Download data/MachineFour_002/annotations/sample_0010005.json from OCR-Data/dataset: direct link, hf CLI and curl.
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hf download hf://datasets/OCR-Data/dataset/data/MachineFour_002/annotations/sample_0010005.json
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curl -L -o sample_0010005.json https://huggingface.co/datasets/OCR-Data/dataset/resolve/main/data/MachineFour_002/annotations/sample_0010005.json
50.6 kB
| { | |
| "markdown": "## ุชุนุฑูู\nููุงู ุดุฑูุท ูุง ุจุฏูู ู ู ุชูุงูุฑูุง (1) ุ ูุฐู ุงูุดุฑูุท ุฅุฐุง ุชููุฑุช ูุฌุจ ุงูุญุฌุ ููุฐู ุงูุดุฑูุท ู ููุง ู ุง ูู ุดุฑูุท ุตุญุฉุ ูู ููุง ู ุง ูู ุดุฑูุท\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ู ุจุฑููุฉ\nูุฌูุจุ ูููุงู ู ูู ูุฌุจ ุนููู ุงูุญุฌ ููุตุญ ู ููุ ูููุงู ู ูู ููุทูุจ ู ููู ูุฐุง ุงููุฑุถ ููู ูุง ูุตุญูู ู ููู ุ ูููุงู ู ูู ูุตุญ ู ููู ุ ููู ูุง ูููููู ุนู ุญุฌุฉ ุงูุฅุณูุงู ุ ูุงูุตุจู (2) ุ\n\\nabla_{\\lambda} J(\\lambda) = \\frac{1}{m} X^T ( \\sigma(X \\lambda) - Y )\n## ู ุจุฑููุฉ\nููุชุถู ุงูู ุดุงุฑูุฉ ุจุงูุฑุจุญุ ูุฅุฐุง ุดุฑุท ุงุฎุชุตุงุต ุฃุญุฏูู ุง ุจุงูุฑุจุญ ููุฏ ุดุฑุท ู ุง ููุงูู ู ูุชุถู ุงูุนูุฏ. ููุฐุง ู ุฐูุจ ุงูุดุงูุนูุฉ ูุงูุญูุงุจูุฉ (1) . ูุงู ุงูุดูุฑุงุฒู: ยซูุฅู ูุงู: ูุงุฑุถุชู ุนูู ุฃู ุงูุฑุจุญ ููู ููุ ุฃู ููู ููุ ุจุทู ุงููุฑุงุถุ ูุฃู ู ูุถูุนู ุนูู ุงูุงุดุชุฑุงู ูู ุงูุฑุจุญุ\n\\vec{F} = m\\vec{a}\n## ูุธุฑูุฉ\nูุฅุฐุง ุดุฑุท ุงูุฑุจุญ ูุฃุญุฏูู ุง ููุฏ ุดุฑุท ู ุง ููุงูู ู ูุชุถุงูุ ูุจุทู. ูุฅู ุฏูุน ุฅููู ุฃูููุงุ ููุงู: ุชุตุฑู ูููุ ูุงูุฑุจุญ ููู ููุ ููู ูุฑุถุ ูุง ุญู ูุฑุจ ุงูู ุงู ูู ุฑุจุญูุ ูุฃู ุงูููุธ ู ุดุชุฑู ุจูู ุงููุฑุงุถ ูุงููุฑุถุ ููุฏ ูุฑู ุจู ุญูู ุงููุฑุถุ ูุงูุนูุฏ ุงููุฑุถ ุจูุ\n\\prod_{x=1}^{n} (1 \\leq j_x) = 0\n## ุชุนุฑูู\nูููุธ ุงูุชู ููู ูู ุง ูุงู ู ุดุชุฑููุง ุจูู ุงูุจูุน ูุงููุจุฉ ุฅุฐุง ูุฑู ุจู ุงูุซู ู ูุงู ุจูุนูุงยป (2) . โ โุงูุฑุงุฌุญ ู ู ุงูุฎูุงู: ุฃุฑ ู ุฃู ููู ุงูู ุงูููุฉ ููู ูุณุทุ ุจูู ุงูุญูููุฉ ุงูุฐูู ุฃูุบูุง ุงูููุธ ูุตุญุญูุง ุงูุนูุฏ ูุญู ููู ุนูู ุนูุฏ ุขุฎุฑุ ูุจูู ุงูุดุงูุนูุฉ ูุงูุญูุงุจูุฉ ุงูุฐูู ุฃูุณุฏูุง ุงูุนูุฏุ ููู ุงุนุชุจุฑูุง\n\\iint_{D} n^2 \\times \\lambda^2 \\, dx \\, dy\n## ุชุนุฑูู\nุงูููุธ ููู ูุฎุฑุฌูู ุนู ุงููุฑุงุถุ ูุตุญุญูุง ุงูุนูุฏุ ูุฌุนููู ู ู ูุจูู ุงูุชุจุฑุน ุจูุตูุจูุ ูุงููู ุฃุนูู . * * *\nj_{n+1} = j_n - \\alpha \\nabla f(j_n) + \\frac{\\theta}{t^2}\n\\sum_{z=0}^{\\infty} \\frac{\\theta^z}{z!} = e^{\\theta}\nP(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{\\lambda}{\\theta^2}\n\\nabla_{\\lambda} J(\\lambda) = \\frac{1}{m} X^T ( \\sigma(X \\lambda) - Y )", | |
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| "text": "ููุงู", | |
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| "text": "ุดุฑูุท", | |
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| "text": "ูุง", | |
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| "text": "ุจุฏูู", | |
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| { | |
| "text": "ู ู", | |
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| "text": "ุชูุงูุฑูุง", | |
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| "text": "ุฅุฐุง", | |
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| "text": "ุชููุฑุช", | |
