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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.{3. department of mathematics,Hubei normal University,Huangshi 43.002,P.R.{3. 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

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, {3.) 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

Note on the number of integral ideals in Galois extensions

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Science china mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2 1School of mathematics,Shandong University,Jinan 250100,china 2department of mathematics,Capital normal University,Beijing 100048,china School of mathematics Shandong University Jinan China department of mathematics Capital Normal University Beijing China

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2,3....).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

THE SOLVABILITY FOR A CLASS OF SINGULARLY PERTURBED QUASI-LINEAR DIFFERENTIAL SYSTEM

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Acta Mathematica Scientia 2008年第3期28卷 495-500页

作者：莫嘉琪王辉林万涛 department of Mathemtics Anhui Normal University Division of Computational Science E-Institutes of Shanghai Universities at SJTUShanghai 200240China department of mathematics Huzhou Teachers'CollegeHuzhou 313000China Chinese Academy of Meteorological Sciences LASG Institute of Atmospheric PhysicsChinese Academy of Sciences

The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using t... 详细信息

关键词： Solvability singular perturbation differential system boundary layer

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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Science china mathematics 2011年第3期54卷 555-572页

作者： DENG ShengFu1, GUO BoLing2 & WANG TingChun2,3.1department of mathematics, Zhanjiang normal University, Zhanjiang 524048, {3. 2Institute of Applied Physics and Computational mathematics, Beijing 100088, {3. 3.College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, {3. department of mathematics Zhanjiang Normal University Zhanjiang China Institute of Applied Physics and Computational mathematics Beijing China College of Math and Physics Nanjing University of Information Science and Technology Nanjing China

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关键词： homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions

ON THE INVERSE IMAGE SET OF RATIONAL FUNCTIONS

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Acta Mathematica Scientia 2007年第3期27卷 541-548页

作者：孙道椿 department of mathematics South China Normal University

This article studies the inverse image of rational functions. Several theorems are obtained on the Julia set expressed by the inverse image, and a mistake is pointed out in ***＇ theorem incidentally.

关键词： Rational dynamical system Julila set Fatou component

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, {3. department of mathematics Shanxi Normal University Linfen 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

AVERAGE σ-K WIDTH OF CLASS OF L_p(R^n) IN L_q (R^n)

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Chinese Annals of mathematics,Series B 1995年第3期16卷 351-360页

作者： LIU YONGPING(department of mathematics, Beijing normal University, Beliing 100875, {3..) BEIJING normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn... 详细信息

关键词： Average σ-K width Optimal subspace,Sobolev-Wiener class,Riesz potential.

ALMOST　PERIODIC　SOLUTIONS　OF　NEUTRAL　FUNCTIONAL　DIFFERENTIAL　EQUATIONS　WITH　NONAUTONOMOUS　OPERATOR

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Chinese Annals of mathematics,Series B 1995年第4期16卷 519-530页

作者： YUAN RONG(department of mathematics, Beijing normal Universityl Beijing 100875, {3..) BEIJING normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

This paper presents some existence theorems on almost periodic solutions for almost periodicneutral functional differential equation and its perturbed systems by means of Liapunov functional, and extends the correspon... 详细信息

关键词： Almost periodic solution Neutral functional differelltial equation Nonautollomous operator