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

The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...

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 ...

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 ...

A stochastic approximation method that functions by placing conditions on iterative step sizes and whose convergence is guaranteed under mild conditions. However, the method ...

The time required for a given principal to double (assuming n=1 conversion period) for compound interest is given by solving 2P=P(1+r)^t, (1) or t=(ln2)/(ln(1+r)), (2) where ...

Let p(n) be the first prime which follows a prime gap of n between consecutive primes. Shanks' conjecture holds that p(n)∼exp(sqrt(n)). Wolf conjectures a slightly different ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...