| [ |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 309, |
| 627, |
| 823, |
| 627, |
| 823, |
| 721, |
| 309, |
| 721 |
| ], |
| "anno_id": 9, |
| "latex": "$$ \\lim _{x\\rightarrow 0}\\frac{x-\\sin x}{x^{3}}=\\lim _{x\\rightarrow 0}\\frac{x-\\left(x-\\frac{x^{3}}{6}+o\\left(x^{4}\\right)\\right)}{x^{3}}=\\lim _{x\\rightarrow 0}\\left(\\frac{1}{6}-\\frac{o\\left(x^{4}\\right)}{x^{3}}\\right)=\\frac{1}{6}: $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 277, |
| 110, |
| 794, |
| 110, |
| 794, |
| 170, |
| 277, |
| 170 |
| ], |
| "anno_id": 10, |
| "latex": "$$\\text{II.} \\sin x=x-\\frac{1}{3 !}x^{3}+\\cdots+\\frac{(-1)^{n-1}}{(2 n-1)!}x^{2n-1}+o\\left(x^{2 n}\\right),\\quad x\\rightarrow 0 $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 278, |
| 296, |
| 863, |
| 296, |
| 863, |
| 348, |
| 278, |
| 348 |
| ], |
| "anno_id": 11, |
| "latex": "$$\n\\text{V.}(1+x)^{p}=1+p x+\\cdots+\\frac{p(p-1) \\cdot \\ldots \\cdot(p-(n-1))}{n !} x^{n}+o\\left(x^{n}\\right), x \\rightarrow 0:\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 278, |
| 176, |
| 794, |
| 176, |
| 794, |
| 234, |
| 278, |
| 234 |
| ], |
| "anno_id": 12, |
| "latex": "$$\\text{III.} \\cos x=1-\\frac{1}{2 !}x^{2}+\\cdots+\\frac{(-1)^{n}}{(2 n)!}x^{2n}+o\\left(x^{2 n+1}\\right),\\quad x\\rightarrow 0;$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 277, |
| 241, |
| 794, |
| 241, |
| 794, |
| 295, |
| 277, |
| 295 |
| ], |
| "anno_id": 13, |
| "latex": "$$\n\\text{IV.} \\ln (1+x)=x-\\frac{1}{2} x^{2}+\\cdots+\\frac{(-1)^{n}}{n} x^{n}+o\\left(x^{n}\\right),\\quad x\\rightarrow 0;\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 308, |
| 575, |
| 495, |
| 575, |
| 495, |
| 627, |
| 308, |
| 627 |
| ], |
| "anno_id": 15, |
| "latex": "$$ \\sin x=x-\\frac{x^{3}}{6}+o\\left(x^{4}\\right), $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 309, |
| 952, |
| 592, |
| 952, |
| 592, |
| 980, |
| 309, |
| 980 |
| ], |
| "anno_id": 16, |
| "latex": "$$ P(x)=(x-x_{1})(x-x_{2})\\cdot\\ldots\\cdot(x-x_{n}) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "hy" |
| }, |
| "image_path": "hy_a32b21bf6d19fcf4682fde2e720070ed_120_60.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 119, |
| 814, |
| 888, |
| 814, |
| 888, |
| 887, |
| 119, |
| 887 |
| ], |
| "anno_id": 8, |
| "latex": "$$\n\\frac{1}{\\mathrm{c}^{2}}\\frac{\\partial^{2} \\mathrm{p}}{\\partial \\mathrm{t}^{2}}=\\frac{\\partial^{2} \\mathrm{p}}{\\partial \\mathrm{r}^{2}}+\\frac{2}{\\mathrm{r}}\\frac{\\partial \\mathrm{p}}{\\partial \\mathrm{r}}\\quad(1)\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 121, |
| 985, |
| 888, |
| 985, |
| 888, |
| 1047, |
| 121, |
| 1047 |
| ], |
| "anno_id": 9, |
| "latex": "$$ \\rho=\\frac{1}{c^{2}}\\mathrm{p}\\quad(3) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 121, |
| 916, |
| 888, |
| 916, |
| 888, |
| 966, |
| 121, |
| 966 |
| ], |
| "anno_id": 10, |
