In this article, we establish the existence of minimizers for energy integrals associated with the p-Laplacian in RN with the admissible set being a rearrangement class of a given function. Some representation formulae of the minimizers are also stated.

In order to achieve a multiple resolution with multiple directional feature analysis, a Laplacian pyramid is combined with directional filter bank. This requires the analysis on the design of both the filter in the Laplacian pyramid and the overall directional decomposition structure. Our analysis shows that the energy distribution of the filter in the Laplacian pyramid should match with the an...

The aim of this paper is to deduce a discrete version of the fractional Laplacian in matrix form defined on the 1D periodic (cyclically closed) linear chain of finite length. We obtain explicit expressions for this fractional Laplacian matrix and deduce also its periodic continuum limit kernel. The continuum limit kernel gives an exact expression for the fractional Laplacian (Riesz fractional d...

Motion editing requires the preservation of spatial and temporal information of the motion. During editing, this information should be preserved at best. We propose a new representation of the motion based on the Laplacian expression of a 3D+t graph: the set of connected graphs given by the skeleton over time. Through this Laplacian representation of the motion, we propose an application which ...

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

This paper presents a Laplacian-based image filtering method. Using a local noise estimator function in an energy functional minimizing scheme we show that Laplacian that has been known as an edge detection function can be used for noise removal applications. The algorithm can be implemented on a 3x3 window and easily tuned by number of iterations. Image denoising is simplified to the reduction...

 In this paper we consider a general setting of skew-symmetric distribution which was constructed by Azzalini (1985), and its properties are presented. A suitable empirical estimator for a skew-symmetric distribution is proposed. In data analysis, by comparing this empirical model with the estimated skew-normal distribution, we show that the proposed empirical model has a better fit in den...