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...

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...

This study introduced new technique which is based on a combination of the least-squares (LST) with Chebyshev and Legendre polynomials for finding approximate solutions higher-order linear Fredholm-Volterra integro-differential equations (FVIDEs) subject to mixed conditions. Two examples second third-order FVIDEs are considered illustrate proposed method, numerical results comprised demonstrate...

A large number of different methods for numerically inverting the Laplace transform are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to various types of functions, numerical accuracy, computational efficiency, and ease of programming and implementation. The methods are presented briefly and classified theoretically into methods whic...

This article provides an overview of some recent developments in quantum dynamic and spectroscopic calculations using the Chebyshev propagator. It is shown that the Chebyshev operator ( Tk (Ĥ)) can be considered as a discrete cosine type propagator ( cos(kΘ̂)), in which the angle operator ( Θ̂ = arccos Ĥ ) is a single-valued mapping of the scaled Hamiltonian ( Ĥ ) and the order (k) is an effectiv...

We introduce a new and eecient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the Legendre-Galerkin and Chebyshev-Galerkin methods.

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is reintroduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by th...