Etude theorique et numerique de deux problemes couples stefan-transport; Application au stockage thermique

In this paper, we study a model of thermal energy storage by solid-liquid phase change. Writing the equations reveals Stefan problems and Transport equations. Reducing them to a variational formulation, we get some results about the existence and uniqueness of solutions using different properties of variational inequalities. Then we propose two finite difference methods of approximation (explicit and implicit) and numerical results.      

Caracteristiques des explications orales en classe de mathematiques : Construction d'un cadre d'analyse pour rendre compte de la pratique des futurs enseignants et futures enseignantes de mathematiques du secondaire 1

Résumé:

De nombreuses études font ressortir l'importance des explications orales des enseignants et enseignantes de mathématiques pour l'apprentissage des élèves. Cette compétence à expliquer les mathématiques en classe apparaît donc centrale à la formation des enseignants et enseignantes. Afin de mieux rendre compte de la construction de cette compétence chez les futurs enseignants et futures enseignantes de mathématiques du secondaire, nous avons élaboré un cadre d'analyse permettant de situer différentes caractéristiques des explications orales. Ce cadre d'analyse a été mis à l'essai, à titre d'exemple illustratif, lors de l'analyse des pratiques de deux futurs enseignants. L'analyse permet de tracer un portrait caractéristique des explications orales pour ces deux futurs enseignants et montre l'intérêt que présente ce cadre d'analyse pour la compréhension des pratiques d'enseignement — tout en suscitant et orientant certaines réflexions pour la formation des enseignants et enseignantes de mathématiques. La façon qu'ont les futurs enseignants et futures enseignantes de ?parler? les mathématiques en classe nous en dit long, en effet, sur leur enseignement et leur compréhension de ce que représente pour eux l'enseignement et l'apprentissage des mathématiques.     

Notions ensemblistes et besoins d’apprentissage dans la transition secondaire-supérieur

Abstract

In set theory, functions present specific conceptual and semiotic properties. In this article, relying on constructs from the anthropological theory of didactics, we analyze the evolution of institutional relationships to set theory functional notions in the transition from high school to university in Tunisia, and the way some characteristics of this evolution can explain the observed difficulties met by successful high school students in the solving of problems involving functions in linear algebra at university.     

Resolution numerique de quelques problemes raides en mecanique des milieux faiblement compressibles

This paper deals with the numerical approximation of some «stiff» problems by asymptotic expansion of the solution. The model problem is the stationary linearized equation of slightly compressible fluids: $$\begin{gathered} \ll Find u_\varepsilon \varepsilon \left[ {H_0^1 (\Omega )} \right]^n s.t. \hfill \\ - \mu \Delta u_\varepsilon - \frac{1}{\varepsilon } grad div u_\varepsilon = f in \Omega \gg \hfill \\ \end{gathered} $$ where ∈ is asmall parameter; numerical treatment of the problem is thus difficult («stiff» problem). We establish existence and unicity of an asymptotic expansion foru, and use it to computeu. In the usual cases, with small divergence, the numerical results are far better than those obtained by direct discretisation of the problem. We also construct asymptotic expansions for the solutions of some nonlinear or non-stationary related problems.     

Simulation de la circulation systemique du sang par des procedes electriques et analogiques

A simulator where arterial and venous vessels are represented directly by systems of resistances, inductances and capacitors specifically controlled is described. Arterioles, capillaries and the left ventricule are also introduced. Some results are given.     

Resolution numerique d'un probleme de controle optimal d'un couplage des equations de navier-stokes et celle de la chaleur

We study by the method of artificial compressibility the numerical solution of an optimal control problem of a system governed by the Navier-Stokes equations coupled with the heat-equation. The control problem is of boundary control—final observation type. A system of equations and an inequality characterizing the optimal control gives rise to an algorithm which permits us to calculate a control satisfying a necessary condition for optimality. The algorithm will be approximated by finite difference schemes based on the fractional step method. We prove the stability and the convergence of the schemes and the convergence of the algorithm. Finally we present some numerical results illustrating the proposed method.     

Un algorithme combinatoire pour la résolution des problemes du type du permanent

A general algorithm for solving the problems of type of the permanent of a matrix is proposed.      

Simulation des phenomenes de reflexion et de transmission des electrons

The determination of reflection and transmission coefficients for electrons going through a zone of variable potential is considered. The method of calculation from the resolution of the Schrödinger equation is indicated. On the other hand, one shows that it is interesting to resolve the equation giving the module of the wave function. An example is presented.     

Generalisations de la transformation de shanks,de la table de Pade et de l'ε-algorithme

This paper deals with a generalization of the Shank's transformation for a sequence of elements of a topological vector space. It is showned how this generalization leads to a generalization of the Padé table. A recursive algorithm for effecting this transformation is given. Its properties are studied and some theorems are proved. This algorithm can be considered as a generalization of the ε-algorithm of Wynn. A second generalization is also studied and a third one which needs less elements of the initial sequence. The paper ends with a discussion on the vector case.      

Methode de determination des invariants radiometriques adaptee au paysage semi-aride de l'Afrique de l'Ouest

The follow-up of changes by multi-temporal spatial remote sensing studies can be carried out by successive classifications or by dynamic study of the radiometric signal. In this last case, a prior stage of radiometric rectification is required. In developing countries, determinist methods of radiometric rectification are not operational due to lack of atmospheric optical properties automatic recorders. Ideally, empirical methods use only data included in the image. They are founded on research of invariant radiometric points. However they are unusable in rural areas of these countries as the usual invariant radiometric points (asphalt road, roof, etc.) are missing. A new approach, an automatic selection of invariant pixels, is proposed in this paper. This is carried out in two stages: firstly, the bare soils are selected by use of a vegetation index, secondly, an index of brightness is used to distinguish the areas of extreme brightness and darkness in the selected areas. On a site of central Senegal, the quality of the algorithm is assessed by an identification of the sets of invariant pixels using high resolution aerial photography and in-situ observations. Dark pixels arise mainly on lateritics and uncultivated lands. Bright pixels are divided between the sandy trails and the crusted surfaces of some fields. Potential applications of multi-temporal spatial data with high resolution are suggested in terms of multi-annual vegetation studies. Resume. Le suivi des changements par etude multi-date d'images de teledetection peut se faire par classification successive ou par etude dynamique du signal radiometrique. Dans ce dernier cas, une etape prealable de correction radiometrique s'impose. Dans les pays en voie de developpement, les methodes deterministes de correction radiometrique ne sont pas operationnelles faute de station d'acquisition des proprietes optiques de l'atmosphere. Ne necessitant pas de donnees exogenes aux images, les methodes empiriques fondees sur la recherche d'invariants radiometriques sont egalement difficiles d'emploi dans les zones rurales de ces pays car les invariants classiques (route goudronnee, toit, etc.) sont absents. Nous presentons ici une methode de selection automatique des invariants. Elle consiste en un double seuillage: le premier, au moyen d'un indice de vegetation, selectionne les zones de sol nu, le second, a l'aide d'un indice de brillance, distingue les extrema sombres et clairs de la droite des sols nus. Dans notre application, sur un site du centre du Senegal, l'identification physique des pixels determines invariants par selection automatique est verifiee par interpretation de photographies aeriennes a haute resolution et par verite terrain. Les invariants sombres se situent principalement sur les surfaces lateritiques et incultes, les invariants clairs se partagent entre les chemins sableux ou les surfaces encroutees de certains champs. L'utilisation de donnees satellitaires multi-dates a haute resolution spatiale, ouvre le champ du suivi interannuel de la vegetation.