空间性

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

Before 1970s, the supply model of government single-center was established and the research was focused on the location and efficiency according to public goods theory; During the l970s-1990s, the spatial equity of the distribution of public service facilities has been researched from theory of dual-main joint supply; From 1 990s to date, based on the theory of diversified purveyance, society differentiation and accessibility has been the research focus from the perspective of social restructuring.

结果表明：战后西方国家城市公共服务设施供给研究历经3个阶段：二战后至70年代，基于公共物品理论和社会公共服务的政府单中心供给模式，布局区位及影响机制是城市公共服务设施研究的重点；70-90年代，从公共服务的双主体联合供给理论出发，重在探讨城市公共服务设施供给的空间公平；90年代以来，在公共服务多元供给理论基础上，从社会结构的深层次视角研究公共服务设施供给的可达性差异及社会空间分异。

Aiming at the deficiency of the current fingerprint segmentation method at pixel and the segment limitation of the linear classifier, a new method of segmentation based on quadric surface model is proposed.

文中分析了指纹的前景点和背景点在指标CMV(C指像素点的方向一致性、M是像素点的平均灰度、V是像素点的平均灰度方差)下的空间分布特点，发现该空间下的指纹前景和背景区域具有线性不可分性，使用线性分类器进行分类具备一定局限性。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

By using techniques from robust statistics, we obtain the approximations of the underlying surfaces. This leads to a conceptually good local patch with precise geometry properties, and as a result, the influence of noises is reduced. In addition, we also present a diffusion method to smooth the geometry properties, including principle curvatures and Frenet frame. The method ensures that the surfaces are smooth in the curvature space, and maintain the details, features and optimize the normals. The results show that, even in a high level noise situation, our algorithm can remove noise effectively, and at the same time keep the details of the model.

与传统的双边滤波去噪算法不同，该算法通过引入鲁棒统计理论获得模型表面较为准确的几何属性；进而在曲率空间中对包含主曲率和Frenet标架的表面几何属性进行各向异性的滤波，既有利于保持模型的细节，又能保证曲面的光滑性；与此同时，优化各个顶点的法向；最后在优化后的几何属性引导下，在几何空间中进行高阶双边滤波去噪。

In Chapter2, we first study the existence of Chebyshev coordinates of time-like (or space-like) submanifolds with a constant sectional curvature in N〓. Afterwards, we generalize the classical Backlund theorem for space-like (or time-like) submanifolds in N〓 and N〓.

在第二章中，首先我们研究了伪黎曼空间形式N〓中常曲率类空子流形的Chebyshev坐标的存在性；然后把经典的Backlund定理推广到高维的伪黎曼空间形式N〓和N〓中。

Here, we characterize sequential separability and prove that l_p is a separable space if and only if E is a separable space and l_p is a GAK_space.

关于Banach序列空间lp，讨论的主要问题之一就是E的几何性质能否提升到lp中去，在文中，刻划了lp的序列可分性，证明了lp是可分的当且仅当E是可分的以及lp是GAK 空间

Entrance is indispensability factor of building, it is keystone of forming the sequence space and control the transform of differ space.

而入口是建筑形态构成不可缺少的基本元素之一，它控制着两种不同空间的转换，是形成空间序列和节奏性的关键所在。

Along with the developing of the molecole characterization of the weighted Herz type Hardy space, the study of the singular integral operator get a plentiful harvest.

本文首先解决了加权Herz型Hardy空间的分子刻画，作为应用，给出了强奇异积分算子T_b在加权Herz型Hardy空间上的有界性的证明。

In the fourth chapter,we discuss theapplication of the atomic decomposition theory to the vector-valued harmonicanalysis.We give the Hardy inequalities in the vector-valued martingale space,we also study the Mikhlin multiplier operator and singular integral operator in thevector-valued Hardy space.

第四章我们主要研究原子分解理论在向量值调和分析中的应用，建立了向量值鞅空间上的Hardy不等式，向量值Hardy空间上的Mikhlin乘子算子及一类奇异积分算子的有界性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。