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Ruixing Long - One of the best experts on this subject based on the ideXlab platform.

  • Spectral controllability for 2D and 3D linear Schrödinger equations
    2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of ℝn, n = 2; 3, subjected to a uniform electric field in space. Under the dipolar moment approximation, the wave function solves a PDE of Schrödinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time (K al) if Ω is the bottom of the well, then for every eigenvalue λ of - ΔDΩ, the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in ℝn. In 3D, our main result states that spectral controllability in finite time never holds for one-directional dipolar moment. The proof uses classical results from trigonometric moment theory and properties about the set of zeros of entire functions. In 2D, we first prove the existence of a minimal time Tmin(Ω) andgt; 0 for spectral controllability i.e., if T andgt; Tmin(Ω), one has spectral controllability in time T if condition (K al) holds true for (Ω) and, if T andlt; T min(Ω) and the dipolar moment is one-directional, then one does not have spectral controllability in time T. We next characterize a necessary and sufficient condition on the dipolar moment insuring that spectral controllability in time T andgt; Tmin(Ω) holds generically with respect to the domain. The proof relies on shape differentiation and a careful study of Dirichlet-to-Neumann operators associated to certain Helmholtz equations. ©2009 IEEE.

  • Spectral controllability for 2D and 3D linear Schrödinger equations
    Journal of Functional Analysis, 2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of RnRn, n=2,3n=2,3, subjected to a control which is a uniform (in space) electric field. Under the dipolar moment approximation, the wave function solves a PDE of Schrödinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time: (Kal ) if Ω is the bottom of the well, then for every eigenvalue λ of View the MathML source−ΔΩD, the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in RnRn. In 3D, our main result states that spectral controllability in finite time never holds for one-directional dipolar moment. The proof uses classical results from trigonometric moment theory and properties about the set of zeros of entire functions. In 2D, we first prove the existence of a minimal time Tmin(Ω)>0Tmin(Ω)>0 for spectral controllability, i.e., if T>Tmin(Ω)T>Tmin(Ω), one has spectral controllability in time T if condition (Kal ) holds true for (Ω ) and, if TTmin(Ω) holds generically with respect to the domain. The proof relies on shape differentiation and a careful study of Dirichlet-to-Neumann operators associated to certain Helmholtz equations. We also show that one can recover exact controllability in abstract spaces from this 2D spectral controllability, by adapting a classical variational argument from control theory.

  • CDC - Spectral controllability for 2D and 3D linear Schrödinger equations
    Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of ℝn, n = 2; 3, subjected to a uniform electric field in space. Under the dipolar moment approximation, the wave function solves a PDE of Schrodinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time: (Kal) if Ω is the bottom of the well, then for every eigenvalue λ of ΔD Ω the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in ℝn.

Lixing Han - One of the best experts on this subject based on the ideXlab platform.

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

  • Sensitivitas Keputusan Terhadap Nilai Eigenvector Dengan Pendekatan Weight Product Model
    2017
    Co-Authors: Akmaludin Akmaludin
    Abstract:

    Analytic Hierarchical Process (AHP) is a widely used method for determining thepriority decision is plural, because it is able to process data with a lot of good data criteria arequalitative, quantitative, or a combination of both. Changes to the value of the decision that isstrong or weak against the decisions that have been treated empirically. Thus the globaldecisions that have been in the synthesis can be amended, if the partial decision experiencingweak sensitivity. Therefore, to prove that local decisions each value tested pairwise matrix ofvalues Normalized Eigenvector results do not necessarily provide perfect power, it can be seen ifthe process is carried out sensitivity tests of each Eigenvector value of the partial decision. Thesensitivity of the test results will give the amount of value judgment which has the value of acertain range of the limit value of the minimum sensitivity and sensitivity maximum value thatcan affect the priority value of the global decisions synthesis results. Keywords: analytic hierarchical process, Eigenvector.priority, sensitivity.

  • Sensitivitas Keputusan Terhadap Nilai Eigenvector DenganPendekatan Weight Product Model
    Lembaga Penelitian dan Pengabdian Masyarakat Universitas Bina Insani, 2017
    Co-Authors: Akmaludin Akmaludin
    Abstract:

