1 Il s'agit du modèle du pendule linéarisé avec frottement visqueux. Le seul point d'équilibre est (x, v) = (0, 0). C'est un point d'équilibre stable, ce qu'on peut vérifier par exemple en utilisant la fonction de Lyapunov H(x, v) = (x 2 + v 2)/2. En fait, on montrera dans la suite que c'est un point d'équilibre asymptotiquement stable. 2 Il suffit de faire le calcul explicitement. On vérifie q...

In the computational geometry field, simplicial complexes have been used to describe an underlying geometric shape knowing a point cloud sampled on it. In this article, an adequate statistical framework is first proposed for the choice of a simplicial complex among a parametrized family. A least squares penalized criterion is introduced to choose a complex, and a model selection theorem states ...

Polynomials are ubiquitous in a variety of applications. A relatively recent theory exploits their sparse structure by associating a point connguration to each polynomial system; however, it has so far mostly dealt with roots having nonzero coordinates. We shift attention to arbitrary aane roots, and improve upon the existing algorithms for counting them and computing them numerically. The one ...

This paper is the continuation of the paper “Autour de nouvelles notions pour l’analyse des algorithmes d’approximation: Formalisme unifié et classes d’approximation” where a new formalism for polynomial approximation and its basic tools allowing an “absolute” (individual) evaluation the approximability properties of NPhard problems have been presented and discussed. In order to be used for exh...

In this paper we describe a new approach for the detection of fine structures in an image. This approach is based on the computation of the topological gradient associated to a cost function defined from a regularization of the data (possibly noisy). We get this approximation by solving a fourth order PDE. The study of the topological sensitivity is made both in the cases of a circular inclusio...

Biodiesel is usually produced from food-grade vegetable oil using trans-esterification process. As an effective factor on the biodiesel characteristics of the biodiesel is the kind of feedstock which is used, so finding a proper feedstock for using initially has an important role for different places. So, in this research, disposal substances of Capparis Spinosa are used as a feedstock for prod...

Let k be a field of characteristic zero and k an algebraic closure of k. For a geometrically integral variety X over k , we write k (X) for the function field of X = X × k k. If X has a smooth k-point , the natural embedding of multiplicative groups k * ֒→ k (X) * admits a Galois-equivariant retraction. In the first part of the paper , over local and then over global fields , equivalent conditio...

We consider a quadratic optimal control problem governed by a nonautonomous affine differential equation subject to nonnegativity control constraints. For a general class of interior penalty functions, we show how to compute the principal term of the pointwise expansion of the state and the adjoint state. Our main argument relies on the following fact: If the control of the initial problem sati...

introduction - les impuretes, meme en faibles teneurs, modifient beaucoup les proprietes physiques des metaux. ainsi, pour une etude profonde de ces proprie, tes , on a besion d'un metal extremement pur. la methode de la zone fondue a permis cette realisation . principe - dans la methode de purification dite de la «zone fondue» decouverte par pfann en 1952, une courte zone liquide est depl...