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The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

Mergelyan's theorem can be stated as follows (Krantz 1999). Let K subset= C be compact and suppose C^*\K has only finitely many connected components. If f in C(K) is ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

Let f be analytic on a domain U subset= C, and assume that f never vanishes. Then if there is a point z_0 in U such that |f(z_0)|<=|f(z)| for all z in U, then f is constant. ...

A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

Let M be a finitely generated module over a commutative Noetherian ring R. Then there exists a finite set {N_i|1<=i<=l} of submodules of M such that 1. intersection ...

The word "number" is a general term which refers to a member of a given (possibly ordered) set. The meaning of "number" is often clear from context (i.e., does it refer to a ...

Given a set S of n nonnegative integers, the number partitioning problem requires the division of S into two subsets such that the sums of number in each subset are as close ...