导出匹配可扩二部图度和条件的改进

研究并改进了导出匹配可扩二部图的度和条件.主要结论如下:若图G是一个有二部划分(A,B)的二部图,且|A|=|B|=n=3k+1(k≥2),如果对图G中任意不相邻的顶点u和v,有d(u)+d(v)≥4k+1,那么图G是导出匹配可扩的,并且该结果是最佳可能的.     

残缺大圆半径的测量

圆弧的测量,测绘在计量中经常遇到,一般说来圆弧尺寸小,形状比较完整,弦高尺寸在1/2～l/3圆弧直径时,测量比较方便,可用标准样板对比、工具显微镜的切线法、座标法等来解决,但遇到R尺寸大,形状较差,弦高尺寸<1/4直径时,要测出其圆弦比较困难。例如,欲测飞机襟翼滑轨之R。如图1,是从旧飞机上拆下的,现要实际测出R尺寸。显然这样将近1米的R. 且形状较差,弦 高不到圆弧1/4 直径,用上述方 法是不行的。根 据实际情况,采 用滚柱测量,具 体步骤是: 1.装夹:将滑轨平卧平板,V型铁垫入沿轨最高端,以保持一个方向的水平。二个千斤顶分别搁于滑轨二端…     

几乎导出匹配可扩图的一些度条件

目的:研究图的完美匹配与几乎导出匹配可扩性的关系,研究无爪图是几乎导出匹配可扩图的度条件。方法:利用无爪图导出匹配的性质和几乎导出匹配可扩图的定义,以及n-可扩图度和条件的Plummer定理,推导证明度条件。结果:得到了几乎导出匹配可扩无爪图的度条件,研究了二部图的几乎导出匹配可扩性。结论:若图G是一个顶点数为2n-1的无爪图,如果对图G中任意不相邻的顶点u和v,有d(u)+d(v)≥2n+1,那么图G是几乎导出匹配可扩的,并证明了不存在几乎导出匹配可扩的二部图。     

匹配覆盖图的阈函数(英文)

一个图G是匹配覆盖的(或1-可扩的)如果它是连通的且G的每条边都被包含在一个完美匹配里.我们称一个图G为双因子临界的,如果对于G中的任意两个不同顶点x,y,Gx-y都有一个完美匹配.一个双因子临界图被称为砖块,如果它是3-连通的.本文对于双因子临界图与匹配覆盖二部图确定了它们的阈函数.对于非二部的匹配覆盖图,我们发现了一个概率序列,其表现就像一个阈.此外,我们证明几乎所有的3-连通图均是砖块.     

部分逆M矩阵2-弦图的完备问题

本文采用图论的方法对任意阶部分逆M矩阵,当其对应的图为2-弦图时,研究了其逆M矩阵的完备问题。给出了完备定理以及具体完备的算法。     

大尺寸R尺

测量小于半圆的圆弧半径时,经常采用弦高法。这里介绍一种按弦高法原理制成的大尺寸R尺。该尺由圆柱、连杆、轴及螺钉、螺帽构成(图1),各零件尺寸可根据所测工件尺寸范围而定。测量时,使三圆柱与所测之圓弧相切后固紧滚轮螺钉4,取下该尺,并测出L、H值(图2),由下式可以算出R尺寸:     

一种样板的两种测量方法

图1示样板要求测量固定弦EF=42.000mm处的h值,在万能工具显微镜上有以下两种测量方法.     

巧用卡尺测量缺圆皮带轮

图１所示是我厂机床设备上一个破碎了的皮带轮,由于其残缺不全,且无图纸,给重新制造该皮带轮带来困难。为此我们采用普通卡尺测量皮带轮剩余圆弧部分弦长和弓高的办法,对皮带轮进行了测绘,使问题得到解决。图１测量原理见图２,从图中我们可知：在直角三角形ＯＡＢ中...     

具有极谱的二部竞赛矩阵

令Γm ,n 表示所有的不可约m×n二部竞赛矩阵 ,获得了如下主要结论 :(1)Γm ,n 中每个 (s,t)半正则二部竞赛矩阵的特征值的代数重数和几何重数相等 ;(2 )刻划了Γm ,n 中恰好有四个不同特征值的 (s ,t) 半正则二部竞赛矩阵 ,这些矩阵与组合设计有关 ;(3)设 lm ,n 表示 Γm ,n 中零特征值的最大代数重数 ,则lm ,n =m +n - 4 ,并给出了使该式成立的二部竞赛图的结构。     

二维彩色多普勒血流图诊断复杂性先天性心脏病的价值

本文介绍二维彩色多普勒血流图检测30例复杂性先天性心脏病。每例均经心血管造影及/或手术证实。诊断敏感性为100%。23例法乐氏四联症者,二维彩色多普勒血流图显示室间隔膜部出现无回声区(室间隔缺损),主动脉向前移位骑跨于室间隔。兰色血流从右室通过主动脉骑跨处注入主动脉,桔红色血流从左室注入主动脉与右室。5例右型大血管转位者,二维彩色多普勒血流图显示主动脉起始于右室,肺动脉起始于解剖左室,收缩期左室内兰色血流通过左室流出道注入肺动脉,而右室内兰色血流通过右室流出道注入主动脉。2例三尖瓣闭锁者,二维彩色多普勒血流图显示三…     

图的测地全控制数

将图的测地集与全控制集的概念结合,引入图的测地全控制集的定义,得到测地全控制数与测地数、测地控制数关系的一个基本结论:设图G为最小度δ≥2的任意图.如果图G的围长至少为6,则g(G)≤gγt(G)=tγ(G);给出路与圈上的测地全控制数的确定值,并证明弦图上的测地全控制集问题是NP-完全的.     

Subdivision surface-based finish machining

Subdivision surfaces combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. Motivated by the idea, this paper presents the study of finish machining of objects represented by subdivision surfaces with emphasis on geometric error control involved in tool-path generation. First, given a design model, chordal error is controlled during finishing model building. A chordal error-driven adaptive subdivision method is used to build finishing models with less data. Second, a surface decomposition machining strategy is used to control the cusp height error. A simple iso-slope curve tracing and surface decomposition algorithm is presented to partition the model into flat and steep regions. Contour-map tool-paths are generated in the steep regions while iso-planar tool-paths are generated in the flat regions. The gouge problem is easily handled through two-dimensional (2D) tool-path correction algorithms. The implementation results demonstrate that subdivision is capable of serving as a unified representation for both geometric modelling and machining.     

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

Graph theory has a significant impact and is crucial in the structure of many real-life situations. To simulate uncertainty and ambiguity, many extensions of graph theoretical notions were created. Planar graphs play a vital role in modelling which has the property of non-crossing edges. Although crossing edges benefit, they have some drawbacks, which paved the way for the introduction of planar graphs. The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph. The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs. The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs, a conceptual blending of Pythagorean Neutrosophic and Planar graphs. The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations. This paper investigates the Pythagorean Neutrosophic planar values, which form the edges of the Pythagorean neutrosophic graphs. The concept of Pythagorean Neutrosophic dual graphs, isomorphism, co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs. A decision-making algorithm was proposed with a numerical illustration by using the Pythagorean Neutrosophic fuzzy graph.     

给定阶及边独立数和圈数的图的谱半径

令U(n,i,r)表示阶是n、边独立数是i和圈数是r的简单连通图的集合,这里图的任意两个圈至多有一个公共顶点。当i≥r 1时,对任意的G∈U(n,i,r),得到了G的谱半径的精确上界和达到上界的所有极图。这一结果推广了树、单圈图和双圈图谱半径的许多已有结论。     

Graph algebras and the graph isomorphism problem

We consider the families of matrix algebras over C associated with graphs. Restricting the multiplicity of the irreducible representations over C produces corresponding classes of graphs. The main result of the paper is a polynomial-time algorithm for recognizing the isomorphism of graphs from these classes. It is a generalization of the well-known Babai-Grigor'ev-Mount algorithm for testing the isomorphism of graphs with bounded eigenvalue multiplicity.     

Sequences of regressions and their independences

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or retrospective studies. Conditional independences are captured by what we name regression graphs, provided the generated distribution shares some properties with a joint Gaussian distribution. Regression graphs extend purely directed, acyclic graphs by two types of undirected graph, one type for components of joint responses and the other for components of the context vector variable. We review the special features and the history of regression graphs, prove criteria for Markov equivalence and discuss the notion of a?simpler statistical covering model. Knowledge of Markov equivalence provides alternative interpretations of a given sequence of regressions, is essential for machine learning strategies and permits to use the simple graphical criteria of regression graphs on graphs for which the corresponding criteria are in general more complex. Under the known conditions that a Markov equivalent directed acyclic graph exists for any given regression graph, we give a polynomial time algorithm to find one such graph.     

一种基于多播路由图的最小子树图搜索算法

提出了一种基于网络编码的新的多播路由算法,该算法在搜索信源节点到各接收者路径族的过程中,考虑了不同路径族之间链路的共享,以降低带宽资源消耗,提高网络性能.基于得到的多播路由图,提出了一种最小子树图搜索算法,并利用最小子树图的性质,对相应于多播路由图的子树图进行化简.最后,在最小子树图上进行有效的网络编码,所有的网络编码问题可以简化为搜索多播网络的最小子树图问题.     

Traffic fatalities, Peltzman's model, and directed graphs

We show how statistical methods based on directed graphs may be useful in modeling traffic fatalities by comparing models specified using directed graphs to a model originally developed by Peltzman. The comparison uses Peltzman's original data, as well as up-dated data (and coefficients) through 1993. Out-of-sample forecasts of traffic fatalities from Peltzman's model are compared with those from a model constructed using directed graphs over data for the more recent period. The directed graphs model outperforms Peltzman's model in root mean squared forecast error.     

完全图的剖分图的线图的谱

如果一个图G的邻接矩阵A(G)的特征多项式的所有特征值全为整数,则称图G是整的.设图L2(Kp):L(s(Kp))是完全图Kp的剖分图S(Kp)的线图.在这篇文章里,我们利用图的理论给出了S(Kp)和L2(Kp)的特征多项式及其谱.对于图L2(Kp),得到了其补图、线图、线图的补图及补图的线图的特征多项式.也证明了这些图都是整图.这些整图的发现是对整图的研究的一个新贡献.     

路图与线图的一个综述

线图的概念最早是由Whitney提出的,在所有图的变换中,线图可能是研究最广泛的一种变换了。关于线图的研究已经有很多结果,路图变换是线图的一种自然推广。在这篇综述中,我们可以看到有时路图与线图的性质差异很大,有些问题对路图而言变得相当复杂和困难。这篇文章主要通过以下几个方面比较和总结了路图与线图的一些结果:基本事实,判定问题,刻画问题,贯穿性,连通度。