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The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

A place nu of a number field k is an isomorphism class of field maps k onto a dense subfield of a nondiscrete locally compact field k_nu. In the function field case, let F be ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

Refer to the above figures. Let X be the point of intersection, with X^' ahead of X on one manifold and X^('') ahead of X of the other. The mapping of each of these points ...