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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 term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

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).

A circle is the set of points in a plane that are equidistant from a given point O. The distance r from the center is called the radius, and the point O is called the center. ...

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 ...