A general framework is introduced to analyze the approximation properties of mapped Legendre polynomials and of interpolations based on mapped Legendre–Gauss–Lobatto points. Optimal error estimates featuring explicit expressions on the mapping parameters for several popular mappings are derived. These results not only play an important role in numerical analysis of mapped Legendre spectral and ...

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...

Object of study in the present paper are slant and Legendre null curves 3-dimensional Sasaki-like almost contact B-metric manifolds. For examined we express general Frenet frame for which original parameter is distinguished, as well corresponding curvatures, terms structure on manifold. We prove that curvatures a framed curve constants if only specific function considered manifolds constant. fi...

We show that Lagrangian and Legendre varieties associated with matrix singularities and singularities of composite functions are stable in a sense which is a natural modification of Givental’s notion of stability of Lagrangian projections. The study of singular Lagrangian and Legendre varieties was initiated about twenty five years ago by Arnold when he was investigating singularities in the va...

The aim of this study was to model the variances and covariances of body weight in Zandi sheep from 60 to 365 days of age using random regression models (RRM). Legendre polynomials of different orders were used to model the direct and maternal covariances. Mean trends were also modeled through a quadratic regression on orthogonal polynomials of age. Homogeneity and heterogeneity of the residual...

Résumé Dans cet article nous allons présenter une méthode de détection d’objets basée sur l’analyse multifractale. La détection d’objets est particulièrement difficile lorsque l’on ne connaît pas les caractéristiques des objets pouvant être présents dans l’image. Contrairement aux méthodes le plus souvent proposées, cette méthode est destinée à détecter des objets artificiels dans des images ph...