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Concatenating construction of the multisymplectic schemes for 2+1-dimensional sine-Gordon equation

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science china mathematics 2004年第1期47卷 18-30页

作者： WANG Yushun, WANG Bin & QIN MengzhaoLASG, institute of atmospheric physics, chinese academy of sciences, beijing 100029, china school of mathematics and computer science, nanjing normal university, nanjing 210097, china school of mathematics and System science, chinese academy of sciences, beijing 100080, china 1. LASG Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing China 2. school of mathematics and computer science Nanjing Normal University 210097 Nanjing China 3. school of mathematics and System science Chinese Academy of Sciences 100080 Beijing China

In this paper, taking the 2+1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.

关键词： 2+l-climensional sine-Gordon equation multisymplectic scheme concatenating method solitons

Multisymplectic five-point scheme for the nonlinear wave equation

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chinese science Bulletin 2003年第S2期48卷 24-29页

作者： WANG Yushun~(1,2), WANG Bin~1, YANG Hongwei~1 & WANG Yunfeng~1 1. LASG, institute of atmospheric physics, chinese academy of sciences, beijing 100029. china 2. Permanent address: school of mathematics and computer science, nanjing normal university, nanjing 210097. china chinese Acad Sci Inst Atmospher Phys LASG Beijing 100029 Peoples R China nanjing normal Univ Sch Math & Comp Sci Nanjing 210097 Peoples R China

In this paper, we introduce the multisymplecticstructure of the nonlinear wave equation, and prove that theclassical five-point scheme for the equation is multisymplec-tic. Numerical simulations of this multisymplectic scheme onhighly oscillatory waves of the nonlinear Klein-Gordonequation and the collisions between kink and anti-kink soli-tons of the sine-Gordon equation are also provided. The mul-tisymplectic schemes do not need to discrete PDEs in thespace first as the symplectic schemes do and preserve notonly the geometric structure of the PDEs accurately, but alsotheir first integrals approximately such as the energy, themomentum and so on. Thus the multisymplectic schemeshave better numerical stability and long-time numerical be-havior than the energy-conserving scheme and the symplec-tic scheme.

关键词： symplectic schelne energy-conserving scheme multisymplectic scheme nonlinear wave equation.

P2P traffic optimization

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science china(Information sciences) 2012年第7期55卷 1475-1492页

作者： ZHANG GuoQiang 1,2 ,TANG MingDong 3 ,CHENG SuQi 2,4 ,ZHANG GuoQing 2 ,SONG HaiBin 5 ,CAO JiGuang 6 & YANG Jing 7 1 school of computer science and Technology,nanjing normal university,nanjing 210046,china 2 institute of Computing Technology,chinese academy of sciences,beijing 100190,china 3 school of computer science and Engineering,Hunan university of science and Technology,Xiangtan 411201,china 4 Graduate university of chinese academy of sciences,beijing 100190,china 5 nanjing R&D Center,Huawei Technologies,nanjing 210012,china 6 china academy of Telecommunication Research of MIIT,beijing 100191,china 7 china Mobile Research institute,beijing 100053,china 1. school of computer science and Technology Nanjing Normal University Nanjing 210046 China2. Institute of Computing Technology Chinese Academy of Sciences Beijing 100190 China3. School of Computer Science and Engineering Hunan University of Science and Technology Xiangtan 411201 China4. Graduate University of Chinese Academy of Sciences Beijing 100190 China5. Nanjing R&D Center Huawei Technologies Nanjing 210012 China6. China Academy of Telecommunication Research of MIIT Beijing 100191 China7. China Mobile Research Institute Beijing 100053 China

Peer-to-peer (P2P) based content distribution systems have emerged as the main form for content distribution on the Internet,which can greatly reduce the distribution cost of content providers and improve the overall system ***,the mismatch between the overlay and underlay networks causes large volume of redundant traffic,which intensifies the tension between P2P content providers and ***,how to efficiently use network resources to reduce the traffic burden on the ISPs is crucial for the sustainable development of P2P *** paper surveys the state-of-art P2P traffic optimization technologies from three perspectives:P2P cache,locality-awareness and data *** details,comparison between these technologies and their applicabilities are presented,followed by a discussion of the issues that remain to be addressed and the direction of future content distribution research.

关键词： P2P traffic localization P2P traffic optimization P2P cache locality-awareness network coding content-centric network

Communication network designing:Transmission capacity,cost and scalability

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science china(Information sciences) 2012年第11期55卷 2454-2465页

作者： ZHANG GuoQiang1,2,3 & ZHANG GuoQing1 1institute of Computing Technology,chinese academy of sciences,beijing 100190,china 2school of computer science and Technology,nanjing normal university,nanjing 210046,china 3Provincial Key Laboratory for computer Information Processing Technology,Soochow university,Suzhou 215000,china 1. institute of Computing Technology Chinese Academy of Sciences Beijing 100190 China2. School of Computer Science and Technology Nanjing Normal University Nanjing 210046 China3. Provincial Key Laboratory for Computer Information Processing Technology Soochow University Suzhou 215000 China

