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Spectra of the Energy Operator of Four-Electron Systems in the Impurity Hubbard Model. Triplet State

Journal of Applied Mathematics and Physics 2021年第11期9卷 2776-2795页

作者： S. M. Tashpulatov R. T. Parmanova Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of four-electron systems in an impurity Hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity Hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

关键词： Hubbard Model essential spectrum Discrete spectrum Four Electron Systems Quintet State Triplet State Singlet State Spectra

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Exponential Stability of a Robot with Safety System

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Journal of Systems Science and Information 2009年第3期7卷 201-214页

作者： Lihua Jin Aidong Jin Yufeng Zhang Department of Mathematics Science College Yanbian University Yanji 133002 China Teachers college Yanbian University Yanji 133002 China

This paper presents the analysis of exponential stability of a system consisting of a robot and its associated safety mechanism. The system have various modes of failures and is repairable. The paper investigates the nonnegative stead-state solution of system,the existence of strictly dominant eigenvalue and restriction of essential spectrum growth bound of the system operator. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that the dynamic solution of the system is exponential stab＇flity and converges to the steady-state solution.

关键词： repairable system nonnegative solution simple eigenvalue strictly domi- nant eigenvalue essential spectrum perturbation exponential stability

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Exponential Stability Analysis of a Redundant Robot Configuration with a Built-in Safety System

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Journal of Systems Science and Information 2009年第4期7卷 289-293页

作者： Xin Zhang North College of Beijing University of Chemical Technology Sanhe 065210 China

The paper presents a model of a redundant robot configuration with a built-in safety. By the method of strong continuous semi-group, the paper analyzes the essential spectrum of the system operator before and after perturbation. The results show that in s special condition, the dynamic solution of the system is exponential stability and tends to the steady solution of the system.

关键词： strictly dominant eigenvalue essential spectrum disturbance exponential stability

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On essential Spectra of 2 × 2 Operator Matrices

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Journal of Mathematical Research and Exposition 2008年第2期28卷 359-365页

作者： LIYuan DUHongKe College of Mathematics and Information Science Shaanxi Normal University Shaanxi 710062 China

Let MX=（A C X B ）be a 2×2 operator matrix acting on the Hilbert space H＋K. For given A∈B（H）,B∈B（K）and C∈B（K,H）the set UX∈B（H,K）^σe（MX）is determined, whereσe（T）denotes the essential spectrum.

关键词： essential spectrum 2 ×2 operator matrices.

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