ocr_dataset / data /Zetati_abdel_002 /annotations /sample_0010036.json
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"markdown": "ูู† ุงู„ุญูˆุงุฑ ูˆุงู„ุฅู‚ู†ุงุน ููŠ ุงู„ุฎุทุงุจ ุงู„ู…ุนุงุตุฑ\nุงู„ู…ู„ุฎุต: ุงู„ุชุณุฌูŠู„ ุนู„ู‰ ุงู„ุณุงู…ุน) ุฃู‰: ูƒุชุงุจุฉ ุงู„ุญูƒู… ุนู„ูŠู‡ ุจูŠู† ูŠุฏู‰ ุงู„ุญุงูƒู… ูƒู…ุง ุฅุฐุง ู‚ุงู„ ุงู„ุญุงูƒู… ู„ุดุงู‡ุฏ ูˆุงู‚ุนุฉ ู‡ู„ ุฃู‚ุฑ ู‡ุฐุง ุนู„ู‰ ู†ูุณู‡ ุจูƒุฐุง ููŠู‚ูˆู„ ุงู„ุดุงู‡ุฏ: ู†ุนู… ุฒูŠุฏ ู‡ุฐุง ุฃู‚ุฑ ุนู„ู‰ ู†ูุณู‡ ุจูƒุฐุง- ููŠุฐูƒุฑ ุงู„ู…ุณู†ุฏ ุฅู„ูŠู‡ ู„ุฆู„ุง ูŠุฌุฏ ุงู„ู…ุดู‡ูˆุฏ ุนู„ูŠู‡ ุณุจูŠู„ุง ู„ู„ุฅู†ูƒุงุฑุŒ ุจุฃู† ูŠู‚ูˆู„ ู„ู„ุญุงูƒู… ุนู†ุฏ\nู‚ุงุฆู…ุฉ ุงู„ู…ุฑุงุฌุน ูˆุงู„ู…ุตุงุฏุฑ ุงู„ุชูˆุซูŠู‚ูŠุฉ\nุงู„ุชุณุฌูŠู„ ุฅู†ู…ุง ูู‡ู… ุงู„ุดุงู‡ุฏ ุฃู†ูƒ ุฃุดุฑุช ุฅู„ู‰ ุบูŠุฑู‰ุ› ูุฃุฌุงุจ ูˆู„ุฐู„ูƒ ู„ู… ุฃู†ูƒุฑ ูˆู„ู… ุฃุทู„ุจ ุงู„ุฅุนุฐุงุฑ ููŠู‡ุŒ ูˆุงุนู„ู… ุฃู† ุงู„ู…ุตู†ู ุชุฑูƒ ู‡ู†ุง ู‚ูˆู„ู‡: ุฃูˆ ู†ุญูˆ ุฐู„ูƒ ุงูƒุชูุงุก ุจุฐูƒุฑู‡ ูู‰ ุงู„ุญุฐู. ู„ุง ู„ูƒูˆู†ู‡ ุงุณุชูˆุนุจ ู†ูƒุงุช ุงู„ุฐูƒุฑุ› ู„ุฃู† ุงู„ู…ู‚ุชุถูŠุงุช ู„ู„ุฎุตูˆุตูŠุงุช ู„ูŠุณุช ุณู…ุงุนูŠุฉ ุจู„ ุงู„ู…ุฏุงุฑ ุนู„ู‰ ุงู„ุฐูˆู‚ ุงู„ุณู„ูŠู… ูู…ุง ุนุฏู‡ ุงู„ุฐูˆู‚ ู…ู‚ุชุถูŠุง ู„ุฎุตูˆุตูŠุฉ ุนู…ู„ ุจู‡ุŒ ูˆุฅู† ู„ู… ูŠุฐูƒุฑู‡ ุฃู‡ู„ ุงู„ูู† [ุชุนุฑูŠู ุงู„ู…ุณู†ุฏ ุฅู„ูŠู‡]: (ู‚ูˆู„ู‡: ุฃู‰ ุฅูŠุฑุงุฏ ุฅู„ุฎ). ุฃู‰: ูˆู„ูŠุณ ุงู„ู…ุฑุงุฏ ุจุชุนุฑูŠูู‡ ุฌุนู„ู‡ ู…ุนุฑูุฉุ› ู„ุฃู† ุฐู„ูƒ ูˆุธูŠูุฉ ุงู„ูˆุงุถุน ุจุฎู„ุงู ุงู„ุฅูŠุฑุงุฏ ู…ุนุฑูุฉ ูุฅู†ู‡ ู…ู† ูˆุธูŠูุฉ ุงู„ุจู„ูŠุบ ุงู„ู…ุณุชุนู…ู„ ูˆุฐู„ูƒ ู‡ูˆ ุงู„ู…ุฑุงุฏ\nู…ุคุดุฑุงุช ุงู„ุฃุฏุงุก ูˆุงู„ู…ุนุงูŠูŠุฑ ุงู„ู…ุนุชู…ุฏุฉ\nู…ู† ูŠูˆู…ู‡ ุญุชู‘ู‰ ู†ุฒู„: {(ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’ ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰)} (1) . ูˆุนู† ุฃู†ุณ ุจู† ู…ุงู„ูƒ ู‚ุงู„: ู‚ุงู„ ุนู…ุฑ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡: (ูˆุงูู‚ู†ูŠ ุฑุจูŠ ููŠ ุซู„ุงุซ: ู‚ู„ุช: ู„ูˆ ุงุชู‘ุฎุฐุช ู…ู† ู…ู‚ุงู… ุฅุจุฑุงู‡ูŠู… ู…ุตู„ู‘ู‰ุ› ูุฃู†ุฒู„ ุงู„ู„ู‡ ุชุนุงู„ู‰ {(ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’ ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰)}. ูˆู‚ู„ุช: ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ุ› ุฅู†ู‘ู‡ ูŠุฏุฎู„ ุนู„ูŠูƒ ุงู„ุจุฑู‘ ูˆุงู„ูุงุฌุฑุ› ูู‡ู„ุงู‘ ุญุฌู‘ุจุช ุฃู…ู‘ู‡ุงุช ุงู„ู…ุคู…ู†ูŠู†ุŸ ูุฃู†ุฒู„ ุงู„ู„ู‡ ุขูŠุฉ ุงู„ุญุฌุงุจ. ู‚ุงู„: ูˆุจู„ุบู†ูŠ ุดูŠุก ูƒุงู† ุจูŠู† ุฃู…ู‘ู‡ุงุช ุงู„ู…ุคู…ู†ูŠู† ูˆุจูŠู† ุงู„ู†ู‘ุจูŠู‘ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุงุณุชูุฒู‘\nุงู„ุชุญุฏูŠุงุช ูˆุงู„ูุฑุต ุงู„ู…ุณุชู‚ุจู„ูŠุฉ\nู…ู†ุงู‚ุดุฉ ูˆุชูุณูŠุฑ ุงู„ู†ุชุงุฆุฌ ุงู„ุนุงู…ุฉ\nt_{n+1} = t_n - \\alpha \\nabla f(t_n) + \\frac{x}{\\lambda^2}\n\\vec{F} = m\\vec{a}\n\n[tbl-0.html](tbl-0.html)\n\nู…ู†ู‡ุฌูŠุฉ ุงู„ุจุญุซ ูˆุฃุฏูˆุงุช ุฌู…ุน ุงู„ุจูŠุงู†ุงุช",
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"content": "<table><tbody><tr><th>ููŠู‡.</th><th>ูƒุงู†</th><th>ุงู„ุฑุฌู„ ู…ู†ู‡ู…</th><th>ูŠุคูˆูŠ ุฅู„ูŠู‡</th></tr><tr><td>ู‚ุงุชู„ ุฃุจูŠู‡ ูู„ุง ูŠุชุนุฑู‘ุถ ู„ู‡. ูˆู…ู† ุงู„ุฃู…ู† ุงู„ุฐูŠ</td><td>ุฌุนู„ู‡ ุงู„ู„ู‡ ููŠู‡: ุงุฌุชู…ุงุน ุงู„ุตูŠุฏ ูˆุงู„ูƒู„ุจ ูˆู„ุง</td><td>ูŠู‡ูŠุฌ ุงู„ูƒู„ุจ ุงู„ุตูŠุฏุŒ</td><td>ูˆู„ุง ูŠู†ูุฑ</td></tr><tr><td>ุงู„ุตูŠุฏ ู…ู† ุงู„ูƒู„ุจ ุญุชู‰ ุฅุฐุง ุฎุฑุฌุง ู…ู†ู‡</td><td>ุนุฏุง ุงู„ูƒู„ุจ</td><td>ุนู„ู‰ ุงู„ุตูŠุฏุŒ</td><td>ูˆุนุงุฏ ุงู„ุตูŠุฏ ุฅู„ู‰ ุงู„ู‡ุฑุจ.</td></tr><tr><td>ู‚ูˆู„ู‡ ุชุนุงู„ู‰: {ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’</td><td>ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰ุ›} ู‚ุฑุฃ ุดูŠุจุฉ</td><td>ูˆู†ุงูุน ูˆุงุจู† ุนุงู…ุฑ</td><td>ูˆุงู„ุญุณู†: ยซ(ูˆุงุชู‘ุฎุฐูˆุง)ยป ุจูุชุญ ุงู„ุฎุงุก ุนู„ู‰ ุงู„ุฎุจุฑ. ูˆู‚ุฑุฃ</td></tr><tr><td>ุงู„ุจุงู‚ูˆู† ุจุงู„ูƒุณุฑ ุนู„ู‰ ุงู„ุฃู…ุฑ. ู‚ุงู„ ุงุจู†</td><td>ูƒูŠุณุงู†: (ุฐูƒุฑูˆุง ุฃู†ู‘ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡</td><td>ูˆุณู„ู… ู…ุฑู‘ ุจุงู„ู…ู‚ุงู…</td><td>ูˆู…ุนู‡ ุนู…ุฑ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ุ›</td></tr><tr><td>ูู‚ุงู„: ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ุ› ุฃู„ูŠุณ</td><td>ู‡ุฐุง ู…ู‚ุงู… ุฃุจูŠู†ุง ุฅุจุฑุงู‡ูŠู…ุŸ ู‚ุงู„: [ุจู„ู‰].ู‚ุงู„: ุฃูู„ุง</td><td>ุชุชู‘ุฎุฐู‡ ู…ุตู„ู‘ู‰ุŸ ู‚ุงู„: [ู„ู… ุฃูˆู…ุฑ ุจุฐู„ูƒ].ูู„ู…</td><td>ุชุบุจ ุงู„ุดู‘ู…ุณ</td></tr></tbody></table>",
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"text": "ููŠู‡.",
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"text": "ูƒุงู†",
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"text": "ุงู„ุฑุฌู„",
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"text": " ู…ู†ู‡ู…",
