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Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

A set of functions {f_1(n,x),f_2(n,x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., int_Rf_1(m,x)f_1(n,x)dx = ...

A base for a neighborhood system of a point x is a collection N of open sets such that x belongs to every member of N, and any open set containing x also contains a member of ...

A tag system in which a list of n tag rules (each of a special form) is applied to a system in sequential order and then starting again from the first rule. In a cyclic tag ...

The x-axis is the horizontal axis of a two-dimensional plot in Cartesian coordinates that is conventionally oriented to point to the right (left figure). In three dimensions, ...

A sequential substitution system is a substitution system in which a string is scanned from left to right for the first occurrence of the first rule pattern. If the pattern ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...

A set of numbers a_0, a_1, ..., a_(m-1) (mod m) form a complete set of residues, also called a covering system, if they satisfy a_i=i (mod m) for i=0, 1, ..., m-1. For ...

A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number ...

A generalization of simple majority voting in which a list of quotas {q_0,...,q_n} specifies, according to the number of votes, how many votes an alternative needs to win ...