Local energy decay for the damped wave equation

We prove local energy decay for the damped wave equation on R^d${\mathbb{R}}^d$. The problem which we consider is given by a long range metric perturbation of the Euclidean Laplacian with a short range absorption index. Under a geometric control assumption on the dissipation we obtain an almost optimal polynomial decay for the energy in suitable weighted spaces. The proof relies on uniform estimates for the corresponding “resolvent”, both for low and high frequencies. These estimates are given by an improved dissipative version of Mourre's commutators method.     

Elimination versus ring opening: a convergent route to alkylidene-cyclobutanes

Functionalized alkylidene-cyclobutanes have been prepared from 2-fluoropyridinyl-6-oxy precursors derived from vinyl cyclobutanols by a radical addition-elimination process. A wide range of functional groups is tolerated, and the alkylidene-cyclobutanes can be further elaborated into cyclopentanones. The limitation of this approach resides in the competition with opening of the cyclobutane ring.     

Synthesis and electrochemical studies of LiMn1−xCuXO4 cathode material

LiMn_1.8Cu_0.2O₄ was investigated in order to improve the electrochemical properties of LiMn₂O₄. We report the synthesis and characterization of materials prepared by solid-state reaction. The structural properties evaluated by the X-ray diffraction and vibrational spectroscopy show that a single phase was formed. Conductivity of LiMn_1.8Cu_0.2O₄ cathode is found to be 8×10⁻⁶ S/cm at 25 °C. The cyclic voltammetry data shows the reversibility of the electrode material. Paper presented at the 7th Euroconference on Ionics, Calcatoggio, Corsica, France, Oct. 1–7, 2000.     

Preparation and characterization of LiCo1−yCryO2 oxides

We report the synthesis, characterization and electrochemical properties of LiCo_0.85Cr_0.15O₂ samples. Powders prepared by wet-chemistry using the poly(vinyl alcohol) gel technique exhibit a well-defined layered structure. We describe the evolution of the local environment of cations when the precursor is heat treated at 750 °C in air. Electrochemical features of Li//LiCo_0.85Cr_0.15O₂ cells show a reversible capacity of 125 mAh/g for the first charge-discharge cycle. Paper presented at the 7th Euroconference on Ionics, Calcatoggio, Corsica, France, Oct. 1–7, 2000.     

Singularités des courants d'Ahlfors

We prove that an algebraic curve charged by a current coming from an entire curve is rational or elliptic. This answers a question by M. P?un.     

Comportement macroscopique des matériaux poreux à microstructure en feuilletsMacroscopic behavior of porous materials with lamellar microstructure

The solid phase of the porous material considered in this Note is made up of lamellar particles. The influence of interaction forces between platelets on the macroscopic behavior is addressed. The results provide a micromechanical basis to the modelling of the behavior of clays of the smectite group, for which repulsive forces arise from the electrical interaction between the solid platelets and the interstitial fluid. To cite this article: L. Dormieux et al., C. R. Mecanique 334 (2006).     

Generation of 20-GHz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers

In this paper, we numerically and experimentally study two methods to generate 20-GHz pulse trains at 1550 nm from a dual-frequency beat-signal. The first method is based on the multiple four-wave mixing temporal compression occurring in the anomalous dispersion regime of a standard optical fiber (SMF). In the second original method, the initial sinusoidal signal is first converted into a parabolic pulses train through nonlinear propagation in a normally dispersive fiber. A subsequent linear compression in an anomalous dispersive fiber leads to well-separated picosecond pulses.     

Structure and electrochemistry of thin-film oxides grown by laser-pulsed deposition

Thin films of V₂O₅, LiCoO₂ and LiMn₂O₄ were grown by pulsed-laser deposition in the view of their use in lithium microbatteries. Lithiated polycrystalline crystalline thin dense films grown without post-deposition annealing were formed onto substrates maintained at low temperature (300 °C) from a sintered composite target including Li₂O as additive. The structural characterizations of these films have been carried out by X-ray diffraction and Raman scattering spectroscopy. The electrochemical features of thin films are investigated by cyclic voltammetry and their charge-discharge profiles in lithium microbatteries are shown. Paper presented at the 7th Euroconference on Ionics, Calcatoggio, Corsica, France, Oct. 1–7, 2000.