几何结构

First the math theory of machining simulation is studied, and the set structure of NC machining simulation system whose components, including time, input, output and so on, are defined. Hereby we set up the hierarchy structure, the logical structure, the static model and the dynamic model of simulation system. The construction method of sweep entity of cutter and rotation parts is researched, and their differential geometry invariants are calculated. NC code is unscrambled, and the recursion division arithmetic of time segment is put forward, which is the driven data of the movement or rotation parts. The CLDATA should be interference-free. To examine if there is interference between cutter flank and the work piece, an arithmetic that discussed the existence of intersecting curve between them is put forward. To examine if there is interference between two turrets, an arithmetic that discussed the existence of intersection set between two polygons is put forward.

首先研究加工过程仿真的数学基础，然后定义数控加工仿真系统的集合结构及时间集、输入集、输出集等概念，建立加工仿真的层次结构和逻辑结构，阐述双刀车削仿真系统的静态模型和动态模型建立方法，分析刀具扫描体和旋转部件扫描体的建立方法及其微分几何性质；研究NC代码解读技术和双刀加工时间段递归子分划技术，为驱动各仿真单元作数据准备；通过讨论后刀面和工件表面交线的存在性判断刀具后刀面与工件间是否干涉，通过求多边形的交集判断刀架与刀架是否干涉。

As basic element of CAGD, representation, design, display, analysis and handle of curve and surface is main task of CAGD.

作为CAGD系统基本几何元素，自由曲线、曲面的表示、设计、显示、分析以及规格、处理(包括数据结构、数据库、图形的信息形式和调整方式等)问题，是计算机辅助几何设计的主要研究对象和内容。

The cable sag effect, the beam-column effect and the large displacement effect are taken into account in the study. The results indicate that geometrical nonlinearity significantly influences the internal force of long span highway and railway cable stayed bridge, so the geometrical nonlinearity must be considered in design.

研究结果表明，几何非线性对大跨度公铁斜拉桥的内力影响比较显著，线性计算结果与非线性计算结果相比偏不安全，在公铁斜拉桥结构设计中，必须计入几何非线性的影响。

Libermann.The early researcheson this kind of manifolds were closely related to Physics and Mechanics.But since1991,S.Kaneyuki published his result on the algebraic condition for the existence ofinvariant〓structures on a coset space,Lie theory has played the most impor-tant role in the study of this kind of manifolds.In particular,dipolarizations in a Liealgebra are closely related to the homogeneous〓manifolds.Dipolarizationsin semisimple Lie algebras and the homogeneous〓manifolds associated withthese dipolarizations have been studied by S.Kaneyuki,Z.X.Hou and S.Q.Deng.Inthe partⅡ of this thesis we study the dipolarizations in some quadratic Lie algebrasand the homogeneous parakahler manifolds associated with these dipolarizations.

Libermann给出的，早期的有关类流形的研究与物理和力学密切相关，自从1991年金行壮二发表了陪集空间上存在不变仿凯勒结构的代数化结果后，李群及李代数理论在这类流形的研究中起着主要作用，特别地，李代数的双极化与这类流形密切相关，半单李代数的双极化的相关几何，金行壮二，候自新和邓少强等人已作了研究，二次李代数是比半单李代数更广且带有非退化不变双线性型的李代数，本文主要研究了二次代数的双极化及相关几何。

Contemporary geometric topology and differential topology , and particular subfields such as Morse theory , would be counted by most mathematicians as part of geometry.

现代微分几何拓扑和拓扑结构，特别是分支如莫尔斯理论，将计算的大多数数学家的一部分几何。

Geometry now is, in large part, the study of structures on manifolds that have a geometric meaning, in the sense of the principle of covariance that lies at the root of general relativity theory in theoretical physics.

现在是几何，在很大程度上是结构的研究流形上具有几何意义，在意义上的原则协在于从根本上广义相对论理论在理论物理。

Also, we can present the geometric representation of biological sequences and structures. So the genometric topology and group theory are important also.

同样我们可以用几何方法来表示生物序列和二级结构，几何拓扑和群论也发挥了很大的作用。

Inaddition, it can be used in the geometrically nonlinear analysis of structures of mixed connection.

同时采用本文提出的的几何非线性分析力学模型和非线性分析方法还可实现刚接与铰接混合连接的空间杆系结构的几何非线性性能分析，且计算效率优于子结构法。

According to the feature of drawing crystal shape from gnomonic projection,a data structure (the single 3 table chain structure )is presented.

根据极平投影绘晶体形态的特点，建立了一种数据结构———单链三表结构，此结构由面表、线表、点表组成，能充分反映晶体形态的拓扑信息和几何信息，并在此基础上设计了一种适合于变换和消隐处理的数据结

By introducing the two dimensional homogeneous coordinates of an infinite point on Euclidian plane,the point coordinates and linear coordinates of an infinite point in straight lines,some theorems and conclusions referred to infinite points are applied in the classifications of structures in this paper.

引入了欧氏平面上无限远点的二维齐次坐标和直线上无限远点的点坐标及线坐标，引用了与无限远点有关的一些定理及结论于结构的分类中。从而给出了可变体系中的常变与瞬变在结构形式上的区别，完善了杆系平面结构几何组成规则的内容

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。