Spectral boundary controllability of networks of strings

In this Note we give a necessary and sufficient condition for the spectral controllability from one simple node of a general network of strings that undergoes transversal vibrations in a sufficiently large time. This condition asserts that no eigenfunction vanishes identically on the string that contains the controlled node. The proof combines the Beurling–Malliavin's theorem and an asymptotic formula for the eigenvalues of the network. The optimal control time may be characterized as twice the sum of the lengths of all the strings of the network. To cite this article: R. Dáger, E. Zuazua, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 545–550.     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Electrochemical reduction of monothiobenzils in the presence of aroyl chlorides. First synthesis of (Z)-α-benzoyloxy-β-benzoylthiostilbenes

The first method for the synthesis of the title compounds has been established involving a stereoselective electrochemical diacylation process. The cathodic reductions of monothiobenzils in an aprotic medium, under constant potential, in the presence of twofold molecular amounts of aroyl chlorides provide previously unknown (Z)-α-benzoyloxy-β-benzoythiostilbenes in high to quantitative yields.     

The spin-S Blume-Capel RG flow diagram

Using the finite-size scaling renormalization group, we obtain the two-dimensional flow diagram of the Blume-Capel model forS=1 andS=3/2. In the first case our results are similar to those of mean-field theory, which predicts the existence of first- and second-order transitions with a tricritical point. In the second case, however, our results are different. While we obtain in theS=1 case a phase diagram presenting a multicritical point, the mean-field approach predicts only a second-order transition and a critical endpoint.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

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).     

Mittlere Schwingungsamplituden von OTeF 5 −

Summary Mean amplitudes of vibration for OTeF ₅ ^– have been calculated from known spectroscopic and structural data in a wide temperature range. The results are briefly discussed in comparison with those of related species.