TREE DECOMPOSITIONS OF MULTIGRAPHS

1.IntroductionInthispaperweconsideronlyfiniteundirectedlooplessgraphs.ForasubgraphHofG,E(H)andP(H)denotethenumberofedgesandthenUmberofcyclesinHrespectively.GiventwodisjointsubsetsXandYofV(G),wewriteEG(X,Y)={acEE(G)IxEX,y6Y}.IfTisatreeinGande=acEG--E(T)with{u,v}CV(T),thenT econtainsauniquecycle.WedenotethiscyclebyC(T,e).Aforestiscalledak-tree-forestifitconsistsofexactlykpairwisedisjointtrees.ForagraphG,ifE(G)canbepartitionedilltoseveralpairwisedisjointsetsas{EI,EZ,...,EI}such…     

VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS

H. Wang considered the minimum degrees condition that G has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let m > 3, n > 2 and k >1 be three integers. Let G = (V1,V2;E) be a bipartite graph with | V1| = | V2| =n > 2k 1. If the minimum degreefor any cycle C of G with length 2m, then G contains k vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.     

LONG DOMINATING CYCLES IN GRAPHS

1.IntroductionAllgraphsconsideredinthispaperwillbefiniteandsimple.WeuseBondyandMurty[1]forterminologyandnotationsnotdefinedhere.LetG=(V,E)beagraphofordernandCbeacycleinG.Ciscalledadominatingcycle,orbrieflyaD--cycle,ifV(G)\V(C)isanindependentsetinG.ForavertexvinG,theneighborhoodofvisdenotedbyN(v),andthedegreeofvisdenotedbyd(v).FortwosubsetsSandTofV(G),wesetNT(S)~{vET\S:N(v)nS/0}.WewriteN(u,v)insteadofNV(G)({u,v})foranyu,vEV(G).IfFandHaretwosubgraphsofG,wealsowriteNF(H)insteado…     

c个修理工同步多重休假的k/n(G)表决可修系统

本文首次将"多个修理工同步多重休假"规则引入到c个修理工的k/n(G)表决可修系统中,在假设部件的工作寿命、故障后的修理时间和修理工的休假时间 分别服从参数λ(>0)、μ(>0)和θ(>0)的负指数分布下,利用拟生灭过程 和矩阵几何解方法,讨论了在稳态下系统处于各状态的概率分布,以及一些刻画系统性能的可靠性指标 和排队指标,如系统的稳态可用度、稳态故障频度和故障部件的等待修理时间等,并且讨论了四种特殊情况: 1) c=1,θ→+∞; 2) c=1,k=1,θ→+∞; 3) c=1,k=n,θ→+∞; 4) c=1,k=n-1,θ→+∞.最后给出了在c=2,n=6,k=3,λ=1/10,μ=1/5,θ=1/2的数值计算例子.     

A NEIGHBORHOOD UNION CONDITION FOR PANCYCLIC GRAPHS

1.IntroductionWeconsideronlysimplefinitegraphs.OurbasicnotationandterminologynotdefinedherefollowthOSeofBondyandMurtyll].ForagraphG,letV(G)andE(G)(orjustVandE)deDOtelievertexsetandedgeset,respectively.Wedenoteapathandacyclecontaining8veniCesbyPaandCarespectively.ThecycleCaiscalledans-cycle.Denotebyg(G)(orbrieflybyg)thegirthofG1.SetNC=min{IN(u)UN(v)l:tv相似文献   

1/2-TRANSITIVE GRAPHS ASSOCIATED WITH LINEAR GROUPS

１／２－ＴＲＡＮＳＩＴＩＶＥＧＲＡＰＨＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨＬＩＮＥＡＲＧＲＯＵＰＳ￥ＤＵＳｈａｏｆｅｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｘｉＵｎｉｖｅｒｓｉｔｙ，Ｔａｉｙｕａｎ０３０００６，Ｃｈｉｎａ）Ａｂｓｔｒａｃ...     

PANCONNECTIVITY AND 2-CONNECTED CLAW-FREE GRAPHS

ＰＡＮＣＯＮＮＥＣＴＩＶＩＴＹＡＮＤ２－ＣＯＮＮＥＣＴＥＤＣＬＡＷ－ＦＲＥＥＧＲＡＰＨＳ￥ＧＡＯＪｉｎｇｚｈｅｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｄｄｏｃｋＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５００１４，Ｃｈｉｎａ）Ｚ...     

A DEGREE CONDITION FOR THE EXISTENCE OF CONNECTED [k, k 1]-FACTORS

ＡＤＥＧＲＥＥＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＥＸＩＳＴＥＮＣＥＯＦＣＯＮＮＥＣＴＥＤ［ｋ，ｋ＋１］－ＦＡＣＴＯＲＳＡＤＥＧＲＥＥＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＥＸＩＳＴＥＮＣＥＯＦＣＯＮＮＥＣＴＥＤ［ｋ，ｋ＋１］－ＦＡＣＴＯＲＳ￥ＣＡＩＭａｏｃｈｅｎ...     