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| "text": "ูุฌุจ", | |
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| "confidence": 1.0, | |
| "start_index": 487 | |
| }, | |
| { | |
| "text": "ู ุฐูุจ", | |
| "confidence": 1.0, | |
| "start_index": 492 | |
| }, | |
| { | |
| "text": "ุงูุดุงูุนูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 497 | |
| }, | |
| { | |
| "text": "ูุงูุญูุงุจูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 506 | |
| }, | |
| { | |
| "text": "(1)", | |
| "confidence": 1.0, | |
| "start_index": 516 | |
| }, | |
| { | |
| "text": ".", | |
| "confidence": 1.0, | |
| "start_index": 520 | |
| }, | |
| { | |
| "text": "ูุงู", | |
| "confidence": 1.0, | |
| "start_index": 522 | |
| }, | |
| { | |
| "text": "ุงูุดูุฑุงุฒู:", | |
| "confidence": 1.0, | |
| "start_index": 526 | |
| }, | |
| { | |
| "text": "ยซูุฅู", | |
| "confidence": 1.0, | |
| "start_index": 536 | |
| }, | |
| { | |
| "text": "ูุงู:", | |
| "confidence": 1.0, | |
| "start_index": 541 | |
| }, | |
| { | |
| "text": "ูุงุฑุถุชู", | |
| "confidence": 1.0, | |
| "start_index": 546 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 553 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 557 | |
| }, | |
| { | |
| "text": "ุงูุฑุจุญ", | |
| "confidence": 1.0, | |
| "start_index": 560 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 566 | |
| }, | |
| { | |
| "text": "ููุ", | |
| "confidence": 1.0, | |
| "start_index": 570 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 574 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 577 | |
| }, | |
| { | |
| "text": "ููุ", | |
| "confidence": 1.0, | |
| "start_index": 581 | |
| }, | |
| { | |
| "text": "ุจุทู", | |
| "confidence": 1.0, | |
| "start_index": 585 | |
| }, | |
| { | |
| "text": "ุงููุฑุงุถุ", | |
| "confidence": 1.0, | |
| "start_index": 589 | |
| }, | |
| { | |
| "text": "ูุฃู", | |
| "confidence": 1.0, | |
| "start_index": 597 | |
| }, | |
| { | |
| "text": "ู ูุถูุนู", | |
| "confidence": 1.0, | |
| "start_index": 601 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 608 | |
| }, | |
| { | |
| "text": "ุงูุงุดุชุฑุงู", | |
| "confidence": 1.0, | |
| "start_index": 612 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 621 | |
| }, | |
| { | |
| "text": "ุงูุฑุจุญุ", | |
| "confidence": 1.0, | |
| "start_index": 624 | |
| }, | |
| { | |
| "text": "\\vec{F}", | |
| "confidence": 1.0, | |
| "start_index": 631 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 639 | |
| }, | |
| { | |
| "text": "m\\vec{a}", | |
| "confidence": 1.0, | |
| "start_index": 641 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 650 | |
| }, | |
| { | |
| "text": "ูุธุฑูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 653 | |
| }, | |
| { | |
| "text": "ูุฅุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 659 | |
| }, | |
| { | |
| "text": "ุดุฑุท", | |
| "confidence": 1.0, | |
| "start_index": 664 | |
| }, | |
| { | |
| "text": "ุงูุฑุจุญ", | |
| "confidence": 1.0, | |
| "start_index": 668 | |
| }, | |
| { | |
| "text": "ูุฃุญุฏูู ุง", | |
| "confidence": 1.0, | |
| "start_index": 674 | |
| }, | |
| { | |
| "text": "ููุฏ", | |
| "confidence": 1.0, | |
| "start_index": 682 | |
