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Let C^omega(I) be the set of real analytic functions on I. Then C^omega(I) is a subalgebra of C^infty(I). A necessary and sufficient condition for a function f in C^infty(I) ...

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical ...

The structure factor S_Gamma of a discrete set Gamma is the Fourier transform of delta-scatterers of equal strengths on all points of Gamma, S_Gamma(k)=intsum_(x in ...

A submonoid is a subset of the elements of a monoid that are themselves a monoid under the same monoid operation. For example, consider the monoid formed by the nonnegative ...

The span of subspace generated by vectors v_1 and v_2 in V is Span(v_1,v_2)={rv_1+sv_2:r,s in R}. A set of vectors m={v_1,...,v_n} can be tested to see if they span ...

Let f_n(z) be a sequence of functions, each regular in a region D, let |f_n(z)|<=M for every n and z in D, and let f_n(z) tend to a limit as n->infty at a set of points ...

A set of three conjectures proposed by Weil in 1942 for extending Riemann hypothesis-like statements to classes of mathematical structures. The conjectures were proved by ...

Two patterns T_1 and T_2 belong to the same Wilf class if |S_n(T_1)|=|S_n(T_2)| for all n, where S_n(T) denotes the set of permutations on {1,...,n} that avoid the pattern T. ...