| { | |
| "markdown": "\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n)\n## ุจุฑูุงู\n\"ุตู ุซูุงุซุฉุ ููู ุฃุฌุฑ ุซู ุงููุฉ\". ููุฐุง ูุฏูุน ูู ุตุฏุฑ ุงูุชุฃููู ุงูุฃููุ ูุงููู ุฃุนูู ุ ุฃูุงุฏู ูู \"ุงููุชุญ\" (1) . ูุงู ุงูุฌุงู ุน ุนูุง ุงููู ุนูู: ุนูุฏู ุงูุฃูุฑุจ ุญู ู ุงูุญุฏูุซ ุนูู ุธุงูุฑูุ ููู ุงูุงุญุชู ุงู\n\\frac{\\partial y}{\\partial j} = \\lim_{h \\to 0} \\frac{\\log(j + h) - \\log(j)}{h} + \\frac{t}{i^2}\n## ูุธุฑูุฉ\nุงูุฃุฎูุฑ ุงูุฐู ู ุฑู ุขููุงู ูู ุนุจุงุฑุฉ \"ุงููุชุญ\"ุ ูุฅูู ุง ููุต ุงูุฃุฌุฑ ู ุน ุฒูุงุฏุฉ ุงูุนู ูุ ููู ูุง ุฐูููุฑ ู ู ุชุฑุชูุจ ุชูููุช ุจุนุถ ุงูุนุจุงุฏุงุช ุจุณุจุจ ู ุดููุฉ ุงูุตูู ุ ูุชุจุตูุฑุ ูุงููู ุชุนุงูู ุฃุนูู ุจุงูุตูุงุจุ ูุฅููู ุงูู ุฑุฌุน ูุงูู ุขุจุ ููู ุญุณุจูุง ููุนู ุงููููู. ูุจุงูุณูุฏ ุงูู ุชูุตู ุฅูู ุงูุฅู ุงู ู ุณูู ุจู ุงูุญุฌุงุฌ ุฑุญู ู ุงููู ุงูู ุฐููุฑ ุฃููู ุงููุชุงุจ ูุงู: [2743]\n\\prod_{i=1}^{n} (1 - n_i) = 0\n## ู ุจุฑููุฉ\n( โฆ ) - (ููุญูุฏููุซูููู ุฒูููููุฑู ุจููู ุญูุฑูุจูุ ููู ูุญูู ููุฏู ุจููู ุญูุงุชูู ูุ ุฌูู ููุนุงู ุนูู ุงุจููู ู ูููุฏููููุ ููุงูู ุฒูููููุฑู: ุญูุฏููุซูููุง ุนูุจูุฏู ุงูุฑููุญูู ููู ุจููู ู ูููุฏููููุ ุญูุฏููุซูููุง ุณููููู ู ุจููู ุญููููุงููุ ุญูุฏููุซูููุง ุณูุนููุฏู ุจููู ู ููููุงุกูุ ููุงูู: ููุงูู ุนูุจูุฏู ุงูููู ุจููู ุนูู ูุฑูู: ููุงูู ููู ุฑูุณูููู ุงูููู ุตูู ุงููู ุนููู ูุณูู :\n\\sum_{\\lambda=0}^{M} \\frac{i^\\lambda}{\\lambda!} = e^{i} + \\frac{i}{x^2}\n## ู ูุงุญุธุฉ\n\"ููุง ุนูุจูุฏู ุงูููู ุจููู ุนูู ูุฑููุ ุจูููุบูููู ุฃูููููู ุชูุตููู ู ุงููููููุงุฑูุ ููุชููููู ู ุงููููููููุ ููููุง ุชูููุนูููุ ููุฅูููู ููุฌูุณูุฏููู ุนููููููู ุญูุธููุงุ ููุจุนููููููู ุนููููููู ุญูุธููุงุ ููุฅูููู ููุฒูููุฌููู ุนููููููู ุญูุธููุงุ ุตูู ูุ ููุฃูููุทูุฑูุ ุตูู ู ู ููู ููููู ุดูููุฑู ุซูููุงุซูุฉู ุฃููููุงู ูุ ููุฐููููู ุตูููู ู ุงูุฏููููุฑู\"ุ ููููุชู: ููุง ุฑูุณูููู ุงูููู ุฅูู ุจูู ูููููุฉูุ ููุงูู:\n\\frac{\\partial \\lambda}{\\partial \\beta} = \\lim_{h \\to 0} \\frac{\\sin(\\beta + h) - \\sin(\\beta)}{h} + \\frac{\\alpha}{j^2}\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ู ุจุฑููุฉ\n\"ููุตูู ู ุตูููู ู ุฏูุงููุฏูุ ุตูู ู ููููู ุงูุ ููุฃูููุทูุฑู ููููู ุงู\"ุ ููููุงูู ููููููู: ููุง ููููุชูููู ุฃูุฎูุฐูุชู ุจูุงูุฑููุฎูุตูุฉู). ุฑุฌุงู ูุฐุง ุงูุฅุณูุงุฏ: ุณุชุฉ: 1 - (ุนูุจูุฏู ุงูุฑููุญูู ููู ุจููู ู ูููุฏูููู) ุจู ุญุณูุงู ุงููุนููุจุฑูู ู ููุงูู ุ ุฃุจู ุณุนูุฏ\nz_{n+1} = z_n - \\alpha \\nabla f(z_n)\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
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| "start_index": 496 | |
| }, | |
| { | |
| "text": "ุงูู ุฑุฌุน", | |
| "confidence": 1.0, | |
| "start_index": 502 | |
| }, | |
| { | |
| "text": "ูุงูู ุขุจุ", | |
| "confidence": 1.0, | |
| "start_index": 509 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 517 | |
| }, | |
| { | |
| "text": "ุญุณุจูุง", | |
| "confidence": 1.0, | |
| "start_index": 521 | |
| }, | |
| { | |
| "text": "ููุนู ", | |
| "confidence": 1.0, | |
| "start_index": 527 | |
| }, | |
| { | |
| "text": "ุงููููู.", | |
| "confidence": 1.0, | |
| "start_index": 532 | |
| }, | |
| { | |
