In this paper, an efficient direct method based on Legendre wavelets is introduced to approximate the solution of Fredholm integral equations of the first kind. These basic functions are orthonormal and have compact support. The properties of the Legendre wavelets are utilized to convert the integral equations into a system of linear algebraic equations. The main characteristic of the method is...

-The discrete Legendre transform is compared to the discrete cosine transform (DCT), which is based on Chebyshev polynomials, in terms of image compression efficiency. Using standard test images in various image compression configurations, the DCT is found to perform marginally better than the discrete Legendre transform in all cases examined. A simplified fundamental matrix theory for construc...

In the generalized Legendre transform construction the Kähler potential is related to a particular function. Here, the form of this function appropriate to the k-monopole metric is calculated from the known twistor theory of monopoles.

The Jacobi-Stirling numbers and the Legendre-Stirling numbers of the first and second kind were first introduced by Everitt et al. (2002) and (2007) in the spectral theory. In this paper we note that Jacobi-Stirling numbers and Legendre-Stirling numbers are specializations of elementary and complete symmetric functions. We then study combinatorial interpretations of this specialization and obta...

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...

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...

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...