Recently, Xu and Cheney (1992) have proved that if all the Legendre coeecients of a zonal function deened on a sphere are positive then the function is strictly positive deenite. It will be shown in this paper, that even if nitely many of the Legendre coeecients are zero, the strict positive deeniteness can be assured. The results are based on approximation properties of singular integrals, and...

In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations usi...

In this paper, for integers n and e such that e|n and 2 − 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2−1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences.

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying RungeKutta m...

We introduce a new join operation on colored simplicial complexes that preserves the CohenMacaulay property. An example of this operation puts the connection between the central Delannoy numbers and Legendre polynomials in a wider context. Résumé. Nous introduisons une nouvelle opération qui joint des complexes simpliciaux équilibrés d’une telle manière que la propriété de Cohen-Macaulay est pr...

In this paper, for integers n and e such that e|n and 2 − 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2n−1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences.

This is to certify that I have examined a copy of a technical report by Kazh Brito and found it satisfactory in all respects, and that any and all revisions required by the examining committee have been made. Abstract This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite...

Low autocorrelation binary sequence (LABS) detection is a classic problem in the literature. We use these sequences in many real-life applications. The detection of these sequences involves many problems. In the literature, various methods have been developed to approach the LABS issue. Based on the length of the sequence, an appropriate method can be selected and implemented. For short length ...