| "latex": "$$\n\\rho_{\\mathrm{s}}\\frac{\\partial \\mathrm {v}}{\\partial \\mathrm{t}}=-\\frac{\\partial \\mathrm{p}}{\\partial \\mathrm{r}}\\quad(2)\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "nn" |
| }, |
| "image_path": "nn_1231a003b6c76b1364de10ce870cc829_207_104.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 925, |
| 1078, |
| 1410, |
| 1078, |
| 1410, |
| 1117, |
| 925, |
| 1117 |
| ], |
| "anno_id": 17, |
| "latex": "$$ \\mathrm{HGeCl}_{3}+\\mathrm{CH}_{2}=\\mathrm{CHCN}\\rightarrow\\mathrm{Cl}_{3}\\mathrm{GeCH}_{2}\\mathrm{CH}_{2}\\mathrm{CN}(53\\%) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 124, |
| 476, |
| 676, |
| 476, |
| 676, |
| 505, |
| 124, |
| 505 |
| ], |
| "anno_id": 18, |
| "latex": "$$ \\mathrm{BrE'}+\\mathrm{HBr}\\rightarrow\\mathrm{BrEH}+\\mathrm{Br'}\\quad\\Delta H=-21\\mathrm{Дж}/\\mathrm{моль} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 124, |
| 443, |
| 676, |
| 443, |
| 676, |
| 471, |
| 124, |
| 471 |
| ], |
| "anno_id": 19, |
| "latex": "$$\n\\ce{Br^{\\cdot} + E <=> BrE^{\\cdot}} \\quad \\Delta H = -46\\text{кДж/моль}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 984, |
| 755, |
| 1382, |
| 755, |
| 1382, |
| 790, |
| 984, |
| 790 |
| ], |
| "anno_id": 20, |
| "latex": "$$\n\\ce {R_{3}MH}+\\ce{XCH}=\\ce{CH_{2}}\\rightarrow \\ce{R_{3}MCH_{2}CH_{2}X}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1135, |
| 217, |
| 1253, |
| 217, |
| 1253, |
| 267, |
| 1135, |
| 267 |
| ], |
| "anno_id": 21, |
| "latex": "$$\n\\mathrm{X}_{2}\\xrightarrow[\\text{или}\\Delta] {hv} 2\\mathrm{X}^{\\cdot}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1100, |
| 132, |
| 1298, |
| 132, |
| 1298, |
| 161, |
| 1100, |
| 161 |
| ], |
| "anno_id": 22, |
| "latex": "$$\nX_{2}+E \\rightarrow X E \\cdot+\\mathrm{X}^{\\cdot}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1125, |
| 270, |
| 1264, |
| 270, |
| 1264, |
| 301, |
| 1125, |
| 301 |
| ], |
| "anno_id": 23, |
| "latex": "$$\n\\mathrm{X}^{\\cdot}+\\mathrm{E}\\rightarrow\\mathrm{XE}^{\\cdot}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ky" |
| }, |
| "image_path": "ky_90f1bdef9edfee8e4369cedaaf2788a9_135_68.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 399, |
| 1045, |
| 549, |
| 1045, |
| 549, |
| 1113, |
| 399, |
| 1113 |
| ], |
| "anno_id": 14, |
| "latex": "$$ t^{\\prime}=t\\sqrt{1-\\frac{v^{2}}{c^{2}}} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 399, |
| 870, |
| 516, |
| 870, |
| 516, |
| 943, |
| 399, |
| 943 |
| ], |
| "anno_id": 15, |
| "latex": "$$ l^{\\prime}=l\\sqrt{1-\\frac{v^{2}}{c^{2}}} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "vi" |
| }, |
| "image_path": "vi_213829ec216d223a5df6892b71cb15d4_166_83.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 251, |
| 1287, |
| 773, |
| 1287, |
| 773, |
| 1333, |
| 251, |
| 1333 |
| ], |
| "anno_id": 15, |
| "latex": "$$ f(\\alpha x+\\beta y)=\\alpha f(x)+\\beta f(y)\\geqslant\\alpha\\lambda+\\beta\\lambda=\\lambda $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 322, |
| 620, |
| 712, |
| 620, |
| 712, |
| 660, |
