dataset / data /MachineTwo_002 /annotations /sample_0010002.json
Abrasive-jet's picture
Upload folder using huggingface_hub
31a6df2 verified
Raw History Blame Contribute Delete
46.9 kB
{
"markdown": "## ู…ู„ุงุญุธุฉ\nู…ู† ู‚ุฑูŠุด ููŠ ุงู„ุฌู†ุฉ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ููŠ ุงู„ุฌู†ุฉ ูˆุฃุจูˆ ุจูƒุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนู…ุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุซู…ุงู† ููŠ ุงู„ุฌู†ุฉ ูˆุนู„ูŠ ููŠ ุงู„ุฌู†ุฉ ูˆุทู„ุญุฉ ููŠ ุงู„ุฌู†ุฉ ูˆุงู„ุฒุจูŠุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุณุนุฏ ููŠ ุงู„ุฌู†ุฉ ูˆุนุจุฏ ุงู„ุฑุญู…ู† ููŠ ุงู„ุฌู†ุฉ ู‚ูŠู„ ู„ุณุนูŠุฏ ูˆู…ู† ุงู„ุนุงุดุฑ ูุจูƒู‰ ุซู… ู‚ุงู„ ุณุนูŠุฏ ุจู† ุฒูŠุฏ ูˆุฑูˆุงู‡ ูŠุฒูŠุฏ ุจู† ุงู„ุญุงุฑุซ ุนู† ุณุนูŠุฏ ุฃุฎุจุฑู†ุงู‡ ุฃุจูˆ ุนุจุฏ ุงู„ู„ู‡ ู…ุญู…ุฏ\n\\iint_{D} \\beta^2 \\times z^2 \\, dx \\, dy\n## ู…ู„ุงุญุธุฉ\nุจู† ุฃุญู…ุฏ ุจู† ุฅุจุฑุงู‡ูŠู… ููŠ ูƒุชุงุจู‡ ุซู… ุฃุฎุจุฑู†ุง ุฃุจูˆ ุนุจุฏ ุงู„ู„ู‡\ni_{n+1} = i_n - \\alpha \\nabla f(i_n)\n## ู…ุจุฑู‡ู†ุฉ\nุฃุดู‡ุฏ ุนู„ู‰ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุจู…ุง ุณู…ุนุชู‡ ุฃุฐู†ุงู† ูˆูˆุนุงู‡ ู‚ู„ุจูŠ ู…ู† ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุฅู†ูŠ ู„ู… ุฃูƒู† ู„ุฃุฑูˆูŠ ุนู†ู‡\nP(A|B) = \\frac{P(A \\cap B)}{P(B)}\n\\vec{F} = m\\vec{a}\n## ุชุนุฑูŠู\nูƒุฐุจุง ูŠุณุฃู„ู†ูŠ ูˆู‚ุงู„ ุงู„ุฏู‡ุณุชุงู†ูŠ ููŠุณุฃู„ู†ูŠ ุนู†ู‡ ุฅุฐุง ู„ู‚ูŠุชู‡ ุฃู†ู‡ ู‚ุงู„ ุฃุจูˆ ุจูƒุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนู…ุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุซู…ุงู† ููŠ ุงู„ุฌู†ุฉ ูˆุนู„ูŠ ููŠ ุงู„ุฌู†ุฉ ูˆุทู„ุญุฉ ููŠ ุงู„ุฌู†ุฉ ูˆุงู„ุฒุจูŠุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุนูˆู ููŠ ุงู„ุฌู†ุฉ ูˆุณุนุฏ ุจู† ู…ุงู„ูƒ ููŠ ุงู„ุฌู†ุฉ ูˆุชุงุณุน ุงู„ู…ุคู…ู†ูŠู† ู„ูˆ ุดุฆุช ุฃู† ุฃุณู…ูŠู‡ ุณู…ูŠุชู‡ ูˆููŠ ุญุฏูŠุซ ุงู„ูุงุฑุณูŠ ู„ุณู…ูŠุชู‡ ู‚ุงู„ ูุฑุฌ ุฃู‡ู„ ุงู„ู…ุณุฌุฏ ูŠู†ุงุดุฏูˆู†ู‡\n\\sigma_{n+1} = \\sigma_n - \\alpha \\nabla f(\\sigma_n) + \\frac{n}{n^2}\n## ู†ุธุฑูŠุฉ\nูŠุง ุตุงุญุจ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ู…ู† ุงู„ุชุงุณุน ู‚ุงู„ ู†ุงุดุฏุชู…ูˆู†ูŠ ุจุงู„ู„ู‡ ูˆุงู„ู„ู‡ ุนุธูŠู… ุฃู†ุง ุชุงุณุน ุงู„ู…ุคู…ู†ูŠู† ูˆุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุงู„ุนุงุดุฑ ุซู… ุฃุชุจุน ุฐู„ูƒ ูŠู…ูŠู†ุง ูˆุงู„ู„ู‡ ู„ู…ุดู‡ุฏ ุดู‡ุฏู‡ ุฑุฌู„ ู…ุน ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูˆุฒุงุฏ ุงู„ุฏู‡ุณุชุงู†ูŠ ุงุบุจุฑ\n\\int_{3}^{100} \\exp(x) \\, dx = x^2 \\geq C\n\\prod_{t=1}^{n} (1 \\geq z_t) = 0\n\\frac{\\partial \\beta}{\\partial i} = \\lim_{h \\to 0} \\frac{\\exp(i + h) - \\exp(i)}{h}",
"images": [],
"tables": [],
"hyperlinks": [],
"header": null,
"footer": null,
"dimensions": {
"dpi": 96,
"height": 1097,
"width": 761
},
"confidence_scores": {
"word_confidence_scores": [
{
"text": "##",
"confidence": 1.0,
"start_index": 0
},
{
"text": "ู…ู„ุงุญุธุฉ",
"confidence": 1.0,
"start_index": 3
},
{
"text": "ู…ู†",
"confidence": 1.0,
"start_index": 10
},
{
"text": "ู‚ุฑูŠุด",
"confidence": 1.0,
"start_index": 13
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 18
