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{
    "markdown": "## ุจุฑู‡ุงู†\nูˆุงู„ุนูŠู† ุงู„ุฎูŠุงุฑ ู…ู† ุงู„ู†ู‘ุงุณุŒ ูˆุงู„ุนูŠู† ุงู„ุฌุงุณูˆุณ. ูˆู…ูุงุฏ ุงู„ู‚ุงุนุฏุฉ: ุฃู†ู‘ ุงู„ู…ุดุชุฑูƒ ู…ู† ุญูŠุซ ุญู…ู„ู‡ ุนู„ู‰ ูƒู„ู‘ ู…ุนุงู†ูŠู‡ ุฃูˆ ุนู„ู‰ ู…ุนู†ู‰ ุฏูˆู† ุขุฎุฑ ู…ุณุฃู„ุฉ ุฎู„ุงููŠู‘ุฉ ุจูŠู† ุงู„ูู‚ู‡ุงุก\n\\prod_{\\sigma=1}^{n} (1 \\geq \\beta_\\sigma) = 0\n## ู…ุจุฑู‡ู†ุฉ\nูˆุงู„ุฃุตูˆู„ูŠู‘ูŠู†. ูู‚ุฏ ุฐู‡ุจ ุงู„ุดู‘ุงูุนูŠ ุฑุญู…ู‡ ุงู„ู„ู‡ ูˆุฌู…ุงุนุฉ ู…ู† ูู‚ู‡ุงุก ูˆุฃุตูˆู„ูŠูŠ ุงู„ุดู‘ุงูุนูŠู‘ุฉ ุฅู„ู‰ ุฌูˆุงุฒู‡ุŒ ูˆุฐู‡ุจ ุขุฎุฑูˆู† ู…ู†ู‡ู… ูˆุนู„ู‰ ุฑุฃุณู‡ู… ุฅู…ุงู… ุงู„ุญุฑู…ูŠู† ูˆุงู„ุบุฒุงู„ูŠ\nn_{n+1} = n_n - \\alpha \\nabla f(n_n)\n\\iint_{D} \\alpha^2 \\times j^2 \\, dx \\, dy\n## ุจุฑู‡ุงู†\nุฑุญู…ู‡ู…ุง ุงู„ู„ู‡ุŒ ูˆุงู„ุญู†ููŠู‘ุฉ ุฅู„ู‰ ู…ู†ุนู‡ ูˆุบูŠุฑู‡ู…. โ€Œ โ€Œุซุงู„ุซุงู‹: ู…ู† ุฃู…ุซู„ุฉ ู‡ุฐู‡ ุงู„ู‚ุงุนุฏุฉ ูˆู…ุณุงุฆู„ู‡ุง: ู„ูˆ ูˆู‚ู‘ู ุฃูˆ ุฃูˆุตู‰ ุนู„ู‰ ู…ูˆุงู„ูŠู‡ุŒ ูˆู„ู‡ ู…ูˆุงู„ู ู…ู† ุฃุนู„ู‰ ูˆู…ูˆุงู„ู ู…ู†\n\\mathbb{E}[j] = \\int x f_j(x) dx + \\frac{i}{z^2}",
    "images": [],
    "tables": [],
    "hyperlinks": [],
    "header": null,
    "footer": null,
    "dimensions": {
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        "height": 645,
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    },
    "confidence_scores": {
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            {
                "text": "##",
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            },
            {
                "text": "ุจุฑู‡ุงู†",
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                "start_index": 3
            },
            {
                "text": "ูˆุงู„ุนูŠู†",
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                "start_index": 9
            },
            {
                "text": "ุงู„ุฎูŠุงุฑ",
                "confidence": 1.0,
                "start_index": 16
            },
            {
                "text": "ู…ู†",
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                "text": "ุงู„ู†ู‘ุงุณุŒ",
                "confidence": 1.0,
                "start_index": 26
            },
            {
                "text": "ูˆุงู„ุนูŠู†",
                "confidence": 1.0,
                "start_index": 34
            },
            {
                "text": "ุงู„ุฌุงุณูˆุณ.",
                "confidence": 1.0,
                "start_index": 41
            },
            {
                "text": "ูˆู…ูุงุฏ",
                "confidence": 1.0,
                "start_index": 50
            },
            {
                "text": "ุงู„ู‚ุงุนุฏุฉ:",
                "confidence": 1.0,
                "start_index": 56
            },
            {
                "text": "ุฃู†ู‘",
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                "start_index": 65
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            {
                "text": "ุงู„ู…ุดุชุฑูƒ",
                "confidence": 1.0,
                "start_index": 69
            },
            {
                "text": "ู…ู†",
                "confidence": 1.0,
                "start_index": 77
            },
            {
                "text": "ุญูŠุซ",
                "confidence": 1.0,
                "start_index": 80
            },
            {
                "text": "ุญู…ู„ู‡",
                "confidence": 1.0,
                "start_index": 84
            },
            {
                "text": "ุนู„ู‰",
                "confidence": 1.0,
                "start_index": 89
            },
            {
                "text": "ูƒู„ู‘",
                "confidence": 1.0,
                "start_index": 93
            },
            {
                "text": "ู…ุนุงู†ูŠู‡",
                "confidence": 1.0,
                "start_index": 97
            },
            {
                "text": "ุฃูˆ",
                "confidence": 1.0,
                "start_index": 104
            },
            {
                "text": "ุนู„ู‰",
                "confidence": 1.0,
                "start_index": 107
            },
            {
                "text": "ู…ุนู†ู‰",
                "confidence": 1.0,
                "start_index": 111
