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"markdown": "## ุชุนุฑูŠู\nู‡ู†ุงูƒ ุดุฑูˆุท ู„ุง ุจุฏู‘ูŽ ู…ู† ุชูˆุงูุฑู‡ุง (1) ุŒ ู‡ุฐู‡ ุงู„ุดุฑูˆุท ุฅุฐุง ุชูˆูุฑุช ูˆุฌุจ ุงู„ุญุฌุŒ ูˆู‡ุฐู‡ ุงู„ุดุฑูˆุท ู…ู†ู‡ุง ู…ุง ู‡ูŠ ุดุฑูˆุท ุตุญุฉุŒ ูˆู…ู†ู‡ุง ู…ุง ู‡ูŠ ุดุฑูˆุท\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n## ู…ุจุฑู‡ู†ุฉ\nูˆุฌูˆุจุŒ ูู‡ู†ุงูƒ ู…ูŽู† ูŠุฌุจ ุนู„ูŠู‡ ุงู„ุญุฌ ูˆูŠุตุญ ู…ู†ู‡ุŒ ูˆู‡ู†ุงูƒ ู…ูŽู† ูŠูุทู„ุจ ู…ู†ู‡ู… ู‡ุฐุง ุงู„ูุฑุถ ู„ูƒู† ู„ุง ูŠุตุญู‘ู ู…ู†ู‡ู…ุŒ ูˆู‡ู†ุงูƒ ู…ูŽู† ูŠุตุญ ู…ู†ู‡ู…ุŒ ู„ูƒู† ู„ุง ูŠูŽูƒููŠู‡ ุนู† ุญุฌุฉ ุงู„ุฅุณู„ุงู…ุ› ูƒุงู„ุตุจูŠ (2) ุŒ\n\\nabla_{\\lambda} J(\\lambda) = \\frac{1}{m} X^T ( \\sigma(X \\lambda) - Y )\n## ู…ุจุฑู‡ู†ุฉ\nูŠู‚ุชุถูŠ ุงู„ู…ุดุงุฑูƒุฉ ุจุงู„ุฑุจุญุŒ ูุฅุฐุง ุดุฑุท ุงุฎุชุตุงุต ุฃุญุฏู‡ู…ุง ุจุงู„ุฑุจุญ ูู‚ุฏ ุดุฑุท ู…ุง ูŠู†ุงููŠ ู…ู‚ุชุถู‰ ุงู„ุนู‚ุฏ. ูˆู‡ุฐุง ู…ุฐู‡ุจ ุงู„ุดุงูุนูŠุฉ ูˆุงู„ุญู†ุงุจู„ุฉ (1) . ู‚ุงู„ ุงู„ุดูŠุฑุงุฒูŠ: ยซูˆุฅู† ู‚ุงู„: ู‚ุงุฑุถุชูƒ ุนู„ู‰ ุฃู† ุงู„ุฑุจุญ ูƒู„ู‡ ู„ูŠุŒ ุฃูˆ ูƒู„ู‡ ู„ูƒุŒ ุจุทู„ ุงู„ู‚ุฑุงุถุ› ู„ุฃู† ู…ูˆุถูˆุนู‡ ุนู„ู‰ ุงู„ุงุดุชุฑุงูƒ ููŠ ุงู„ุฑุจุญุŒ\n\\vec{F} = m\\vec{a}\n## ู†ุธุฑูŠุฉ\nูุฅุฐุง ุดุฑุท ุงู„ุฑุจุญ ู„ุฃุญุฏู‡ู…ุง ูู‚ุฏ ุดุฑุท ู…ุง ูŠู†ุงููŠ ู…ู‚ุชุถุงู‡ุŒ ูุจุทู„. ูˆุฅู† ุฏูุน ุฅู„ูŠู‡ ุฃู„ูู‹ุงุŒ ูˆู‚ุงู„: ุชุตุฑู ููŠู‡ุŒ ูˆุงู„ุฑุจุญ ูƒู„ู‡ ู„ูƒุŒ ูู‡ูˆ ู‚ุฑุถุŒ ู„ุง ุญู‚ ู„ุฑุจ ุงู„ู…ุงู„ ููŠ ุฑุจุญู‡ุ› ู„ุฃู† ุงู„ู„ูุธ ู…ุดุชุฑูƒ ุจูŠู† ุงู„ู‚ุฑุงุถ ูˆุงู„ู‚ุฑุถุŒ ูˆู‚ุฏ ู‚ุฑู† ุจู‡ ุญูƒู… ุงู„ู‚ุฑุถุŒ ูุงู†ุนู‚ุฏ ุงู„ู‚ุฑุถ ุจู‡ุŒ\n\\prod_{x=1}^{n} (1 \\leq j_x) = 0\n## ุชุนุฑูŠู\nูƒู„ูุธ ุงู„ุชู…ู„ูŠูƒ ู„ู…ุง ูƒุงู† ู…ุดุชุฑูƒู‹ุง ุจูŠู† ุงู„ุจูŠุน ูˆุงู„ู‡ุจุฉ ุฅุฐุง ู‚ุฑู† ุจู‡ ุงู„ุซู…ู† ูƒุงู† ุจูŠุนู‹ุงยป (2) . โ€Œ โ€Œุงู„ุฑุงุฌุญ ู…ู† ุงู„ุฎู„ุงู: