Algorithm CPLCL (Classification by Preferential Clustered Link) for the classification graphs of syntactic variations, introduced by Ibekwe SanJuan in [10, 6], has the mathematical properties of single link clustering, since it is partly founded on the concept of component related to a subgraph, while avoiding the chain effect as much as possible. In spite of these properties, this algorithm of...

in this paper, we prove that the wrapped Butterfly graph WBF(d; n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2. Key-words: Butterfly graph, graph theory, Hamiltonism, Hamilton decomposition, Hamilton cycle, Hamilton circuit, perfect matching. (Résumé : tsvp) This work has been supported by the C...

The purpose of this work is to show how algebraic and symbolic techniques such as Smith normal forms and Gröbner basis techniques can be used to develop new Schwarz-like algorithms and preconditioners for linear systems of partial differential equations. Key-words: Systems of partial differential equations, domain decomposition methods, symbolic computation, systems theory, algebraic analysis, ...

This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that the input matrix is identical with the preconditioner on a given filtering vector. This vector is chosen to alleviate the effect of low frequency modes on con...

Les fruits de Curry-Howard. Depuis la mise en évidence via la correspondance de CurryHoward [21], des relations entre démonstrations mathématiques et programmes informatiques, théorie de la programmation et théorie de la démonstration s’enrichissent mutuellement. Parmi les nombreux allers-retours fructueux entre preuves et programmes, la logique linéaire [13] tient une place exemplaire. Girard ...

— Beam propagation in an optical fiber is usuatty described by the Helmholtz équation. Feit and Fleck have proposed a splitting method algorithm (the Beam Propagation Method or B.P.M.) in order to approximate this équation. In this work, we discuss their procedure and dérive the équation which is consistent with this algorithm. We give a functionnal framework that allows one to solve this équat...

1. Le problème de l’apprentissage statistique 2 1.1. Cadre général 2 1.2. Exemple : prédiction 2 1.3. Exemple : régression 2 1.4. Exemple alternatif : régression sur un plan d’expérience fixe 3 1.5. Autres exemples 4 2. Estimateurs 4 2.1. Définition générale 4 2.2. Consistance, No Free Lunch 5 2.3. Exemples : Estimateurs par minimum de contraste 5 2.4. Exemple : Estimateurs des moindres carrés ...

— Tofind a zero of the sum of two maximal monotone operators, we analyze a twosteps algorithm where the problem is first approximated by a regularized one and the regularization parameter is then reduced to converge to a solution of the original problem. We give a formai proof of the convergence which, in that case, is not ergodic. The main resuit is a generalization of one given by Brezis [4] ...

Résumé. Soit f ∈ Z[x] un polynôme de degré r ≥ 3 sans racines de multiplicité r ou (r − 1). Supposons que f(x) 6≡ 0 mod p admette une solution dans (Z/p) pour tout p. Erdős a conjecturé que f(p) est donc sans facteurs puissances (r − 1)ièmes pour un nombre infini de premiers p. On prouve cela pour toutes les fonctions f dont une racine génère le corps de décomposition, et également pour d’autre...

In this study we present first the main theorem of the unfolding method in linearized elasticity. Then we prove that every displacement of a thin structure (curved rod or shell) is the sum of an elementary displacement and a warping. Thanks to the previous theorem we obtain sharp estimates of the displacements of this decomposition. Résumé. Dans cette étude on présente d’abord le théorème fonda...