The Experts below are selected from a list of 165 Experts worldwide ranked by ideXlab platform

Chris Judge - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Simplicity and Asymptotic Separation of Variables
    Communications in Mathematical Physics, 2011
    Co-Authors: Luc Hillairet, Chris Judge
    Abstract:

    We describe a method for comparing the spectra of two real-analytic families, ( a _ t ) and ( q _ t ), of quadratic forms that both degenerate as a positive parameter t tends to zero. We suppose that the family ( a _ t ) is amenable to ‘separation of variables’ and that each eigenSpace of a _ t is 1-dimensional for some t . We show that if ( q _ t ) is asymptotic to ( a _ t ) at first order as t → 0, then the eigenSpaces of ( q _ t ) are also 1-dimensional for all but countably many t . As an application, we prove that for the generic triangle (simplex) in Euclidean Space (Constant curvature Space form) each eigenSpace of the Laplacian acting on Dirichlet functions is 1-dimensional.

  • Spectral simplicity and asymptotic separation of variables
    Communications in Mathematical Physics, 2011
    Co-Authors: Luc Hillairet, Chris Judge
    Abstract:

    We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean Space (Constant curvature Space form) each eigenSpace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.

C. V. Usenko - One of the best experts on this subject based on the ideXlab platform.

  • Scalar Charged Particle in Weyl–Wigner–Moyal Phase Space. Constant Magnetic Field
    Journal of Russian Laser Research, 2002
    Co-Authors: B. I. Lev, A. A. Semenov, C. V. Usenko
    Abstract:

    A relativistic phase-Space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables) is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and Constant magnetic field). The differences in the equations are connected with the peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.

  • Scalar charged particle in Weyl--Wigner--Moyal phase Space. Constant magnetic field
    arXiv: Quantum Physics, 2001
    Co-Authors: B. I. Lev, A. A. Semenov, C. V. Usenko
    Abstract:

    A relativistic phase-Space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables)is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and Constant magnetic field). The differences in the equations are connected with peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.

Zhengling Huang - One of the best experts on this subject based on the ideXlab platform.

  • Study on correlation between the surround Space Constant of Retinex center/surround algorithm and images
    2010 IEEE International Conference on Mechatronics and Automation, 2010
    Co-Authors: Ziwu Wang, Fei Bei, Zhengling Huang
    Abstract:

    Generally the surround Space Constant of Retinex's center/surround algorithm is an empirical value that is between 25 and 250, and it is of small images. For the larger engineering images, how much should the parameter value be? In addition, in this algorithm, convolution is an operation whose efficiency is very low. It is a bottleneck that has impact on this algorithm's application in image engineering. How to solve this problem will have impact on the algorithm's application in the practical engineering.

Luc Hillairet - One of the best experts on this subject based on the ideXlab platform.

  • Spectral Simplicity and Asymptotic Separation of Variables
    Communications in Mathematical Physics, 2011
    Co-Authors: Luc Hillairet, Chris Judge
    Abstract:

    We describe a method for comparing the spectra of two real-analytic families, ( a _ t ) and ( q _ t ), of quadratic forms that both degenerate as a positive parameter t tends to zero. We suppose that the family ( a _ t ) is amenable to ‘separation of variables’ and that each eigenSpace of a _ t is 1-dimensional for some t . We show that if ( q _ t ) is asymptotic to ( a _ t ) at first order as t → 0, then the eigenSpaces of ( q _ t ) are also 1-dimensional for all but countably many t . As an application, we prove that for the generic triangle (simplex) in Euclidean Space (Constant curvature Space form) each eigenSpace of the Laplacian acting on Dirichlet functions is 1-dimensional.

  • Spectral simplicity and asymptotic separation of variables
    Communications in Mathematical Physics, 2011
    Co-Authors: Luc Hillairet, Chris Judge
    Abstract:

    We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean Space (Constant curvature Space form) each eigenSpace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.

B. I. Lev - One of the best experts on this subject based on the ideXlab platform.

  • Scalar Charged Particle in Weyl–Wigner–Moyal Phase Space. Constant Magnetic Field
    Journal of Russian Laser Research, 2002
    Co-Authors: B. I. Lev, A. A. Semenov, C. V. Usenko
    Abstract:

    A relativistic phase-Space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables) is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and Constant magnetic field). The differences in the equations are connected with the peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.

  • Scalar charged particle in Weyl--Wigner--Moyal phase Space. Constant magnetic field
    arXiv: Quantum Physics, 2001
    Co-Authors: B. I. Lev, A. A. Semenov, C. V. Usenko
    Abstract:

    A relativistic phase-Space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables)is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and Constant magnetic field). The differences in the equations are connected with peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed.