ocr_dataset / data /MachineThree_001 /annotations /sample_0000042.json
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"markdown": "## ุชุนุฑูŠู\nุฃู† ูŠุฏุฎู„ ุญุฒู…ูƒ ูˆู‡ู†ุŒ ุฃูˆ ูŠุดูˆุจ ุนุฒู…ูƒ ุฅูŠุซุงุฑุŒ ุฃูˆ ูŠุฎู„ุท ุฑุฃูŠูƒ ุถูŠุงุนุŒ ูˆุงู„ู„ู‡ ูŠุณุชูˆุฏุน ุฃู…ูŠุฑ ุงู„ู…ุคู…ู†ูŠู† ู†ูุณูƒ ูˆุฏูŠู†ูƒ (1). ุฅุฐุง ูƒู†ุช ู…ู† ุนุฏูˆูƒ ุนู„ู‰ ู…ุณุงูุฉ\n\\int_{1}^{N} \\cos(\\lambda) \\, d\\lambda = j^2 \\leq C\n## ุจุฑู‡ุงู†\nุฏุงู†ูŠุฉุŒ ูˆุณู†ู† (2) ู„ู‚ุงุก ู…ุฎุชุตุฑุŒ ูˆูƒุงู† ู…ู† ุนุณูƒุฑูƒ ู…ู‚ุชุฑุจุงุŒ ู‚ุฏ ุดุงู…ุช (3) ุทู„ุงุฆุนูƒ ู…ู‚ุฏู‘ู…ุงุช ุถู„ุงู„ุชู‡ุŒ ูˆุญู…ุงุฉ ูุชู†ุชู‡ุŒ ูุชุฃู‡ู‘ุจ ุฃู‡ุจุฉ ุงู„ู…ู†ุงุฌุฒุŒ ูˆุฃุนุฏู‘ ุฅุนุฏุงุฏ\n\\int_{3}^{100} \\max(k) \\, dk = t^2 \\leq C + \\frac{k}{\\alpha^2}\n\\iint_{D} k^2 \\cdot \\beta^2 \\, dx \\, dy\n\\mathbb{E}[\\alpha] = \\int x f_\\alpha(x) dx + \\frac{t}{\\sigma^2}\n## ู…ู„ุงุญุธุฉ\nุงู„ุญุฐุฑุŒ ูˆูƒุชู‘ุจ ุฎูŠูˆู„ูƒุŒ ูˆุนุจู‘ ุฌู†ูˆุฏูƒุŒ ูˆุฅูŠุงูƒ ูˆุงู„ู…ุณูŠุฑ ุฅู„ุง ูู‰ ู…ู‚ุฏู‘ู…ุฉ ูˆู…ูŠู…ู†ุฉ ูˆู…ูŠุณุฑุฉ ูˆุณุงู‚ุฉ (4)ุŒ ู‚ุฏ ุดู‡ุฑูˆุง ุงู„ุฃุณู„ุญุฉุŒ ูˆู†ุดุฑูˆุง ุงู„ุจู†ูˆุฏ (5) ูˆุงู„ุฃุนู„ุงู…ุŒ ูˆุนุฑู‘ู ุฌู†ุฏูƒ ู…ุฑุงูƒุฒู‡ู… ุณุงุฆุฑูŠู† ุชุญุช ุฃู„ูˆูŠุชู‡ู…ุŒ ู‚ุฏ ุฃุฎุฐูˆุง ุฃู‡ุจุฉ ุงู„ู‚ุชุงู„ุŒ ูˆุงุณุชุนุฏูˆุง ู„ู„ู‘ู‚ุงุกุŒ ู…ู„ุชุฌุฆูŠู† (6) ุฅู„ู‰ ู…ูˆุงู‚ูู‡ู…ุŒ ุนุงุฑููŠู† ุจู…ูˆุงุถุนู‡ู… ูู‰ ู…ุณูŠุฑู‡ู… ูˆู…ุนุณูƒุฑู‡ู…ุŒ ูˆู„ูŠูƒู†\n\\int_{1}^{N} \\ln(\\lambda) \\, d\\lambda = k^2 \\approx C\n## ู…ู„ุงุญุธุฉ\nุชุฑุญู‘ู„ู‡ู… ูˆุชู†ุฒู‘ู„ู‡ู… ุนู„ู‰ ุฑุงูŠุงุชู‡ู… ูˆุฃุนู„ุงู…ู‡ู… ูˆู…ุฑุงูƒุฒู‡ู…ุŒ ู‚ุฏ ุนุฑู‘ู ูƒู„ู‘ ู‚ุงุฆุฏ ู…ู†ู‡ู… ุฃุตุญุงุจู‡ ู…ูˆุงู‚ูู‡ู…ุŒ ู…ู† ุงู„ู…ูŠู…ู†ุฉ ูˆุงู„ู…ูŠุณุฑุฉ ูˆุงู„ู‚ู„ุจ ูˆุงู„ุณู‘ุงูุฉ ูˆุงู„ุทู‘ู„ูŠุนุฉุŒ ู„ุงุฒู…ูŠู† ู„ู‡ุงุŒ ุบูŠุฑ ู…ุฎู„ู‘ูŠู† ุจู…ุง ุงุณุชู†ุฌุฏุชู‡ู… ู„ู‡ุŒ ูˆู„ุง ู…ุชู‡ุงูˆู†ูŠู† ุจู…ุง ุฃู‡ุจุช ุจู‡ู… ุฅู„ูŠู‡ุŒ ุญุชู‰ ุชูƒูˆู† ุนุณุงูƒุฑูƒ ูู‰ ูƒู„ ู…ู†ู‡ู„ ุชุตู„ ุฅู„ูŠู‡ุŒ ูˆู…ุณุงูุฉ ุชุฌุชุงุฒู‡ุง (7)ุŒ ูƒุฃู†ู‡ุง ุนุณูƒุฑ ูˆุงุญุฏ ูู‰ ุงุฌุชู…ุงุนู‡ุง ุนู„ู‰ ุงู„ุนุฏูˆู‘ ูˆุฃุฎุฐู‡ุง ุจุงู„ุญุฒู…ุŒ ูˆู…ุณูŠุฑู‡ุง ุนู„ู‰ ุฑุงูŠุงุชู‡ุงุŒ\n\\int_{4}^{N} \\log(i) \\, di = y^2 - C\n\\frac{\\partial \\sigma}{\\partial \\lambda} = \\lim_{h \\to 0} \\frac{\\sin(\\lambda + h) - \\sin(\\lambda)}{h} + \\frac{y}{z^2}\n\\sum_{t=0}^{N} \\frac{\\theta^t}{t!} = e^{\\theta}\n## ุชุนุฑูŠู\nูˆู†ุฒูˆู„ู‡ุง ุนู„ู‰ ู…ุฑุงูƒุฒู‡ุงุŒ ูˆู…ุนุฑูุชู‡ุง ุจู…ูˆุงุถุนู‡ุงุŒ ุฅู† ุฃุถู„ู‘ุช ุฏุงุจุฉ ู…ูˆุถุนู‡ุงุŒ ุนุฑู ุฃู‡ู„ ุงู„ุนุณูƒุฑ: ู…ู† ุฃู‰ ุงู„ู…ุฑุงูƒุฒ ู‡ู‰ุŸ ูˆู…ู† ุตุงุญุจู‡ุงุŸ ูˆูู‰ ุฃู‰ ุงู„ู…ุญู„ ุญู„ูˆู„ู‡ ู…ู†ู‡ุงุŸ ูุฑุฏู‘ุช ุฅู„ูŠู‡ ู‡ุฏุงูŠุฉ ู…ุนุฑูˆูุฉ\n\\prod_{\\alpha=1}^{n} (1 \\times \\theta_\\alpha) = 0 + \\frac{\\alpha}{\\alpha^2}",
