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An inner automorphism of a group G is an automorphism of the form phi(g)=h^(-1)gh, where h is a fixed element of G. An outer automorphism of G is an automorphism which cannot ...

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

The path traced out by a fixed point at a radius b>a, where a is the radius of a rolling circle, also sometimes called an extended cycloid. The prolate cycloid contains ...

A regular patch is a patch x:U->R^n for which the Jacobian J(x)(u,v) has rank 2 for all (u,v) in U. A patch is said to be regular at a point (u_0,v_0) in U provided that its ...

A natural transformation Phi_Y:B(AY)->Y is called unital if the leftmost diagram above commutes. Similarly, a natural transformation Psi_Y:Y->A(BY) is called unital if the ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

The inverse secant sec^(-1)z (Zwillinger 1995, p. 465), also denoted arcsecz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 315; Jeffrey 2000, p. 124), is ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number theta is given by |_theta_|, ...