dataset / data /run_test_2_002 /annotations /sample_0000238.json
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{
"markdown": "\\frac{\\partial n}{\\partial t} = \\lim_{h \\to 0} \\frac{\\sin(t + h) - \\sin(t)}{h}\n## ู…ุจุฑู‡ู†ุฉ\nุฃูˆ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุŸ ููŠ ู‚ูˆู„ ุนู†ุฏ ุฃุจูŠ ูŠูˆุณู ุฑุญู…ู‡ ุงู„ู„ู‡ ูŠู‚ุชุตุฑ ููŠ ุงู„ู†ู‘ุตู‘ ุนู„ู‰ ู…ูˆุฑุฏู‡ุ› ู„ุฃู†ู‘ู‡ ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงู„ู†ู‘ุตู‘. ูˆุฃูˆู„ุงุฏ ุงู„ุฃุฎูˆุฉ ู„ุฃู…ู‘ ู„ูŠุณูˆุง ููŠ ู…ุนู†ู‰ ุงู„ุขุจุงุกุ› ู„ุฃู†ู‘ู‡ู… ู„ุง ูŠุฑุซูˆู† ุจุงู„ูุฑุถูŠู‘ุฉ ุดูŠุฆุงู‹. ูˆู…ู†ู‡ุง: ุฃู†ู‘ ุงู„ู…ุดุชุฑูŠ ู„ู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชุญู‚ู‘ุฉ\n\\iint_{D} \\mu^2 - \\mu^2 \\, dx \\, dy\n\\frac{\\partial \\mu}{\\partial \\alpha} = \\lim_{h \\to 0} \\frac{\\min(\\alpha + h) - \\min(\\alpha)}{h}\n\\lambda_{n+1} = \\lambda_n - \\alpha \\nabla f(\\lambda_n)\n## ุจุฑู‡ุงู†\nูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ ุงู„ูˆู„ุฏุŒ ูˆู‡ุฐุง ู‡ูˆ ุงู„ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงุชู‘ูุงู‚ ุงู„ุตู‘ุญุงุจุฉ. ู„ูƒู† ุฅุฐุง ูˆุทุฆ\n\\nabla_{z} J(z) = \\frac{1}{m} X^T ( \\sigma(X z) - Y )\n## ู†ุธุฑูŠุฉ\nุงู„ู…ุดุชุฑูŠ ุงู„ุฌุงุฑูŠุฉ ููŠุฌุจ ุนู„ูŠู‡ ู…ู‡ุฑู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุงุŒ ูˆูŠู‚ุถู‰ ุจู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุง ุฃูŠุถุงู‹ุŒ ูˆุงู„ู…ุดุชุฑูŠ ูŠุนูˆุฏ ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ู„ูƒู† ู„ุง ูŠุนูˆุฏ ุนู„ูŠู‡ ุจุงู„ู…ู‡ุฑุ› ู„ุฃู†ู‘ ุงู„ู…ู‡ุฑ ุฅู†ู‘ู…ุง ู„ุฒู…ู‡ ุนูˆุถุงู‹ ุนู…ู‘ุง ุงุณุชูˆูู‰ ุจุงู„ูˆุทุก ูู„ุง ูŠุฑุฌุน ุจุจุฏู„ู‡ ุนู„ู‰ ุบูŠุฑู‡. ูˆู„ุง ูŠู‚ุงุณ ุนู„ู‰ ูˆู„ุฏ ุงู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชูˆู„ุฏุฉ. ูˆู„ูƒู† ุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุฅู†ู‘ ุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ\n\\nabla_{j} J(j) = \\frac{1}{m} X^T ( \\sigma(X j) - Y ) + \\frac{k}{\\sigma^2}\n## ุจุฑู‡ุงู†\nุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘\n\\int_{1}^{M} \\cos(\\sigma) \\, d\\sigma = \\beta^2 - C\nj_{n+1} = j_n - \\alpha \\nabla f(j_n)\n## ู†ุธุฑูŠุฉ\nุงู„ู‚ูŠุงุณ ุจุงู„ู†ู‘ุตู‘. ูˆุฃูˆู„ุงุฏ ุงู„ุฃุฎูˆุฉ ู„ุฃู…ู‘ ู„ูŠุณูˆุง ููŠ ู…ุนู†ู‰ ุงู„ุขุจุงุกุ› ู„ุฃู†ู‘ู‡ู… ู„ุง ูŠุฑุซูˆู† ุจุงู„ูุฑุถูŠู‘ุฉ ุดูŠุฆุงู‹. ูˆู…ู†ู‡ุง: ุฃู†ู‘ ุงู„ู…ุดุชุฑูŠ ู„ู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชุญู‚ู‘ุฉ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ\nx_{n+1} = x_n - \\alpha \\nabla f(x_n) + \\frac{n}{\\mu^2}",
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"content": "\\iint_{D} \\mu^2 - \\mu^2 \\, dx \\, dy",
