On the symplectic phase space of KdV

We prove that the Birkhoff map \Om for KdV constructed on H^{-1}_0(\T) can be interpolated between H^{-1}_0(\T) and L^2_0(\T). In particular, the symplectic phase space H^{1/2}_0(\T) can be described in terms of Birkhoff coordinates. As an application, we characterize the regularity of a potential q\in H^{-1}(\T) in terms of the decay of the gap lengths of the periodic spectrum of Hill's operator on the interval $[0,2]$

Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.Comment: 20 page

Studies of the Influence of Al Doping Agents Nature on the Physical Properties Al:ZnO Films Deposited by Spin-Coating Technique

Date du colloque : 09/2010International audienc

Influence of Al doping agents nature on the physical properties of Al: ZnO films deposited by spin-coating technique

cited By 14International audienceIn this paper we present the morphological,structural, optical and electrical properties of aluminium doped zinc oxide films prepared by spin coating technique from a zinc acetate dihydrate and 2-methoxyethanol (0.5M) solution. AlCl3and Al(NO3)3were used as doping agents in different concentrations (1at%, 4at% and 6at% in starting solution). After deposition, films were dried at 100°C and then annealed at temperatures between 400°C and 500°C. The characterization of deposited layer was performed by Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM) and UV-Vis spectroscopy. The results show that the optical and electrical properties of the structures strongly depend on the deposition conditions of ZnO:Al.In addition, the resistivity can be easily varied depending on ZnO:Al annealing temperatures and Al concentration