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Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

The Carlson elliptic integrals, also known as the Carlson symmetric forms, are a standard set of canonical elliptic integrals which provide a convenient alternative to ...

Let X be a normed space, M and N be algebraically complemented subspaces of X (i.e., M+N=X and M intersection N={0}), pi:X->X/M be the quotient map, phi:M×N->X be the natural ...

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample ...

The dot product can be defined for two vectors X and Y by X·Y=|X||Y|costheta, (1) where theta is the angle between the vectors and |X| is the norm. It follows immediately ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...

Given a set y=f(x) of n equations in n variables x_1, ..., x_n, written explicitly as y=[f_1(x); f_2(x); |; f_n(x)], (1) or more explicitly as {y_1=f_1(x_1,...,x_n); |; ...

The Johnson circumconic, a term used here for the first time, is the circumconic that passes through the vertices of both the reference triangle and the Johnson triangle. It ...

The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...