            },
            {
                "text": "ุฏูˆู†",
                "confidence": 1.0,
                "start_index": 116
            },
            {
                "text": "ุขุฎุฑ",
                "confidence": 1.0,
                "start_index": 120
            },
            {
                "text": "ู…ุณุฃู„ุฉ",
                "confidence": 1.0,
                "start_index": 124
            },
            {
                "text": "ุฎู„ุงููŠู‘ุฉ",
                "confidence": 1.0,
                "start_index": 130
            },
            {
                "text": "ุจูŠู†",
                "confidence": 1.0,
                "start_index": 138
            },
            {
                "text": "ุงู„ูู‚ู‡ุงุก",
                "confidence": 1.0,
                "start_index": 142
            },
            {
                "text": "\\prod_{\\sigma=1}^{n}",
                "confidence": 1.0,
                "start_index": 150
            },
            {
                "text": "(1",
                "confidence": 1.0,
                "start_index": 171
            },
            {
                "text": "\\geq",
                "confidence": 1.0,
                "start_index": 174
            },
            {
                "text": "\\beta_\\sigma)",
                "confidence": 1.0,
                "start_index": 179
            },
            {
                "text": "=",
                "confidence": 1.0,
                "start_index": 193
            },
            {
                "text": "0",
                "confidence": 1.0,
                "start_index": 195
            },
            {
                "text": "##",
                "confidence": 1.0,
                "start_index": 197
            },
            {
                "text": "ู…ุจุฑู‡ู†ุฉ",
                "confidence": 1.0,
                "start_index": 200
            },
            {
                "text": "ูˆุงู„ุฃุตูˆู„ูŠู‘ูŠู†.",
                "confidence": 1.0,
                "start_index": 207
            },
            {
                "text": "ูู‚ุฏ",
                "confidence": 1.0,
                "start_index": 220
            },
            {
                "text": "ุฐู‡ุจ",
                "confidence": 1.0,
                "start_index": 224
            },
            {
                "text": "ุงู„ุดู‘ุงูุนูŠ",
                "confidence": 1.0,
                "start_index": 228
            },
            {
                "text": "ุฑุญู…ู‡",
                "confidence": 1.0,
                "start_index": 237
            },
            {
                "text": "ุงู„ู„ู‡",
                "confidence": 1.0,
                "start_index": 242
            },
            {
                "text": "ูˆุฌู…ุงุนุฉ",
                "confidence": 1.0,
                "start_index": 247
            },
            {
                "text": "ู…ู†",
                "confidence": 1.0,
                "start_index": 254
            },
            {
                "text": "ูู‚ู‡ุงุก",
                "confidence": 1.0,
                "start_index": 257
            },
            {
                "text": "ูˆุฃุตูˆู„ูŠูŠ",
                "confidence": 1.0,
                "start_index": 263
            },
            {
                "text": "ุงู„ุดู‘ุงูุนูŠู‘ุฉ",
                "confidence": 1.0,
                "start_index": 271
            },
            {
                "text": "ุฅู„ู‰",
                "confidence": 1.0,
                "start_index": 282
            },
            {
                "text": "ุฌูˆุงุฒู‡ุŒ",
                "confidence": 1.0,
                "start_index": 286
            },
            {
                "text": "ูˆุฐู‡ุจ",
                "confidence": 1.0,
                "start_index": 293
            },
            {
                "text": "ุขุฎุฑูˆู†",
                "confidence": 1.0,
                "start_index": 298
            },
            {
                "text": "ู…ู†ู‡ู…",
                "confidence": 1.0,
                "start_index": 304
            },
            {
                "text": "ูˆุนู„ู‰",
                "confidence": 1.0,
                "start_index": 309
