Abstract The temperature distribution of human body tissues, when electromagnetic waves are applied, is studied with the help bioheat equation, which characterised by several thermal parameters, such as conductivity, perfusion frequency or metabolic heat. There also electrical conductivity and dielectric constant. Besides, therapy applied power should be considered. If values all these paramete...

In this correspondence we determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result of this correspondence shows that Legendre sequences are quite good from the linear complexity viewpoint.

 This paper deals with a short term forecasting non-stationary time series using wavelets and splines. Wavelets can decompose the series as the sum of two low and high frequency components. Aminghafari and Poggi (2007) proposed to predict high frequency component by wavelets and extrapolate low frequency component by local polynomial fitting. We propose to forecast non-stationary process u...

This paper proposes and investigates a method for reducing potential numerical instability in the fast spherical harmonic transform algorithms proposed previously in [5,11]. The key objective of this study is a numerically reliable fast algorithm for computing the discrete Legendre transform (DLT); that is, the projection of sampled data onto the associated Legendre functions within a specified...

Abstract We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, thus, the whole series, converge to zero much more rapidly compared to the Taylor expansion of the same order. Furthermore, using numerical analysis with sixth-order polynomial expansion, we demonstrate ...

Optimality Theory (henceforth OT) (Prince and Smolensky 1993/2004) is based upon lexicographic optimization. It differs in this respect from Harmonic Grammar (henceforth HG) (Legendre et al. 1990a, Legendre et al. 1990b), which is based upon linear numeric optimization. Differences between the two have been discussed in several places, including (Legendre et al. 2006, Pater et al. 2007a, Prince...

The main result of this paper is a homotopy theoretic classification of Legendre immersions from a compact manifold into a contact manifold. The paper also includes normal form theorems for Legendre submanifolds as well as a multi-jet transversality theorem for Legendre

In this paper, summation formulae for the 2-variable Legendre polynomials in terms of certain multi-variable special polynomials are derived. Several summation formulae for the classical Legendre polynomials are also obtained as applications. Further, Hermite-Legendre polynomials are introduced and summation formulae for these polynomials are also established.

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.

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...