On spectral projections of elliptic operators
On spectral properties of adiabatically perturbed Schroedinger operators with periodic potentials
On spectral properties of the Laplace operator via boundary perturbation.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On the acoustic impedence condition for ondulated boundary
On the antimaximum principle for parabolic periodic problems with weight.
On the approximation of the spectrum of the Stokes operator
On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator H... W in a spectral gap of H.
On the asymptotics of scattering phases for the Schrödinger equation
On the average value for nonconstant eigenfunctions of the -Laplacian assuming Neumann boundary data.
On the backward heat problem: evaluation of the norm of .
On the best observation of wave and Schrödinger equations in quantum ergodic billiards
This paper is a proceedings version of the ongoing work [20], and has been the object of the talk of the second author at Journées EDP in 2012.In this work we investigate optimal observability properties for wave and Schrödinger equations considered in a bounded open set , with Dirichlet boundary conditions. The observation is done on a subset of Lebesgue measure , where is fixed. We denote by the class of all possible such subsets. Let . We consider first the benchmark problem of maximizing...
On the Bethe-Sommerfeld conjecture
We consider the operator in , of the form with a function periodic with respect to a lattice in . We prove that the number of gaps in the spectrum of is finite if . Previously the finiteness of the number of gaps was known for . Various approaches to this problem are discussed.
On the completeness in three body scattering
On the convergence of eigenvalues for mixed formulations
On the convergence of SCF algorithms for the Hartree-Fock equations
On the convergence of SCF algorithms for the Hartree-Fock equations
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
On the curvature and torsion effects in one dimensional waveguides
We consider the Laplace operator in a thin tube of with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube's cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube's central axis and on the rotation of the cross section with respect to the Frenet frame. The main argument is a Γ-convergence theorem for a suitable sequence of quadratic energies.
On the diffraction of high-frequency waves by arbitrary shape cone. Neumann case