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Completely regular paracompact reflection of locales

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Science china mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of mathematics, Nanjing normal university, Nanjing 210097, china department of mathematics, Sichuan university, Chengdu 610064, china department of mathematics Nanjing Normal University Nanjing 210097 China department of mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

Note on families of semistable curves over P^1 with 4 singular fibers whose Jacobian are non-compact

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Science china mathematics 2010年第7期53卷 1710-1713页

作者： YU Fei 1, 2 1 Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, china 2 department of mathematics, east china normal university, shanghai 2.0062. china Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China department of mathematics East China Normal University Shanghai China

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian

Problems in Homoclinic Bifurcation with Higher Dimensions

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Acta Mathematica Sinica,English Series 1998年第3期14卷 341-352页

作者： Zhu Deming department of mathematics, east china normal university. shanghai 2.0062. china department of mathematics East China Normal University 200062 Shanghai China

In this paper, a suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.

关键词： Exponential dichotomy Local coordinates Homoclinic bifurcation Periodic orbit

SINGLE BIRTH PROCESSES

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Chinese Annals of mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of mathematics,Beijing normal university,Beijing 100875,china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Uniform blow-up profiles and boundary layer for a parabolic system with localized nonlinear reaction terms

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Science china mathematics 2005年第2期48卷 185-197页

作者： LI Huiling & WANG Mingxin department of mathematics, Southeast university, Nanjing 210018, china department of mathematics, Xuzhou normal university, Xuzhou 221116, china 1. department of mathematics Southeast University 210018 Nanjing China 2. department of mathematics Xuzhou Normal University 221116 Xuzhou China

This paper deals with the blow-up properties of the solution to a semilinear parabolic system with localized nonlinear reaction terms, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the classical solution blows up in the finite time, secondly give necessary conditions and a sufficient condition for that two components blow up simultaneously, and then obtain the uniform blow-up profiles in the interior. Finally we describe the asymptotic behavior of the blow-up solution in the boundary layer.

关键词： parabolic system, localized nonlinear reaction terms, blow-up profiles, boundary layer size.

Dispersion of Soluble Matters in Newton-dipolar Stratified Fluid and Effects of Peripheral Layer

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 236-241页

作者： Zhangji LU, Shousheng DONG, Yu SHEN and Guangping ZHENG (department of Mechanics and Engineering Science, Fudan university, shanghai 200433,china)(department of Physics, east china normal university, shanghai 2.0062. china) Dept. of Mechanics and Eng. Science Fudan University Shanghai 200433 China department of Physics East China Normal University Shanghai 200062 China

In the paper, the dispersion law and the concentration distributions of soluble matters in Newton-dipolar fluids flowing through a circular tube have been investigated. Main results are: (1) for the dependence of M on A (or H), the completely opposite trends are obtained in the cases with and without the peripheral layer. (2) effects of δ on　M have the minimum values near 8=0.85-0.9. (3) various models such as couple stress,micropolar, dipolar, Newton-newtonian, Newton-couple stress and Newton-micropolar　model etc. are all special cases of Newton-dipolar fluid (where Mz=0). WhenMz≠ 0,however, there are evident differences between the Newton-dipolar fluid and the Newtoncouple stress fluid, the Newton-micropolar fluid.

关键词： dipolar fluid dispersion effects of a peripheral layer tube flow of complex fluid

Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of (?)~n

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Acta Mathematica Sinica,English Series 1995年第1期11卷 29-36页

作者： Ren Fuyao department of mathematics Fudan university shanghai,200433 china Xiao Jianbin department of mathematics Hunan normal university Changsha,410081 china harm.showa-u.ac.jp

In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are *** exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).... 详细信息

关键词： Bounded Projections and Duality on Spaces of Holomorphic Functions in the Unit Ball of Math Ball

MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (department of mathematics, Capital normal university, Beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

DECOMPOSITIONS OF BOSONIC MODULES OF LIE ALGEBRAS W_(1+∞) AND W_(1+∞)(gl_N)

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Chinese Annals of mathematics,Series B 2005年第4期26卷 633-642页

作者： HU NAIHONG LIU DONG department of mathematics East China Normal University Shanghai 200062 China. department of mathematics Changzhou Institute of Technology Changzhou 213002 Jiangsu China.

A bosonic construction (with central charge c = 2) of Lie algebras W1+∞ and W1+∞ (glN), as well as the decompositions into irreducible modules are described. And for W1+∞, when restricted to its Virasoro subalgebra... 详细信息

关键词： Bosonic representation Virasoro algebra