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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.

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

A commutative Noetherian unit ring having only finitely many maximal ideals. A ring having the same properties except Noetherianity is called quasilocal. If K is a field, the ...

A proper ideal I of a ring R is called semiprime if, whenever J^n subset I for an ideal J of R and some positive integer, then J subset I. In other words, the quotient ring ...

An algebraic surface which can be represented implicitly by a polynomial of degree six in x, y, and z. Examples of quartic surfaces include the Barth sextic, Boy surface, ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

Given a Hilbert space H, the sigma-strong operator topology is the topology on the algebra L(H) of bounded operators from H to itself defined as follows: A sequence S_i of ...

The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = ...

The small retrosnub icosicosidodecahedron, also called the small inverted retrosnub icosicosidodecahedron, is the uniform polyhedron with Maeder index 72 (Maeder 1997), ...

The small snub icosicosidodecahedron is the uniform polyhedron with Maeder index 32 (Maeder 1997), Wenninger index 110 (Wenninger 1989), Coxeter index 41 (Coxeter et al. ...