邻域拓扑

A topological space is an minimal CH space if and only if each open CH-filterbase with only one adherent point converges to this point.

4拓扑空间 X是极小 CH空间，当且仅当对任意的 x∈X和任意开 CH滤基μ，若{ x}=∩U∈μU=∩U∈μcl U，则μ是 x的一个邻域基。

The proof is given that the category of linear fuzzy neighborhood spaces in the sense of Katsaras is isomorphic to that of co-towers of topological vector spaces and the intersection of the category of linear fuzzy neighborhood spaces with the category of type fuzzy topological vector spaces is the extract category of induced fuzzy topological vector spaces.

证明了Katsaras的线性fuzzy邻域空间范畴与分明线性拓扑空间的余塔空间范畴同构，而Katsaras的线性fuzzy邻域空间范畴与型fuzzy拓扑线性空间范畴的交集恰为诱导的fuzzy拓扑线性空间范畴。

In this paper, based on fundamental topology theories, the concept of complete set is proposed and the closed ball model is constructed.

基于闭球模型可以直接推导出拓扑关系的完备集和概念邻域以及复合表。

Based upon the idea of space partition and object decomposition, topological components of an area object with holes are defined by the use of the concept of neighborhood in the point set topology, which is a natural extension of the definitions for topological components of a simple area.

本文基于空间划分和目标分解的思想，利用点集理论中的邻域概念详细分析和描述带孔洞面目标的点集拓扑分量，这种描述方法实质上是简单面目标点集拓扑分量描述的一种自然延展。

Based on data cloud, which is measured from 3-coordinate measuring machine or so, an algorithm to search lopological structure from 3D unorganized points using Envelopment-box technology is proposed in this thesis. Based on this method, we searching neighbor points of sampling point. We also improve the Max-Min angle criteria to realize local triangulation, and then get the normal of sampling point from the triangulation. Using the normal and neighbor relationship, classification of scattered data points is realized according to the quadric surface.

本文以测量得到的曲面数据点点云为基础，提出了一种基于包围盒的自动寻找三维散乱数据点之间拓扑结构的方法，采用该方法寻找采样点的邻域结点，并对三角剖分中的典型优化准则—最小内角最大准则提出了改进，按照改进后的优化准则实现了采样点的局部三角划分，并进一步求解得到采样点的法向量，依据法向量及邻域拓扑关系在二次曲面的基础上实现了散乱数据曲面重构中的数据点的自动分类。

The method includes the following steps: firstly, a spherical neighborhood of present sample points is established by using the geometric spherical-modelling theory and all the sample points contained in the spherical neighborhood are adopted as candidate neighbor points, thus not only preserving the effectivity of the dimension reduction capability when data sets are sparse but also getting the advantages of low-sensitivity to isolated points and good stability of the preserved topological structure; then a data relevance matrix more matching semantics can be obtained by relevance measurement based on route clusters to update the candidate neighbor points in the spherical neighborhood and optimize the regular neighborhood space of the present sample points, thus improving the phenomenon that the dimension reduction of sample sets provided with folded curved faces is apt to suffer the integrated-structure distortion in case of heterogeneous data distribution.

首先利用几何开球原理建立当前样本点的球状邻域，将包含在球状邻域内的所有样本点作为候选近邻点，不但能够保持在数据集稀疏情况下的降维性能的有效性，而且具有对孤立点敏感性不高、保留拓扑结构稳定性好的优点。然后利用基于路径聚类的相关性度量得到更符合语义的数据相关性矩阵，用来对球状邻域内的候选近邻点进行更新，优化当前样本点的规则邻域空间，改善了当数据不均匀分布时在带有折叠弯曲面的样本集上降维容易出现整体结构扭曲的现象。

It is proved that the topological neighborhood is self-adaptive and goes to triviality with the increase of the dimension.

对拓扑邻域进行了理论分析，说明其是自适应的，随着维数的不断升高，趋于平凡拓扑邻域。

Coordinate sequence method is made up of the instruct information of polygon boundary x, y coordinate. It is the easiest polygon vector encoding method. The file structure of this method is easy, but because of the polygon boundary has stored two times, it will produce data redundancy, moreover, short of neighbor threshold information; Tree index encoding method make all the boundary points digitizing, store the coordinate sequence, connect the point index to boundary line, and then connect the line index to other polygons, so as to the tree index structure has came into being. It eliminates neighbor polygons boundary data redundancy problems; Topology structure encoding method is a method which by setting up a complete topology relationship structure, resolve the neighbor threshold and island information process problem. However, it makes arithmetic more complicated and makes database bigger.

坐标序列法是由多边形边界的x，y坐标对集合及说明信息组成，是最简单的一种多边形矢量编码法，文件结构简单，但多边形边界被存储两次产生数据冗余，而且缺少邻域信息；树状索引编码法是将所有边界点进行数字化，顺序存储坐标对，由点索引与边界线号相联系，以线索引与各多边形相联系，形成树状索引结构，消除了相邻多边形边界数据冗余问题；拓扑结构编码法是通过建立一个完整的拓扑关系结构，彻底解决邻域和岛状信息处理问题的方法，但增加了算法的复杂性和数据库的大小。

The above problems are studied in this thesis. First, the implicit NND scheme with mix flux splitting method proposed by Zhang Hanxin that is first order accurate in time and second order in space is modified. The modified scheme keeps the characteristics of fast convergence and is second order accurate both in time and space. It can be capable of simulating the unsteacly flow. Second, the topological method founded by Zhang Hanxin is improved to study the characteristics of vortex near the singular point on its axis and the cross streamlines on the longitudinal section passing the vortex axis. On the basis of topological results, a program which visualises numerical results is made out. It can help us analyse the characteristics of vortex motion.

本文对上述问题做了研究：第一，在数值模拟方面，借助于张涵信提出的NND算法和混合通量法，我们将他建立的时间为一阶、空间为二阶精度的快速隐式算法推广为时间和空间均为二阶精度的算法，这样做保留了原格式收敛快的特点，而且能适用于真实的非定常流态的计算；第二，将张涵信的拓扑分析方法加以推广，研究了涡轴附近及破裂点邻域内流场的空间特征，并以这些拓扑分析结果为指导，研制了一套显示计算结果的软件，这一软件能很好地帮助我们分析流场的计算结果和旋涡演变的特征。

Therefore, this paper presented a more robust and more topologically stable ISOMAP algorithm, i.

为此，根据最小连通邻域图能有效避免&短路&边的特点，提出了一种能有效删除&短路&边因而更具鲁棒性和拓扑稳定性的ISOMAP算法－基于最小连通邻域图的ISOMAP (MCNC-ISOMAP)算法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。