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"content": "\\frac{\\partial \\mu}{\\partial \\alpha} = \\lim_{h \\to 0} \\frac{\\min(\\alpha + h) - \\min(\\alpha)}{h}",
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"content": "ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ ุงู„ูˆู„ุฏุŒ ูˆู‡ุฐุง ู‡ูˆ ุงู„ู…ุฎุตูˆุต ู…ู† ุงู„ู‚ูŠุงุณ ุจุงุชู‘ูุงู‚ ุงู„ุตู‘ุญุงุจุฉ. ู„ูƒู† ุฅุฐุง ูˆุทุฆ",
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"content": "\\nabla_{z} J(z) = \\frac{1}{m} X^T ( \\sigma(X z) - Y )",
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"content": "ู†ุธุฑูŠุฉ",
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"content": "ุงู„ู…ุดุชุฑูŠ ุงู„ุฌุงุฑูŠุฉ ููŠุฌุจ ุนู„ูŠู‡ ู…ู‡ุฑู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุงุŒ ูˆูŠู‚ุถู‰ ุจู‡ุง ู„ู…ุณุชุญู‚ู‘ู‡ุง ุฃูŠุถุงู‹ุŒ ูˆุงู„ู…ุดุชุฑูŠ ูŠุนูˆุฏ ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ู„ูƒู† ู„ุง ูŠุนูˆุฏ ุนู„ูŠู‡ ุจุงู„ู…ู‡ุฑุ› ู„ุฃู†ู‘ ุงู„ู…ู‡ุฑ ุฅู†ู‘ู…ุง ู„ุฒู…ู‡ ุนูˆุถุงู‹ ุนู…ู‘ุง ุงุณุชูˆูู‰ ุจุงู„ูˆุทุก ูู„ุง ูŠุฑุฌุน ุจุจุฏู„ู‡ ุนู„ู‰ ุบูŠุฑู‡. ูˆู„ุง ูŠู‚ุงุณ ุนู„ู‰ ูˆู„ุฏ ุงู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชูˆู„ุฏุฉ. ูˆู„ูƒู† ุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุฅู†ู‘ ุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ",
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"content": "\\nabla_{j} J(j) = \\frac{1}{m} X^T ( \\sigma(X j) - Y ) + \\frac{k}{\\sigma^2}",
"type": "text",
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"reading_index": 12
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"content": "ุจุฑู‡ุงู†",
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"content": "ุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘",
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"content": "\\int_{1}^{M} \\cos(\\sigma) \\, d\\sigma = \\beta^2 - C",
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"content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n)",
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"content": "ุงู„ู‚ูŠุงุณ ุจุงู„ู†ู‘ุตู‘. ูˆุฃูˆู„ุงุฏ ุงู„ุฃุฎูˆุฉ ู„ุฃู…ู‘ ู„ูŠุณูˆุง ููŠ ู…ุนู†ู‰ ุงู„ุขุจุงุกุ› ู„ุฃู†ู‘ู‡ู… ู„ุง ูŠุฑุซูˆู† ุจุงู„ูุฑุถูŠู‘ุฉ ุดูŠุฆุงู‹. ูˆู…ู†ู‡ุง: ุฃู†ู‘ ุงู„ู…ุดุชุฑูŠ ู„ู„ุฌุงุฑูŠุฉ ุงู„ู…ุณุชุญู‚ู‘ุฉ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู†ุŒ ูˆู„ูˆ ุงุณุชูˆู„ุฏู‡ุง ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจู‚ูŠู…ุฉ",
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"content": "x_{n+1} = x_n - \\alpha \\nabla f(x_n) + \\frac{n}{\\mu^2}",
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