| 322, |
| 660 |
| ], |
| "anno_id": 16, |
| "latex": "$$ \\alpha\\geqslant 0\\quad,\\quad\\beta\\geqslant 0\\quad,\\quad\\alpha+\\beta=1 $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ar" |
| }, |
| "image_path": "ar_d1894282773ebdc78299310446047d7d_568_284.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 347, |
| 636, |
| 960, |
| 636, |
| 960, |
| 763, |
| 347, |
| 763 |
| ], |
| "anno_id": 12, |
| "latex": "$$ \\frac{\\partial\\theta}{\\partial t}=\\frac{Q}{c(\\alpha t)^{3/2}}\\left\\{-\\frac{3}{2 t}\\cdot f-\\frac{1}{2 t}\\xi\\cdot f^{\\prime}(\\xi)\\right\\} $$ $$ \\frac{\\partial\\theta}{\\partial r}=\\frac{Q}{c(\\alpha t)^{3/2}}\\cdot\\frac{1}{(\\alpha t)^{1/2}}\\cdot f^{\\prime}(\\xi) ;\\frac{\\partial^{2}\\theta}{\\partial r^{2}}=\\frac{Q}{c(\\alpha t)^{3/2}}\\cdot\\frac{1}{\\alpha t}f^{\\prime\\prime}(\\xi)\\quad\\text {(14)} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 418, |
| 441, |
| 957, |
| 441, |
| 957, |
| 499, |
| 418, |
| 499 |
| ], |
| "anno_id": 13, |
| "latex": "$$ \\theta=\\frac{Q}{c(\\alpha t)^{3/2}\\cdot f(\\xi)} ;\\quad\\xi=\\pi_{1}=\\frac{r}{(\\alpha t)^{1/2}}\\quad(13) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 452, |
| 184, |
| 959, |
| 184, |
| 959, |
| 240, |
| 452, |
| 240 |
| ], |
| "anno_id": 14, |
| "latex": "$$ \\pi=\\frac{\\theta\\cdot c}{Q(\\alpha t)^{-3/2}};\\pi_{1}=\\frac{r}{(\\alpha t)^{1/2}}\\quad(10) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 452, |
| 848, |
| 958, |
| 848, |
| 958, |
| 904, |
| 452, |
| 904 |
| ], |
| "anno_id": 15, |
| "latex": "$$ \\frac{d^{2} f}{d\\xi^{2}}+\\frac{2}{\\xi}\\cdot\\frac{d f}{d\\xi}+\\frac{1}{2}\\xi\\frac{d f}{d\\xi}+\\frac{3}{2} f=0\\quad(15) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 500, |
| 1074, |
| 952, |
| 1074, |
| 952, |
| 1136, |
| 500, |
| 1136 |
| ], |
| "anno_id": 16, |
| "latex": "$$ f=K\\cdot\\exp\\left(-\\frac{\\xi^{2}}{4}\\right)\\quad(16) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 477, |
| 1193, |
| 953, |
| 1193, |
| 953, |
| 1233, |
| 477, |
| 1233 |
| ], |
| "anno_id": 17, |
| "latex": "$$ 4\\pi c\\int_{0}^{\\infty} r^{2}\\theta(r, t)dr=Q\\quad(17) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 506, |
| 302, |
| 957, |
| 302, |
| 957, |
| 330, |
| 506, |
| 330 |
| ], |
| "anno_id": 18, |
| "latex": "$$ \\theta=f(t,\\alpha, Q,c,r)\\quad(11) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 529, |
| 372, |
| 955, |
| 372, |
| 955, |
| 400, |
| 529, |
| 400 |
| ], |
| "anno_id": 19, |
| "latex": "$$ \\pi=\\phi\\left(\\pi_{1}\\right)\\quad(12) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ca" |
| }, |
| "image_path": "ca_2bbcea1721f9dc27e488bf20abca52db_461_231.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 231, |
| 1029, |
| 710, |
| 1029, |
| 710, |
| 1070, |
| 231, |
| 1070 |
| ], |
| "anno_id": 13, |
| "latex": "$$ \\mathrm{CH}_{3}\\mathrm{COOH}+\\mathrm{CN}^{-}\\rightleftarrows\\mathrm{HCN}+\\mathrm{CH}_{3}\\mathrm{COO}^{-} ;\\mathrm{k} ? $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "eu" |
