Rangs Stables De Certaines Extensions

M. A. Rieffel [24] a introduit le rang stable topologique (tsr),pour généraliser aux C*-algèbres, le conceptde dimension de recouvrement pour les espaces compacts, affirmantainsi le principe selon lequel une C*-algèbre est ‘unespace localement compact non commutatif’. II a montréque l'on a tsr ((A)) = [dim (Â)] + 1, pour toute C*-algèbre commutative A etque trs (B/J) tsr (B), pour toute C*-algèbre B et pourtout idéal bilatère fermé J dans B (généralisantle fait que, si X est un espace compact et F un sous-ensemblefermé dans X, alors on a dim (F) dim (X), oùdim(X) est la dimension de recouvrement de X [19]). D'autrepart, le rang stable topologique peut être utilisépour obtenir des théorèmes de ‘cancellation’pour les modules projectifs, comme ceci est fait dans [25, 2].Un peu plus tard, R. H. Herman et L. N. Vaserstein [14] ontmontré que pour toute C*-algèbre unitaire A, lerang stable topologique de A et le rang stable de Basse de Acoincident, done, pour toute C*-algèbre unitaire A, onnote sr(A) cette valeur commune appelée rang stable deA. Les C*-algèbres unitaires de rang stable 1 ont étéétudiée géométriquement par M. Rørdam[27], il a montré que l'on a sr(A) = 1 si et seulementsi l'enveloppe convexe des unitaires de A est égale àla boule unité fermé de A. D'autre part, Rieffel[24] avait introduit le rang stable connexe (csr) d'une C*-algèbre,sur lequel V. Nistor [18] a publié un article trésintéressant. Mon travail dans ce papier consiste àcompléter certains travaux déjà entreprisdans les articles qui sont cités ci-dessus.     

Fibres of width 3 ordered sets

We show that in an ordered setP of width 3 there always exists a fibre (i.e., a subset intersecting each maximal nontrivial antichain) of size at most 11/18|P|. This improves previously known results.Research supported by Polish KBN Grant 2 2037 92 03.     

Materials Reinforced by Almost Inextensible Fibres

This paper is concerned with extending the theory of Everstine& Pipkin (1973) for elastic materials reinforced by inextensiblefibres to allow for slight fibre-extensibility. Small deformationsonly are considered. The stress-strain relation for a materialreinforced by two distinct families of extensible fibres isderived and compared with the similar equation for inextensiblefibres to deduce the effect on the elastic constants of approachingthe limit of fibre-inextensibility. It is then shown by twosimple examples how some problems which are indeterminate iffibre inextensibility is assumed b initio are solvable if fibreextensibility is assumed first and the limit of fibre-inextensibilityapproached in the solution. Finally the phenomenon of singularsheets of fibres carrying infinite stress predicted by the inextensibletheory in many cases is examined in a particular problem bya boundary layer technique.     

Jacobiennes de Courbes Algebriques de Genre 2 et 3 de Grand Rang Sur Q

Infinite families of curves are constructed of genus 2 and 3over Q whose jacobians have high rank over Q. More precisely,if E is an elliptic curve with rank at least r over Q, an infinitefamily of curves are constructed of genus 2 whose jacobianshave rank at least r+4 over Q, and, under certain conditions,an infinite family of curves are constructed of genus 3 whosejacobians have rank at least 2r over Q. On specialisation, afamily of curves are obtained of genus 2 whose jacobians haverank at least 27 and a family of curves are obtained of genus3 whose jacobians have rank at least 26; one of these has rankat least 42.     

Quotient Volumique et Espaces de Banach de Type 2 Faible

The Banach spaces for which all finite dimensional quotient spaces have uniformly bounded volume ratio are characterized by a weak type 2 property. This is the dual form of a recently published result of V. Milman and G. Pisier on weak cotype 2 Banach spaces.      

Ensembles de module maximum des domaines rigides de C2

Sans résumé Received 25 April 1994; in final form 27 June 1995     

Convergence en moyenne de l'information pour l'action de Z 2

Résumé On démontre la convergence en moyenne de 1'information (théoréme de Mac-Millan) pour 1'action de Z².     

Espaces Homogenes Principaux et Points de 2-Division de Courbes Elliptiques

Dans cet article, nous nous intéressons aux problèmesde structure galoisienne associés aux couples (E/L, a),où E désigne une courbe elliptique définiesur le corps de nombres L et a un endomorphisme de E. Si E està multiplication complexe, nous notons k le corps quadratiqueimaginaire dont l'anneau des entiers décrit End(E) etL une extension de k. Ainsi a est-il selon les cas un entieralgébrique de k ou un élément de Z.     

Geometrical and Topological Properties of Real Polynomial Fibres

We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of ⁿ . For this we need to study topological properties of a generic hyperplane section of this fibre.     

Loss and Birefringence for Arbitrarily Bent Optical Fibres

We present a calculation to determine the radiation losses forarbitrarily bent, weakly guiding optical fibres. Our resultsare derived for the full set of vector Maxwell's equations,and show that the rate of energy loss due to radiation differsfor the various modes. These results are different from thatcalculated from a scalar theory, where the so-called linearlypolarized (LP) modes are used to approximate the electromagneticfield distributions, showing that in this case scalar theoriesgive incorrect loss rates. We also show that different rangesfor the size of the curvature and torsion produce quite differenteffects. In particular, we show that, for smaller amounts ofcurvature and torsion, the modes retain the basic structureof the modes in the straight fibre while losing energy slowlyat differing rates, while, for larger amounts of curvature andtorsion, the modes become distorted by the bending.     

Constante de Bers en genre 2

We introduce a new tool, the contiguity graph, which enables us to determine the Bers’s constant in genus two.     

Theoremes de congruence pour triplets de points dans les varietes de GrassmannG 2(ℝ N )

La classe di congruenza di una terna {A, B, C} inG ₂(? ⁿ ), sotto l’azione del gruppo ortogonale 0(n, ?), dipende da 9 parametri al più. Possiamo associare in modo naturale a questa terna, una terna di proiettori ortogonali {P _A ,P _B ,P _C }. Utilizzando la teoria algebrica degli invarianti, viene dato un sistema completo di invarianti ortogonali composto da tracce di opportune combinazioni diP _A ,P _B , eP _C che consentono di determinare in modo unico la classe di congruenza della terna di partenza.     

A propos de l'espace des modules de fibrés de rang 2 sur une courbe

Sans résumé

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Partiellement financé par le contrat Science Geometry of Algebraic Varieties, contrat n^o SCI-0398-C