| "text": "ูุจุงูุณูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 540 | |
| }, | |
| { | |
| "text": "ุงูู ุชูุตู", | |
| "confidence": 1.0, | |
| "start_index": 548 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 556 | |
| }, | |
| { | |
| "text": "ุงูุฅู ุงู ", | |
| "confidence": 1.0, | |
| "start_index": 560 | |
| }, | |
| { | |
| "text": "ู ุณูู ", | |
| "confidence": 1.0, | |
| "start_index": 567 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 572 | |
| }, | |
| { | |
| "text": "ุงูุญุฌุงุฌ", | |
| "confidence": 1.0, | |
| "start_index": 575 | |
| }, | |
| { | |
| "text": "ุฑุญู ู", | |
| "confidence": 1.0, | |
| "start_index": 582 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 587 | |
| }, | |
| { | |
| "text": "ุงูู ุฐููุฑ", | |
| "confidence": 1.0, | |
| "start_index": 592 | |
| }, | |
| { | |
| "text": "ุฃููู", | |
| "confidence": 1.0, | |
| "start_index": 600 | |
| }, | |
| { | |
| "text": "ุงููุชุงุจ", | |
| "confidence": 1.0, | |
| "start_index": 605 | |
| }, | |
| { | |
| "text": "ูุงู:", | |
| "confidence": 1.0, | |
| "start_index": 612 | |
| }, | |
| { | |
| "text": "[2743]", | |
| "confidence": 1.0, | |
| "start_index": 617 | |
| }, | |
| { | |
| "text": "\\prod_{i=1}^{n}", | |
| "confidence": 1.0, | |
| "start_index": 624 | |
| }, | |
| { | |
| "text": "(1", | |
| "confidence": 1.0, | |
| "start_index": 640 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 643 | |
| }, | |
| { | |
| "text": "n_i)", | |
| "confidence": 1.0, | |
| "start_index": 645 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 650 | |
| }, | |
| { | |
| "text": "0", | |
| "confidence": 1.0, | |
| "start_index": 652 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 654 | |
| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 657 | |
| }, | |
| { | |
| "text": "(", | |
| "confidence": 1.0, | |
| "start_index": 664 | |
| }, | |
| { | |
| "text": "โฆ", | |
| "confidence": 1.0, | |
| "start_index": 666 | |
| }, | |
| { | |
| "text": ")", | |
| "confidence": 1.0, | |
| "start_index": 668 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 670 | |
| }, | |
| { | |
| "text": "(ููุญูุฏููุซูููู", | |
| "confidence": 1.0, | |
| "start_index": 672 | |
| }, | |
| { | |
| "text": "ุฒูููููุฑู", | |
| "confidence": 1.0, | |
| "start_index": 686 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 695 | |
| }, | |
| { | |
| "text": "ุญูุฑูุจูุ", | |
| "confidence": 1.0, | |
| "start_index": 700 | |
| }, | |
| { | |
| "text": "ููู ูุญูู ููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 708 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 720 | |
| }, | |
| { | |
| "text": "ุญูุงุชูู ูุ", | |
| "confidence": 1.0, | |
| "start_index": 725 | |
| }, | |
| { | |
| "text": "ุฌูู ููุนุงู", | |
| "confidence": 1.0, | |
| "start_index": 734 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 743 | |
| }, | |
| { | |
| "text": "ุงุจููู", | |
| "confidence": 1.0, | |
| "start_index": 747 | |
| }, | |
| { | |
| "text": "ู ูููุฏููููุ", | |
| "confidence": 1.0, | |
| "start_index": 753 | |
| }, | |
| { | |
| "text": "ููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 764 | |
| }, | |
| { | |
| "text": "ุฒูููููุฑู:", | |
| "confidence": 1.0, | |
| "start_index": 770 | |
| }, | |
| { | |
| "text": "ุญูุฏููุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 780 | |
| }, | |
| { | |
| "text": "ุนูุจูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 791 | |
| }, | |
| { | |
| "text": "ุงูุฑููุญูู ููู", | |
| "confidence": 1.0, | |
| "start_index": 798 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 810 | |
| }, | |
| { | |
| "text": "ู ูููุฏููููุ", | |
| "confidence": 1.0, | |
| "start_index": 815 | |
| }, | |
| { | |
| "text": "ุญูุฏููุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 826 | |
| }, | |
| { | |
| "text": "ุณููููู ู", | |
| "confidence": 1.0, | |
| "start_index": 837 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 845 | |
| }, | |
| { | |
| "text": "ุญููููุงููุ", | |
| "confidence": 1.0, | |
| "start_index": 850 | |
| }, | |
| { | |
| "text": "ุญูุฏููุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 860 | |
| }, | |
| { | |
| "text": "ุณูุนููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 871 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 879 | |
| }, | |
| { | |
| "text": "ู ููููุงุกูุ", | |
| "confidence": 1.0, | |
| "start_index": 884 | |
| }, | |
| { | |
| "text": "ููุงูู:", | |
| "confidence": 1.0, | |
| "start_index": 894 | |
| }, | |
| { | |
| "text": "ููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 901 | |
| }, | |
| { | |
| "text": "ุนูุจูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 907 | |
| }, | |
| { | |
| "text": "ุงูููู", | |
| "confidence": 1.0, | |
| "start_index": 914 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 920 | |
| }, | |
| { | |
| "text": "ุนูู ูุฑูู:", | |
| "confidence": 1.0, | |
| "start_index": 925 | |
| }, | |
| { | |
| "text": "ููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 934 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 940 | |
| }, | |
| { | |
| "text": "ุฑูุณูููู", | |
| "confidence": 1.0, | |
| "start_index": 944 | |
| }, | |
| { | |
| "text": "ุงูููู", | |
| "confidence": 1.0, | |
| "start_index": 952 | |
| }, | |
| { | |
| "text": "ุตูู", | |
| "confidence": 1.0, | |
| "start_index": 958 | |
| }, | |
| { | |
| "text": "ุงููู", | |
| "confidence": 1.0, | |
| "start_index": 962 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 967 | |
| }, | |
| { | |
| "text": "ูุณูู :", | |
| "confidence": 1.0, | |
| "start_index": 972 | |
| }, | |
| { | |
| "text": "\\sum_{\\lambda=0}^{M}", | |
| "confidence": 1.0, | |
| "start_index": 978 | |
| }, | |
| { | |
| "text": "\\frac{i^\\lambda}{\\lambda!}", | |
| "confidence": 1.0, | |
| "start_index": 999 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1026 | |
| }, | |
| { | |
| "text": "e^{i}", | |
| "confidence": 1.0, | |
| "start_index": 1028 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 1034 | |
| }, | |
| { | |
| "text": "\\frac{i}{x^2}", | |
| "confidence": 1.0, | |
| "start_index": 1036 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 1050 | |
| }, | |
| { | |