| }, |
| "image_path": "eu_22e270ee941d52266c94001f312dac80_336_168.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 336, |
| 1430, |
| 797, |
| 1430, |
| 797, |
| 1470, |
| 336, |
| 1470 |
| ], |
| "anno_id": 8, |
| "latex": "$$ 6=1+5=1^{2}-i^{2}\\cdot 5=(1+i\\sqrt{5})(1-i\\sqrt{5}): $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 174, |
| 446, |
| 468, |
| 446, |
| 468, |
| 480, |
| 174, |
| 480 |
| ], |
| "anno_id": 10, |
| "latex": "$$\n|a|^{2}=4,\\text {bpp} u=\\pm 2,v=0,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 174, |
| 484, |
| 468, |
| 484, |
| 468, |
| 518, |
| 174, |
| 518 |
| ], |
| "anno_id": 11, |
| "latex": "$$\n|a|^{2}=5,\\text {bpp}u=0,v=\\pm 1,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 174, |
| 408, |
| 468, |
| 408, |
| 468, |
| 442, |
| 174, |
| 442 |
| ], |
| "anno_id": 12, |
| "latex": "$$\n|a|^{2}=1,\\text {bpp}u=\\pm 1,v=0,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 174, |
| 369, |
| 409, |
| 369, |
| 409, |
| 404, |
| 174, |
| 404 |
| ], |
| "anno_id": 13, |
| "latex": "$$\n|a|^{2}=0,\\text {bpp}u,v=0,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "hy" |
| }, |
| "image_path": "hy_1dbd7add147fd261be9e4805b24c194c_376_188.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 377, |
| 506, |
| 757, |
| 506, |
| 757, |
| 588, |
| 377, |
| 588 |
| ], |
| "anno_id": 14, |
| "latex": "$$\n\\frac{ \\mathrm{A}_{1}}{ \\mathrm{a x+b}}+\\frac{ \\mathrm{A}_{2}}{( \\mathrm{a x+b)}^{2}}+\\cdots+\\frac{ \\mathrm{A}_{ \\mathrm{p}}}{( \\mathrm{a x+b})^{ \\mathrm{p}}}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 386, |
| 1307, |
| 741, |
| 1307, |
| 741, |
| 1384, |
| 386, |
| 1384 |
| ], |
| "anno_id": 15, |
| "latex": "$$\n\\frac{\\mathrm{x^{2}-3}}{\\mathrm{(x-2)(x^{2}+4)}}=\\frac{\\mathrm{A}}{\\mathrm{x-2}}+\\frac{\\mathrm{B x+C}}{\\mathrm{x^{2}+4}}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 384, |
| 229, |
| 742, |
| 229, |
| 742, |
| 304, |
| 384, |
| 304 |
| ], |
| "anno_id": 16, |
| "latex": "$$\n\\frac{x+4}{(x+7)(2 x-1)}=\\frac{\\mathrm{A}}{x+7}+\\frac{\\mathrm{B}}{2 x-1}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 418, |
| 717, |
| 712, |
| 717, |
| 712, |
| 794, |
| 418, |
| 794 |
| ], |
| "anno_id": 18, |
| "latex": "$$\n\\frac{3 x-1}{(x+4)^{2}}=\\frac{\\mathrm{A}}{x+4}+\\frac{{\\mathrm{B}}}{(x+4)^{2}}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 498, |
| 984, |
| 633, |
| 984, |
| 633, |
| 1052, |
| 498, |
| 1052 |
| ], |
| "anno_id": 19, |
| "latex": "$$ \\frac { A x + B } { a x ^ { 2 } + b x + c } $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ar" |
| }, |
| "image_path": "ar_9b5d2f8bc9e12611d0b0346415af0eed_143_72.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 452, |
| 978, |
| 673, |
| 978, |
| 673, |
| 1008, |
| 452, |
| 1008 |
| ], |
| "anno_id": 10, |
| "latex": "$$\nExtA=(\\mathbf{R}-\\mathbf{Z})\\times\\mathbf{R},\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 465, |
