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Rule 94 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Let X be a set of urelements, and let V(X) be the superstructure with X as its set of individuals. Let kappa be a cardinal number. An enlargement V(^*X) is kappa-saturated ...

Schur's partition theorem lets A(n) denote the number of partitions of n into parts congruent to +/-1 (mod 6), B(n) denote the number of partitions of n into distinct parts ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

A sequence of functions {f_n}, n=1, 2, 3, ... is said to be uniformly convergent to f for a set E of values of x if, for each epsilon>0, an integer N can be found such that ...

A vector space V is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space R^n, where every element ...

Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...