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- CONTENTS
- 1987 - VOLUME 305 - SECTION I - N° 7
- Algebra
- .......... Page(s) .......... 287
- Let a field of characteristic zero, deg , and . Suppose that Q vanishes on all the common zeros of . We establish somewhat more general versions of the following results. For . For , there are with deg such that .
- Mathematical Analysis
- .......... Page(s) .......... 291
- We study the long time behavior of the solutions of the nonlinear Schrödinger equations in presence of an external excitation and a zero order damping term. We show that an attractor, compact in the energy space, captures all the trajectories. We prove that its dimension is finite using a quadratic functional on the exterior products of the phase space, this functional depending on the trajectory.
- .......... Page(s) .......... 295
- We give the generalization of the Gagliardo-Nirenberg inequality:
- on nilpotent Lie groups.
- Functional Analysis
- .......... Page(s) .......... 299
- In this Note the comparison is made between an asymptotic behaviour of sequences of entropy numbers
and of u and its dual u*, for any compact operator u with values in a Hilbert space. It is shown that these sequences belong to the same symmetric sequence Banach spaces and that their norms are equivalent. Under natural regularity conditions one can compare individual entropy numbers and .
- Optimal Control
- In this paper, we show the validity of the model function concept, because a mathematical model originating from a given biological system could be used for another biological field. This model, so-called model for the regulation of agonistic-antagonistic couples, included its own optimal control device. In case of imbalance of the system, this control pointed out that it was better to resort to two agents with opposite actions than only to the agent already deficient in the system.
- Differential Geometry
- .......... Page(s) .......... 307
- We consider two natural families of almost hermitian structures on a twistor space and determine their types according to the Gray-Hervella classification of almost hermitian manifolds.
- Numerical Analysis
- The solution of the Neumann problem in a plane domain with a polygonal boundary is expressed either as the double layer potential of a function , which is the solution of a coercive variational problem on , or as the simple layer potential of the charge q, which is the solution of a Fredholm integral equation of the second kind on . We adapt the mesh near the corners in order to get rid of the polluting effect of the singularities on the order of convergence.
- .......... Page(s) .......... 315
- We develop a semi-lagrangian numerical scheme for two-dimensional turbulence. This scheme has two important advantages: its time step is limited by an optimal criterion and its computational cost is function of the local dynamic of the flow.
- COMPTES RENDUS DE L'ACADEMIE DES SCIENCES
- MATHEMATIQUE 1987 - Tome 305 - Série I - n° 7Contents with Enghish abstracts I, II
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