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A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...

The sequence of six 9s which begins at the 762nd decimal place of pi, pi=3.14159...134999999_()_(six 9s)837... (Wells 1986, p. 51). The positions of the first occurrences of ...

The Fourier sine transform is the imaginary part of the full complex Fourier transform, F_x^((s))[f(x)](k) = I[F_x[f(x)](k)] (1) = int_(-infty)^inftysin(2pikx)f(x)dx. (2) The ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and ...

Consider a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then the Herbrand universe H of S is defined by the following rules. 1. All constants ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...