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An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.

The (n,k)-arrangement graph A_(n,k) is defined as the graph on the vertex set consisting of the permutations of {1,2,...,n} containing at most k elements where vertices are ...

The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

A type of abstract space which occurs in spline and rational function approximations. The Besov space B_(p,q)^alpha is a complete quasinormed space which is a Banach space ...

Let V(r) be the volume of a ball of radius r in a complete n-dimensional Riemannian manifold with Ricci curvature tensor >=(n-1)kappa. Then V(r)<=V_kappa(r), where V_kappa is ...

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded ...

A bridgeless graph, also called an isthmus-free graph, is a graph that contains no graph bridges. Examples of bridgeless graphs include complete graphs on n>2 nodes, cycle ...

A description of an object by properties that are different from those mentioned in its definition, but are equivalent to them. The following list gives a number of examples. ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...