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Periodic Solution for Diffusive Predator-Prey System with Functional Response

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wuhan university Journal of Natural Sciences 2002年第3期7卷 267-273页

作者： Li Bi\|wen 1,2., Cheng Jian 1 1. Department of mathematics, hubei Normal {2., Huangshi 435002. hubei,china 2. school of mathematics and statistics, wuhan {2., wuhan 430072, hubei,china hubei Normal university Department of Mathematics Huangshi Hubei China (GRID:grid.462271.4) (ISNI:***) wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) hubei Normal university Department of Mathematics Huangshi Hubei China (GRID:grid.462271.4) (ISNI:***)

In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence ... 详细信息

关键词： diffusive model functional nesponse positive periodic solution continuation theorem of coincidence degree fopological degree

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B值拟鞅差序列加权和的收敛性与大数律

武汉大学学报（理学版） 2002年第3期48卷 281-284页

作者：邱德华甘师信衡阳师范学院数学系湖南衡阳421008 武汉大学数学与统计学院湖北武汉430072

{Xn,Fn,n≥1}为B值P拟鞅,{anj}为实值常数阵列,在{}关于{}一致可积的条件下,建立了anjdjX的收敛性与Banach空间p光滑性的关系,并在p光滑Banach空间中,给出anjdjX的强大数定律及完全收敛定理.

关键词： B值似鞅差序列加权和收敛性大数律

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随机环境马氏链中的几种等价关系

武汉大学学报（理学版） 2003年第5期49卷 567-570页

作者：郭光耀胡迪鹤曾华武汉化工学院计算机系湖北武汉430074 武汉大学数学与统计学院湖北武汉430072

假设Xn是定义在随机环境下具有有限或者可列的马氏链,本文利用Hopf马氏链和绕积马氏链的方法,研究了随机环境马氏链中的互通、相遇等等价关系,获得了一些与经典马氏链类似的结果,这些结果对进一步研究随机环境马氏链是有意义的.

关键词：随机环境马氏链等价关系 Hopf马氏链绕积马氏链互通相遇保守集

Non-Homogeneous Riemann Boundary Value Problem with Radicals

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wuhan university Journal of Natural Sciences 2002年第4期7卷 379-382页

作者： Lu Jian-ke school of mathematics and {2.,wuhan university,wuhan 430072, hubei,china wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2. together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for t... 详细信息

关键词： Riemann boundary value problem branch points of radicals index order at infinity sectionally holomorphic functions

Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises

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Science china mathematics 2010年第11期53卷 2949-2972页

作者： ZHANG XiCheng school of mathematics and {2., wuhan university, wuhan 430072, china 1. school of mathematics and {2. Wuhan University Wuhan 430072 China

In this paper, we study the regularity of solutions of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noises in the framework of Hilbert scales. Then we apply our abstract result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau equations on the real line, stochastic 2. Navier-Stokes equations (SNSEs) in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their smooth solutions respectively. In particular, we also get the existence of local smooth solutions for 3D SNSEs.

关键词： smooth solutions stochastic partial differential equations stochastic Navier-Stokes equations

The construction of Markov processes in random environments and the equivalence theorems

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Science china mathematics 2004年第4期47卷 481-496页

作者： HU Diheschool of mathematics and {2., wuhan university, wuhan 430072, china 1. school of mathematics and {2. Wuhan University 430072 Wuhan China

In sec.1, we introduce several basic concepts such as random transition function, p-m process and Markov process in random environment and give some examples to construct a random transition function from a non-homogeneous density function. In sec.2. we construct the Markov process in random enviromment and skew product Markov process by p - m process and investigate the properties of Markov process in random environment and the original process and environment process and skew product process. In sec. 3, we give several equivalence theorems on Markov process in random environment.

关键词： radom transition function, p -m process, Markov process in random environment, skew product Markov process, density function.

Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails

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Science china mathematics 2010年第6期53卷 1421-1434页

作者： LIU Li school of mathematics and {2.,wuhan university,wuhan 430072,china 1. school of mathematics and {2. Wuhan University Wuhan 430072 China

This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying *** moderate deviations of partial sums are first *** results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.

关键词： moderate deviation extended negative dependence consistently varying tail random sum

Some Index Classes of Singularity of Vector Fields on Manifolds with Boundary

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wuhan university Journal of Natural Sciences 2002年第4期7卷 388-390页

作者： Xu Xu, Liu Heng-xing school of mathematics and {2., wuhan university, wuhan 430072, hubei, china wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

V. I. Arnold defined some particular classes of index for singularities of adapted fields. We generalize these index classes for general fields on manifolds with boundary and get some relations of these index classes.

关键词： adapted fields singularity index

A Principal Theorem of Normal Discretization Schemes for Operator Equations of the First Kind

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wuhan university Journal of Natural Sciences 2001年第4期6卷 767-768页

作者： Du Nai lin 1, Wang Hannah 2.1.school of mathematics and {2., wuhan university, wuhan 430072, china 2. school of Foreign Languages and Literature,wuhan university,wuhan 430072,{12. wuhan university School of Mathematics and Statistics Wuhan China (GRID:grid.49470.3e) (ISNI:***) wuhan university School of Foreign Languages and Literature Wuhan China (GRID:grid.49470.3e) (ISNI:***)

The authors announce a newly-proved theorem of theirs. This theorem is of principal significance to numerical computation of operator equations of the first kind.

关键词： operator equation of the first kind normal discretization scheme pure pseudoinverse