| 795, |
| 654, |
| 795, |
| 654, |
| 828, |
| 465, |
| 828 |
| ], |
| "anno_id": 11, |
| "latex": "$$ (x,z)\\in A\\cap\\mathcal{B}(q,\\varepsilon) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 450, |
| 1010, |
| 636, |
| 1010, |
| 636, |
| 1040, |
| 450, |
| 1040 |
| ], |
| "anno_id": 12, |
| "latex": "$$ \\bar{A}=\\mathcal{F} A=\\mathbf{Z}\\times\\mathbf{R} . $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 452, |
| 935, |
| 521, |
| 935, |
| 521, |
| 974, |
| 452, |
| 974 |
| ], |
| "anno_id": 13, |
| "latex": "$$ \\stackrel{\\circ}{A}=\\emptyset, $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ca" |
| }, |
| "image_path": "ca_ffde9e04a6368323e7db09075e660dd6_300_150.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1041, |
| 1003, |
| 1501, |
| 1003, |
| 1501, |
| 1047, |
| 1041, |
| 1047 |
| ], |
| "anno_id": 18, |
| "latex": "$$ V_{2}=V_{\\delta}+V_{z 2}+\\frac{1}{2} V_{j2}=\\mathrm{f}(\\Phi) .\\quad(3) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1069, |
| 910, |
| 1501, |
| 910, |
| 1501, |
| 953, |
| 1069, |
| 953 |
| ], |
| "anno_id": 19, |
| "latex": "$$ V_{1}=V_{p}+\\frac{1}{2} V_{j1}=\\mathrm{f}\\left(\\Phi_{p}\\right) .\\quad(2) $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 1118, |
| 326, |
| 1498, |
| 326, |
| 1498, |
| 353, |
| 1118, |
| 353 |
| ], |
| "anno_id": 20, |
| "latex": "$$ \\Phi_{p}=\\Phi+\\Phi_{s},\\quad{(1)} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "bs" |
| }, |
| "image_path": "bs_919fe8db159d816e405b8ec8c9c638f9_130_65.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 227, |
| 614, |
| 904, |
| 614, |
| 904, |
| 651, |
| 227, |
| 651 |
| ], |
| "anno_id": 7, |
| "latex": "$$ V=250z_{oro}+0,945z_{b}=250\\times 3-0,945\\times 640=145,2\\text {mill.euros.} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 486, |
| 340, |
| 810, |
| 340, |
| 810, |
| 377, |
| 486, |
| 377 |
| ], |
| "anno_id": 8, |
| "latex": "$$ s=1:280z_{\\text {oro}}+1z_{b}=200\\mathrm{mill}. $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 485, |
| 387, |
| 798, |
| 387, |
| 798, |
| 424, |
| 485, |
| 424 |
| ], |
| "anno_id": 9, |
| "latex": "$$ s=2:230z_{\\text {oro}}+1z_{b}=50\\text {mill.} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 441, |
| 483, |
| 721, |
| 483, |
| 721, |
| 517, |
| 441, |
| 517 |
| ], |
| "anno_id": 10, |
| "latex": "$$ \\Rightarrow z_{b}=-640\\text {mill.euros.} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 441, |
| 436, |
| 677, |
| 436, |
| 677, |
| 472, |
| 441, |
| 472 |
| ], |
| "anno_id": 11, |
| "latex": "$$\n\\Rightarrow z_{oro}=3 \\text { mill. onzas }\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "es" |
| }, |
| "image_path": "es_60c95dc22fa725fb675b7b42dcc7a1d5_286_143.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 467, |
| 1229, |
| 708, |
| 1229, |
| 708, |
| 1298, |
| 467, |
| 1298 |
| ], |
| "anno_id": 16, |
| "latex": "$$\nA_{эш}=\\int\\limits_{l} dA_{эш}=\\frac{1}{2}\\int\\limits_{0}^{l}\\frac{M_{б}^{2} dx}{GJ_{p}};\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 518, |
