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Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

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Acta Mathematica Sinica,English Series 2002年第1期18卷 199-208页

作者： JIN Yin Lai ZHU De Ming department of mathematics. Linyi Teachers university. Shandong 276005. P. R. china department of mathematics. east china normal university. shanghai 200062. P. R. china department of mathematics. east china normal university. shanghai 200062. P. R. china department of mathematics Linyi Teachers' University Shandong P. R. China department of mathematics East China Normal University Shanghai P. R. China

In this paper, we study the bifurcation problems of rough heteroclinic loups cormecting threc saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition. the existence. uniqueness. nd incoexistencc of thc l-heteroclinic loop with threc or two saddle pomts. l-homoclinic orbit and l-periodic orbit near T are obtained. Nleanwhile, the bifurcation surfaces and existence regions are also given. Moreover. the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.

关键词： Local coordinates Heteroclinic loop Homoclinic orbit Periodic orbit Bifurcation surface

Global Existence of Positive Periodic Solutions for a Distributed Delay Competition Model

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 491-498页

作者： Xian-yi Li, De-ming Zhudepartment of mathematics, east china normal university, shanghai 200062, china department of mathematics and Physics, Nanhua university, Hengyang 421001, china department of mathematics East China Normal University Shanghai China department of mathematics and Physics Nanhua University Hengyang China

By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r 1 and r 2 are continuous ω-periodic functions in R + = [0,∞) with are positive continuous ω-periodic functions in R + = [0,∞), b i (i = 1, 2) is nonnegative continuous ω-periodic function in R + = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.

关键词： Global existence positive periodic solution coincidence degree distributed delay model

DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA

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Chinese Annals of mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU department of mathematics, shanghai normal university, shanghai 200234, china. 上海师范大学数学系上海

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

Algebraic Surfaces of General Type with K^2 = 2p_g-1, p_g■5

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Acta Mathematica Sinica,English Series 1996年第3期12卷 234-243页

作者： Liu Xianfang, department of mathematics east china normal university shanghai, 200062 chinaCurrent address: Institute of systems science Beijing, 100080 china department of mathematics East China Normal University Shanghai China

This paper mainly deals with minimal algebraic surfaces of general type with K^2= 2p_g-1. We prove that for p_g 7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces with p_g=5, 6. Lastly we show that when p_g 13 all these surfaces are simply-connected.

关键词： Double cover Canonical resolution Fibration Singular fiber Ramification divisor Branch locus

The Tracial Rokhlin Property for Automorphisms on Non-simple C~*-Algebras

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Chinese Annals of mathematics,Series B 2010年第2期31卷 191-200页

作者： Jiajie HUA department of mathematics East China Normal University Shanghai 200241 China.

Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊... 详细信息

关键词： Rokhlin property Tracial rank zero AF-algebra

Rose solutions with three petals for planar 4-body problems

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Science china mathematics 2010年第12期53卷 3085-3094页

作者： DENG ChunHua 1,2 , ZHANG ShiQing 1, & ZHOU Qing 3 1 Yangtze Center of mathematics and College of mathematics, Sichuan university, Chengdu 610064, china 2 Faculty of mathematics and Physics, Huaiyin Institute of Technology, Huai’an 223001, china 3 department of mathematics, east china normal university, shanghai 200062, china Yangtze Center of mathematics and College of mathematics Sichuan University Chengdu China Faculty of mathematics and Physics Huaiyin Institute of Technology Huai’an China department of mathematics East China Normal University Shanghai China

For planar Newtonian 4-body problems with equal masses, we use variational methods to prove the existence of a non-collision periodic choreography solution such that all bodies move on a rose-type curve with three pet... 详细信息

关键词： 4-body problems with Newtonian potentials rose solutions with three petals winding numbers variational minimization methods

THE PROJECTIVE PLANE CROSSING NUMBERS OF CIRCULAR GRAPHS

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Journal of Systems Science & Complexity 2008年第2期21卷 316-322页

作者： Dengju MA Han REN School of Science Nantong University Nantong 226007 China department of mathematics East China Normal University Shanghai 200062 China

The authors give an upper bound for the projective plane crossing number of a circular graph. Also, the authors prove the projective plane crossing numbers of circular graph C （8, 3） and C （9, 3） are 2 and 1, resp... 详细信息

关键词： Circular graph crossing number projective plane crossing number.

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 200062. 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

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian hongjiong & Kuang Jiaoxun (department of mathematics, shanghai normal university, shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.