| }, | |
| { | |
| "text": "ุดุฑุท", | |
| "confidence": 1.0, | |
| "start_index": 686 | |
| }, | |
| { | |
| "text": "ู ุง", | |
| "confidence": 1.0, | |
| "start_index": 690 | |
| }, | |
| { | |
| "text": "ููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 693 | |
| }, | |
| { | |
| "text": "ู ูุชุถุงูุ", | |
| "confidence": 1.0, | |
| "start_index": 699 | |
| }, | |
| { | |
| "text": "ูุจุทู.", | |
| "confidence": 1.0, | |
| "start_index": 707 | |
| }, | |
| { | |
| "text": "ูุฅู", | |
| "confidence": 1.0, | |
| "start_index": 713 | |
| }, | |
| { | |
| "text": "ุฏูุน", | |
| "confidence": 1.0, | |
| "start_index": 717 | |
| }, | |
| { | |
| "text": "ุฅููู", | |
| "confidence": 1.0, | |
| "start_index": 721 | |
| }, | |
| { | |
| "text": "ุฃูููุงุ", | |
| "confidence": 1.0, | |
| "start_index": 726 | |
| }, | |
| { | |
| "text": "ููุงู:", | |
| "confidence": 1.0, | |
| "start_index": 733 | |
| }, | |
| { | |
| "text": "ุชุตุฑู", | |
| "confidence": 1.0, | |
| "start_index": 739 | |
| }, | |
| { | |
| "text": "ูููุ", | |
| "confidence": 1.0, | |
| "start_index": 744 | |
| }, | |
| { | |
| "text": "ูุงูุฑุจุญ", | |
| "confidence": 1.0, | |
| "start_index": 749 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 756 | |
| }, | |
| { | |
| "text": "ููุ", | |
| "confidence": 1.0, | |
| "start_index": 760 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 764 | |
| }, | |
| { | |
| "text": "ูุฑุถุ", | |
| "confidence": 1.0, | |
| "start_index": 768 | |
| }, | |
| { | |
| "text": "ูุง", | |
| "confidence": 1.0, | |
| "start_index": 773 | |
| }, | |
| { | |
| "text": "ุญู", | |
| "confidence": 1.0, | |
| "start_index": 776 | |
| }, | |
| { | |
| "text": "ูุฑุจ", | |
| "confidence": 1.0, | |
| "start_index": 779 | |
| }, | |
| { | |
| "text": "ุงูู ุงู", | |
| "confidence": 1.0, | |
| "start_index": 783 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 789 | |
| }, | |
| { | |
| "text": "ุฑุจุญูุ", | |
| "confidence": 1.0, | |
| "start_index": 792 | |
| }, | |
| { | |
| "text": "ูุฃู", | |
| "confidence": 1.0, | |
| "start_index": 798 | |
| }, | |
| { | |
| "text": "ุงูููุธ", | |
| "confidence": 1.0, | |
| "start_index": 802 | |
| }, | |
| { | |
| "text": "ู ุดุชุฑู", | |
| "confidence": 1.0, | |
| "start_index": 808 | |
| }, | |
| { | |
| "text": "ุจูู", | |
| "confidence": 1.0, | |
| "start_index": 814 | |
| }, | |
| { | |
| "text": "ุงููุฑุงุถ", | |
| "confidence": 1.0, | |
| "start_index": 818 | |
| }, | |
| { | |
| "text": "ูุงููุฑุถุ", | |
| "confidence": 1.0, | |
| "start_index": 825 | |
| }, | |
| { | |
| "text": "ููุฏ", | |
| "confidence": 1.0, | |
| "start_index": 833 | |
| }, | |
| { | |
| "text": "ูุฑู", | |
| "confidence": 1.0, | |
| "start_index": 837 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 841 | |
| }, | |
| { | |
| "text": "ุญูู ", | |
| "confidence": 1.0, | |
| "start_index": 844 | |
| }, | |
| { | |
| "text": "ุงููุฑุถุ", | |
| "confidence": 1.0, | |
| "start_index": 848 | |
| }, | |
| { | |
| "text": "ูุงูุนูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 855 | |
| }, | |
| { | |
| "text": "ุงููุฑุถ", | |
| "confidence": 1.0, | |
| "start_index": 862 | |
| }, | |
| { | |
| "text": "ุจูุ", | |
