拓扑学

Its theoretic foundation is integration geometry, random theory of set, topology, modern probability, algebra, theory of set, graph theory, and so on.

其最基本的数学理论基础是积分几何和随机集论，同时还涉及到拓扑学、现代概率论、近代代数、集合论、图论等一系列数学分支。

The dissertation gives a self-contained definition of Complex boundary and interior based on point set topology so that the Complex was consistent with the common description of spatial objects. It is in favor of a unifying between nature description and theory representation of spatial entities in 3DGIS.

本文基于点集拓扑学理论，对复形的边界和内部进行了完备性定义，使得空间实体的复形表达符合人类对空间对象的直观认识，有助于在3DGIS中实现空间实体的自然描述与理论表达的统一。

As the layer structure of lattice, relative separation properties and relative compactness in L-fuzzy topological spaces are more complex than that in general topological spaces.

由于层次结构的存在，L-fuzzy拓扑空间中的相对分离性和相对紧性较一般拓扑学中的相对分离性与相对紧性复杂得多。

A new group of autocorrelation topological index (At、Bt、Ct and Dt) was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. The autocorrelation functions were calculated from the square root of the vertex degree、modified vertex degree and their combination, that is d i、、 and . The matrix description method and the algorithm of computer software have been developed for the new topological index calculation.

针对目前自相关拓扑指数的计算完全依赖于实验参数而存在的问题，以分子拓扑学点价和自相关函数研究为基础，将点价、修正点价及其组合：、、、的平方根分别作为自相关函数中的f，设计开发出一组新的以点价计算为基础的自相关拓扑指数At、Bt、Ct和Dt。

Firstly, based on the generalized function,φ-mapping topological current are rigorously proved to be of delta-function form δ and can be labelled by the nodal indices of the vector field, namely by Hopf indices and Brouwer degrees of this vector field, which reveals the inner relationships between our theory and the topology of vector bundle.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

Firstly,based on the generalized function,φ-mapping topological currentare rigorously proved to be of delta-function formδand can be labelledby the nodal indices of the vector field,namely by Hopf indices and Brouwerdegrees of this vector field,which reveals the inner relationships between ourtheory and the topology of vector bundle.A singular divergence theorem isalso presented.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

These toxic data(TC50,SDH and LDH) were used as dependent variable and 10 topological indices of 25 aminobenzene derivatives were used as independent variable.QSAR was analyzed with multiple stepwise linear regression.The results indicated that there is different toxicity with different structure of compounds.

内容摘要以大鼠游离肝细胞半数中毒浓度(TC50)和细胞逸出酶为观察指标，研究了25种苯胺类化合物的肝细胞毒性，并利用这些毒性效应数据为因变量，以这些化合物的10种拓扑学指数为自变量，利用多元逐步回归统计分析方法进行了定量结构-活性关系的深入探讨。

These toxic data(TC50,SDH and LDH) were used as dependent variable and 10 topological indices of 25 aminobenzene derivatives were used as independent variable.QSAR was analyzed with multiple stepwise linear regression.The results indicated that there is different toxicity with different structure of compounds.

卫生毒理学杂志990108 内容摘要以大鼠游离肝细胞半数中毒浓度(TC50)和细胞逸出酶为观察指标，研究了25种苯胺类化合物的肝细胞毒性，并利用这些毒性效应数据为因变量，以这些化合物的10种拓扑学指数为自变量，利用多元逐步回归统计分析方法进行了定量结构-活性关系的深入探讨。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

Coding;Communication;Communication systems;Communication technology;Components;Data;Data description;Data processing;Data processing system;Data records;Data representation;Data transfer;Definition;Definitions;Earth's surface;Encoding;Geodesy;Geographic information;Geographical;Geography;Geology;Geomatics;Geotechnics;Information;Information exchange;Information processing;Information technology;Schemes;Topology

中文标题地质信息。数据描述。传输中文主题词信息技术；信息；数据处理；地质的；信息交流；地球表面；地质信息管理；地质信息；定义；图表；数据处理系统；大地构造学；地质学；拓扑学；数据传送；信息处理；数据记录；通信系统；元部件；地理学；数据表示；传播技术；传播学；数据；编码；编码；数据描述；大地测量学

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。