同胚

Furthermore,it shows that if E is a barrelled space with continuousdual 〓,then 〓 contains no copy of 〓 if and only if each〓 is compact operator.

据此证明了若E是桶型空间，那么〓〓不拓扑同胚地包含〓的充要条件是每个〓都是紧算子。

Next,it proves that if E is a barrelled space and F〓 is a locally convex space,Kis all the compact operators of L,then the weak operator topology and the uniformly operator topology have the same sub-series convergence series in Kif and only if 〓 contains no copyof 〓.

其次又得到，若E是桶型空间，〓是局部凸空间，那么紧算子空间K中弱算子拓扑与一致算子拓扑具有相同子级数收敛的充要条件是〓不拓扑同胚地包含〓。

The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.

本文讨论了定义在上述非柱形区域中的半线性抛物方程零能控性，我们使用的方法主要是通过同胚映射将非柱形区域中的抛物方程转化为柱形区域中的抛物方程，再利用不动点方法得到半线性抛物方程的有关结果。

The article roughs out some result about the mapping class group of a toms,including a classical theorem about the classification of all automorphisms of a toms.

文章介绍了关于环面的映射类群的一些结果，包括环面到自身的自同胚类的分类的经典结果。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

But diffeomorphism invariant theory leaves some problems to be explained, and the meanings of spacetime and physical theory are still in question.

但微分同胚不变理论存在需要解释的问题，空时及物理理论的意义仍不明确。

Further, when the coefficients are smooth, the solutions form a stochastic diffeomorphism flow.

而且，若系数是光滑的，则方程的解形成一随机微分同胚流。

It is proved that two sequences of Markov maps on the circle generated homeomorphic inverse limit spaces if each pair of the bounding maps with the same subscript are of the same Markov type with respect to a fixed arrangement of the two partitions.

证明了圆周上两个关于两组固定分点的Markov映射列在相同下标的两个约束映射总是关于两组分点的固定次序Markov同型的条件下生成同胚的逆极限空间。

In the last chapter, on the basis of theories in paper [4, 5], the notions of strong mixing, weak mixing, generator and expansion of the variable-parametric dynamical system are introduced, it turns out that in variable-parametric dynamical system strong mixing implies weak mixing and then implies transitivity; it is proved that if and both are variable-parametric dynamical system, F conjugates with G , the members of F are communicate with each other and the members of G are also communicate with each other, what's more, they are both homeomorphism, then F is strong mixing implies G has the same properties; futhermore, we prove that F is strong mixing implies F Devaney chaos in the sense of modification in variable-parametric dynamical system and that F Devaney chaos in the sense of modification if and only if G Devaney chaos in the sense of modification when semi-conjugate with and they both are communicate and homeomorphism; at last, we illustrate that F has generator if and only if it has weak generator, and we also prove that if F is expansion, then F has generator.

在第三章中，我们在文[4，5]的基础上，提出了变参数动力系统拓扑强混合、拓扑弱混合以及变参数动力系统的生成子、扩张的概念；证明了变参数动力系统拓扑强混合蕴含拓扑弱混合，进而蕴含拓扑传递；证明了：如果，为两个变参数动力系统，F与G拓扑半共轭，且F两两可交换，G两两可交换，它们均为同胚映射，那么F拓扑强混合，则G也有同样的性质；本章还证明了变参数动力系统拓扑强混合蕴含F在修改的意义下Devaney混沌；在此基础上得出了：如果变参数动力系统与变参数动力系统拓扑半共轭，它们都两两可交换，并且它们均为同胚映射，那么F在修改的意义下Devaney混沌当且仅当G在修改的意义下Devaney混沌；得出了F有生成子当且仅当F有弱生成子；如果F是扩张的，则F有生成子。

In section 3, the theorem is applied to interval analysis.

本文将Banach空间之间的同胚问题归之为一类动力系统非负解的存在性问题，证明了一个全局微分同胚定理，给出了一些推论，并应用于区间分析，推广了一些已有的结果。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。