查询词典 locally compact space

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

It separated 3-D space, 2-D space, temporal space and abstract space (focused on the first 3). 3-D space/2-D space belong to the same category in syntactic model; but 2-D space/ temporal space /abstract space share the same category when we talked about how to confirm the spatial direction. 2. It investigated a spatial system proposed by Mr. Qi Huyang, and argued that there is necessity to modify this system. 3. It enumerated a series of grammatical forms which are involved in the "Spatial System", and pointed out that there exits a relation among these forms: words representing "Spatial and Locative"→ phrases representing "Spatial and Locative"→ sentences representing "Spatial and Locative".

第三章研究"空间系统"的子系统。1、分出立体空间、线性空间、时间和抽象空间几大领域，在句法上，立体空间/线性空间是一类；但在如何确定方向场的问题上，线性空间/时间/抽象空间是一类。2、省视了齐沪扬先生已提出的一个空间系统体系，指出很有改进的必要。3、归纳了"空间系统"所涉及的各种语法形式，并指出它们构成"表示空间方位意义的词→表示空间方位意义的短语→表示空间方位意义的句子"的层次关系。4、辨析各种语法形式的语义域及其语义结构，并考察语法意义与语法形式的对应情况。

On the basis of Earth surface space using reference ellipsoid as height basis, map space using Gauss-Kruger projection plane as height basis, a viewpoint is proposed that map projection actually establishes corresponding relationship between the height bases of two different spaces above. From the viewpoint of projection and visible representation, the relationships among earth surface space, RS imagery space and map space are analyzed; the differences among different representations of earth surface space are identified theoretically; virtual reality is applied to the representation of land surface space, and a prototype of real 3D virtual reality system based on spatial information is developed. By means of digital simulation, virtual reality representation of land surface space in visual image space is realized.

在以参考椭球面为高程基准面表征地表空间、以高斯-克吕格地图平面为高程基准面表征地图空间的思想基础上，提出了地图投影实质上是建立两个空间的高程基准面之间关系的观点；从投影和可视表达的角度，分析了地表空间、遥感图像空间、地图空间之间的关系，从理论上区分了对地表空间的不同表达方式之间存在的差别；将虚拟现实技术应用于地表空间的表达，研制了空间信息三维虚拟现实系统原型，利用数字模拟技术在视像空间实现了对地表空间的真三维虚拟现实表达。

The results prove that T*1 S-closed space and T2 S-closed space are identical and that the regular S-closed space and normal S-closed space are the same. Therefore, to make T*1 space X become the complete conditions of S-closed space is the X extremely unconnected H-closed space, while S-closed space X can be measured as the complete condition X of S-closed T1 normal (A1) space.

首先讨论了S-闭空间的分离性，证明T*1型的S-闭空间与T2型S-闭空间是相同的，正则的S-闭空间与正规的S-闭空间是相同的，从而得到要使T*1型空间X成为S-闭空间的充要条件是X为极不连通的H-闭空间， S-闭空间X可度量化的充要条件是X为S-闭的T1型正则(A1)空间。

Besides, the author also give a detailed analysis and conclusion from the four levels of the total layout, building flat surface layout, building space and the exterior space shape. First, the thesis analyzed the race building, aim at the special natural environment and social milieu, i.e. how its total layout is; the concrete nature adaptability to the natural and social features. Second, this thesis analyzes the feature of layout in this origin with the examples of store, house, general residence, house, courtyard, public buildings and the clues of person's living mode. Furthermore, the thesis launches from street space, courtyard space, indoors space to explore the villages and living room of the nationalities such as 汉,土家,苗,侗. Finally, the thesis gives a specific analysis of the exterior space and nature factor, unreasoned composition of exterior space and fortuity, the relationship between the exterior space and function, the exterior space and geography and hang feet floor and horoscope doors and fence etc.

首先，论文分析了民族建筑针对特殊的自然环境与社会环境，其总体布局如何；具体体现自然适应性和社会适应性的特色：其次，论文以店宅、一般住宅、宅院、公共建筑四种湘西民族建筑类型为主，以相应的人的生活模式为线索，分析湘西民族建筑的平面布局特色；再者，论文从街道空间、院落空间、室内空间三个部分展开，同时对湘西地区汉族、土家族、苗族、侗族的村镇和民居建筑空间分别进行了颇有民族特色的着力探寻；最后，论文分外部空间造型与自然因素、外部空间造型的非理性与偶成、外部空间造型与功能关系、外部空间造型与地形关系、吊脚楼及八字门与围墙等六个部分，具体分析湘西民族建筑外部空间造型特色。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

Under the plastic-mulched ridge and furrow cultivation, the average soil water content of furrow (12.7%) was significantly higher than that of ridge (9.1%) at the soil depths of 20-100 cm. The locally compacted ridge served as a water flow barrier and a rainfall collection area under locally compacted ridge and furrow cultivation, and the water content of furrow was significantly higher than that of ridge in the same soil depths, which was similar to the characteristic of soil water distribution under plastic-mulched ridge and furrow cultivation. No significant differences were found in soil water content of furrow between locally compacted ridge and furrow cultivation and plastic-mulched ridge and furrow cultivation, with the same efficiency of water collection.

相对于自然垄沟，膜垄的集雨效果明显，沟中土壤平均含水量显著高于垄中，20～100cm土层范围内平均土壤含水量分别为12.7％和9.1％；成垄压实土壤水分在剖面分布状况与盖膜垄沟的水分分布相似，水分向沟内集中，沟中土壤水分含量显著高于同一土层深度处垄中土壤含水量，且与盖膜垄沟处理下沟中土壤水分含量无显著差异，在集水和聚水方面表现出和膜垄的相似性。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

在这个结果的基础上，我们定义了局部有限树集的概念，利用这个概念又定义了局部有限树鞅，通过局部有限树鞅给出了树鞅分解定理。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

基于这个分解，证明了树鞅指标集同构于一个有向森林，这个森林中的每一棵树都是有向局部有限树，这就证明了树鞅指标集有一个分解，它的每一部分同构于一个有向无限、局部有限树。

You think you're a big shot.

你认为你是一个大人物？

All states are equal, and none can receive special treatment from the federal government.

所有的州都是平等的，任何州都不能获得联邦政府的特别待遇。