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 21
},
{
"text": "ุฑุณูˆู„",
"confidence": 1.0,
"start_index": 27
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 32
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 37
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 41
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 46
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 51
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 56
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 59
},
{
"text": "ูˆุฃุจูˆ",
"confidence": 1.0,
"start_index": 65
},
{
"text": "ุจูƒุฑ",
"confidence": 1.0,
"start_index": 70
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 74
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 77
},
{
"text": "ูˆุนู…ุฑ",
"confidence": 1.0,
"start_index": 83
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 88
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 91
},
{
"text": "ูˆุนุซู…ุงู†",
"confidence": 1.0,
"start_index": 97
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 104
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 107
},
{
"text": "ูˆุนู„ูŠ",
"confidence": 1.0,
"start_index": 113
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 118
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 121
},
{
"text": "ูˆุทู„ุญุฉ",
"confidence": 1.0,
"start_index": 127
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 133
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 136
},
{
"text": "ูˆุงู„ุฒุจูŠุฑ",
"confidence": 1.0,
"start_index": 142
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 150
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 153
},
{
"text": "ูˆุณุนุฏ",
"confidence": 1.0,
"start_index": 159
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 164
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 167
},
{
"text": "ูˆุนุจุฏ",
"confidence": 1.0,
"start_index": 173
},
{
"text": "ุงู„ุฑุญู…ู†",
"confidence": 1.0,
"start_index": 178
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 185
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 188
},
{
"text": "ู‚ูŠู„",
"confidence": 1.0,
"start_index": 194
},
{
"text": "ู„ุณุนูŠุฏ",
"confidence": 1.0,
"start_index": 198
},
{
"text": "ูˆู…ู†",
"confidence": 1.0,
"start_index": 204
},
{
"text": "ุงู„ุนุงุดุฑ",
"confidence": 1.0,
"start_index": 208
},
{
"text": "ูุจูƒู‰",
"confidence": 1.0,
"start_index": 215
},
{
"text": "ุซู…",
"confidence": 1.0,
"start_index": 220
},
{
"text": "ู‚ุงู„",
"confidence": 1.0,
"start_index": 223
},
{
"text": "ุณุนูŠุฏ",
"confidence": 1.0,
"start_index": 227
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 232
},
{
"text": "ุฒูŠุฏ",
"confidence": 1.0,
"start_index": 235
},
{
"text": "ูˆุฑูˆุงู‡",
"confidence": 1.0,
"start_index": 239
},
{
"text": "ูŠุฒูŠุฏ",
"confidence": 1.0,
"start_index": 245
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 250
},
{
"text": "ุงู„ุญุงุฑุซ",
"confidence": 1.0,
"start_index": 253
},
{
"text": "ุนู†",
"confidence": 1.0,
"start_index": 260
},
{
"text": "ุณุนูŠุฏ",
"confidence": 1.0,
"start_index": 263
