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Highest weight representations of a Lie algebra of Block type

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Science China Mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu WU & Yu-cai SU Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China Department of Mathematics, Qufu Normal University, Qufu 273165, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China Department of Mathematics Shanghai Jiaotong University Shanghai China Department of Mathematics Qufu Normal University Qufu China Department of Mathematics University of Science and Technology of China Hefei China

For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i + 1)β- (j + 1)α)Lα+β,i+j +αδα,-βδi+j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it 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.

关键词： Verma modules Lie algebras of Block type irreducibility

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On Nonexistence of Algebraic Curve Solutions to Second-order Polynomial Autonomous Systems Over the Complex Field

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 657-662页

作者： Zhao-sheng FengDepartment of Mathematics. Texas A&M University, College Station, TX 77843, USA Department of Mathematics Texas A&M University College Station TX USA

In this paper, by using the method of algebraic analysis, the results in our previous work are generalized. These results are of importance in the qualitative theory of polynomial autonomous systems.

关键词： Autonomous system existence algebraic curve irreducibility

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Neo-Confucian Theory of Mind as a Discourse of the Infinite： The Lu-Wang School

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Frontiers of Philosophy in China 2015年第1期10卷 75-94页

作者： ZHAO Dongming Department of Philosophy College of Arts Shenzhen University Shenzhen 518060 China

This paper is a second-order study ofxinxue 心學（the Neo-Confucian theory of mind from the Lu-Wang school）. Having shown the difficulty of fitting the theory into philosophical or religious discourse, the paper will argue that it is more appropriate to see xinxue as a special variety of the ＂discourse of the infinite,＂ that is, discourse concerning the infinite, which will bring forth action. In this light, Lu Xiangshan 陸象山 and Wang Yangming＇s 王陽明 theory on the internal experience of the unity of mind is to be seen less as description of mental life than as an effort to adhere to the spirit of Mencius： they insist on the unity of the internal experience of mind, without allowing its intensity to be reduced in the explanatory theory of lixue 理學（theory of principles） espoused by Cheng Yi 程頤 and Zhu Xi 朱熹, and, in this way, strive to reaffirm Mencius＇s proclamation about the goodness of human nature. More importantly, the discourse as a whole works to enhance the status of the sage as someone who embodies tianli 天理（the highest moral principle of the universe）. This mode of discourse has the performative force of bringing forth moral actions. The real subject ofxinxue is not what Lu and Wang claim it to be, e.g. the essentially good human nature or the infinite moral mind. Rather, the subject of xinxue is that which reveals itself through a series of effortful discursive activities and in the moral practice thereby produced. The subject of xinxue that emerges from this continuous process of striving is a special subject even within the Confucian tradition, whose attention is directed mainly towards the internal experience of the unity of mind. This subject threatens to interrupt the intellectual as well as socio-political operations established by lixue, and therefore engenders a series of conflicts.

关键词： xinxue discourse of the infinite metaphysics irreducibility subject

Asymptotic Stability of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations

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World Journal of Engineering and Technology 2015年第3期3卷 277-283页

作者： Abdukerim Haji College of Mathematics and System Sciences Xinjiang University Urumqi 830046 China

We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By analysing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

关键词： Gaver’s Parallel Pystem C0-Semigroup irreducibility Asymptotic Stability

Asymptotic Stability of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman

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Journal of Applied Mathematics and Physics 2017年第1期5卷 185-193页

作者： Tursunjan Keyim Abdukerim Haji College of Mathematics and System Sciences Xinjiang University Urumqi China

We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

关键词： Series-Parallel Repairable System C0-Semigroup irreducibility Asymptotic Stability

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广义对角占优矩阵的判定准则

高等学校计算数学学报 2012年第1期34卷 23-29页

作者：王峰菏泽学院数学系

1引言广义对角占优矩阵在理论上和应用上都十分重要,它的研究已广泛引起人们的注意.最近,许多文章都在寻求它的简单实用的判别([1-8]).本文在文[1-7]的基础上,讨论了广

关键词： generalized diagonally dominant matrix strictly diagonally dominant matrix irreducibility chain of nonzero elements

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广义严格对角占优矩阵的充分条件

高等学校计算数学学报 2009年第4期31卷 310-318页

作者：丁碧文刘建州湘潭大学数学与计算科学学院

1引言广义严格对角占优矩阵是一类在数值代数、数学物理和控制论等领域有着广泛应用的特殊矩阵,例如:线性方程组Ax=b,当系数矩阵A为广义严格对角占优矩阵时,许多经典的迭代算法均是收敛的,同时对目前提出的一些修正算法也是收敛的,因此... 详细信息

1引言广义严格对角占优矩阵是一类在数值代数、数学物理和控制论等领域有着广泛应用的特殊矩阵,例如:线性方程组Ax=b,当系数矩阵A为广义严格对角占优矩阵时,许多经典的迭代算法均是收敛的,同时对目前提出的一些修正算法也是收敛的,因此,寻找广

关键词： strictly diagonally dominant matrix generalized strictly diagonally dominant matrix irreducibility nonzero elements chain

The Geometrical Theory of the Structure of Nuclei, Atoms, and Molecules

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Applied Mathematics 2014年第15期5卷 2209-2215页

作者： Amagh Nduka Department of Physics and Mathematics Federal University of Technology Owerri Nigeria

Quantum geometrodynamics (QGD) has established the following fundamental facts: First, every elementary particle is the physical realization of a certain irreducible 4-quantum operator of spin (rank) 0, 1/2 or 1. A photon (boson) is the physical realization of an irreducible 4-quantum operator of spin zero. A fermion is the physical realization of an irreducible 4-quantum operator of spin 1/2. A graviton (boson) is the physical realization of an irreducible 3-quantum operator of spin zero, and the Ws and mesons (bosons) are the physical realizations of irreducible 3-quantum operator of rank one. Second, the particles of every composite fermion system (nuclei, atoms, and molecules) reside in a certain 4-quantum space which is partitioned into an infinite set of subspaces of dimension 4n (n = 1, 2, 3, L,?∞;n is the index of the subspace and n is called principal quantum number by physicists, and period by chemists) each of which is reducible to a set of 2-level cells [1]. With these two fundamental facts, the complexities associated with atomic, nuclear, and molecular many-body problems have evaporated. As an application of the reducibility scenario we discuss in this paper the explicit construction of the periodic table of the chemical elements. In particular we show that each chemical element is characterized by a state ket |En;l, m1;s, ms〉where l is orbital angular momentum, s = 1/2, En = E1 + khv (k = 1, 2, 3, L, ∞, E1 is the Schr?dinger first energy level, and v is the Lamb-Retherford frequency).

关键词： Reducibility irreducibility Periodicity Fermion Quantum Number Index

Asymptotic Stability of the Dynamic Solution of an N-Unit Series System with Finite Number of Vacations

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Journal of Applied Mathematics and Physics 2018年第11期6卷 2202-2218页

作者： Abdugeni Osman Abdukerim Haji Askar Ablimit College of Mathematics and System Sciences Xinjiang University Urumqi China School of Mathematics and Physics Xinjiang Education Institute Urumqi China

We investigate an N-unit series system with finite number of vacations. By analyzing the spectral distribution of the system operator and taking into account the irreducibility of the semigroup generated by the system operator we prove that the dynamic solution converges strongly to the steady state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.

关键词： N-Unit Series System C0-Semigroup irreducibility Asymptotic Stability