{
"NTCIR12-MathWiki-1": ["math:-0.026838601\\ldots"],
"NTCIR12-MathWiki-2": ["math:\\mathfrak{P}"],
"NTCIR12-MathWiki-3": ["math:N=\\left\\lfloor 0.5-\\log_{2}\\left(\\frac{\\text{Frequency of this item}}{\\text{\nFrequency of most common item}}\\right)\\right\\rfloor"],
"NTCIR12-MathWiki-4": ["math:\\mathbf{\\nabla}\\times\\mathbf{B}=\\mu_{0}\\mathbf{J}+\\underbrace{\\mu_{0}\\epsilon_%\n{0}\\frac{\\partial}{\\partial t}\\mathbf{E}}_{\\mathrm{Maxwell^{\\prime}s\\ term}}"],
"NTCIR12-MathWiki-5": ["math:1+\\cfrac{1}{2+\\cfrac{1}{5+\\cfrac{1}{5+\\cfrac{1}{4+\\ddots}}}}"],
"NTCIR12-MathWiki-6": ["math:\\,{}^{238}_{92}\\mathrm{U}+\\,^{64}_{28}\\mathrm{Ni}\\to\\,^{302}_{120}\\mathrm{Ubn}%\n^{*}\\to\\ \\mathit{fission\\ only}"],
"NTCIR12-MathWiki-7": ["math:0\\to G^{\\wedge}\\stackrel{\\pi^{\\wedge}}{\\to}X^{\\wedge}\\stackrel{\\imath^{\\wedge}%\n}{\\to}H^{\\wedge}\\to 0"],
"NTCIR12-MathWiki-8": ["math:w=\\begin{cases}w^{*}&\\mbox{if }w^{*}>\\frac{1}{2},\\\\\n\\frac{1}{2}&\\mbox{if }w^{*}\\leq\\frac{1}{2}.\\\\\n\\end{cases}"],
"NTCIR12-MathWiki-9": ["math:\\begin{bmatrix}V_{1}\\\\\nI_{2}\\end{bmatrix}=\\begin{bmatrix}h_{11}&h_{12}\\\\\nh_{21}&h_{22}\\end{bmatrix}\\begin{bmatrix}I_{1}\\\\\nV_{2}\\end{bmatrix}"],
"NTCIR12-MathWiki-10": ["math:L(\\lambda,\\alpha,s)=\\sum_{n=0}^{\\infty}\\frac{\\exp(2\\pi i\\lambda n)}{(n+\\alpha)%\n^{s}}."],
"NTCIR12-MathWiki-11": ["math:\\ ax^{2}+bx+c=0"],
"NTCIR12-MathWiki-12": ["math:O(mn\\log m)"],
"NTCIR12-MathWiki-13": ["math:A\\oplus B=(A^{c}\\ominus B^{s})^{c}"],
"NTCIR12-MathWiki-14": ["math:\\cos\\alpha=-\\cos\\beta\\cos\\gamma+\\sin\\beta\\sin\\gamma\\cosh\\frac{a}{k},\\,"],
"NTCIR12-MathWiki-15": ["math:\\forall x,y\\in A\\;[x\\neq y\\rightarrow\\neg\\exists z\\in X\\;[z\\leq x\\land z\\leq y%\n]]."],
"NTCIR12-MathWiki-16": ["math:\\tau_{\\text{rms}}=\\sqrt{\\frac{\\int_{0}^{\\infty}(\\tau-\\overline{\\tau})^{2}A_{c}%\n(\\tau)d\\tau}{\\int_{0}^{\\infty}A_{c}(\\tau)d\\tau}}"],
"NTCIR12-MathWiki-17": ["math:x-1-\\frac{1}{2}-\\frac{1}{4}-\\frac{1}{5}-\\frac{1}{6}-\\frac{1}{9}-\\cdots=1"],
"NTCIR12-MathWiki-18": ["math:P_{i}^{x}=\\frac{N!}{n_{x}!(N-n_{x})!}p_{x}^{n_{x}}(1-p_{x})^{N-n_{x}}"],
"NTCIR12-MathWiki-19": ["math:H_{ij}=\\begin{bmatrix}{\\partial^{2}V_{ij}\\over\\partial x_{i}\\partial x_{j}}&{%\n\\partial^{2}V_{ij}\\over\\partial x_{i}\\partial y_{j}}&{\\partial^{2}V_{ij}\\over%\n\\partial x_{i}\\partial z_{j}}\\\\\n{\\partial^{2}V_{ij}\\over\\partial y_{i}\\partial x_{j}}&{\\partial^{2}V_{ij}\\over%\n\\partial y_{i}\\partial y_{j}}&{\\partial^{2}V_{ij}\\over\\partial y_{i}\\partial z%\n_{j}}\\\\\n{\\partial^{2}V_{ij}\\over\\partial z_{i}\\partial x_{j}}&{\\partial^{2}V_{ij}\\over%\n\\partial z_{i}\\partial y_{j}}&{\\partial^{2}V_{ij}\\over\\partial z_{i}\\partial z%\n_{j}}\\end{bmatrix}"],
