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- CONTENTS 1988 - VOLUME 306 - SECTION I - N° 1
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- Let K be a number field with r1 and r2 real and complex absolute values, degree , discriminant , class number h and regulator R. Let w be the number of roots of unity belonging to K; let B be the Minkowski constant (); let S be the set of prime ideals of K with norm and P(B) the product of terms (). We prove that the product h. R of class number and regulator is bounded by the expression .
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- We explicitly construct the dimension sequence of each Pn VD, characterize the set of such dimension sequences and show that each dimension sequence can be realized by a semilocal integrally closed integral domain which is locally Pn VD.
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- As a generalization of an example given by Jaffard [2] we introduce a class of filtered ordered (abelian) groups which are not groups of divisibility.
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- In this Note we show that the union of Lusztig series of irreducible characters of associated to a section of the dual group (where G is a connected reductive algebraie group defined over is a union of blocks, and that the Brauer morphism is compatible to this partition of the irreducible characters.
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- The adapted Fourier transform, in the case of a nilpotent Lie group, gives the decomposition of the regular representation in the space of square integrable functions on the group; the usual Fourier transform does not. This adapted transform has an integral kernel which is precisely the * exponential, introduced in the deformation program.
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- Constrained global optimization of nonlinear nonconvex functions of several variables can be done following an analytical approach. This leads to branch-and-bound procedures, combining symbolic computation, especially in the exploitation of monotonicity properties and the elimination of variables, with many tests similar to those of combinatorial optimization. A program using the MACSYMA computer algebra system allows to solve many problems from the literature.
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- We present two new theorems concerning the existence and the regularity of certain real solutions to a class of semilinear wave equations in . Those solutions are Bohr almost-periodic in time and converge exponentially rapidly to a constant equilibrium solution as the spatial variable goes to plus or minus infinity.
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- Counterexample in the framework of gaussian differential calculus.
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- Let us consider the non-linear Schrödinger equation: (1) .
- When one looks for physically convenient solutions to (1) (for instance, of soliton type), it appears an ordinary differential equation ([2], [7]), and the existence of solutions to this equation is a necessary and sufficient condition to solve the initial problem. We show here that in the case of the harmonic oscillator this latter equation has positive solutions with Gaussian decay.
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- The index of a vector field on the boundary of a compact manifold allows us to define a singularity index for a compact hypersurface in a pseudo-riemannian manifold. When this manifold is locally conformally flat, singularity index of a generic hypersurface can be expressed in terms the of topological invariants of the induced pseudo-metric's singular set.
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- We give an answer to a question of A. Katok by showing the existence, for a generic area-preserving twist map of the annulus, of a dense open set of such that every Aubry-Mather set whose number of rotation belongs to it is hyperbolic.
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- We determine the set of such that every germ of holomorphic diffeomorphism of (C, 0) with linear part is linearizable. For such , we obtain a best possible bound from below for the size of the linearization domain.
- COMPTES RENDUSDE L'ACADEMIE DES SCIENCES
- .......... Page(s) .......... I
- Logique
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- Théorie des nombres
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- Algèbre
- Théorie des groupes
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- Algèbres de Lie
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- Analyse mathématique
- Equations différentielles
- Géométrie différentielle
- Systèmes dynamiques
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, Bruno SCARPELLINI and Pierre-A.VUILLERMOTLe taux de reconnaissance estimé pour ce document est de 91.07%.
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Le texte affiché peut comporter un certain nombre d'erreurs. En effet, le mode texte de ce document a été généré de façon automatique par un programme de reconnaissance optique de caractères (OCR). Le taux de reconnaissance estimé pour ce document est de 91.07%.
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