关于紧优双环网络的无限族

双环网络是计算机互连网络和通讯系统的一类重要拓扑结构．1993年,李乔等人提出一个系统的构造方法,构造出69类0紧优和33类1紧优双环网络的无限族,并提出研究下述问题:求k(k>1)紧优双环网络的无限族．2003年,徐俊明等人给出一个4紧优双环网络的无限族．本文首先证明从每一个具体的0紧优双环网络出发,都可以构造若干0紧优双环网络无限族;结合同余方程组理论和数论中的素数理论,给出若干求一般k(k≥0)紧优双环网络无限族(包括非单位步长双环网络无限族)的方法．     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.     

Pregelation Behaviour of Coagulation Processes with the Constant-Reaction-Number Kernel

We propose an irreversible binary coagulation model with a constant-reaction-number kernel, in which, among all the possible binary coagulation reactions, only p reactions are permitted to take place at every time. By means of the generalized rate equation we investigate the kinetic behaviour of the system with the reaction rate kernel K（i;j） = （ij）^w （0 ≤w〈1/2）, at which an i-mer and a j-mer coagulate together to form a large one. It is found that for such a system there always exists a gelation transition at a finte time to, which is in contrast to the ordinary binary coagulation with the same rate kernel. Moreover, the pre-gelation behaviour of the cluster size distribution near the gelation point falls in a scaling regime and the typical cluster size grows as （to - t）-1/（1-2w）. On the other hand, our model can also provide some predictions for the evolution of the cluster distribution in multicomponent complex networks.     

关于图的直径和平均距离

图的直径和平均距离是度量网络有效性的两个重要参数．Ore通过图的顶点数和直径给出无向图的最大边数．Entringer，Jakson，Slater和Ng，Teh通过图的顶点数和边数分别给出无向图和有向图平均距离的下界．该文提供这两个结果的简单证明，给出有向图类似Ore的结果，并通过图的直径改进Entringer等人的结果到更一般的情形．结合本文和Ore的结果，可以得到一个无向图和有向图平均距离的下界，它比Plesnik得到的下界更好．     

EXPONENTIAL STABILITY AND PERIODIC SOLUTION OF HYBRID BIDIRECTIONAL ASSOCIATIVE MEMORY NEURAL NETWORKS WITH DISCRETE DELAYS

In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.     

带有边集限制的最均匀支撑树问题

本在无向网络中，建立了带有边集限制的最均匀支撑树问题的网络模型．中首先解决最均匀支撑树问题，并给出求无向网络中最均匀支撑树的多项式时间算法；然后，给出了求无向网络中带有边集限制的最小树多项式时间算法；最后，在已解决的两个问题的基础上解决了带有边集限制的最均匀支撑树问题．     

随机需求条件下的延迟发运策略模型及性质

本针对随机需求条件下物流配送中心的库存和运输联合决策问题，在基本库存和自身运输能力不足的情况下，提出对剩余客户订货需求采取部分延迟到下一期与部分利用第三方物流立即发运两相结合的策略，并在具有一般惩罚(损失)费延迟发运量限制的条件下，建立运输和库存相关总成本数学期望最小的优化模型，论证了该模型的主要性质，在此基础上很容易构造求解该类问题的优化方法。     

ULTIMATE BOUNDEDNESS FOR A DIFFERENTIAL DELAY MODEL

This paper considers the scalar differential delay equation x(t) = -μx(t)-f(x(t-Τ(t)), t). By using the mapping method we obtain that the solutionswill be ultimately in some interval.     

综合运用、多位一体的实验教学模式

介绍了在新的教学环境下 ,通过教学形式、教学手段、教学方法等多方面的改革来建立一种新的实验教学模式 ,以及该教学模式的特点和效果     

全光网中基于FBG的OADM设计研究

提出一种全新的OADM(Optical Add—Drop Multiplexers)结构设计，此结构仅采用一个多端口环行器，大大减少了环行器的数量，节约了成本。若要上／下路一个波长．则只需要一个FBG(Fiber Bragg Grating)；若要同时上／下路多个波长，则需要2m个FBG。计算机仿真实验证明此结构比H．Yuan提出的结构具有更低的损耗．对全光网络的实现具有重大的意义。