},
{
"text": "ุฃุฎุจุฑู†ุงู‡",
"confidence": 1.0,
"start_index": 268
},
{
"text": "ุฃุจูˆ",
"confidence": 1.0,
"start_index": 276
},
{
"text": "ุนุจุฏ",
"confidence": 1.0,
"start_index": 280
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 284
},
{
"text": "ู…ุญู…ุฏ",
"confidence": 1.0,
"start_index": 289
},
{
"text": "\\iint_{D}",
"confidence": 1.0,
"start_index": 294
},
{
"text": "\\beta^2",
"confidence": 1.0,
"start_index": 304
},
{
"text": "\\times",
"confidence": 1.0,
"start_index": 312
},
{
"text": "z^2",
"confidence": 1.0,
"start_index": 319
},
{
"text": "\\,",
"confidence": 1.0,
"start_index": 323
},
{
"text": "dx",
"confidence": 1.0,
"start_index": 326
},
{
"text": "\\,",
"confidence": 1.0,
"start_index": 329
},
{
"text": "dy",
"confidence": 1.0,
"start_index": 332
},
{
"text": "##",
"confidence": 1.0,
"start_index": 335
},
{
"text": "ู…ู„ุงุญุธุฉ",
"confidence": 1.0,
"start_index": 338
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 345
},
{
"text": "ุฃุญู…ุฏ",
"confidence": 1.0,
"start_index": 348
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 353
},
{
"text": "ุฅุจุฑุงู‡ูŠู…",
"confidence": 1.0,
"start_index": 356
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 364
},
{
"text": "ูƒุชุงุจู‡",
"confidence": 1.0,
"start_index": 367
},
{
"text": "ุซู…",
"confidence": 1.0,
"start_index": 373
},
{
"text": "ุฃุฎุจุฑู†ุง",
"confidence": 1.0,
"start_index": 376
},
{
"text": "ุฃุจูˆ",
"confidence": 1.0,
"start_index": 383
},
{
"text": "ุนุจุฏ",
"confidence": 1.0,
"start_index": 387
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 391
},
{
"text": "i_{n+1}",
"confidence": 1.0,
"start_index": 396
},
{
"text": "=",
"confidence": 1.0,
"start_index": 404
},
{
"text": "i_n",
"confidence": 1.0,
"start_index": 406
},
{
"text": "-",
"confidence": 1.0,
"start_index": 410
},
{
"text": "\\alpha",
"confidence": 1.0,
"start_index": 412
},
{
"text": "\\nabla",
"confidence": 1.0,
"start_index": 419
},
{
"text": "f(i_n)",
"confidence": 1.0,
"start_index": 426
},
{
"text": "##",
"confidence": 1.0,
"start_index": 433
},
{
"text": "ู…ุจุฑู‡ู†ุฉ",
"confidence": 1.0,
"start_index": 436
},
{
"text": "ุฃุดู‡ุฏ",
"confidence": 1.0,
"start_index": 443
},
{
"text": "ุนู„ู‰",
"confidence": 1.0,
"start_index": 448
},
{
"text": "ุฑุณูˆู„",
"confidence": 1.0,
"start_index": 452
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 457
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 462
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 466
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 471
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 476
},
{
"text": "ุจู…ุง",
"confidence": 1.0,
"start_index": 481
},
{
"text": "ุณู…ุนุชู‡",
"confidence": 1.0,
"start_index": 485
},
{
"text": "ุฃุฐู†ุงู†",
"confidence": 1.0,
"start_index": 491
},
{
"text": "ูˆูˆุนุงู‡",
"confidence": 1.0,
"start_index": 497
},
{
"text": "ู‚ู„ุจูŠ",
"confidence": 1.0,
"start_index": 503
},
{
"text": "ู…ู†",
"confidence": 1.0,
"start_index": 508
},
{
"text": "ุฑุณูˆู„",
"confidence": 1.0,
"start_index": 511
