Absence of localization in a class of Schrödinger operators with quasiperiodic potential

We prove that a class of discrete Schrödinger operators with a quasiperiodic potential taking only a finite number of values, exhibits purely continuous spectrum; in particular they cannot have localized eigenvectors.Groupe de Recherche 048 of C.N.R.S.     

The service allocation problem at the Gioia Tauro Maritime Terminal

The Service Allocation Problem (SAP) is a tactical problem arising in the yard management of a container transshipment terminal. The objective is the minimization of the container rehandling operations inside the yard. This study of the SAP was undertaken for the Gioia Tauro port which is located in Italy and is the main hub terminal for container traffic in the Mediterranean Sea. The SAP can be formulated as a Generalized Quadratic Assignment Problem (GQAP) with side constraints. Two mixed integer linear programming formulations are presented. The first one exploits characteristics of the yard layout at Gioia Tauro where the berth and the corresponding yard positions extend along a line. The second formulation is an adaptation of a linearization for the GQAP. In both cases only small instances can be solved optimally. An evolutionary heuristic was therefore developed. For small size instances the heuristic always yields optimal solutions. For larger sizes it is always better than a truncated branch-and-bound algorithm applied to the exact formulations.     

Stabilisation des vinyl- et ethynyl-phosphines secondaires par complexation du phosphore

A stable divinylphosphine P-W(CO)₅ complex is prepared in 2 steps from the corresponding divinyl-diethylaminophosphine complex by cleavage of the P-N bond by HCl followed by reduction of the P-Cl bond thus formed by LiAlH₄; a similar scheme is used for the synthesis of stable tungsten complexes of vinyl- and phenylethynyl-diethylaminophosphines.     

Scattering pour l'équation de Schrödinger en présence d'un potentiel répulsif

We study scattering theory for linear Schrödinger equations, when the reference Hamiltonian is ?Δ?〈x〉^α, in $\text{R}{}^{\mathrm{n}}$, with 0<α?2. The notion of short range perturbative potential is much weaker than for the usual reference Hamiltonian ?Δ. We also consider the case where 〈x〉² is replaced by a general second order polynomial. To cite this article: J.-F. Bony et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Electron charge density of alkali halides beyond the rigid-ion approximation

The dependence of the electron charge distribution in alkali halides on the lattice constant is examined. It is found that in the case of NaCl the non-rigid behavior of the electron charge density calculated from first principles can be well understood if one starts from the free-ion functions and takes into account the mutual overlap between them. The relevance of our results for the structural properties of alkali halides is pointed out in connection with recent ab-initio calculations.     

Poisson boundaries of discrete groups of matrices

If μ is a probability measure on a countable group there is defined a notion of the Poisson boundary for μ which enables one to represent all bounded μ-harmonic functions on the group. It is shown that for discrete groups of matrices this boundary can be identified with the boundary of the corresponding Lie group.     

On minimum congestion routing in rearrangeable multihop lightwave networks

In this article we consider the problem of minimizing the congestion in logically rearrangeable multihop lightwave networks. Namely, we consider a network in which each node is equipped with a small number of transmitters and receivers, and tuning a transmitter at nodei and a receiver at nodej to the same wavelength creates a logical link (i, j) through which traffic could be sent. For a given traffic matrix-the matrix of flows between nodes—the objective is to find the best connectivity diagram and the corresponding flow assignment so that the maximal flow on any link is minimized. We develop a tabu search heuristic that yields a suboptimal connectivity diagram and an optimal flow assignment on it. Computational experiments are conducted on some benchmark data sets, on a real-world traffic matrix, and on some randomly generated problems of larger dimension. The results are compared with known results from the literature and with a known greedy approach. The results suggest that a tabu search—based heuristic is a promising approach for handling this NP-hard combinatorial problem. In addition, we discuss the performance of the method in view of different patterns of input data.