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The finite field (Galois field) GF(125) = GF(5 3) has degree 3 over its subfield GF(5). More generally, if p is a prime and n, m are positive integers with n dividing m, then [GF(p m):GF(p n)] = m/n. The field extension C(T)/C, where C(T) is the field of rational functions over C, has infinite degree (indeed it is a purely transcendental extension
Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe. Since many central theorems of model theory do not hold when restricted to finite ...
Finite model property. In mathematical logic, a logic L has the finite model property (fmp for short) if any non- theorem of L is falsified by some finite model of L. Another way of putting this is to say that L has the fmp if for every formula A of L, A is an L -theorem if and only if A is a theorem of the theory of finite models of L .
Subshift of finite type. In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state machine. The most widely studied shift spaces are the subshifts of finite type.
Locally finite group. In mathematics, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous to a finite group. Sylow subgroups, Carter subgroups, and abelian subgroups of locally finite groups have been studied. The concept is credited to work in the 1930s by Russian mathematician Sergei ...
The Infinite sites model (ISM) is a mathematical model of molecular evolution first proposed by Motoo Kimura in 1969. [1] Like other mutation models, the ISM provides a basis for understanding how mutation develops new alleles in DNA sequences. Using allele frequencies, it allows for the calculation of heterozygosity, or genetic diversity, in a ...
Five-point stencil. An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".
The finite element method ( FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential .