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If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

The algebra A is called a pre-C^*-algebra if it satisfies all conditions to be a C^*-algebra except that its norm need not be complete.

If A is true precisely unless B, then B implies not-A and not-B implies A. J. H. Conway has suggested the term "unlesss" for this state of affairs, by analogy with iff.

A vector whose elements are real numbers.

A ringoid is a set R with two binary operators, conventionally denoted addition (+) and multiplication (×), where × distributes over + left and right: a(b+c)=ab+ac and ...

The logical axiom R(x,y)=!(!(x v y) v !(x v !y))=x, where !x denotes NOT and x v y denotes OR, that, when taken together with associativity and commutativity, is equivalent ...

An estimation technique which is insensitive to small departures from the idealized assumptions which have been used to optimize the algorithm. Classes of such techniques ...

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z and 2. f(0)=0. Then |f(z)|<=|z| and |f^'(0)|<=1. If either |f(z)|=|z| for some z!=0 or if ...