dataset / data /run_test_001 /annotations /sample_0000008.json
Zetati's picture
Upload folder using huggingface_hub
6032230 verified
Raw History Blame Contribute Delete
30.2 kB
{
"markdown": "## ู…ู„ุงุญุธุฉ\nูˆูŽุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู ูููŠ ู‡ูŽุฐูู‡ู ุงุณู’ุชูุญู’ุจูŽุงุจู ุงู†ู’ุชูุธูŽุงุฑูู‡ูุ› ู„ูุฃูŽู†ู‘ูŽ ุงู„ุฑู‘ูŽูƒู’ุนูŽุฉูŽ ุชูุญู’ุณูŽุจู ุนูŽู†ู’ ุงู„ู’ู…ูŽุฃู’ู…ููˆู…ู ูููŠ ุฅุณู’ู‚ูŽุงุทู ุญูุฑู’ู…ูŽุฉู ุงู„ู’ูˆูŽู‚ู’ุชู. ููŽุฑู’ุนูŒ ูˆูŽุฌูŽุฏูŽ ู…ูุตูŽู„ู‘ููŠู‹ุง ุฌูŽุงู„ูุณู‹ุง ูˆูŽุดูŽูƒู‘ูŽ ู‡ูŽู„ู’ ู‡ููˆูŽ ูููŠ ุงู„ุชู‘ูŽุดูŽู‡ู‘ูุฏู ุฃูŽูˆู’ ุงู„ู’ู‚ููŠูŽุงู…ู ู„ูุนูŽุฌู’ุฒูู‡ู ููŽู‡ูŽู„ู’ ู„ูŽู‡ู ุฃูŽู†ู’ ูŠูŽู‚ู’ุชูŽุฏููŠูŽ ุจูู‡ู ุฃูŽูˆู’ ู„ูŽุงุŸ ูˆูŽูƒูŽุฐูŽุง ู„ูŽูˆู’ ุฑูŽุขู‡ู ูููŠ ูˆูŽู‚ู’ุชู ุงู„ู’ูƒูุณููˆูู ูˆูŽุดูŽูƒู‘ูŽ ูููŠ ุฃูŽู†ู‘ูŽู‡ู ูƒูุณููˆููŒ ุฃูŽูˆู’ ุบูŽูŠู’ุฑูู‡ูุŸ\n\\sum_{x=0}^{100} \\frac{x^x}{x!} = e^{x}\n\\prod_{z=1}^{n} (1 \\geq i_z) = 0\n\\mathbb{E}[i] = \\int x f_i(x) dx\n## ู…ุจุฑู‡ู†ุฉ\nู‚ูŽุงู„ูŽ ุงู„ุฒู‘ูŽุฑู’ูƒูŽุดููŠู‘ู: ุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู ุนูŽุฏูŽู…ู ุงู„ุตู‘ูุญู‘ูŽุฉู. ุชูŽู†ู’ุจููŠู‡ูŒ: ุงู„ุถู‘ูŽู…ููŠุฑู ูููŠ ู‚ูŽูˆู’ู„ู ุงู„ู’ู…ูุตูŽู†ู‘ููู ูˆูŽู„ูŽูˆู’ ุฃูŽุญูŽุณู‘ูŽ ูŠูŽุนููˆุฏู ุนูŽู„ูŽู‰ ุงู„ู’ุฅูู…ูŽุงู…ู ู„ูุชูŽู‚ูŽุฏู‘ูู…ู ุฐููƒู’ุฑูู‡ูุŒ ูˆูŽูŠูุญู’ุชูŽู…ูŽู„ู ุนูŽูˆู’ุฏูู‡ู ุนูŽู„ูŽู‰ ุงู„ู’ู…ูุตูŽู„ู‘ููŠ ู„ูู„ู’ุนูู„ู’ู…ู ุจูู‡ู ู„ููŠูŽุดู’ู…ูŽู„ูŽ ุงู„ู’ู…ูู†ู’ููŽุฑูุฏูŽ ุจูŽู„ู’ ู‡ููˆูŽ ุฃูŽูˆู’ู„ูŽู‰ ุจูุงู„ูุงู†ู’ุชูุธูŽุงุฑู ู…ูู†ู’ ุงู„ู’ุฅูู…ูŽุงู…ู ู„ูุงุญู’ุชููŠูŽุงุฌูู‡ู ุฅู„ูŽู‰ ุชูŽุญู’ุตููŠู„ู ุงู„ู’ุฌูŽู…ูŽุงุนูŽุฉูุŒ ูˆูŽู„ูŽู…ู’\n\\prod_{i=1}^{n} (1 = j_i) = 0\n\\sum_{\\sigma=0}^{100} \\frac{\\beta^\\sigma}{\\sigma!} = e^{\\beta}\nP(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{i}{x^2}\ni_{n+1} = i_n - \\alpha \\nabla f(i_n) + \\frac{j}{\\sigma^2}\n\\int_{1}^{M} \\exp(j) \\, dj = x^2 \\cdot C\n\\sum_{\\alpha=0}^{100} \\frac{\\lambda^\\alpha}{\\alpha!} = e^{\\lambda} + \\frac{j}{x^2}\n\\int_{3}^{100} \\log(j) \\, dj = \\theta^2 \\leq C + \\frac{\\sigma}{\\alpha^2}",
"images": [],
"tables": [],
"hyperlinks": [],
"header": null,
"footer": null,
"dimensions": {
"dpi": 96,
"height": 1034,
"width": 735
},
"confidence_scores": {
"word_confidence_scores": [
{
"text": "##",
"confidence": 1.0,
"start_index": 0
},
{
"text": "ู…ู„ุงุญุธุฉ",
"confidence": 1.0,
"start_index": 3
},
{
