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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

Commission Strategy of the Auction House

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wuhan university Journal of Natural Sciences 2006年第3期11卷 507-510页

作者： WANG Yan~ 1,2.1. College of Economics, Fudan university, Shanghai 2.0433, china {2., wuhan university , wuhan 430072. hubei, china College of Economics Fudan University 200433 Shanghai China school of mathematics statistics Wuhan University 430072 Wuhan Hubei China

In a SIPV model, when the commission proportion is not certain, but related with bargain price, generally, it is a linear function of the bargain price, this paper gives bidders＇ equilibrium bidding strategies in the first-and secondprice auctions. We find that the equilibrium strategies in second-price auction are dominant strategies. For seller or auction house, whether the fixed proportion or the unfixed proportion is good is not only related with constant item and the linear coefficient of the linear function, the size of the fixed commission proportion, but also related with the value of the item auctioned. So, in the practical auctions, the seller and the auction house negotiated with each other to decide the commission rules for their own advantage.

关键词： auction commission proportion Bayesian equilibrium bidding strategy

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.china 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

On the Symmetry Classes of Functions

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wuhan university Journal of Natural Sciences 2005年第5期10卷 813-816页

作者： ZHU Ping~1,2. FAN Yun~3 1. school of mathematics and {2., wuhan university, wuhan 430072. hubei, china 2. school of Science, Beijing university of Posts and Telecommunications, Beijing 100876, china 3. school of mathematics and {2., Huazhong Normal university, wuhan 430079, hubei, china wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Beijing university of Posts and Telecommunications School of Science Beijing China (GRID:grid.31880.32) Huazhong Normal university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.411407.7) (ISNI:***)

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

关键词： symmetry class strict symmetry class blockcharacter ξi-symmetric function block idempotent

A General Solution for a Class of Non-Homogeneous Recurrence Relations with Two Indices

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wuhan university Journal of Natural Sciences 2010年第4期15卷 287-291页

作者： YU Chang’an school of mathematics and {2., wuhan university, wuhan 430072. hubei, china school of mathematics and {2. Wuhan University Wuhan Hubei China

In this paper,we present the formula of a solution for a class of recurrence relations with two indices by applying iteration and induction according to the principle of solving algebraic equa-tions. It provides a con... 详细信息

关键词： two indices non-homogeneous recurrence relation formula of general solution

Evaluation Method of Web Site Structure Based on Web Structure Mining

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wuhan university Journal of Natural Sciences 2003年第3A期8卷 791-796页

作者： Li Jun\|e 1 , Zhou Dong\|ru 2.1. Computer Center,wuhan university,{2., china 2. school of Computer,wuhan university,{2.,china wuhan university Computer Center Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) wuhan university School of Computer Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

The structure of Web site became more complex than before. During the design period of a Web site, the lack of model and method results in improper Web structure, which depend on the designer's experience. From the point of view of software engineering, every period in the software life must be evaluated before starting the next period's work. It is very important and essential to search relevant methods for evaluating Web structure before the site is completed. In this work, after studying the related work about the Web structure mining and analyzing the major structure mining methods (Page\|rank and Hub/Authority), a method based on the Page\|rank for Web structure evaluation in design stage is proposed. A Web structure modeling language WSML is designed, and the implement strategies for evaluating system of the Web site structure are given out. Web structure mining has being used mainly in search engines before. It is the first time to employ the Web structure mining technology to evaluate a Web structure in the design period of a Web site. It contributes to the formalization of the design documents for Web site and the improving of software engineering for large scale Web site, and the evaluating system is a practical tool for Web site construction.

关键词： web structure mining page\|rank web structure evaluation modeling language for web structure