| "text": "ู ูุงุญุธุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1053 | |
| }, | |
| { | |
| "text": "\"ููุง", | |
| "confidence": 1.0, | |
| "start_index": 1060 | |
| }, | |
| { | |
| "text": "ุนูุจูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 1065 | |
| }, | |
| { | |
| "text": "ุงูููู", | |
| "confidence": 1.0, | |
| "start_index": 1072 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 1078 | |
| }, | |
| { | |
| "text": "ุนูู ูุฑููุ", | |
| "confidence": 1.0, | |
| "start_index": 1083 | |
| }, | |
| { | |
| "text": "ุจูููุบูููู", | |
| "confidence": 1.0, | |
| "start_index": 1092 | |
| }, | |
| { | |
| "text": "ุฃูููููู", | |
| "confidence": 1.0, | |
| "start_index": 1102 | |
| }, | |
| { | |
| "text": "ุชูุตููู ู", | |
| "confidence": 1.0, | |
| "start_index": 1110 | |
| }, | |
| { | |
| "text": "ุงููููููุงุฑูุ", | |
| "confidence": 1.0, | |
| "start_index": 1118 | |
| }, | |
| { | |
| "text": "ููุชููููู ู", | |
| "confidence": 1.0, | |
| "start_index": 1130 | |
| }, | |
| { | |
| "text": "ุงููููููููุ", | |
| "confidence": 1.0, | |
| "start_index": 1140 | |
| }, | |
| { | |
| "text": "ููููุง", | |
| "confidence": 1.0, | |
| "start_index": 1151 | |
| }, | |
| { | |
| "text": "ุชูููุนูููุ", | |
| "confidence": 1.0, | |
| "start_index": 1157 | |
| }, | |
| { | |
| "text": "ููุฅูููู", | |
| "confidence": 1.0, | |
| "start_index": 1167 | |
| }, | |
| { | |
| "text": "ููุฌูุณูุฏููู", | |
| "confidence": 1.0, | |
| "start_index": 1175 | |
| }, | |
| { | |
| "text": "ุนููููููู", | |
| "confidence": 1.0, | |
| "start_index": 1186 | |
| }, | |
| { | |
| "text": "ุญูุธููุงุ", | |
| "confidence": 1.0, | |
| "start_index": 1195 | |
| }, | |
| { | |
| "text": "ููุจุนููููููู", | |
| "confidence": 1.0, | |
| "start_index": 1203 | |
| }, | |
| { | |
| "text": "ุนููููููู", | |
| "confidence": 1.0, | |
| "start_index": 1215 | |
| }, | |
| { | |
| "text": "ุญูุธููุงุ", | |
| "confidence": 1.0, | |
| "start_index": 1224 | |
| }, | |
| { | |
| "text": "ููุฅูููู", | |
| "confidence": 1.0, | |
| "start_index": 1232 | |
| }, | |
| { | |
| "text": "ููุฒูููุฌููู", | |
| "confidence": 1.0, | |
| "start_index": 1240 | |
| }, | |
| { | |
| "text": "ุนููููููู", | |
| "confidence": 1.0, | |
| "start_index": 1251 | |
| }, | |
| { | |
| "text": "ุญูุธููุงุ", | |
| "confidence": 1.0, | |
| "start_index": 1260 | |
| }, | |
| { | |
| "text": "ุตูู ูุ", | |
| "confidence": 1.0, | |
| "start_index": 1268 | |
| }, | |
| { | |
| "text": "ููุฃูููุทูุฑูุ", | |
| "confidence": 1.0, | |
| "start_index": 1274 | |
| }, | |
| { | |
| "text": "ุตูู ู", | |
| "confidence": 1.0, | |
| "start_index": 1286 | |
| }, | |
| { | |
| "text": "ู ููู", | |
| "confidence": 1.0, | |
| "start_index": 1291 | |
| }, | |
| { | |
| "text": "ููููู", | |
| "confidence": 1.0, | |
| "start_index": 1296 | |
| }, | |
| { | |
| "text": "ุดูููุฑู", | |
| "confidence": 1.0, | |
| "start_index": 1302 | |
| }, | |
| { | |
| "text": "ุซูููุงุซูุฉู", | |
| "confidence": 1.0, | |
| "start_index": 1309 | |
| }, | |
| { | |
| "text": "ุฃููููุงู ูุ", | |
| "confidence": 1.0, | |
