查询词典 underlying topological space

XEX ~ Arg min{FIy E ~2} where the upper level is about topological structure optimization(a~ is a topological structure varable), and the lower level is a constrained programming about continuous variable y. 2 Apply graph, the action of permutation group on a graph, equiva- lent class, orbit etc.

取得的主要成果有： 1 依点到集的映射、集值映射、二元映射和分离定理等理论首次建立了具有拓扑结构双层规划的数学模型 min F s.t.x∈X y∈Arg min｛F|y∈Ω｝其上层规划为关于离散变量x的拓扑结构优化，下层规划是关于连续变量的约束规划。

This dissertation summarizes all kinds of topological relationships and spatial operations, and uses the conception realms to design the data structure of spatial region objects, and devises the red、blue planar graph algorithm, and makes use of red and blue sweep-line algorithm to implement the spatial topological analysis operations on layers of region objects. At the end, further works and improvements are presented.

本文 对空间拓扑分析操作进行了归纳总结，并且基于 Realms 概念探讨了空间区域对象的数据结构以及红蓝区域平面图算法，文章详细讨论了针对双层红蓝区域对象的各种空间拓扑分析算法的实现，最后是该类问题的进一步改进和构想。

The theory of topological perception argued that a primitive and general function of the visual system was the perception of global topological properties.

客体的形状、大小、明度、颜色、甚至拓扑结构等特征都与知觉组织有关，它们分别在知觉过程中起着不同的作用。

Based on twenty yearss research, Chen Lin developed the holistic processing hypothesis of Gestalt psychology into topology property perception theory, and thought of the human perception as a processing from holistic property to local property of perceptual object. From the viewpoint of Chen, a primitive and general function of the visual system is the perception of topological properties, and perceptual organization should be understood in the perspective of transformation and perception of invariance over transformation in the topological approach.

基于二十余年的研究积累，陈霖的拓扑性质知觉理论从格式塔心理学的整体加工思想出发，试图结合拓扑学的相关研究，对人类的知觉加工给出一个"大范围到局部"的说明，认为视觉系统的基本单元和一般功能是拓扑性质的知觉，知觉组织应当从变换和变换中的不变性知觉的角度进行理解。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

In this note, various definitions of lower semicontinuous set- valued mapping are extended to topological spaces without any metric topological and are compared.

文章的目的是要把各类下半连续型集值映射的定义推广到不带有任何度量的拓扑空间中并且作仔细的比较。

The topological bodies were introduced to express the topological relationships between complicated objects based on the point set topology.

5基于点集拓扑学理论，引入了拓扑体来描述矿山复杂对象间的拓扑关系。

This paper aims at the prominent issue that current models of spatial topological relations can not represent complex object, among which 9-Intersections Model (9IM) is well known. Therefore, taking cadastral data as example, one model of topological relations between complex and spatio-temporal objects based on 9IM is put forward. And the improved sweep-line algorithm is designed. Specific studies as follows:(1)According to the concepts of point set topology, the author distinguishes the complexity of the object, redefines the spatial point, line and region. For instance, in the simple region, concave one is more complex than convex, composite regions can be composed of many parts or with holes, and so on.

本文针对当前空间拓扑关系模型无法表达复杂对象的突出问题，以地籍对象为实例，以9I模型为基础，探索了一种适合复杂对象和时空对象的拓扑关系表达模型，较好地解决了地籍对象中各类要素间拓扑关系的描述和应用，实现了地籍变更中变化语义类型的推理和历史回溯；通过对现有的拓扑关系计算方法进行了改进，设计了相关算法，给出了C语言程序示例；最后通过实验系统的实现，验证了模型和算法的可行性。

Thirdly, based on the φ-mapping theory the topological field theory of various topological structures in two-and three-component spinor Bose-Einstein condensates is established.

第三，本文应用Φ-映射理论建立了两分量和三分量旋量玻色-爱因斯坦凝聚体中包含多种拓扑结构的拓扑场论。

It is found that topological charge of vortex beam influences the interference pattern, i.e., by compared with the straight interference pattern of plane wave, the interference pattern of vortex beam is shifted in the transverse direction as we look from the top of the interference to the bottom, and the magnitude and direction of shift are related to the topological charge.

详细介绍了涡旋光束的拓扑荷数对干涉条纹分布的影响。发现同平面波的竖直干涉条纹相比较，涡旋光束的干涉条纹，从顶部向底部看去，沿着横向出现移动，并且移动的大小和方向与拓扑荷数的取值有关。

A carrier gas such as nitrogen is directed through line 20 and valve 22 to connect with line 26 and mix with the gas sample.

如氮气之类的载体通过管线20和阀22引入，与管线26相通，与气体样品混合。

But for the most part, knaves and parasites had the command of his fortune

然而支配他的家产的大多是恶棍和寄生虫。