"NTCIR12-MathWiki-20": ["math:r_{xy}=\\frac{\\sum\\limits_{i=1}^{n}(x_{i}-\\bar{x})(y_{i}-\\bar{y})}{(n-1)s_{x}s_%\n{y}}=\\frac{\\sum\\limits_{i=1}^{n}(x_{i}-\\bar{x})(y_{i}-\\bar{y})}{\\sqrt{\\sum%\n\\limits_{i=1}^{n}(x_{i}-\\bar{x})^{2}\\sum\\limits_{i=1}^{n}(y_{i}-\\bar{y})^{2}}},"],
"NTCIR12-MathWiki-21": ["math:-0.\\qvar{*1*}\\ldots"],
"NTCIR12-MathWiki-22": ["math:\\mathfrak{P}^{\\qvar{*1*}}"],
"NTCIR12-MathWiki-23": ["math:\\qvar{*1*}\\left(\\frac{\\text{Frequency \\qvar{*2*}}}{\\text{Frequency \\qvar{*3*}}%\n}\\right)"],
"NTCIR12-MathWiki-24": ["math:\\underbrace{\\qvar{*1*}}_{\\qvar{*2*}}"],
"NTCIR12-MathWiki-25": ["math:1+\\cfrac{1}{\\qvar{*1*}+\\cfrac{1}{\\qvar{*2*}}}"],
"NTCIR12-MathWiki-26": ["math:\\,{}^{238}_{92}\\mathrm{U}+\\qvar{*1*}\\to\\qvar{*2*}"],
"NTCIR12-MathWiki-27": ["math:\\qvar{*1*}^{\\wedge}\\stackrel{\\qvar{*2*}^{\\wedge}}{\\to}\\qvar{*3*}^{\\wedge}"],
"NTCIR12-MathWiki-28": ["math:\\qvar{*1*}=\\{\\begin{array}[]{ll}\\qvar{*2*}&\\mbox{if }\\qvar{*3*}>\\frac{1}{2}\\\\\n\\qvar{*4*}&\\mbox{if }\\qvar{*3*}\\leq\\frac{1}{2}\\\\\n\\end{array}"],
"NTCIR12-MathWiki-29": ["math:\\qvar{*1*}=\\begin{bmatrix}\\qvar{*2*}&\\qvar{*3*}\\\\\n\\qvar{*4*}&\\qvar{*5*}\\end{bmatrix}\\begin{bmatrix}\\qvar{*6*}\\\\\n\\qvar{*7*}\\end{bmatrix}"],
"NTCIR12-MathWiki-30": ["math:L(\\qvar{*1*},\\qvar{*2*},\\qvar{*3*})=\\sum_{\\qvar{*4*}=0}^{\\infty}\\frac{\\exp(2%\n\\pi i\\qvar{*1*}\\qvar{*4*})}{(\\qvar{*4*}+\\qvar{*2*})^{\\qvar{*3*}}}"],
"NTCIR12-MathWiki-31": ["math:\\qvar{*1*}x^{2}+\\qvar{*2*}x+\\qvar{*3*}=0"],
"NTCIR12-MathWiki-32": ["math:O(\\qvar{*1*}\\log\\qvar{*2*})"],
"NTCIR12-MathWiki-33": ["math:A~{}\\qvar{*1*}~{}B=(\\qvar{*2*})^{\\qvar{*3*}}"],
"NTCIR12-MathWiki-34": ["math:\\qvar{*1*}\\alpha=-\\qvar{*1*}\\beta\\qvar{*1*}\\gamma+\\qvar{*2*}\\beta\\qvar{*2*}%\n\\gamma\\qvar{*3*}"],
"NTCIR12-MathWiki-35": ["math:\\forall x,y\\in\\qvar{*1*}\\;[x\\neq y\\rightarrow\\qvar{*2*}]"],
"NTCIR12-MathWiki-36": ["math:\\qvar{*1*}=\\sqrt{\\frac{\\int_{0}^{\\infty}\\qvar{*2*}^{2}\\qvar{*3*}~{}d\\qvar{*1*}%\n}{\\int_{0}^{\\infty}\\qvar{*3*}~{}d\\qvar{*1*}}}"],
"NTCIR12-MathWiki-37": ["math:\\frac{1}{\\qvar{*1*}}-\\frac{1}{\\qvar{*2*}}-\\frac{1}{\\qvar{*3*}}-\\frac{1}{\\qvar{%\n*4*}}-\\frac{1}{\\qvar{*5*}}"],
"NTCIR12-MathWiki-38": ["math:\\frac{N!}{\\qvar{*1*}!(N-\\qvar{*1*})!}p^{\\qvar{*1*}}(1-p)^{N-\\qvar{*1*}}"],
"NTCIR12-MathWiki-39": ["math:H_{\\qvar{*1*}}=\\begin{bmatrix}{\\partial^{2}\\qvar{*2*}\\over\\qvar{*3*}}\\end{bmatrix}"],
"NTCIR12-MathWiki-40": ["math:\\frac{\\sum\\limits_{i=1}^{n}(\\qvar{*1*}_{i}-\\bar{\\qvar{*1*}})(\\qvar{*2*}_{i}-%\n\\bar{\\qvar{*2*}})}{\\sqrt{\\sum\\limits_{i=1}^{n}(\\qvar{*1*}_{i}-\\bar{\\qvar{*1*}}%\n)^{2}\\sum\\limits_{i=1}^{n}(\\qvar{*2*}_{i}-\\bar{\\qvar{*2*}})^{2}}}"],
}