On the domain dependence of solutions to the compressible Navier–Stokes equations of a barotropic fluid

We prove a general compactness result for the solution set of the compressible Navier–Stokes equations with respect to the variation of the underlying spatial domain. Among various corollaries, we then prove a general existence theorem for the system in question with no restrictions on smoothness of the spatial domain. Copyright © 2002 John Wiley & Sons, Ltd.     

Isometries of the Dirichlet space among the composition operators

We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem.

     

Scaled-oscillation and regularity

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

     

New examples of Osserman metrics with nondiagonalizable Jacobi operators

Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators.     

Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.     

An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Capillary Electrophoresis Chiral Separation for Enantiomeric Purity Determination of a Basic Drug in Pharmaceutical Formulations

Capillary electrophoresis using a running buffer composed of β-cyclodextrin as the chiral selector and ethanolamine mesylate at pH 9.6 is being used to monitor the stereochemical stability of a hydrophobic drug, containing two chiral centers, in two different formulated self-emulsifying drug delivery system (SEDDS) products. The separation takes place in less than 25 min. Strategies for enhancing the method reproducibility and detection sensitivity in the lower potency formulation are presented. The results demonstrating the specificity, assay precision, recovery, linearity and range achieved during the method validation experiments are presented in this paper.Presented at: CE in the Biotechnology and Pharmaceutical Industries: 7th Symposium on the Practical Applications for the Analysis of Proteins, Nucleotides and Small Molecules, Montreal, Canada, August 12–16, 2005.     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.