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The triangle space T is the set of triples (a,b,c) of real numbers that are side lengths of a (Euclidean) triangle, i.e., T={(a,b,c):0<a<b+c,0<b<c+a,0<c<a+b} (Kimberling ...

The trimean is defined to be TM=1/4(H_1+2M+H_2), where H_i are the hinges and M is the statistical median. Press et al. (1992) call this Tukey's trimean. It is an L-estimate.

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

A witness is a number which, as a result of its number theoretic properties, guarantees either the compositeness or primality of a number n. Witnesses are most commonly used ...

On an algebraic curve, the sum of the number of coincidences at a noncuspidal point C is the sum of the orders of the infinitesimal distances from a nearby point P to the ...

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

The Kneser graphs are a class of graph introduced by Lovász (1978) to prove Kneser's conjecture. Given two positive integers n and k, the Kneser graph K(n,k), often denoted ...

Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...