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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, {2. University of Chemical Technology, {2. 10002., 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 {2. 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

ON THE OBSERVABILITY AND DETECTABILITY OF LINEAR STOCHASTIC systems WITH MARKOV JUMPS AND MULTIPLICATIVE NOISE

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Journal of systems science & Complexity 2010年第1期23卷 102-115页

作者： Yuanhua NI Weihai ZHANG Haitao FANG Key Laboratory of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China. College of Information and Electrical Engineering Shandong University of Science and Technology Qingdao China.

This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Ito type with multiplieative noise （for short, MJLSS）. Stochastic Popov-Belevith-Hautus （PBH） Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2.H∞ control for such MJLSS is discussed under exact detectability.

关键词： Exact detectability exact observability Markov jump systems multiplicative noise PBH Criterion stochastic H2.H∞ control.

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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science China mathematics 2011年第3期54卷 555-572页

作者： DENG ShengFu1, GUO BoLing2.& WANG TingChun2.3.1Department of mathematics, Zhanjiang Normal University, Zhanjiang 52.048, China 2.1} of {2. Physics and Computational mathematics, beijing 100088, China 3.College of Math and Physics, Nanjing University of Information science and Technology, Nanjing 2.0044, China 1. Department of mathematics Zhanjiang Normal University Zhanjiang 524048 China2. Institute of Applied Physics and Computational Mathematics Beijing 100088 China3. College of Math and Physics Nanjing University of Information Science and Technology Nanjing 210044 China

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关键词： homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions

Influence factors of sparse microwave imaging radar system performance:approaches to waveform design and platform motion analysis

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science China(Information sciences) 2012年第10期55卷 2301-2317页

作者： ZHANG Zhe 1,2.3.ZHANG BingChen 1,2.JIANG ChengLong 1,2.3.XIANG Yin 1,2.HONG Wen 1,2.& WU YiRong 1,2.1 science and Technology on Microwave Imaging Laboratory,beijing 100190,China 2.{2. of Electronics,chinese Academy of sciences,beijing 100190,China 3.Graduate University,chinese Academy of sciences,beijing 100190,China 1. science and Technology on Microwave Imaging Laboratory Beijing 100190 China 2. institute of Electronics Chinese Academy of Sciences Beijing 100190 China 3. Graduate University Chinese Academy of Sciences Beijing 100190 China

Sparse microwave imaging radar is a newly developed concept of microwave imaging system,which tries to combine the traditional radar imaging system with sparse signal processing theories,achieving the aim of reducing the complexity of microwave imaging systems and enhancing the system *** this paper,we introduce some basic concepts of sparse signal processing theory,and then apply it to the traditional radar imaging system to get the mathematical model of sparse microwave imaging *** analyze the factors that determine the performance of sparse microwave imaging radar,including scene,waveform and *** to the radar model,we analyze how these factors influence the radar system and how to optimize *** results of the sparse microwave imaging radar system are also provided.

关键词： sparse microwave imaging radar synthetic aperture radar compressive sensing Lq regularization waveform design

Two remarks on quenching phenomenon for semilinear parabolic equations

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chinese science Bulletin 1997年第3期42卷 258-259页

作者： DAI Qiuyi and GU Yonggeng1 Xiangtan Mining institute, Xiangtan 4112.1, China 2.institute of {2. science, chinese Academy of sciences, beijing 100080, China Xiangtan Mining institute Xiangtan China institute of systems {2. Chinese Academy of Sciences Beijing China

THIS letter discusses the following initial-boundary value problem: where (?)Ω is the boundary of domain Ω, f(s): [0, b)→(0, +∞) satisfy Because this problem has strong background of physics and geometry, it has attracted much attention in recent years. The main results can be found in ref. [1]. Here we give only a result of reference [2..

关键词： Two remarks on quenching phenomenon for semilinear parabolic equations

SrGa_2._4∶Ce blue TFEL in new structure

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chinese science Bulletin 1998年第7期43卷 603-605页

作者： XU Chunxiang+1, LOU Zhidong+2. XU Zheng+3.and XU Xurong+3.. National Laboratory of Molecular and Biomolecular Electronics, Southeast University, Nanjing 2.0096, China 2. Department of {3. Physics, Tianjin University, Tianjin 3.003., China 3. Institu National Laboratory of Molecular and Biomolecular Electronics Southeast University Nanjina China Department of applied Physics Tianjin University Tianjin China institute of Photoelectronic Technology Northern Jiaotong University Beijing China

SrGa-2.-4∶Ce blue TFEL device with a novel structure was prepared by electron beam evaporation. The dielectric constant of insulator layer in this structure is far less than that in the conventional structure, so the hot-electrons can be accelerated in SiO-2.layers. The stable TFEL with good chromaticity was achieved and the basic characteristics were investigated.

关键词： SrGa-2.-4∶Ce bule TFEL low dielectric constant insulator layer.

Existence of SURU estimators in SURE model with special covariance structures

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chinese science Bulletin 1997年第14期42卷 1149-1151页

作者： WU Qiguanginstitute of systems {2., {3. Academy of sciences, beijing 100080, China institute of systems {2. Chinese Academy of Sciences Beijing China

THROUGHOUT this note, the following notations are used: For a matrix A, A>0 means thatA is positive definite symmetric; R （A）, A′and A- stand for the column space, transposeand any g-inverse of A respectively; PA = A （A′A）- A′and PA = Ik - PA, where Ik is theidentity matrix of order k that is the number of rows in A. Rm×n is the totality of m×n realmatrices.

关键词： seemingly unrelated regression equations (SURE) model uniformly minimum risk unbiased (UMRU) estimator uniform covariance structure serial covariance structure.

A simple proof of the formal duality of the Kerdock and Preparata codes

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chinese science Bulletin 2000年第14期45卷 1279-1282页

作者： WAN Zhexianinstitute of systems {2., {3. Academy of sciences, beijing 100080, China institute of systems {2. Chinese Academy of Sciences Beijing China

The nonlinearity of the Z2.Kerdock code Km+1, where m is an odd integer ≥3. is not at all obvious. By regarding Km+1 as the binary image of the Z4-Kerdock code .,K(m) under the Gray map[1], a simple proof can be achieved (cf. Theorems 8.7 and 8.9 of [2.). Similarly, the formal duality of the Z2.Kerdock code Km+1 and the Z2.Preparata code Pm+1 is even more not at all obvious. A simple proof is given in the present note, by regarding Km+1 as the binary image of .K (m) and using the duality of .K(m) and the Z4-Preparata code . (m) established in [1].

关键词： 4-code. Kerdock code Preparata code formal duality.

Cleaning of Chromate Manufacture Process

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 132-134页

作者： Xing Zou Yi Zhang(applied science School, University of science and Technology {3., {3. 100083. China)(institute of Engineering Chemistry and Metallurgy, chinese Academy of sciences, beijing 100080, China) applied science School University of Science and Technology Beijing Beijing 100083 China institute of Engineering Chemistry and Metallurgy Chinese Academy of Sciences Beijing 100080 China

Sodium chromate solubility is determined in the range of NaOH concentrations from 450 to 810 g/L andsolution temperatUres from 3. to 110℃. The optimized conditions to separate sodium chromate from NaOH inleached solution are resolved. It is first found the method to efficiently separate sbdium chromate from NaOH andsodium altuninate in crude sodium chromate. Bench-scale studies on the separating are performed. Finally, goodseparation results are achieved.

关键词： chromate separation clean process