Search Results for ""

Let A be a relational system, and let L be a language which is appropriate for A. Let phi be a well-formed formula of L, and let s be a valuation in A. Then A|=_sphi is ...

Let A be a closed convex subset of a Banach space and assume there exists a continuous map T sending A to a countably compact subset T(A) of A. Then T has fixed points.

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

An orientable surface with one boundary component such that the boundary component of the surface is a given knot K. In 1934, Seifert proved that such a surface can be ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

A "split" extension G of groups N and F which contains a subgroup F^_ isomorphic to F with G=F^_N^_ and F^_ intersection N^_={e} (Ito 1987, p. 710). Then the semidirect ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

A series is an infinite ordered set of terms combined together by the addition operator. The term "infinite series" is sometimes used to emphasize the fact that series ...

A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...