The Stochastic Reflection Problem in Hilbert Spaces

We construct a Markov process X associated with the stochastic reflection problem on a closed convex subset with non empty interior and smooth boundary in a Hilbert space, as a solution to a random convex control problem. The transition semigroup corresponding to X is exactly that defined by the Kolmogorov equation with Neumann homogeneous boundary conditions (see [3 Barbu , V. , Da Prato , G. , Tubaro , L. ( 2011 ). Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II . Ann. Inst. H. Poincaré 4 : 699 – 724 .[Crossref] , [Google Scholar]]).     

Phase equilibria experiments and calculations for carbon dioxide + methanol binary system

Vapor-liquid equilibria (VLE) data for the carbon dioxide + methanol system was measured at 293.15, 298.15, 310.15, and 323.15 K. Phase behavior measurements were made in a high-pressure visual cell with variable volume, based on the static-analytic method. The pressure range under investigation was between 4.8 and 95.1 bar. The Soave-Redlich-Kwong (SRK)-EOS coupled with Huron-Vidal (HV) mixing rules and a reduced UNIQUAC model, was used in a semi-predictive approach, in order to represent the phase behavior (critical curve, isothermal VLE) of the system. The topology of the phase behavior of the carbon dioxide + methanol system is satisfactory predicted with the SRK/HV-residual UNIQUAC model.      

Finite-dimensional controller design for semilinear parabolic systems

This paper considers the stabilization of steady-state solutions of a semilinear parabolic system using finite-dimensional feedback controllers with support in an arbitrary open subset and which are active in one equation only. It is shown that such a controller, with dimension given by the largest algebraic multiplicity of the unstable eigenvalues of the linearized system, exponentially stabilizes the steady-state solution. An optimal design methodology for these types of controllers, which is based on the finite element approximation of the semilinear parabolic system, is introduced and illustrated by numerical simulation examples.     

Invariance of cohomologicalq-completeness under finite holomorphic surjections

It is proved that cohomologicalq-completeness (cohomologicalq-convexity) is invariant under finite surjective holomorphic mappings. A related result in the non-proper case is also proved.     

Hamiltoniens àN corps avec champs magnétiques très singuliers du type ‘courte portée’

We study the spectral properties of a large class ofN-body Hamiltonians, in the Agmon formalism, considering magnetic fields with strong singularities and of short-range type. More precisely, we obtain the essential spectrum (a problem that has been solved in a more general setting by Iftimie by a different method), we control the point spectrum embeded in the continuous spectrum, we prove the absence of singularly continuous spectrum and a Limiting Absorption Principle. Our method consists in performing a gauge transformation (obtained by a procedure similar to that used by Boutet-de Monvel-Berthier and Purice that eliminates the magnetic field by adding some perturbation to the electric potential. The perturbation is a first-order differential operator, generally of the long-range type. At this stage we can use the theory without the magnetic field given by Amreinet al.

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Résumé Nous étudions le spectre d'une classe trés générale d'hamiltoniens à N corps dans le formalisme d'Agmon avec des champs magnétiques très singuliers. Il s'agit notamment de calculer le spectre essentiel (probléme deja résolu par Iftimie dans des conditions plus générales, par une autre méthode), de contrôler le spectre ponctuel plongé dans le spectre continu, d'établir l'absence du spectre singulier continu et de prouver un principe d'absorption limite. Par un changement de jauge (dont la construction est basée sur une idée de Boutet de Monvel-Berthier et Purice) on se ramène au cas d'un hamiltonien sans champ magnétique, mais avec les potentiels électriques modifiés, les perturbations étant des opérateurs différentiels du premier ordre, en général du type longue portée. À ce moment là on peut utiliser la théorie sans champ magnétique de Amreinet al.

     

The Stochastic Nonlinear Damped Wave Equation

We prove the existence of an invariant measure for the transition semigroup associated with a nonlinear damped stochastic wave equation in Rⁿ of the Klein--Gordon type. The uniqueness of the invariant measure and the structure of the corresponding Kolmogorov operator are also studied.     

Optimal control problems with two-point boundary conditions

We study convex as well as some nonconvex optimal control problems for infinite-dimensional first-order linear differential systems with two-point boundary conditions of antiperiodic type. The main advance of this paper over existing related papers consists in the fact that the domains of the possible nonlinear operators involved in the boundary conditions have empty interior. Applications to boundary control systems governed by partial differential equations describing incompressible flows with fading memory and steering a temperature field are given.This work was supported in part by the National Science Foundation under Grant No. DMS-91-11794.     

Radiation stability of methionine-35S and selenomethionine-75Se

The radiation stability of methionine-³⁵S and selenomethionine⁷⁵Se was investigated using the methods of thin-layer chromatography, gas chromatography and ESR. Radiation decomposition of methionine-³⁵S mainly consists in an oxidation process and in the release of volatile products. The ESR-spectra of irradiated DL-methionine indicated a strong localization of the unpaired electrons on sulfur atoms. Radiation damage to selenomethionine-⁷⁵Se as a function of radiation dose proved an increased stability of this compound, and its radiation decomposition consists in the formation of oxidized products and by direct rupture of the selenium bonds accompanied by the formation of volatile compounds like CH₃SeH and SeH₂. The self-radiolysis of the aqueous solution of selenomethionine-⁷⁵Se during its storage in air leads, however, to a lower decomposition rate which consists in the release of inorganic selenium and in an oxidation process.