查询词典 relatively bounded space

That is, any function from a discrete metric space to another bounded metric space is Lipschitz continuous, and any function from a discrete metric space to another metric space bounded by 1 is short.

就是说，从离散度量空间到另一个有界度量空间的函数是李普希茨连续的，而任何从离散度量空间到另一个有界于 1 的度量空间的函数是短映射。

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。

We proved that this kind of operators were bounded from Hardy space to Lebesgue space, and they were bounded operators on the Hardy space if they satisfied some special conditions.

利用Hardy空间和Herz型Hardy空间的原子和分子分解特征，文中首先给出了此类算子从Hardy空间到Lebesgue空间上的有界性，而且，在满足一定的消失矩时，它又是Hardy空间上的有界算子。

In chapter four, we prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its excess is bounded by some function of its conjugate radius.

第四章，我们证明了对于Ricci曲率具负下界的完备开Riemannian流形，当其共轭半径有正下界且它的Excess被其共轭半径的某个函数所界定时，它就有有限拓扑型。

Based on the concepts of bounded operator, positive bounded operator and possible bounded operator their connections are discussed such that the contents are deeper.

在有界算子，肯定有界算子以及可能有界算子这些概念的基础上，进一步讨论它们之间的联系，使得关于这方面的内容更全面深刻。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

At the every relative momentary point of time time-space, is to the situation of observe identity mutuality gravitation and space-energy quantum spatial measurement cosmic energy at relatively determine, namely to the difference of quantity quantum of the original spatial measurement and the spatial measurement limit of cosmic energy, to the quantity of quantum spatial measurement cosmic energy, to the situation of spatial measurement and spatial curvature relative time-space cosmic energy, to the difference of spatial measurement of the gravitation exceed the space-energy of quantum spatial measurement cosmic energy, to the situation of the average density spatial energy and the temperature spatial background of relative time-space cosmic energy, to the situation of spatial measurement and spatial curvature relative vacuum cosmic energy all at relatively determine.

在时空时间的每一个相对时刻点，是对宇宙能量的宇称量子的引力与空间能的守恒状况的相对确定。即是对宇宙能量的原初宇称量子与极限宇称量子的数量差，宇宙能量的宇称量子数量，宇宙能量的相对时空的宇称及空间的曲率状况，宇宙能量的宇称量子的引力大于空间能的宇称差，宇宙能量的相对时空空间的能量平均密度及空间的背景温度状况，以及对宇宙能量的相对真空的宇称及空间的曲率状况全都在相对地确定。

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。