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In this thesis, we mainly study the homeomorphism flow properties of solutions for SDEs with jumps and backward stochastic differential equations, and also give some applications.

本文我们将上述结果作了以下两方面的推广，一方面是带跳随机微分方程解的同胚流及其应用，另一方面是倒向随机微分方程解的同胚流及其应用。

It is proved that if a homeomorphism f on a compact metric space with the POTP is distal homeomorphism, then f does not have the average shadowing property.

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性，并给出了有平均跟踪性的同胚是极小的一个充分条件。

Homtopy theory is the study of topological spaces using a broader equivalence than homeomorphism.

等变同伦满态与等变同伦单态方体定理

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。

Since 1950s,a series of such new economic phenomena as"Mystery of Modem Economic Growth"and"Mystery of Leontief,Wassily"have posed great challenge to the traditional theories,particularly such basic economic hypothesis as Capital Homogeny and Work Force Homogeny.

二十世纪五十年代以来，一系列新的经济现象，如"现代经济增长之谜"、"里昂惕夫之谜"等对传统经济理论，尤其是资本同质、劳动力同质等经济学基本假设提出了严峻挑战。

In the third chapter, identical words have been divided into synonymy and homograph from semanteme.

第三章从词义的角度出发，将同形词分为同形同义词和同形异义词。

The synonymy and homograph problem appearing in retrieval are resolved, trying hard to improve the effect of retrievals.

解决检索中出现的同义异形和同形异义词问题，尽可能地减少关键词匹配检索中的漏检和歧义的发生。

On the basis of division, the synonymy has been divided into absolute synonymy and relative synonymy, and the homograph has been divided into partial homograph and absolute homograph according to the differences of application area and sense of language.

在此基础上，按照使用范围以及语感的不同，将同形同义词分为完全同义词和相对同义词；将同形异义词分为部分异义词和完全异义词。

With the general toolbox in Maple,the principle and realization of a new homology continuation algorithm is put forward by constructing a new type homology function.

通过构造新型同伦函数并结合Maple高级程序设计语言的通用工具箱，提出了同伦算法的原理与实现方法。

This paper proves that the maximal right quasinormal band homomorphic image of free product of right quasinormal bands in semigroup category is isomorphic to their free product in right quasinormal band category.

证明了右拟正规带在半群范畴中的自由积的极大右拟正规带同态象同构于它们在右拟正规带范畴中的自由积。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。