同胚

The nonlinear dynamic model was expressed based on the format of SISO affine nonlinear system. Then the system was represented into the standard Byres-Isidori format base on the diffeomorphism transform.

使用SISO仿射非线性系统描述了所建立的自行车机器人非线性动力学模型，利用非线性微分同胚变换将该系统化成了Byres-Isidori非线性系统的标准型形式。

The reduced dynamic model including motor dynamics is developed for nonholonomic mobile manipulators. The system is then decomposed into four lower-dimensional subsystems by applying diffeomorphism and nonlinear input transformation to the reduced model. The design of robust controller is also addressed for the output tracking of mobile manipulators.

首先给出了包括驱动电机动态特性的非完整移动机械臂的简化动态模型，然后通过微分同胚和输入变换将其分解为四个低阶子系统，并给出了其输出跟踪的滑模控制器设计方法。

After defining the normal forms and quasi—linearization forms, the simplified forms of uncertain nonlinear systems abtained by means of state feedback/disturbance feedforward/diffeomorphism are derived.

通过定义不确定非线性系统的规范型和准线性化形式，推出了不确定非线性系统经状态反馈/干扰前馈/微分同胚变换后所具有的简化形式。

Firstly, the reduced dynamic model including motor dynamics is developed for mobile manipulators. The system is then decomposed into four lower-dimensional subsystems by applying diffeomorphism and nonlinear input transformation to the reduced model. The design of the second order dynamical sliding mode controller is then addressed for the output tracking of mobile manipulators.

首先给出了包括驱动电机动态特性的移动机械臂的简化动态模型，然后通过微分同胚和输入变换将其分解为四个低阶子系统，并给出了其输出跟踪的二阶动态滑模控制器的设计方法。

A class of affine nonlinear system of single input-single output is investigated. Firstly, the nonlinear system is transformed into an equivalent linear system through a diffeomorphism transformation. The networked control problems for the delays are constant, stochastic and shorter than a sampling period, and long and stochastic are investigated respectively.

针对一类单输入-单输出仿射非线性系统，首先通过微分同胚变换实现了仿射非线性系统的无反馈精确线性化；然后基于精确化线性模型，分别讨论网络延时为常时滞，随机时滞小于一个采样周期和随机长时滞情况的控制问题。

In differentiable manifolds, one studies for instance differentiable structure, definition of differential manifolds, diffeomorphism, tangent space, Embedding theorem, partitions of unity etc.

微分流形部分主要涉及微分结构，微分流形的定义及例子，可微映射，微分同胚，切空间与余切空间，流形的嵌入，单位分解定理等。

In Chapter 3,the concept of obstruction set for diffeomorphisms is introduced.And then we givesan important relation between obstruction set and dual mapping.

在第三章我们对微分同胚引入了阻碍集的概念，随后给出了阻碍集与对偶映射之间的一个重要关系。

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。

Minimality ; minimal set ; compact metric space ; open cover ; equicontinuous homeomorphism

极小性；极小集；紧致度量空间；开覆盖；等度连续同胚

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 。