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An algebraic group is a variety (or scheme) endowed with a group structure such that the group operations are morphisms of varieties (or schemes). The concept is similar to ...

An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, ...

An Anosov diffeomorphism is a C^1 diffeomorphism phi of a manifold M to itself such that the tangent bundle of M is hyperbolic with respect to phi. Very few classes of Anosov ...

A method for finding solutions u and v to a linear congruence au+bv=d by constructing a matrix formed by adjoining a vector containing a and b with a unit matrix, M=[a 1 0; b ...

Let B={b_1,b_2,...} be an infinite Abelian semigroup with linear order b_1<b_2<... such that b_1 is the unit element and a<b implies ac<bc for a,b,c in B. Define a Möbius ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

In general, a cross is a figure formed by two intersecting line segments. In linear algebra, a cross is defined as a set of n mutually perpendicular pairs of vectors of equal ...

The inversion of a convolution equation, i.e., the solution for f of an equation of the form f*g=h+epsilon, given g and h, where epsilon is the noise and * denotes the ...

Consider the length of the diagonal of a unit square as approximated by piecewise linear steps that may only be taken in the right and up directions. Obviously, the length so ...

An implicit method for solving an ordinary differential equation that uses f(x_n,y_n) in y_(n+1). In the case of a heat equation, for example, this means that a linear system ...