基于Hausdorff距离的区间数据的系统聚类分析

基于Hausdorff距离用于定义两个紧集之间距离的考虑,将区间数视为一个紧集,定义了区间数之间的距离,并研究了区间向量的距离,从而得到聚类分析中两个样品间的距离。进一步定义了两个类之间的Hausdorff距离。为消除量纲对聚类结果的影响,研究了区间数据的标准化。基于此,给出了区间数据系统聚类算法。采用随机模拟的方法,对文中方法进行有效性评价,结论表明,Hausdorff距离法的聚类有效性在所有设计的实验条件下都要优于传统的欧式距离法。最后,基于符号数据分析的思想构造区间数据,给出了对多种动物群体按其身高、体重等生理特征进行聚类分析的算例。     

公式与理论的最近距离和最远距离及在近似推理中的应用

本文引入了公式与有限理论之间的最近距离和最远距离,讨论了公式与有限理论之间的最近距离和最远距离的一些简单性质;得到了当有限理论Γ中有根A,且公式B满足一定条件时,公式B与理论Γ之间的最近距离就是ρ(A,B)。基于最近距离和最远距离,给出了逻辑系统L中的可能Γ-结论的定义,并讨论了逻辑系统L中相应的近似推理。     

基于直觉模糊距离的群决策专家意见聚合分析

提出了一种基于直觉模糊距离来聚合专家个人意见为一个优化的群体意见一致度的新方法.首先,根据直觉模糊集的几何意义,定义了两个直觉模糊集之间的距离;然后,利用直觉模糊距离来聚合专家两两之间对备选方案意见的一致度,综合考虑每位专家的相对重要权重,得到专家群体对备选方案意见的综合一致度;最后通过一个具体实例来说明这种方法的具体应用及计算过程.     

关于相对Bousfield类和相对Bousfield等价关系

本文研究了有限群的群代数上的有限生成模的相对Bousfield类,定义了相对Bousfield等价关系和相对Bousfield等价类,建立了群与子群的相对Bousfield等价类之间的对应关系.     

直觉模糊集之间的距离测度

介绍了直觉模糊集之间距离测度公理化的定义,引入了一些新的距离测度并给出了这些距离测度性质的证明.讨论了相似测度与距离测度之间的关系.最后,指出直觉模糊集距离测度在模式识别中的应用.     

Banach 空间上算子的几种不可约性

本文根据Cowen-Douglas 算子的定义引入两类与强不可约算子有紧密联系的算子类— B_n 算子与B 算子. 说明了在可分Banach 空间上存在B_n 算子与B 算子. 文章详细讨论了几种具有不可约性的算子类之间的关系并得到了一个关系图. 本文还给出这些算子类的一些性质, 包括算子的(拟) 相似不变性等.     

Pre-Schwarz导数意义下区域之间的距离

Lehto曾用Schwarz导数定义了边界多于一点的两个单连通区域的Mbius等价类之间的"距离",并猜测它是一个距离.但最近Bozin和Markovic否定了这一猜想.一个自然的问题就是:在Pre-Schwarz导数意义相应情况如何?用Pre-Schwarz导数给出了边界多于一点的两个单连通区域的仿射等价类之间的"距离",并证明了这样定义的"距离"是一个伪距离,即使将其限制在由具有解析边界的单连通区域的仿射等价类空间上也是如此.     

经典逻辑系统中公式的真度及公式间伪距离的一种等价定义

给出了经典命题逻辑中公式的向量表示形式,利用向量表示形式给出公式的真度和公式间伪距离的定义,说明了这种定义与原有的概率形式的定义等价,得到了公式间的伪距离的一些简单性质以及在伪距离空间(F(s),ρ)中,逻辑连接词都是连续的.     

直观模糊集的熵、距离测度、相似测度及它们的关系

熵、距离测度和相似测度是模糊集理论中的三个重要概念.首先系统地给出了直观模糊集的熵、距离测度和相似测度的公理化定义,并讨论了它们之间的一些基本关系.然后在距离测度公理化定义的基础上产生了一些新的直观模糊集的熵公式.     