| "confidence": 1.0, | |
| "start_index": 868 | |
| }, | |
| { | |
| "text": "\\prod_{x=1}^{n}", | |
| "confidence": 1.0, | |
| "start_index": 872 | |
| }, | |
| { | |
| "text": "(1", | |
| "confidence": 1.0, | |
| "start_index": 888 | |
| }, | |
| { | |
| "text": "\\leq", | |
| "confidence": 1.0, | |
| "start_index": 891 | |
| }, | |
| { | |
| "text": "j_x)", | |
| "confidence": 1.0, | |
| "start_index": 896 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 901 | |
| }, | |
| { | |
| "text": "0", | |
| "confidence": 1.0, | |
| "start_index": 903 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 905 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 908 | |
| }, | |
| { | |
| "text": "ูููุธ", | |
| "confidence": 1.0, | |
| "start_index": 914 | |
| }, | |
| { | |
| "text": "ุงูุชู ููู", | |
| "confidence": 1.0, | |
| "start_index": 919 | |
| }, | |
| { | |
| "text": "ูู ุง", | |
| "confidence": 1.0, | |
| "start_index": 927 | |
| }, | |
| { | |
| "text": "ูุงู", | |
| "confidence": 1.0, | |
| "start_index": 931 | |
| }, | |
| { | |
| "text": "ู ุดุชุฑููุง", | |
| "confidence": 1.0, | |
| "start_index": 935 | |
| }, | |
| { | |
| "text": "ุจูู", | |
| "confidence": 1.0, | |
| "start_index": 943 | |
| }, | |
| { | |
| "text": "ุงูุจูุน", | |
| "confidence": 1.0, | |
| "start_index": 947 | |
| }, | |
| { | |
| "text": "ูุงููุจุฉ", | |
| "confidence": 1.0, | |
| "start_index": 953 | |
| }, | |
| { | |
| "text": "ุฅุฐุง", | |
| "confidence": 1.0, | |
| "start_index": 960 | |
| }, | |
| { | |
| "text": "ูุฑู", | |
| "confidence": 1.0, | |
| "start_index": 964 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 968 | |
| }, | |
| { | |
| "text": "ุงูุซู ู", | |
| "confidence": 1.0, | |
| "start_index": 971 | |
| }, | |
| { | |
| "text": "ูุงู", | |
| "confidence": 1.0, | |
| "start_index": 977 | |
| }, | |
| { | |
| "text": "ุจูุนูุงยป", | |
| "confidence": 1.0, | |
| "start_index": 981 | |
| }, | |
| { | |
| "text": "(2)", | |
| "confidence": 1.0, | |
| "start_index": 988 | |
| }, | |
| { | |
| "text": ".", | |
| "confidence": 1.0, | |
| "start_index": 992 | |
| }, | |
| { | |
| "text": "โ", | |
| "confidence": 1.0, | |
| "start_index": 994 | |
| }, | |
| { | |
| "text": "โุงูุฑุงุฌุญ", | |
| "confidence": 1.0, | |
| "start_index": 996 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 1004 | |
| }, | |
| { | |
| "text": "ุงูุฎูุงู:", | |
| "confidence": 1.0, | |
| "start_index": 1007 | |
| }, | |
| { | |
| "text": "ุฃุฑ", | |
| "confidence": 1.0, | |
| "start_index": 1015 | |
| }, | |
| { | |
| "text": "ู", | |
| "confidence": 1.0, | |
| "start_index": 1018 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 1020 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 1023 | |
| }, | |
| { | |
| "text": "ุงูู ุงูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1027 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 1036 | |
| }, | |
| { | |
| "text": "ูุณุทุ", | |
| "confidence": 1.0, | |
| "start_index": 1040 | |
| }, | |
| { | |
| "text": "ุจูู", | |
| "confidence": 1.0, | |
| "start_index": 1045 | |
| }, | |
| { | |
| "text": "ุงูุญูููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1049 | |
| }, | |
| { | |
| "text": "ุงูุฐูู", | |
