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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.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.

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 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.

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 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 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) SHANGHAI normal UNIV DEPT MATHSHANGHAIPEOPLES R CHINA

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

Finite p-groups all of whose maximal abelian subgroups are soft

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Science china mathematics 2010年第11期53卷 3037-3040页

作者： QU HaiPeng department of mathematics, Shanxi normal university, Linfen 041004, china 1. department of mathematics Shanxi Normal University Linfen 041004 China

A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4.

关键词： soft subgroup p-group of maximal class