Superposition, Entanglement, and Product of States

The superposition relation extended to the statistical operators is shown to be invariant under tensor product and partial trace operations. Particular mathematical examples of superposition are characterized as well as the nature of the Schmidt decomposition of pure states superposition of other pure states.     

Semigroups Generated by Ordinary Differential Operators in L 1(I)*

In this paper we give necessary and sufficient conditions for the existence of a C> ₀-semigroup in L ¹(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Existence of global attractors for a class of periodic Kolmogorov systems

In this paper we use a continuation argument to prove the existence of global attractors for a class of periodic Kolmogorov systems.     

On the maximum principle for complete second-order elliptic operators in general domains

This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

Memory effects in gas chromatographic detection with a microwave-induced plasma

Capillary gas chromatography coupled to microwave-inducedplasma detection furnishes sensitivity adequate for trace analysis when the signal is monitored at a carbon emission line. Work performed with one of these systems at high electronic gain for the carbon signal has revealed solvent band widths in excess of four minutes; these impeded quantification of peaks eluting after the solvent. This report discusses two phenomena which could be related to the unexpected intensity of this solvent response: photomultiplier tube saturation and carbon deposits in the quartz plasma discharge tube.     

Nonconservation of the net current of Dirac particles in Tolman-Bondi and Robertson-Walker geometries

A straightforward calculation shows that, in contrast to what happens for the Dirac equation in the Kerr metric, the net current of particles is not conserved in the case of the Dirac equation in the Tolman-Bondi and Robertson-Walker space-times.