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First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

Let O be an incidence geometry, i.e., a set with a symmetric, reflexive binary relation I. Let e and f be elements of O. Let an incidence plane be an incidence geometry whose ...

An important result in valuation theory which gives information on finding roots of polynomials. Hensel's lemma is formally stated as follows. Let (K,|·|) be a complete ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

Given a set y=f(x) of n equations in n variables x_1, ..., x_n, written explicitly as y=[f_1(x); f_2(x); |; f_n(x)], (1) or more explicitly as {y_1=f_1(x_1,...,x_n); |; ...

The Johnson circumconic, a term used here for the first time, is the circumconic that passes through the vertices of both the reference triangle and the Johnson triangle. It ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...