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| "markdown": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}\n\\sum_{\\beta=0}^{\\infty} \\frac{n^\\beta}{\\beta!} = e^{n}\n## ุจุฑูุงู\n5371 - ุญุฏูุซ: ูุง ุนุฏูู ููุง ุทูุฑุฉ ููุง ูุงู ุฉ ููุง ุฌุฏ ูุงูุนูู ุญู (2: 222) ุญุฏุซูุง ูุชูุจุฉุ ุซูุง ุฑุดุฏูู ุจู ุณุนุฏุ ุนู ุงูุญุณู ุจู ุซูุจุงูุ ุนูู ุจูุฐุง.\n\\frac{\\partial j}{\\partial t} = \\lim_{h \\to 0} \\frac{\\max(t + h) - \\max(t)}{h} + \\frac{n}{x^2}\n## ุจุฑูุงู\nููุญูููู ุจููู ู ูุญูู ููุฏู ุจููู ููุญููููุ ุซูููุง ู ูุณูุฏููุฏูุ ุซูููุง ููุญููููุ ุนููู ุซูููุฑู ุจููู ููุฒููุฏูุ ุนููู ุฑูุงุดูุฏู ุจููู ุณูุนูุฏูุ ุนููู ุนูุจูุฏู ุงูููููู ุจููู ููุญููููุ ุนููู\n\\nabla_{i} J(i) = \\frac{1}{m} X^T ( \\sigma(X i) - Y )\n\\nabla_{\\mu} J(\\mu) = \\frac{1}{m} X^T ( \\sigma(X \\mu) - Y ) + \\frac{x}{n^2}\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ุชุนุฑูู\nุนูุจูุฏู ุงูููููู ุจููู ููุฑูุทูุ ููุงูู: ููุงูู ุฑูุณูููู ุงูููููู ุตูู ุงููู ุนููู ูุณูู : ยซุฃูุนูุธูู ู ุงููุฃููููุงู ู ุนูููุฏู ุงูููููู ููููู ู ุงููููุญูุฑู ุซูู ูู ููููู ู ุงููููุฑููยป ููููุฏูู ู ุฅูููู ุงููููุจูููู ุตูู ุงููู ุนููู ูุณูู ุจูุฏูููุงุชู ุฎูู ูุณู ุฃููู ุณูุชูู ููุทููููููู\n\\mathbb{E}[x] = \\int x f_x(x) dx\ni_{n+1} = i_n - \\alpha \\nabla f(i_n) + \\frac{y}{i^2}\n\\int_{5}^{M} \\tan(i) \\, di = \\lambda^2 \\approx C\n## ูุธุฑูุฉ\nููุฒูุฏููููููู ุจูุฃููููุชูููููู ููุจูุฏูุฃู ุจูููุง ููููู ููุง ููุฌูุจูุชู ุฌููููุจูููุง - ููุงูู ููููู ูุฉู ุฎููููููุฉู ููู ู ุฃูููููู ูููุง ููุณูุฃูููุชู ู ููู ููููููู ููููุงูู - ููุงูู: ยซู ููู ุดูุงุกู ุงููุชูุทูุนูยป ููุฐูุง ุญูุฏููุซู ุตูุญููุญู ุงููุฅูุณูููุงุฏู ููููู ู ููุฎูุฑููุฌูุงูู \" 7522 - ุตุญูุญ\n\\frac{\\partial \\alpha}{\\partial \\alpha} = \\lim_{h \\to 0} \\frac{\\tan(\\alpha + h) - \\tan(\\alpha)}{h}", | |
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| }, | |
| { | |
| "text": "ุฑูุณูููู", | |
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| }, | |
| { | |
| "text": "ุงูููููู", | |
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| }, | |
| { | |
| "text": "ุตูู", | |
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| "start_index": 717 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 721 | |
| }, | |
| { | |
| "text": "ุนููู", | |
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| "start_index": 726 | |
| }, | |
| { | |
| "text": "ูุณูู :", | |
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| "start_index": 731 | |
| }, | |
| { | |
| "text": "ยซุฃูุนูุธูู ู", | |
| "confidence": 1.0, | |
| "start_index": 737 | |
| }, | |
| { | |
| "text": "ุงููุฃููููุงู ู", | |
| "confidence": 1.0, | |
| "start_index": 747 | |
| }, | |
| { | |
| "text": "ุนูููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 759 | |
| }, | |
| { | |
| "text": "ุงูููููู", | |
| "confidence": 1.0, | |
| "start_index": 766 | |
| }, | |
| { | |
| "text": "ููููู ู", | |
| "confidence": 1.0, | |
| "start_index": 774 | |
| }, | |
| { | |
| "text": "ุงููููุญูุฑู", | |
| "confidence": 1.0, | |
| "start_index": 781 | |
| }, | |
| { | |
| "text": "ุซูู ูู", | |
| "confidence": 1.0, | |
| "start_index": 791 | |
| }, | |
| { | |
| "text": "ููููู ู", | |
| "confidence": 1.0, | |
| "start_index": 797 | |
| }, | |
| { | |
| "text": "ุงููููุฑููยป", | |
| "confidence": 1.0, | |
| "start_index": 804 | |
| }, | |
| { | |
| "text": "ููููุฏูู ู", | |
| "confidence": 1.0, | |
| "start_index": 814 | |
| }, | |
| { | |
| "text": "ุฅูููู", | |
| "confidence": 1.0, | |
| "start_index": 823 | |
| }, | |
| { | |
| "text": "ุงููููุจูููู", | |
| "confidence": 1.0, | |
| "start_index": 829 | |
