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The Fourier cosine transform of a real function is the real part of the full complex Fourier transform, F_x^((c))[f(x)](k) = R[F_x[f(x)](k)] (1) = ...

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 ...

The fractional derivative of f(t) of order mu>0 (if it exists) can be defined in terms of the fractional integral D^(-nu)f(t) as D^muf(t)=D^m[D^(-(m-mu))f(t)], (1) where m is ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

The girth of a graphs is the length of one of its (if any) shortest graph cycles. Acyclic graphs are considered to have infinite girth (Skiena 1990, p. 191). The girth of a ...

If T is a set of axioms in a first-order language, and a statement p holds for any structure M satisfying T, then p can be formally deduced from T in some appropriately ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra are therefore special cases of a trigonal trapezohedron as well as ...