ุฃุฑ ู‰ ุฃู† ู‚ูˆู„ ุงู„ู…ุงู„ูƒูŠุฉ ู‚ูˆู„ ูˆุณุทุŒ ุจูŠู† ุงู„ุญู†ููŠุฉ ุงู„ุฐูŠู† ุฃู„ุบูˆุง ุงู„ู„ูุธ ูˆุตุญุญูˆุง ุงู„ุนู‚ุฏ ูˆุญู…ู„ูˆู‡ ุนู„ู‰ ุนู‚ุฏ ุขุฎุฑุŒ ูˆุจูŠู† ุงู„ุดุงูุนูŠุฉ ูˆุงู„ุญู†ุงุจู„ุฉ ุงู„ุฐูŠู† ุฃูุณุฏูˆุง ุงู„ุนู‚ุฏุŒ ูู‡ู… ุงุนุชุจุฑูˆุง\n\\iint_{D} n^2 \\times \\lambda^2 \\, dx \\, dy\n## ุชุนุฑูŠู\nุงู„ู„ูุธ ูู„ู… ูŠุฎุฑุฌูˆู‡ ุนู† ุงู„ู‚ุฑุงุถุŒ ูˆุตุญุญูˆุง ุงู„ุนู‚ุฏุŒ ูˆุฌุนู„ูˆู‡ ู…ู† ู‚ุจูŠู„ ุงู„ุชุจุฑุน ุจู†ุตูŠุจู‡ุŒ ูˆุงู„ู„ู‡ ุฃุนู„ู…. * * *\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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"content": "ูˆุฌูˆุจุŒ ูู‡ู†ุงูƒ ู…ูŽู† ูŠุฌุจ ุนู„ูŠู‡ ุงู„ุญุฌ ูˆูŠุตุญ ู…ู†ู‡ุŒ ูˆู‡ู†ุงูƒ ู…ูŽู† ูŠูุทู„ุจ ู…ู†ู‡ู… ู‡ุฐุง ุงู„ูุฑุถ ู„ูƒู† ู„ุง ูŠุตุญู‘ู ู…ู†ู‡ู…ุŒ ูˆู‡ู†ุงูƒ ู…ูŽู† ูŠุตุญ ู…ู†ู‡ู…ุŒ ู„ูƒู† ู„ุง ูŠูŽูƒููŠู‡ ุนู† ุญุฌุฉ ุงู„ุฅุณู„ุงู…ุ› ูƒุงู„ุตุจูŠ (2) ุŒ",
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"content": "ูŠู‚ุชุถูŠ ุงู„ู…ุดุงุฑูƒุฉ ุจุงู„ุฑุจุญุŒ ูุฅุฐุง ุดุฑุท ุงุฎุชุตุงุต ุฃุญุฏู‡ู…ุง ุจุงู„ุฑุจุญ ูู‚ุฏ ุดุฑุท ู…ุง ูŠู†ุงููŠ ู…ู‚ุชุถู‰ ุงู„ุนู‚ุฏ. ูˆู‡ุฐุง ู…ุฐู‡ุจ ุงู„ุดุงูุนูŠุฉ ูˆุงู„ุญู†ุงุจู„ุฉ (1) . ู‚ุงู„ ุงู„ุดูŠุฑุงุฒูŠ: ยซูˆุฅู† ู‚ุงู„: ู‚ุงุฑุถุชูƒ ุนู„ู‰ ุฃู† ุงู„ุฑุจุญ ูƒู„ู‡ ู„ูŠุŒ ุฃูˆ ูƒู„ู‡ ู„ูƒุŒ ุจุทู„ ุงู„ู‚ุฑุงุถุ› ู„ุฃู† ู…ูˆุถูˆุนู‡ ุนู„ู‰ ุงู„ุงุดุชุฑุงูƒ ููŠ ุงู„ุฑุจุญุŒ",
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"content": "\\vec{F} = m\\vec{a}",
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"content": "ู†ุธุฑูŠุฉ",
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"content": "ูุฅุฐุง ุดุฑุท ุงู„ุฑุจุญ ู„ุฃุญุฏู‡ู…ุง ูู‚ุฏ ุดุฑุท ู…ุง ูŠู†ุงููŠ ู…ู‚ุชุถุงู‡ุŒ ูุจุทู„. ูˆุฅู† ุฏูุน ุฅู„ูŠู‡ ุฃู„ูู‹ุงุŒ ูˆู‚ุงู„: ุชุตุฑู ููŠู‡ุŒ ูˆุงู„ุฑุจุญ ูƒู„ู‡ ู„ูƒุŒ ูู‡ูˆ ู‚ุฑุถุŒ ู„ุง ุญู‚ ู„ุฑุจ ุงู„ู…ุงู„ ููŠ ุฑุจุญู‡ุ› ู„ุฃู† ุงู„ู„ูุธ ู…ุดุชุฑูƒ ุจูŠู† ุงู„ู‚ุฑุงุถ ูˆุงู„ู‚ุฑุถุŒ ูˆู‚ุฏ ู‚ุฑู† ุจู‡ ุญูƒู… ุงู„ู‚ุฑุถุŒ ูุงู†ุนู‚ุฏ ุงู„ู‚ุฑุถ ุจู‡ุŒ",
