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Bifurcation and Chaos in a Weakly Nonlinear system Subjected to Combined Parametric and External Excitation

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 501-512页

作者： Wei Li, Peng-cheng XuInstitute of mathematics, beijing University of Chemical Technology, beijing 100029, chinaInstitute of Applied mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Institute of mathematics Beijing University of Chemical Technology Beijing China Institute of Applied mathematics Academy of Mathematics and System Sciences Chinese Academy of Science Beijing China

In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.

关键词： Bifurcation chaos transversal homoclinic orbit

WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

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chinese Annals of mathematics,Series B 2005年第1期26卷 75-88页

作者： HUOZHAOHUI JIAYUELING GraduateSchool ChinaAcademyofEngineeringPhysicsP.O.Box2101Beijing100088China academyofmathematicsandsystemsciences ChineseAcademyofSciencesBeijing100080China

The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s ≥ -1-4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s ＞ 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.

关键词： Fourier restriction norm Trilinear estimates Hirota equation Low regularity Global well-posedness

A new trust region algorithm for image restoration

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Science china mathematics 2005年第2期48卷 169-184页

作者： WEN Zaiwen & WANG Yanfei State Key Laboratory of Scientific Engineering Computing, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china National Key Laboratory on Remote Sensing Science, Institute of Remote Sensing Applications, chinese academy of sciences, beijing 100101, china 1. State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. National Key Laboratory on Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China

The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter a. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious finding the regularization parameters and truncation levels. Some numerical tests on remotely sensed images are given to show that the trust region method is promising.

关键词： trust region algorithm, image restoration, Lanczos method, Kronecker matrix-vector product, preconditioning.

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R^(2*)

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Science china mathematics 2004年第z1期47卷 181-189页

作者： WU Zhengpeng, KANG Tong & YU DehaoInstitute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Department of Applied mathematics, beijing Broadcasting Institute, beijing 100024, china Combinatorial and Computational mathematics Center, Pohang University of Science and Technology, Phoang 790-784, Republic of Korea chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China beijing Broadcasting Inst Dept Appl Math Beijing 100024 Peoples R China Pohang Univ Sci & Technol Combinatorial & Computat Math Ctr Phoang 790784 South Korea

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with *** provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.

关键词： natural boundary integral method, finite element method, coupling method, error estimate.

A New Statistic for Variable Selection in Questionnaire Analysis

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Journal of systems Science and systems Engineering 2001年第3期13卷 315-322页

作者： ZHANG Jun-hua, FANG Wei-wu Institute of Applied mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Institute of Applied mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper, a new statistic is proposed for variable selection which is one of the important problems in analysis of questionnaire data. Contrasting to other methods, the approach introduced here can be used not on... 详细信息

关键词： questionnaire variable selection information divergence statistic

Optimal Harvesting and Stability for a Predator-prey system with Stage Structure

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 423-430页

作者： Xin-yu Song, Lan-sun ChenDepartment of mathematics. Xinyang Teachers College, Henan 464000, chinaInstitute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing100080, china Department of mathematics Xinyang Teachers College Henan China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.

关键词： Optimal harvesting stage structure predator-prey system global asymptotic stability

Periodic Solutions of a Model of Mitosis in Prog Eggs

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 625-628页

作者： Bei-ye Feng, Zuo-huan ZhengInstitute of Applied mathematics, academy of mathematics and system sciences, chinese academy of sciences beijing 100080, china

In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.

关键词： Model of Mitosis frog eggs limit cycle

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2* and CHEN Qiuhui3(1. Department of mathematics, beijing Jiaotong University, beijing 100044, china 2. Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china 3. Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 510275, china) Department of mathematics Beijing Jiaotong University Beijing 100044 China. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. Department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization

REMARK ON UNIQUE CONTINUATION OF SOLUTIONS TO THE STOKES AND THE NAVIER-STOKES EQUATIONS

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Acta Mathematica Scientia 2005年第4期25卷 594-598页

作者： Jin Kim Tu 常谦顺 TuInstitute of mathematics Academy of Sciences of DPR of Korea Pyonyang DPR of Korea Institute of Applied mathematics Academy of Mathematics and System SciencesChinese Academy of Sciences Beijing 100080 China

New simple proofs of unique continuation of solutions for the Stokes equation and Navier-Stokes equations is presented under weaker conditions.

关键词： Stokes equation Navier-Stokes equation