We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical algorithm to get closer to satisfying the zero mean curvature condition. We report values for both the bilinear and improved areas, suggesting a quantitative ...

Using our recently developed Chebyshev expansion technique for finite-temperature dynamical correlation functions we numerically study the AC conductivity σ(ω) of the Anderson model on large cubic clusters of up to 100 sites. Extending previous results we focus on the role of the boundary conditions and check the consistency of the DC limit, ω → 0, by comparing with direct conductance calculati...

A fast Chebyshev–Fourier algorithm for Poisson-type equations in polar geometries is presented in this paper. The new algorithm improves upon the algorithm of Jie Shen (1997), by taking advantage of the odd–even parity of the Fourier expansion in the azimuthal direction, and it is shown to be more efficient in terms of CPU and memory.  2000 IMACS. Published by Elsevier Science B.V. All rights ...

Abstract— A new wavelet based approximation method for solving the second order differential equations arising science and engineering is presented in this paper. Such differential equation is often applied to model phenomena in various fields of science and engineering. In this study, shifted second kind Chebyshev wavelet (CW) operational matrices of derivatives is introduced and applied for s...

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...

The performance analysis of high rate space–time trellis-coded modulation (HR-STTCM) using the Gauss–Chebyshev quadrature technique is presented. HR-STTCM is an example of space– time codes that combine the idea used in trellis coded modulation (TCM) design that is signal set expansion and set partitioning into its construction. HR-STTCM construction is based on the concatenation of an outer TC...

I present an algorithm to simulate low-frequency electromagnetic propagation in an anisotropic earth, described by a general (non-diagonal) conductivity tensor. I solve the electric formulation by explicitly imposing an approximate form of the condition ∇ · J = 0, where J is the current density vector, which includes the source and the induced current. The numerical algorithm consists of a full...

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...