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Method of Characteristic for Functional Equations in Polynomial Form

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Acta Mathematica Sinica,English Series 1997年第3期13卷 421-432页

作者： janusz matkowski (Department of mathematics,technical university of bielsko-biala 43-309 bielsko-biala,poland)zhang weinian (Department of mathematics,Sichung Union university,East Area,Chengdu 610041,China) Department of mathematics Technical University of Bielsko-Biala Department of mathematics Sichung Union University

Properties of continuous solutions of a second order polynomial-like iterated functional equation are given by considering its characteristic.A useful method to discuss the general case is described indeed in this pro... 详细信息

关键词： Functional equation Iterative root Characteristic equation Recursive construction

Persistence of bounded solutions to degenerate Sobolev-Galpern equations

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Science China mathematics 2010年第11期53卷 2831-2846页

作者： ZHU ChangRong1.& zhang {1.2, 1.chool of mathematics, Chongqing university, Chongqing 400044, China 2Yangtze Center of mathematics and Department of mathematics, Sichuan university, Chengdu 61.064, China 1. School of mathematics Chongqing University Chongqing 400044 China2. Yangtze Center of Mathematics and Department of Mathematics Sichuan University Chengdu 610064 China

In this paper the persistence of bounded solutions to degenerate evolution equations of Sobolev-Galpern type is discussed. In order to define the evolution operator well, we study the existence and uniqueness of solutions to its linear form. On this basis we discuss exponential dichotomies of the evolution operator and give the Fredholm alternative result for bounded solutions of nonhomogeneous linear degenerate equations. This result enables us to give a condition for the persistence of bounded solutions of a general degenerate nonlinear autonomous equation under a nonautonomous perturbation.

关键词： degenerate evolution equation Sobolev-Galpern type boundedness Fredholm alternative exponential dichotomy

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science China mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1.zhang Baolin~(1.2) & LIU Yang~1.1. Department of {1.,Wuhan university,Wuhan 430072,China 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational {1.,Beijing 1.0088. China 1. Department of mathematics Wuhan University 430072 Wuhan China 2. Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

Research on the Low Detonation Velocity Explosives Containing Nitroesters

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含能材料 2002年第1期10卷 24-26页

作者： Andrzej WOJEWσDKA 1.andrzej MARANDA 2 (1. Silesian{1. of Gliwice,44-1.0 Gliwice, poland 2. Military university of Technology,00-908 Warsaw, poland) Silesian technical university of Gliwice Gliwice 波兰Military university of Technology Warsaw

Some explosive mixtures detonating at low velocity were experimentally investigated. Detonation velocity and critical diameter were measured for mixtures,being different in composition and density. An attempt of physi... 详细信息

关键词：爆炸速度硝基盐硝基酯引爆采矿工业混合物低速度临界参数

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： zhang Dexue {1. YANG Zhongqiang 2.1. Department of mathematics, Sichuan university, Chengdu 61.064, China 2. Department of mathematics, Shaanxi Normal university, Xi’an 71.062, China Department of mathematics Sichuan University Chengdu China Department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science China mathematics 2005年第9期48卷 1245-1259页

作者： zhang Xiaoxia~(1.2) & GUO Maozheng~(1.3) 1. School of Mathematical Sciences,Peking {1.,Beijing 1.0871.China 2. Department of mathematics,Yantai {1.,Yantai 264005,China 3. LMAM,Peking {1.,Beijing 1.0871.China 1. School of Mathematical Sciences Peking University 100871 Beijing China 2. Department of mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

Mechanical model of vulnerable atherosclerotic plaque rupture

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Science China(Physics,Mechanics & Astronomy) 2004年第4期47卷 452-462页

作者： SU Haijun1. zhang Mei2 & zhang Yun2.1. School of mathematics and System Science, Shandong university, Jinan 2501.0, China 2. Qilu Hospital, Shandong university, Jinan 25001., China 1. School of mathematics and System Science Shandong University 250100 Jinan China 2. Qilu Hospital Shandong University 250012 Jinan China

Rupture of atherosclerotic plaque is the main trigger of acute cardiovascular events, but the mechanism of plaque rupture is still unknown. We have constructed a model describing the motion of the fibrous cap of the plaque using the theory of elastic mechanics and studied the stability of the plaque theoretically. It has shown that plaque rupture is the result of a dynamic interplay between factors intrinsic to the plaque itself and extrinsic factors. We have proposed a new mechanism of plaque rupture, given a new explanation about the nonlinear dynamic progress of atherosclerosis and suggested a method to identify the vulnerable plaques to manage atherosclerosis.

关键词： fibrous cap, parametric resonance, stability, mechanism, identification.

Global convergence property of s-dependent GFR conjugate gradient method

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Chinese Science Bulletin 1998年第23期43卷 1959-1965页

作者： WANG Changyu 1.2 and zhang Yuzhong\+1.1. Institute of Operations Research in Qufu Normal {1., Qufu 2731.5, China 2. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 1.0080, China Institute of Operations Research Qufu Normal University Qufu China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

An \%S\%_dependent GFR method and a generalized conjugate gradient method are designed. Two estimated values of upper bounds for the ratio of β k to β FR k are given. The two convergence theorems are proved. The global convergent properties of \%s\%_dependent GFR method are obtained adopting several choice strategies of steplength and some results in recent literature are extended.

关键词： steplength linear search global convergence conjugate gradient.

Weighted composition operators between μ-Bloch spaces on the unit ball

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Science China mathematics 2005年第10期48卷 1349-1368页

作者： zhang Xuejun~1.& XIAO Jianbin~{1. College of mathematics and Computer Science,Hunan Normal university,Changsha 41.006,China(email:xuejunttt@263. net) 2. The School of Science,Hangzhou Dianzi university,Hangzhou 31.037,China 1. College of mathematics and Computer Science Hunan Normal University 410006 Changsha China 2. The School of Science Hangzhou Dianzi University 310037 Hangzhou China

In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^***... 详细信息

关键词： μ-Bloch space, weighted composition operator, boundedness, compactness.