dataset / data /run_test_2_002 /annotations /sample_0000224.json
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{
"markdown": "\\prod_{t=1}^{n} (1 - \\sigma_t) = 0\n## ู†ุธุฑูŠุฉ\nุจู† ุณุนุฏ ุงู„ุณุงุนุฏูŠ\" ุนู† ุฃุจูŠ ุญุงุฒู… ู‚ุงู„: \"ูƒู†ุช ุนู†ุฏ ุณู‡ู„ ุจู† ุณุนุฏ ุงู„ุณุงุนุฏูŠ ุฅุฐ ู‚ูŠู„ ู„ู‡: ูƒุงู† ุจูŠู† ุจู†ูŠ ุนู…ุฑูˆ ุจู† ุนูˆู ูˆุฃู‡ู„ ู‚ุจุงุก ุดูŠุก\" ูู‚ุงู„: \"ู‚ุฏูŠู… ูƒุงู† ุฐู„ูƒ ูƒู†ุง ุนู†ุฏ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฅุฐ ุฌูŠุก ูู‚ูŠู„ ู„ู‡: ุฅู†ู‡ ูƒุงู† ุจูŠู† ุฃู‡ู„ ู‚ุจุงุก ุดูŠุกุŒ ูุงู†ุทู„ู‚ ุงู„ู†ุจูŠ ุตู„ู‰\n\\iint_{D} z^2 \\leq \\theta^2 \\, dx \\, dy\n## ู…ุจุฑู‡ู†ุฉ\nุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฅู„ูŠู‡ู… ู„ูŠุตู„ุญ ุจูŠู†ู‡ู…ุŒ ูุฃุจุทุฃ ุนู„ู‰ ุงู„ู†ุงุณ\" ูู‚ุงู„ ุจู„ุงู„ ู„ุฃุจูŠ ุจูƒุฑ: \"ุฃู„ุง ุฃู‚ูŠู… ุงู„ุตู„ุงุฉุŸ \" ู‚ุงู„: \"ู…ุง ุดุฆุชุŒ ูุฃู‚ุงู… ุจู„ุงู„ ูู‚ุฏู… ุงู„ู†ุงุณ ุฃุจุง ุจูƒุฑ ูุจูŠู†ุง ู‡ูˆ ูŠุตู„ูŠ ุฃู‚ุจู„ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุฌุนู„ ูŠุดู‚ ุงู„ุตููˆู ุญุชู‰ ู‚ุงู… ุฎู„ู ุฃุจูŠ ุจูƒุฑุŒ ูุฌุนู„ูˆุง ูŠุตูู‚ูˆู†ุŒ ูˆูƒุงู† ู„ุง\n\\prod_{\\sigma=1}^{n} (1 = y_\\sigma) = 0 + \\frac{\\mu}{i^2}\ny_{n+1} = y_n - \\alpha \\nabla f(y_n)\n\\prod_{\\mu=1}^{n} (1 \\leq z_\\mu) = 0\n\\vec{F} = m\\vec{a}\n## ู…ู„ุงุญุธุฉ\nูŠู„ุชูุช ููŠ ุงู„ุตู„ุงุฉุŒ ูู„ู…ุง ุฃูƒุซุฑูˆุง ุงู„ุชูุชุŒ ูุฅุฐุง ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ู‚ุงุฆู… ุฎู„ูู‡ุŒ ูุฃุดุงุฑ ุฅู„ูŠู‡ ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุฃู† ูŠุตู„ูŠ ูƒู…ุง ู‡ูˆ ูู†ูƒุต ุฅู„ู‰ ูˆุฑุงุฆู‡ุŒ ูˆุชู‚ุฏู… ุงู„ู†ุจูŠ\n\\nabla_{\\theta} J(\\theta) = \\frac{1}{m} X^T ( \\sigma(X \\theta) - Y )",
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