| "start_index": 1319 | |
| }, | |
| { | |
| "text": "ููุฐููููู", | |
| "confidence": 1.0, | |
| "start_index": 1329 | |
| }, | |
| { | |
| "text": "ุตูููู ู", | |
| "confidence": 1.0, | |
| "start_index": 1338 | |
| }, | |
| { | |
| "text": "ุงูุฏููููุฑู\"ุ", | |
| "confidence": 1.0, | |
| "start_index": 1345 | |
| }, | |
| { | |
| "text": "ููููุชู:", | |
| "confidence": 1.0, | |
| "start_index": 1357 | |
| }, | |
| { | |
| "text": "ููุง", | |
| "confidence": 1.0, | |
| "start_index": 1365 | |
| }, | |
| { | |
| "text": "ุฑูุณูููู", | |
| "confidence": 1.0, | |
| "start_index": 1369 | |
| }, | |
| { | |
| "text": "ุงูููู", | |
| "confidence": 1.0, | |
| "start_index": 1377 | |
| }, | |
| { | |
| "text": "ุฅูู", | |
| "confidence": 1.0, | |
| "start_index": 1383 | |
| }, | |
| { | |
| "text": "ุจูู", | |
| "confidence": 1.0, | |
| "start_index": 1387 | |
| }, | |
| { | |
| "text": "ูููููุฉูุ", | |
| "confidence": 1.0, | |
| "start_index": 1391 | |
| }, | |
| { | |
| "text": "ููุงูู:", | |
| "confidence": 1.0, | |
| "start_index": 1400 | |
| }, | |
| { | |
| "text": "\\frac{\\partial", | |
| "confidence": 1.0, | |
| "start_index": 1407 | |
| }, | |
| { | |
| "text": "\\lambda}{\\partial", | |
| "confidence": 1.0, | |
| "start_index": 1422 | |
| }, | |
| { | |
| "text": "\\beta}", | |
| "confidence": 1.0, | |
| "start_index": 1440 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1447 | |
| }, | |
| { | |
| "text": "\\lim_{h", | |
| "confidence": 1.0, | |
| "start_index": 1449 | |
| }, | |
| { | |
| "text": "\\to", | |
| "confidence": 1.0, | |
| "start_index": 1457 | |
| }, | |
| { | |
| "text": "0}", | |
| "confidence": 1.0, | |
| "start_index": 1461 | |
| }, | |
| { | |
| "text": "\\frac{\\sin(\\beta", | |
| "confidence": 1.0, | |
| "start_index": 1464 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 1481 | |
| }, | |
| { | |
| "text": "h)", | |
| "confidence": 1.0, | |
| "start_index": 1483 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1486 | |
| }, | |
| { | |
| "text": "\\sin(\\beta)}{h}", | |
| "confidence": 1.0, | |
| "start_index": 1488 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 1504 | |
| }, | |
| { | |
| "text": "\\frac{\\alpha}{j^2}", | |
| "confidence": 1.0, | |
| "start_index": 1506 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
| "confidence": 1.0, | |
| "start_index": 1525 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1532 | |
| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 1534 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 1544 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
| "start_index": 1549 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 1559 | |
| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1562 | |
| }, | |
| { | |
| "text": "\"ููุตูู ู", | |
| "confidence": 1.0, | |
| "start_index": 1569 | |
| }, | |
| { | |
| "text": "ุตูููู ู", | |
| "confidence": 1.0, | |
| "start_index": 1577 | |
| }, | |
| { | |
| "text": "ุฏูุงููุฏูุ", | |
| "confidence": 1.0, | |
| "start_index": 1584 | |
| }, | |
| { | |
| "text": "ุตูู ู", | |
| "confidence": 1.0, | |
