Analogy between Abel's integral equation and the integral of fractional order of a given function, j^α f(t), is discussed. Two different numerical methods are presented and an approximate formula for j^α f(t) is obtained. The first approach considers the case when the function, f(t), is smooth and a quadrature formula is obtained. A modified formula is deduced in case the function has one or more simple pole. In the second approach, a procedure is presented to weaken the singularities. Both two approaches could be used to solve numerically Abel's integral equation. Some numerical examples are given to illustrate our results.
Le Sémantique étend les principes du Web en permettant aux ordinateurs de comprendre et d'explorer le Web de façon intelligente. Ces dernières années, RDF s'est largement répandu comme format de données du Web Sémantique. Il y a un réel besoin de stocker et de rechercher de façon efficiente les données RDF vu que le nombre et la taille des données du Web Sémantique utilisées dans les applications du monde réél est en progression continue. Etant donné que les sources de données sont de plus en plus volumineuses et de plus en plus liées, le passage à l'échelle devient plus que necessaire. Le stockage efficace de données et le traitement de requête à l'échelle de grande sources de données souvent sans schémas est devenu un sujet de recherche très important. Cet article présente les caractéristiques des différentes propositions pour le stockage de données RDF.
A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of an energy error functional. Several numerical experiments are conducted which show the efficiency of the method.
A new interpolation error estimate for a finite element method for image processing is proved in this paper. The suggested scheme is based on the Raviart-Thomas one, extended to a non linear formulation. The numerical trials run confirm the accuracy of the restoration algorithm.
Recently, Azari et al (2006) showed that (AIC) criterion and its corrected versions cannot be directly applied to model selection for longitudinal data with correlated errors. They proposed two model selection criteria, AICc and RICc, by applying likelihood and residual likelihood approaches. These two criteria are estimators of the Kullback-Leibler's divergence distance which is asymmetric. In this work, we apply the likelihood and residual likelihood approaches to propose two new criteria, suitable for small samples longitudinal data, based on the Kullback's symmetric divergence. Their performance relative to others criteria is examined in a large simulation study
In this paper we propose a mathematical model of the Typha growth and analyse its stability. The model that we plan to study describes the dynamics of the plant population. The theoretical study of this model determines the key factors of the Typha proliferation. We present the analysis of equilibrium solutions and lead a study of their local stability.This constitutes a first step towards a more detailed study of the nonlinear dynamics of this model.
