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CDS Simulation and Pattern Formation of Phase Separation

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 233-236页

作者： Zhanaji LIU Men CHENG Jiong RUAN and Shouji CHENG (department of Mechanics and Engineering Science, fudan university, shanghai 200433,china)(department of Mathematics, fudan university, shanghai 200433, china) Dept. of Mechanics and Eng. Science Fudan University Shanghai 200433 China department of Mathematics Fudan University Shanghai 200433 China

Several properties of the generation and evolution of phase separating patterns for binary material studied by CDS model are proposed. The main conclusions are (1) for alloys spinodal decomposition, the conceptions of "macro-pattern" and "micropattern" are posed by "black-and- white graph" and "gray-scale graph" *** find that though the four forms of map f that represent the self-evolution of order parameter in a cell(lattice) are similar to each other in "macro-pattern" , there are evident differences in their micro-pattern, e.g., some different fine netted structures in the blackdomain and the white domain are found by the micro-pattern, so that distinct mechanical and physical behaviors shall be obtained. (2) If the two constitutions of block copolymers are not symmetric (i.e. r ≠ 0.5), a pattern called "grain-strip cross pattern"is discovered,in the 0.43 < r < 0.45.

关键词： lattice gas automata CDS phase separation Pattern formation

SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 651-658页

作者： WANG MENG department of Mathematics, Zhejiang university, Hangzhou 310027, china school of Mathematical sciences, Pudan university, shanghai 200433, china. department of Mathematics Zhejiang University Hangzhou 310027 China school of Mathematical sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

An optimal adaptive filtering algorithm with a polynomial prediction model

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Science china(Information sciences) 2011年第1期54卷 153-162页

作者： TAN JiaJia & ZHANG JianQiu department of Electronic Engineering,fudan university,shanghai 200433,china department of Electronic Engineering Fudan University Shanghai China

A new approach to the optimal adaptive filtering is proposed in this *** this approach,a polynomial prediction model is used to describe the time-variant/invariant impulse response coeffcients of an identified *** the polynomial prediction model is viewed as the state equations of the identified impulse response coeffcients and the relationships between the inputs and outputs of the system are regarded as the measurements of the states,our adaptive filtering can be achieved in the framework of the Kalman filter. It is understood that Kalman filter is optimal in the sense of the MAP(maximum a posteriori),ML(most likelihood)and MMSE(minimum mean square error)under the linear and Gaussian white noise *** a result,our algorithm is also optimal in the statistical senses as Kalman filter does,provided that the impulse response coeffcients can be modeled by a *** only do the analytical results of the algorithm but also the simulation results show that our algorithm outperforms the traditional known algorithms.

关键词： adaptive filters polynomial prediction model impulse response coeffcients process equation Kalman filter optimal

Synchronization of Chaotic Systems by Linear Feedback Controller

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 27-30页

作者： Zhenxun HUANG and Jiong RUAN (department of Mathematics, fudan university, shanghai 200433, china) department of Mathematics Fudan University Shanghai 200433 China

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ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｙｎｃｈｒｏｎｉｚａｔｉｏｎａｎｄｃｏｎｔｒｏｌｏｆｃｈａｏｔｉｃｓｙｓｔｅｍｓｈａｖｅｒｅｃｅｎｔｌｙａｒｏｕｓｅｄａｇｒｅａｔｄｅａｌｏｆｉｎｔｅｒｅｓｔ［１－５］．Ｍａｎｙｄｉｆｅｒｅｎｔｍｅｔｈｏｄｓｈａｖｅ...

关键词： control and synchronization of chaos heterogeneous synchronization ω limit point global asymptotical stability

Chaos in A Class of Impulsive DifferentialEquation

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 165-169页

作者： Jiong RUAN Wei LIN(department of Mathematics, fudan university, shanghai 200433, china) department of Mathematics Fudan University Shanghai 200433 China

In this paper, the chaotic differential equation with impulse effect is introduced including its foundamental theory. For illustrating the chaotic characteristic ofthis kind of system, the theory of the dynamics is ap... 详细信息

关键词： chaos impulsive differential equation impulse effect

Optimal variational principle for backward stochastic control systems associated with Lévy processes

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Science china Mathematics 2012年第4期55卷 745-761页

作者： TANG MaoNing 1 & ZHANG Qi 2,1 department of Mathematical sciences,Huzhou university,Huzhou 313000,china 2 school of Mathematical sciences,fudan university,shanghai 200433,china department of Mathematical sciences Huzhou University Huzhou China school of Mathematical sciences Fudan University Shanghai China

The paper is concerned with optimal control of backward stochastic differentiM equation （BSDE） driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, where Teugel＇s martingales are a family of pairwise strongly orthonormal martingales associated with L6vy processes （see e.g., Nualart and Schoutens＇ paper in 2000）. We derive the necessary and sufficient conditions for the existence of the optimal control by means of convex variation methods and duality techniques. As an application, the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria （or backward linear-quadratic problem, or BLQ problem for short） is discussed and characterized by a stochastic Hamilton system.

关键词： stochastic control stochastic maximum principle Ldvy processes Teugel's martingales backwardstochastic differential equations

An Improved Method in Synchronization ofChaotic Systems

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 140-143页

作者： Jiong RUAN and Lijuan LI(department of Mathematics, fudan university, shanghai 200433, china) department of Mathematics Fudan University Shanghai 200433 China

An improved strategy in srnchrohization of chaotic dynamics as contrastedwith PC(*** and ***) method and KSC(Kocarev L, Shang A, Chua,L.O.)control idea is presented in this paper. Computer simulations are included to ... 详细信息

关键词： synchronization conditional Lyapunov exponents drive-response

Complexity Analysis and Its Application

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Communications in Nonlinear Science and Numerical Simulation 1999年第1期4卷 48-50页

作者： Jiong RUAN (department of Mathematics, fudan university, shanghai 200433, china) Wei LIN and Dajun XIN (department of physiology and biophysics, fudan university, shanghai 200433, china) department of Mathematics Fudan University Shanghai 200433 China department of physiology and biophysics Fudan University Shanghai 200433 China

In this paper, we introduce a nonlinear method named as "Complexity Analysis" by which we study the chaotic and other behavior in heart rate of the patients suffer from AMI, STSDS and VPB, or normal healthy subjects. The results show that the nolinear parameter-complexity reflects the dynamic state of heart. It can be used to measure the complexity of biologic systems quantitatively. It is possible to use such a method to analyze and diagnose cardiovascular disease in clinics.

关键词： heart rate variability complexity nonlinear time series analysis

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

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Applied Mathematics(A Journal of Chinese Universities) 2007年第2期22卷 181-200页

作者： Guo Fei school of Mathematical sciences, fudan university, shanghai 200433, china department of Mathematics, Qufu Normal university, Shandong, 273165, china. school of Mathematical sciences Fudan University Shanghai China department of Mathematics Qufu Normal University Shandong China

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x）｜ t ≥ 0, x ≥0} is considered. A suffic... 详细信息

关键词： quasilinear hyperbolic system mixed initial-boundary value problem global weakly discontinu-ous solution weak linear degeneracy