    Abstrak: Analytic Hierarchical Process (AHP) merupakan suatu metode yang cukup banyakdigunakan untuk menentukan prioritas keputusan yang bersifat majemuk, karena mampumengolah data dengan banyak kriteria baik data yang bersifat kualitatif, kuantitatif, maupunkombinasi keduanya. Perubahan terhadap nilai keputusan ada yang bersifat kuat atau lemahterhadap hasil keputusan yang telah diproses secara empiris. Dengan demikian keputusanglobal yang telah di sintesis dapat mengalami perubahan, jika keputusan parsial mengalaminilai sensitivitas yang lemah. Oleh karena itu untuk membuktikan bahwa keputusan local setiapnilai pairwise matrix yang diuji dari nilai Eigenvector hasil normalisasi belum tentu memberikankekuatan keputusan yang sempurna, hal ini dapat terlihat jika dilakukan proses uji sensitivitas dari masing-masing nilai Eigenvector keputusan parsial. Hasil pengujian sensitivitas ini akanmemberikan besaran nilai keputusan yang memiliki nilai jangkauan tertentu terhadap batas nilaisensitivitas minimum dan sensitivias nilai maksimum yang dapat mempengaruhi prioritas nilaikeptusan global hasil sintesis. Kata kunci: analytic hierarchical process, Eigenvector, prioritas, sensitivitas. Abstract: Analytic Hierarchical Process (AHP) is a widely used method for determining thepriority decision is plural, because it is able to process data with a lot of good data criteria arequalitative, quantitative, or a combination of both. Changes to the value of the decision that isstrong or weak against the decisions that have been treated empirically. Thus the globaldecisions that have been in the synthesis can be amended, if the partial decision experiencingweak sensitivity. Therefore, to prove that local decisions each value tested pairwise matrix ofvalues Normalized Eigenvector results do not necessarily provide perfect power, it can be seen ifthe process is carried out sensitivity tests of each Eigenvector value of the partial decision. Thesensitivity of the test results will give the amount of value judgment which has the value of acertain range of the limit value of the minimum sensitivity and sensitivity maximum value thatcan affect the priority value of the global decisions synthesis results. Keywords: analytic hierarchical process, Eigenvector.priority, sensitivity.  

Karine Beauchard - One of the best experts on this subject based on the ideXlab platform.

  • Spectral controllability for 2D and 3D linear Schrödinger equations
    2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of ℝn, n = 2; 3, subjected to a uniform electric field in space. Under the dipolar moment approximation, the wave function solves a PDE of Schrödinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time (K al) if Ω is the bottom of the well, then for every eigenvalue λ of - ΔDΩ, the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in ℝn. In 3D, our main result states that spectral controllability in finite time never holds for one-directional dipolar moment. The proof uses classical results from trigonometric moment theory and properties about the set of zeros of entire functions. In 2D, we first prove the existence of a minimal time Tmin(Ω) andgt; 0 for spectral controllability i.e., if T andgt; Tmin(Ω), one has spectral controllability in time T if condition (K al) holds true for (Ω) and, if T andlt; T min(Ω) and the dipolar moment is one-directional, then one does not have spectral controllability in time T. We next characterize a necessary and sufficient condition on the dipolar moment insuring that spectral controllability in time T andgt; Tmin(Ω) holds generically with respect to the domain. The proof relies on shape differentiation and a careful study of Dirichlet-to-Neumann operators associated to certain Helmholtz equations. ©2009 IEEE.

  • Spectral controllability for 2D and 3D linear Schrödinger equations
    Journal of Functional Analysis, 2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of RnRn, n=2,3n=2,3, subjected to a control which is a uniform (in space) electric field. Under the dipolar moment approximation, the wave function solves a PDE of Schrödinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time: (Kal ) if Ω is the bottom of the well, then for every eigenvalue λ of View the MathML source−ΔΩD, the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in RnRn. In 3D, our main result states that spectral controllability in finite time never holds for one-directional dipolar moment. The proof uses classical results from trigonometric moment theory and properties about the set of zeros of entire functions. In 2D, we first prove the existence of a minimal time Tmin(Ω)>0Tmin(Ω)>0 for spectral controllability, i.e., if T>Tmin(Ω)T>Tmin(Ω), one has spectral controllability in time T if condition (Kal ) holds true for (Ω ) and, if TTmin(Ω) holds generically with respect to the domain. The proof relies on shape differentiation and a careful study of Dirichlet-to-Neumann operators associated to certain Helmholtz equations. We also show that one can recover exact controllability in abstract spaces from this 2D spectral controllability, by adapting a classical variational argument from control theory.

  • CDC - Spectral controllability for 2D and 3D linear Schrödinger equations
    Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
    Co-Authors: Karine Beauchard, Yacine Chitour, Djalil Kateb, Ruixing Long
    Abstract:

    We consider a quantum particle in an infinite square potential well of ℝn, n = 2; 3, subjected to a uniform electric field in space. Under the dipolar moment approximation, the wave function solves a PDE of Schrodinger type. We study the spectral controllability in finite time of the linearized system around the ground state. We characterize one necessary condition for spectral controllability in finite time: (Kal) if Ω is the bottom of the well, then for every eigenvalue λ of ΔD Ω the projections of the dipolar moment onto every (Normalized) Eigenvector associated to λ are linearly independent in ℝn.

Shmuel Friedland - One of the best experts on this subject based on the ideXlab platform.