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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.Beijing normal university,Beijing 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

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.

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, Beijing 100871, china) 北京大学数学系北京

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

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, 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 department of mathematics Zhejiang University (Xixi Campus) Hangzhou China School of Mathematical Sciences Beijing Normal University Beijing China department of mathematics University of Wisconsin-Milwaukee Milwaukee USA department of mathematics Central China Normal University Wuhan 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.

He原子和BH分子碰撞体系的转动激发能量转移

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物理学报 2011年第7期60卷 244-248页

作者：宫明艳安徽师范大学物理与电子信息学院芜湖241000

在碰撞体系He+BH的CCSD(T)二维势能面基础上,应用密耦方法,研究了He+BH分子碰撞转动激发过程.计算了该体系的转动态-态激发的弹性和非弹性的微分和积分截面,分析了计算结果与势能面特征间的关系.结果表明:He原子以从H原子端共线形式碰... 详细信息

在碰撞体系He+BH的CCSD(T)二维势能面基础上,应用密耦方法,研究了He+BH分子碰撞转动激发过程.计算了该体系的转动态-态激发的弹性和非弹性的微分和积分截面,分析了计算结果与势能面特征间的关系.结果表明:He原子以从H原子端共线形式碰撞BH分子对j=0→j'=2的激发最为有效;短程排斥对Δj=2的激发作用较大;态-态跃迁总截面出现振荡结构,长程部分分波只对j=0→j'=1的跃迁总截面有较大贡献,j'≥3的激发截面几乎完全由各向异性的短程部分贡献;低能下,Δj=1的激发较为有效,但较大能量则对Δj=2的激发最为有效.

关键词： He+BH体系转动激发散射截面

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 Institute of Operations Research Qufu Normal University Qufu China department of Applied mathematics Dalian University of Technology Dalian China department of Applied mathematics The Hong Kong Polytechnic University Hong Kong China department of mathematics Chongqing Normal University 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.

Harmonic maps with potential from complete manifolds

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Chinese Science Bulletin 1998年第21期43卷 1780-1786页

作者： CHEN Qun mathematics department, Central china normal university, Wuhan 430079, china Institute of mathematics, Fudan university, Shanghai 200433, china mathematics department Central China Normal University Wuhan China Institute of mathematics Fudan University Shanghai China

Harmonic maps with potential from complete manifolds are considered. This is a new kind of maps more general than the usual harmonic maps relating to many interesting problems such as equilibrium system of ferromagnetic spin chain and Neumann motion. Aiming at the general properties, the author derives basic gradient estimates and then Liouville type results for these maps, which are interesting in constrast to those of the usual harmonic maps for the presence of potentials.

关键词： harmonic maps potential ferromagnetic chain gradient estimate.

On solving equations of algebraic sum of equal powers

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Science china mathematics 2006年第9期49卷 1153-1157页

作者： WANG Xinghua & YANG Shijun department of mathematics, Zhejiang university, Hangzhou 310028, china department of mathematics, Hangzhou normal College, Hangzhou 310036, china department of mathematics Zhejiang University Hangzhou China department of mathematics Hangzhou Normal College Hangzhou China

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.

The Principal Eigenvalue for Jump Processes

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Acta Mathematica Sinica,English Series 2000年第3期16卷 361-368页

作者： Mufa Chen department of mathematics,Beijing normal university,Beijing 100875,P.R.china department of mathematics Beijing Normal University Beijing 100875 P. R. China

A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is *** result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov... 详细信息

关键词： Principal eigenvalue Jump processes Variational formula for Dirichlet form

ON THE SPLITTINGS FOR RECTANGULAR SYSTEMS

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Journal of Computational mathematics 1995年第4期13卷 337-342页

作者： H.J. Tian(department of mathematics, Shanghai normal university, Shanghai, china) 上海师范大学数学系上海

Recently, M. Hanke and M. Neumann([4]) have derived a necessary and sufficient condition on a splitting of A = U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum a-norm of the system Ax = b. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system Ax = b for every to is an element of C-n and every b is an element of C-m. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every to x(0) is an element of C-n.

关键词： AR Math ON THE SPLITTINGS FOR RECTANGULAR SYSTEMS