Analyse locale des droites discrètes. Généralisation et application à la connexité des plans discrets

When studying a Reveillès digital straight line defined by a doubleinequality (I): γ ≤ ax + by < γ + Γ with (a,b,Γ)∈ℕ^*3 and γ∈ℤ, we are naturally led to study fibers from a digital plane P of ℤ³. Local results concerning the existence of connectivity paths between neighbouring legos provide a construction of a special infinite graph G with finite period. The deterministic algorithm for recognizing connectivity of infinite graphs we give below also permits us to know the connectivity of P using G.     

Sur la cohomologie à support des fibrés en droites sur les variétés symétriques complètes

Let X be a complete symmetric variety, i.e., the wonderful compactification of a symmetric G-homogeneous space (where G is a simply connected semi-simple linear algebraic group). If L is a line bundle over X and if C is a Bialynicki-Birula cell of codimension c in X, then the Lie algebra $ \mathfrak{g} $ of G operates naturally on the cohomology group with support H _C ^c (L). A necessary condition on C for the existence of a finite-dimensional simple subquotient of this $ \mathfrak{g} $ -module is given. As applications one calculates the Euler–Poincaré characteristic of L over X, estimates the higher cohomology group H ^d (X, L), d ≥ 0, and obtains the exact formulas in some cases including that of the complete conic variety.     

Dérivabilité globale et locale des fonctionnelles de Wiener

In this Note we give sufficient conditions which imply the global Sobolev differentiability of locally differentiable Wiener functionals.     

Existence locale et unicité d'écoulements de fluides viscoélastiques dans des domaines non bornés

In this Note, we present a result of local existence and uniqueness, for any initial data, of the solutions to the equations of viscoelastic fluids of Jeffreys type (differential constitutive law). The system of equations is supposed to be verified in an unbounded domain Ω ⊂ ℝ^N (N = 2 or 3)), uniformly regular. The difficulty comes essentially from the loss of compactness in the case of unbounded domains. To overcome this difficulty we use a local compactness method, which allows us to construct a sequence of solutions on subdomains ;inn whi_n which union covers Ω After that, we pass to the limit to define a solution over the whole domain. Finally we show the uniqueness of this solution in its class of regularity, by using an energy estimate.     

Caractérisation par l'uniformité des fibrés universels sur la Grassmanienne

Conclusion SoitE un fibré uniforme surG(d,n). Nous avons étudié exhaustivement les cas où rangEd. montrant queE est soit somme directe de fibrés ou droites, soit, sir=d, indécomposable et isomorphe àH _d O _G () où àH _d ^* O _G ().Si rangE=(n-d), nous avons étudié les cas oùE est décomposable en fibrés en droites ou indécomposable et isomorphe àQ _{n d} O _G () où àQ _n ^* _d O _G (). L'étude des fibrés indécomposables de rangd, et (n-d) nous a montré que les quatre fibrés universels surG(d,n), sont caractérisés par leur rang, leur polynôme de Chern et al propriété d'uniformité.     

Configurations combinatoires des polynômes fibrés de degré 2

In this Note, we are interested in quadratic fibered polynomials which are skew products of the kind P_c : X × C → X × C, P_c(x, z) = (ƒ(x),z² + c(x)), where X is a compact set, ƒ is a continuous map from X into X, and c is a continuous complex valued function on X considered as a parameter. We construct a compact connected configuration space which gives a combinatorial model of a subset of the parameters space. Then, we explain in which way an abstract configuration can be realized by a quadratic fibered polynomial.     

Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale

Sans résumé Oblatum 28-XII-1998 & 3-V-1999 / Published online: 5 August 1999     

Enveloppe d'holomorphie locale des variétés CR et élimination des singularités pour les fonctions CR intégrables

Let M be a locally embeddable CR manifold and Φ ⊂M be a closed set. We give sufficient conditions in order that L_loc¹ functions on M which are CR on M #x003A6; are CR on M.     

Rationalité des séries de poincaré et des fonctions zêta motiviques

Soient k un corps de caractéristique 0 et X une k[[t]]-variété (éventuellement singulière) plate, purement de dimension relative d. Nous prouvons la rationalité des séries de Poincaré motiviques et de fonctions Zêta dIgusa motiviques, associées à X, à laide de lintégration motivique, du théorème de désingularisation plongée dHironaka, de la théorie des modèles de Néron faibles pour les schémas formels et dun théorème délimination des quantificateurs en théorie des modèles.Revised version: 17 March 2004     

Annulation et pureté des groupes de cohomologie rigide associés à des sommes exponentielles

We show a purity property for the rigid cohomology groups associated to exponential sums on a smooth and affine variety. For this purpose, we compare these groups with the p-adic Banach spaces of Dwork's theory constructed by Adolphson and Sperber [1].     

Frottement interne et anélasticité des solides

Summary Having recalled a few essential definitions in the theory of internal friction in solids, the authors, in a first chapter, study the propagation of longitudinal waves in a rod; they start from a simple law relating locally stress, strain and their first derivatives with respect to time. This law which is more general thanHooke's law has been proposed first byZener to explain the anelastic behaviour of a standard linear solid. The authors calculate the internal friction resulting from energy dissipation when the vibration is forced then free. The second chapter deals with problems arising when one tries to measure the internal friction in flexure of metallic specimens having the shape of rods or circular plates. The authors develop the basic flexure equations applied to the two types of specimen; then they determine the fundamental characteristics, which appear in internal friction measurement purposes.

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Recherche bénéficant d'un subside du Fonds National Suisses de la Recherche Scientifique (Commission pour la Science Atomique, FN A 176).     

Schémas en groupe et modules filtrés

Let k be a perfect field of characteristic p > 0. When p ≥ 3, Fontaine has classified p-divisible groups and finite flat commutative p-groups over the Witt vectors W(k) in terms of filtered modules ([9]+[6],[7]). Still assuming p ≥ 3, we extend these classifications over an arbitrary complete discrete valuation ring of unequal characteristic and residue field k by using “generalized” filtered modules. In particular, there is no restriction on the ramification index.