| "start_index": 1593 | |
| }, | |
| { | |
| "text": "ููููู ุงูุ", | |
| "confidence": 1.0, | |
| "start_index": 1598 | |
| }, | |
| { | |
| "text": "ููุฃูููุทูุฑู", | |
| "confidence": 1.0, | |
| "start_index": 1607 | |
| }, | |
| { | |
| "text": "ููููู ุงู\"ุ", | |
| "confidence": 1.0, | |
| "start_index": 1618 | |
| }, | |
| { | |
| "text": "ููููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 1628 | |
| }, | |
| { | |
| "text": "ููููููู:", | |
| "confidence": 1.0, | |
| "start_index": 1636 | |
| }, | |
| { | |
| "text": "ููุง", | |
| "confidence": 1.0, | |
| "start_index": 1645 | |
| }, | |
| { | |
| "text": "ููููุชูููู", | |
| "confidence": 1.0, | |
| "start_index": 1649 | |
| }, | |
| { | |
| "text": "ุฃูุฎูุฐูุชู", | |
| "confidence": 1.0, | |
| "start_index": 1659 | |
| }, | |
| { | |
| "text": "ุจูุงูุฑููุฎูุตูุฉู).", | |
| "confidence": 1.0, | |
| "start_index": 1668 | |
| }, | |
| { | |
| "text": "ุฑุฌุงู", | |
| "confidence": 1.0, | |
| "start_index": 1684 | |
| }, | |
| { | |
| "text": "ูุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 1689 | |
| }, | |
| { | |
| "text": "ุงูุฅุณูุงุฏ:", | |
| "confidence": 1.0, | |
| "start_index": 1693 | |
| }, | |
| { | |
| "text": "ุณุชุฉ:", | |
| "confidence": 1.0, | |
| "start_index": 1702 | |
| }, | |
| { | |
| "text": "1", | |
| "confidence": 1.0, | |
| "start_index": 1707 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1709 | |
| }, | |
| { | |
| "text": "(ุนูุจูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 1711 | |
| }, | |
| { | |
| "text": "ุงูุฑููุญูู ููู", | |
| "confidence": 1.0, | |
| "start_index": 1719 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 1731 | |
| }, | |
| { | |
| "text": "ู ูููุฏูููู)", | |
| "confidence": 1.0, | |
| "start_index": 1736 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 1747 | |
| }, | |
| { | |
| "text": "ุญุณูุงู", | |
| "confidence": 1.0, | |
| "start_index": 1750 | |
| }, | |
| { | |
| "text": "ุงููุนููุจุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 1756 | |
| }, | |
| { | |
| "text": "ู ููุงูู ุ", | |
| "confidence": 1.0, | |
| "start_index": 1767 | |
| }, | |
| { | |
| "text": "ุฃุจู", | |
| "confidence": 1.0, | |
| "start_index": 1775 | |
| }, | |
| { | |
| "text": "ุณุนูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 1779 | |
| }, | |
| { | |
| "text": "z_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 1784 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1792 | |
| }, | |
| { | |
| "text": "z_n", | |
| "confidence": 1.0, | |
| "start_index": 1794 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1798 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 1800 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 1807 | |
| }, | |
| { | |
| "text": "f(z_n)", | |
| "confidence": 1.0, | |
| "start_index": 1814 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
| "confidence": 1.0, | |
| "start_index": 1821 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1828 | |
| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 1830 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 1840 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
| "start_index": 1845 | |
| } | |
| ], | |
| "average_page_confidence_score": 1.0, | |
| "minimum_page_confidence_score": 1.0 | |
| }, | |
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| "top_left_x": 40, | |
| "top_left_y": 46, | |
| "bottom_right_x": 731, | |
| "bottom_right_y": 87, | |
| "content": "\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n)", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 1 | |
| }, | |
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| "content": "ุจุฑูุงู", | |
| "type": "title", | |
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| "reading_index": 2 | |
| }, | |
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| "top_left_x": 52, | |
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| "bottom_right_x": 715, | |
| "bottom_right_y": 171, | |
| "content": "\"ุตู ุซูุงุซุฉุ ููู ุฃุฌุฑ ุซู ุงููุฉ\". ููุฐุง ูุฏูุน ูู ุตุฏุฑ ุงูุชุฃููู ุงูุฃููุ ูุงููู ุฃุนูู ุ ุฃูุงุฏู ูู \"ุงููุชุญ\" (1) . ูุงู ุงูุฌุงู ุน ุนูุง ุงููู ุนูู: ุนูุฏู ุงูุฃูุฑุจ ุญู ู ุงูุญุฏูุซ ุนูู ุธุงูุฑูุ ููู ุงูุงุญุชู ุงู", | |
| "type": "text", | |
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| "top_left_x": 52, | |
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| "bottom_right_x": 715, | |
| "bottom_right_y": 232, | |
| "content": "\\frac{\\partial y}{\\partial j} = \\lim_{h \\to 0} \\frac{\\log(j + h) - \\log(j)}{h} + \\frac{t}{i^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
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| "content": "ูุธุฑูุฉ", | |
| "type": "title", | |
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| "content": "ุงูุฃุฎูุฑ ุงูุฐู ู ุฑู ุขููุงู ูู ุนุจุงุฑุฉ \"ุงููุชุญ\"ุ ูุฅูู ุง ููุต ุงูุฃุฌุฑ ู ุน ุฒูุงุฏุฉ ุงูุนู ูุ ููู ูุง ุฐูููุฑ ู ู ุชุฑุชูุจ ุชูููุช ุจุนุถ ุงูุนุจุงุฏุงุช ุจุณุจุจ ู ุดููุฉ ุงูุตูู ุ ูุชุจุตูุฑุ ูุงููู ุชุนุงูู ุฃุนูู ุจุงูุตูุงุจุ ูุฅููู ุงูู ุฑุฌุน ูุงูู ุขุจุ ููู ุญุณุจูุง ููุนู ุงููููู. ูุจุงูุณูุฏ ุงูู ุชูุตู ุฅูู ุงูุฅู ุงู ู ุณูู ุจู ุงูุญุฌุงุฌ ุฑุญู ู ุงููู ุงูู ุฐููุฑ ุฃููู ุงููุชุงุจ ูุงู: [2743]", | |
| "type": "text", | |
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| { | |
| "top_left_x": 52, | |
| "top_left_y": 372, | |
| "bottom_right_x": 715, | |
| "bottom_right_y": 436, | |
| "content": "\\prod_{i=1}^{n} (1 - n_i) = 0", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 7 | |
| }, | |
| { | |
| "top_left_x": 52, | |
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| "bottom_right_x": 715, | |
| "bottom_right_y": 497, | |
| "content": "ู ุจุฑููุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 8 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 502, | |
| "bottom_right_x": 715, | |
| "bottom_right_y": 547, | |
| "content": "( โฆ ) - (ููุญูุฏููุซูููู ุฒูููููุฑู ุจููู ุญูุฑูุจูุ ููู ูุญูู ููุฏู ุจููู ุญูุงุชูู ูุ ุฌูู ููุนุงู ุนูู ุงุจููู ู ูููุฏููููุ ููุงูู ุฒูููููุฑู: ุญูุฏููุซูููุง ุนูุจูุฏู ุงูุฑููุญูู ููู ุจููู ู ูููุฏููููุ ุญูุฏููุซูููุง ุณููููู ู ุจููู ุญููููุงููุ ุญูุฏููุซูููุง ุณูุนููุฏู ุจููู ู ููููุงุกูุ ููุงูู: ููุงูู ุนูุจูุฏู ุงูููู ุจููู ุนูู ูุฑูู: ููุงูู ููู ุฑูุณูููู ุงูููู ุตูู ุงููู ุนููู ูุณูู :", | |
