{
"NTCIR11-Math-1": [["math:\\qvar{square}(\\qvar{phi})=id"], ["math:\\qvar{phi}\\neq id"], ["text:hyperelliptic", "text:surface"], ["text:riemann"]],
"NTCIR11-Math-2": [["math:ImP^{\\qvar{+}}_{\\gamma}=C^{\\qvar{+}}_{\\mu}(\\gamma)"], ["text:lisboa"], ["text:cauchy"]],
"NTCIR11-Math-3": [["math:\\qvar{L}\\prime_{d-\\qvar{k}}=\\qvar{L}_{\\qvar{k}}"], ["text:geodesic", "text:interval"], ["text:symmetric"]],
"NTCIR11-Math-4": [["math:\\qvar{B}\\sigma_{3}\\qvar{B}=\\sigma_{3}"], ["text:invariance"], ["text:point"], ["text:interaction"]],
"NTCIR11-Math-5": [["math:S_{EH}=\\frac{1}{G_{3}}\\qvar{o}d^{3}x\\,\\sqrt{-g^{(3)}}"], ["text:entropy"], ["text:bound"], ["text:bekenstein", "text:hawking"]],
"NTCIR11-Math-6": [["math:\\qvar{S}=-\\qvar{T}_{\\qvar{p}}\\int\\qvar{d}^{\\qvar{p}+1}\\qvar{x}\\sqrt{\\qvar{g}}"], ["text:brane"], ["text:action"], ["text:cosmological"]],
"NTCIR11-Math-7": [["math:\\qvar{x}\\frac{\\qvar{y}}{\\qvar{z}}-\\qvar{u}\\frac{\\qvar{v}}{\\qvar{w}}"], ["text:non", "text:gaussianity"], ["text:curvatons"], ["text:density", "text:perturbations"], ["text:energy", "text:potential"]],
"NTCIR11-Math-8": [["math:\\qvar{x}\\leq\\frac{6}{2^{\\qvar{n}}}+12\\epsilon"], ["text:invariant", "text:subspace", "text:property"], ["text:banach", "text:spaces"]],
"NTCIR11-Math-9": [["math:\\qvar{x}^{\\qvar{i}}_{\\qvar{n}}=(1-\\epsilon)\\qvar{f}+\\frac{\\epsilon}{2}[\\qvar{g%\n}+\\qvar{h}]"], ["text:ecosystems"], ["text:power", "text:law", "text:distributions"]],
"NTCIR11-Math-10": [["math:f(\\qvar{x})=\\frac{1}{\\sigma\\sqrt{2\\pi}}\\qvar{z}"], ["text:gaussian", "text:distribution"], ["text:random", "text:sequence"], ["text:algorithm"], ["text:code"]],
"NTCIR11-Math-11": [["math:p^{2}+x^{2}(ix)^{\\epsilon}"], ["text:eigenvalue"]],
"NTCIR11-Math-12": [["math:L_{\\infty}"], ["text:construct"], ["text:differential", "text:graded", "text:algebra"]],
"NTCIR11-Math-13": [["math:(D)"], ["text:type"], ["text:maximal", "text:monotone"]],
"NTCIR11-Math-14": [["math:-tr(\\qvar{x}ln\\qvar{x})"], ["text:neumann"], ["text:entropy"]],
"NTCIR11-Math-15": [["math:\\frac{1}{n^{\\qvar{s}}}"], ["text:riemann"], ["text:zeta"]],
"NTCIR11-Math-16": [["math:\\qvar{f}(\\qvar{x})=\\qvar{x}"], ["text:fixed", "text:point"]],
"NTCIR11-Math-17": [["math:\\qvar{f}(\\qvar{z})=\\qvar{z}^{\\qvar{d}}+c"], ["text:mandelbrot"], ["text:dynamical", "text:plane"]],
"NTCIR11-Math-18": [["math:\\frac{a\\qvar{z}+b}{c\\qvar{z}+d}"], ["text:mobius"], ["text:mo", "text:bius"], ["text:automorphism"]],