| 169, |
| 691, |
| 169, |
| 691, |
| 233, |
| 518, |
| 233 |
| ], |
| "anno_id": 17, |
| "latex": "$$ \\theta=\\frac{M_{\\kappa p}}{G\\cdot J_{P}}\\leq\\theta_{a dm}, $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 532, |
| 395, |
| 675, |
| 395, |
| 675, |
| 466, |
| 532, |
| 466 |
| ], |
| "anno_id": 18, |
| "latex": "$$ d\\geq\\sqrt[4]{\\frac{M_{\\kappa p}}{G\\cdot\\theta_{a dm}}}. $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 525, |
| 1041, |
| 683, |
| 1041, |
| 683, |
| 1098, |
| 525, |
| 1098 |
| ], |
| "anno_id": 19, |
| "latex": "$$\ndA_{эш}=\\frac{1}{2} M_{\\sigma}d\\varphi,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 524, |
| 1337, |
| 651, |
| 1337, |
| 651, |
| 1407, |
| 524, |
| 1407 |
| ], |
| "anno_id": 20, |
| "latex": "$$\nA_{эш}=\\frac{M_{б}^{2} l}{2GJ_{p}}.\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 518, |
| 1131, |
| 656, |
| 1131, |
| 656, |
| 1194, |
| 518, |
| 1194 |
| ], |
| "anno_id": 21, |
| "latex": "$$\nd\\varphi=\\frac{M_{\\sigma}}{G J_{p}}dx,\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 556, |
| 775, |
| 648, |
| 775, |
| 648, |
| 803, |
| 556, |
| 803 |
| ], |
| "anno_id": 22, |
| "latex": "$$\nM=N/\\omega\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "tt" |
| }, |
| "image_path": "tt_7e8e64f5d6b4bd4b1f9b9bdf1fb5a365_83_42.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 191, |
| 653, |
| 703, |
| 653, |
| 703, |
| 788, |
| 191, |
| 788 |
| ], |
| "anno_id": 20, |
| "latex": "$$\n\\underline{I_{s}}=\\frac{s}{s_{p}}\\sqrt{\\frac{1+\\left(\\frac{s_{p n}}{s_{n}}\\right)^{2}}{1+\\left(\\frac{s}{s_{p}}\\right)^{2}}} \\quad \\text{ (11-44)}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 194, |
| 847, |
| 707, |
| 847, |
| 707, |
| 938, |
| 194, |
| 938 |
| ], |
| "anno_id": 21, |
| "latex": "$$\nI_{s0}=\\sqrt{\\frac{1+\\left(\\frac{s_{pn}}{s_{n}}\\right)^{2}}{1+s_{p}^{2}}} \\quad \\text (11-45)\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 184, |
| 319, |
| 693, |
| 319, |
| 693, |
| 403, |
| 184, |
| 403 |
| ], |
| "anno_id": 22, |
| "latex": "$$\nI_{s}=\\frac{U_{s}}{\\omega_{s}\\Lambda\\sqrt{1+\\left(\\frac{s_{p}}{s}\\right)^{2}}} \\quad \\text{(11-41)}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 186, |
| 426, |
| 696, |
| 426, |
| 696, |
| 510, |
| 186, |
| 510 |
| ], |
| "anno_id": 23, |
| "latex": "$$\nI_{sn}=\\frac{U_{s}}{\\omega_{s}\\Lambda\\sqrt{1+\\left(\\frac{s_{pn}}{s_{n}}\\right)^{2}}} \\quad(11-42)\n$$\n\n$$\nI_{sn}=\\frac{U_{s}}{\\omega_{s}\\Lambda\\sqrt{1+\\left(\\frac{s_{pn}}{s_{n}}\\right)^{2}}} \\quad\\text{(11-42})\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 182, |
| 216, |
| 691, |
| 216, |
| 691, |
| 293, |
| 182, |
| 293 |
| ], |
| "anno_id": 24, |
| "latex": "$$\nI_{s}=\\frac{U_{s}}{\\sqrt{\\left(\\frac{R_{r}}{s}\\right)^{2}+\\left(\\omega_{s}\\Lambda\\right)^{2}}}\\quad \\text{(11-40)}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 898, |
