蛙卵有丝分裂模型的定性分析

本文对M.T.Borisuk和J.J.Tyson在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了大范围周期解的存在性，给出了周期解所在的空间区域和所对应的参数区域及周期解不存在的空间区域和参数区域，所得结果严格地证明了[1]中给出的数值结果，最后我们证明在[1]的数值结果所用的参数下极限环的唯一性。     

有限区间上积分-微分算子的逆结点问题

研究Dirichlet边界条件下的积分-微分算子逆结点问题.证明了积分-微分算子稠定的结点子集能够唯一确定[0,π]上的势函数q(x)和区域Do上的积分扰动核M(x-t)且给出了这个逆结点问题的解的重构算法.     

关于集值优化问题的若干结果

引入了集值集值C-τ-半预不变凸概念，证明了集值集值C-τ-半预不变凸优化问题的局部弱有效元是弱有效元，给出了集值预不变凸变分不等式作为集值C-τ-半预不变凸优化问题的充分条件和必要条件，这些结果推广了文[1-4]的相应结果。     

平面上含两鞍结点和一鞍点的余维三多角环的三参数开折

本文应用有限光滑正规形理论，研究了平面上含有两个重数为２的鞍结点和一个双曲比率≠１的双曲鞍点的三类余维三多角环的一般三参数开折．证明了这三类多角环至多能分支出三条极限环，给出了分支图．     

弱Silnikov现象中的全局分支问题

本文考虑在一条同宿于具一对纯虚特征值的鞍－焦点的轨道邻域内的分支问题，证明了在同宿分支值的邻域内，存在着可数无穷多个鞍结点分支值，倍周期分支值和２－脉冲同宿分支值，并且两相邻鞍结点分支值的比趋于常数１。     

平面上含鞍结点与中心型鞍点的余维3环的三参数开折

本文应用有限光滑正规形理论研究了含有一个重数为2的鞍结点与一个中心型双曲鞍点（双曲比率为1）的余维3的平面环（Polycycle）的一般三参数开折与环性,证明了这类环至多分支出三条极限环,并且在一般性条件下环性为3,给出了分支图和相应的相图．作为应用,证明了文［4］提出的图（I192）环性为1的猜想．     

锥映象的K.Fan逼近定理及其应用

本文在Banach空间中分别就锥内的闭球、环形区域及球面，对半紧的1－集压缩映象证明了著名的K.Fan逼近定理，本质上改进和推广了文[2]的所有结果。并且应用所得结果给出了关于Banach空间中两点边值问题正固有元和正解的几个存在定理，这也是文[3]主要结果的推广和补充。     

关于耗散过程的若干结果

本文讨论Banach空间上的离散动力系统,给出了一类耗散过程存在稳定的最大紧不变集的充分条件,所得结果改进和推广了Hale[1] [2]和Massatt[7]的一些结果。     

微分同胚族共轭中的刚性现象

证明了对于仅有有限次光滑性的微分同胚族,即使在退化的鞍结点上,其刚性现象也成立,即:强拓扑共轭蕴含着共轭变换在鞍结点的中心流形上有某种光滑性。     

具有重结点的B-样条曲面G1的连续条件

本文得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G1光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G1光滑造型.     

Periodic Solutions of a Model of Mitosis in Prog Eggs

In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.     

THE UNIQUENESS OF BIFURCATION TO SEPARATRIX LOOPS IN SUPERCRITICAL CASES

ＴＨＥＵＮＩＱＵＥＮＥＳＳＯＦＢＩＦＵＲＣＡＴＩＯＮＴＯＳＥＰＡＲＡＴＲＩＸＬＯＯＰＳＩＮＳＵＰＥＲＣＲＩＴＩＣＡＬＣＡＳＥＳ￥ＳＵＮＪＩＡＮＨＵＡ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２...     

Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III

In this paper we study a generalized Gause model with prey harvesting and a generalized Holling response function of type III: . The goal of our study is to give the bifurcation diagram of the model. For this we need to study saddle-node bifurcations, Hopf bifurcation of codimension 1 and 2, heteroclinic bifurcation, and nilpotent saddle bifurcation of codimension 2 and 3. The nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram. The Hopf bifurcation is studied by means of a generalized Liénard system, and for b=0 we discuss the potential integrability of the system. The nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4. But because it occurs with an invariant line, the effective highest codimension is 3. We develop normal forms (in which the invariant line is preserved) for studying of the nilpotent saddle bifurcation. For b=0, the reversibility of the nilpotent saddle is discussed. We study the type of the heteroclinic loop and its cyclicity. The phase portraits of the bifurcations diagram (partially conjectured via the results obtained) allow us to give a biological interpretation of the behavior of the two species.     

关于混合图的谱扰动

本文刻画了如下的混合图:在添加一个环时,它恰有一个 Laplace特征值以整数增加,其它的 Laplace特征值保持不变.本文是文章[Linear Algebra and its Applications 374(2003):307-316]的一个延续性的文章.     

血生成模型的全局吸引性

在本文中，我们进一步研究时滞微分方程它由Ｍａｃｋｅｙ和Ｌａｄａｓ［２］提出作为血生成模型．我们建立了（＊）的平衡是全局吸引子的新的充分条件，我们还改进了Ｇｏｐａｌｓａｍｙ，Ｋｕｌｅｎｏｖｉｃ和Ｌａｄａｓ［１］所得到的某些结果．     

Examples of non-Kähler Hamiltonian torus actions

An important question with a rich history is the extent to which the symplectic category is larger than the K?hler category. Many interesting examples of non-K?hler symplectic manifolds have been constructed [T] [M] [G]. However, sufficiently large symmetries can force a symplectic manifolds to be K?hler [D] [Kn]. In this paper, we solve several outstanding problems by constructing the first symplectic manifold with large non-trivial symmetries which does not admit an invariant K?hler structure. The proof that it is not K?hler is based on the Atiyah-Guillemin-Sternberg convexity theorem [At] [GS]. Using the ideas of this paper, C. Woodward shows that even the symplectic analogue of spherical varieties need not be K?hler [W]. Oblatum IX-1995 & 3-III-1997     

Submanifolds in Cauchy Riemann Geometry

In this paper I would like to make a report on the results about hypersurfaces in the Heisenberg group and invariant curves and surfaces in CR geometry. The results are contained in the papers [8, 9, 16] and [14]. Besides, I would also report on the results about the strong maximum principle for a class of mean curvature type operators in [10].