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Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then for ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

The angular distance traveled around a circle is the number of radians the path subtends, theta=l/(2pir)2pi=l/r.

An ANOVA in which the number of replicates (sets of identical observations) is restricted to be the same for each factor level (treatment group).

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

The number of "prime" boxes is always finite, where a set of boxes is prime if it cannot be built up from one or more given configurations of boxes.

If the total group of the canonical series is divided into two parts, the difference between the number of points in each part and the double of the dimension of the complete ...