The scene for Interpretive Systemology

In this introductory paper to the special issue ofSystems Practice devoted to Interpretive Systemology, some of the conditions under which this trend in systems thinking has come to life are briefly depicted. For that purpose a wider and a narrower scene are presented. The wider scene presents the general questions and problems that are to be tackled by Interpretive Systemology, within a wide international perspective of systems thinking and practice. The narrower scene, which is related to more particular conditions, shows how some circumstances connected to the socalled Third World or underdeveloped countries have helped to trigger the launching of Interpretive Systemology. Finally, a brief outline of the research program for Interpretive Systemology is introduced.     

On LCD Negacyclic Codes over Finite Fields

This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2 n, the authors obtain the parameters of LCD negacyclic codes of lengths n =(q+1)/2,(q~m-1)/2(q-1)and q~(t·2~τ)-1/2(q~t +1), respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n |(q-1)/2 and n |(q+1)2, respectively.     

DECOMPOSITION OF MATRICES INTO COMMUTATORS OF REFLECTIONS

Let F be a field and let resA=rank(A-I) for any A in GLnF.We prove that every matrix in SLnF is a product of at most [resA/2] 2 commutators of reflections for n≥2 except for n=2 and F=F2.     

On suicidal rabbits: A relativity of systems

This festschrift paper, written in honour of Russell Ackoff, hinges on three of his characteristic approaches: the use of fables, his acceptance of messes as distinct from well-formulated problems, and his concept of idealized planning. Current thoughts of the author, dealing respectively with recursive logic, the implementation of change, and the theory of democratic organization, are attached to these hinges and among them, express his own theme as to a relativity of systems.     

复杂系统的演化过程,n(n-1)律,自聚集

研究一类复杂系统的演化过程,给出一个网络模型,由此导出f(n)=n(n-1),用以在某种程度上定性地描写演化过程中聚集与功能变化的规律。这里n表示agents的聚集数量。熟知的关系式1+1>2是n=2时的特例。当n为小数时,n的增减对系统整体功能的影响显著,此情况将称为“小n机制”。当n充分大时,系统的整体功能将有大跃升,并可用n2度量,称此为“n2效应”。一般情况下,n(n-1)描写聚集-相互作用-功能跃升的模式,用此模式可对不同领域的演化过程作某种解释。     

环形不同部件相邻2/3(G或F)可修系统的可靠性分析

本文考虑了相邻２／３（Ｇ或Ｆ）不同部件的这类环形可修系统,给出了这类系统可靠度的Ｌａｐｌａｃｅ变换表达式、首次故障前的平均时间（ＭＴＴＦＦ）等可靠性指标,为进一步探索环形不同部件相邻ｋ／ｎ（Ｇ或Ｆ）可修系统、复杂串并联和复杂并串联系统提供了一条新途径。     

任意分布的冷备表决系统可靠度求解

k/n: M(G)冷备表决系统包含n个工作部件, M个冷储备件, 至少有k个部件工作时系统工作。然而, 现有对于k/n: M(G)冷备表决系统的研究集中在同型指数分布的情况, 缺乏针对其工作部件非同型且服从任意分布的情况的研究。本文研究了k/n: M(G)冷备表决系统的可靠度, 系统部件服从任意分布, 冷备件服从同一分布。对k=n的情况, 给出了M取任意值时部件同型和非同型情况下的系统可靠度解析式。对于k＜n的情况, 考虑了两种不同的冷备件替换策略, 给出了部件同型情况和非同型M取特定值情况下的系统可靠度解析式。蒙特卡罗仿真实验证明了所提方法的准确性。     

基于任务的k/n(G)系统舰船备件需求预测

针对k/n(G)系统在事后维修与任务后检修相结合条件下的舰船备件需求预测问题,在备件寿命服从指数分布的条件下,首先建立了k/n(G)系统的备件需求预测模型,并给出了备件需求特征。然后,基于方便理解和简便计算的需要,以伽马型单部件需求为基础,给出了备件需求模型的工程解释和近似计算方法,并对近似算法的精度进行了验证。结果表明,备件需求模型可以更好地描述k/n(G)系统在一次海上任务期内的备件需求,近似算法具有较高的精度,可以为舰船装备备件配置问题提供参考。     

Two-Weight Norm Inequality for Imaginary Powers of a Laplace Operator

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I： G/M（n）/1/K

In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.     

On the Meromorphic Solutions of Linear Differential Equations

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.     

n/k(G)表决冗余多阶段任务系统可靠性优化模型

提出采用多阶段任务系统（phased mission systems, PMS）冗余故障树模型和PMS冗余二元决策图（binary decision diagram, BDD）模型来描述冗余多阶段任务系统;通过递归法实现PMS冗余故障树模型到PMS冗余BDD模型的转换,从而得到整个PMS的最小割集;在分析n/k(G)表决冗余模块在PMS中可靠度计算模型的基础上得到整个PMS的可靠性计算模型。以费用最小为目标,构建多阶段任务系统可靠性冗余优化模型,并应用微粒群算法对模型进行求解。算例通过一个三个阶段n/k(G)表决系统来阐述该方法的应用,并验证了模型的合理性及算法的有效性。