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⌀ | json
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{
"height": 35,
"id": "1710.09075_1204",
"lines": 1,
"tex": "\\[ u_{t}=u_{0}+tv, \\]",
"tokens": 12,
"width": 89
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1710_09075_1204
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
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"tex": "\\[ x:=\\log|z|^{2} \\]",
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}
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1710_09075_1913
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
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"id": "1710.09075_1960",
"lines": 1,
"tex": "\\[ u_{t}:=\\phi_{t}^{*} \\]",
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"width": 62
}
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1710_09075_1960
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 49,
"id": "1710.09075_3893",
"lines": 1,
"tex": "\\[ \\mathcal{L}(v)=0. \\]",
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1710_09075_3893
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
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"tex": "\\begin{equation} \\rho=\\sqrt{\\eta_x}. \\end{equation}",
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1710_05484_529
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 24,
"id": "1710.05484_3559",
"lines": 1,
"tex": "$$Z_t+uZ_x+Z^2=-F,$$",
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"width": 94
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1710_05484_3559
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 28,
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"tex": "\\begin{equation} \\Delta + g_3 \\varphi > 0~~. \\end{equation}",
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1710_06686_3556
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 38,
"id": "1710.08618_2155",
"lines": 1,
"tex": "\\[ DRF\\hookrightarrow RFRF \\xrightarrow{R\\epsilon F}RF, \\]",
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"width": 174
}
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1710_08618_2155
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 28,
"id": "1710.08618_3172",
"lines": 1,
"tex": "\\[ F\\to F'\\to F'', \\]",
"tokens": 9,
"width": 85
}
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1710_08618_3172
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 24,
"id": "1710.08618_4198",
"lines": 1,
"tex": "\\[\\Psi F\\simeq {\\mathscr F}.\\]",
"tokens": 9,
"width": 51
}
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1710_08618_4198
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 81,
"id": "1710.08618_5186",
"lines": 1,
"tex": "\\[ \\Sigma_2^*\\Sigma_{2*}F''\\simeq F'. \\]",
"tokens": 15,
"width": 215
}
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1710_08618_5186
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 101,
"id": "1710.08618_5233",
"lines": 1,
"tex": "\\[ F[1]\\simeq T_{\\Sigma_2^*}F''. \\]",
"tokens": 14,
"width": 252
}
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1710_08618_5233
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 92,
"id": "1710.08618_6885",
"lines": 1,
"tex": "\\[ \\Sigma_{n*}F\\simeq 0. \\]",
"tokens": 11,
"width": 209
}
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1710_08618_6885
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 51,
"id": "1710.08618_7487",
"lines": 1,
"tex": "\\[ \\varpi^*F \\textrm{and} \\varpi^*\\Sigma_n^*, \\]",
"tokens": 14,
"width": 140
}
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1710_08618_7487
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 166,
"id": "1710.06205_1608",
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"tex": "\\begin{align} X =X_n. \\end{align}",
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1710_06205_1608
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 153,
"id": "1710.07888_1862",
"lines": 1,
"tex": "\\begin{align} k^2=\\mu v. \\end{align}",
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"width": 824
}
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1710_07888_1862
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 63,
"id": "1710.05549_2261",
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"tex": "\\begin{equation} \\Delta E = -\\mu N b . \\end{equation}",
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1710_05549_2261
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 55,
"id": "1710.07507_1608",
"lines": 1,
"tex": "$$SW_k(G) = SH_k'(G,1).$$",
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"width": 200
}
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1710_07507_1608