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"text": "ูŠุคูˆูŠ",
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"text": " ุฅู„ูŠู‡",
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{
"text": "ู‚ุงุชู„",
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{
"text": " ุฃุจูŠู‡",
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{
"text": " ูู„ุง",
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"text": " ูŠุชุนุฑู‘ุถ",
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{
"text": " ู„ู‡.",
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{
"text": " ูˆู…ู†",
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"text": " ุงู„ุฃู…ู†",
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{
"text": " ุงู„ุฐูŠ",
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{
"text": "ุฌุนู„ู‡",
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"text": " ุงู„ู„ู‡",
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"text": " ููŠู‡:",
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"text": " ุงุฌุชู…ุงุน",
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{
"text": " ุงู„ุตูŠุฏ",
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{
"text": " ูˆุงู„ูƒู„ุจ",
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"text": " ูˆู„ุง",
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{
"text": "ูŠู‡ูŠุฌ",
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{
"text": " ุงู„ูƒู„ุจ",
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{
"text": " ุงู„ุตูŠุฏุŒ",
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{
"text": "ูˆู„ุง",
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"text": " ูŠู†ูุฑ",
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"text": "ุงู„ุตูŠุฏ",
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"text": " ู…ู†",
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{
"text": " ุงู„ูƒู„ุจ",
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{
"text": " ุญุชู‰",
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{
"text": " ุฅุฐุง",
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{
"text": " ุฎุฑุฌุง",
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"text": " ู…ู†ู‡",
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{
"text": "ุนุฏุง",
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{
