A graph theory approach to subcontracting, machine duplication and intercell moves in cellular manufacturing

We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance.     

Synthese de derives mono- ou disilicies au niveau d'un carbone fonctionnel

Aliphatic saturated amides treated with Me₃SiCl/Li/THF were found to react in two ways. Either alkoxysilanes, mono- or di-silylated at the functional carbon, or C-silylated amines were obtained dependent of the original amide structure and the experimental conditions. (Me₃Si)₂CHN(SiMe₃)₂ exhibited Physicochemical properties that are particular for hindered rotation about the CN bond. A general mechanism is proposed to explain these results.     

Renormalisation du produit, Jacobiens et transformations de Riesz

The “correction algorithm”, applied in probability theory to the pointwise product of two martingales, has a natural analogue in the real-variable setting. It turns out that the corresponding bilinear operators obtained in this way provide us with a new “renormalization algorithm”, in the sense of Coifman, Dobyinski and Meyer. We give a few examples of applications, regarding multidimensional Hardy spaces and various nonlinear quantities.     

Espaces de Thom et contre-exemples de J.L. Verdier et M. Goresky

Résumé SoitS une variété algébrique complexe singulière, de dimension réelle 2s. M.H. Schwartz et R. Mac-Pherson ont défini des classes caractéristiques, généralisation des classes de Chern, dans l'homologie deS (de telles classes n'existent pas en cohomologie). D'autre part l'homomorphisme de PoincaréH ^2s−⋆ (S)→H _⋆ (S) n'est en géneral, ni injectif, ni surjectif. Cet homomorphisme se factorise par l'homologie d'intersectionIH _⋆ (S). Il est naturel de se demander quel est le “comportement” des classes deS (classes de M.H. Schwartz-R. Mac-Pherson) vis-à-vis du morphisme canonique α:IH _⋆(S)→H_⋆(S). J. L. Verdier a construit un exemple dans lequel, le morphisme canonique α n'étant pas injectif, les classes deS peuvent ètre réalisées de plusieurs manières comme images de classes de Chern de variétés lisses, désingularisations deS, et dont l'homologie est isomorphe àIH _⋆ (S). M. Goresky a construit une variation de cet exemple dans laquelle les classes de Chern ne sont pas dans l'image de α. Nous montrons que ces deux exemples sont cas particuliers d'une même situation:S est un espace de Thom associé à un plongement d'une variétéB dans un espaceIP ^k . L'essentiel de cet article a été écrit lors d'un séjour des auteurs à l'Université du Rio Grande do Sul (Porto-Alegre-Brésil), sur invitation de M. Sebastiani. Nous le remercions ici, ainsi que l'Université de Porto-Alegre, de leur accueil et de leur hospitalité      

Modélisation de fissures elliptiques internes par hybridation de fonctions de poidsEmbedded elliptical cracks modeling with hybridization of weight functions

A method improving the evaluation of the stress intensity factor by hybridization of two weight functions is presented and applied to embedded elliptical cracks under various loadings. The hybridization consists in using one or the other function in the zone of the crack where it is the most efficient. The delimitation of the two zones is achieved after optimizing the axes ratio and the curvature radius of the crack. During this optimization we seek to reduce the effects of the singularities present in the weight functions as well as to take better into account the influence of the ellipse curvature. To cite this article: B. El Khalil Hachi et al., C. R. Mecanique 334 (2006).     

Numerical approximation of a viscoelastic frictional contact problemApproximation numérique d'un problème viscoélastique de contact avec frottement

We consider a fully discrete scheme for a quasistatic frictional contact problem between a viscoelastic body and an obstacle. The contact is bilateral, the friction is modeled with Tresca's law and the behavior of the material is described with a viscoelastic constitutive law with long memory. We state an existence and uniqueness result for the discrete solution, followed by error estimate results. Then, we present numerical simulations in the study of a two-dimensional test example. To cite this article: Á. Rodríguez-Arós et al., C. R. Mecanique 334 (2006).     

Exterior products of forms and the cohomology ring of a complex space

In recent publications, we have defined complexes of differential forms on analytic spaces which are resolutions of the constant sheaf. These complexes were used to prove the existence of a mixed Hodge structure on the cohomology of analytic spaces which possess kählerian hypercoverings, in particular, projective algebraic varieties. We define an exterior product on these forms, which induces the cup product on the cohomology of analytic spaces. The main difficulty is to prove that this exterior product is functorial with respect to morphisms of analytic spaces. This exterior product can be used to prove that the cup product is compatible with the mixed Hodge structure on the cohomology.     

Étude par spectroscopie infrarouge de la structure du cation mg(h2o)62+ dans quelques sels de magnésium hydratés

The infrared spectra of eight hexahydrated magnesium salts have been investigated in the 4000-2000 cm^?1 range. The stretching H₂O, D₂O and HDO water bands are discussed. Two types of hydrogen bond depending on the acceptor properties of the anion can be distinguished: the water molecules are bonded to anions or to other water molecules.     

Stability of roll waves in open channel flowsStabilité de trains d'ondes dans un canal découvert

The stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section is studied. In the framework of shallow water theory with turbulent friction the modulation equations for wave series are derived and a nonlinear stability criterion is obtained. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 330 (2002) 291–295.