[ { "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": {} } ]