Despite the growing number of works centering around the traffic dynamics on complex networks,these researches still have some common shortcomings,e.g.,too simple traffic flow model and lack of considerations for the designing cost and scalability *** paper builds on a more realistic traffic flow model,and offers a holistic view on the network designing *** addition to the extensively studied transmission capacity,this paper takes designing cost and scalability as two other designing objectives,and presents a quantitative study of how different designing choices independently and collectively influence these objectives by the introduction of a cartesian coordinate *** is shown that different kinds of network topologies display different shapes of achievable solution spaces and exhibit different abilities to achieve cost-effective and scalable *** particular,we find the philosophy underlying empirical network designing and engineering today fails to meet the cost-effective and scalable designing requirements,and propose a cost-effective and scalable designing scheme for BA-like networks,i.e.,the efficient routing combined with effective betweenness based link bandwidth *** addition,when designing a thoroughly new network from the beginning,we find that ER network is a good candidate to achieve cost-effective and scalable designing in most settings.

关键词： cost-effective communication network designing network transmission efficiency network topology traffic dynamics next generation network scalable network designing

Symbolic Computation Study of (2+1)-Dimensional Dispersive Long Wave Equations

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Communications in Theoretical physics 2006年第8期46卷 199-202页

作者： LU Zhuo-Sheng~(1,2,+) and XIE Fu-Ding~(2,3) ~1school of science, beijing university of Post and Telecommunications, beijing 100876, china ~2Key Laboratory of mathematics Mechanization, academy of mathematics and System sciences, the chinese academy of sciences, beijing 100080, china ~3Department of computer science, Liaoning normal university, Dalian 116029, china Department of Otolaryngology University Hospital VU P.O. Box 7057 1007 MB Amsterdam The Netherlands school of science Beijing University of Post and Telecommunications Beijing 100876 China

Seeking exact analytical solutions of nonlinear evolution equations is of fundamental importance in mathematical physics. In this paper, based on a constructive algorithm and symbolic computation, abundant new exact solutions of the (2+1)-dimensional dispersive long wave equations are obtained, among which there are soliton-like solutions, mult-soliton-like solutions and formal periodic solutions, etc. Certain special solutions are considered and some interesting localized structures are revealed.

关键词： dispersive long wave equations symbolic computation exact solution localized structure

三维热传导型半导体问题的交替方向特征有限元方法

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系统科学与数学 2002年第4期22卷 395-405页

作者：张志跃南京师范大学数学与计算机科学学院南京2100972

提出交替方向特征有限元方法,对电场位势方程采用混合元格式,对电子,空穴浓度方程采用交替方向特征有限元格式,对温度方程提出交替方向格式.应用向量积计算及先验估计理论和技巧,得到最佳的L2误差估计.

关键词：热传导型半导体交替方向特征有限元方法最优误差估计半导体器件

CONSENSUS CONTROL FOR LEADER-FOLLOWING MULTI-AGENT SYSTEMS WITH MEASUREMENT NOISES

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Journal of Systems science & Complexity 2010年第1期23卷 35-49页

作者： Cuiqin MA Tao LI Jifeng ZHANG school of Mathematical sciences Qufu Normal University Qufu 273165 China. Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

This work is concerned with consensus control for a class of leader-following multi-agentsystems (MASs).The information that each agent received is corrupted by measurement *** the impact of noises on consensus,time-varying consensus gains are adopted,based on whichconsensus protocols are *** using the tools of stochastic analysis and algebraic graph theory,asufficient condition is obtained for the protocol to ensure strong mean square consensus under the *** condition is shown to be necessary and sufficient in the noise-free ***,by using a common Lyapunov function,the result is extended to the switching topology case.

关键词： Consensus protocol leader-following multi-agent system stochastic noise.

Wave Solutions for the GinzburgLandau-BBM Equations (I)

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Communications in Nonlinear science and Numerical Simulation 1998年第4期3卷 218-221页

作者： Murong JIANG and Yawei TIAN(Department of mathematics, Yunnan university, Kunming 650091, china)(Graduate school of china academy of Engineering and physics, P.O.Box 2010 beijing100081, china)(computer Department, Shaanxi normal university, Xi’an 710062, Department of mathematics Yunnan University Kunming 650091 China Graduate school of china Academy of Engineering and Physics P.O.Box 2010 Beijing 100081 China computer Department Shanxi Normal University Xi'an 710062 China

In this paper, the stability of plane wave solutions for the GinzburgLandau-BBM equations are considered. When the coefficients are suitably constrained,these waves are stable.

关键词： stability the Ginzburg- Landau- BBM equations plane wave solutions

On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations

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Journal of Mathematical Research with Applications 2012年第4期32卷 423-430页

作者： Jianren LONG 1,2 1.school of mathematics and computer science,Guizhou normal university,Guizhou 550001,P.R.china 2.academy of mathematics and Systems science,chinese academy of sciences,beijing 100190,P.R.china school of mathematics and computer science Guizhou Normal University Guizhou 550001

In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential *** that A is a transcendental entire function with ρ(A)<1/*** that k≥2 and f(k)+A(z)f=0 has a solution f with λ(f)<ρ(A),and suppose that A1=A+h,where h≡0 is an entire function with ρ(h)<ρ(A).Then g(k)+A1(z)g=0 does not have a solution g with λ(g)<∞.

关键词： complex differential equations entire function the growth of order the exponent of convergence of the zeros.