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A hex number, also called a centered hexagonal number, is given by H_n = 1+6T_n (1) = 3n^2+3n+1, (2) where T_n=n(n+1)/2 is the nth triangular number and the indexing with ...

The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

The conjugate gradient method can be applied on the normal equations. The CGNE and CGNR methods are variants of this approach that are the simplest methods for nonsymmetric ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

A quartic equation is a fourth-order polynomial equation of the form z^4+a_3z^3+a_2z^2+a_1z+a_0=0. (1) While some authors (Beyer 1987b, p. 34) use the term "biquadratic ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

The Harries-Wong graph is one of the three (3,10)-cage graphs, the other two being the (10,3)-cage known as the Balaban 10-cage and the Harries graph. The Harries-Wong graph ...

A strongly regular graph with parameters (n,k,a,c) has graph eigenvalues k, theta, and tau, where theta = ((a-c)+sqrt(Delta))/2 (1) tau = ((a-c)-sqrt(Delta))/2 (2) where ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

Probability and Statistics