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AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

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Acta Mathematica Scientia 2006年第4期26卷 639-645页

作者：李波刘禄勤 school of mathematics and statistics Huazhong Normal university Wuhan 430079China School of Mathematics and StatisticsWuhan UniversityWuhan 430072China school of mathematics and statistics Wuhan university Wuhan 430072China

Let Ls be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of Ls is obtained, and the sufficient and necessary condition for E^x（L^κB）〈∞ is pr... 详细信息

关键词： Last exit time moment transience distribution diffusion process

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 statistics,Wuhan university,Wuhan 430072,China school of mathematics and statistics Wuhan University Wuhan 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

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 statistics, Wuhan university, Wuhan 430072, China school of mathematics and statistics Wuhan University Wuhan 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 2D 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 extension of the first main theorem for π-blocks

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Science China mathematics 2006年第5期49卷 620-625页

作者： HAI Jinke Department of mathematics, qingdao university, qingdao 266071, China College of mathematics ,Shandong university, Jinan 250100, China Department of mathematics Qingdao University Qingdao China College of mathematics Shandong University Jian China

Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.

关键词： π-block, π-separable group, π-regular classes, defect group.

ON RAYLEIGH QUOTIENT MATRICES: THEORY ANDAPPLICATIONS

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Journal of Computational mathematics 1999年第6期17卷 629-638页

作者： Xin-guo Liu(Department of Applied mathematics Ocean university of qingdao, qingdao 266003, China) 青岛海洋大学应用数学系山东青岛 266003

Many authors have studied the Rayleigh quotient and Rayleigh quotient matrix. This paper consists of two parts. First, generalizations of some results on the Rayleigh quotient are proved. Second, we give some applicat... 详细信息

关键词： Rayleigh quotient matrix eigenvalue approximation

A general type of twisted anomaly cancellation formulas

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Science China mathematics 2010年第7期53卷 1684-1695页

作者： WANG Yong school of mathematics and statistics, Northeast Normal university, Changchun 130024, China school of mathematics and statistics Northeast Normal University Changchun China

For even-dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteris... 详细信息

关键词： modular invariance transgression cancellation formulas

Characterization of Type p Banach Spaces by the Weak Law of Large Numbers

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Wuhan university Journal of Natural Sciences 2002年第1期7卷 14-19页

作者： Gan Shi-xin school of mathematics and statistics, Wuhan university, Wuhan 430072, Hubei, China school of mathematics and statistics Wuhan University Wuhan Hubei China

For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.

关键词： Key words Banach space of typep array of random elements weighted sums weak law of large numbers {a nj } uniform integrability L r convergence convergence in probability

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 statistics, Wuhan university, Wuhan 430072, Hubei, China 2. school of Science, Beijing university of Posts and Telecommunications, Beijing 100876, China 3. school of mathematics and statistics, Huazhong Normal university, Wuhan 430079, Hubei, China school of mathematics and statistics Wuhan University Wuhan Hubei China school of Science Beijing University of Posts and Telecommunications Beijing China school of mathematics and statistics Huazhong Normal University Wuhan Hubei China

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

The closures of (U+K)-orbits of essentially normal triangular operator models

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Science China mathematics 2010年第11期53卷 1045-1066页

作者： ZHAI FaHui 1,& GUO XianZhou 2 1 Department of mathematics,qingdao university of Science and Technology,qingdao 266061,China 2 school of Sciences,Hebei university of Technology,Tianjin 300401,China Department of mathematics Qingdao University of Science and Technology Qingdao China school of Sciences Hebei University of Technology Tianjin China

The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator *** generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article "A survey of (U + K)-orbits".

关键词： (U+K)-orbit essentially normal operator triangular operator