基于关键节点和多播节点的多播路由算法

在视频会议等多播应用中，降低多播树网络费用非常重要。本文提出了基于关键节点和目的节点的多播路由KDDMC算法。由于在算法中优先考虑采用关键节点，实现更多链路的共享，从而降低网络费用。在随机网络上的仿真结果表明，KDDMC算法的多播树网络费用优于SPH算法。同时证明了KDDMC算法的复杂度为O(n^3)，且利用所提出的路由表算法易于分布式实现。     

一种增强型冲突分解算法

冲突分解算法是一种能有效改善无线信道多址接入协议的方式。本文对传统的冲突分解算法——树形冲突分解算法和先到先服务冲突分解算法进行了深入研究和仿真，探讨了这两种算法的优点和不足之处，提出了一种增强型的冲突分解算法（Enhanced Splitting Algorithm，ESA）。该算法继承了树形冲突分解算法和先到先服务算法的优点，不仅考虑了碰撞分组产生的时间，还考虑了分组的产生间隔，从而有效地提高了冲突分解算法的性能。仿真结果显示ESA算法是一种可行的算法。     

一种基于树形结构显示关联数据的设计

论述了在程序设计过程中 ,使用树形控件、SQL 语句、临时表等多种手段 ,达到多个关联数据库的数据由一个可视化树形结构控件显示的方法和技巧     

Analytic continuation and identities involving heat,Poisson, wave and Bessel kernels

In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．     

On lattices embeddable into subsemigroup lattices. V. Trees

We prove that the class of finite lattices embeddable into the subsemilattice lattices of semilattices which are (n-ary) trees can be axiomatized by identities within the class of finite lattices, whence it forms a pseudovariety.     

求解无线传感器网络路由问题的蚁群最优化算法及其收敛性

首先将无线传感器网络的路由问题转化成求解最小Steiner树问题,然后给出了求解无线传感器网络路由的蚁群优化算法,并对算法的收敛性进行了证明．最后对找到最优解后信息素值的变化进行了分析．即在限制信息素取值的条件下,当迭代次数充分大时,该算法能以任意接近于1的概率找到最优解,并且当最优解找到后,最优树边上的信息素单调增加,而最优解以外边上的信息素在有限步达到最小值．     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

求解最小Steiner树的蚁群优化算法及其收敛性

最小Steiner树问题是NP难问题,它在通信网络等许多实际问题中有着广泛的应用．蚁群优化算法是最近提出的求解复杂组合优化问题的启发式算法．本文以无线传感器网络中的核心问题之一,路由问题为例,给出了求解最小Steiner树的蚁群优化算法的框架．把算法的迭代过程看作是离散时间的马尔科夫过程,证明了在一定的条件下,该算法所产生的解能以任意接近于1的概率收敛到路由问题的最优解．     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.