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The following integral transform relationship, known as the Abel transform, exists between two functions f(x) and g(t) for 0<alpha<1, f(x) = int_0^x(g(t)dt)/((x-t)^alpha) (1) ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

The Bailey mod 9 identities are a set of three Rogers-Ramanujan-like identities appearing as equations (1.6), (1.8), and (1.7) on p. 422 of Bailey (1947) given by A(q) = ...

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 ...

A bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board). To form the ...

A polyhedron is said to be canonical if all its polyhedron edges touch a sphere and the center of gravity of their contact points is the center of that sphere. In other ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...

A category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary ...

Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels. ...

The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi ...