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A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

A Diophantine problem (i.e., one whose solution must be given in terms of integers) which seeks a solution to the following problem. Given n men and a pile of coconuts, each ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

If a distribution has a single mode at mu_0, then P(|x-mu_0|>=lambdatau)<=4/(9lambda^2), where tau^2=sigma^2+(mu-mu_0)^2.

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

A multiple integral is a set of integrals taken over n>1 variables, e.g., int...int_()_(n)f(x_1,...,x_n)dx_1...dx_n. An nth-order integral corresponds, in general, to an ...

There are several fractal curves associated with Sierpiński. The area for the first Sierpiński curve illustrated above (Sierpiński curve 1912) is A=1/3(7-4sqrt(2)). The curve ...

A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane. Von Staudt (1847) classified space ...