拓扑指数在烷烃同分异构体中的应用

运用拓扑指数基本原理来定量阐述烃类的分子结构及性质变化趋势，有很高的准确性和适用性。     

浅议方中通"九九图说"中的数学思想

方中通是清初数学家,“九九图说”是他重要的数学成果之一。“九九图说”主要对中国古代组合图形进行了深入的研究,给出了各类纵横图的一般性定义,从中反映出方氏对数学对称性、统一性的追求,以及对辩证方法的运用。     

Non-linear autoregressive time series with multivariate Gaussian mixtures as marginal distributions

A new form of non-linear autoregressive time series is proposed to model solar radiation data, by specifying joint marginal distributions at low lags to be multivariate Gaussian mixtures. The model is also a type of multiprocess dynamic linear model, but with the advantage that the likelihood has a closed form.     

一类Weierstrass函数图像的K-维数式

Weierstrass函数是一类处处连续不可微的函数,其函数图像具有分形性质。研究Weierstrass函数图像的分形维数在分形几何中具有非常重要的地位。K-维数是介于Hausdorff维数和Box维数之间的分形维数,通过研究一类Weierstrass函数图像的K-维数,证明了这类函数图像的K-维数为1,从而进一步揭示出这类Weierstrass函数图像的Hausdorff维数、Box维数和K-维数之间的关系。     

Information seeking in secondary schools: A multilevel network approach

In this study, we investigate information seeking interactions in secondary schools from a multilevel network approach. Based on network-related theories, we examine the facilitating role of formal subunits. We apply exponential random graph models for multilevel networks and summarize our findings by using a meta-analysis technique. Our results indicate that formal subunits (e.g. subject departments) can, to some extent, facilitate interactions, in loosely coupled organizations (e.g. secondary schools). Finally, this study shows that a multilevel network approach can provide a more informative representation of information seeking ties in knowledge-intensive organizations.     

T—S图上任意循环的卡诺循环分解

本文用T－S图代替了常用的P－V图，用直观易画的台阶形代替了锯齿形，避免了因分解不同而引出的不统一的看法，并且给出了一个形象、直观、准确无误、易于接受的分析及解答。     

Who are the objects of positive and negative gossip at work?: A social network perspective on workplace gossip

Gossip is informal talking about colleagues. Taking a social network perspective, we argue that group boundaries and social status in the informal workplace network determine who the objects of positive and negative gossip are. Gossip networks were collected among 36 employees in a public child care organization, and analyzed using exponential random graph modeling (ERGM). As hypothesized, both positive and negative gossip focuses on colleagues from the own gossiper's work group. Negative gossip is relatively targeted, with the objects being specific individuals, particularly those low in informal status. Positive gossip, in contrast, is spread more evenly throughout the network.     

A multiple stream generator based on de Bruijn digraph homomorphisms

We propose a method to obtain several streams of pseudorandom numbers based on a backbone generator of the generalized shift register type. The method is based on inverting one cycle in a de Bruijn digraph into many sequences in a higher-order de Bruijn graph via an appropriate graph homomorphism. We apply this technique to twisted generalized feedback shift register generators and to the Mersenne Twister MT19937. Positive results of statistical testing are reported.     

On Approximate Graph Colouring and MAX-k-CUT Algorithms Based on the θ-Function

The problem of colouring a k-colourable graph is well-known to be NP-complete, for k 3. The MAX-k-CUT approach to approximate k-colouring is to assign k colours to all of the vertices in polynomial time such that the fraction of `defect edges' (with endpoints of the same colour) is provably small. The best known approximation was obtained by Frieze and Jerrum (1997), using a semidefinite programming (SDP) relaxation which is related to the Lovász -function. In a related work, Karger et al. (1998) devised approximation algorithms for colouring k-colourable graphs exactly in polynomial time with as few colours as possible. They also used an SDP relaxation related to the -function.In this paper we further explore semidefinite programming relaxations where graph colouring is viewed as a satisfiability problem, as considered in De Klerk et al. (2000). We first show that the approximation to the chromatic number suggested in De Klerk et al. (2000) is bounded from above by the Lovász -function. The underlying semidefinite programming relaxation in De Klerk et al. (2000) involves a lifting of the approximation space, which in turn suggests a provably good MAX-k-CUT algorithm. We show that of our algorithm is closely related to that of Frieze and Jerrum; thus we can sharpen their approximation guarantees for MAX-k-CUT for small fixed values of k. For example, if k = 3 we can improve their bound from 0.832718 to 0.836008, and for k = 4 from 0.850301 to 0.857487. We also give a new asymptotic analysis of the Frieze-Jerrum rounding scheme, that provides a unifying proof of the main results of both Frieze and Jerrum (1997) and Karger et al. (1998) for k 0.     

图的相对断裂度的若干结果

文献[1]引入了图的相对断裂度的概念,讨论了相对断裂度与1-因子和带宽的关系,并在文献[1]的基础上进一步刻划了相对断裂度与图的结构。