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A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...

The standard deviation sigma of a probability distribution is defined as the square root of the variance sigma^2, sigma = sqrt(<x^2>-<x>^2) (1) = sqrt(mu_2^'-mu^2), (2) where ...

For some constant alpha_0, alpha(f,z)<alpha_0 implies that z is an approximate zero of f, where alpha(f,z)=(|f(z)|)/(|f^'(z)|)sup_(k>1)|(f^((k))(z))/(k!f^'(z))|^(1/(k-1)). ...

A searching algorithm which works on a sorted table by testing the middle of an interval, eliminating the half of the table in which the key cannot lie, and then repeating ...