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If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

It is conjectured that any convex body in n-dimensional Euclidean space has an interior point lying on normals through 2n distinct boundary points (Croft et al. 1991). This ...

The second-order ordinary differential equation xy^('')+(c-x)y^'-ay=0, sometimes also called Kummer's differential equation (Slater 1960, p. 2; Zwillinger 1997, p. 124). It ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

The convexity coefficient chi(D) of a region D is the probability that the line segment connecting two random points in D is contained entirely within D. For a convex region, ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...