网络的容错性是指当网络中出现故障时，该网络仍然具有的一些好的性质，它是衡量一个网络可靠性的重要标准。文章研究了二维网络的边容错哈密尔顿性，证明了在一种条件故障假设以及排除一种禁止圈的情况下，对给定的偶数k≥6，F是Torus-（ k，k）中故障边的集合。若F中元素个数至多为4时，则Torus-（ k，k）-F中仍存在哈密尔顿圈。

Fault-tolerant of network means that the network will still have some good properties when it fails,which plays an important role in measuring the reliability of a network. In this paper,the edge fault-tolerant hamiltonicity of two-dimensional torus network was investigated to prove that that under the conditional fault assumption and the assumption of exclude a forbidden cycle,to a given even integer k≥6,F is a set which contains faulty edges. If the number of elements in the F is up to 4,the Torus-( k,k)-F still exists a Hamiltonian cycle.

目的探讨小脑性眩晕伴焦虑的原因及其抗焦虑治疗的疗效。方法自2009年1月开始,对三家医院收治的小脑性眩晕伴焦虑患者82例随机分为治疗组和对照组,治疗组进行常规治疗+氟哌塞顿美利曲辛联合度洛西汀抗焦虑治疗,对照组进行常规治疗。在入院时及治疗2、4、8周末给予眩晕量表和哈密尔顿焦虑量表(HAMA)评分。结果治疗组与对照组在入院时眩晕量表及HAMA量表评分两者无显著性差异(均P0.05)。治疗后,治疗组在2周末、4周末和8周末眩晕量表及HAMA量表评分较对照组明显偏低(均P0.05)。对照组8周末时眩晕量表评分较4周末时反而上升,差异有极显著性意义(P0.01)。结论小脑性眩晕伴焦虑患者,积极进行抗焦虑治疗有益于改善患者焦虑及眩晕症状。

Objective To explore the causes of anxiety in cerebellum vertigo and evaluate the efficacy of anxiolytic therapy.Method Since January, 2008, patients of cerebellar vertigo with anxiety were randomly divided into an experimental group and a control group in three hospitals .The experimental group were treated with routine therapy plus anxiolytic therapy with droperidol seton melitracen and duloxetine , while the control group were administered with conventional treatment .The patients received evaluation with Dizziness Scale and Hamilton Anxiety Scale ( HAMA) on admission and 2,4,8 weeks after treatment.Findings At the time of admission, no significant differences were found in the vertigo and HAMA scale scores between the two groups ( P>0.05).After treatment, the experimental group scored significantly lower than the control group in the vertigo and HAMA scale at the end of 2,4,8 weeks(P<0.05).The control group for 8 weeks at the vertigo score over 4 weeks at the rise.The difference wa

图G的线图L(G)是指以G的边集E(G)为顶点集且L(G)的2个顶点邻接当且仅当它们在G中有公共顶点.n次迭代线图Ln(G)递归地定义为L0(G)=G,Ln(G)=L(Ln-1(G))(n∈N={0,1,2,…}),其中L1(G)=L(G)并且假设Ln-1(G)非空,使得Ln(G)是哈密尔顿的最小整数n称为哈密尔顿指数,用h(G)表示.该文综述了(类)哈密尔顿指数的一些结果.

Let G be a simple graph. The line graph L( G)of a graph G is a graph which has E( G)as its vertex set and two vertices are adjacent in L( G)if and only if they share an end vertex in G. The n-th iterated line graph Ln(G)is defined recursively by L0(G)=G,Ln(G)=L(Ln-1(G))(n∈N={0,1,2,…}),where L1(G)=L(G) and Ln-1( G)is assumed to be nonempty. The hamiltonian index of a graph G,denoted by h( G),is the smallest in-teger n such that Ln(G)is hamiltonian. The results of hamiltonian(like)indices of graphs have been summaric-zed.

求解完全图上的哈密尔顿圈是典型的组合优化问题，遗传算法是解决此类NP问题的一种较理想的方法。对基本的遗传算法进行改进，在选择操作和变异操作中加入贪心优化思想，使算法获得更优的全局最优解。在MATLAB环境下模拟实现了哈密尔顿圈的经典问题———TSP( travelling salesman problem)旅行商问题，从而验证了该算法的可行性和正确性。

Solving Hamilton-circle on a complete graph is a typical combinatorial optimization problem. Genetic algorithm is a good way to solve such an NP problem. In this paper, the basic genetic algorithm is improved. Particularly, the greedy optimization i-deas are applied to the selection and mutation operation in order to obtain global optimal solutions with the algorithm. In the MATLAB environment, the algorithm was simulated to implement classical Hamilton circle-TSP ( Travelling Salesman Problem) and the results verify the feasibility and correctness of the algorithm.

通过引入一个新的显式李代数得到了一个孤子族的非线性可积耦合,利用相应圈代数上的变分恒等式给出了非线性可积耦合的哈密尔顿结构.本文所给的方法也可以应用于其它孤子族的非线性可积耦合.

A new explicit Lie algebra structure is introduced for which the nonlinear inte-grable couplings of a soliton hierarchy is obtained. Variational identity over the corresponding loop algebras is used to furnish Hamiltonian structures for the re-sulting nonlinear integrable couplings. The approach presented in the paper can also provide nonlinear integrable couplings for other soliton hierarchies.