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A linear operator A:D(A)->H from its domain D(A) into a Hilbert space H is closable if it has a closed extension B:D(B)->H where D(A) subset D(B). Closable operators are ...

A coequalizer of a pair of maps f,g:X->Y in a category is a map c:Y->C such that 1. c degreesf=c degreesg, where degrees denotes composition. 2. For any other map c^':Y->C^' ...

The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

A completely multiplicative function, sometimes known as linear or totally multiplicative function, is an arithmetic function f(n) such that f(mn)=f(m)f(n) holds for each ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

The composite number problem asks if for a given positive integer N there exist positive integers m and n such that N=mn. The complexity of the composite number problem was ...

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...

Computation time (also called "running time") is the length of time required to perform a computational process. Representation a computation as a sequence of rule ...

A concordant form is an integer triple (a,b,N) where {a^2+b^2=c^2; a^2+Nb^2=d^2, (1) with c and d integers. Examples include {14663^2+111384^2=112345^2; ...