{
"NTCIR11-Math-1": [["math:(", "math:(", "math:?", "math:U!times", "math:?", "math:)", "math:U!eq", "math:(", "math:V!i", "math:U!times", "math:V!d", "math:)", "math:)"], ["math:(", "math:?", "math:U!neq", "math:(", "math:V!i", "math:U!times", "math:V!d", "math:)", "math:)"], ["text:hyperelliptic", "text:surface"], ["text:riemann"]],
"NTCIR11-Math-2": [["text:lisboa"], ["text:cauchy"]],
"NTCIR11-Math-3": [["text:geodesic", "text:interval"], ["text:symmetric"]],
"NTCIR11-Math-4": [["text:invariance"], ["text:point"], ["text:interaction"]],
"NTCIR11-Math-5": [["text:entropy"], ["text:bound"], ["text:bekenstein", "text:hawking"]],
"NTCIR11-Math-6": [["text:brane"], ["text:action"], ["text:cosmological"]],
"NTCIR11-Math-7": [["math:(", "math:(", "math:?", "math:U!times", "math:(", "math:?", "math:O!divide", "math:?", "math:)", "math:)", "math:O!minus", "math:(", "math:?", "math:U!times", "math:(", "math:?", "math:O!divide", "math:?", "math:)", "math:)", "math:)"], ["text:non", "text:gaussianity"], ["text:curvatons"], ["text:density", "text:perturbations"], ["text:energy", "text:potential"]],
"NTCIR11-Math-8": [["text:invariant", "text:subspace", "text:property"], ["text:banach", "text:spaces"]],
"NTCIR11-Math-9": [["text:ecosystems"], ["text:power", "text:law", "text:distributions"]],
"NTCIR11-Math-10": [["math:(", "math:(", "math:V!f", "math:U!times", "math:?", "math:)", "math:U!eq", "math:(", "math:(", "math:N!1", "math:O!divide", "math:(", "math:V!\u03c3", "math:U!times", "math:O!root", "math:(", "math:(", "math:N!2", "math:U!times", "math:V!\u03c0", "math:)", "math:,", "math:N!2", "math:)", "math:)", "math:)", "math:U!times", "math:?", "math:)", "math:)"], ["text:gaussian", "text:distribution"], ["text:random", "text:sequence"], ["text:algorithm"], ["text:code"]],
"NTCIR11-Math-11": [["text:eigenvalue"]],
"NTCIR11-Math-12": [["text:construct"], ["text:differential", "text:graded", "text:algebra"]],
"NTCIR11-Math-13": [["math:V!D"], ["text:type"], ["text:maximal", "text:monotone"]],
"NTCIR11-Math-14": [["math:(", "math:V!t", "math:U!times", "math:V!r", "math:U!times", "math:(", "math:?", "math:U!times", "math:V!l", "math:U!times", "math:V!n", "math:U!times", "math:?", "math:)", "math:)"], ["text:neumann"], ["text:entropy"]],
"NTCIR11-Math-15": [["text:riemann"], ["text:zeta"]],
"NTCIR11-Math-16": [["math:(", "math:(", "math:?", "math:U!times", "math:?", "math:)", "math:U!eq", "math:?", "math:)"], ["text:fixed", "text:point"]],
"NTCIR11-Math-17": [["text:mandelbrot"], ["text:dynamical", "text:plane"]],
"NTCIR11-Math-18": [["math:(", "math:(", "math:(", "math:V!a", "math:U!times", "math:?", "math:)", "math:U!plus", "math:V!b", "math:)", "math:O!divide", "math:(", "math:(", "math:V!c", "math:U!times", "math:?", "math:)", "math:U!plus", "math:V!d", "math:)", "math:)"], ["text:mobius"], ["text:mo", "text:bius"], ["text:automorphism"]],
"NTCIR11-Math-19": [["text:homology"], ["text:duality"]],
"NTCIR11-Math-20": [["text:golden", "text:ratio"], ["text:fibonacci"]],
