同胚的

Finally,as to an equicontinuous homeomorphism on a compact metric space,...

最后，针对紧致度量空间上的等度连续同胚，利用空间的极小性和紧致性，得到以空间中某有限个点的有限长轨道为中心，以ε2为半径的开邻域构成的有限子覆盖，并利用f的等度连续性，由该子覆盖构造出以空间任一点的有限长轨道为中心的开邻域所作成的有限子覆盖，进而得到所要结论。

Let be a homeomorphism, the following statements were obtained: if is distal and has POTP ,then does not have the average shadowing property; if is equicontinuous and has the average shadowing property, then f is minimal; let :X→X be distal and chaintransitive, then does not have POTP; is distal if and only if is distal.

设是个同胚映射，得到了如下结果：若有POTP且是distal的，则不具有平均跟踪性；若有平均跟踪性且是等度连续的，则是极小的；若是distal的且是链可迁的，则不具有POTP；是distal的当且仅当是distal的。

In chapter 3,we prove that a complete noncompact n-dimensional Riemannian manifold M whose Ricci curvature Ric_M ≥(n- 1) has finite topological type or diffeomorphic to R~n if its Excess function has some upper bound at a point.

第三章，我们证明了对于Ricci曲率Ric_M≥-(n-1)的完备非紧n维Riemann流形M，若它的共轭半径有正的下界且共轭半径的某个函数为M在某一点的Excess的上界时，它就有有限拓扑型或者微分同胚于n维欧几里德空间。

If the dynamicmapping thus determined is continuous,the two topological spaces is said to be homeomorphic and their respective energy shellsdo have the same dynamic property of being subdividable into invariant subspaces according to the same set of quantum num-bers.

如果这样决定的动力学映射是连续的，它就是两个拓扑空间之间的同胚映射，而两个系统的能量壳有同样的动力学性质，即可以按同一套量子数划分不变子空间。

The so-call'exportable equation'is found by nonlinear geometry method for general non-autonomous chaotic control systems which coefficient matrix of control term is functional matrix contained system variables. The homeomorphic transformation of coordinate is found under specified conditions, the coefficient matrix of control term can be transformed as constant matrix, the synchronization among chaotic systems can be realized by common control methods.

针对一般的非自治混沌控制系统中控制项系数矩阵是含有系统变量的函数矩阵，利用非线性几何线性化的方法找出所谓的"输出方程"，在一定的条件下求出坐标的同胚变换，将控制项系数矩阵变换为常矩阵，然后利用常规的控制方法进行混沌系统之间的同步化。

Paul Erds once posed the following problem about real line R: is it true that, for every infinite set X, there is a closed set E with positive lebesgue measure such that E doesn't contain any subset similar to X (I.e., there is no subset of E, which is a linear homeomorphic image of X). In 1984, K. J. Falconer proved the following: for a decreasing sequence of positive numbers {xn} such that \%lim\%xn=0 and \%lim\%(xn+1)/=1, Erds problem has a partial positive answer.

叶盛 Paul Erds曾提出如下关于实直线R的问题：是否对R的每一个无限子集X，都存在一个具有正测度的闭子集E，使得E的任何子集都不相似于X(E的任何子集都不与X线性同胚)。1984年，Falconer证明了如下结论：对于一个满足limxn=0和lim(xn+1)/=1的单调递减的正实数列{x n}，Erds问题有一个部分肯定的解答。

We prove in this paper that topological entropy is zero, in systems of equivariant mapping, that systems of compression mapping, and systems of the homeomorphism of unit circle onto itself, while the toppological entropy is positive, that extensible mapping in the compact toppological metric space.

证明了在一般的紧致度量空间上，等距映射的系统，压缩映射的系统，单位圆上的自同胚映射的系统等的拓扑熵都为零，而可扩映射的系统有正的拓扑熵。

A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms.

给出一类非线性系统的实现简单的多项式逼近的建模方法，在此方法中，将输入输出数据通过拓扑同胚变换，变换到[0，1]区间内，用多项式逼近的方法进行建模，对初始给定的多项式模型，通过反复的参数辨识、去除模型中的冗余项，得到非线性系统的多项式逼近模型，再利用拓扑反变换，将数据还原回原始数据区间。

The arguments on the necessary for quantized evaluation toward quality of services of multicast in Overlay networks are given. The concept of twodegree homeomorphism reduction multicast tree is introduced, extend Bowman's method for evaluating QoS of unicast dataflow by using stochastic process algebra is promoted, a modeling scheme is proposed for quantized evaluating QoS of concrete multicast instances in Overlay networks with simulation tool PEPA workbench.

论述了对Overlay网络中组播的服务质量进行量化评价的必要性，引入了组播树二度同胚约简的概念，推广了Bowman评价单播数据流服务质量的随机进程代数方法，提出用随机进程代数对Overlay网络中组播的服务质量进行评价的建模方案，并用PEPA workbench模拟工具针对具体的组播实例的服务质量进行了定量分析。

A key problem is: is it true that the supremum of the ratios of the moduli of quadrilaterals equals to the extremal maximal dilatation?In this chapter, firstly, for a class of quasisymmetric homeomorphisms with substantial boundary points, we apply a result of Chen Jixiu etc.

在第二章中，我们首先利用了文[16]的结果，研究了单位圆周上一类具有本质边界点的拟对称同胚，证明了它的极值拟共形延拓的最大伸缩商等于四边形模之比的上确界，改进了文[128]的有关结果。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。