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If X is any compact space, let A be a subalgebra of the algebra C(X) over the reals R with binary operations + and ×. Then, if A contains the constant functions and separates ...

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e., f^((k))(x)>=0 (1) for a<x<b and k=0, 1, 2, ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

Analytic number theory is the branch of number theory which uses real and complex analysis to investigate various properties of integers and prime numbers. Examples of topics ...

An angle theta drawn on the coordinate plane is said to be in standard position if its initial side lies on the positive x-axis so that its vertex coincides with the origin ...

An anti-analytic function is a function f satisfying the condition (df)/(dz)=0. (1) Using the result ...

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...

The kernel of a symmetric bilinear form Q:V×V-->R is the set Ker(Q)={v in V|Q(v,w)=0 for all w in V}.