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Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2.1 Nonlinear Mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contem- porary Applied Mathematics School of Mathematical Sciences, fudan university,{2., china. 2.School of Mathematical Sciences, fudan university,{2., china department of Mathematics, North university of china, Taiyuan 030051, china. Nonlinear Mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2.and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992.. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2.∑i=1n δx^^2. is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2. with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

Synchronization of Chaotic Systems byFeedback

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 162-165页

作者： Xiping ZENG Jiong RUAN Lijuan LI(department of Mathematics, fudan university,{2., china) department of Mathematics Fudan University Shanghai 200433 China

A sufficient condition of the asymptotical stability of the zero solutionabout the nonautonomous equation dz/dt=A(t)z+o(||z||) .is .presented,in this paper. Furthermore, this sufficient condition is used to analyze the synchronization of chaotic Rosslersystem, a new method without any limitation on the response system in the synchronization is proposed in the meantime,

关键词： synchronization drive-response asymptotical stability

Direct CP violation in hadronic B decays

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Science china(physics,Mechanics & Astronomy) 2006年第3期49卷 357-366页

作者： HONG Bihai1,2.& Lü Caidian3 1. department of physics, Lishui {2., Lishui 32.000,china 2. department of physics, shanghai Jiaotong {2., shanghai 2.0030, china 3. Institute of High Energy physics, Beijing 100049,china department of physics Lishui University Lishui 323000 China department of physics Shanghai Jiaotong University Shanghai 200030 China Institute of High Energy physics Beijing 100049 China

There are different approaches for the hadronic B decay calculations, recently. In this paper, we upgrade three of them, namely factorization, QCD factorization and the perturbative QCD approach based on kT factorization, using new parameters and full wave functions. Although they get similar results for many of the branching ratios, the direct CP asymmetries predicted by them are different, which can be tested by recent experimental measurements of B factories.

关键词： CP violation hadronic B decay factorization.

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2.and LI Zhenqi 1, 3 1. Institute of Mathematics, fudan university, shanghai 200433,{2. 2. department of Mathematics,Sichuan Union university, Chengdu 610064,{2. 3. department of Mathematics, Nanchang university, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of Mathematics Sichuan Union University Chengdu China department of Mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

Controlling Chaotic Discrete System via the Improved Closed-loop Control

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 134-139页

作者： Wei LIN Jiong RUAN and Zhenxun HUANG(department of Mathematics, fudan university.{2.. china) department of Mathematics Fudan University Shanghai 200433 China

In this paper. we use the improved closed-loop control method to realizethat the discrete chaotic system stabilizes to any arbitrarily chosen dynamics. We givethe strict proof as well as the general result of 2.dimensional system to show the feasibiltyof our method and criterion. Furthermore, the well-known Henon system is chosen foran example and the corresponding computer simulation results are given to support ourmethod.

关键词： controlling chaotic system gain matrix asymptotical stability

A UNICITY THEOREM FOR ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

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Chinese Annals of Mathematics,Series B 2004年第4期25卷 483-492页

作者： JINLU departmentofMathematics FudanUniversityShanghai200433China

A unicity theorem concerning the total derivative for entire functions of several complex variables is proved.

关键词： Unicitv theorem Entire function Total derivative

A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information

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Science china Mathematics 2009年第7期52卷 1579-1588页

作者： MENG QingXin1,2.1 department of Mathematical Sciences,Huzhou university,Zhejiang 313000,{2. 2.Institute of Mathematics,fudan university,shanghai 200433,{2. 1. department of Mathematical Sciences Huzhou University Zhejiang 313000 China 2. Institute of Mathematics Fudan University Shanghai 200433 China

The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian *** is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian *** this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are *** control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.

关键词： maximum principle stochastic optimal control partial information 93E2. 60H10 60H30

PIXE and INAA studies on ancient potteries from Guangfulin relics in shanghai

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Progress in Natural Science:Materials International 2007年第11期17卷 1348-1356页

作者： Lin Jiawei1, Cheng Huansheng1, Zhang Zhengquan1, Zhang Bin1, Feng Songlin2. Song Jian3, Gao Menghe4 and Zhu Dan1(1. Applied Ion Beam physics Laboratory, Key Laboratory of the Ministry of Education, Institute of Modern physics,{2., shanghai 200433, china 2. Key Laboratory of Nuclear Analytical Techniques, Institute of High Energy physics, Beijing 100039, china 3. shanghai Museum, shanghai 2.0003, china 4. department of Cultural Heritage and Museology,{2., shanghai 200433, china) Applied Ion Beam physics Laboratory Key Laboratory of the Ministry of Education Institute of Modern Physics Fudan University Shanghai 200433 China Key Laboratory of Nuclear Analytical Techniques Institute of High Energy Physics Beijing 100039 China shanghai Museum Shanghai 200003 China department of Cultural Heritage and Museology Fudan University Shanghai 200433 China

This paper reports the study of ancient potteries unearthed from the Guangfulin site in shanghai. From the external features of these potteries, archeologists can classify them into two different cultural types: Liangzhu culture (local culture) and a new culture which might be derived elsewhere, but they can not recognize whether they were produced in the same place. Proton induced X-ray emission (PIXE) and instrumental neutron activation analysis (INAA) were used to measure the chemical compositions of the samples and the results were analyzed using multivariate statistics. We found that the two methods can complement each other and their database can be mutually referenced in the study of ancient potteries. Experimental results show that the compositions of the potteries from the two cultural types are different, which means that the materials for ancient potteries of new culture originate from elsewhere. This supports the archaeologists’ speculation that a group of ancient people migrated to shanghai from some other places 4000 years ago.

关键词： PIXE INAA factor analysis Guangfulin ancient pottery

Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china Mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong School of Mathematical Sciences, fudan university, shanghai 200433,{2. School of Mathematics, Sichuan university, Chengdu 610064,{2. department of Applied Mathematics, shanghai university of Finance & Economics, shanghai 200433,{2. School of Mathematical Sciences Fudan University Shanghai 200433 China School of Mathematics Sichuan University Chengdu 610064 China department of Applied Mathematics Shanghai University of Finance & Economics Shanghai 200433 China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-