| "confidence": 1.0, | |
| "start_index": 1057 | |
| }, | |
| { | |
| "text": "ุฃูุบูุง", | |
| "confidence": 1.0, | |
| "start_index": 1063 | |
| }, | |
| { | |
| "text": "ุงูููุธ", | |
| "confidence": 1.0, | |
| "start_index": 1069 | |
| }, | |
| { | |
| "text": "ูุตุญุญูุง", | |
| "confidence": 1.0, | |
| "start_index": 1075 | |
| }, | |
| { | |
| "text": "ุงูุนูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 1082 | |
| }, | |
| { | |
| "text": "ูุญู ููู", | |
| "confidence": 1.0, | |
| "start_index": 1088 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 1095 | |
| }, | |
| { | |
| "text": "ุนูุฏ", | |
| "confidence": 1.0, | |
| "start_index": 1099 | |
| }, | |
| { | |
| "text": "ุขุฎุฑุ", | |
| "confidence": 1.0, | |
| "start_index": 1103 | |
| }, | |
| { | |
| "text": "ูุจูู", | |
| "confidence": 1.0, | |
| "start_index": 1108 | |
| }, | |
| { | |
| "text": "ุงูุดุงูุนูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1113 | |
| }, | |
| { | |
| "text": "ูุงูุญูุงุจูุฉ", | |
| "confidence": 1.0, | |
| "start_index": 1122 | |
| }, | |
| { | |
| "text": "ุงูุฐูู", | |
| "confidence": 1.0, | |
| "start_index": 1132 | |
| }, | |
| { | |
| "text": "ุฃูุณุฏูุง", | |
| "confidence": 1.0, | |
| "start_index": 1138 | |
| }, | |
| { | |
| "text": "ุงูุนูุฏุ", | |
| "confidence": 1.0, | |
| "start_index": 1145 | |
| }, | |
| { | |
| "text": "ููู ", | |
| "confidence": 1.0, | |
| "start_index": 1152 | |
| }, | |
| { | |
| "text": "ุงุนุชุจุฑูุง", | |
| "confidence": 1.0, | |
| "start_index": 1156 | |
| }, | |
| { | |
| "text": "\\iint_{D}", | |
| "confidence": 1.0, | |
| "start_index": 1164 | |
| }, | |
| { | |
| "text": "n^2", | |
| "confidence": 1.0, | |
| "start_index": 1174 | |
| }, | |
| { | |
| "text": "\\times", | |
| "confidence": 1.0, | |
| "start_index": 1178 | |
| }, | |
| { | |
| "text": "\\lambda^2", | |
| "confidence": 1.0, | |
| "start_index": 1185 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 1195 | |
| }, | |
| { | |
| "text": "dx", | |
| "confidence": 1.0, | |
| "start_index": 1198 | |
| }, | |
| { | |
| "text": "\\,", | |
| "confidence": 1.0, | |
| "start_index": 1201 | |
| }, | |
| { | |
| "text": "dy", | |
| "confidence": 1.0, | |
| "start_index": 1204 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 1207 | |
| }, | |
| { | |
| "text": "ุชุนุฑูู", | |
| "confidence": 1.0, | |
| "start_index": 1210 | |
| }, | |
| { | |
| "text": "ุงูููุธ", | |
| "confidence": 1.0, | |
| "start_index": 1216 | |
| }, | |
| { | |
| "text": "ููู ", | |
| "confidence": 1.0, | |
| "start_index": 1222 | |
| }, | |
| { | |
| "text": "ูุฎุฑุฌูู", | |
| "confidence": 1.0, | |
| "start_index": 1226 | |
| }, | |
| { | |
| "text": "ุนู", | |
| "confidence": 1.0, | |
| "start_index": 1233 | |
| }, | |
| { | |
| "text": "ุงููุฑุงุถุ", | |
| "confidence": 1.0, | |
| "start_index": 1236 | |
| }, | |
| { | |
| "text": "ูุตุญุญูุง", | |
| "confidence": 1.0, | |
| "start_index": 1244 | |
| }, | |
| { | |
| "text": "ุงูุนูุฏุ", | |
| "confidence": 1.0, | |
| "start_index": 1251 | |
| }, | |
| { | |
| "text": "ูุฌุนููู", | |
| "confidence": 1.0, | |
| "start_index": 1258 | |
| }, | |
| { | |
| "text": "ู ู", | |
| "confidence": 1.0, | |