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 516
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 521
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 525
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 530
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 535
},
{
"text": "ูุฅู†ูŠ",
"confidence": 1.0,
"start_index": 540
},
{
"text": "ู„ู…",
"confidence": 1.0,
"start_index": 545
},
{
"text": "ุฃูƒู†",
"confidence": 1.0,
"start_index": 548
},
{
"text": "ู„ุฃุฑูˆูŠ",
"confidence": 1.0,
"start_index": 552
},
{
"text": "ุนู†ู‡",
"confidence": 1.0,
"start_index": 558
},
{
"text": "P(A|B)",
"confidence": 1.0,
"start_index": 562
},
{
"text": "=",
"confidence": 1.0,
"start_index": 569
},
{
"text": "\\frac{P(A",
"confidence": 1.0,
"start_index": 571
},
{
"text": "\\cap",
"confidence": 1.0,
"start_index": 581
},
{
"text": "B)}{P(B)}",
"confidence": 1.0,
"start_index": 586
},
{
"text": "\\vec{F}",
"confidence": 1.0,
"start_index": 596
},
{
"text": "=",
"confidence": 1.0,
"start_index": 604
},
{
"text": "m\\vec{a}",
"confidence": 1.0,
"start_index": 606
},
{
"text": "##",
"confidence": 1.0,
"start_index": 615
},
{
"text": "ุชุนุฑูŠู",
"confidence": 1.0,
"start_index": 618
},
{
"text": "ูƒุฐุจุง",
"confidence": 1.0,
"start_index": 624
},
{
"text": "ูŠุณุฃู„ู†ูŠ",
"confidence": 1.0,
"start_index": 629
},
{
"text": "ูˆู‚ุงู„",
"confidence": 1.0,
"start_index": 636
},
{
"text": "ุงู„ุฏู‡ุณุชุงู†ูŠ",
"confidence": 1.0,
"start_index": 641
},
{
"text": "ููŠุณุฃู„ู†ูŠ",
"confidence": 1.0,
"start_index": 651
},
{
"text": "ุนู†ู‡",
"confidence": 1.0,
"start_index": 659
},
{
"text": "ุฅุฐุง",
"confidence": 1.0,
"start_index": 663
},
{
"text": "ู„ู‚ูŠุชู‡",
"confidence": 1.0,
"start_index": 667
},
{
"text": "ุฃู†ู‡",
"confidence": 1.0,
"start_index": 673
},
{
"text": "ู‚ุงู„",
"confidence": 1.0,
"start_index": 677
},
{
"text": "ุฃุจูˆ",
"confidence": 1.0,
"start_index": 681
},
{
"text": "ุจูƒุฑ",
"confidence": 1.0,
"start_index": 685
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 689
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 692
},
{
"text": "ูˆุนู…ุฑ",
"confidence": 1.0,
"start_index": 698
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 703
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 706
},
{
"text": "ูˆุนุซู…ุงู†",
"confidence": 1.0,
"start_index": 712
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 719
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 722
},
{
"text": "ูˆุนู„ูŠ",
"confidence": 1.0,
"start_index": 728
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 733
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 736
},
{
"text": "ูˆุทู„ุญุฉ",
"confidence": 1.0,
"start_index": 742
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 748
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 751
},
{
"text": "ูˆุงู„ุฒุจูŠุฑ",
"confidence": 1.0,
"start_index": 757
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 765
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 768
},
{
"text": "ูˆุนุจุฏ",
"confidence": 1.0,
"start_index": 774
},
{
