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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 ...

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 set of n cells in an n×n square such that no two come from the same row and no two come from the same column. The number of transversals of an n×n square is n! (n ...

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 ...

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. ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...