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A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all ...

If (1-z)^(alpha+beta-gamma-1/2)_2F_1(2alpha,2beta;2gamma;z)=sum_(n=0)^inftya_nz^n, (1) where _2F_1(a,b;c;z) is a hypergeometric function, then (2) where (a)_n is a Pochhammer ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

The symmetric statistic k_(r,s,...) defined such that <k_(r,s,...)>=kappa_rkappa_s..., (1) where kappa_r is a cumulant. These statistics generalize k-statistic and were ...

A symbol used to distinguish one quantity x^' ("x prime") from another related x. Prime marks are most commonly used to denote 1. Transformed coordinates, 2. Conjugate ...