Titre : Comptes rendus de l'Académie des sciences. Série 1, Mathématique
Auteur : Académie des sciences (France). Auteur du texte
Éditeur : Elsevier (Paris)
Éditeur : Centrale des revuesCentrale des revues (Montrouge)
Éditeur : ElsevierElsevier (Paris)
Date d'édition : 1988-08-15
Notice du catalogue : http://catalogue.bnf.fr/ark:/12148/cb34394200t
Type : texte texte
Type : publication en série imprimée publication en série imprimée
Langue : français
Format : Nombre total de vues : 29122 Nombre total de vues : 29122
Description : 15 août 1988 15 août 1988
Description : 1988/08/15 (SER1,T307,N7). 1988/08/15 (SER1,T307,N7).
Droits : Consultable en ligne
Identifiant : ark:/12148/bpt6k5490736g
Source : Archives de l'Académie des sciences, 2008-94315
Conservation numérique : Bibliothèque nationale de France
Date de mise en ligne : 19/01/2011
- Aller à la page de la table des matièresI
- CONTENTS 1988 - VOLUME 307 - SECTION I - N° 7
- Homological Algebra
- (see Tome 307, Series I, 1988, p. 329)
- .......... Page(s) .......... 287
- .......... Page(s) .......... 287
- We construct a new family of factor traces on inductive limits of classical Hecke algebras of type An, Bn, Cnand Dn These traces are "weak generalized Markov traces". That is, they satisfy a property weaker than the generalized Markov property enjoyed by the traces constructed in [9], which is a generalization to Hecke algebras of type An, Bn, Cn and Dn, of the Markov property of the traces constructed in ([6], [10]) on Hecke algebras of type An.
- .......... Page(s) .......... 289
- We define two different classes of solutions (regular and singular) for the problem . We show there exists no singular solution for greater than the critical parameter , then that the set of regular solutions is relatively compact in the class of singular solutions. We make the situation precise in the case of a ball, by exhibiting a singular solution.
- .......... Page(s) .......... 293
- We study the density of smooth maps between two compact manifolds M and N in Sobolev spaces. We prove that, if N is such that is trivial, then is dense in
- .......... Page(s) .......... 297
- Non-standard analysis enables one to define an integral a sum of infinitely many contributions each of which is infinitely small. It is therefore possible to construct Lebesgue's integral using Riemann sums. We solve in this set-up the main stability problem pertaining to the change of subdivision of an interval. As an application, we state a decomposition theorem of an integrable function into a rapidly oscillating part and a tame part. This provides a rational foundation for the widely used averaging methods such as mean field, etc.
- .......... Page(s) .......... 303
- Let (, P) be a probability measure space and E a separable Banach space. We establish an integral representation theorem for disjointly additive inf-compact functionals defined on L1 (P; E). Applications include a functional version of the Dunford-Pettis theorem and an extension of de la Vallée-Poussin's theorem.
- .......... Page(s) .......... 307
- To look for transverse invariants for some foliations with singularities, we build up the involutive normed algebra of half-densities on a differntiable groupoid with paracompact basis. This algebra allows to generalise the construction of the C*-algebra of a foliation.
- In this Note, we consider a general class of dynamical semi-systems which have a first integral. In this setting, we can show that the asymptotic behaviour of solutions depends only on the first integral.
- .......... Page(s) .......... 317
- .......... Page(s) .......... 317
- We give a formula, "à la Riemann-Roch-Grothendieck", for the curvature of the Quillen metric on the determinant line bundle associated with a holomorphic vector bundle over a family of complex curves, whose singularities are ordinary double points.
- .......... Page(s) .......... 321
- Let D, C" be bounded domains with smooth real-analytic boundaries and a proper holomorphic map. It is an old conjecture that in this case f can be holomorphically extended to a neighbourhood of D. For n>1 the conjecture has recently been verified by Baouendi-Rothschild [1] and by Diederich-Fornaess [7] under the additional hypothesis that f is already known to extend in a way to D and that , where v means normal direction to in z resp. to . This hypothesis is automatically satisfied if D and D' are pseudoconvex (see [4] and [6]) whereas it is, in general, unknown for non-pseudoconvex D. The purpose of this Note is to show that f also extends holomorphically to a neighborhood of D and are algebraic and f is biholomorphic. Further supplementary results are obtained.
- .......... Page(s) .......... 325
- We apply the abstract methods introduced in [1] for the study of classical solutions of problems of the type
- .......... Page(s) .......... 329
- .......... Page(s) .......... 329
- We prove that both the "discrete" and "continuous" cyclic homology groups of a stable C*-algebra vanish in all dimensions. This fact, which may be regarded as an "additive" version of Karoubi's conjecture, is a consequence of the excision properties of C*-algebras which were established in [15] (cf. also[14]).
- .......... Page(s) .......... 335
- .......... Page(s) .......... 335
- One proves the existence of minimal hypersurfaces with infinite focal radius and arbitrarily large principal curvatures in Riemannian manifolds whose Ricci curvatures are bounded from below by a negative constant. Hence the hypothesis "N totally umbilic" is necessary in Heintze and Karcher's comparison theorem in this case.
- .......... Page(s) .......... 339
- .......... Page(s) .......... 339
- We determine the integer cohomology algebra of the classifying space of the gauge group of a principal S3bundle over a closed simply connected 4-manifold minus a point. As an application, we obtain some information on divisibility of S. Donaldson's "polynomial invariants".
- .......... Page(s) .......... 343
- .......... Page(s) .......... 343
- A theorem is proved which is the sub-analytic version of Mostowski's theorem on regular projections for complex analytic hypersurfaces. This theorem leads to some corollaries concerning the distance to sub-analytic sets and the metric properties of these sets. The method of proof used gives also a stronger theorem of regular projections in the complex case.
- .......... Page(s) .......... 349
- Absolute continuity of the law of the maximum of a continuous process, David NUALART and Josep VIVES.......... Page(s) .......... 349
- We consider a stochastic process with continuous paths, which is measurable with respect to the -field generated by a Gaussian process. Using the stochastic calculus of variations we show that the maximum of such a process belongs to the Sobolev space , and we give sufficient conditions for its law to be absolutely continuous.
- .......... Page(s) .......... 355
- .......... Page(s) .......... 355
- The problem of testing a null hypothesis of ARMA dependence with unspecified, symmetric w.r.t. the origin, innovation density, is considered. The use of signed-rank tests then naturally follows from invariance arguments. A locally asymptotically maximin signed-rank test for this problem is derived.
- .......... Page(s) .......... 359
- .......... Page(s) .......... 359
- An efficient numerical method is proposed for solving steady Navier-Stokes equations in the driven cavity (0,1) x (0,1). The primitive variables, pressure and velocity components, are discretized on staggered grids and a multigrid procedure with a cell by cell relaxation is used to achieve a good convergence. A new upwind differences scheme is proposed for the convection terms. Stable solutions exhibiting good representation of secondary vortices are obtained. The transition to turbulence is observed numerically for Re = 10,000.
- .......... Page(s) .......... 363
- Under some mild assumptions, one shows that a non linear system given in a usual state space form can always be described locally by a set of input-output differential equations.
- MATHEMATIQUE 1988 - Tome 307 - Série I - n° 7
1988 - DEUXIÈME SEMESTRE
CASMEI ISSN 0249-6291
CASMEI ISSN 0249-6291
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