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A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

The number of staircase walks on a grid with m horizontal lines and n vertical lines is given by (m+n; m)=((m+n)!)/(m!n!) (Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube I=[0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

Strang's strange figures are the figures produced by plotting a periodic function f(z) as a function of an integer argument n for n=1, 2, .... Unexpected patterns and ...

A pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime. A number n with (n,2a)=1 is a strong Frobenius pseudoprime with respect ...

An integer n is called a super unitary perfect number if sigma^*(sigma^*(n))=2n, where sigma^*(n) is the unitary divisor function. The first few are 2, 9, 165, 238, 1640, ... ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

The taxicab metric, also called the Manhattan distance, is the metric of the Euclidean plane defined by g((x_1,y_1),(x_2,y_2))=|x_1-x_2|+|y_1-y_2|, for all points ...