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.     

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.

     

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.     

Design of an experimental procedure for energy evaluation from biomass

The rational and sustainable exploitation of nature resources is one of the priority objectives of our society. In this article a method is proposed to evaluate and exploit the energetic resources contained in different forest formations. This method is based on the use of a combustion bomb calorimeter to determine the calorific values of the different samples studied. These results were complemented with chemical analysis of the samples and with environmental and geomorphological studies of the zones were samples were taken. The results obtained during the last 3 years for the residual biomass originated from the forest formations existing in Galicia ensure the reliability and usefulness of the method that can be extended to any forest formation all over the world.     

On I-fuzzy topologies derived from a decreasing family of I-topologies

The aim of this paper is to study I-fuzzy topologies (fuzzy topologies in ostak's sense) derived from decreasing families of I-topologies (fuzzy topologies in Chang's sense), defined on a set X.