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CRITERIONS AND ALGORITHMS FOR irreducibility AND APERIODICITY OF NONNEGATIVE MATRICES

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Chinese Science Bulletin 1992年第24期37卷 2029-2031页

作者：周作领肖金声 Zhongshan University Guangzhou 510275 PRC

The irreducibility and aperiodicity (primitivity)are two basic notions in the theory of nonnegative matrices. As we know, for a nonnegative matrix, there exist no feasible algorithms for judging them, especially for aperiodicity. Usually, for a k×k nonnegative matrix, one can form an associated directed graph which has k vertices and whose directed

关键词： nonnegafive matrices irreducibility aperiodicity

Sufficient Conditions for Amalgamated 3-Manifolds to be ∂-Irreducible

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 161-172页

作者： Bing FANG Fengchun LEI Liang LIANG School of Mathematical Sciences Dalian University of TechnologyDalian 116024LiaoningChina School of Mathematics Liaoning Normal UniversityDalian 116029LiaoningChina

In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets ... 详细信息

关键词： ∂-irreducibility irreducibility Amalgamated 3-manifold Curve complex Arc complex

Isotropic polynomial invariants of Hall tensor

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Applied Mathematics and Mechanics(English Edition) 2018年第12期39卷 1845-1856页

作者： Jinjie LIU Weiyang DING Liqun QI Wennan ZOU Department of Applied Mathematics The Hong Kong Polytechnic University Department of Mathematics Hong Kong Baptist University Institute for Advanced Study Nanchang University

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.

关键词： isotropic polynomial invariant irreducibility function basis integrity basis Hall tensor

Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations

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Acta Mathematica Sinica,English Series 2011年第1期27卷 45-72页

作者： Ling CHEN Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P. R. China

We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu＇s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.

关键词： Hamiltonian Lie algebras representation simplicity irreducibility

ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

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Acta Mathematica Scientia 2020年第3期40卷 805-823页

作者： Abdul-Majeed AL-IZERI Khalid LATRACH UniversitéClermont Auvergne CNRSLMBPF-63000 Clermont-FerrandFrance

In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these *** close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

关键词： Compactness properties transport operator abstract boundary conditions asymptotic spectrum irreducibility leading eigenvalue

Modules for double affine Lie algebras

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Frontiers of Mathematics in China 2016年第1期11卷 89-108页

作者： Naihuan JING Chunhua WANG School of Mathematics South China University of Technology Guangzhou 510640 China Department of Mathematics North Carolina State University Raleigh NC 27695 USA

Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.

关键词： Double affine Lie algebra Verma module irreducibility Weylmodule

l^k,8-Singular values and spectral radius of rectangular tensors

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Frontiers of Mathematics in China 2013年第1期8卷 63-83页

作者： Chen LING Liqun QI School of Science Hangzhou Dianzi University Hangzhou 310018 China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of/k,S-singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of lk,S-singular values /vectors, some properties of the related /k＇S-spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.

关键词： Nonnegative rectangular tensor /k,S-singular value /k'S-spectralradius irreducibility weak irreducibility

Highest Weight Representations of a Family of Lie Algebras of Block Type

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Acta Mathematica Sinica,English Series 2008年第4期24卷 687-696页

作者： Xiao Qing YUE Yu Cai SU Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 P. R. China Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China

For an additive subgroup G of a field F of characteristic zero, a Lie algebra B（G） of Block type is defined with basis {Lα,i｜ α∈G, i∈Z＋} and relations [Lα,i, Lβ,j] = （β-α）Lα＋β,i＋j＋（αj-βi）Lα＋β,Lα＋β,i＋*** is proved that an irreducible highest weight B（Z）-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B（G）0^＊（the dual space of B（G）0 = span{L0,i｜i∈Z＋}）, a Verma B（G）-module M（∧,λ） is defined, and the irreducibility of M（A,λ） is completely determined.

关键词： Verma modules Lie algebras of Block type irreducibility quasifinite

Periodic solutions of hybrid jump diffusion processes

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Frontiers of Mathematics in China 2021年第3期16卷 705-725页

作者： Xiaoxia GUO Wei SUN School of Applied Mathematics Shanxi University of Finance and EconomicsTaiyuan030006China School of Mathematics and Information Sciences Guangzhou UniversityGuangzhou510006China Department of Mathematics and Statistics Concordia UniversityMontrealH3G 1M8Canada

We investigate periodic solutions of regime-switching jump *** first show the well-posedness of solutions to stochastic differential equations corresponding to the hybrid ***,we derive the strong Feller property and irreducibility of the associated time-inhomogeneous ***,we establish the existence and uniqueness of periodic *** examples are presented to illustrate the results.

关键词： Hybrid system regime-switching jump diffusion periodic solution strong Feller property irreducibility