A method for the design of ultraspherical window functions that achieves prescribed spectral characteristics is proposed. The method comprises a collection of techniques that can be used to determine the three independent parameters of the ultraspherical window such that a specified ripple ratio and main-lobe width or null-to-null width along with a user-defined side-lobe pattern can be achieve...

In this paper, the free vibration characteristics of various coupled composite laminated doubly curved revolution shells are investigated under generalized boundary conditions (BCs). The joint shell structure consists a shell–cylindrical shell–doubly structure, and here, unlike previous structures, inversely joined together. such as elliptical, paraboloidal, spherical considered. first order sh...

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

Mohammad Masjed-Jamei c a, Wolfram Koepf b a Department of Mathematics, K.N.Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran, E-mail: [email protected] , [email protected] b Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany, E-mail: [email protected] c School of Mathematics, Institute for Research in Fundamental Science...

In this paper, Chebyshev polynomials—which are ultraspherical in the first and second kind hence symmetric, while third fourth order not non-symmetric—are used for simulation of two-dimensional mass transfer equation arising during convective air drying processes food products subject to Robin Neumann boundary conditions. These simulations improve quality dried prediction moisture distributions...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...