"text": "ุงู„ุฑุญู…ู†",
"confidence": 1.0,
"start_index": 779
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 786
},
{
"text": "ุนูˆู",
"confidence": 1.0,
"start_index": 789
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 793
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 796
},
{
"text": "ูˆุณุนุฏ",
"confidence": 1.0,
"start_index": 802
},
{
"text": "ุจู†",
"confidence": 1.0,
"start_index": 807
},
{
"text": "ู…ุงู„ูƒ",
"confidence": 1.0,
"start_index": 810
},
{
"text": "ููŠ",
"confidence": 1.0,
"start_index": 815
},
{
"text": "ุงู„ุฌู†ุฉ",
"confidence": 1.0,
"start_index": 818
},
{
"text": "ูˆุชุงุณุน",
"confidence": 1.0,
"start_index": 824
},
{
"text": "ุงู„ู…ุคู…ู†ูŠู†",
"confidence": 1.0,
"start_index": 830
},
{
"text": "ู„ูˆ",
"confidence": 1.0,
"start_index": 839
},
{
"text": "ุดุฆุช",
"confidence": 1.0,
"start_index": 842
},
{
"text": "ุฃู†",
"confidence": 1.0,
"start_index": 846
},
{
"text": "ุฃุณู…ูŠู‡",
"confidence": 1.0,
"start_index": 849
},
{
"text": "ุณู…ูŠุชู‡",
"confidence": 1.0,
"start_index": 855
},
{
"text": "ูˆููŠ",
"confidence": 1.0,
"start_index": 861
},
{
"text": "ุญุฏูŠุซ",
"confidence": 1.0,
"start_index": 865
},
{
"text": "ุงู„ูุงุฑุณูŠ",
"confidence": 1.0,
"start_index": 870
},
{
"text": "ู„ุณู…ูŠุชู‡",
"confidence": 1.0,
"start_index": 878
},
{
"text": "ู‚ุงู„",
"confidence": 1.0,
"start_index": 885
},
{
"text": "ูุฑุฌ",
"confidence": 1.0,
"start_index": 889
},
{
"text": "ุฃู‡ู„",
"confidence": 1.0,
"start_index": 893
},
{
"text": "ุงู„ู…ุณุฌุฏ",
"confidence": 1.0,
"start_index": 897
},
{
"text": "ูŠู†ุงุดุฏูˆู†ู‡",
"confidence": 1.0,
"start_index": 904
},
{
"text": "\\sigma_{n+1}",
"confidence": 1.0,
"start_index": 913
},
{
"text": "=",
"confidence": 1.0,
"start_index": 926
},
{
"text": "\\sigma_n",
"confidence": 1.0,
"start_index": 928
},
{
"text": "-",
"confidence": 1.0,
"start_index": 937
},
{
"text": "\\alpha",
"confidence": 1.0,
"start_index": 939
},
{
"text": "\\nabla",
"confidence": 1.0,
"start_index": 946
},
{
"text": "f(\\sigma_n)",
"confidence": 1.0,
"start_index": 953
},
{
"text": "+",
"confidence": 1.0,
"start_index": 965
},
{
"text": "\\frac{n}{n^2}",
"confidence": 1.0,
"start_index": 967
},
{
"text": "##",
"confidence": 1.0,
"start_index": 981
},
{
"text": "ู†ุธุฑูŠุฉ",
"confidence": 1.0,
"start_index": 984
},
{
"text": "ูŠุง",
"confidence": 1.0,
"start_index": 990
},
{
"text": "ุตุงุญุจ",
"confidence": 1.0,
"start_index": 993
},
{
"text": "ุฑุณูˆู„",
"confidence": 1.0,
"start_index": 998
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1003
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 1008
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1012
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 1017
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 1022
},
{
"text": "ู…ู†",
"confidence": 1.0,
"start_index": 1027
},
{
"text": "ุงู„ุชุงุณุน",
"confidence": 1.0,
"start_index": 1030
},
{
"text": "ู‚ุงู„",
"confidence": 1.0,
"start_index": 1037
},
{
"text": "ู†ุงุดุฏุชู…ูˆู†ูŠ",
"confidence": 1.0,
"start_index": 1041
},
{