■距离及随机场的失真率函数

本文将距离的概念推广到了随机场情形，证明了该推广定义的合理性，并导出了一些上界和下届估计.特别地，我们证明了有相变情况下２维Ｉｓｉｎｇ模型的两个极端测度μ＋，μ－间的距离大于１／３．我们着重研究了距离和失真率函数之间的关系，得到了一些重要性质．这些性质可以用来证明编码定理．     

Weighted distances based on neighborhood sequences for point-lattices

A path-based distance is defined as the minimal cost-path between two points. One such distance function is the weighted distance based on a neighborhood sequence. It can be defined using any number of neighborhood relations and weights in conjunction with a neighborhood sequence. The neighborhood sequence restricts some steps in the path to a smaller neighborhood. We give formulas for computing the point-to-point distance and conditions for metricity for weighted distances based on neighborhood sequences with two neighborhood relations for the general case of point-lattices.     

Construction of proximal distances over symmetric cones

Abstract

This paper is devoted to the study of proximal distances defined over symmetric cones, which include the non-negative orthant, the second-order cone and the cone of positive semi-definite symmetric matrices. Specifically, our first aim is to provide two ways to build them. For this, we consider two classes of real-valued functions satisfying some assumptions. Then, we show that its corresponding spectrally defined function defines a proximal distance. In addition, we present several examples and some properties of this distance. Taking into account these properties, we analyse the convergence of proximal-type algorithms for solving convex symmetric cone programming (SCP) problems, and we study the asymptotic behaviour of primal central paths associated with a proximal distance. Finally, for linear SCP problems, we provide a relationship between the proximal sequence and the primal central path.     

相对拓扑的一些性质

讨论了相对超正则的充要条件及相对拓扑空间在映射下的一些性质，并定义了两类新的相对拓扑空间，给出了它们的一些性质．     

Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

Lower bounds for the complexity of the graph of the Hausdorff distance as a function of transformation

The Hausdorff distance is a measure defined between two sets in some metric space. This paper investigates how the Hausdorff distance changes as one set is transformed by some transformation group. Algorithms to find the minimum distance as one set is transformed have been described, but few lower bounds are known. We consider the complexity of the graph of the Hausdorff distance as a function of transformation, and exhibit some constructions that give lower bounds for this complexity. We exhibit lower-bound constructions for both sets of points in the plane, and sets of points and line segments; we consider the graph of the directed Hausdorff distance under translation, rigid motion, translation and scaling, and affine transformation. Many of the results can also be extended to the undirected Hausdorff distance. These lower bounds are for the complexity of the graph of the Hausdorff distance, and thus do not necessarily bound algorithms that search this graph; however, they do give an indication of how complex the search may be. This work was supported in part by National Science Foundation PYI Grant IRI-9057928 and matching funds from General Electric, Kodak, and Xerox, and in part by Air Force Contract AFOSR-91-0328.     

Regularized Riesz energies of submanifolds

Given a closed submanifold, or a compact regular domain, in Euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two different regularization techniques (Hadamard's finite part and analytic continuation), and show that they give essentially the same result. We prove that some of these energies are invariant under Möbius transformations, thus giving a generalization to higher dimensions of the Möbius energy of knots.     

上图像拓扑与多目标优化问题加权解的通有稳定性

用函数的上图象之间的Hausdorff距离定义向量值函数间的距离,在此弱拓扑下研究了多目标优化问题加权解关于权因子和目标函数的稳定性,指出加权解关于权因子和目标函数是通有稳定的．     

Characterization of balls by generalized Riesz energy

We show that balls, circles and 2‐spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension 0, where the Riesz energy is defined as the double integral of some power of the distance between pairs of points. As a consequence, we obtain the identification by the interpoint distance distribution.     

混合长度为{4,5,6}的完备删位纠错码的存在性

依据刻画空间中向量间距离方式的不同,可定义不同的纠错码.Levenshtein定义了莱文斯坦距离,由此定义了删位纠错码.本文借助组合设计理论中的成对平衡设计以及初等数论的方法和技巧,给出参数为T{2,{4,5,6},v}的完备删位纠错码存在的两个必要条件,并确定了,当v≥4且v■{8,9,14}时,存在参数为T{2,{4,5,6},v}的完备删位纠错码.