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 127,
"id": "1710.07507_2501",
"lines": 1,
"tex": "$$n_{ij}^{kl} = |N_{ij}^{kl}|.$$",
"tokens": 16,
"width": 269
}
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1710_07507_2501
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 43,
"id": "1710.09850_1690",
"lines": 1,
"tex": "$$\\text{\\it IR}(G,H)\\ \\ge\\ 2\\omega.$$",
"tokens": 15,
"width": 142
}
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1710_09850_1690
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 119,
"id": "1710.09850_2053",
"lines": 1,
"tex": "$$\\text{\\it IR}(G,H)\\ \\ge\\ \\alpha\\omega.$$",
"tokens": 15,
"width": 381
}
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1710_09850_2053
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 70,
"id": "1710.09850_2213",
"lines": 1,
"tex": "$$\\text{\\it IR}(kK_2,K_n)\\ =\\ kn.$$",
"tokens": 14,
"width": 247
}
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1710_09850_2213
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 65,
"id": "1710.08914_6096",
"lines": 1,
"tex": "\\[ \\tilde{g}(n) \\ll n^{-2}. \\]",
"tokens": 13,
"width": 154
}
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1710_08914_6096
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 104,
"id": "1710.08914_6520",
"lines": 1,
"tex": "\\[ z := V^{10/49}. \\]",
"tokens": 10,
"width": 269
}
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1710_08914_6520
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 133,
"id": "1710.04932_1195",
"lines": 1,
"tex": "$$h_{PST}^{(2N)}=Dh_1D^\\dagger.$$",
"tokens": 14,
"width": 369
}
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1710_04932_1195
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 77,
"id": "1710.04932_2386",
"lines": 1,
"tex": "$$ X(t)=e^{-B}Xe^{A} $$",
"tokens": 15,
"width": 245
}
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1710_04932_2386
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 121,
"id": "1710.04932_2592",
"lines": 1,
"tex": "$$ X\\mapsto X+\\delta(XA-BX). $$",
"tokens": 12,
"width": 522
}
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1710_04932_2592
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 43,
"id": "1710.04932_2630",
"lines": 1,
"tex": "$$X\\rightarrow e^{-B}Xe^A.$$",
"tokens": 12,
"width": 126
}
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1710_04932_2630
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 90,
"id": "1710.04932_4192",
"lines": 1,
"tex": "$$ H_1=e^{-B}H_0e^{A} $$",
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"width": 258
}
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1710_04932_4192
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 62,
"id": "1710.04932_4356",
"lines": 1,
"tex": "$$ H_0\\mapsto e^{-A}H_0e^A, $$",
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"width": 195
}
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1710_04932_4356
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 98,
"id": "1710.04932_4947",
"lines": 1,
"tex": "$$ e^{-i\\lambda_mt_0}=\\pm e^{i\\phi} $$",
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"width": 294
}
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1710_04932_4947
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 32,
"id": "1710.06968_133",
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"tex": "\\[ \\delta:\\Delta\\times \\Delta \\to W \\]",
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}
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1710_06968_133
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 82,
"id": "1710.06968_730",
"lines": 1,
"tex": "\\[gh=g;h=h\\circ g\\]",
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"width": 261
}
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1710_06968_730
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 78,
"id": "1710.06968_873",
"lines": 1,
"tex": "\\[\\delta(gh)\\geq \\delta(g)\\delta(h).\\]",
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"width": 258
}
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1710_06968_873
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 116,
"id": "1710.06968_1146",
"lines": 1,
"tex": "\\[1=\\delta(h) \\in \\{w,ws\\} .\\]",
"tokens": 15,
"width": 432
}
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1710_06968_1146
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 24,
"id": "1710.06968_1330",
"lines": 1,
"tex": "\\[ \\delta(k)=\\delta(gh)\\geq st . \\]",
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"width": 80
}
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1710_06968_1330
