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Let U subset= C be a domain, and let f be an analytic function on U. 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. The ...

The largest value of a set, function, etc. The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted ...

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

The Jacobi symbol (a/y)=chi(y) as a number theoretic character can be extended to the Kronecker symbol (f(a)/y)=chi^*(y) so that chi^*(y)=chi(y) whenever chi(y)!=0. When y is ...

A local maximum, also called a relative maximum, is a maximum within some neighborhood that need not be (but may be) a global maximum.

A global maximum, also known as an absolute maximum, the largest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm ...

A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The ...

The maximum degree, sometimes simply called the maximum degree, of a graph G is the largest vertex degree of G, denoted Delta.