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一类四正则小世界网络的生成树数目的算法
Spanning Trees in a Class of Four Regular Small World Network
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贾环身, 海兴
Computer Science and Application (CSA) , 2014, DOI: 10.12677/CSA.2014.43009
Abstract:
生成树是表征网络结构性质的一个重要物理量,然而精确地确定网络上的生成树数目是一个巨大的理论挑战。本文提出了一个四正则小世界网络模型。介绍了其概念及演化过程,详细计算了四正则图的相关拓扑特性,例如直径、聚类系数等。给出了此类四正则网络的生成树数目计算方法,得出生成树数目公式及熵。研究发现,所研究网络的生成树的熵与具有相同平均度的其他网络形成了鲜明的对比,因为后者的生成树的熵小于所研究网络。因此,这一四正则小世界网络上的生成树数目比其他具有自相似结构网络生成树的数目要多
Spanning tree is an important quantity characterizing the reliability of a network; however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we present a class of four regular network model with small world phenomenon. We introduce the concept and evolving process and determine the relevant topological characteristics of the four regular network, such as diameter and clustering coefficient. We give a calculation method of number of spanning trees in such four regular network and derive the formulas and the entropy of number of spanning trees. We find that the entropy of spanning trees in the studied network is in sharp contrast to other small world with the same average degree, of which the entropy is less than the studied network. Thus, the number of spanning trees in such four regular network is more than that of other self-similar networks.
一种确定性小世界网络模型平均路径长度的逼近方法
An Approximation Algorithm for Average Path Length in A Small-World Network Model
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张科, 海兴, 李峰
Advances in Applied Mathematics (AAM) , 2014, DOI: 10.12677/AAM.2014.31004
Abstract:
确定性小世界网络是复杂网络中的一个重要的研究分支。2008年,章忠志等人(Eur.Phys.J.B 63)在复杂网络的视角下对确定性均匀递归树作了详尽地分析,得到了其拓扑属性。尽管确定性均匀递归树的平均路径长度表现出了网络大小的对数规模,但是它的聚类系数为零。2012年,陆哲明等人(Physica A 391)通过在确定性均匀递归树的基础上以一个简单的规则添加一些边得到一个确定性小世界网络模型。本文根据网络模型的结构用分析的方法给出了文献Physica A 391中的模型的平均路径长度的逼近方法。
Deterministic small-world network is an important branch of study of complex networks. In 2008, Zhang et al. in Eur.Phys.J.B 63 have offered detailed topological characteristics of the deterministic uniform recursive tree from the viewpoint of complex network. They derived topological characteristics of the deterministic uniform recursive tree. It shows a logarithmic scaling with the size of the network, however, its clustering coefficient is zero. In 2012, Lu, et al. in Physica A 391, based on the deterministic uniform recursive tree, by a simple rule to add some edges, got a deterministic small-world network model. In this paper, using an approximation algorithm based on the network construction, we show explicitly the average path length of the model constructed in Physica A 391.
一种星–树结构的确定性的小世界网络
A Star-Tree-Structured Deterministic Small-World Network
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侯鹏锋, 海兴
Computer Science and Application (CSA) , 2014, DOI: 10.12677/CSA.2014.411038
Abstract:
在过去的的几十年,人们运用各种机制建构了许多不确定性的和确定性的小世界网络。最近,郭世泽等人通过在星图K1,2上运用一个简单的算法在每个迭代步添加一些边首次形成了一个二叉树结构的确定性的小世界网络。本文通过一个星图K1,6在每个迭代步连接每个树的各祖父节点和它的四个孙子节点,由此构建一个二叉树结构的新的确定性的小世界网络模型。此外,我们给出了一些拓扑属性的分析结果,它表明构建的模型是小世界网络。
In the past dozen years, many probabilistic small-world networks and some deterministic small- world networks have been proposed utilizing various mechanisms. Recently, Guo et al. proposed a deterministic small-world network model by first constructing a binary-tree structure from star K1,2 by adding some edges in each iteration with a simple mechanism. In this paper, we propose a new deterministic small-world network model by constructing a binary-tree structure from a star K1,6 and then adding links between each grandfather node and its four grandson nodes for each tree in each iteration. Furthermore, we give the analytic solution to several topological characteristics, which shows that the proposed model is a small-world network.