| 145, |
| 1407, |
| 145, |
| 1407, |
| 212, |
| 898, |
| 212 |
| ], |
| "anno_id": 25, |
| "latex": "$$\n\\underline{I_{s0}}=\\sqrt{\\frac{2 v\\sqrt{v^{2}-1}}{1+s_{p}^{2}}}\\approx v\\sqrt{\\frac{2}{1+s_{p}^{2}}} \\quad (11-46)\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 187, |
| 531, |
| 700, |
| 531, |
| 700, |
| 578, |
| 187, |
| 578 |
| ], |
| "anno_id": 26, |
| "latex": "$$\ns_{pn}=\\frac{R_{r n}}{\\omega_{s}\\Lambda}\\quad\\text{(11-43)}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "sl" |
| }, |
| "image_path": "sl_b9942dda6c476248e59e33f605e2cf4f_144_72.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 196, |
| 693, |
| 1075, |
| 693, |
| 1075, |
| 770, |
| 196, |
| 770 |
| ], |
| "anno_id": 24, |
| "latex": "$$( 3\\ce{CH2=CH2} + 2\\ce{KMnO4} + 4\\ce{H2O} \\longrightarrow 3\\underset{\\ce{OH}}{\\underset{|}{\\ce{CH2}}}-\\underset{\\ce{OH}}{\\underset{|}{\\ce{CH2}}} + 2\\ce{MnO2} + 2\\ce{KOH} )$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "pnb" |
| }, |
| "image_path": "pnb_cc7044fdfc9e991d31e5669aa947c9c5_224_112.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 276, |
| 1376, |
| 943, |
| 1376, |
| 943, |
| 1442, |
| 276, |
| 1442 |
| ], |
| "anno_id": 14, |
| "latex": "$$\n\\beta-\\text {магнетон Бора, } \\beta=\\frac{\\mathrm{e} \\hbar}{2 \\mathrm{mc}}=9.2741 \\cdot 10^{-21} \\text { эрг } \\mathrm{Э}^{-1},\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 453, |
| 1249, |
| 1054, |
| 1249, |
| 1054, |
| 1293, |
| 453, |
| 1293 |
| ], |
| "anno_id": 15, |
| "latex": "$$\n\\text{hv}=\\text{gβH}_0,\\quad(5.7)\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ko" |
| }, |
| "image_path": "ko_aa4ba03f650301bebed229802f13ac85_124_62.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 321, |
| 1395, |
| 811, |
| 1395, |
| 811, |
| 1451, |
| 321, |
| 1451 |
| ], |
| "anno_id": 14, |
| "latex": "$$\n\\mathcal{Q}_{\\mathrm{xп.ф}}=\\frac{12950 \\cdot 0,3}{1000} 365 \\cdot 2500=3,55 \\cdot 10^{6} \\mathrm{MДж} / \\mathrm{год} ;\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 326, |
| 1196, |
| 807, |
| 1196, |
| 807, |
| 1252, |
| 326, |
| 1252 |
| ], |
| "anno_id": 15, |
| "latex": "$$ \\mathcal{Q}_{\\text {бол }}=\\frac{12950}{1000} 8(3200+9200)=1,28 \\cdot 10^{6} \\mathrm{МДж}/\\text {год. } $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 328, |
| 1280, |
| 804, |
| 1280, |
| 804, |
| 1336, |
| 328, |
| 1336 |
| ], |
| "anno_id": 16, |
| "latex": "$$\nQ_{\\mathrm{пр}}=\\frac{12950\\cdot 0,3\\cdot 100}{1000}18800=7,3\\cdot 10^{6}\\mathrm{MДж}/\\text { год. }\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 170, |
| 683, |
| 909, |
| 683, |
| 909, |
| 714, |
| 170, |
| 714 |
| ], |
| "anno_id": 17, |
| "latex": "$$\n=(35,88\\cdot 98,7+64,3\\cdot 0,33+93,18\\cdot 0,12+123,5\\cdot 0,04)0,01=35,841\\text{MДж/м}^{3}.\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 173, |
| 653, |
| 806, |
| 653, |
| 806, |
| 683, |
| 173, |
| 683 |
| ], |
| "anno_id": 18, |
