Search Results for ""

The scalar curvature, also called the "curvature scalar" (e.g., Weinberg 1972, p. 135; Misner et al. 1973, p. 222) or "Ricci scalar," is given by R=g^(mukappa)R_(mukappa), ...

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), ...