| "start_index": 1265 | |
| }, | |
| { | |
| "text": "ูุจูู", | |
| "confidence": 1.0, | |
| "start_index": 1268 | |
| }, | |
| { | |
| "text": "ุงูุชุจุฑุน", | |
| "confidence": 1.0, | |
| "start_index": 1273 | |
| }, | |
| { | |
| "text": "ุจูุตูุจูุ", | |
| "confidence": 1.0, | |
| "start_index": 1280 | |
| }, | |
| { | |
| "text": "ูุงููู", | |
| "confidence": 1.0, | |
| "start_index": 1288 | |
| }, | |
| { | |
| "text": "ุฃุนูู .", | |
| "confidence": 1.0, | |
| "start_index": 1294 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 1300 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 1302 | |
| }, | |
| { | |
| "text": "*", | |
| "confidence": 1.0, | |
| "start_index": 1304 | |
| }, | |
| { | |
| "text": "j_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 1306 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "j_n", | |
| "confidence": 1.0, | |
| "start_index": 1316 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1320 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 1322 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 1329 | |
| }, | |
| { | |
| "text": "f(j_n)", | |
| "confidence": 1.0, | |
| "start_index": 1336 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 1343 | |
| }, | |
| { | |
| "text": "\\frac{\\theta}{t^2}", | |
| "confidence": 1.0, | |
| "start_index": 1345 | |
| }, | |
| { | |
| "text": "\\sum_{z=0}^{\\infty}", | |
| "confidence": 1.0, | |
| "start_index": 1364 | |
| }, | |
| { | |
| "text": "\\frac{\\theta^z}{z!}", | |
| "confidence": 1.0, | |
| "start_index": 1384 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1404 | |
| }, | |
| { | |
| "text": "e^{\\theta}", | |
| "confidence": 1.0, | |
| "start_index": 1406 | |
| }, | |
| { | |
| "text": "P(A|B)", | |
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| "start_index": 1417 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1424 | |
| }, | |
| { | |
| "text": "\\frac{P(A", | |
| "confidence": 1.0, | |
| "start_index": 1426 | |
| }, | |
| { | |
| "text": "\\cap", | |
| "confidence": 1.0, | |
| "start_index": 1436 | |
| }, | |
| { | |
| "text": "B)}{P(B)}", | |
| "confidence": 1.0, | |
| "start_index": 1441 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
| "start_index": 1451 | |
| }, | |
| { | |
| "text": "\\frac{\\lambda}{\\theta^2}", | |
| "confidence": 1.0, | |
| "start_index": 1453 | |
| }, | |
| { | |
| "text": "\\nabla_{\\lambda}", | |
| "confidence": 1.0, | |
| "start_index": 1478 | |
| }, | |
| { | |
| "text": "J(\\lambda)", | |
| "confidence": 1.0, | |
| "start_index": 1495 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 1506 | |
| }, | |
| { | |
| "text": "\\frac{1}{m}", | |
| "confidence": 1.0, | |
| "start_index": 1508 | |
| }, | |
| { | |
| "text": "X^T", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "(", | |
| "confidence": 1.0, | |
| "start_index": 1524 | |
| }, | |
| { | |
| "text": "\\sigma(X", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\lambda)", | |
| "confidence": 1.0, | |
| "start_index": 1535 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 1544 | |
| }, | |
| { | |
| "text": "Y", | |
| "confidence": 1.0, | |
| "start_index": 1546 | |
| }, | |
| { | |