"text": "ูˆูŽุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู",
"confidence": 1.0,
"start_index": 10
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 25
},
{
"text": "ู‡ูŽุฐูู‡ู",
"confidence": 1.0,
"start_index": 29
},
{
"text": "ุงุณู’ุชูุญู’ุจูŽุงุจู",
"confidence": 1.0,
"start_index": 36
},
{
"text": "ุงู†ู’ุชูุธูŽุงุฑูู‡ูุ›",
"confidence": 1.0,
"start_index": 49
},
{
"text": "ู„ูุฃูŽู†ู‘ูŽ",
"confidence": 1.0,
"start_index": 63
},
{
"text": "ุงู„ุฑู‘ูŽูƒู’ุนูŽุฉูŽ",
"confidence": 1.0,
"start_index": 71
},
{
"text": "ุชูุญู’ุณูŽุจู",
"confidence": 1.0,
"start_index": 83
},
{
"text": "ุนูŽู†ู’",
"confidence": 1.0,
"start_index": 92
},
{
"text": "ุงู„ู’ู…ูŽุฃู’ู…ููˆู…ู",
"confidence": 1.0,
"start_index": 97
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 110
},
{
"text": "ุฅุณู’ู‚ูŽุงุทู",
"confidence": 1.0,
"start_index": 114
},
{
"text": "ุญูุฑู’ู…ูŽุฉู",
"confidence": 1.0,
"start_index": 123
},
{
"text": "ุงู„ู’ูˆูŽู‚ู’ุชู.",
"confidence": 1.0,
"start_index": 132
},
{
"text": "ููŽุฑู’ุนูŒ",
"confidence": 1.0,
"start_index": 143
},
{
"text": "ูˆูŽุฌูŽุฏูŽ",
"confidence": 1.0,
"start_index": 150
},
{
"text": "ู…ูุตูŽู„ู‘ููŠู‹ุง",
"confidence": 1.0,
"start_index": 157
},
{
"text": "ุฌูŽุงู„ูุณู‹ุง",
"confidence": 1.0,
"start_index": 168
},
{
"text": "ูˆูŽุดูŽูƒู‘ูŽ",
"confidence": 1.0,
"start_index": 177
},
{
"text": "ู‡ูŽู„ู’",
"confidence": 1.0,
"start_index": 185
},
{
"text": "ู‡ููˆูŽ",
"confidence": 1.0,
"start_index": 190
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 195
},
{
"text": "ุงู„ุชู‘ูŽุดูŽู‡ู‘ูุฏู",
"confidence": 1.0,
"start_index": 199
},
{
"text": "ุฃูŽูˆู’",
"confidence": 1.0,
"start_index": 212
},
{
"text": "ุงู„ู’ู‚ููŠูŽุงู…ู",
"confidence": 1.0,
"start_index": 217
},
{
"text": "ู„ูุนูŽุฌู’ุฒูู‡ู",
"confidence": 1.0,
"start_index": 228
},
{
"text": "ููŽู‡ูŽู„ู’",
"confidence": 1.0,
"start_index": 239
},
{
"text": "ู„ูŽู‡ู",
"confidence": 1.0,
"start_index": 246
},
{
"text": "ุฃูŽู†ู’",
"confidence": 1.0,
"start_index": 251
},
{
"text": "ูŠูŽู‚ู’ุชูŽุฏููŠูŽ",
"confidence": 1.0,
"start_index": 256
},
{
"text": "ุจูู‡ู",
"confidence": 1.0,
"start_index": 267
},
{
"text": "ุฃูŽูˆู’",
"confidence": 1.0,
"start_index": 272
},
{
"text": "ู„ูŽุงุŸ",
"confidence": 1.0,
"start_index": 277
},
{
"text": "ูˆูŽูƒูŽุฐูŽุง",
"confidence": 1.0,
"start_index": 282
},
{
"text": "ู„ูŽูˆู’",
"confidence": 1.0,