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 40,
"id": "1710.06968_1558",
"lines": 1,
"tex": "\\[\\delta(g)=\\delta(g_1)\\dots \\delta(g_n).\\]",
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"width": 158
}
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1710_06968_1558
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 122,
"id": "1710.06968_1866",
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"tex": "\\[gh=g_1\\dots g_n\\]",
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"width": 322
}
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1710_06968_1866
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 47,
"id": "1710.06968_1999",
"lines": 1,
"tex": "\\[\\delta(gh)\\geq \\delta(g)\\delta(h)\\]",
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"width": 152
}
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1710_06968_1999
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 124,
"id": "1710.06968_2608",
"lines": 1,
"tex": "\\[G\\twoheadrightarrow B \\backslash G/ B, g\\mapsto B g B\\]",
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"width": 617
}
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1710_06968_2608
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 102,
"id": "1710.06968_2613",
"lines": 1,
"tex": "\\[\\delta_{B}: B \\backslash G/B\\to W.\\]",
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"width": 352
}
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1710_06968_2613
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 127,
"id": "1710.04940_1690",
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"tex": "\\begin{equation} L_{tot}=L_h+L_s. \\end{equation}",
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}
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1710_04940_1690
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 65,
"id": "1710.06939_4198",
"lines": 1,
"tex": "$$[Eq[f],R\\vee S]=\\Delta_{X}.$$",
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"width": 251
}
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1710_06939_4198
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 44,
"id": "1710.06939_4346",
"lines": 1,
"tex": "$$[Eq[f],R]=\\Delta_{X}.$$",
"tokens": 12,
"width": 135
}
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1710_06939_4346
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 124,
"id": "1710.06939_5518",
"lines": 1,
"tex": "\\[\\cdot : Ker[d]\\times Ker[c]\\to X_1.\\]",
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"width": 593
}
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1710_06939_5518
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 44,
"id": "1710.07304_10026",
"lines": 1,
"tex": "\\[ b = b_1 + \\dots + b_n \\]",
"tokens": 9,
"width": 139
}
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1710_07304_10026
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 39,
"id": "1710.07304_14252",
"lines": 1,
"tex": "\\[ B = C_1 \\cdot q_1 + \\dots + C_k \\cdot q_k \\]",
"tokens": 13,
"width": 178
}
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1710_07304_14252
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 68,
"id": "1710.07304_15323",
"lines": 1,
"tex": "\\[ b = k \\operatorname{p}(b) c_1 \\cdots c_n. \\]",
"tokens": 15,
"width": 237
}
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1710_07304_15323
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 78,
"id": "1710.07304_16527",
"lines": 1,
"tex": "\\[ B = D_1 \\cdot q_1 + \\dots + D_k \\cdot q_k \\]",
"tokens": 13,
"width": 369
}
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1710_07304_16527
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 49,
"id": "1710.07304_17705",
"lines": 1,
"tex": "\\[ b = k \\operatorname{p}(b) c_1 \\cdots c_n. \\]",
"tokens": 15,
"width": 165
}
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1710_07304_17705
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 73,
"id": "1710.05105_1600",
"lines": 1,
"tex": "$$\\operatorname{Dom}(B)\\subseteq \\operatorname{Dom}[\\mathfrak{b}]$$",
"tokens": 16,
"width": 264
}
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1710_05105_1600
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 80,
"id": "1710.05105_2205",
"lines": 1,
"tex": "$$ JR=-RJ. $$",
"tokens": 8,
"width": 205
}
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1710_05105_2205
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 113,
"id": "1710.05105_2492",
"lines": 1,
"tex": "$$QT\\subseteq TQ,$$",
"tokens": 6,
"width": 240
}
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1710_05105_2492
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 28,
"id": "1710.05105_3821",