"NTCIR11-Math-21": [["math:(", "math:(", "math:?", "math:U!times", "math:(", "math:(", "math:?", "math:U!times", "math:V!x", "math:)", "math:U!plus", "math:(", "math:?", "math:U!times", "math:V!y", "math:)", "math:)", "math:)", "math:O!lt", "math:(", "math:(", "math:?", "math:U!times", "math:?", "math:U!times", "math:V!x", "math:)", "math:U!plus", "math:(", "math:?", "math:U!times", "math:?", "math:U!times", "math:V!y", "math:)", "math:)", "math:)"], ["text:convex"], ["text:convexity"]],
"NTCIR11-Math-22": [["text:integral"], ["text:surface"]],
"NTCIR11-Math-23": [["text:definition"], ["text:inner"], ["text:product"]],
"NTCIR11-Math-24": [["text:arithmetic"], ["text:chow"], ["text:group"]],
"NTCIR11-Math-25": [["text:theorem"], ["text:arithmetic"], ["text:chern"], ["text:number"]],
"NTCIR11-Math-26": [["text:vessel"]],
"NTCIR11-Math-27": [["text:electron", "text:energy"], ["text:quantum"], ["text:dynamics"], ["text:njl"]],
"NTCIR11-Math-28": [["text:quantum"], ["text:field"], ["text:theory"]],
"NTCIR11-Math-29": [["text:heat"], ["text:kernel"], ["text:asymptotic"]],
"NTCIR11-Math-30": [["text:complex"], ["text:projective"], ["text:space"]],
"NTCIR11-Math-31": [["math:(", "math:?", "math:U!plus", "math:(", "math:N!1", "math:O!divide", "math:(", "math:(", "math:N!3", "math:U!times", "math:?", "math:)", "math:U!plus", "math:?", "math:)", "math:)", "math:)"], ["text:graph"], ["text:covering"], ["text:fractional", "text:arboricity"]],
"NTCIR11-Math-32": [["text:cauchy"], ["text:schwarz"]],
"NTCIR11-Math-33": [["text:hoelder"], ["text:ho", "text:lder"]],
"NTCIR11-Math-34": [["text:dominated", "text:convergence"], ["text:lebesgue"]],
"NTCIR11-Math-35": [["text:invertible"], ["text:banach", "text:algebra"]],
"NTCIR11-Math-36": [["text:spectral", "text:radius"], ["text:matrix"]],
"NTCIR11-Math-37": [["text:singular", "text:value", "text:decomposition"], ["text:matrix"]],
"NTCIR11-Math-38": [["text:minkowski"], ["text:inequality"]],
"NTCIR11-Math-39": [["text:markov", "text:inequality"]],
"NTCIR11-Math-40": [["text:weak", "text:law"], ["text:large", "text:number"]],
"NTCIR11-Math-41": [["text:strong", "text:law"], ["text:large", "text:number"]],
"NTCIR11-Math-42": [["text:eigenvalues"]],
"NTCIR11-Math-43": [["text:ampere"], ["text:line", "text:integral"]],
"NTCIR11-Math-44": [["math:(", "math:M!L-0", "math:(", "math:?", "math:,", "math:?", "math:,", "math:?", "math:,", "math:?", "math:)", "math:O!in", "math:V!N", "math:)"], ["text:diophantine", "text:equations"]],
"NTCIR11-Math-45": [["text:fibonacci"]],
"NTCIR11-Math-46": [["text:graph"], ["text:chromatic", "text:polynomials"]],
"NTCIR11-Math-47": [["text:recurrence", "text:relation"], ["text:pell", "text:number"]],
"NTCIR11-Math-48": [["math:(", "math:(", "math:F!normal- \u0307", "math:(", "math:V!x", "math:)", "math:U!times", "math:V!t", "math:)", "math:U!eq", "math:(", "math:(", "math:?", "math:U!times", "math:V!x", "math:U!times", "math:V!t", "math:)", "math:U!plus", "math:(", "math:?", "math:U!times", "math:V!u", "math:U!times", "math:V!t", "math:)", "math:)", "math:)"], ["math:(", "math:V!t", "math:O!in", "math:V!R", "math:)"], ["text:pole", "text:placement"], ["text:state", "text:feedback"], ["text:eigenstructure", "text:assigment"]],
"NTCIR11-Math-49": [["text:gauss", "text:sums"], ["text:finite", "text:sums"]],
"NTCIR11-Math-50": [["text:acyclic", "text:index"], ["text:acyclic", "text:edge", "text:coloring"], ["text:graph"]],
}