"start_index": 290
},
{
"text": "ุฑูŽุขู‡ู",
"confidence": 1.0,
"start_index": 295
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 301
},
{
"text": "ูˆูŽู‚ู’ุชู",
"confidence": 1.0,
"start_index": 305
},
{
"text": "ุงู„ู’ูƒูุณููˆูู",
"confidence": 1.0,
"start_index": 312
},
{
"text": "ูˆูŽุดูŽูƒู‘ูŽ",
"confidence": 1.0,
"start_index": 323
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 331
},
{
"text": "ุฃูŽู†ู‘ูŽู‡ู",
"confidence": 1.0,
"start_index": 335
},
{
"text": "ูƒูุณููˆููŒ",
"confidence": 1.0,
"start_index": 343
},
{
"text": "ุฃูŽูˆู’",
"confidence": 1.0,
"start_index": 351
},
{
"text": "ุบูŽูŠู’ุฑูู‡ูุŸ",
"confidence": 1.0,
"start_index": 356
},
{
"text": "\\sum_{x=0}^{100}",
"confidence": 1.0,
"start_index": 366
},
{
"text": "\\frac{x^x}{x!}",
"confidence": 1.0,
"start_index": 383
},
{
"text": "=",
"confidence": 1.0,
"start_index": 398
},
{
"text": "e^{x}",
"confidence": 1.0,
"start_index": 400
},
{
"text": "\\prod_{z=1}^{n}",
"confidence": 1.0,
"start_index": 406
},
{
"text": "(1",
"confidence": 1.0,
"start_index": 422
},
{
"text": "\\geq",
"confidence": 1.0,
"start_index": 425
},
{
"text": "i_z)",
"confidence": 1.0,
"start_index": 430
},
{
"text": "=",
"confidence": 1.0,
"start_index": 435
},
{
"text": "0",
"confidence": 1.0,
"start_index": 437
},
{
"text": "\\mathbb{E}[i]",
"confidence": 1.0,
"start_index": 439
},
{
"text": "=",
"confidence": 1.0,
"start_index": 453
},
{
"text": "\\int",
"confidence": 1.0,
"start_index": 455
},
{
"text": "x",
"confidence": 1.0,
"start_index": 460
},
{
"text": "f_i(x)",
"confidence": 1.0,
"start_index": 462
},
{
"text": "dx",
"confidence": 1.0,
"start_index": 469
},
{
"text": "##",
"confidence": 1.0,
"start_index": 472
},
{
"text": "ู…ุจุฑู‡ู†ุฉ",
"confidence": 1.0,
"start_index": 475
},
{
"text": "ู‚ูŽุงู„ูŽ",
"confidence": 1.0,
"start_index": 482
},
{
"text": "ุงู„ุฒู‘ูŽุฑู’ูƒูŽุดููŠู‘ู:",
"confidence": 1.0,
"start_index": 488
},
{
"text": "ุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู",
"confidence": 1.0,
"start_index": 504
},
{
"text": "ุนูŽุฏูŽู…ู",
"confidence": 1.0,
"start_index": 517
},
{
"text": "ุงู„ุตู‘ูุญู‘ูŽุฉู.",
"confidence": 1.0,
"start_index": 524
},
{
"text": "ุชูŽู†ู’ุจููŠู‡ูŒ:",
"confidence": 1.0,
"start_index": 536
},
{
"text": "ุงู„ุถู‘ูŽู…ููŠุฑู",
"confidence": 1.0,
"start_index": 547
},
{
"text": "ูููŠ",
"confidence": 1.0,
"start_index": 558
},
