有机醇的结构与色谱保留指数的相关性拓扑指数法研究

通过计算40种有机醇化合物分子结构的拓扑指数，用多元线性回归将它与气相色谱保留指数进行关联分析，结果获得了良好的相关性，因此，对有机醇各组分在气相色谱上保留指数的理论预测，可作为在色谱分离过程中识别各组分的一种参考方法。     

A database system of mechanical components based on geometric and topological similarity. Part I: representation

A database of mechanical components is an important issue for some manufacturing activities such as cost estimation, process planning, and design by case-based reasoning. In this paper, we give the representation scheme of the CAD model in such a database. Components are represented using attributed graphs in which the nodes correspond to the surfaces of the component and the links correspond to the edges of the component. The graph is based on the standard for the exchange of product information (STEP) physical file of the component. STEP file should be unique for a single component regardless of the underlying CAD system. The process of creating the graph of a component constitutes two sub-tasks: (i) importing the CAD model from the CAD system in STEP format and (ii) transforming the STEP data into attributed graph-based representation. The graph and its attributes describe the topology of the component completely together with some geometric data that are not dependent on any coordinate system such as surface type and curve type. These geometric data are helpful in the retrieval and matching processes in the database.     

Two-point higher-order BVPs with singularities in phase variables

The existence of solutions for singular higher-order differential equations with the Lidstone or the (n,p) boundary conditions is proved. The right-hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities. Proofs are based on the method of a priori estimates, the degree theory arguments and on Vitali's convergence theorem.     

道路网拓扑模型的数据结构和生成方法

针对路径规划所需数据的特点，采用“混合数据结构”组织地图道路网数据，通过路段提取、节点分离、目标点区域确定，快速生成了起始点至目标点的路径规划道路网拓扑模型。     

有教师的线性基本函数前向三层神经网络结构研究

优化选择隐节点数是人们在应用基于误差反传算法的有教师的线性基本函数前向三层神经网络过程中首先遇到的一个十分重要而又困难的问题。本文从国内外大量应用裕列中陪结归纳出了一个初定这种网络隐节点数的经验公式，提出了一种判断所选隐节点数是否多余的具体方法，并从理论上做了详细的推导。     

On fuzzy sobriety

This paper mainly shows that sober fuzzy topological spaces form the epireflective hull of the fuzzy Sierpinski space in the category of T₀-fuzzy topological spaces.     

Preserving Topology by a Digitization Process

The main task of digital image processing is to recognize properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and represented as finite sets of points that are assigned some value in a gray-level or color scale. Based on technical properties of sampling devices, these points are usually assumed to form a square grid and are modeled as finite subsets of Z². Therefore, a fundamental question in digital image processing is which features in the digital image correspond, under certain conditions, to properties of the underlying objects. In practical applications this question is mostly answered by visually judging the obtained digital images. In this paper we present a comprehensive answer to this question with respect to topological properties. In particular, we derive conditions relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. These conditions also imply that two digital images of a given object are topologically equivalent. This means, for example, that shifting or rotating an object or the camera cannot lead to topologically different images, i.e., topological properties of obtained digital images are invariant under shifting and rotation.     

一种可视外壳的快速拓扑生成算法

针对各种传统可视外壳生成算法中数据冗余及壮健性不足等问题，提出了一种新的从阴影图像中快速重构物体可视外壳的壮健的算法，即首先利用物体表面的拓扑结构直接生成外壳，然后使用改进的SurfaceNet算法光滑三维表面，从而在保留经典的体求交方法壮健性的基础上，克服了对于物体内部点的冗余计算和存储问题，不仅使得计算的时间复杂度降低到仅线性依赖于外壳上结点的数目，而且降低了像片数对算法复杂度产生的影响，实验结果表明，在算法复杂度和壮健性上优于诸如八叉树等传统可视外壳算法。     

Mappings of Figure Spaces and Systems of These Spaces

The formation of an informal theory of figure spaces is considered. In particular, interesting and natural generalizations of such fundamental mathematical concepts as continuous and uniformly continuous mappings are proposed.     

Research on Constructing Contours from Regular Terrain Grids Containing Invalid Data

A new method for constructing contours from complicated terrain elevation grids containing invalid data is put forward. By using this method, the topological consistency of contours in groups can be maintained effectively and the contours can be drawn smoothly based on boundaries pre-searching and local correction. An experimental example is given to demonstrate that the contours constructed by this method are of good quality.