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Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science china mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,Zhejiang normal university,Jinhua 321004,china 2 department of mathematics,Tongji university,shanghai 200092,china 1. department of mathematics Zhejiang Normal University Jinhua 321004 China2. Department of Mathematics Tongji University Shanghai 200092 China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion

THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES

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Chinese Annals of mathematics 1988年第2期9卷 197-206页

作者：朱德明 department of mathematics east china normal university shanghai china.

Four topological and dynamical properties of nonorientable surfaces are *** is that for every continuous flow defined on any nonorientable closed surface,thereexist periodic or singular closed *** the case of the projective plane,it confirms aconjecture of professor Ye Yian-qian in his lecture notes“dynamical systems on surfaces”.Secondly,the author gives an exact upper bound of the number of closed curves onnonorientable surfaces,which do not intersect each other and the complement of their sumis still *** third is concerned with the upper and lower bound of the number ofthe periodic or singular closed orbits with certain *** last is related to theconnectedness of the complement of a lifting curve on two-fold covering *** firstproperty may be considered as a generalization of Kneser theorem from Klein bottle togeneral nonorientable surfaces and the second as a generalization of[4]Theorem 9.3.6from orientable surfaces to nonorientable surfaces.

关键词： Th THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES PCO

SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

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Chinese Annals of mathematics 1987年第4期8卷 466-478页

作者：朱德明 department of mathematics east china normal university shanghai china.

In the first section of the paper,the first three saddle values R1,R2,R3 of the realquadratic differential system（QDE） are computed by use of the method with which Poincaréresearchs on Hopf *** the second section,by applying the method and results ofDulac seeking integrability conditions of QDE it is proved that the system is integrable ifand only if R1=R2=R3=0,and it is also true when the system is *** integrabilityconditions given here can be applied much more easily then Dulac’*** the last part ofthe paper,it is pointed out that iR1,iR2,iR3 are the first three focal values of the weakfocus of the complex *** the formulae of R1,R2,R3 and the result in section 2,one can easily give the formulae of the focal values for the real QDE with Bautin formand give a new proof of Bautin’s famous result.

关键词：鲁一 Za SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science china(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & SUN JiTao 11 department of mathematics, Tongji university,shanghai 200092,china 2 department of mathematics,Luoyang normal university, Luoyang 471022,china 1. department of mathematics Tongji University Shanghai 200092 China2. Department of Mathematics Luoyang Normal University Luoyang 471022 China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES

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Journal of Computational mathematics 2003年第5期21卷 569-584页

作者： Er-xiong Jiang (department of mathematics, shanghai university, shanghai 200436, china) department of mathematics Shanghai University 上海 200436

Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.

关键词： Symmetric tridiagonal matrix Jacobi matrix Eigenvalue problem Inverse eigenvalue problem.

Finite element analysis for general elastic multi-structures

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Science china mathematics 2006年第1期49卷 109-129页

作者： HUANG Jianguo, SHI Zhongci & XU Yifeng department of mathematics, shanghai Jiao long university, shanghai 200240, china Division of Computational Science, E-lnstitute of shanghai Universities, shanghai normal university, shanghai 200234, china Institute of Computational mathematics, Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, china department of mathematics, Chinese university of Hong Kong, Shatin, N. T., Hong Kong, china department of mathematics Shanghai Jiao Tong University Shanghai 200240 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China Institute of Computational mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China department of mathematics Chinese University of Hong Kong Shatin N. T. Hong Kong China

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

关键词： elastic multi-structures, finite elements, generalized Korn's inequality, unique solvability, error estimates.

THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

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Journal of Computational mathematics 1998年第3期16卷 203-212页

作者： Xin-ming Xiang (shanghai normal university, shanghai 200234, china) 上海师范大学上海

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.

关键词： Kuramoto- Sivashinsky equation,large time convergence Approximate attractor Upper semicontinuity of attractors.

Issues of the Holocene transgression on the southern plain of the Changjiang Delta

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Acta Oceanologica Sinica 1988年第4期7卷 578-590页

作者： Yan Qinshang and Hong Xueqing department of Geography, east china normal university, shanghai, china Dept. of Geography East China Normal Univ. Shanghai China. China

The paper deals with the question of Holocene transgression on the southern plain of the Changjiang *** the beginning of the transgression, the paleovalleys of the Changjiang and Qiantang Rivers were covered by sea water at *** shoreline of 8000-7500 yr BP coincided with the -7m isobath of paleotopography. Sea level had already been the present level about 7000-6500 years ago, and the Holocene transgression reached its maximum extent. During the period, the Changjiang and Qiantang Rivers and the Dongtiaoxi valley were turned into estuaries; the eastern area of shanghai became a shallow sea; some of the bays and lagoons were distributed on the Hang-Jia-Hu and Tao-Ge Plain; the hilly region around the Taihu Lake was coastal marsh and freshwater swamp. Gangshen on the west of shanghai was formed 7000-4000 yr BP, and during the last 4000 years, the eastern coastal plain of shanghai advanced quickly toward the sea, and partial clear land of the western Taihu Lake was enclosed and charged into a fre

关键词： Ho Issues of the Holocene transgression on the southern plain of the Changjiang Delta

An improvement in stability of delay difference systems

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Chinese Science Bulletin 1998年第7期43卷 544-547页

作者： ZHANG Shunian department of Applied mathematics, shanghai Jiaotong university, shanghai 200240, china department of Applied mathematics Shanghai Jiaotong University Shanghai China

A new result on the stability of delay difference equations is established, in which a kind of weighted norm for x is adopted in order to estimate the upper bound of Liapunov functional.

关键词： delay difference systems uniform asymptotic stability in terms of two measures Liapunov functionals.