{
"text": "ู‚ูŽูˆู’ู„ู",
"confidence": 1.0,
"start_index": 562
},
{
"text": "ุงู„ู’ู…ูุตูŽู†ู‘ููู",
"confidence": 1.0,
"start_index": 569
},
{
"text": "ูˆูŽู„ูŽูˆู’",
"confidence": 1.0,
"start_index": 582
},
{
"text": "ุฃูŽุญูŽุณู‘ูŽ",
"confidence": 1.0,
"start_index": 589
},
{
"text": "ูŠูŽุนููˆุฏู",
"confidence": 1.0,
"start_index": 597
},
{
"text": "ุนูŽู„ูŽู‰",
"confidence": 1.0,
"start_index": 605
},
{
"text": "ุงู„ู’ุฅูู…ูŽุงู…ู",
"confidence": 1.0,
"start_index": 611
},
{
"text": "ู„ูุชูŽู‚ูŽุฏู‘ูู…ู",
"confidence": 1.0,
"start_index": 622
},
{
"text": "ุฐููƒู’ุฑูู‡ูุŒ",
"confidence": 1.0,
"start_index": 634
},
{
"text": "ูˆูŽูŠูุญู’ุชูŽู…ูŽู„ู",
"confidence": 1.0,
"start_index": 644
},
{
"text": "ุนูŽูˆู’ุฏูู‡ู",
"confidence": 1.0,
"start_index": 657
},
{
"text": "ุนูŽู„ูŽู‰",
"confidence": 1.0,
"start_index": 666
},
{
"text": "ุงู„ู’ู…ูุตูŽู„ู‘ููŠ",
"confidence": 1.0,
"start_index": 672
},
{
"text": "ู„ูู„ู’ุนูู„ู’ู…ู",
"confidence": 1.0,
"start_index": 684
},
{
"text": "ุจูู‡ู",
"confidence": 1.0,
"start_index": 695
},
{
"text": "ู„ููŠูŽุดู’ู…ูŽู„ูŽ",
"confidence": 1.0,
"start_index": 700
},
{
"text": "ุงู„ู’ู…ูู†ู’ููŽุฑูุฏูŽ",
"confidence": 1.0,
"start_index": 711
},
{
"text": "ุจูŽู„ู’",
"confidence": 1.0,
"start_index": 725
},
{
"text": "ู‡ููˆูŽ",
"confidence": 1.0,
"start_index": 730
},
{
"text": "ุฃูŽูˆู’ู„ูŽู‰",
"confidence": 1.0,
"start_index": 735
},
{
"text": "ุจูุงู„ูุงู†ู’ุชูุธูŽุงุฑู",
"confidence": 1.0,
"start_index": 743
},
{
"text": "ู…ูู†ู’",
"confidence": 1.0,
"start_index": 759
},
{
"text": "ุงู„ู’ุฅูู…ูŽุงู…ู",
"confidence": 1.0,
"start_index": 764
},
{
"text": "ู„ูุงุญู’ุชููŠูŽุงุฌูู‡ู",
"confidence": 1.0,
"start_index": 775
},
{
"text": "ุฅู„ูŽู‰",
"confidence": 1.0,
"start_index": 790
},
{
"text": "ุชูŽุญู’ุตููŠู„ู",
"confidence": 1.0,
"start_index": 795
},
{
"text": "ุงู„ู’ุฌูŽู…ูŽุงุนูŽุฉูุŒ",
"confidence": 1.0,
"start_index": 805
},
{
"text": "ูˆูŽู„ูŽู…ู’",
"confidence": 1.0,
"start_index": 819
},
{
"text": "\\prod_{i=1}^{n}",
"confidence": 1.0,
"start_index": 826
},
{
"text": "(1",
"confidence": 1.0,
"start_index": 842
},
{
"text": "=",
"confidence": 1.0,
"start_index": 845
},
{
"text": "j_i)",
"confidence": 1.0,
"start_index": 847
},
{
"text": "=",
"confidence": 1.0,
"start_index": 852
},
{
"text": "0",
"confidence": 1.0,
"start_index": 854
},
{
"text": "\\sum_{\\sigma=0}^{100}",
"confidence": 1.0,