一类确定性小世界网络模型及特性分析
A Kind of Deterministic Small-World Networks Model and Analysis of Their Characteristics
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张科, 海兴, 李发旭, 肖玉芝, 李峰
Computer Science and Application (CSA) , 2014, DOI: 10.12677/CSA.2014.42006
Abstract:
确定性小世界网络是复杂网络中的一个重要的研究分支2008章忠志等人(Eur.Phys.J.B 63)在复杂网络的视角下对确定性均匀递归树作了详尽地分析,得到了其拓扑属性尽管确定性均匀递归树的平均路径长度表现出了网络大小的对数规模但是它的聚类系数为零2012陆哲明等人(Physica A 391)通过在确定性均匀递归树的基础上以一个简单的规则添加一些边得到一个确定性小世界网络模型本文在新的视角下对文献Physica A 391中的模型的构造规律进行了探究并自然地对其进行了推广构造了一类确定性小世界网络模型然后运用分析的方法给出了所构造网络模型的几个重要拓扑属性包括呈幂律分布的累积度分布、高的聚类系数和小的直径
Deterministic small-world network is an important branch of study of complex networks. In 2008, Zhang et al. in Eur.Phys.J.B 63 have offered detailed topological characteristics of the deterministic uniform recursive tree from the viewpoint of complex network. They derived topological characteristics of the deterministic uniform recursive tree. It shows a logarithmic scaling with the size of the network; however its clustering coefficient is zero. In 2012, Lu et al. in Physica A 391, based on the deterministic uniform recursive tree and by a simple rule, added some edges and got a deterministic small-world network model. In this paper, we study the law of the structure on the basis of the model constructed
有向三角形树的匹配数
On the Matching Number of Directed Triangle Trees
 [PDF]

李梦英, 海兴
Computer Science and Application (CSA) , 2016, DOI: 10.12677/CSA.2016.65036
Abstract: 有向图G的一个匹配是由其一组没有公共起点也没有公共终点的有向边构成的集合。图G的k匹配是指含k (k = 1, 2, …, n)条有向边的匹配;图G的k-匹配数是指含k (k = 1, 2, …, n)条有向边的匹配的选择方法数;图G的匹配数指所有k-匹配数的和。刘和Barabasi等人提出:有向网络的可控节点数等于有向网络的顶点数减去最大匹配包含的边数。说明有向网络的可控性与有向网络的匹配数有着密切的联系。因此,研究有向网络的所有匹配数目具有一定的应用意义。这篇文章主要研究一类有向三角形树的所有匹配数的计数问题和极值问题。给出了一类含n个三角形的有向三角形树匹配数的计算方法,以及有向三角形树匹配数的上下界和相应的结构。
A matching of a directed graph G is a set of some directed edges without common starting-node and end-node. K-matching of a digraph G is the matching with the k (k = 1, 2,…, n) edges; k-matching number of a graph G is the number of distinct matchings containing k (k = 1, 2,…, n) edges. The matching of a graph G refers to the number of all k-matchings. Liu and Barabasi put forward: the number of controllable nodes in directed networks is equal to the number of nodes of directed networks minus the number of edges of the maximum matching. It illustrates that the matching number and controllability of directed networks have a close connection. Thus, the research of the number of all matchings of directed networks is of applied significance. This article mainly studies the counting problems and the extremal problems on the number of matchings in a class of directed triangle trees. We investigate the calculation method and the expression of the matching number in a class of directed triangle trees with n triangles and determine the bounds for the matching number in directed triangle trees with n triangles and the correspond graphs.
基于耦合映像格子的有向网络相继故障
马秀娟,马福祥,海兴
计算机应用 , 2011,
Abstract: ?针对现实世界中存在大量的有向网络,根据有向网络中边的有向性,提出适合描述有向网络耦合映像格子(cml)的相继故障模型,利用仿真分析的方法研究了ba无标度有向网络和er随机图有向网络在该模型作用下的相继故障行为。仿真中,对节点数固定的网络采用蓄意攻击和随机攻击两种策略进行攻击,并记录相关数据。通过对所得数据的分析发现:1)这两类有向网络的相继故障进程比同规模的无向网络要剧烈;2)当网络遭受攻击时,有向网络比无向网络更加脆弱;3)er随机图网络相继故障发生过程中引起网络相继故障规模增长的4个临界值之间存在线性关系。
基于dlp的自认证代理签密方案
俞惠芳,海兴,王之仓,王小红?
计算机科学 , 2010,
Abstract: 自认证密码体制可以实现无公钥证书和密钥托管,代理签密是将代理签名和签密相结合的一种方案。在已有研究的基础上,集成自认证密码体制和代理签密,提出了一种新的基于dlp的自认证代理签密方案,并在有限域上离散对数问题的难解性下,给出了其正确性和安全性证明。
静电
海兴
现代物理知识 , 1992,
Abstract: 人类对电现象的认识始于静电.从古希腊哲学家塞利斯记载的木头摩擦琥珀能吸引草屑,到十六世纪英国的吉尔伯特的各种摩擦电实验,基本上都是对静电现象的观察和定性的总结.定量研究则始于十八世纪英国的卡文迪许和法国的库伦.自从1800年意大利的伏打发明电堆、获得了持续、稳定的电流之后,静电似乎已完成了历史的使命而与技术无缘.然而进入二十世纪,特别是50年代以来,随着石油化工的兴起,高分子绝缘材料的涌现,静电科学逐渐转向静电技术,其应用领域日趋扩大,静电已成为物理学领域中既古老而又年轻的一门分支学科.
微粗糙平面上Chaplygin球永久转动的稳定性
海兴
力学学报 , 1989, DOI: 10.6052/0459-1879-1989-6-1989-368
Abstract: 本文讨论微粗糙平面上chaplygin球绕铅垂轴永久转动的稳定性,严格证明了在粘性摩擦条件下球绕最小和中间惯量主轴永久转动的不稳定性,以及在粘性和库仑两种摩擦条件下绕最大惯量主轴永久转动的一致稳定性。
在微粗糙平面上滚动的Chaplygin球的稳定性
海兴
力学学报 , 1991, DOI: 10.6052/0459-1879-1991-3-1995-848
Abstract: 本文利用文献[1]的结果,继续讨论Chaplygin球在微粗糙平面上滚动的稳定性。严格证明了在粘性和库仓两种磨擦条件下球绕最大惯量主轴滚动的一致稳定性,和在粘性摩擦条件及球的最大与中间主惯量矩十分接近的前提下球绕最小惯量主轴滚动的不稳定性。
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