"text": "ุจุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1051
},
{
"text": "ูˆุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1057
},
{
"text": "ุนุธูŠู…",
"confidence": 1.0,
"start_index": 1063
},
{
"text": "ุฃู†ุง",
"confidence": 1.0,
"start_index": 1068
},
{
"text": "ุชุงุณุน",
"confidence": 1.0,
"start_index": 1072
},
{
"text": "ุงู„ู…ุคู…ู†ูŠู†",
"confidence": 1.0,
"start_index": 1077
},
{
"text": "ูˆุฑุณูˆู„",
"confidence": 1.0,
"start_index": 1086
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1092
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 1097
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1101
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 1106
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 1111
},
{
"text": "ุงู„ุนุงุดุฑ",
"confidence": 1.0,
"start_index": 1116
},
{
"text": "ุซู…",
"confidence": 1.0,
"start_index": 1123
},
{
"text": "ุฃุชุจุน",
"confidence": 1.0,
"start_index": 1126
},
{
"text": "ุฐู„ูƒ",
"confidence": 1.0,
"start_index": 1131
},
{
"text": "ูŠู…ูŠู†ุง",
"confidence": 1.0,
"start_index": 1135
},
{
"text": "ูˆุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1141
},
{
"text": "ู„ู…ุดู‡ุฏ",
"confidence": 1.0,
"start_index": 1147
},
{
"text": "ุดู‡ุฏู‡",
"confidence": 1.0,
"start_index": 1153
},
{
"text": "ุฑุฌู„",
"confidence": 1.0,
"start_index": 1158
},
{
"text": "ู…ุน",
"confidence": 1.0,
"start_index": 1162
},
{
"text": "ุฑุณูˆู„",
"confidence": 1.0,
"start_index": 1165
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1170
},
{
"text": "ุตู„ู‰",
"confidence": 1.0,
"start_index": 1175
},
{
"text": "ุงู„ู„ู‡",
"confidence": 1.0,
"start_index": 1179
},
{
"text": "ุนู„ูŠู‡",
"confidence": 1.0,
"start_index": 1184
},
{
"text": "ูˆุณู„ู…",
"confidence": 1.0,
"start_index": 1189
},
{
"text": "ูˆุฒุงุฏ",
"confidence": 1.0,
"start_index": 1194
},
{
"text": "ุงู„ุฏู‡ุณุชุงู†ูŠ",
"confidence": 1.0,
"start_index": 1199
},
{
"text": "ุงุบุจุฑ",
"confidence": 1.0,
"start_index": 1209
},
{
"text": "\\int_{3}^{100}",
"confidence": 1.0,
"start_index": 1214
},
{
"text": "\\exp(x)",
"confidence": 1.0,
"start_index": 1229
},
{
"text": "\\,",
"confidence": 1.0,
"start_index": 1237
},
{
"text": "dx",
"confidence": 1.0,
"start_index": 1240
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1243
},
{
"text": "x^2",
"confidence": 1.0,
"start_index": 1245
},
{
"text": "\\geq",
"confidence": 1.0,
"start_index": 1249
},
{
"text": "C",
"confidence": 1.0,
"start_index": 1254
},
{
"text": "\\prod_{t=1}^{n}",
"confidence": 1.0,
"start_index": 1256
},
{
"text": "(1",
"confidence": 1.0,
"start_index": 1272
},
{
"text": "\\geq",
"confidence": 1.0,
"start_index": 1275
},
{
"text": "z_t)",
"confidence": 1.0,
"start_index": 1280
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1285
},
{
"text": "0",
"confidence": 1.0,
"start_index": 1287
},
{
"text": "\\frac{\\partial",
"confidence": 1.0,
"start_index": 1289
},
{
"text": "\\beta}{\\partial",
"confidence": 1.0,
"start_index": 1304
},
{
"text": "i}",
"confidence": 1.0,
"start_index": 1320
