扑

Firstly, based on the generalized function,φ-mapping topological current are rigorously proved to be of delta-function form δ and can be labelled by the nodal indices of the vector field, namely by Hopf indices and Brouwer degrees of this vector field, which reveals the inner relationships between our theory and the topology of vector bundle.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

For inheriting the dynamic constraint information of the multibody simulation model, topological configuration of the multibody simulation model was built, and simplified constraint form was put forward with the topological mapping of the multibody simulation model in the heterogeneous systems. To transform the information of the multibody simulation model, the offset matrix which transformed the location and orientation of constraints and the matrix which transformed the location and orientation of parts were computed.

利用多体动力学仿真模型在异构系统的拓扑映射，建立多体动力学仿真拓扑构型，提出仿真模型动力学约束的约束简型表示法，实现动力学约束信息的关联继承，并通过约束偏置变换矩阵和构件位姿变换矩阵的求取，驱动多体动力学仿真模型构件和约束位姿的自动调整，实现多体动力学仿真模型的动态转化。

A method of the surface combination based on classification or Euler Operation and the computation of the surface boundaries of a surface is offered to finish the geometry mapping of surfaces between half-edge model and the closed_shell branch of manifold surface model. Moreover, the concepts of conformal-shape geometrical mapping and topological mapping are given. The bi-directional conformal-shape topological mapping between half-edge model and the closed_shell branch of manifold surface model is proved.

提出了一种基于等价分类和欧拉操作的面片合成和曲面边界计算方法，完成了半边模型到流形曲面模型closed shell枝的曲面几何映射；给出了保形几何和保形拓扑映射概念，证明了半边模型到流形曲面模型的closed_shell分枝的双向保形拓扑映射。

Firstly,based on the generalized function,φ-mapping topological currentare rigorously proved to be of delta-function formδand can be labelledby the nodal indices of the vector field,namely by Hopf indices and Brouwerdegrees of this vector field,which reveals the inner relationships between ourtheory and the topology of vector bundle.A singular divergence theorem isalso presented.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

Moreover, a sufficient and necessary condition for an I -topological vector space to be determined by its level topological spaces is discussed.

此外，还讨论了I型fuzzy线性拓扑由其水平拓扑确定的充要条件。

In this thesis, we mainly study several problems on geometry and topology of Rieman-nian submanifolds, which contains the geometric rigidity, topological sphere theorems and eigenvalue problems of Laplace-Beltrami operator on Riemannian submanifolds.

本文着重研究黎曼子流形上几何与拓扑的若干问题，主要内容包括子流形的几何刚性、拓扑球面定理和Laplace-Beltrami算子的特征值问题。

The crucial point of topology relationships is the building of topological structure.

拓扑关系的关键点在于拓扑结构的构建。

It has been shown in practice that the proposed method can describe topological structure exactly and be of fairly high practical value.

经过实际应用表明，本文提出的基于GIS的农村配电网络拓扑分析方法能够正确描述系统的拓扑结构，具有很大的实用性和推广价值。

Besides,we study the topology of Riemannian manifolds with some curvature conditions via comparisonsl geometry methods,and we get some results towards the topological type and the finiteness of isomorphism classes of fundamental groups of some Riemannian manifolds.

另外，我们在比较几何的框架下研究了具特定曲率条件的Riemannian流形的拓扑，得到了有关有限拓扑型和基本群同构类的一些结果。

Based on these researches,a full theoretical method is established, which is an applicable to determine all possible STPR mechanisms of anyone usable topological limb.Finally,this family of STPR mechanisms is determined one by one.Each mechanism in the family is depicted by means of the type of its topological limb,the actuated layout,and the structure parameter.

基于这些工作，形成一套完整的理论方法，用来确定任何一种可用分支拓扑组成的所有可能的STPR机构，一类STPR机构最终逐个被确定，每个机构都可以根据其分支拓扑类型、驱动布局类型和结构参数给以唯一的描述。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。