Search Results for ""

Given a set y=f(x) of n equations in n variables x_1, ..., x_n, written explicitly as y=[f_1(x); f_2(x); |; f_n(x)], (1) or more explicitly as {y_1=f_1(x_1,...,x_n); |; ...

The Jordan matrix decomposition is the decomposition of a square matrix M into the form M=SJS^(-1), (1) where M and J are similar matrices, J is a matrix of Jordan canonical ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

A multiple integral is a set of integrals taken over n>1 variables, e.g., int...int_()_(n)f(x_1,...,x_n)dx_1...dx_n. An nth-order integral corresponds, in general, to an ...

An outer-totalistic cellular automaton is a generalization of the totalistic cellular automaton. Totalistic rules are a proper superset of outer-totalistic rules. In ...

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The ...