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A marked point process with mark space E is a double sequence (T,Y)=((T_n)_(n>=1),(Y_n)_(n>=1)) of R^^^+-valued random variables and E^_-valued random variables Y_n defined ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

Amazingly, the distribution of a sum of two normally distributed independent variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively is ...

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively ...

A univariate function f(x) is said to be odd provided that f(-x)=-f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, ...

The word "order" is used in a number of different ways in mathematics. Most commonly, it refers to the number of elements in (e.g., conjugacy class order, graph order, group ...

Ore algebra is an algebra of noncommutative polynomials representing linear operators for functional equations such as linear differential or difference equations. Ore ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

A quotient of two polynomials P(z) and Q(z), R(z)=(P(z))/(Q(z)), is called a rational function, or sometimes a rational polynomial function. More generally, if P and Q are ...