度量拓扑

We have also shown that the collection of prime event structures on N can be endowed with the structure of a complete metric space, and in this space the collection of all universal homogeneous prime event structures is topologically large: it is the complement of a meager set.

我们也表明，集的主要事件结构对N可以赋予一个完整的度量空间结构，在该空间的主要活动是普遍均匀结构拓扑大：它是相辅相成的微薄的集合。

It solves the problem that the unitary contour presentation can not correctly extract face contour in a face image which suffers from scale, rotation etc. The definition of the internal and external energy function is provided. At the same time, the global matching algorithm and local matching algorithm is given. The experiment shows that this presentation and the accompanying matching algorithm can be used to extract the face contour very well. So the image segmentation can be implemented by using it.②By analyzing the recognition principle of PCA method, we can conclude that the face images coming from different surrounding consist of different face image space. This is the essential reason that makes the generality of PCA method worse. Also, we give a measurement means to measure the distance from different face image space, so we can analyze face image space more conveniently.③We also construct various scale models and rotation pose models to detect the scale and rotating angle of face image to be recognized. The experiment results show that the detecting precision is very high. So it is good for face image feature extraction and face image representation.④Similarly, we construct local feature models of face image and utilize them to detect the local feature of face image. At the same time, we put forward a novel face image local feature detection algorithm, locating step by step. The experiment results show that this method can accurately detect the location of local face feature in a image.⑤A novel face image presentation model, dual attribute graph , is put forward. Firstly, it utilizes attribute graph to present the face image, then exact the local principal component coefficient and Gabor transform coefficient of thc pixels which corresponds to the nodes of the graph as the attribute of the nodes. This representation fully makes use of the statistical characteristic of the local face feature and utilizes Gabor transform to present the topographical structure of face image. So DAG has more general property.⑥Based on the DAG presentation, we give a DAG matching function and matching algorithm. During the design of the function and algorithm, the noise factor, e. g., lighting, scale and rotation pose are considered and tried to be eliminated. So the algorithm can give more general property.⑦A general face image recognition system is implemented. The experiment show the system can get better recognition performance under the noise surrounding of lighting, scale and rotation pose.

本文在上述研究的基础上，取得了如下主要研究成果：①构造了一个通用的人脸轮廓模型表示，解决了由于人脸图象尺度、旋转等因素而使得仅用单一轮廓表示无法正确提取人脸轮廓的问题，并给出了模型内、外能函数的定义，同时给出了模型的全局与局部匹配算法，实验表明，使用这种表示形式以及匹配算法，能够较好地提取人脸图象的轮廓，可实际用于人脸图象的分割；②深入分析了PCA方法的识别机制，得出不同成象条件下的人脸图象构成不同的人脸图象空间的结论，同时指出这也是造成PCA方法通用性较差的本质原因，并给出了不同人脸空间距离的一种度量方法，使用该度量方法能够直观地对人脸图象空间进行分析；③构造了各种尺度模板、旋转姿势模板以用于探测待识人脸图象的尺度、旋转角度，实验结果表明，探测精确度很高，从而有利于人脸图象特征提取，以及图象的有效表示；④构造了人脸图象的各局部特征模板，用于人脸图象局部特征的探测；同时提出了一种新的人脸图象局部特征探测法---逐步求精定位法，实验结果表明，使用这种方法能够精确地得到人脸图象各局部特征的位置；⑤提出了一种新的人脸图象表示法---双属性图表示法；利用属性图来表示人脸图象，并提取图节点对应图象位置的局部主成分特征系数以及Gabor变换系数作为图节点的属性，这种表示方法充分利用了人脸图象的局部特征的统计特性，并且使用Gabor变换来反映人脸图象的拓扑结构，从而使得双属性图表示法具有较强的通用性；⑥在双属性图表示的基础上，给出双属性图匹配函数及匹配算法，在函数及算法设计过程中，考虑并解决了光照、尺度、旋转姿势变化等因素对人脸图象识别的影响，使得匹配算法具有较强的通用性；⑦设计并实现了一个通用的人脸图象识别系统，实验结果表明，该系统在图象光照、尺度、旋转姿势情况下，得到了较好的识别效果。

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

The research conducted in this paper solves the symbolic structure of the devils carpet and the metrization of the plateau of an equal topological entropy class, and presents the symbolic description and visual realization of equal entropy fractals.

本研究解决了拓扑熵魔毯的符号结构和等拓扑熵类平台的度量刻划；获得了等熵分形的符号刻划及直观实现。

Lacking necessary metrization, RCC only describe spatial topological relations roughly without further accurateness, and it is also not easy to describe spatial relations such as distance, direction and so on, with the exclusion of topological relation.

但由于缺乏必要的度量，RCC只是粗略地描述空间拓扑关系而难以对其更准确地描述，也难以利用RCC描述除拓扑关系之外的其它空间关系，如距离、方向等。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

To get the low dimensional data with regular structure,the measure of the regularity is constructed and then the dimension reduction is brought forward.

为了寻求具有规则拓扑结构的低维数据集，构造了数据结构规则性的度量，提出了保持数据集拓扑结构不变的降维方法。

Since the commonly-used parameter analysis method is liable to cause the diversity of results in style investment analysis, the method of subdominant ultra-metric space is introduced to the study of style investment. Subdominant ultra-metric space is provided with the exactly defined topology sequence, and corresponded with index hierarchical structure and style.

针对常用的参数分析方法在证券风格投资分析中容易导致结果的差异性问题，提出将亚超度量空间方法引入到风格投资研究中，因为具有准确定义拓扑序列的亚超度量空间与指数分层结构、风格能够一一对应。

Based on the description of uncertain linear and area objects, intersection degrees for parts of uncertain linear and area objects are represented quantitatively. By calculating correlation degrees between spatial vectors composed of these measurement units and spatial relation vectors determined by 9-intersection model, a new model is presented for topological relations between uncertain linear objects and fuzzy region, which could distinguish the type of topological relations through quantitative analysis method.

在时不确定线状目标和面状目标进行描述的基础上，对不确定线状目标与面状目标各组成部分之间的相交程度进行了定量表达，通过计算这些度量组成的空间向量与9-交集模型确定的空间关系向量之间的相关度，提出了一种不确定线状目标和面状目标之间拓扑关系的描述模型，通过定量的方法来对其空间拓扑关系进行判别。

Graphs are often as models for the multiprocessor interconnect networks, in which the vertex set corresponds to processors, and the edge set corresponds to communication links. In this case, some properties of the graphs correspond to the capability of the networks.

多处理机系统的互连网络拓扑通常以图为数学模型，这时图的顶点代表处理机，而一对处理机之间的直接通信联系则用连接这对顶点的边来表示，因此网络拓扑的性能可以通过图的性质和参数来度量。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。