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Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,East china university of Science and Technology,shanghai 200237,china 2 department of mathematics,Anhui Normal university,Wuhu 241000,china 3.department of mathematics,donghua university,shanghai 201620,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

Property A and Uniform Embeddability of Metric Spaces Under Decompositions of Finite Depth

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Chinese Annals of mathematics,Series B 2010年第1期31卷 21-34页

作者： Yujuan DUAN Qin WANG Xianjin WANG department of Applied mathematics Donghua University Shanghai 201620 China Corresponding author. department of Applied mathematics Donghua University Shanghai 201620 China

Property A and uniform embeddability are notions of metric geometry which imply the coarse Baum-Connes conjecture and the Novikov *** this paper,the authors prove the permanence properties of property A and uniform em... 详细信息

关键词： Metric space Uniform embedding Property A Large scale decomposition Permanence property

Remarks on the Operator Norm Localization Property

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Chinese Annals of mathematics,Series B 2011年第4期32卷 593-604页

作者： Xianjin WANG department of Applied mathematics Donghua University Shanghai 201620 China.

The author studies the metric spaces with operator norm localization property. It is proved that the operator norm localization property is coarsely invariant and is preserved under certain infinite union. In the case... 详细信息

关键词： Metric space Asymptotic dimension Operator norm localization Coarse invariance Roe algebra

Fault Estimation for a Class of Markov Jump Piecewise-Affine Systems: Current Feedback Based Iterative Learning Approach

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IEEE/CAA Journal of Automatica Sinica 2024年第2期11卷 418-429页

作者： Yanzheng Zhu Nuo Xu Fen Wu Xinkai Chen donghua Zhou IEEE College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China College of Mechanical Engineering and Automation Huaqiao UniversityXiamen 361021China department of Mechanical and Aerospace Engineering North Carolina State UniversityRaleigh NC 27695 USA department of Electronic and Information Systems Shibaura Institute of TechnologySaitama 337-8570Japan

In this paper, the issues of stochastic stability analysis and fault estimation are investigated for a class of continuoustime Markov jump piecewise-affine(PWA) systems against actuator and sensor faults. Firstly, a novel mode-dependent PWA iterative learning observer with current feedback is designed to estimate the system states and faults, simultaneously, which contains both the previous iteration information and the current feedback mechanism. The auxiliary feedback channel optimizes the response speed of the observer, therefore the estimation error would converge to zero rapidly. Then, sufficient conditions for stochastic stability with guaranteed performance are demonstrated for the estimation error system, and the equivalence relations between the system information and the estimated information can be established via iterative accumulating ***, two illustrative examples containing a class of tunnel diode circuit systems are presented to fully demonstrate the effectiveness and superiority of the proposed iterative learning observer with current feedback.

关键词： Current feedback fault estimation iterative learning observer Markov jump piecewise-affine system

A NONLINEAR GALERKIN METHOD WITH VARIABLEMODES FOR KURAMOTO-SIVASHINSKY EQUATION

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Journal of Computational mathematics 1999年第3期17卷 243-256页

作者： Yu-jiang wu(Depadrtment of mathematics, shanghai university, Jiadiap shanghai 201800, china department of mathematics, Lanzhou university, Lanzhou 750000, china) 上海大学数学系上海

This article proposes a kind of nonlinear Galerkin methods with variable modes for the long-term integration of Kuramoto-Sivashinsky equation. It consists of finding an appropriate or best number of modes in the correction of the method. Convergence results and error estimates are derived for this method. Numerical examples show also the efficiency and advantage of our method over the usual nonlinear Galerkin method and the classical Galerkin method.

关键词： Kuramoto-Sivaskinsky equation nonlinear Galerkin method approximation convergence

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, shanghai Normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (department of mathematics, shanghai Jiaotong university, shanghai 200240, china) department of mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, shanghai Normal university, shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, East china Normal university, shanghai 200062, china) E china Normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number