| }, | |
| { | |
| "text": "ุตูู", | |
| "confidence": 1.0, | |
| "start_index": 840 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 844 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 849 | |
| }, | |
| { | |
| "text": "ูุณูู ", | |
| "confidence": 1.0, | |
| "start_index": 854 | |
| }, | |
| { | |
| "text": "ุจูุฏูููุงุชู", | |
| "confidence": 1.0, | |
| "start_index": 859 | |
| }, | |
| { | |
| "text": "ุฎูู ูุณู", | |
| "confidence": 1.0, | |
| "start_index": 869 | |
| }, | |
| { | |
| "text": "ุฃููู", | |
| "confidence": 1.0, | |
| "start_index": 876 | |
| }, | |
| { | |
| "text": "ุณูุชูู", | |
| "confidence": 1.0, | |
| "start_index": 881 | |
| }, | |
| { | |
| "text": "ููุทููููููู", | |
| "confidence": 1.0, | |
| "start_index": 887 | |
| }, | |
| { | |
| "text": "\\mathbb{E}[x]", | |
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| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\int", | |
| "confidence": 1.0, | |
| "start_index": 914 | |
| }, | |
| { | |
| "text": "x", | |
| "confidence": 1.0, | |
| "start_index": 919 | |
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| { | |
| "text": "f_x(x)", | |
| "confidence": 1.0, | |
| "start_index": 921 | |
| }, | |
| { | |
| "text": "dx", | |
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| }, | |
| { | |
| "text": "i_{n+1}", | |
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| }, | |
| { | |
| "text": "=", | |
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| { | |
| "text": "i_n", | |
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| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 945 | |
| }, | |
| { | |
| "text": "\\alpha", | |
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| "start_index": 947 | |
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| { | |
| "text": "\\nabla", | |
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| }, | |
| { | |
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| }, | |
| { | |
| "text": "+", | |
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| }, | |
| { | |
| "text": "\\frac{y}{i^2}", | |
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| "start_index": 970 | |
| }, | |
| { | |
| "text": "\\int_{5}^{M}", | |
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| "start_index": 984 | |
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| { | |
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| { | |
| "text": "di", | |
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| }, | |
| { | |
| "text": "=", | |
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| }, | |
| { | |
| "text": "\\lambda^2", | |
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| { | |
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| { | |
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| }, | |
| { | |
| "text": "ููุฒูุฏููููููู", | |
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| "start_index": 1042 | |
| }, | |
| { | |
| "text": "ุจูุฃููููุชูููููู", | |
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| "start_index": 1055 | |
| }, | |
| { | |
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| "confidence": 1.0, | |
| "start_index": 1070 | |
| }, | |
| { | |
| "text": "ุจูููุง", | |
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| "start_index": 1079 | |
| }, | |
| { | |
| "text": "ููููู ููุง", | |
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| }, | |
| { | |
| "text": "ููุฌูุจูุชู", | |
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| { | |
| "text": "ุฌููููุจูููุง", | |
