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Rank of loop, constraint degree of path, coupling degree of graph and their application

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Progress in Natural Science:Materials International 2005年第2期15卷 79-85页

作者： YANG Tingli1*, LUO Yufeng2, ZHANG Ce3.and YAO Fanghua1(1. SINOPIC Jinling Petrochemical Corp., Nanjing 21003., China 2. department of Mechanical Engineering, nanchang university, nanchang 3.0029, China 3. department of Mechanical Engineering, Tianjin university, Tianjin 3.0072, China) SINOPIC Jinling Petrochemical Corp. Nanjing 210037 China. department of Mechanical Engineering Nanchang University Nanchang 330029 China. department of Mechanical Engineering Tiánjin University Tianjin 300072 China

Some new concepts (rank of a loop, degree of freedom of a graph, path unit and ordered path arrangement, constraint degree of path, coupling degree of a graph, basic graph, etc.), formulas, and algorithms, are proposed in this paper. Based on these concepts, a new systematic theory and practical method for the design of topological structure, kinematics and dynamics of mechanical systems is established. Some conjectures and problems needed to be researched are also put forward. The concepts, formulae and algorithms presented in this paper will find wide potential applications.

关键词： rank of loop degree of freedom of graph constraint degree of path coupling degree of graph

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (Shum Kar-ping) 3.. department of mathematics, Xi’an university of Architecture & Technology, Xi’an 710055, China 2. department of mathematics, Yunnan university, Kunming 650091, China 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

Modified Wave Particle Duality and Black Hole Physics

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Communications in Theoretical Physics 2007年第7期48卷 93-98页

作者： LI Xiang department of Physics,nanchang university,nanchang 3.0047,China department of Physics Nanchang University

de Broglie relation is revisited,in consideration of a generalization of canonical commuting *** effects on particle's localization and black hole physics are also discussed,in a heuristic manner.

关键词： wave-particle duality dispersion relation localization limit black hole entropy

Synthesis of vertically aligned carbon nanotube arrays on silicon substrates

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Science China(Technological Sciences) 2004年第5期47卷 616-624页

作者： ZHENG Ruiting1, CHENG Guoan1, PENG Yibin1, 2, ZHAO Yong1, 3. LIU Huaping1 & LIANG Changlin1 1. Key Laboratory of Radiation Beam Technology and Materials Modification of Ministry of Education, department of Materials Science and Engineering, Beijing Normal university, Beijing 100875, China 2. School of Science, Civil Aviation university of China, Tianjin 3.03.0, China 3. department of Physics, nanchang university, nanchang 3.0047, China Correspondence should be addressed to Zheng Ruiting 1. Key Laboratory of Radiation Beam Technology and Materials Modification of Ministry of Education Department of Materials Science and Engineering Beijing Normal University 100875 Beijing China 2. School of Science Civil Aviation University of China 300300 Tianjin China 3. department of Physics Nanchang University 330047 Nanchang China

The growth of well-aligned carbon nanotube (CNT) arrays using a heat chemical vapor deposition system on silicon substrates is reported. The growth properties of CNT arrays are studied as a function of synthesis conditions. It is found that 750°C and 10 nm Fe film are suitable conditions for the growth of well-aligned CNT arrays. CNT arrays with a uniform diameter, thick tube wall and firm cohesion to the Si substrate can be grown for C2H2 concentration of 27%. Based on the experiment, the processes of improving the alignment of CNT arrays and cohesion between CNT arrays and Si substrates are discussed.

关键词： carbon nanotubes, vertically aligned, silicon substrate, chemical vapor deposition.

PRE-IMAGE ENTROPY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

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Journal of Systems Science & Complexity 2008年第3期21卷 441-445页

作者： Xianjiu HUANG Xi WEN Fanping ZENG department of mathematics Nanchang University Nanchang 330031 China department of Computer Nanchang University Nanchang 330031 China department of mathematics Liuzhou Theachers College Liuzhou 545004 China

The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.

关键词： Equiconjugacy non-autonomous pre-image entropy sequence of continuous self-maps

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3. XIE Chunhong 1 1. department of mathematics, Nanjing university, Nanjing 210093. China 2. department of mathematics, Henan university, Kaifeng 475001, China 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2 and YU Yuanhong 3.1. department of Applied mathematics, Beijing Institute of Technology, Beijing 100081, China 2. department of mathematics, Yunnan university, Kunming 650091, China 3. Institute of Applied mathematics, C department of Applied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

Study on the two and three-parameter working stability regions of 3.-TZP suspension

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Science China(Technological Sciences) 2006年第5期49卷 547-568页

作者： CHEN Youqiang1, 2, ZHANG Xinni3. CHEN Sha’ou3.& QI Ping3.1. department of Chemistry, Qingdao university, Qingdao 266071, China 2. department of Chemistry, Tsinghua university, Beijing 100084, China 3. department of Physics, Qingdao university, Qingdao 266071, China 1. department of Chemistry Qingdao University Qingdao 266071 China 2. department of Chemistry Tsinghua University Beijing 100084 China 3. department of Physics Qingdao University Qingdao 266071 China

We determined the variation tendency of viscosity (η) at various solids load- ing (α) for 3.-TZP suspension as a function of dispersant concentration (Cw) using vis- cosity measurement, measured the diameter of particles as a function of Cw in very dilute suspension using light scattering method, and obtained the surface features of the sedi- ment of suspension with different Cw using SEM. We also discussed the influence of the microstructure of adsorbed polymer layers on particles and their interactions in the dis- persing medium on the stability of suspension. Then two different stable states and two different unstable states for 3.-TZP suspension were given. Accordingly, the (Cw, η), (Cw, α), and (α, η) two-parameter, and (Cw, α, η) three-parameter stability maps were con- structed. Based on the DLVO theory calculations, the dispersant concentration, particle distance (r), and interparticle potential energy (VT) maps with various solids loading for 3.-TZP aqueous suspension were also constructed. In (Cw, r) two-parameter coordinate system, the stable motion region map for particles was established. The Cw, α, and VT,max (the highest potential energy) surface of the potential barrier map was obtained through calculation and simulation on the basis of the surfaces of Cw, r, VT maps introduced above. The (Cw, α) two-parameter stability map was then obtained from the Cw, α, VT,max map. The results showed that this theoretical map can qualitatively prove the experimentally obtained results—the existence of different dispersed states of particles in suspension system and the variation tendency of suspension stability with changing each parame- ter—were reasonable.

关键词： 3.-TZP, suspension, stability, DLVO theory, interparticle potential energy.

Online uniform machine covering with the known largest size

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Progress in Natural Science:Materials International 2007年第11期17卷 1271-1278页

作者： Cao Shunjuan1,2 and Tan Zhiyi1,3.1. department of mathematics, Zhejiang university, Hangzhou 3.0027, China 2. department of mathematics, Zhejiang Forestry university, Hangzhou 3.13.0, China 3. State Key Laboratory of CAD & CG, Zhejiang university, Hangzhou 3.0027, China) department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Zhejiang Forestry University Hangzhou 311300 China State Key Laboratory of CAD & CG Zhejiang University Hangzhou 310027 China

This paper investigates the semi-online scheduling problem with the known largest size on two uniform machines. The objective is to maximize the minimum machine completion time. Both lower bounds and algorithms are given. Algorithms are optimal for the majority values of s≥1, where s is the speed ratio of the two machines. The largest gap between the competitive ratio and the lower bound is about 0.064. Moreover, the overall competitive ratio 2 matches the overall lower bound.

关键词： scheduling and covering uniform machine design and analysis of algorithm online competitive ratio