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Stability of Solution of a Class of Quasilinear Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 461-470页

作者： Qi-kang Ran, Ai-nong FangDepartment of Applied mathematics, Shanghai university of finance and economics, Shanghai 200433, chinaDepartment of Applied mathematics, Shanghai Jiaotong university, Shanghai 200030, china Department of Applied mathematics Shanghai University of Finance and Economics Shanghai China Department of Applied mathematics Shanghai Jiaotong University Shanghai China

In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.

关键词： Nonhoraogeneous quasilinear elliptic equations capacity stability

Latent ancestral graph of structure vector autoregressive models

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Journal of Systems Engineering and Electronics 2010年第2期21卷 233-238页

作者： Wei Gao1,2and Zheng Tian2,3 1.School of statistics,Xi’an university of finance&economics,Xi’an 710061,P.R.china 2.Department of Applied mathematics,Northwestern Polytechnical university,Xi’an 710072,P.R.china 3.State Key Laboratory of Remote Sensing Science,Institute of Remote Sensing Applications,Chinese Academy of Sciences,Beijing 100101,P.R.china School of statistics Xi'an University of Finance & EconomicsXi'an 710061P.R.China Department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China Department of Applied mathematics Northwestern Polytechnical UniversityXi'an 710072P.R.China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing ApplicationsChinese Academy of SciencesBeijing 100101P.R.China

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

关键词： multivariate time series latent ancestral graph itera- tive conditional fitting.

BIFURCATIONS OF PERIODIC ORBITS IN THREE-WELL DUFFING SYSTEM WITH A PHASE SHIFT

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Journal of Systems Science & Complexity 2011年第3期24卷 519-531页

作者： Jicai HUANG Han ZHANG School of mathematics and statistics Central China Normal University Wuhan 430079 China college of Information Technical Science Nankai University Tianjin 300071 China.

Bifurcations of periodic orbits of three-well Duffing system with a phase shift are investigated in detail. The conditions of the existence and bifurcations for harmonics, subharmonics （2-order, 3- order and m-order） and superharmonics under small perturbations are given by using second-order averaging method and Melnikov＇s method. The influence of the phase shift on the dynamics is also obtained.

关键词： Bifurcations Melnikov's method periodic orbits second-order averaging three-well Duffing system.

Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI School of Mathematical Sciences, Fudan university, Shanghai 200433, china School of mathematics and statistics, Northeast Normal university, Changchun 130024, china. School of Mathematical Sciences Fudan University Shanghai 200433 China School of mathematics statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

The Cauchy problem about Dirac-wave map from the 2-dimension Minkowski space to a complete Riemannian manifold

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Science china mathematics 2007年第6期50卷 859-874页

作者： Yan ZHANG School of statistics and mathematics , Zhejiang Gongshang university, Hangzhou 310018, china Department of Physics, Zhejiang university, Hangzhou 310027, china 1. School of statistics and mathematics Zhejiang Gongshang University Hangzhou 310018 China 2. Department of Physics Zhejiang University Hangzhou 310027 China

When a target manifold is complete with a bounded curvature, we prove that there exists a unique global solution which satisfies the Euler-lagrange equation of for the given Cauchy data.

关键词： Dirac-wave map nonlinear σ-model spin bundle harmonic map 53C43

*** CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS

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Chinese Annals of mathematics,Series B 2002年第4期23卷 461-468页

作者： HU DIHEcollege of mathematics and statistics, Wuhan university, Wuhan 430072, china. E-mail: dhhu@***. college of mathematics and statistics Wuhan University Wuhan 430072 China

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.

关键词： Hausdorff metric Statistical contraction operator Statistically self-similar set Statistically self-similar measure

OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIAL EQUATIONS IN THE ABSENCE OF CONVEXITY

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Journal of Systems Science & Complexity 2010年第2期23卷 321-333页

作者： Shu LUAN Hang GAO School of mathematics and Computation Science Zhanjiang Normal College Zhanjiang 524048 China. School of mathematics and statistics Northeast Normal University Changchun 130024 China.

In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of *** overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are *** the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is *** the end of this paper,the authors discuss the applicationof the maximum principle by an example.

关键词： Multisolution ODEs optimal control Pontryagin's maximum principle relaxed controls.

The Willmore functional and the containment problem in R^4

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Science china mathematics 2007年第3期50卷 325-333页

作者： Jia-zu ZHOU School of mathematics and statistics, Southwest university, Chongqing 400715, china Department of mathematics, Polytechnic university, Brooklyn, NY 11201, USA School of mathematics and statistics Southwest University Chongqing 400715China

Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.

关键词： mean curvature scalar curvature kinematic formula Minkowski quermassintegrals convex body convex hypersurface 52A22 53C65 51C16

Tests for nonparametric parts on partially linear single index models

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Science china mathematics 2007年第3期50卷 439-449页

作者： Ri-quan ZHANG Department of statistics, East china Normal university, Shanghai 200062, china Department of mathematics, Shanxi Datong university, Datong 037009, china Department of statistics East China Normal University Shanghai 200062China

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

关键词： local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ 2-distribution 62G10 62G20