"text": " ุงู„ูƒู„ุจ",
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"text": "ุนู„ู‰",
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"text": " ุงู„ุตูŠุฏุŒ",
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{
"text": "ูˆุนุงุฏ",
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{
"text": " ุงู„ุตูŠุฏ",
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{
"text": " ุฅู„ู‰",
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{
"text": " ุงู„ู‡ุฑุจ.",
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{
"text": "ู‚ูˆู„ู‡",
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"text": " ุชุนุงู„ู‰:",
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"text": " {ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง",
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{
"text": " ู…ูู†ู’",
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"text": "ู…ูŽู‚ุงู…ู",
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"content": "ุงู„ุชุณุฌูŠู„ ุฅู†ู…ุง ูู‡ู… ุงู„ุดุงู‡ุฏ ุฃู†ูƒ ุฃุดุฑุช ุฅู„ู‰ ุบูŠุฑู‰ุ› ูุฃุฌุงุจ ูˆู„ุฐู„ูƒ ู„ู… ุฃู†ูƒุฑ ูˆู„ู… ุฃุทู„ุจ ุงู„ุฅุนุฐุงุฑ ููŠู‡ุŒ ูˆุงุนู„ู… ุฃู† ุงู„ู…ุตู†ู ุชุฑูƒ ู‡ู†ุง ู‚ูˆู„ู‡: ุฃูˆ ู†ุญูˆ ุฐู„ูƒ ุงูƒุชูุงุก ุจุฐูƒุฑู‡ ูู‰ ุงู„ุญุฐู. ู„ุง ู„ูƒูˆู†ู‡ ุงุณุชูˆุนุจ ู†ูƒุงุช ุงู„ุฐูƒุฑุ› ู„ุฃู† ุงู„ู…ู‚ุชุถูŠุงุช ู„ู„ุฎุตูˆุตูŠุงุช ู„ูŠุณุช ุณู…ุงุนูŠุฉ ุจู„ ุงู„ู…ุฏุงุฑ ุนู„ู‰ ุงู„ุฐูˆู‚ ุงู„ุณู„ูŠู… ูู…ุง ุนุฏู‡ ุงู„ุฐูˆู‚ ู…ู‚ุชุถูŠุง ู„ุฎุตูˆุตูŠุฉ ุนู…ู„ ุจู‡ุŒ ูˆุฅู† ู„ู… ูŠุฐูƒุฑู‡ ุฃู‡ู„ ุงู„ูู† [ุชุนุฑูŠู ุงู„ู…ุณู†ุฏ ุฅู„ูŠู‡]: (ู‚ูˆู„ู‡: ุฃู‰ ุฅูŠุฑุงุฏ ุฅู„ุฎ). ุฃู‰: ูˆู„ูŠุณ ุงู„ู…ุฑุงุฏ ุจุชุนุฑูŠูู‡ ุฌุนู„ู‡ ู…ุนุฑูุฉุ› ู„ุฃู† ุฐู„ูƒ ูˆุธูŠูุฉ ุงู„ูˆุงุถุน ุจุฎู„ุงู ุงู„ุฅูŠุฑุงุฏ ู…ุนุฑูุฉ ูุฅู†ู‡ ู…ู† ูˆุธูŠูุฉ ุงู„ุจู„ูŠุบ ุงู„ู…ุณุชุนู…ู„ ูˆุฐู„ูƒ ู‡ูˆ ุงู„ู…ุฑุงุฏ",
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"content": "ู…ู† ูŠูˆู…ู‡ ุญุชู‘ู‰ ู†ุฒู„: {(ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’ ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰)} (1) . ูˆุนู† ุฃู†ุณ ุจู† ู…ุงู„ูƒ ู‚ุงู„: ู‚ุงู„ ุนู…ุฑ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡: (ูˆุงูู‚ู†ูŠ ุฑุจูŠ ููŠ ุซู„ุงุซ: ู‚ู„ุช: ู„ูˆ ุงุชู‘ุฎุฐุช ู…ู† ู…ู‚ุงู… ุฅุจุฑุงู‡ูŠู… ู…ุตู„ู‘ู‰ุ› ูุฃู†ุฒู„ ุงู„ู„ู‡ ุชุนุงู„ู‰ {(ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’ ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰)}. ูˆู‚ู„ุช: ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ุ› ุฅู†ู‘ู‡ ูŠุฏุฎู„ ุนู„ูŠูƒ ุงู„ุจุฑู‘ ูˆุงู„ูุงุฌุฑุ› ูู‡ู„ุงู‘ ุญุฌู‘ุจุช ุฃู…ู‘ู‡ุงุช ุงู„ู…ุคู…ู†ูŠู†ุŸ ูุฃู†ุฒู„ ุงู„ู„ู‡ ุขูŠุฉ ุงู„ุญุฌุงุจ. ู‚ุงู„: ูˆุจู„ุบู†ูŠ ุดูŠุก ูƒุงู† ุจูŠู† ุฃู…ู‘ู‡ุงุช ุงู„ู…ุคู…ู†ูŠู† ูˆุจูŠู† ุงู„ู†ู‘ุจูŠู‘ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุงุณุชูุฒู‘",
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"content": "ุงู„ุชุญุฏูŠุงุช ูˆุงู„ูุฑุต ุงู„ู…ุณุชู‚ุจู„ูŠุฉ",
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"content": "t_{n+1} = t_n - \\alpha \\nabla f(t_n) + \\frac{x}{\\lambda^2}",
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"content": "\\vec{F} = m\\vec{a}",
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"content": "<table><tbody><tr><th>ููŠู‡.</th><th>ูƒุงู†</th><th>ุงู„ุฑุฌู„ ู…ู†ู‡ู…</th><th>ูŠุคูˆูŠ ุฅู„ูŠู‡</th></tr><tr><td>ู‚ุงุชู„ ุฃุจูŠู‡ ูู„ุง ูŠุชุนุฑู‘ุถ ู„ู‡. ูˆู…ู† ุงู„ุฃู…ู† ุงู„ุฐูŠ</td><td>ุฌุนู„ู‡ ุงู„ู„ู‡ ููŠู‡: ุงุฌุชู…ุงุน ุงู„ุตูŠุฏ ูˆุงู„ูƒู„ุจ ูˆู„ุง</td><td>ูŠู‡ูŠุฌ ุงู„ูƒู„ุจ ุงู„ุตูŠุฏุŒ</td><td>ูˆู„ุง ูŠู†ูุฑ</td></tr><tr><td>ุงู„ุตูŠุฏ ู…ู† ุงู„ูƒู„ุจ ุญุชู‰ ุฅุฐุง ุฎุฑุฌุง ู…ู†ู‡</td><td>ุนุฏุง ุงู„ูƒู„ุจ</td><td>ุนู„ู‰ ุงู„ุตูŠุฏุŒ</td><td>ูˆุนุงุฏ ุงู„ุตูŠุฏ ุฅู„ู‰ ุงู„ู‡ุฑุจ.</td></tr><tr><td>ู‚ูˆู„ู‡ ุชุนุงู„ู‰: {ูˆูŽุงุชู‘ูŽุฎูุฐููˆุง ู…ูู†ู’</td><td>ู…ูŽู‚ุงู…ู ุฅูุจู’ุฑุงู‡ููŠู…ูŽ ู…ูุตูŽู„ู‘ู‹ู‰ุ›} ู‚ุฑุฃ ุดูŠุจุฉ</td><td>ูˆู†ุงูุน ูˆุงุจู† ุนุงู…ุฑ</td><td>ูˆุงู„ุญุณู†: ยซ(ูˆุงุชู‘ุฎุฐูˆุง)ยป ุจูุชุญ ุงู„ุฎุงุก ุนู„ู‰ ุงู„ุฎุจุฑ. ูˆู‚ุฑุฃ</td></tr><tr><td>ุงู„ุจุงู‚ูˆู† ุจุงู„ูƒุณุฑ ุนู„ู‰ ุงู„ุฃู…ุฑ. ู‚ุงู„ ุงุจู†</td><td>ูƒูŠุณุงู†: (ุฐูƒุฑูˆุง ุฃู†ู‘ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡</td><td>ูˆุณู„ู… ู…ุฑู‘ ุจุงู„ู…ู‚ุงู…</td><td>ูˆู…ุนู‡ ุนู…ุฑ ุฑุถูŠ ุงู„ู„ู‡ ุนู†ู‡ุ›</td></tr><tr><td>ูู‚ุงู„: ูŠุง ุฑุณูˆู„ ุงู„ู„ู‡ุ› ุฃู„ูŠุณ</td><td>ู‡ุฐุง ู…ู‚ุงู… ุฃุจูŠู†ุง ุฅุจุฑุงู‡ูŠู…ุŸ ู‚ุงู„: [ุจู„ู‰].ู‚ุงู„: ุฃูู„ุง</td><td>ุชุชู‘ุฎุฐู‡ ู…ุตู„ู‘ู‰ุŸ ู‚ุงู„: [ู„ู… ุฃูˆู…ุฑ ุจุฐู„ูƒ].ูู„ู…</td><td>ุชุบุจ ุงู„ุดู‘ู…ุณ</td></tr></tbody></table>",
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