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Poisson kernel and Cauchy formula of a non-symmetric transitive domain

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science china Mathematics 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng institute of Mathematics, academy of Mathematics and System science, chinese academy of sciences, beijing 100190, china institute of Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.

关键词： Poisson kernel Cauchy formula

DISTRIBUTED FINITE-TIME χ-CONSENSUS ALGORITHMS FOR MULTI-AGENT systems WITH VARIABLE COUPLING TOPOLOGY

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Journal of systems science & Complexity 2010年第2期23卷 209-218页

作者： Xiaoli WANG·Yiguang HONG Key Laboratory of systems and Control,chinese academy of sciences,beijing 100190,china. Key Laboratory of systems and Control Chinese Academy of Sciences Beijing China

This paper considers finite-time χ-consensus problem for a multi-agent system with firstorderindividual dynamics and switching interaction *** distributed finite-time consensusrules are constructed for multi-agent dynamics in a unified way with the help of Lyapunovfunction and graph theory as well as ***-invariant non-smooth forms of finite-timeneighbor-based controllers are proposed and a numerical example is shown for illustration.

关键词： χ-consensus distributed control multi-agent networks non-smoothness switching graphs.

Markov chain approach to identifying Wiener systems

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science china(Information sciences) 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 Key Laboratory of systems and Control Institute of Systems Science AMSS Chinese Academy of Sciences Beijing China National Center for Mathematics and Interdisciplinary sciences Chinese Academy of Sciences Beijing 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

A quasi-local mass for 2-spheres with negative Gauss curvature

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science china Mathematics 2008年第9期51卷 1644-1650页

作者： ZHANG Xiao institute of Mathematics, academy of Mathematics and systems science, chinese academy of sciences, beijing 100080, china institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We extend our previous definition of quasi-local mass to 2-spheres whose Gauss curvature is negative, and prove its positivity.

关键词： general relativity quasi-local mass positivity 53C27 53C50 83C60

Euler solution using adaptive Cartesian grid with a gridless boundary treatment

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Acta Mechanica Sinica 2009年第2期25卷 187-196页

作者： L. Xiang G. Yang LHD of institute of Mechanics, chinese academy of sciences, 100190 beijing, china LHD of institute of Mechanics Chinese Academy of Sciences Beijing China

A quadtree-based adaptive Cartesian grid generator and flow solver were developed. The grid adaptation based on pressure or density gradient was performed and a gridless method based on the least-square fashion was used to treat the wall surface boundary condition, which is generally difficult to be handled for the common Cartesian grid. First, to validate the technique of grid adaptation, the benchmarks over a forward-facing step and double Mach reflection were computed. Second, the flows over the NACA 0012 airfoil and a two-element airfoil were calculated to validate the developed gridless method. The computational results indi- cate the developed method is reasonable for complex flows.

关键词： Cartesian grid Gridless method Adaptation technique Euler solution

Fiducial inference in the pivotal family of distributions

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science china Mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying Department of Mathematics, beijing institute of Technology, beijing 100081, china academy of Mathematics and systems science, chinese academy of sciences, beijing 100080, china Department of Mathematics Beijing Institute of Technology Beijing China academy of Mathematics and systems science Chinese Academy of Sciences Beijing China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

Onset of cavitation by the strong tension spike from a tube-arrest apparatus

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science china(Physics,Mechanics & Astronomy) 2010年第2期53卷 301-305页

作者： YING ChongFu & LI Chao institute of Acoustics,chinese academy of sciences,beijing 100190,china institute of Acoustics Chinese Academy of Sciences Beijing China

Our earlier paper has identified a wave of Type 1 that is the pressure wave generated in the liquid-filled glass tube through the tube-arrest method by pulling and arresting the tube,when cavitation is prohibited. If cavitation is produced,a wave of Type 2 generally appears. The present paper takes the transition between wave types as indication of cavitation onset,and looks for a liquid parameter which controls the onset. One such an attempt shows the concentration of a dissolved gas in the liquid is the controlling factor with the result that the threshold of cavitation onset decreases with the increase of the concentration. Then a specially designed experiment reveals that possibly the mobility of the gas molecules (and also that of the liquid molecules) transiently affects the threshold so as to induce a large rise and fall in time of hours. The threshold finally settles down to some stable value under atmospheric pressure.

关键词： tube-arrest method cavitation onset controlling parameter concentration of dissolved gas mobile gas molecules liq-uid tensile strength

Effect of internal bubbly flow on pipe vibrations

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science china(Technological sciences) 2010年第2期53卷 423-428页

作者： ZHANG MingMing & XU JianZhong institute of Engineering Thermophysics, chinese academy of sciences, beijing 100190, china institute of Engineering Thermophysics Chinese Academy of Sciences Beijing China

This paper presents an experimental investigation on wall vibrations of a pipe due to injection of a uniform bubble cloud into the pipe flow. For different bubble void fractions and averaged bubble sizes, the vibrations were measured using accelerometers. To understand the underlying physics, the evolution of the vibration spectra along the streamwise direction was examined. Results showed that wall vibrations were greatly enhanced up to 25 dB, compared with no bubble case. The characteristics of the vibration were mainly dependent on void fraction. These vibrations were believed to be caused by two mechanisms: acoustic resonance and normal modes of the bubble cloud. The former, originating from the interaction between the first mode of the bubble cloud and the first acoustic mode of the pipe, persisted along the entire pipe to enhance the vibration over a broad band frequency range, while the later, due to the process of bubble formation, successively decayed in the streamwise direction.

关键词： pipe vibration bubbly flow acoustic resonance normal mode decay rate

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

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science china Mathematics 2012年第8期55卷 1597-1612页

作者： DING YuTao 1,2,& ZHANG LiQun 1,2 1 institute of Mathematics,academy of Mathematics and systems science,chinese academy of sciences,beijing 100190,china 2 Hua Loo-Keng Key Laboratory of Mathematics,chinese academy of sciences,beijing 100190,china institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing China

We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial *** related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral op... 详细信息

关键词： integral operators eigenvalues heat equation