查询词典 hilbert space

Also prove that every bounded linear approximately local Hilbert space representation of a abelian von Neumann algebra is a representation,every bounded linear approximately 2- local Hilbert space representation of a von Neumann algebra is a representation.

同时证明了交换von Neumann代数的有界近似局部表示是表示，每个von Neumann代数的有界近似2—局部表示是表示。

There is a bijection between the set of all the projections on Hilbert space H and the set of all the closed subspaces of Hilbert space H.

我们都知道Hilbert空间上的正交投影和Hilbert空间的闭子空间是一一对应的。

Hilbert space and generalized Fourier series in Hilbert space,etc.

Hilbert空间与广义Fourier级数，主要讲授内积空间内积空间中的正交系，投景定理，与广义Fourier级数。

Using two new methods, this paper prores one pertubation theorem on the finite Hilbert space of 2×2 operator matrices, and gereralizes this theorem to the infinite Hilbert space of selfadjoint operators.

给出了有限维Hilbert空间中2×2算子矩阵的数值域扰动定理的两种证明方法，并且将该定理推广到无限维Hilbert空间上的自伴算子。

In chapter 1, we introduce the notions of the approximately 2-local automorphisms, the approximately local Hilbert space representations and the approximately 2- local Hilbert space representations;We prove that every surjective and multiplicative approximately local *-automorphisms of a C*- algebra with a unique faithful tracial state is *-automorphisms;surjective approximately 2- local *- automorphisms of C*-algebra with unique faithful tracial states are Jordan *- automorphisms;Surjective approximately 2- local *- automorphisms of a finit factor are *-automorphisms;Approximately 2- local *- automorphisms of M_n are *-automorphisms.

第一章定义了近似2—局部自同构，近似局部表示，近似2—局部表示；证明了有唯一忠实迹态的C~*-代数上的满可乘近似局部*—自同构是*—自同构，满近似2—局部*—自同构是Jordan *—自同构，有限因子上的满近似2—局部*—自同构是*—自同构，以及矩阵代数M_n上的近似2—局部*—自同构是*—自同构。

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。

The simulation and test results show that the space-filling feature of Hilbert fractal structure antenna can be effectively transformed into the size-reducing feature, and that the RFID tag antenna with one-dimension Hilbert fractal structure is of higher efficiency.

仿真和实测结果表明，Hilbert分形结构天线的空间填充特性可有效转化为标签天线的尺寸缩减特性，而且一维Hilbert标签天线具有更高的天线效率。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。