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1323
},
{
"text": "\\lim_{h",
"confidence": 1.0,
"start_index": 1325
},
{
"text": "\\to",
"confidence": 1.0,
"start_index": 1333
},
{
"text": "0}",
"confidence": 1.0,
"start_index": 1337
},
{
"text": "\\frac{\\exp(i",
"confidence": 1.0,
"start_index": 1340
},
{
"text": "+",
"confidence": 1.0,
"start_index": 1353
},
{
"text": "h)",
"confidence": 1.0,
"start_index": 1355
},
{
"text": "-",
"confidence": 1.0,
"start_index": 1358
},
{
"text": "\\exp(i)}{h}",
"confidence": 1.0,
"start_index": 1360
}
],
"average_page_confidence_score": 1.0,
"minimum_page_confidence_score": 1.0
},
"blocks": [
{
"top_left_x": 52,
"top_left_y": 52,
"bottom_right_x": 705,
"bottom_right_y": 71,
"content": "ู…ู„ุงุญุธุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 1
},
{
"top_left_x": 52,
"top_left_y": 76,
"bottom_right_x": 705,
"bottom_right_y": 143,
"content": "ู…ู† ู‚ุฑูŠุด ููŠ ุงู„ุฌู†ุฉ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ููŠ ุงู„ุฌู†ุฉ ูˆุฃุจูˆ ุจูƒุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนู…ุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุซู…ุงู† ููŠ ุงู„ุฌู†ุฉ ูˆุนู„ูŠ ููŠ ุงู„ุฌู†ุฉ ูˆุทู„ุญุฉ ููŠ ุงู„ุฌู†ุฉ ูˆุงู„ุฒุจูŠุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุณุนุฏ ููŠ ุงู„ุฌู†ุฉ ูˆุนุจุฏ ุงู„ุฑุญู…ู† ููŠ ุงู„ุฌู†ุฉ ู‚ูŠู„ ู„ุณุนูŠุฏ ูˆู…ู† ุงู„ุนุงุดุฑ ูุจูƒู‰ ุซู… ู‚ุงู„ ุณุนูŠุฏ ุจู† ุฒูŠุฏ ูˆุฑูˆุงู‡ ูŠุฒูŠุฏ ุจู† ุงู„ุญุงุฑุซ ุนู† ุณุนูŠุฏ ุฃุฎุจุฑู†ุงู‡ ุฃุจูˆ ุนุจุฏ ุงู„ู„ู‡ ู…ุญู…ุฏ",
"type": "text",
"confidence_scores": null,
"reading_index": 2
},
{
"top_left_x": 52,
"top_left_y": 149,
"bottom_right_x": 705,
"bottom_right_y": 204,
"content": "\\iint_{D} \\beta^2 \\times z^2 \\, dx \\, dy",
"type": "text",
"confidence_scores": null,
"reading_index": 3
},
{
"top_left_x": 52,
"top_left_y": 248,
"bottom_right_x": 705,
"bottom_right_y": 267,
"content": "ู…ู„ุงุญุธุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 4
},
{
"top_left_x": 52,
"top_left_y": 272,
"bottom_right_x": 705,
"bottom_right_y": 294,
"content": "ุจู† ุฃุญู…ุฏ ุจู† ุฅุจุฑุงู‡ูŠู… ููŠ ูƒุชุงุจู‡ ุซู… ุฃุฎุจุฑู†ุง ุฃุจูˆ ุนุจุฏ ุงู„ู„ู‡",
"type": "text",
"confidence_scores": null,
"reading_index": 5
},
{
"top_left_x": 52,
"top_left_y": 300,
"bottom_right_x": 705,
"bottom_right_y": 338,
"content": "i_{n+1} = i_n - \\alpha \\nabla f(i_n)",
"type": "text",
"confidence_scores": null,
"reading_index": 6
},
{
"top_left_x": 52,
"top_left_y": 382,
"bottom_right_x": 705,
"bottom_right_y": 401,
"content": "ู…ุจุฑู‡ู†ุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 7
},
{
"top_left_x": 52,
"top_left_y": 406,
"bottom_right_x": 705,
"bottom_right_y": 429,
"content": "ุฃุดู‡ุฏ ุนู„ู‰ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุจู…ุง ุณู…ุนุชู‡ ุฃุฐู†ุงู† ูˆูˆุนุงู‡ ู‚ู„ุจูŠ ู…ู† ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูุฅู†ูŠ ู„ู… ุฃูƒู† ู„ุฃุฑูˆูŠ ุนู†ู‡",
"type": "text",
"confidence_scores": null,
"reading_index": 8
},
{
"top_left_x": 52,
"top_left_y": 435,
"bottom_right_x": 705,
"bottom_right_y": 491,
"content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)}",
