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Weak Index Theorem

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  • Weak solution — In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives appearing in the equation may not all exist but which is nonetheless deemed to satisfy… …   Wikipedia

  • Kleene's recursion theorem — In computability theory, Kleene s recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions. The theorems were first proved by Stephen Kleene in 1938.This article uses the… …   Wikipedia

  • Sonnenschein–Mantel–Debreu theorem — The Sonnenschein–Mantel–Debreu theorem (named after Gérard Debreu, Rolf Ricardo Mantel, and Hugo Freund Sonnenschein) is a result in general equilibrium economics. It states that the excess demand function for an economy is not restricted by the… …   Wikipedia

  • Sonnenschein-Mantel-Debreu Theorem — The Sonnenschein Mantel Debreu Theorem is a result in General equilibrium economics. It states that the system of excess demand functions pertaining to an economy with sufficiently many agents is in no way restricted by the usual rationality… …   Wikipedia

  • Central limit theorem — This figure demonstrates the central limit theorem. The sample means are generated using a random number generator, which draws numbers between 1 and 100 from a uniform probability distribution. It illustrates that increasing sample sizes result… …   Wikipedia

  • Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia

  • Noisy-channel coding theorem — In information theory, the noisy channel coding theorem (sometimes Shannon s theorem), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information)… …   Wikipedia

  • Focal subgroup theorem — In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1958) and is the first major application of the transfer according to… …   Wikipedia

  • Multi-index notation — The mathematical notation of multi indices simplifies formulae used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.… …   Wikipedia

  • Lefschetz fixed-point theorem — In mathematics, the Lefschetz fixed point theorem is a formula that counts the number of fixed points of a continuous mapping from a compact topological space X to itself by means of traces of the induced mappings on the homology groups of X . It …   Wikipedia

  • König's theorem (set theory) — For other uses, see König s theorem. In set theory, König s theorem (named after the Hungarian mathematician Gyula König) colloquially states that if the axiom of choice holds, I is a set, mi and ni are cardinal numbers for every i in I , and m i …   Wikipedia

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