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The Fourier transform of a Gaussian function f(x)=e^(-ax^2) is given by F_x[e^(-ax^2)](k) = int_(-infty)^inftye^(-ax^2)e^(-2piikx)dx (1) = ...

Given an infinitive sequence {x_n} with associative array a(i,j), then {x_n} is said to be a fractal sequence 1. If i+1=x_n, then there exists m<n such that i=x_m, 2. If h<i, ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning graph. It has 9 vertices, 16 edges (consisting of 3 ...

A special case of nim played by the following rules. Given a heap of size n, two players alternately select a heap and divide it into two unequal heaps. A player loses when ...

An abstract algebra concerned with results valid for many different kinds of spaces. Modules are the basic tools used in homological algebra.

Let f be a function defined on a set A and taking values in a set B. Then f is said to be an injection (or injective map, or embedding) if, whenever f(x)=f(y), it must be the ...

A particular solution to a differential equation corresponding to a specific value of the equation's free parameters. For example, the integral curves of the differential ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

Let S be a mathematical statement, then the Iverson bracket is defined by [S]={0 if S is false; 1 if S is true, (1) and corresponds to the so-called characteristic function. ...