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The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

The sigmoid function, also called the sigmoidal curve (von Seggern 2007, p. 148) or logistic function, is the function y=1/(1+e^(-x)). (1) It has derivative (dy)/(dx) = ...

The small retrosnub icosicosidodecahedron, also called the small inverted retrosnub icosicosidodecahedron, is the uniform polyhedron with Maeder index 72 (Maeder 1997), ...

The small snub icosicosidodecahedron is the uniform polyhedron with Maeder index 32 (Maeder 1997), Wenninger index 110 (Wenninger 1989), Coxeter index 41 (Coxeter et al. ...

Special affine curvature, also called as the equi-affine or affine curvature, is a type of curvature for a plane curve that remains unchanged under a special affine ...

The special orthogonal group SO_n(q) is the subgroup of the elements of general orthogonal group GO_n(q) with determinant 1. SO_3 (often written SO(3)) is the rotation group ...

The square gyrobicupola is a convex equilateral solid that is Johnson solid J_(29). The unit square gyrobicupola has volume V=2+4/3sqrt(2) (1) and Dehn invariant D = 24<3>_2 ...

The first Strehl identity is the binomial sum identity sum_(k=0)^n(n; k)^3=sum_(k=0)^n(n; k)^2(2k; n), (Strehl 1993, 1994; Koepf 1998, p. 55), which are the so-called Franel ...

A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

Let V be a real vector space (e.g., the real continuous functions C(I) on a closed interval I, two-dimensional Euclidean space R^2, the twice differentiable real functions ...