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An array B=b_(ij), i,j>=1 of positive integers is called a dispersion if 1. The first column of B is a strictly increasing sequence, and there exists a strictly increasing ...

The function defined by y_+^alpha={y^alpha for y>0; 0 for y<=0. (1)

A normed vector space X=(X,||·||_X) is said to be uniformly convex if for sequences {x_n}={x_n}_(n=1)^infty, {y_n}={y_n}_(n=1)^infty, the assumptions ||x_n||_X<=1, ...

A cube whose edge lengths are 1. The unit cube therefore has unit volume.

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

The base 2 method of counting in which only the digits 0 and 1 are used. In this base, the number 1011 equals 1·2^0+1·2^1+0·2^2+1·2^3=11. This base is used in computers, ...

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

A prime circle of order 2n is a free circular permutation of the numbers from 1 to 2n with adjacent pairs summing to a prime. The number of prime circles for n=1, 2, ..., are ...