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If X_i for i=1, ..., m has a multivariate normal distribution with mean vector mu=0 and covariance matrix Sigma, and X denotes the m×p matrix composed of the row vectors X_i, ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a model of population growth first published by Pierre Verhulst (1845, 1847). The ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...