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"content": "ุงู„ุญุฐุฑุŒ ูˆูƒุชู‘ุจ ุฎูŠูˆู„ูƒุŒ ูˆุนุจู‘ ุฌู†ูˆุฏูƒุŒ ูˆุฅูŠุงูƒ ูˆุงู„ู…ุณูŠุฑ ุฅู„ุง ูู‰ ู…ู‚ุฏู‘ู…ุฉ ูˆู…ูŠู…ู†ุฉ ูˆู…ูŠุณุฑุฉ ูˆุณุงู‚ุฉ (4)ุŒ ู‚ุฏ ุดู‡ุฑูˆุง ุงู„ุฃุณู„ุญุฉุŒ ูˆู†ุดุฑูˆุง ุงู„ุจู†ูˆุฏ (5) ูˆุงู„ุฃุนู„ุงู…ุŒ ูˆุนุฑู‘ู ุฌู†ุฏูƒ ู…ุฑุงูƒุฒู‡ู… ุณุงุฆุฑูŠู† ุชุญุช ุฃู„ูˆูŠุชู‡ู…ุŒ ู‚ุฏ ุฃุฎุฐูˆุง ุฃู‡ุจุฉ ุงู„ู‚ุชุงู„ุŒ ูˆุงุณุชุนุฏูˆุง ู„ู„ู‘ู‚ุงุกุŒ ู…ู„ุชุฌุฆูŠู† (6) ุฅู„ู‰ ู…ูˆุงู‚ูู‡ู…ุŒ ุนุงุฑููŠู† ุจู…ูˆุงุถุนู‡ู… ูู‰ ู…ุณูŠุฑู‡ู… ูˆู…ุนุณูƒุฑู‡ู…ุŒ ูˆู„ูŠูƒู†",
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"content": "\\int_{1}^{N} \\ln(\\lambda) \\, d\\lambda = k^2 \\approx C",
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"content": "ุชุฑุญู‘ู„ู‡ู… ูˆุชู†ุฒู‘ู„ู‡ู… ุนู„ู‰ ุฑุงูŠุงุชู‡ู… ูˆุฃุนู„ุงู…ู‡ู… ูˆู…ุฑุงูƒุฒู‡ู…ุŒ ู‚ุฏ ุนุฑู‘ู ูƒู„ู‘ ู‚ุงุฆุฏ ู…ู†ู‡ู… ุฃุตุญุงุจู‡ ู…ูˆุงู‚ูู‡ู…ุŒ ู…ู† ุงู„ู…ูŠู…ู†ุฉ ูˆุงู„ู…ูŠุณุฑุฉ ูˆุงู„ู‚ู„ุจ ูˆุงู„ุณู‘ุงูุฉ ูˆุงู„ุทู‘ู„ูŠุนุฉุŒ ู„ุงุฒู…ูŠู† ู„ู‡ุงุŒ ุบูŠุฑ ู…ุฎู„ู‘ูŠู† ุจู…ุง ุงุณุชู†ุฌุฏุชู‡ู… ู„ู‡ุŒ ูˆู„ุง ู…ุชู‡ุงูˆู†ูŠู† ุจู…ุง ุฃู‡ุจุช ุจู‡ู… ุฅู„ูŠู‡ุŒ ุญุชู‰ ุชูƒูˆู† ุนุณุงูƒุฑูƒ ูู‰ ูƒู„ ู…ู†ู‡ู„ ุชุตู„ ุฅู„ูŠู‡ุŒ ูˆู…ุณุงูุฉ ุชุฌุชุงุฒู‡ุง (7)ุŒ ูƒุฃู†ู‡ุง ุนุณูƒุฑ ูˆุงุญุฏ ูู‰ ุงุฌุชู…ุงุนู‡ุง ุนู„ู‰ ุงู„ุนุฏูˆู‘ ูˆุฃุฎุฐู‡ุง ุจุงู„ุญุฒู…ุŒ ูˆู…ุณูŠุฑู‡ุง ุนู„ู‰ ุฑุงูŠุงุชู‡ุงุŒ",
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