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In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

Assume X, Y, and Z are lotteries. Denote "X is preferred to Y" as X≻Y, and indifference between them by X∼Y. One version of the probability axioms are then given by the ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

The theory of non-uniformly hyperbolic diffeomorphisms.

In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

The truncated square pyramid is a special case of a pyramidal frustum for a square pyramid. Let the base and top side lengths of the truncated pyramid be a and b, and let the ...

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. ...

There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where zeta(z,a) is a ...

Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. 1. ...