"type": "text",
"confidence_scores": null,
"reading_index": 9
},
{
"top_left_x": 40,
"top_left_y": 523,
"bottom_right_x": 721,
"bottom_right_y": 567,
"content": "\\vec{F} = m\\vec{a}",
"type": "text",
"confidence_scores": null,
"reading_index": 10
},
{
"top_left_x": 52,
"top_left_y": 585,
"bottom_right_x": 705,
"bottom_right_y": 604,
"content": "ุชุนุฑูŠู",
"type": "title",
"confidence_scores": null,
"reading_index": 11
},
{
"top_left_x": 52,
"top_left_y": 609,
"bottom_right_x": 705,
"bottom_right_y": 676,
"content": "ูƒุฐุจุง ูŠุณุฃู„ู†ูŠ ูˆู‚ุงู„ ุงู„ุฏู‡ุณุชุงู†ูŠ ููŠุณุฃู„ู†ูŠ ุนู†ู‡ ุฅุฐุง ู„ู‚ูŠุชู‡ ุฃู†ู‡ ู‚ุงู„ ุฃุจูˆ ุจูƒุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนู…ุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุซู…ุงู† ููŠ ุงู„ุฌู†ุฉ ูˆุนู„ูŠ ููŠ ุงู„ุฌู†ุฉ ูˆุทู„ุญุฉ ููŠ ุงู„ุฌู†ุฉ ูˆุงู„ุฒุจูŠุฑ ููŠ ุงู„ุฌู†ุฉ ูˆุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุนูˆู ููŠ ุงู„ุฌู†ุฉ ูˆุณุนุฏ ุจู† ู…ุงู„ูƒ ููŠ ุงู„ุฌู†ุฉ ูˆุชุงุณุน ุงู„ู…ุคู…ู†ูŠู† ู„ูˆ ุดุฆุช ุฃู† ุฃุณู…ูŠู‡ ุณู…ูŠุชู‡ ูˆููŠ ุญุฏูŠุซ ุงู„ูุงุฑุณูŠ ู„ุณู…ูŠุชู‡ ู‚ุงู„ ูุฑุฌ ุฃู‡ู„ ุงู„ู…ุณุฌุฏ ูŠู†ุงุดุฏูˆู†ู‡",
"type": "text",
"confidence_scores": null,
"reading_index": 12
},
{
"top_left_x": 52,
"top_left_y": 682,
"bottom_right_x": 705,
"bottom_right_y": 729,
"content": "\\sigma_{n+1} = \\sigma_n - \\alpha \\nabla f(\\sigma_n) + \\frac{n}{n^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 13
},
{
"top_left_x": 52,
"top_left_y": 773,
"bottom_right_x": 705,
"bottom_right_y": 792,
"content": "ู†ุธุฑูŠุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 14
},
{
"top_left_x": 52,
"top_left_y": 797,
"bottom_right_x": 705,
"bottom_right_y": 842,
"content": "ูŠุง ุตุงุญุจ ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ู…ู† ุงู„ุชุงุณุน ู‚ุงู„ ู†ุงุดุฏุชู…ูˆู†ูŠ ุจุงู„ู„ู‡ ูˆุงู„ู„ู‡ ุนุธูŠู… ุฃู†ุง ุชุงุณุน ุงู„ู…ุคู…ู†ูŠู† ูˆุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ุงู„ุนุงุดุฑ ุซู… ุฃุชุจุน ุฐู„ูƒ ูŠู…ูŠู†ุง ูˆุงู„ู„ู‡ ู„ู…ุดู‡ุฏ ุดู‡ุฏู‡ ุฑุฌู„ ู…ุน ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูˆุฒุงุฏ ุงู„ุฏู‡ุณุชุงู†ูŠ ุงุบุจุฑ",
"type": "text",
"confidence_scores": null,
"reading_index": 15
},
{
"top_left_x": 52,
"top_left_y": 848,
"bottom_right_x": 705,
"bottom_right_y": 906,
"content": "\\int_{3}^{100} \\exp(x) \\, dx = x^2 \\geq C",
"type": "text",
"confidence_scores": null,
"reading_index": 16
},
{
"top_left_x": 40,
"top_left_y": 938,
"bottom_right_x": 721,
"bottom_right_y": 1008,
"content": "\\prod_{t=1}^{n} (1 \\geq z_t) = 0",
"type": "text",
"confidence_scores": null,
"reading_index": 17
},
{
"top_left_x": 40,
"top_left_y": 1014,
"bottom_right_x": 721,
"bottom_right_y": 1067,
"content": "\\frac{\\partial \\beta}{\\partial i} = \\lim_{h \\to 0} \\frac{\\exp(i + h) - \\exp(i)}{h}",
"type": "text",
"confidence_scores": null,
"reading_index": 18
}
],
"meta": {
"template": "math_proof",
"hybrid": null,
"page_font": "haradh-semibold.otf",
"title_font": "ge-jarida-heavy-italic.otf",
"language": "ar",
"script": "arabic",
"direction": "rtl",
"augmentation": null
}
}