Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...

We describe the development of a scoring function designed to model the hydrophobic effect in protein folding. An optimization technique is used to determine the best functional form of the hydrophobic potential. The scoring function is expanded using the Chebyshev polynomials, for which the coefficients are determined by minimizing the Z-score of native structures in the ensembles of alternate...

Rational Chebyshev approximations are given for the complete Fermi-Dirac integrals of orders — \, \ and f. Maximal relative errors vary with the function and interval considered, but generally range down to 10~9 or less.

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. Comp. Phys. 45 (1982), 45-49) for infinite or semi-infinite domains. Like Chebyshev series, the He...

We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L2-norm for the interval [0,1], using the weight function wðxÞ 1⁄4 1= ffiffiffiffiffiffiffi...