"lines": 1,
"tex": "$$ UP=QU, $$",
"tokens": 7,
"width": 57
}
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1710_05105_3821
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hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
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{
"height": 41,
"id": "1710.05105_3905",
"lines": 1,
"tex": "$$\\dot U=U|_{\\dot{\\mathcal H}}\\;.$$",
"tokens": 15,
"width": 81
}
|
1710_05105_3905
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 101,
"id": "1710.05105_4583",
"lines": 1,
"tex": "$$I-Y^2=(I-Y)(I+Y)$$",
"tokens": 15,
"width": 450
}
|
1710_05105_4583
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 95,
"id": "1710.05105_5055",
"lines": 1,
"tex": "$$Q\\tilde y= x\\oplus Xx.$$",
"tokens": 10,
"width": 264
}
|
1710_05105_5055
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 85,
"id": "1710.05105_5066",
"lines": 1,
"tex": "$$Q^\\bot \\tilde x=-X^\\ast y\\oplus y.$$",
"tokens": 14,
"width": 286
}
|
1710_05105_5066
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 42,
"id": "1710.08250_327",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n:Y_n\\in S^*\\}\\]",
"tokens": 13,
"width": 167
}
|
1710_08250_327
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 91,
"id": "1710.08250_1192",
"lines": 1,
"tex": "\\[\\tau^*\\in\\{\\sigma_m:0\\leq m\\leq \\infty\\}.\\]",
"tokens": 16,
"width": 372
}
|
1710_08250_1192
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 115,
"id": "1710.08250_1444",
"lines": 1,
"tex": "\\[Z_m=\\rho^{\\sigma_m}g(Y_{\\sigma_m}).\\]",
"tokens": 16,
"width": 342
}
|
1710_08250_1444
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 32,
"id": "1710.08250_2050",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n\\geq 0:Y_n\\geq \\alpha^*\\}\\]",
"tokens": 15,
"width": 144
}
|
1710_08250_2050
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 72,
"id": "1710.08250_2065",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n\\geq 0:Y_n>\\alpha^*\\}\\]",
"tokens": 15,
"width": 333
}
|
1710_08250_2065
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 78,
"id": "1710.08250_2091",
"lines": 1,
"tex": "\\[\\tau'=\\inf\\{n>0:Y_n\\geq \\alpha^*\\}\\]",
"tokens": 15,
"width": 367
}
|
1710_08250_2091
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 25,
"id": "1710.08250_2357",
"lines": 1,
"tex": "\\[Y_n^y=y+S_n\\]",
"tokens": 9,
"width": 61
}
|
1710_08250_2357
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 68,
"id": "1710.08250_2414",
"lines": 1,
"tex": "\\[E_y\\rho^{\\tau_y}=E\\rho^{\\tau_+},\\]",
"tokens": 14,
"width": 176
}
|
1710_08250_2414
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 102,
"id": "1710.08250_2482",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n\\geq 0:Y_n\\geq \\alpha^*\\}\\]",
"tokens": 15,
"width": 491
}
|
1710_08250_2482
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 27,
"id": "1710.08250_2497",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n\\geq 0:Y_n>\\alpha^*\\}\\]",
"tokens": 15,
"width": 127
}
|
1710_08250_2497
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 93,
"id": "1710.08250_2690",
"lines": 1,
"tex": "\\[g(y)=(y^+)^\\nu,\\]",
"tokens": 10,
"width": 232
}
|
1710_08250_2690
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 82,
"id": "1710.08250_2889",
"lines": 1,
"tex": "\\[g(y)=(K-\\exp(y))^+\\]",
"tokens": 13,
"width": 316
}
|
1710_08250_2889
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 35,
"id": "1710.08250_2957",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{n\\geq 0:Y_n\\leq a^*\\}\\]",
"tokens": 15,
"width": 149
}
|
1710_08250_2957
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 86,
"id": "1710.08250_2970",
"lines": 1,
"tex": "\\[\\tau_-=\\inf\\{m>0:S_m<0\\}.\\]",
"tokens": 16,
"width": 399
}
|
1710_08250_2970
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 74,
"id": "1710.08250_2990",
"lines": 1,
"tex": "\\[a^*=\\log\\left(KE\\exp(I_T)\\right),\\]",
"tokens": 14,
"width": 290
}
|
1710_08250_2990
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 45,
"id": "1710.08250_3305",
"lines": 1,
"tex": "\\[r=\\rho\\mu<1,\\]",
"tokens": 9,
"width": 107
}
|
1710_08250_3305
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 24,
"id": "1710.08250_3338",
"lines": 1,
"tex": "\\[S^*=[a^*,\\infty)\\]",
"tokens": 9,
"width": 60
}
|
1710_08250_3338
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 30,
"id": "1710.08250_3460",
"lines": 1,
"tex": "\\begin{equation} \\tau_y\\leq \\tau_{y'}. \\end{equation}",
"tokens": 16,
"width": 48
}
|
1710_08250_3460
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 165,
"id": "1710.08250_4126",
"lines": 1,