"start_index": 856
},
{
"text": "\\frac{\\beta^\\sigma}{\\sigma!}",
"confidence": 1.0,
"start_index": 878
},
{
"text": "=",
"confidence": 1.0,
"start_index": 907
},
{
"text": "e^{\\beta}",
"confidence": 1.0,
"start_index": 909
},
{
"text": "P(A|B)",
"confidence": 1.0,
"start_index": 919
},
{
"text": "=",
"confidence": 1.0,
"start_index": 926
},
{
"text": "\\frac{P(A",
"confidence": 1.0,
"start_index": 928
},
{
"text": "\\cap",
"confidence": 1.0,
"start_index": 938
},
{
"text": "B)}{P(B)}",
"confidence": 1.0,
"start_index": 943
},
{
"text": "+",
"confidence": 1.0,
"start_index": 953
},
{
"text": "\\frac{i}{x^2}",
"confidence": 1.0,
"start_index": 955
},
{
"text": "i_{n+1}",
"confidence": 1.0,
"start_index": 969
},
{
"text": "=",
"confidence": 1.0,
"start_index": 977
},
{
"text": "i_n",
"confidence": 1.0,
"start_index": 979
},
{
"text": "-",
"confidence": 1.0,
"start_index": 983
},
{
"text": "\\alpha",
"confidence": 1.0,
"start_index": 985
},
{
"text": "\\nabla",
"confidence": 1.0,
"start_index": 992
},
{
"text": "f(i_n)",
"confidence": 1.0,
"start_index": 999
},
{
"text": "+",
"confidence": 1.0,
"start_index": 1006
},
{
"text": "\\frac{j}{\\sigma^2}",
"confidence": 1.0,
"start_index": 1008
},
{
"text": "\\int_{1}^{M}",
"confidence": 1.0,
"start_index": 1027
},
{
"text": "\\exp(j)",
"confidence": 1.0,
"start_index": 1040
},
{
"text": "\\,",
"confidence": 1.0,
"start_index": 1048
},
{
"text": "dj",
"confidence": 1.0,
"start_index": 1051
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1054
},
{
"text": "x^2",
"confidence": 1.0,
"start_index": 1056
},
{
"text": "\\cdot",
"confidence": 1.0,
"start_index": 1060
},
{
"text": "C",
"confidence": 1.0,
"start_index": 1066
},
{
"text": "\\sum_{\\alpha=0}^{100}",
"confidence": 1.0,
"start_index": 1068
},
{
"text": "\\frac{\\lambda^\\alpha}{\\alpha!}",
"confidence": 1.0,
"start_index": 1090
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1121
},
{
"text": "e^{\\lambda}",
"confidence": 1.0,
"start_index": 1123
},
{
"text": "+",
"confidence": 1.0,
"start_index": 1135
},
{
"text": "\\frac{j}{x^2}",
"confidence": 1.0,
"start_index": 1137
},
{
"text": "\\int_{3}^{100}",
"confidence": 1.0,
"start_index": 1151
},
{
"text": "\\log(j)",
"confidence": 1.0,
"start_index": 1166
},
{
"text": "\\,",
"confidence": 1.0,
"start_index": 1174
},
{
"text": "dj",
"confidence": 1.0,
"start_index": 1177
},
{