| "latex": "$$\n\\mathcal{Q}_{\\mathrm{H}}=\\left(35,88 \\mathrm{CH}_{4}+64,3 \\mathrm{C}_{2} \\mathrm{H}_{6}+93,18 \\mathrm{C}_{3} \\mathrm{H}_{8}+123,5 \\mathrm{C}_{4} \\mathrm{H}_{10}\\right) 0,01=\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 309, |
| 1105, |
| 820, |
| 1105, |
| 820, |
| 1139, |
| 309, |
| 1139 |
| ], |
| "anno_id": 19, |
| "latex": "$$\n\\mathcal{Q}_{\\mathrm{CT}}=12950\\cdot 0,2(4,2+2,1)365=5,96\\cdot 10^{6}\\mathrm{MДж}/\\text {год.}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 171, |
| 766, |
| 744, |
| 766, |
| 744, |
| 795, |
| 171, |
| 795 |
| ], |
| "anno_id": 20, |
| "latex": "$$\n\\text{В нашем случае} N=(7+10+5+8+3+4)350=12950 \\text{чел.}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 327, |
| 959, |
| 802, |
| 959, |
| 802, |
| 993, |
| 327, |
| 993 |
| ], |
| "anno_id": 21, |
| "latex": "$$ Q_{\\text {быт }}=12950 \\cdot 0,8 \\cdot 10000=103,6 \\cdot 10^{6} \\mathrm{MДж}/\\text {год. } $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 343, |
| 1048, |
| 786, |
| 1048, |
| 786, |
| 1077, |
| 343, |
| 1077 |
| ], |
| "anno_id": 22, |
| "latex": "$$\n\\mathcal{Q}_{6}=12950\\cdot 0,20\\cdot 52\\cdot 40=5,4\\cdot 10^{6}\\text {МДж/год. }\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "ko" |
| }, |
| "image_path": "ko_4cef6faf62400640334d0c6e82767a0f_148_74.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 119, |
| 1372, |
| 860, |
| 1372, |
| 860, |
| 1437, |
| 119, |
| 1437 |
| ], |
| "anno_id": 5, |
| "latex": "$$ \\text {तथैव,}\\quad\\frac{\\mathrm{AM}}{\\mathrm{AP}}=\\frac{\\mathrm{AB}}{\\mathrm{AC}}=\\cos\\mathrm{A},\\frac{\\mathrm{MP}}{\\mathrm{AM}}=\\frac{\\mathrm{BC}}{\\mathrm{AB}}=\\tan\\mathrm{A}\\text {इत्यादय:} $$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 120, |
| 1267, |
| 685, |
| 1267, |
| 685, |
| 1330, |
| 120, |
| 1330 |
| ], |
| "anno_id": 6, |
| "latex": "$$\n\\mathrm{इत:}\\quad\\frac{\\mathrm{MP}}{\\mathrm{AP}}=\\frac{\\mathrm{BC}}{\\mathrm{AC}}=\\sin \\mathrm{A}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| }, |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 120, |
| 1162, |
| 671, |
| 1162, |
| 671, |
| 1226, |
| 120, |
| 1226 |
| ], |
| "anno_id": 7, |
| "latex": "$\\text{अत:}\\quad\\frac{\\mathrm{AM}}{\\mathrm{AB}}=\\frac{\\mathrm{AP}}{\\mathrm{AC}}=\\frac{\\mathrm{MP}}{\\mathrm{BC}}$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "sa" |
| }, |
| "image_path": "sa_5dad288bf1417e5c08fa22e68b7bf492_418_209.jpg" |
| }, |
| "extra": {} |
| }, |
| { |
| "layout_dets": [ |
| { |
| "category_type": "equation_isolated", |
| "poly": [ |
| 184, |
| 469, |
| 597, |
| 469, |
| 597, |
| 499, |
| 184, |
| 499 |
| ], |
| "anno_id": 22, |
| "latex": "$$\n\\text{- V - - / V V - - / V V - - / V V -}\n$$", |
| "attribute": { |
| "formula_type": "print" |
| } |
| } |
| ], |
| "page_info": { |
| "page_attribute": { |
| "language": "cy" |
| }, |
| "image_path": "cy_425a7a53a38365498eb46a529fd7ba24_266_133.jpg" |
| }, |
| "extra": {} |
| } |
| ] |
