基础拓扑空间

In order to eliminate the influence caused by the nonminimum phase characteristic of a common Boost DC／DC converter, Viswanathan K has proposed a novel tristate Boost DC／DC converter. For enhancing performance, the statespace averaging model of this converter was first presented in this paper. Due to the nonlinear nature in this model, an inputoutput feedback linearization technique was adopted, and a complete controllable linear system was obtained. Then a statefeedback control strategy was designed based on this linear system. Simulation results show that the proposed control strategy can assure constant output voltage in a wide range, so as to realize the stability of the system during large fluctuation of power supply and load disturbance. Good dynamic performance can also be achieved.

针对 Viswanathan K为消除普通BOOST DC／DC变换器的非最小相位特性而提出的三态Boost DC／DC变换器，为进一步提高这种电路拓扑的性能，在建立了变换器状态空间平均模型的基础上，针对其多变量、非线性特点，采用输入输出线性化将其转化为一个完全可控的线性系统，在此基础上应用现有成熟的线性控制策略进行了控制系统的设计，并且采用MATLAB进行仿真验证，结果表明：这种非线性控制策略可以确保输出电压在大范围内恒定可调，且即使存在大范围扰动(输入电压和负载变化均较大)的情况下，系统也可以确保稳定性和良好的动态性能。

The research of this paper is began with the analysis the geographic spatial character of the UPTN, and designs the UPTN data mode based on GIS. Then, based on the good exhibiting all kinds of topology of the UPTN, and combined with the technology evaluation standards of the UPTN, this paper builds the UPTN planning mathematic model, and puts forward the quantitative calculation of the UPTN evaluation standards based on GIS; brings forward the arithmetic of the optimal path of the UPTN based on the public traffic network storage structure; designs the bus lines grouping management model, and realizes the contradistinctive evaluation of the UPTN planning projects based on GIS.

论文研究的重点内容是从分析城市公交网络中地理空间实体的特征开始，设计基于GIS的城市公交网络数据模型，在有效表现公交网络拓扑关系的基础上，根据公交线网技术评价指标，建立基于GIS的公交线网规划的数学模型，并给出公交线网评价指标的GIS量化计算方法；提出以公交线网数据存储结构为基础的公交网络最优路径算法；设计公交线路分组管理模型，实现公交线网规划方案对比分析。

Taking a heavy truck cab as the example, a model of the spotweld space based on finite element was built to analyse the torsional stiffness of the model, and the amount and layout of the spotweld using the discrete variable topology optimization were optimized. Comparing with the original model in welding spot's number and the torsional stiffness, the optimized model has less number of welding spot, but the torsional stiffness of the two model is almost the same.

以某重型卡车驾驶室为例，在有限元模型基础上建立焊点空间模型进行扭转刚度分析，并采用离散变量拓扑优化方法对焊点的数量及空间布局进行优化，通过优化前后的对比可知，优化后在不降低扭转刚度的同时减少了焊点数目。

An algorithm of searching and computing two adjacent polygons' closest distance based on restricted circle has been proposed in this paper, which can be fitted for the situations of undistinguished shapes and location relationships of the two adjacent polygons.

空间方向关系、空间拓扑关系和空间相似关系、相关关系的研究都离不开空间距离这个基础(闫浩文2003)。二维空间目标间的距离关系，尤其是面状目标间的距离，描述和计算都相当复杂[1-2]。

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。

Compared with traditional DEM or TIN based methods, this pure vector approach obtains not only the topological structure of drainage system in planar graph, but also the valley distribution polygon range. Depending on geometrical computation and judgment of vector line, polygon, the structured properties in drainage representation is enhanced, avoiding the case of noise disturbance in DEM based method. The core algorithm makes use of the ability of Delaunay triangulation in detecting hierarchical structure of each contour line.

中文摘要：基于Delaunay三角网模型在矢量等高线基础上通过弯曲特征分析，给出了一种地形结构特征提取及谷地树组织的方法，与传统的基于DEM或TIN数据结构提取地形特征的方法相比，该方法不仅得到了谷地系统在平面图上的拓扑结构，还获得了河谷在空间分布上的汇水范围，依托矢量线、多边形的几何关系判断，增强了谷地树组织中的结构化，避免了DEM方法中的噪音干扰，方法的核心是Delaunay三角网在单根等高线弯曲深度表达上的层次结构识别。

A multi-level hierarchical image representation that preserves topological relation equivalency and a set of well-complete functional architecture that efficiently reflects this representation are presented, and the digital Jordan curve theorem is validated.

基于复形理论定义了数字图像空间的拓扑元素及其性质，在此基础上提出一套完备的保持拓扑等价性的层次表达数字图像的数学模型体系框架，并验证了层次表达结构中的Jordan曲线定理。

As an example, the time series of China composite stock index is considered Firstly, the distribution of five days return on China composite stock index is studied. Secondly, based on the R/S analysis Hurst exponent is worked out and determination detecting can be done . Lastly, the topological characteristics such as correlation dimension and maximum Lyapunov exponent are extracted from time series.

作为例子，本文对中国股票指数时间序列做了实证分析，首先研究了中国股票指数的五天收益率的分布规律，然后运用重标极差分析方法计算出赫斯特指数，并以此为基础进行确定性检验，最后在相空间重构的基础上提取吸引子的拓扑特征指数。

Based on the topological dimension reduction method presented by B. Zhang et al for the problem of motion planning in the environment consisting of precisely known polygonal or polyhedral obstacles, we further discuss the problem of motion planning for a multi—joint robotic arm.

对由完全精确已知的多边形或多面体组成的障碍环境中的运动规划问题，在张钹等提出的拓扑降维法的基础上，本论文进一步探讨了应用拓扑法的多关节机械手的运动规划问题，其中重点解决了状态空间中连通块的划分问题和连通块之间连通性的判别问题。

The spatial topologic relation is the foundation of spatial syntactic research.

空间拓扑关系是空间句法研究的基础。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。