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COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

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Acta Mathematica Scientia 2011年第1期31卷 353-360页

作者：邓勤涛 Department of mathematics Sun Yat-Sen University Laboratory of Nonlinear Analysis and School of Mathematics and StatisticsHuazhong Normal University

In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4（-1）（H5（-1）） with constant mean curvature H satisfying H2 6634 （H2 114785 respectively） must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4（-1）（resp. H5（-1）） with constant mean curvature H satisfying H2 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].

关键词： k-weighted bi-Ricci curvature finite index constant mean curvature

Adaptive quasi-likelihood estimate in generalized linear models

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Science china mathematics 2005年第6期48卷 829-846页

作者： CHEN Xia & CHEN Xiru School of mathematics and statistics, Wuhan university, Wuhan 430072, china Graduate School, Chinese Academy of Science, Beijing 100049, china 1. School of mathematics and statistics Wuhan University 430072 Wuhan China 2. Graduate School Chinese Academy of Science 100049 Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

CONTACT PROCESS ON HEXAGONAL LATTICE

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Acta Mathematica Scientia 2010年第3期30卷 769-790页

作者：姚强李群昌 Department of statistics and Actuarial Science School of Finance and Statistics East China Normal University School of Mathematical Sciences Peking University

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

关键词： Hexagonal lattice contact process critical value complete convergence theorem rate of growth

Isometric Immersions into Warped Product Spaces

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Acta Mathematica Sinica,English Series 2010年第12期26卷 2269-2282页

作者： Qun CHEN Cai Rong XIANG~1) School of mathematics and statistics, Wuhan university, Wuhan 430072, P.R. china School of mathematics and statistics Wuhan University Wuhan 430072 China

This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.

关键词： Isometric immersion hypersurface warped product the fundamental theorem

Regular solutions for multiplicative stochastic Landau-Lifshitz-Gilbert equation and blow-up phenomena

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Science china mathematics 2010年第12期53卷 3115-3130页

作者： PU XueKe 1, & GUO BoLing 2 1 college of mathematics and statistics, Chongqing university, Chongqing 400044, china 2 Institute of Applied Physics and Computational mathematics, P. O. Box 8009, Beijing 100088, china 1. college of mathematics and statistics Chongqing University Chongqing 400044 China2. Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China

The two-dimensional Landau-Lifshitz-Gilbert equation of motion for a classical magnetic moment perturbed by a multiplicative noise is considered. This equation is highly nonlinear in nature and, for this reason, many mathematical results in stochastic partial differential equations (SPDEs) cannot be applied. The aim of this work is to introduce the difference method to handle SPDEs and prove the existence of regular martingale solutions in dimension two. Some blow-up phenomena are presented, which are drastically different from the deterministic case. Finally, to yield correct thermal-equilibrium properties, Stratonovitch integral is used instead of Ito integral.

关键词： stochastic Landau-Lifshitz-Gilbert equation regular solution difference method blow up

DYNAMIC CHARACTERISTICS OF LIQUID SLOSHING IN A TRANSVERSELY VIBRATING SPHERICAL TANK WITH A SPACER UNDER LOW GRAVITY

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Journal of Hydrodynamics 2008年第6期20卷 762-769页

作者： CHENG Xu-duo HU Mei-zhu WEN Ji-hua School of Food Science and Engineering Nanjing University of Finance and Economics Nanjing 210003 China Department of Physics Anqing Teachers College Anqing 246011 China

The dynamic characteristics of liquid sloshing in a transversely vibrating spherical tank with spacer under low gravity were investigated. By expanding the characteristic functions, the frequencies and velocity potentials of liquid free-sloshing were obtained. The dynamic equations and boundary conditions of liquid sloshing in the traverse vibrational spherical tank with spacer under low gravity were derived. By modifying the velocity potentials of liquid free-sloshing, the velocity potentials of liquid sloshing in the traverse vibrating spherical tank with a spacer were obtained. Furthermore, the forces and the moments acting on tank wall were given. The numerical results show when a spacer is inserted in the tank, the sloshing frequencies of liquid and the forces acting on tank wall will decrease, but the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer will occur.

关键词： low gravity liquid forced sloshing sloshing suppression

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

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Science china mathematics 2004年第6期47卷 882-893页

作者： YUE Li & CHEN Xiru School of mathematics and statistics, Wuhan university, Wuhan 430072, china Graduate School, Chinese Academy of Sciences, Beijing 100039, china 1. School of mathematics and statistics Wuhan University 430072 Wuhan China 2. Graduate School Chinese Academy of Sciences 100039 Beijing China

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

关键词： quasi-likelihood function generalized linear models strong consistency

DYNAMIC CHARACTERISTICS OF LIQUID FORCED SLOSHING IN A TURNING SPHERICAL TANK WITH A SPACER UNDER LOW GRAVITY

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Journal of Hydrodynamics 2008年第2期20卷 202-209页

作者： CHENG Xu-duo HU Mei-zhu WEN Ji-hua School of Food Science and Engineering Nanjing University of Finance and Economics Nanjing 210003China Department of Physics Anqing Teachers College Anging 246011 China

Under the condition of low gravity the characteristics of liquid forced sloshing in a turning spherical tank with a spacer were investigated. The static shape of the liquid surface was analyzed. By expanding the characteristic functions, the frequencies and velocity potential of liquid free-sloshing were derived. The governing equations and boundary conditions for the forced sloshing of liquid under the tank turning were established. The transverse force of liquid acting on the tank and the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer were given. Numerical results were compared with the ones of the spherical tank without a spacer. The results show that when a spacer is inserted in the tank, the sloshing frequency of liquid and the transverse force of liquid acting on the tank will decrease, but the moment of force to the centre of the tank which is caused by the force of liquid acting on the spacer will occur.

关键词： low gravity forced sloshing of liquid sloshing suppression

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2 ,DU Jin-yuan 1,3 1. School of mathematics and statistics, Wuhan university, Wuhan 430072, Hubei, china 2. School of mathematics and Computer, Ningxia university, Yinchuan 750021, Ningxia, china 3. Department of mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, china Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningxia university School of Mathematics and Computer Yinchuan Ningxia China (GRID:grid.260987.2) (ISNI:***) Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Hubei Institute for Nationalities Department of Mathematies Enshi Hubei China (GRID:grid.34418.3a) (ISNI:***)

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order