Volume 15, 2012

1. Two numerical methods for Abel's integral equation with comparison

Abdallah Ali Badr.
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.

2. A survey of RDF storage approaches

David C. Faye ; Olivier Curé ; Guillaume Blin.
The Semantic Web extends the principles of the Web by allowing computers to understand and easily explore the Web. In recent years RDF has been a widespread data format for the Semantic Web. There is a real need to efficiently store and retrieve RDF data as the number and scale of Semantic Web in real-word applications in use increase. As datasets grow larger and more datasets are linked together, scalability becomes more important. Efficient data storage and query processing that can scale to large amounts of possibly schema-less data has become an important research topic. This paper gives an overview of the features of techniques for storing \textttRDF data.

3. Minimization of an energy error functional to solve a Cauchy problem arising in plasma physics: the reconstruction of the magnetic flux in the vacuum surrounding the plasma in a Tokamak

Blaise Faugeras ; Amel Ben Abda ; Jacques Blum ; Cedric Boulbe.
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.

4. An error estimate in image processing

Philippe Destuynder ; Mohamed Jaoua ; Hela Sellami.
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.

5. Criteria for longitudinal data model selection based on Kullback’s symmetric divergence

Bezza Hafidi ; Nourddine Azzaoui.
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

6. Comportement asymptotique d’un modèle à commutation de la prolifération du Typha

Mamadou Lamine Diagne ; Papa Ibrahima Ndiaye ; Mary Teuw Niane ; Tewfik Sari.
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.