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| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}", | |
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| "content": "ูุฌูุจุ ูููุงู ู ูู ูุฌุจ ุนููู ุงูุญุฌ ููุตุญ ู ููุ ูููุงู ู ูู ููุทูุจ ู ููู ูุฐุง ุงููุฑุถ ููู ูุง ูุตุญูู ู ููู ุ ูููุงู ู ูู ูุตุญ ู ููู ุ ููู ูุง ูููููู ุนู ุญุฌุฉ ุงูุฅุณูุงู ุ ูุงูุตุจู (2) ุ", | |
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| "content": "\\nabla_{\\lambda} J(\\lambda) = \\frac{1}{m} X^T ( \\sigma(X \\lambda) - Y )", | |
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| "content": "ููุชุถู ุงูู ุดุงุฑูุฉ ุจุงูุฑุจุญุ ูุฅุฐุง ุดุฑุท ุงุฎุชุตุงุต ุฃุญุฏูู ุง ุจุงูุฑุจุญ ููุฏ ุดุฑุท ู ุง ููุงูู ู ูุชุถู ุงูุนูุฏ. ููุฐุง ู ุฐูุจ ุงูุดุงูุนูุฉ ูุงูุญูุงุจูุฉ (1) . ูุงู ุงูุดูุฑุงุฒู: ยซูุฅู ูุงู: ูุงุฑุถุชู ุนูู ุฃู ุงูุฑุจุญ ููู ููุ ุฃู ููู ููุ ุจุทู ุงููุฑุงุถุ ูุฃู ู ูุถูุนู ุนูู ุงูุงุดุชุฑุงู ูู ุงูุฑุจุญุ", | |
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| "content": "\\vec{F} = m\\vec{a}", | |
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| "content": "ูุฅุฐุง ุดุฑุท ุงูุฑุจุญ ูุฃุญุฏูู ุง ููุฏ ุดุฑุท ู ุง ููุงูู ู ูุชุถุงูุ ูุจุทู. ูุฅู ุฏูุน ุฅููู ุฃูููุงุ ููุงู: ุชุตุฑู ูููุ ูุงูุฑุจุญ ููู ููุ ููู ูุฑุถุ ูุง ุญู ูุฑุจ ุงูู ุงู ูู ุฑุจุญูุ ูุฃู ุงูููุธ ู ุดุชุฑู ุจูู ุงููุฑุงุถ ูุงููุฑุถุ ููุฏ ูุฑู ุจู ุญูู ุงููุฑุถุ ูุงูุนูุฏ ุงููุฑุถ ุจูุ", | |
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| "content": "\\prod_{x=1}^{n} (1 \\leq j_x) = 0", | |
| "type": "text", | |
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| "content": "ูููุธ ุงูุชู ููู ูู ุง ูุงู ู ุดุชุฑููุง ุจูู ุงูุจูุน ูุงููุจุฉ ุฅุฐุง ูุฑู ุจู ุงูุซู ู ูุงู ุจูุนูุงยป (2) . โ โุงูุฑุงุฌุญ ู ู ุงูุฎูุงู: ุฃุฑ ู ุฃู ููู ุงูู ุงูููุฉ ููู ูุณุทุ ุจูู ุงูุญูููุฉ ุงูุฐูู ุฃูุบูุง ุงูููุธ ูุตุญุญูุง ุงูุนูุฏ ูุญู ููู ุนูู ุนูุฏ ุขุฎุฑุ ูุจูู ุงูุดุงูุนูุฉ ูุงูุญูุงุจูุฉ ุงูุฐูู ุฃูุณุฏูุง ุงูุนูุฏุ ููู ุงุนุชุจุฑูุง", | |
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| "content": "\\iint_{D} n^2 \\times \\lambda^2 \\, dx \\, dy", | |
| "type": "text", | |
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| "content": "ุชุนุฑูู", | |
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| { | |
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| "content": "ุงูููุธ ููู ูุฎุฑุฌูู ุนู ุงููุฑุงุถุ ูุตุญุญูุง ุงูุนูุฏุ ูุฌุนููู ู ู ูุจูู ุงูุชุจุฑุน ุจูุตูุจูุ ูุงููู ุฃุนูู . * * *", | |
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| "bottom_right_y": 1002, | |
| "content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n) + \\frac{\\theta}{t^2}", | |
| "type": "text", | |
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| "content": "\\sum_{z=0}^{\\infty} \\frac{\\theta^z}{z!} = e^{\\theta}", | |
| "type": "text", | |
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| "content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{\\lambda}{\\theta^2}", | |
| "type": "text", | |
| "confidence_scores": null, | |
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| "content": "\\nabla_{\\lambda} J(\\lambda) = \\frac{1}{m} X^T ( \\sigma(X \\lambda) - Y )", | |
| "type": "text", | |
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