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Remarks on Hard Lefschetz conjectures on Chow groups Dedicated in celebration of science china on the occasion of its 60th birthday

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science china Mathematics 2010年第1期53卷 105-114页

作者： FU BaoHua institute of Mathematics, academy of Mathematic and {2. science, chinese academy of sciences, Beijing 100190, china institute of Mathematics Academy of Mathematic and Systems Science Chinese Academy of Sciences Beijing China

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we show that they are equivalent to the well-known conjectures of Beauville and Murre.

关键词： Chow groups abelian varieties Bloch-Beilinson conjectures Beauville conjecture Murre conjecture

Holomorphic invariant forms of a bounded domain

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science china Mathematics 2008年第11期51卷 1945-1964页

作者： LU QiKeng institute of Mathematics, academy of Mathematics and {2. science, chinese academy of sciences, Beijing 100190, china institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Given a complete ortho-normal system ? = (?0,?1,?2.…) of L 2.H( $ \mathcal{D} $ ), the space of holomorphic and absolutely square integrable functions in the bounded domain $ \mathcal{D} $ of ? n , we construct a holomorphic imbedding $ \iota _\phi :\mathcal{D} \to \mathfrak{F}(n,\infty ) $ , the complex infinite dimensional Grassmann manifold of rank n. It is known that in $ \mathfrak{F}(n,\infty ) $ there are n closed (μ, μ)-forms τμ (μ = 1,…,n) which are invariant under the holomorphic isometric automorphism of $ \mathfrak{F}(n,\infty ) $ and generate algebraically all the harmonic differential forms of $ \mathfrak{F}(n,\infty ) $ . So we obtain in $ \mathcal{D} $ a set of (μ, μ)-forms ι ? * τμ (μ = 1,…, n), which are independent of the system ? chosen and are invariant under the bi-holomorphic transformations of $ \mathcal{D} $ . Especially the differential metric ds 2.1 associated to the K?hler form ι ? * τ1 is a K?hler metric which differs from the Bergman metric ds 2.of $ \mathcal{D} $ in general, but in case that the Bergman metric is an Einstein metric, ds 1 2.differs from ds 2.only by a positive constant factor.

关键词： complete ortho-normal system holomorphic invariant forms 32.36 32.65

PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF EUROPEAN OPTIONS

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Journal of Computational Mathematics 2001年第6期19卷 591-600页

作者： Dong-sheng Wu (institute of systems {2., academy of Mathematics and systems sciences, chinese academy of sciences, Beijing 100080, china ) 中科院系统科学所北京 100080

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of European Options.

关键词： Brownian motion probabilistic numerical solution European Options

Study on the generator f of the operators I_n and I_t

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science china Mathematics 2010年第10期53卷 2589-2603页

作者： CHEN HanLin academy of Mathematics and systems {2.,chinese academy of sciences,Beijing 100190,china 1. academy of Mathematics and systems {2. Chinese Academy of Sciences Beijing 100190 China

Define two operators In and It,the inner product operator In(g)(x) := j∈Zs(g,f(·-j))f(x-j) and the interpolation operator It(g)(x) := j∈Zs g(j)f(x-j),where f belongs to some space and integer s *** call f the generator of the operators In and *** is well known that there are many results on operators In and *** there remain some important problems to be further *** application we first need to find the available generators (that can recover polynomials as It(p) = p or In(p) = p,p ∈Πm-1) for constructing the relative *** this paper,we focus on the available generator in the class of spline *** shall see that not all spline functions can be used to construct available ***,we do find a spline function in S,of degree m-1,where m is even and S is a class of *** for odd m the problem is still *** on spline functions in this paper are new.

关键词： generator available generator inner product operator spline interpolation operator two-closed refinable

CONVERGENCE AND SUPERCONVERGENCE OF HERMITE BICUBIC ELEMENT FOR EIGENVALUE PROBLEM OF THE BIHARMONIC EQUATION

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Journal of Computational Mathematics 2001年第2期19卷 139-142页

作者： Dong-sheng Wu (institute of systems {2., academy of Mathematics and systems sciences, chinese academy of sciences, Beijing 100080, china ) 中科院系统科学所北京 100080

Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.

关键词： Hermite bicubic element biharmonic equation interpolation postprocessing eigenvalue problem

Markov chain approach to identifying Wiener systems

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science china(Information {2.) 2012年第5期55卷 1201-1217页

作者： ZHAO WenXiao 1,2.& CHEN HanFu 1,2.1 Key Laboratory of systems and Control,institute of systems science,AMSS,chinese academy of sciences,Beijing 100190,china 2.National Center for Mathematics and Interdisciplinary sciences,chinese academy of sciences,Beijing 100190,china 1. Key Laboratory of systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing 100190 China2. National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China

Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is *** recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approx-imation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly *** comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.

关键词： Wiener system recursive identification stochastic approximation Markov chain strong consis-tency

MULTI-AGENT TRACKING OF A HIGH-DIMENSIONAL ACTIVE LEADER WITH SWITCHING TOPOLOGY

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Journal of systems science & Complexity 2009年第4期22卷 722-731页

作者： Yiguang HONG Xiaoli WANG Key Lab of systems and Control,institute of systems science,academy of Mathematics and systems science,chinese academy of sciences,Beijing 100190,china. Key Lab of systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper considers a multi-agent tracking problem for a high-dimensional active leaderand variable interconnection topology. The state of the leader not only keeps changing but also maynot be measured. To estimate the state such a leader individually, a neighbor-based local controllertogether with a neighbor-based state-estimation rule is given for each autonomous agent. Then, theauthors prove that, with the help of a constructed common Lyapunov function (CLF), each agent cantrack the active leader with unmeasurable states. Finally, the authors explicitly construct a CLF foran active leader with unknown periodic input for illustration.

关键词： Active leader distributed algorithms multi-agent systems switching topology.

Simulation of aerodynamic performance affected by vortex generators on blunt trailing-edge airfoils

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science china(Technological {2.) 2010年第1期53卷 1-7页

作者： YANG Ke1,2.ZHANG Lei1,3 & XU JianZhong1,2.1 institute of Engineering Thermophysics,chinese {2. of sciences,Beijing 100190,china 2.Key Laboratory of Wind Energy Utilization,chinese {2. of sciences,Beijing 100190,china 3 Graduate School of chinese academy of sciences,Beijing 100190,china 1. institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Wind Energy Utilization Chinese Academy of Sciences Beijing 100190 China3. Graduate School of Chinese Academy of Sciences Beijing 100190 China

An investigation was carried out by numerical simulation on a wind turbine airfoil and a blunt trailing-edge airfoil with and without vortex generators (VGs), and the performance of the airfoils was analyzed. By the simulation of airfoil DU 91-W2.2.0 it was verified that the numerical method and model were credible. Based on this airfoil, a new one with a blunt trailing edge of 6% chord was blended by symmetrically adding thickness, and its characteristics curves were obtained through computing at key angles of attack. Additionally, the pressure distribution on blended airfoil was analyzed by comparing to the airfoil without blend. The interaction of streamwise vortices induced by VGs with trailing vortex or separation vortex was considered, followed by the uncovery of how VGs can suppress the boundary layer separation.

关键词： vortex generators airfoil blunt trailing-edge

BOUNDARY FEEDBACK STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH A TIPLOAD

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chinese Annals of Mathematics,Series B 2001年第4期22卷 485-494页

作者： YAN QINGXU, FENG DEXING institute of systems {2., academy of Mathematics and systems {2., chinese academy of sciences, Beijing 100080, china. institute of systems {2., academy of Mathematics and systems {2., chinese academy of sciences, Be institute of systems {2. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.

关键词： Timoshenko beam Boundary feedback control C0 semigroups Exponential stability Multiplier method