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An experiment in which s trials are made of an event, with probability p of success in any given trial.

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

If g(theta) is a trigonometric polynomial of degree m satisfying the condition |g(theta)|<=1 where theta is arbitrary and real, then g^'(theta)<=m.

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 ...

Let x^__1 and s_1^2 be the observed mean and variance of a sample of N_1 drawn from a normal universe with unknown mean mu_((1)) and let x^__2 and s_2^2 be the observed mean ...

A distribution with probability function P(x)=(x^(alpha-1)(1+x)^(-alpha-beta))/(B(alpha,beta)), where B is a beta function. The mode of a variate distributed as ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

Integers (lambda,mu) for a and b that satisfy Bézout's identity lambdaa+mub=GCD(a,b) are called Bézout numbers. For integers a_1, ..., a_n, the Bézout numbers are a set of ...

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...