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A semiring is a set together with two binary operators S(+,*) satisfying the following conditions: 1. Additive associativity: For all a,b,c in S, (a+b)+c=a+(b+c), 2. Additive ...

Let A be a C^*-algebra, then a state is a positive linear functional on A of norm 1.

Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a ...

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

Let A be a C^*-algebra, then two element a,b of A are called unitarily equivalent if there exists a unitary u in A such that b=uau^*.

A closed subspace of a Banach space X is called weakly complemented if the dual i^* of the natural embedding i:M↪X has a right inverse as a bounded operator. For example, the ...

A pole of multiplicity less than p+1.

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...