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- CONTENTS 1987 - VOLUME 305 - SECTION I - N° 10
- .......... Page(s) .......... 393
- .......... Page(s) .......... 393
- A new proof of existence for "strong Frobenius structure" of the hypergeometric differential equation is given. The interest of this proof lies in the fact that the geometric interpretation of the equation as "Picard-Fuchs equation" is not used.
- .......... Page(s) .......... 397
- It is shown that the set of squares
and, more generally, a set of the form where p(n) is any polynomial taking integer values, satisfies the pointwise ergodic theorem for L2-functions. This gives an affirmative answer to a problem considered by A. Bellow and H. Furstenberg. The previous result generalizes to commuting systems of transformations.
- .......... Page(s) .......... 403
- .......... Page(s) .......... 403
- The aim of this Note is to show by an explicit verification, that the stable category of a self injective finite dimensional algebra over a field, graded by the inverse of the equivalence induced by the Heller operator, is triangulated (cf. [2]).
- .......... Page(s) .......... 407
- To every homogeneous polynomial P on Rk we associate a triplet of differential operators (X_, X0, X+) on the same space, which satisfies the commutation relations of the usual basis of sl (2, R) and such that X+ = Cte P(x). We examine more closely the case where P is the relative invariant of a prehomogeneous vector space and give, in some cases, the decomposition of the space of regular functions on the open orbit.
- .......... Page(s) .......... 411
- We consider the uniqueness of the inverse scattering problem for the wave equation . If and if the asymptotic wave profiles related to coincide for , then .
- .......... Page(s) .......... 415
- We study the Klein-Gordon symbolic calculus of operators acting on solutions of the free Klein-Gordon equation. It contracts to the Weyl calculus as . Mathematically, it may also be considered as a pseudodifferential analysis on the unit ball of Rn.
- .......... Page(s) .......... 419
- .......... Page(s) .......... 419
- Let E be a holomorphic vector bundle of rank r over a compact complex manifold X of dimension n. If E is positive in the sense of Griffiths, it is shown that the Dolbeault cohomology groups vanish for and . The proof rests on the well-known fact that any tensor power splits into irreductible representations of Gl(E), each component being canonically isomorphic to the space of sections of a positive homogeneous line bundle over a flag manifold of E. The vanishing property is then obtained by a combination of Le Potier's isomorphism theorem with a new curvature estimate for the bundle of X-relative differential forms on the flag manifold of E.
- .......... Page(s) .......... 431
- .......... Page(s) .......... 431
- We propose a particle method of resolution of convection-diffusion equations which is a generalization of the one proposed in [1]. The method is based on the approximation of a diffusion operator by an integral operator and consists in two steps: the approximation of the solution of the convection-diffusion problem by the solution of the obtained integro-differential equation and the resolution of the integro-differential equation by a particle method.
- All rational curves are determined with Bernstein polynomials by a polygon of control weighted points and control vectors. Stable algorithms for computing any point are given with a view to their applications in CAD. CAM and robotics.
- .......... Page(s) .......... 441
- .......... Page(s) .......... 441
- We determine, by homogenization, the limit load of a periodic nonhomogeneous structure. For a structure clamped on its boundary it was proposed [1] and proved [4] that the problem reduces to a limit load problem for an homogenized structure the strength capacity of which was characterized. For a structure loaded on its boundary the present work shows that the limit load problem must include an additional strength criterion on the stress vector on the boundary. This strength criterion is more restrictive than the condition which can be deduced from the bulk strength capacity.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- MATHEMATIQUE 1987 - Tome 305 - Série I - n° 10
- Théorie des nombres
- Algèbre
- .......... Page(s) .......... 403
- Théorie des groupes
- .......... Page(s) .......... 407
- Analyse mathématique
- .......... Page(s) .......... 415
- Analyse complexe
- Analyse fonctionnelle
- .......... Page(s) .......... 423
- Géométrie différentielle
- .......... Page(s) .......... 427
- Analyse numérique
- .......... Page(s) .......... 431
- Problèmes mathématiques de la mécanique
- .......... Page(s) .......... 441