"text": "=",
"confidence": 1.0,
"start_index": 1180
},
{
"text": "\\theta^2",
"confidence": 1.0,
"start_index": 1182
},
{
"text": "\\leq",
"confidence": 1.0,
"start_index": 1191
},
{
"text": "C",
"confidence": 1.0,
"start_index": 1196
},
{
"text": "+",
"confidence": 1.0,
"start_index": 1198
},
{
"text": "\\frac{\\sigma}{\\alpha^2}",
"confidence": 1.0,
"start_index": 1200
}
],
"average_page_confidence_score": 1.0,
"minimum_page_confidence_score": 1.0
},
"blocks": [
{
"top_left_x": 52,
"top_left_y": 52,
"bottom_right_x": 679,
"bottom_right_y": 76,
"content": "ู…ู„ุงุญุธุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 1
},
{
"top_left_x": 52,
"top_left_y": 81,
"bottom_right_x": 679,
"bottom_right_y": 126,
"content": "ูˆูŽุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู ูููŠ ู‡ูŽุฐูู‡ู ุงุณู’ุชูุญู’ุจูŽุงุจู ุงู†ู’ุชูุธูŽุงุฑูู‡ูุ› ู„ูุฃูŽู†ู‘ูŽ ุงู„ุฑู‘ูŽูƒู’ุนูŽุฉูŽ ุชูุญู’ุณูŽุจู ุนูŽู†ู’ ุงู„ู’ู…ูŽุฃู’ู…ููˆู…ู ูููŠ ุฅุณู’ู‚ูŽุงุทู ุญูุฑู’ู…ูŽุฉู ุงู„ู’ูˆูŽู‚ู’ุชู. ููŽุฑู’ุนูŒ ูˆูŽุฌูŽุฏูŽ ู…ูุตูŽู„ู‘ููŠู‹ุง ุฌูŽุงู„ูุณู‹ุง ูˆูŽุดูŽูƒู‘ูŽ ู‡ูŽู„ู’ ู‡ููˆูŽ ูููŠ ุงู„ุชู‘ูŽุดูŽู‡ู‘ูุฏู ุฃูŽูˆู’ ุงู„ู’ู‚ููŠูŽุงู…ู ู„ูุนูŽุฌู’ุฒูู‡ู ููŽู‡ูŽู„ู’ ู„ูŽู‡ู ุฃูŽู†ู’ ูŠูŽู‚ู’ุชูŽุฏููŠูŽ ุจูู‡ู ุฃูŽูˆู’ ู„ูŽุงุŸ ูˆูŽูƒูŽุฐูŽุง ู„ูŽูˆู’ ุฑูŽุขู‡ู ูููŠ ูˆูŽู‚ู’ุชู ุงู„ู’ูƒูุณููˆูู ูˆูŽุดูŽูƒู‘ูŽ ูููŠ ุฃูŽู†ู‘ูŽู‡ู ูƒูุณููˆููŒ ุฃูŽูˆู’ ุบูŽูŠู’ุฑูู‡ูุŸ",
"type": "text",
"confidence_scores": null,
"reading_index": 2
},
{
"top_left_x": 52,
"top_left_y": 132,
"bottom_right_x": 679,
"bottom_right_y": 198,
"content": "\\sum_{x=0}^{100} \\frac{x^x}{x!} = e^{x}",
"type": "text",
"confidence_scores": null,
"reading_index": 3
},
{
"top_left_x": 40,
"top_left_y": 230,
"bottom_right_x": 695,
"bottom_right_y": 300,
"content": "\\prod_{z=1}^{n} (1 \\geq i_z) = 0",
"type": "text",
"confidence_scores": null,
"reading_index": 4
},
{
"top_left_x": 40,
"top_left_y": 306,
"bottom_right_x": 695,
"bottom_right_y": 369,
"content": "\\mathbb{E}[i] = \\int x f_i(x) dx",
"type": "text",
"confidence_scores": null,
"reading_index": 5
},
{
"top_left_x": 52,
"top_left_y": 387,
"bottom_right_x": 679,
"bottom_right_y": 411,
"content": "ู…ุจุฑู‡ู†ุฉ",
"type": "title",
"confidence_scores": null,
"reading_index": 6
},
{
"top_left_x": 52,
"top_left_y": 416,
"bottom_right_x": 679,
"bottom_right_y": 460,
