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By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

A simple directed graph is a directed graph having no multiple edges or graph loops (corresponding to a binary adjacency matrix with 0s on the diagonal). The number of simple ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

n weighings are sufficient to find a bad coin among (3^n-1)/2 coins (Steinhaus 1999, p. 61). vos Savant (1993) gives an algorithm for finding a bad ball among 12 balls in ...

An affine geometry is a geometry in which properties are preserved by parallel projection from one plane to another. In an affine geometry, the third and fourth of Euclid's ...

The quartic curve given by the implicit equation (x^2-a^2)(x-a)^2+(y^2-a^2)^2=0, (1) so-named because of its resemblance to a tooth. The bicuspid curve has cusps at (a,-a) ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

The fractal-like two-dimensional function f(x,y)=((x^2-y^2)sin((x+y)/a))/(x^2+y^2). The function is named for the appearance of a butterfly-like pattern centered around the ...

A check which can be used to verify correct computations in a table of grouped classes. For example, consider the following table with specified class limits and frequencies ...