The first ruthenium-alkyne-dihydride reported is now recognized as an intermediate in the homogeneous hydrogenation of diphenylacetylene: Crystal structure of (μ-H)2Ru3(CO)9(μ3-η2-∥-C2Ph2)

The title complex (complex1) was the first alkyne-substituted triruthenium dihydrido cluster to be reported and was characterized by spectroscopy as a triangular cluster with the alkyne parallel to a Ru-Ru edge. Recently, we have found that1 is a key intermediate in the homogeneous hydrogenation of diphenylacetylene catalyzed by tetrahedral Ru₄ and FeRu₃ clusters. Since the discovery of1, a great number of complexes with alkynes parallel to a cluster edge have been reported; at present this is the more common bonding mode for alkynes on trinuclear clusters. The structural features of1 allow a comparison with those of other ruthenium-containing derivatives and help to draw suggestions of the role of1 in hydrogenation catalysis.     

Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

Long‐range dependence and performance in telecom networks

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long‐range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM; (b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long‐range dependence in the data versus the alternative of short‐range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Obituary Gilbert Grynberg (1948-2003)

We mourn the death of Professor Dr. Gilbert Grynberg, April 17, 1948 - January 27, 2003. We have lost an excellent and highly esteemed scientist, an outstanding character and a good friend. He has been a very active colleague in the merger of Zeitschrift für Physik and Journal de Physique in the early days. As one of the Co-Editors-in-Chief of The European Physical Journal D, from its start, he has formed the scienti.c standards of EPJ. Untiringly he has served our Journal with greatest dedication. We are grateful that he has been with us. The editorial board and o.ce of EPJ B Siegfried Grossmann, Denis Jérome, Antonio Paoletti     

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).