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| "text": "ููููู ูุฉู", | |
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| { | |
| "text": "ููู ู", | |
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| { | |
| "text": "ุฃูููููู ูููุง", | |
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| "start_index": 1146 | |
| }, | |
| { | |
| "text": "ููุณูุฃูููุชู", | |
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| }, | |
| { | |
| "text": "ู ููู", | |
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| { | |
| "text": "ููููููู", | |
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| }, | |
| { | |
| "text": "ููููุงูู", | |
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| { | |
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| "text": "ยซู ููู", | |
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| { | |
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| { | |
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| { | |
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| { | |
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| }, | |
| { | |
| "text": "ููุฎูุฑููุฌูุงูู", | |
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| { | |
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| { | |
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| "content": "ุนูุจูุฏู ุงูููููู ุจููู ููุฑูุทูุ ููุงูู: ููุงูู ุฑูุณูููู ุงูููููู ุตูู ุงููู ุนููู ูุณูู : ยซุฃูุนูุธูู ู ุงููุฃููููุงู ู ุนูููุฏู ุงูููููู ููููู ู ุงููููุญูุฑู ุซูู ูู ููููู ู ุงููููุฑููยป ููููุฏูู ู ุฅูููู ุงููููุจูููู ุตูู ุงููู ุนููู ูุณูู ุจูุฏูููุงุชู ุฎูู ูุณู ุฃููู ุณูุชูู ููุทููููููู", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 12 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 714, | |
| "bottom_right_x": 732, | |
| "bottom_right_y": 768, | |
| "content": "\\mathbb{E}[x] = \\int x f_x(x) dx", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 13 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 800, | |
| "bottom_right_x": 748, | |
| "bottom_right_y": 847, | |
| "content": "i_{n+1} = i_n - \\alpha \\nabla f(i_n) + \\frac{y}{i^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 14 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 853, | |
| "bottom_right_x": 748, | |
| "bottom_right_y": 911, | |
| "content": "\\int_{5}^{M} \\tan(i) \\, di = \\lambda^2 \\approx C", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 15 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 929, | |
| "bottom_right_x": 732, | |
| "bottom_right_y": 955, | |
| "content": "ูุธุฑูุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 16 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 960, | |
| "bottom_right_x": 732, | |
| "bottom_right_y": 1005, | |
| "content": "ููุฒูุฏููููููู ุจูุฃููููุชูููููู ููุจูุฏูุฃู ุจูููุง ููููู ููุง ููุฌูุจูุชู ุฌููููุจูููุง - ููุงูู ููููู ูุฉู ุฎููููููุฉู ููู ู ุฃูููููู ูููุง ููุณูุฃูููุชู ู ููู ููููููู ููููุงูู - ููุงูู: ยซู ููู ุดูุงุกู ุงููุชูุทูุนูยป ููุฐูุง ุญูุฏููุซู ุตูุญููุญู ุงููุฅูุณูููุงุฏู ููููู ู ููุฎูุฑููุฌูุงูู \" 7522 - ุตุญูุญ", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 17 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 1011, | |
| "bottom_right_x": 732, | |
| "bottom_right_y": 1064, | |
| "content": "\\frac{\\partial \\alpha}{\\partial \\alpha} = \\lim_{h \\to 0} \\frac{\\tan(\\alpha + h) - \\tan(\\alpha)}{h}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 18 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "digi-hamishe-regular.ttf", | |
| "title_font": "digi-hamishe-regular.ttf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |