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ON THE RAngE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of mathematics, beij.ng normal university, beij.ng 100875, china.) beij.ng normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (department of mathematics, Shanghai normal university, Shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12.(t) + b11 u(t - τ1) + b12.(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.

Pairing problem of generators in Kac-Moody algebras

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Chinese Science Bulletin 1998年第22期43卷 1872-1879页

作者： LU Caihui department of mathematics, Capital normal university, beij.ng 100037, china department of mathematics Capital Normal University Beijing China

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that th... 详细信息

关键词： generator root system real root vector.

On quasi-convex mappings of order α in the unit ball of a complex Banach space

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Science china mathematics 2006年第11期49卷 1451-1457页

作者： LIU Taishun & XU Qinghua department of mathematics, Huzhou Teachers College, Huzhou, 313000, china department of mathematics, Jiangxi normal university, Nanchang, 330022, china department of mathematics Huzhou Teachers College Huzhou 313000 China department of mathematics Jiangxi Normal University Nanchang 330022 China

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.

关键词： coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order a.

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

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Acta Mathematica Sinica,English Series 2000年第2期16卷 261-270页

作者： Shaoyi Zhangdepartment of mathematics.beij.ng normal university,beij.ng 100875,P.R.china department of mathematics,Hubei normal university,Huangshi 435002,P.R.china department of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Hubei Normal University Huangshi 435002 P. R. China

In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is *** an application of this result,the well-known Strassen’s theorem is ***,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.

关键词： Transition probability Markovian coupling Jump process

THE PHYSICAL ENTROPY OF SIngLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, beij.ng 100871, china) beij.ng Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Regular n-simplices in R^n with vertices in Z^(n)

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Science china mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN Hourongdepartment of mathematics, Nanjing normal university, Nanjing 210097, china (email: jgxia@***) department of mathematics, Nanjing university, Nanjing 210093, china Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

Littlewood-Paley operators with variable kernels

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Science china mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, DIng Yong & FAN Dashan department of mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, china School of Mathematical Sciences, beij.ng normal university, beij.ng 100875, china department of mathematics, university of Wisconsin-Milwaukee, Milwaukee WI 53201, USA department of mathematics, Central china normal university, Wuhan 430074, china department of mathematics Zhejiang University [Xixi Campus] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

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Science china mathematics 2005年第2期48卷 261-276页

作者： WAng Changyu, YAng Xiaoqi & YAng Xinmin Institute oi Operations Research, Qufu normal university, Qufu 273165, china department of Applied mathematics, Dalian university of Technology, Dalian 116024, china department of Applied mathematics, The Hong Kong Polytechnic university, Hong Kong, china department of mathematics, Chongqing normal university, Chongqing 400047, china 1. Institute of Operations Research Qufu Normal University 273165 Qufu China 2. department of Applied mathematics Dalian University of Technology 116024 Dalian China 3. department of Applied mathematics The Hong Kong Polytechnic University Hong Kong China 4. department of mathematics Chongqing Normal University 400047 Chongqing China

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subdifferential characterizations of optimal value functions are given. Using these properties,we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.

关键词： optimal value function, directional derivative, subdifferential, semi-infinite programming, first order optimality condition.