In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomial functions. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind, as has been proposed in reference [1]. A multi-resolution analysis is implemented and illustrated with analytical data and real-life signals from turbulent flow fields.

We consider the sequences over the finite field of four elements obtained by inverse Gray mapping from a pair of binary sequences. We derive the linear complexity and the minimal polynomial of sequences constructed from Legendre sequences, Hall’s sextic sequences and twin-prime sequences using the technique proposed by Tang, Ding, Lim, Kim et al.

The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

A conducting spherical shell with a circular orifice of half angle θ0 is at electric potential V0. Show that the difference between the charge densities on the inner and outer surfaces is independent of position, and estimate the ratio of the electric charge on the inner surface to that on the outer. Correct results can be inferred from “elementary” arguments based on superposition, and more “e...

The three-dimensional high-order simulation algorithm HOSIM is developed to simulate complex nonlinear and non-Gaussian systems. HOSIM is an alternative to the current MP approaches and it is based upon new high-order spatial connectivity measures, termed high-order spatial cumulants. The HOSIM algorithm implements a sequential simulation process, where local conditional distributions are gener...

3FunMap is a windows software that can be used to construct genetic linkage maps and perform functional QTL mapping with molecular markers generated in a full-sib family. For linkage analysis, the software utilizes seven segregation types of markers to estimate the recombination and simultaneously predict the linkage phase between any two markers. After two-point linkage analysis, markers are c...

Abstract— This paper introduces a new set of orthogonal moments function hypergeometric based on the discrete Legendre polynomials. The Legendre moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain o...

have many applications in pure mathematics as in other branches of science. They are named by Karlin and Szegő in [8], Turán-type inequalities because the first of these type of inequalities was introduced by Turán in [18]. More precisely, he used some results of Szegő in [17] to prove the previous inequality for x ∈ (−1, 1), where fn is the Legendre polynomial of degree n. This classical resul...