"NTCIR11-Math-19": [["math:H_{\\qvar{n}-\\qvar{k}}(\\qvar{X})"], ["text:homology"], ["text:duality"]],
"NTCIR11-Math-20": [["math:\\qvar{x}^{2}-\\qvar{x}-1=0"], ["text:golden", "text:ratio"], ["text:fibonacci"]],
"NTCIR11-Math-21": [["math:\\qvar{f}(\\qvar{a}x+\\qvar{b}y)<\\qvar{a}\\qvar{f}(x)+\\qvar{b}\\qvar{f}(y)"], ["text:convex"], ["text:convexity"]],
"NTCIR11-Math-22": [["math:\\int_{\\qvar{M}}\\qvar{f}dS"], ["text:integral"], ["text:surface"]],
"NTCIR11-Math-23": [["math:\\langle\\cdot,\\cdot\\rangle"], ["text:definition"], ["text:inner"], ["text:product"]],
"NTCIR11-Math-24": [["math:\\widehat{\\mathrm{CH}}^{\\qvar{p}}(\\qvar{A})\\cong\\qvar{Y}"], ["text:arithmetic"], ["text:chow"], ["text:group"]],
"NTCIR11-Math-25": [["math:\\displaystyle\\widehat{\\deg}(\\qvar{x}_{1}^{\\qvar{k}_{1}}\\qvar{x}_{2}^{\\qvar{k}_%\n{2}}\\cdots\\qvar{x}_{n}^{\\qvar{k}_{n}})"], ["text:theorem"], ["text:arithmetic"], ["text:chern"], ["text:number"]],
"NTCIR11-Math-26": [["math:det(\\qvar{a}_{1}\\qvar{b}_{2}-\\qvar{a}_{2}\\qvar{b}_{1}+\\qvar{c})"], ["text:vessel"]],
"NTCIR11-Math-27": [["math:E(\\lambda)=-m^{2}_{\\rm dyn}(\\lambda)"], ["text:electron", "text:energy"], ["text:quantum"], ["text:dynamics"], ["text:njl"]],
"NTCIR11-Math-28": [["math:\\Phi^{4}"], ["text:quantum"], ["text:field"], ["text:theory"]],
"NTCIR11-Math-29": [["math:\\sum_{{\\qvar{n}}=0}^{\\infty}t^{\\qvar{m}}a_{k}(x)"], ["text:heat"], ["text:kernel"], ["text:asymptotic"]],
"NTCIR11-Math-30": [["math:\\mathbb{C}P^{\\qvar{n}}"], ["text:complex"], ["text:projective"], ["text:space"]],
"NTCIR11-Math-31": [["math:\\qvar{k}+1/(3\\qvar{k}+\\qvar{c})"], ["text:graph"], ["text:covering"], ["text:fractional", "text:arboricity"]],
"NTCIR11-Math-32": [["math:|\\qvar{u}\\cdot\\qvar{v}|\\leq||\\qvar{u}||||\\qvar{v}||"], ["text:cauchy"], ["text:schwarz"]],
"NTCIR11-Math-33": [["math:||\\qvar{f}\\qvar{g}||_{1}\\leq||\\qvar{f}||_{p}||\\qvar{g}||_{q}"], ["text:hoelder"], ["text:ho", "text:lder"]],
"NTCIR11-Math-34": [["math:\\lim\\limits_{n\\rightarrow\\infty}\\int\\limits_{\\qvar{X}}\\qvar{f}_{n}d\\qvar{u}=%\n\\int\\limits_{\\qvar{X}}\\lim\\limits_{n\\rightarrow\\infty}\\qvar{f}_{n}d\\qvar{u}"], ["text:dominated", "text:convergence"], ["text:lebesgue"]],
"NTCIR11-Math-35": [["math:||\\qvar{x}-\\qvar{a}||\\leq\\frac{1}{||\\qvar{a}^{-1}||}"], ["text:invertible"], ["text:banach", "text:algebra"]],