"tex": "\\[c=\\frac{\\mu-\\log(b)}{\\mu}.\\]",
"tokens": 14,
"width": 354
}
|
1710_08250_4126
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 120,
"id": "1710.08250_4336",
"lines": 1,
"tex": "\\[P_k(\\tau_k=\\infty)=g(k).\\]",
"tokens": 13,
"width": 415
}
|
1710_08250_4336
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 158,
"id": "1710.08250_4490",
"lines": 1,
"tex": "\\[M_n=\\sup_{m\\leq n}Y_m,\\]",
"tokens": 13,
"width": 342
}
|
1710_08250_4490
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 77,
"id": "1710.08250_4538",
"lines": 1,
"tex": "\\[\\inf\\{n\\geq 0:Y_n>a^*\\}\\]",
"tokens": 13,
"width": 282
}
|
1710_08250_4538
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 113,
"id": "1710.08250_4752",
"lines": 1,
"tex": "\\[\\inf\\{n\\geq 0:Y_n>a^*\\}.\\]",
"tokens": 14,
"width": 423
}
|
1710_08250_4752
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 65,
"id": "1710.08250_5357",
"lines": 1,
"tex": "\\[\\tau^*=\\inf\\{t\\geq 0:Y_t\\geq \\alpha^*\\}\\]",
"tokens": 15,
"width": 291
}
|
1710_08250_5357
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 32,
"id": "1710.08250_5596",
"lines": 1,
"tex": "\\[g(x)<v_n(x)\\leq v(x). \\]",
"tokens": 15,
"width": 120
}
|
1710_08250_5596
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 55,
"id": "1710.06728_5018",
"lines": 1,
"tex": "\\begin{equation} M(k)\\cdot X=0 \\end{equation}",
"tokens": 16,
"width": 139
}
|
1710_06728_5018
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 104,
"id": "1710.09221_2718",
"lines": 1,
"tex": "\\begin{equation} J = \\sigma E, \\end{equation}",
"tokens": 13,
"width": 181
}
|
1710_09221_2718
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 111,
"id": "1710.05263_328",
"lines": 1,
"tex": "\\begin{eqnarray} Y = G(X)+\\varepsilon \\end{eqnarray}",
"tokens": 15,
"width": 288
}
|
1710_05263_328
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 73,
"id": "1710.10113_1926",
"lines": 1,
"tex": "$$(V, v_1,v_2) \\mapsto \\det(x_0 v_1 + x_1 v_2)$$",
"tokens": 16,
"width": 397
}
|
1710_10113_1926
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 41,
"id": "1710.10113_2279",
"lines": 1,
"tex": "$$f:W \\to \\mathcal{F}^{\\circ}$$",
"tokens": 11,
"width": 104
}
|
1710_10113_2279
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 61,
"id": "1710.10113_3687",
"lines": 1,
"tex": "$$h=(A,(\\lambda,...,\\lambda), \\operatorname{Id})$$",
"tokens": 13,
"width": 226
}
|
1710_10113_3687
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 74,
"id": "1710.11281_273",
"lines": 1,
"tex": "$$c(G)\\le 2g+3.$$",
"tokens": 10,
"width": 206
}
|
1710_11281_273
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 89,
"id": "1710.11281_833",
"lines": 1,
"tex": "$$ c(g) \\ge \\Omega(g^{1/3}). $$",
"tokens": 15,
"width": 266
}
|
1710_11281_833
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 97,
"id": "1710.05428_834",
"lines": 1,
"tex": "\\begin{align} y \\equiv ag^x \\pmod p. \\end{align}",
"tokens": 16,
"width": 587
}
|
1710_05428_834
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 83,
"id": "1710.07470_1580",
"lines": 1,
"tex": "$$RSV_t = 100 \\times \\frac{P_t-L_t}{H_t-L_t},$$",
"tokens": 16,
"width": 274
}
|
1710_07470_1580
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 89,
"id": "1710.07470_1583",
"lines": 1,
"tex": "$$\\%J_t = 3\\%K_t-2\\%D_t.$$",
"tokens": 12,
"width": 332
}
|
1710_07470_1583
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 109,
"id": "1710.09992_1487",
"lines": 1,
"tex": "$$ \\zeta_n=(1,2,\\ldots,n). $$",
"tokens": 13,
"width": 358
}
|
1710_09992_1487
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 68,
"id": "1710.09992_4880",
"lines": 1,
"tex": "$$ [x^ny^k] f(x,y) $$",
"tokens": 15,
"width": 179
}
|
1710_09992_4880
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 38,
"id": "1710.09992_6230",
"lines": 1,
"tex": "$$ i,j+1, \\cdots , j, i+1$$",
"tokens": 15,
"width": 130
}
|
1710_09992_6230
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 101,
"id": "1710.09992_10051",
"lines": 1,
"tex": "$$ n\\leq 30-3(c_1+c_2+c_3). $$",
"tokens": 14,
"width": 458
}
|
1710_09992_10051
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 111,
"id": "1710.09992_10279",
"lines": 1,
"tex": "$$ z(\\beta)=1+\\frac{n-c_1}{2}, $$",
"tokens": 16,
"width": 321
}
|
1710_09992_10279
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
|
{
"height": 92,
"id": "1710.09992_10294",
"lines": 1,
"tex": "\\begin{equation} n\\leq 24-3c_1. \\end{equation}",
"tokens": 15,
"width": 249
}
|
1710_09992_10294
|
hf://datasets/topdu/MER-17M@0a8d647367b1ea9da0d7b9a4b212d7cd2968437a/tokens_0_16/a-part-000000.tar
|
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