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A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by x_(n+1)=mu(1-2|x_n-1/2|). (1) The first few iterations of (1) give x_1 ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

The topology on the Cartesian product X×Y of two topological spaces whose open sets are the unions of subsets A×B, where A and B are open subsets of X and Y, respectively. ...

The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

The Kermack-McKendrick model is an SIR model for the number of people infected with a contagious illness in a closed population over time. It was proposed to explain the ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Lehmer (1938) showed that every positive irrational number x has a unique infinite continued cotangent representation of the form x=cot[sum_(k=0)^infty(-1)^kcot^(-1)b_k], (1) ...

The series h_q(-r)=sum_(n=1)^infty1/(q^n+r) (1) for q an integer other than 0 and +/-1. h_q and the related series Ln_q(-r+1)=sum_(n=1)^infty((-1)^n)/(q^n+r), (2) which is a ...

The first definition of the logarithm was constructed by Napier and popularized through his posthumous pamphlet (Napier 1619). It this pamphlet, Napier sought to reduce the ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...