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Michel Vittot - One of the best experts on this subject based on the ideXlab platform.

  • perturbation of an eigen value from a dense Point spectrum a general floquet hamiltonian
    Annales De L Institut Henri Poincare-physique Theorique, 1999
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We consider a perturbed Floquet Hamiltonian i@t + H + �V (!t) in the Hilbert space L 2 ((0,T),H,dt). Here H is a self-adjoint operator in H with a discrete spectrum obeying a growing gap condition, V (t) is a symmetric bounded operator in H depending on t 2�-periodically, ! = 2�/T is a frequency andis a coupling constant. The spectrum Spec( i@t + H) of the unperturbed part is pure Point and dense in R for almost every !. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all ! and provided V (t) is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set I which need not be an interval but 0 is still a Point of Density of I. Second, the Rayleigh- Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector.

  • perturbation of an eigen value from a dense Point spectrum an example
    arXiv: Quantum Physics, 1997
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure Point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that $\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a Point of Density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series represents an asymptotic series for the function $\lambda(\beta)$. All ideas are developed and demonstrated when treating an explicit example but some of them are expected to have an essentially wider range of application.

P Duclos - One of the best experts on this subject based on the ideXlab platform.

  • perturbation of an eigen value from a dense Point spectrum a general floquet hamiltonian
    Annales De L Institut Henri Poincare-physique Theorique, 1999
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We consider a perturbed Floquet Hamiltonian i@t + H + �V (!t) in the Hilbert space L 2 ((0,T),H,dt). Here H is a self-adjoint operator in H with a discrete spectrum obeying a growing gap condition, V (t) is a symmetric bounded operator in H depending on t 2�-periodically, ! = 2�/T is a frequency andis a coupling constant. The spectrum Spec( i@t + H) of the unperturbed part is pure Point and dense in R for almost every !. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all ! and provided V (t) is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set I which need not be an interval but 0 is still a Point of Density of I. Second, the Rayleigh- Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector.

  • perturbation of an eigen value from a dense Point spectrum an example
    arXiv: Quantum Physics, 1997
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure Point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that $\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a Point of Density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series represents an asymptotic series for the function $\lambda(\beta)$. All ideas are developed and demonstrated when treating an explicit example but some of them are expected to have an essentially wider range of application.

P Stovicek - One of the best experts on this subject based on the ideXlab platform.

  • perturbation of an eigen value from a dense Point spectrum a general floquet hamiltonian
    Annales De L Institut Henri Poincare-physique Theorique, 1999
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We consider a perturbed Floquet Hamiltonian i@t + H + �V (!t) in the Hilbert space L 2 ((0,T),H,dt). Here H is a self-adjoint operator in H with a discrete spectrum obeying a growing gap condition, V (t) is a symmetric bounded operator in H depending on t 2�-periodically, ! = 2�/T is a frequency andis a coupling constant. The spectrum Spec( i@t + H) of the unperturbed part is pure Point and dense in R for almost every !. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all ! and provided V (t) is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set I which need not be an interval but 0 is still a Point of Density of I. Second, the Rayleigh- Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector.

  • perturbation of an eigen value from a dense Point spectrum an example
    arXiv: Quantum Physics, 1997
    Co-Authors: P Duclos, P Stovicek, Michel Vittot
    Abstract:

    We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure Point and dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that $\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a Point of Density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series represents an asymptotic series for the function $\lambda(\beta)$. All ideas are developed and demonstrated when treating an explicit example but some of them are expected to have an essentially wider range of application.

Jib Huh - One of the best experts on this subject based on the ideXlab platform.

  • bandwidth selections based on cross validation for estimation of a discontinuity Point in Density
    Journal of the Korean Data and Information Science Society, 2012
    Co-Authors: Jib Huh
    Abstract:

    The cross-validation is a popular method to select bandwidth in all types of kernel estimation. The maximum likelihood cross-validation, the least squares cross-validation and biased cross-validation have been proposed for bandwidth selection in kernel Density estimation. In the case that the probability Density function has a discontinuity Point, Huh (2012) proposed a method of bandwidth selection using the maximum likelihood cross-validation. In this paper, two forms of cross-validation with the one-sided kernel function are proposed for bandwidth selection to estimate the location and jump size of the discontinuity Point of Density. These methods are motivated by the least squares cross-validation and the biased cross-validation. By simulated examples, the finite sample performances of two proposed methods with the one of Huh (2012) are compared.

C. Ocampo-martinez - One of the best experts on this subject based on the ideXlab platform.

  • Distributed MPC with time-varying communication network: A Density-dependent population games approach
    2016 IEEE 55th Conference on Decision and Control (CDC), 2016
    Co-Authors: J. Barreiro-gomez, N. Quijano, C. Ocampo-martinez
    Abstract:

    This work addresses distributed control design by using Density-dependent population dynamics. Furthermore, stability of the equilibrium Point under this proposed class of population dynamics is studied, and the relationship between the equilibrium Point of Density-dependent population games (DDPG) and the solution of constrained optimization problems is shown. Finally, a distributed predictive control is designed with the proposed Density-dependent dynamics, and contemplating a time-varying communication network.