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"content": "\\prod_{x=1}^{n} (1 \\leq j_x) = 0",
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"content": "ุชุนุฑูŠู",
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"content": "ูƒู„ูุธ ุงู„ุชู…ู„ูŠูƒ ู„ู…ุง ูƒุงู† ู…ุดุชุฑูƒู‹ุง ุจูŠู† ุงู„ุจูŠุน ูˆุงู„ู‡ุจุฉ ุฅุฐุง ู‚ุฑู† ุจู‡ ุงู„ุซู…ู† ูƒุงู† ุจูŠุนู‹ุงยป (2) . โ€Œ โ€Œุงู„ุฑุงุฌุญ ู…ู† ุงู„ุฎู„ุงู: ุฃุฑ ู‰ ุฃู† ู‚ูˆู„ ุงู„ู…ุงู„ูƒูŠุฉ ู‚ูˆู„ ูˆุณุทุŒ ุจูŠู† ุงู„ุญู†ููŠุฉ ุงู„ุฐูŠู† ุฃู„ุบูˆุง ุงู„ู„ูุธ ูˆุตุญุญูˆุง ุงู„ุนู‚ุฏ ูˆุญู…ู„ูˆู‡ ุนู„ู‰ ุนู‚ุฏ ุขุฎุฑุŒ ูˆุจูŠู† ุงู„ุดุงูุนูŠุฉ ูˆุงู„ุญู†ุงุจู„ุฉ ุงู„ุฐูŠู† ุฃูุณุฏูˆุง ุงู„ุนู‚ุฏุŒ ูู‡ู… ุงุนุชุจุฑูˆุง",
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"content": "\\iint_{D} n^2 \\times \\lambda^2 \\, dx \\, dy",
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"content": "ุชุนุฑูŠู",
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"content": "ุงู„ู„ูุธ ูู„ู… ูŠุฎุฑุฌูˆู‡ ุนู† ุงู„ู‚ุฑุงุถุŒ ูˆุตุญุญูˆุง ุงู„ุนู‚ุฏุŒ ูˆุฌุนู„ูˆู‡ ู…ู† ู‚ุจูŠู„ ุงู„ุชุจุฑุน ุจู†ุตูŠุจู‡ุŒ ูˆุงู„ู„ู‡ ุฃุนู„ู…. * * *",
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"content": "j_{n+1} = j_n - \\alpha \\nabla f(j_n) + \\frac{\\theta}{t^2}",
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"content": "\\sum_{z=0}^{\\infty} \\frac{\\theta^z}{z!} = e^{\\theta}",
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"content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{\\lambda}{\\theta^2}",
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