"NTCIR11-Math-36": [["math:\\rho(\\qvar{A})=\\lim\\limits_{n\\rightarrow\\infty}||\\qvar{A}^{n}||^{1/n}"], ["text:spectral", "text:radius"], ["text:matrix"]],
"NTCIR11-Math-37": [["math:\\qvar{A}=\\qvar{U}\\qvar{S}\\qvar{V}^{T}"], ["text:singular", "text:value", "text:decomposition"], ["text:matrix"]],
"NTCIR11-Math-38": [["math:||\\qvar{x}+\\qvar{y}||_{\\qvar{p}}\\leq||\\qvar{x}||_{\\qvar{p}}+||\\qvar{y}||_{%\n\\qvar{p}}"], ["text:minkowski"], ["text:inequality"]],
"NTCIR11-Math-39": [["math:\\mathbb{P}[\\qvar{X}\\geq\\qvar{t}]\\leq\\frac{\\mathbf{E}[\\qvar{X}]}{\\qvar{t}}"], ["text:markov", "text:inequality"]],
"NTCIR11-Math-40": [["math:\\lim\\limits_{n\\rightarrow\\infty}\\mathbb{P}[|\\qvar{A}_{n}-\\mathbf{E}[\\qvar{X}]|%\n>\\qvar{e}]=0"], ["text:weak", "text:law"], ["text:large", "text:number"]],
"NTCIR11-Math-41": [["math:\\mathbb{P}[\\lim\\limits_{n\\rightarrow\\infty}\\qvar{A}_{n}=\\mathbf{E}[\\qvar{X}]]=1"], ["text:strong", "text:law"], ["text:large", "text:number"]],
"NTCIR11-Math-42": [["math:\\qvar{E}=\\bigoplus\\limits_{\\qvar{i}=0}^{\\infty}\\qvar{E}_{\\qvar{i}}"], ["text:eigenvalues"]],
"NTCIR11-Math-43": [["math:\\oint_{C}\\mathbf{B}\\cdot\\mathrm{d}\\ell=\\mu_{0}I"], ["text:ampere"], ["text:line", "text:integral"]],
"NTCIR11-Math-44": [["math:\\qvar{x}^{\\qvar{n}}+\\qvar{y}^{\\qvar{n}}=\\qvar{z}^{\\qvar{n}}"], ["math:\\qvar{x},\\qvar{y},\\qvar{z},\\qvar{n}\\in{\\mathbb{N}}"], ["text:diophantine", "text:equations"]],
"NTCIR11-Math-45": [["math:\\frac{1+\\sqrt{5}}{2}^{n}"], ["text:fibonacci"]],
"NTCIR11-Math-46": [["math:1024k^{1}0-2560k^{9}+3840k^{8}-4480k^{7}+4096k^{6}-2944k^{5}+1696k^{4}-760k^{3%\n}+236k^{2}-40k"], ["text:graph"], ["text:chromatic", "text:polynomials"]],
"NTCIR11-Math-47": [["math:P_{n}=2P_{n-1}+P_{n-2}"], ["text:recurrence", "text:relation"], ["text:pell", "text:number"]],
"NTCIR11-Math-48": [["math:\\dot{x}(t)=\\qvar{A}x(t)+\\qvar{B}u(t)"], ["math:t\\in\\mathbb{R}"], ["math:x(t)\\in\\mathbb{R}^{\\qvar{n}}"], ["math:u(t)\\in\\mathbb{R}^{\\qvar{m}}"], ["text:pole", "text:placement"], ["text:state", "text:feedback"], ["text:eigenstructure", "text:assigment"]],
"NTCIR11-Math-49": [["math:\\sum_{\\qvar{n}=1}^{2*\\qvar{k}-1}(-1)^{\\qvar{n}}*cos(1/4*\\pi)*\\qvar{n}^{2/\\qvar%\n{k}}=\\qvar{R}"], ["text:gauss", "text:sums"], ["text:finite", "text:sums"]],
"NTCIR11-Math-50": [["math:\\chi^{\\prime}_{a}(\\qvar{G})\\leq\\Delta(\\qvar{G})+6"], ["text:acyclic", "text:index"], ["text:acyclic", "text:edge", "text:coloring"], ["text:graph"]],
}