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A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

Let N samples be taken from a population with central moments mu_n. The sample variance m_2 is then given by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ is the sample mean. ...

A stable isolated (i.e., solitary) traveling nonlinear wave solution to a set of equations that obeys a superposition-like principle (i.e., solitons passing through one ...

The biharmonic operator, also known as the bilaplacian, is the differential operator defined by del ^4=(del ^2)^2, where del ^2 is the Laplacian. In n-dimensional space, del ...

The parameter r (sometimes also denoted mu) in the logistic equation x_(n+1)=rx_n(1-x_n).

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

A fractal produced by iteration of the equation z_(n+1)=z_n^2 (mod m) which results in a Moiré-like pattern.

K=(dT)/(ds), where T is the tangent vector defined by T=((dx)/(ds))/(|(dx)/(ds)|).

The probability that a random integer between 1 and x will have its greatest prime factor <=x^alpha approaches a limiting value F(alpha) as x->infty, where F(alpha)=1 for ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...