            },
            {
                "text": "ุฑุฃุณู‡ู…",
                "confidence": 1.0,
                "start_index": 314
            },
            {
                "text": "ุฅู…ุงู…",
                "confidence": 1.0,
                "start_index": 320
            },
            {
                "text": "ุงู„ุญุฑู…ูŠู†",
                "confidence": 1.0,
                "start_index": 325
            },
            {
                "text": "ูˆุงู„ุบุฒุงู„ูŠ",
                "confidence": 1.0,
                "start_index": 333
            },
            {
                "text": "n_{n+1}",
                "confidence": 1.0,
                "start_index": 342
            },
            {
                "text": "=",
                "confidence": 1.0,
                "start_index": 350
            },
            {
                "text": "n_n",
                "confidence": 1.0,
                "start_index": 352
            },
            {
                "text": "-",
                "confidence": 1.0,
                "start_index": 356
            },
            {
                "text": "\\alpha",
                "confidence": 1.0,
                "start_index": 358
            },
            {
                "text": "\\nabla",
                "confidence": 1.0,
                "start_index": 365
            },
            {
                "text": "f(n_n)",
                "confidence": 1.0,
                "start_index": 372
            },
            {
                "text": "\\iint_{D}",
                "confidence": 1.0,
                "start_index": 379
            },
            {
                "text": "\\alpha^2",
                "confidence": 1.0,
                "start_index": 389
            },
            {
                "text": "\\times",
                "confidence": 1.0,
                "start_index": 398
            },
            {
                "text": "j^2",
                "confidence": 1.0,
                "start_index": 405
            },
            {
                "text": "\\,",
                "confidence": 1.0,
                "start_index": 409
            },
            {
                "text": "dx",
                "confidence": 1.0,
                "start_index": 412
            },
            {
                "text": "\\,",
                "confidence": 1.0,
                "start_index": 415
            },
            {
                "text": "dy",
                "confidence": 1.0,
                "start_index": 418
            },
            {
                "text": "##",
                "confidence": 1.0,
                "start_index": 421
            },
            {
                "text": "ุจุฑู‡ุงู†",
                "confidence": 1.0,
                "start_index": 424
            },
            {
                "text": "ุฑุญู…ู‡ู…ุง",
                "confidence": 1.0,
                "start_index": 430
            },
            {
                "text": "ุงู„ู„ู‡ุŒ",
                "confidence": 1.0,
                "start_index": 437
            },
            {
                "text": "ูˆุงู„ุญู†ููŠู‘ุฉ",
                "confidence": 1.0,
                "start_index": 443
            },
            {
                "text": "ุฅู„ู‰",
                "confidence": 1.0,
                "start_index": 453
            },
            {
                "text": "ู…ู†ุนู‡",
                "confidence": 1.0,
                "start_index": 457
            },
            {
                "text": "ูˆุบูŠุฑู‡ู….",
                "confidence": 1.0,
                "start_index": 462
            },
            {
                "text": "โ€Œ",
                "confidence": 1.0,
                "start_index": 470
            },
            {
                "text": "โ€Œุซุงู„ุซุงู‹:",
                "confidence": 1.0,
                "start_index": 472
            },
            {
                "text": "ู…ู†",
                "confidence": 1.0,
                "start_index": 481
            },
            {
                "text": "ุฃู…ุซู„ุฉ",
                "confidence": 1.0,
                "start_index": 484
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