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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 5
- .......... Page(s) .......... 155
- .......... Page(s) .......... 155
- In [3] que have established several algebraic characterizations of the logical notion of elementar extension. In paticular, in hte presence of the continuum hypothesis, wa have characterized up to an isomorphism of ordered fields a certain elementary extension R* of the ful structure on the real numbers R*. In the present Note, we apply there results, as whell as other results from [4] on the order structure of hyperreal lines to pin down further properties of R* and to obtain a direct characterization of the system N* of hyperintegers in R*.
- .......... Page(s) .......... 163
- The orthogonal polynomials investigated belong to a class characterized by a weight which is the product of a classical weight ans a rational funciton. For such a class a proposed procedure gives excplicitely the second order differential equation satisafied by theser orthogonal polynomials. This procedure is adapted from Shohat and gives in this cas the orgin of apparent singularities.
- .......... Page(s) .......... 167
- Toeplitz extension theorems for generalized Hankel forms are proved for both the discrete and the continuous cases. A generalization of the Bochner-Schwartz theorem, as well as extensions of and simplifications to results or a previous paper by the outhors, follow as applications.
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- In this Note we prove the global existence of classical solutions to the Cauchy problem for general nonlinear wave equations with small initial data.
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- This parper is concerned with a natural point of view for proving the main result of the study of singularities on the bondary for linear partial diffential equations. This proof leads to a simple method for computing these singularities with the help of any approximation of the equation by a finite element method.
- .......... Page(s) .......... 183
- .......... Page(s) .......... 183
- Let the associated Kac-Moody Lie-algebra and G(A) the associated Kac-Moody group. Let P be a (maximal) parabolic subgroup of G(A). Let W (resp. Wp) be the Weyl group of G(A) (resp. P). For let be the Schubert variety in G(A)/P associated to . We construct explicit bases for , in terms of "standard monomials" where L denotes the tautological line bundle on PN [as well as its restriction to ] for some canonical profective embedding . As a consequence, we obtain similar results for Schubert varietis in .
- .......... Page(s) .......... 187
- .......... Page(s) .......... 187
- We define, from the concept of algebric microlocalization, in Fitting ideals associated to a filtered module. Some applications to D-modules are given. We prove that the Oth fitting ideal associated to the filtered moduel and the Oth fitting ideal of the associated graded module on the associated garded ring, wich is assumed commutative, are equal.
- .......... Page(s) .......... 191
- .......... Page(s) .......... 191
- A negatively cured compact manifold has the Poisson property if the harmonic measure class and the visibility measure class coïncie./ We give a necessary condition for the Poisson property to hold. For surfaces, this condition reduces to the curvature being constant, a recent result of Katok's [3].
- .......... Page(s) .......... 195
- We prove some conditions of the non-existence of asymptotically euclidean solutions g for the Ricci equation, h=Ric g, where h positive definite is given in given in some weighted Sobolev spaces on a manifold wich is euclidean at infinity.
- .......... Page(s) .......... 203
- Conditions for ergodicity of the first-order general autoregressive process are developed; is a real-valued random sequence of i.i.d. random variables. The function is allowed to have countably many jumb discontinuities. Fluctuations of T are shown to be related to the ergodic distribution. Sufficient conditions about T and Mill's ratio implying the existence of moments for the ergodic distribution are stated. Our poffs use Leray-Schauder fixed point Theorem.
- .......... Page(s) .......... 207
- We analyze the classical method of approximation of thin shell problems by an assemblage of flat facets of Clough and Johnson and we show its "pseudo-convergence" for a class of shallow shells. Next we propose a peturbation of the flexural term wich leads to a convergent method valid for arbitrary thin shells.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- .......... Page(s) .......... I
- Logique
- .......... Page(s) .......... 155
- Théorie des nombres
- .......... Page(s) .......... 159
- Analyse mathématique
- Prolongements des formes de Hankel généralisées en formes de Toeplitz. Mischa COTLAR et Cora SADOSKY.......... Page(s) .......... 167
- Equations aux dérivées partielles
- .......... Page(s) .......... 175
- Analyse fonctionnelle
- .......... Page(s) .......... 179
- Géométrie algébrique
- .......... Page(s) .......... 183
- Géométrie analytique
- .......... Page(s) .......... 187
- Géométrie différentielle
- Topologie différentielle
- .......... Page(s) .......... 199
- Probabilités
- Analyse numérique
L2. Venkatramani LAKSHMIBAI et Conjeeveram S. SESHADRI