"content": "ู‚ูŽุงู„ูŽ ุงู„ุฒู‘ูŽุฑู’ูƒูŽุดููŠู‘ู: ุงู„ู’ู…ูุชู‘ูŽุฌูŽู‡ู ุนูŽุฏูŽู…ู ุงู„ุตู‘ูุญู‘ูŽุฉู. ุชูŽู†ู’ุจููŠู‡ูŒ: ุงู„ุถู‘ูŽู…ููŠุฑู ูููŠ ู‚ูŽูˆู’ู„ู ุงู„ู’ู…ูุตูŽู†ู‘ููู ูˆูŽู„ูŽูˆู’ ุฃูŽุญูŽุณู‘ูŽ ูŠูŽุนููˆุฏู ุนูŽู„ูŽู‰ ุงู„ู’ุฅูู…ูŽุงู…ู ู„ูุชูŽู‚ูŽุฏู‘ูู…ู ุฐููƒู’ุฑูู‡ูุŒ ูˆูŽูŠูุญู’ุชูŽู…ูŽู„ู ุนูŽูˆู’ุฏูู‡ู ุนูŽู„ูŽู‰ ุงู„ู’ู…ูุตูŽู„ู‘ููŠ ู„ูู„ู’ุนูู„ู’ู…ู ุจูู‡ู ู„ููŠูŽุดู’ู…ูŽู„ูŽ ุงู„ู’ู…ูู†ู’ููŽุฑูุฏูŽ ุจูŽู„ู’ ู‡ููˆูŽ ุฃูŽูˆู’ู„ูŽู‰ ุจูุงู„ูุงู†ู’ุชูุธูŽุงุฑู ู…ูู†ู’ ุงู„ู’ุฅูู…ูŽุงู…ู ู„ูุงุญู’ุชููŠูŽุงุฌูู‡ู ุฅู„ูŽู‰ ุชูŽุญู’ุตููŠู„ู ุงู„ู’ุฌูŽู…ูŽุงุนูŽุฉูุŒ ูˆูŽู„ูŽู…ู’",
"type": "text",
"confidence_scores": null,
"reading_index": 7
},
{
"top_left_x": 52,
"top_left_y": 466,
"bottom_right_x": 679,
"bottom_right_y": 531,
"content": "\\prod_{i=1}^{n} (1 = j_i) = 0",
"type": "text",
"confidence_scores": null,
"reading_index": 8
},
{
"top_left_x": 40,
"top_left_y": 563,
"bottom_right_x": 695,
"bottom_right_y": 641,
"content": "\\sum_{\\sigma=0}^{100} \\frac{\\beta^\\sigma}{\\sigma!} = e^{\\beta}",
"type": "text",
"confidence_scores": null,
"reading_index": 9
},
{
"top_left_x": 40,
"top_left_y": 647,
"bottom_right_x": 695,
"bottom_right_y": 703,
"content": "P(A|B) = \\frac{P(A \\cap B)}{P(B)} + \\frac{i}{x^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 10
},
{
"top_left_x": 40,
"top_left_y": 709,
"bottom_right_x": 695,
"bottom_right_y": 757,
"content": "i_{n+1} = i_n - \\alpha \\nabla f(i_n) + \\frac{j}{\\sigma^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 11
},
{
"top_left_x": 40,
"top_left_y": 763,
"bottom_right_x": 695,
"bottom_right_y": 821,
"content": "\\int_{1}^{M} \\exp(j) \\, dj = x^2 \\cdot C",
"type": "text",
"confidence_scores": null,
"reading_index": 12
},
{
"top_left_x": 40,
"top_left_y": 827,
"bottom_right_x": 695,
"bottom_right_y": 899,
"content": "\\sum_{\\alpha=0}^{100} \\frac{\\lambda^\\alpha}{\\alpha!} = e^{\\lambda} + \\frac{j}{x^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 13
},
{
"top_left_x": 40,
"top_left_y": 905,
"bottom_right_x": 695,
"bottom_right_y": 963,
"content": "\\int_{3}^{100} \\log(j) \\, dj = \\theta^2 \\leq C + \\frac{\\sigma}{\\alpha^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 14
}
],
"meta": {
"template": "math_proof",
"hybrid": null,
"page_font": "IBMPlexSansArabic-ExtraLight.ttf",
"title_font": "IBMPlexSansArabic-ExtraLight.ttf",
"language": "ar",
"script": "arabic",
"direction": "rtl",
"augmentation": null
}
}