"ุ ุฃู: ุฃูุงู ู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ู ูุงู ู ููุณู ูู ุงูู ุณุฌุฏ ูู ุงูู ุฏููุฉ ุญูู ุฎุฑุฌ ุฅูู ุงูุบุฒู. \"ูุคู ูู ุงููุงุณ ููู ุฃุนู ู\": ููุฏ ุฌุงุก ูู ุจุนุถ ุงูุฑูุงูุงุช: ุฃูููู ุนููู ุงูุตูุงุฉ ูุงูุณูุงู ุงุณุชุฎููู ูู ุซูุงุซ ุนุดุฑุฉ ุบุฒูุฉ ู ู ุบุฒูุงุชูุ ููุฐุง ูุฏู ุนูู", | |
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| "top_left_x": 52, | |
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| "bottom_right_x": 734, | |
| "bottom_right_y": 358, | |
| "content": "z_{n+1} = z_n - \\alpha \\nabla f(z_n) + \\frac{t}{z^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 6 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 390, | |
| "bottom_right_x": 750, | |
| "bottom_right_y": 448, | |
| "content": "\\int_{2}^{N} \\ln(\\mu) \\, d\\mu = \\beta^2 \\approx C", | |
| "type": "text", | |
| "confidence_scores": null, | |
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| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 466, | |
| "bottom_right_x": 734, | |
| "bottom_right_y": 488, | |
| "content": "ู ูุงุญุธุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 8 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 493, | |
| "bottom_right_x": 734, | |
| "bottom_right_y": 515, | |
| "content": "ุฌูุงุฒ ุฅู ุงู ุฉ ุงูุฃุนู ูุ ูุงููุฑุงูุฉ ุฅูู ุง ูู ุฅุฐุง ูุงู ูู ุงูููู ุณููู ู ุฃุนูู ู ูู ุฃู ู ุณุงูู ูู ุนูู ูุง. * * *", | |
| "type": "text", | |
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| { | |
| "top_left_x": 52, | |
| "top_left_y": 521, | |
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| "bottom_right_y": 569, | |
| "content": "\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n) + \\frac{y}{\\theta^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 10 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 613, | |
| "bottom_right_x": 734, | |
| "bottom_right_y": 635, | |
| "content": "ูุธุฑูุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 11 | |
| }, | |
| { | |
| "top_left_x": 52, | |
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| "content": "ุงููุนูุชููููููุ ุซูููุง ู ูุญูู ููุฏู ุจููู ุฃูุญูู ูุฏู ุจููู ุฃูููุณู ุงููููุฑูุดููููุ ุซูููุง ุฃูุจูู ุนูุงุตูู ูุ ุซูููุง ุนูุจููุงุฏู ุจููู ู ูููุตููุฑูุ ุนููู ุนูููุฑูู ูุฉูุ ุนููู ุงุจููู ุนูุจููุงุณูุ ุฑุถู ุงููู ุนููู ุง ููุงูู: ููุงูู ุฑูุณูููู ุงูููููู ุตูู ุงููู ุนููู ูุณูู : ยซุฎูููุฑู ู ูุง ุชูุฏูุงููููุชูู ู", | |
| "type": "text", | |
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| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 690, | |
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| "bottom_right_y": 755, | |
| "content": "\\prod_{k=1}^{n} (1 \\times \\mu_k) = 0", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 13 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 787, | |
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| "content": "\\vec{F} = m\\vec{a} + \\frac{\\sigma}{z^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 14 | |
| }, | |
| { | |
| "top_left_x": 52, | |
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| "bottom_right_y": 876, | |
| "content": "ุชุนุฑูู", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 15 | |
| }, | |
| { | |
| "top_left_x": 52, | |
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| "bottom_right_y": 904, | |
| "content": "ุจููู ุงูุณููุนููุทู ููุงููููุฏููุฏู ููุงููุญูุฌูุงู ูุฉู ููุงููู ูุดูููยป ููุฐูุง ุญูุฏููุซู ุตูุญููุญู ุงููุฅูุณูููุงุฏู ููููู ู ููุฎูุฑููุฌูุงูู \" 7472 - ุนุจุงุฏ ุจู ู ูุตูุฑ ุถุนููู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 16 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 910, | |
| "bottom_right_x": 734, | |
| "bottom_right_y": 979, | |
| "content": "\\sum_{\\beta=0}^{100} \\frac{t^\\beta}{\\beta!} = e^{t}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 17 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "ge-jarida-heavy-italic.otf", | |
| "title_font": "ge-jarida-heavy-italic.otf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |