THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR ｜x｜^α

This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f（z） =｜x｜^α（1〈α〈2） on [-1,1] can diverge everywhere in the interval except at zero and the end-points.     

ON LAGRANGE INTERPOLATION TO ｜x｜^α（1 〈α 〈 2） WITH EQUALLY SPACED NODES

S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [−1,1], In 2000, M. Rever generalized S.M. Lozinskii’s result to |x|^α(0≤α≤1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|^α(1<α<2).     

基于网络拓扑结构的重要节点发现算法

复杂网络中的重要节点发现在现实生活中有着广泛的应用价值。传统重要节点发现方法可分为局部发现和全局发现两类算法,全局发现算法中最具代表性的是特征向量中心性算法(Eigenvector Centrality, EC),EC算法将所有节点归为一个社区并利用邻居节点重要性反馈计算节点的影响力大小,具有较高的计算效率和识别精度。但是,EC算法忽略了网络的拓扑结构,未考虑到真实网络中节点所在社区的结构特征。为此,本文提出一种基于网络拓扑结构的可达中心性算法(Accessibility Centrality, AC),首先利用邻接矩阵作为反馈路径,在反馈过程中计算不同路径下的节点整体影响力。同时,利用影响力传递过程中的噪音干扰特性,修正每一路径长度下节点整体影响力大小,最后利用修正结果得到AC值。为评估AC算法,本文利用两种传染病模型模拟节点影响力在四组真实网络中的传播过程,并引入其他四种算法进行对比验证。实验结果表明,与其他算法相比,AC算法可以更准确、有效地识别出有具有影响力的重要节点。     

推荐重要节点部署防御策略的优化模型

当前网络安全防御策略集中部署于高连接度节点主要有2个方面的不足: 一是高连接度节点在很多场合中并不是网络通信的骨干节点; 二是该类节点对信息的转发和传播并非总是最有效的.针对以上传统部署策略的不足, 改进了恶意病毒程序传播的离散扩散模型并采用中间路径跳数来衡量网络节点的重要程度, 提出了基于介数中心控制力和接近中心控制力模型的重要节点优先推荐部署技术.实验结果显示具有高介数中心控制力和低接近中心控制力的节点相对于传统的高连接度节点无论在无标度网络还是小世界网络均能够对恶意病毒程序的疫情扩散和早期传播速度起到更加有效的抑制作用, 同时验证了网络分簇聚类行为产生的簇团特性也将对恶意程序的传播起到一定的负面影响.     

On Residue Symbols and the Mullineux Conjecture

This paper is concerned with properties of the Mullineux map, which plays a rôle in p-modular representation theory of symmetric groups. We introduce the residue symbol for a p-regular partitions, a variation of the Mullineux symbol, which makes the detection and removal of good nodes (as introduced by Kleshchev) in the partition easy to describe. Applications of this idea include a short proof of the combinatorial conjecture to which the Mullineux conjecture had been reduced by Kleshchev.     

面内裂纹扩展问题的虚拟裂纹闭合法和离散内聚力模型

论文介绍了处理面内裂纹扩展问题的两种断裂单元,分别为处理线性问题的VCCT哑节点断裂单元和处理非线性问题的DCZM断裂单元.并与有限元软件ABAQUS的断裂单元相对比,以验证其计算准确性和对网格、步长等不敏感性,以及计算效率高等特点.     

Parameters choosing for a time-of-flight momentum mapping system with truncated cone-shaped head

Based on the operating principle, we analyzed the restrictive interrelationship of the key parameters of the COLTRIMS (cold target recoil ion momentum spectroscopy)-type time-of-flight (TOF) momentum mapping system with truncated cone-shaped head. The analysis demonstrated how to appropriately choose and even optimize these parameters, the axial uniform magnetic field B, the relative position of the differential aperture relative to the electrons source sc and the aperture radius rc for the given energy range to be detected. The conclusion also showed that the cone-shaped head can be optimized by making a compromise between the relative position of the differential aperture relative to the electrons source sc and the differential pumping effect according to the actual acceptance angle. The presented example gave a good demonstration for the conclusion.     

Computing logarithms digit-by-digit

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but rather exploits properties of the radix-d representation of a logarithm in base d. As such, the algorithm is accessible to anyone familiar with the elementary properties of exponents and logarithms.     

Identifying influential nodes in weighted networks based on evidence theory

The design of an effective ranking method to identify influential nodes is an important problem in the study of complex networks. In this paper, a new centrality measure is proposed based on the Dempster–Shafer evidence theory. The proposed measure trades off between the degree and strength of every node in a weighted network. The influences of both the degree and the strength of each node are represented by basic probability assignment (BPA). The proposed centrality measure is determined by the combination of these BPAs. Numerical examples are used to illustrate the effectiveness of the proposed method.     

基于多属性决策的复杂网络节点重要性综合评价方法

复杂网络中的节点重要性评价在实际应用中有着重要意义.现有的一些重要性评价指标如度、介数等存在适用范围有限,评价结果不够全面等缺点,因为节点在复杂网络中的重要性不仅仅受单一因素的影响.为此,本文提出了一种基于多属性决策的复杂网络节点重要性综合评价方法.该方法将复杂网络中的每一个节点看作一个方案,其多个重要性评价指标作为该方案的属性,通过计算每个方案到理想方案的接近程度,最终得到该节点的重要性综合评价结果.该方法不仅可以用于不同类型复杂网络的节点重要性评价,而且便于扩展,实验结果表明了该方法的有效性.