dataset / data /MachineThree_001 /annotations /sample_0000036.json
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{
"markdown": "\\frac{\\partial \\alpha}{\\partial \\theta} = \\lim_{h \\to 0} \\frac{\\min(\\theta + h) - \\min(\\theta)}{h}\n\\frac{\\partial \\mu}{\\partial \\alpha} = \\lim_{h \\to 0} \\frac{\\min(\\alpha + h) - \\min(\\alpha)}{h}\n## ุชุนุฑูŠู\nูŠุณุชุบู†ู‰ ุนู†ู‡. ูˆุงู„ุฐูŠ ูŠูˆุฌุจู‡ ุงู„ู„ูุธ ุนู„ู‰ ุธุงู‡ุฑู‡ ุฃู† ูŠูƒูˆู† ุงู„ุถู…ูŠุฑ ููŠ (ูŠูŽู‚ู’ุฏูุฑููˆู†ูŽ) ยซ3ยป ู„ู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุขู„ู‡ ูˆุงู„ู…ุคู…ู†ูŠู†. ูˆุงู„ู…ุนู†ู‰: ู„ุฆู„ุง ูŠุนู„ู… ุงู„ูŠู‡ูˆุฏ ูˆุงู„ู†ุตุงุฑู‰ ุฃู† ุงู„ู†ุจูŠ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุขู„ู‡ ูˆุงู„ู…ุคู…ู†ูŠู† ู„ุง ูŠู‚ุฏุฑูˆู† ุนู„ู‰ ุฐู„ูƒุŒ ูˆุฅุฐุง ู„ู… ูŠุนู„ู…ูˆุง ุฃู†ู‡ู…\n\\iint_{D} t^2 \\geq \\alpha^2 \\, dx \\, dy\n\\prod_{\\sigma=1}^{n} (1 - i_\\sigma) = 0\n## ุชุนุฑูŠู\nู„ุง ูŠู‚ุฏุฑูˆู† ูู‚ุฏ ุนู„ู…ูˆุง ุฃู†ู‡ู… ูŠู‚ุฏุฑูˆู† ุนู„ูŠู‡. ุฃูŠ ุฅู† ุขู…ู†ุชู… ูƒู…ุง ุฃู…ุฑุชู… ุขุชุงูƒู… ุงู„ู„ู‡ ู…ู† ูุถู„ู‡ ูุนู„ู… ุฃู‡ู„ ุงู„ูƒุชุงุจ ุฐู„ูƒ ูˆู„ู… ูŠุนู„ู…ูˆุง ุฎู„ุงูู‡. ูˆุงู„ุนู„ู…\n\\mathbb{E}[\\lambda] = \\int x f_\\lambda(x) dx\n\\frac{\\partial n}{\\partial \\theta} = \\lim_{h \\to 0} \\frac{\\sin(\\theta + h) - \\sin(\\theta)}{h}\n## ุจุฑู‡ุงู†\nููŠ ู‡ุฐุง ูˆู…ุซู„ู‡ ูŠูˆุถุน ู…ูˆุถุน ูˆู‚ูˆุน ุงู„ูุนู„ ู„ุฃู†ู‡ ุฅู†ู…ุง ูŠุนู„ู… ุงู„ุฃุดูŠุงุก ูˆุงู‚ุนุฉ ุจุนุฏ ูˆู‚ูˆุนู‡ุง. ู‚ุงู„ ุฃุจูˆ ุณุนูŠุฏ ุงู„ุณูŠุฑุงููŠ ยซ4ยป : ุฅู† ู„ู… ุชุฌุนู„ ยซู„ุงยป ุฒุงุฆุฏุฉ ุฌุงุฒ ู„ุฃู† ู‚ูˆู„ู‡: (ูŠูุคู’ุชููƒูู…ู’ ูƒููู’ู„ูŽูŠู’ู†ู ู…ูู†ู’ ุฑูŽุญู’ู…ูŽุชูู‡ู ูˆูŽูŠูŽุฌู’ุนูŽู„ู’ ู„ูŽูƒูู…ู’ ู†ููˆุฑุงู‹ ุชูŽู…ู’ุดููˆู†ูŽ ุจูู‡ู ูˆูŽูŠูŽุบู’ููุฑู’ ู„ูŽูƒูู…ู’ ูˆูŽุงู„ู„ู‘ูŽู‡ู ุบูŽูููˆุฑูŒ ุฑูŽุญููŠู…ูŒ ู„ูุฆูŽู„ู‘ูŽุง ูŠูŽุนู’ู„ูŽู…ูŽ ุฃูŽู‡ู’ู„ู ุงู„ู’ูƒูุชุงุจู) ยซ5ยป ุฃูŠ: ูŠูุนู„ ุจูƒู… ู‡ุฐู‡ ุงู„ุฃุดูŠุงุก ู„ูŠุชุจูŠู† ุฌู‡ู„ ุฃู‡ู„ ุงู„ูƒุชุงุจ ูˆุฃู†ู‡ู…\n\\sum_{\\lambda=0}^{M} \\frac{\\theta^\\lambda}{\\lambda!} = e^{\\theta} + \\frac{\\beta}{n^2}\n\\int_{0}^{\\infty} \\ln(\\beta) \\, d\\beta = z^2 = C\n## ุชุนุฑูŠู\nู„ุง ูŠุนู„ู…ูˆู† ู…ุง ูŠุคุชูŠูƒู… ุงู„ู„ู‡ ู…ู† ูุถู„ู‡ุŒ ู„ุง ูŠู‚ุฏุฑูˆู† ุนู„ู‰ ุชุบูŠูŠุฑู‡ ูˆุฅุฒุงู„ุชู‡ ุนู†ูƒู…. ูุนู„ู‰ ู‡ุฐุง ู„ุง ูŠุญุชุงุฌ ุฅู„ู‰ ุฒูŠุงุฏุฉ ยซู„ุงยป .\n\\prod_{i=1}^{n} (1 \\cdot \\sigma_i) = 0\n\\prod_{t=1}^{n} (1 \\times \\theta_t) = 0",
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"content": "ู„ุง ูŠุนู„ู…ูˆู† ู…ุง ูŠุคุชูŠูƒู… ุงู„ู„ู‡ ู…ู† ูุถู„ู‡ุŒ ู„ุง ูŠู‚ุฏุฑูˆู† ุนู„ู‰ ุชุบูŠูŠุฑู‡ ูˆุฅุฒุงู„ุชู‡ ุนู†ูƒู…. ูุนู„ู‰ ู‡ุฐุง ู„ุง ูŠุญุชุงุฌ ุฅู„ู‰ ุฒูŠุงุฏุฉ ยซู„ุงยป .",
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"content": "\\prod_{i=1}^{n} (1 \\cdot \\sigma_i) = 0",
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