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A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

A formula for the Bell polynomial and Bell numbers. The general formula states that B_n(x)=e^(-x)sum_(k=0)^infty(k^n)/(k!)x^k, (1) where B_n(x) is a Bell polynomial (Roman ...

A two-player game, also called crosscram, in which player H has horizontal dominoes and player V has vertical dominoes. The two players alternately place a domino on a board ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

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 ...

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, ...

A differential evolution method used to minimize functions of real variables. Evolution strategies are significantly faster at numerical optimization than traditional genetic ...

Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...