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| "content": "\\sum_{\\lambda=0}^{M} \\frac{i^\\lambda}{\\lambda!} = e^{i} + \\frac{i}{x^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 10 | |
| }, | |
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| "bottom_right_x": 715, | |
| "bottom_right_y": 681, | |
| "content": "ู ูุงุญุธุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 11 | |
| }, | |
| { | |
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| "content": "\"ููุง ุนูุจูุฏู ุงูููู ุจููู ุนูู ูุฑููุ ุจูููุบูููู ุฃูููููู ุชูุตููู ู ุงููููููุงุฑูุ ููุชููููู ู ุงููููููููุ ููููุง ุชูููุนูููุ ููุฅูููู ููุฌูุณูุฏููู ุนููููููู ุญูุธููุงุ ููุจุนููููููู ุนููููููู ุญูุธููุงุ ููุฅูููู ููุฒูููุฌููู ุนููููููู ุญูุธููุงุ ุตูู ูุ ููุฃูููุทูุฑูุ ุตูู ู ู ููู ููููู ุดูููุฑู ุซูููุงุซูุฉู ุฃููููุงู ูุ ููุฐููููู ุตูููู ู ุงูุฏููููุฑู\"ุ ููููุชู: ููุง ุฑูุณูููู ุงูููู ุฅูู ุจูู ูููููุฉูุ ููุงูู:", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 12 | |
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| "top_left_x": 52, | |
| "top_left_y": 760, | |
| "bottom_right_x": 715, | |
| "bottom_right_y": 815, | |
| "content": "\\frac{\\partial \\lambda}{\\partial \\beta} = \\lim_{h \\to 0} \\frac{\\sin(\\beta + h) - \\sin(\\beta)}{h} + \\frac{\\alpha}{j^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 13 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 847, | |
| "bottom_right_x": 731, | |
| "bottom_right_y": 903, | |
| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 14 | |
| }, | |
| { | |
| "top_left_x": 52, | |
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| "bottom_right_x": 715, | |
| "bottom_right_y": 938, | |
| "content": "ู ุจุฑููุฉ", | |
| "type": "title", | |
| "confidence_scores": null, | |
| "reading_index": 15 | |
| }, | |
| { | |
| "top_left_x": 52, | |
| "top_left_y": 943, | |
| "bottom_right_x": 715, | |
| "bottom_right_y": 987, | |
| "content": "\"ููุตูู ู ุตูููู ู ุฏูุงููุฏูุ ุตูู ู ููููู ุงูุ ููุฃูููุทูุฑู ููููู ุงู\"ุ ููููุงูู ููููููู: ููุง ููููุชูููู ุฃูุฎูุฐูุชู ุจูุงูุฑููุฎูุตูุฉู). ุฑุฌุงู ูุฐุง ุงูุฅุณูุงุฏ: ุณุชุฉ: 1 - (ุนูุจูุฏู ุงูุฑููุญูู ููู ุจููู ู ูููุฏูููู) ุจู ุญุณูุงู ุงููุนููุจุฑูู ู ููุงูู ุ ุฃุจู ุณุนูุฏ", | |
| "type": "text", | |
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| "top_left_x": 52, | |
| "top_left_y": 993, | |
| "bottom_right_x": 715, | |
| "bottom_right_y": 1032, | |
| "content": "z_{n+1} = z_n - \\alpha \\nabla f(z_n)", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 17 | |
| }, | |
| { | |
| "top_left_x": 40, | |
| "top_left_y": 1064, | |
| "bottom_right_x": 731, | |
| "bottom_right_y": 1128, | |
| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 18 | |
| } | |
| ], | |
| "meta": { | |
| "template": "math_proof", | |
| "hybrid": null, | |
| "page_font": "Almarai-ExtraBold.ttf", | |
| "title_font": "Almarai-ExtraBold.ttf", | |
| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
| } | |
| } |