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In a noncommutative ring R, a right ideal is a subset I which is an additive subgroup of R and such that for all r in R and all a in I, ar in I. (1) For all a in R, the set ...

If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n (1) means exists N such that P(n) ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

For a connection A and a positive spinor phi in Gamma(V_+), Witten's equations (also called the Seiberg-Witten invariants) are given by D_Aphi = 0 (1) F_+^A = ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

Fisheye perspective is a two-part projection. First, three-dimensional space is projected onto the surface of a hemisphere, by connecting every external point to the center ...