THE NORMALITY OF CAYLEY GRAPHS OF SIMPLE GROUP A_5 WITH SMALL VALENCIES

1.IntroductionLetGbeafinitegroup.ForaCayleysubsetSofGnotcontainingtheidentityelement1,theCayley(di)graphX~Cay(G,S)ofGwithrespecttoSisdefinedasthedirectedgraphwithvertexsetV(X)=GandedgesetE(X)={(g,sg)IgEG,s6S}.IfS=S--',thentheadjacencyrelationissymmet...     

ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

In this paper we obtain the necessary and sufficient condition for the connec-tivity of the Cayley color graphs or the Cayley graphs to be equal to their minimum degree.The sharp lower bounds of connectivity of Cayley color graphs and the Cayley graphs arealso obtained. Our results generalize the previous results obtained in [1] to [3].     

A NOTE ON THE PAPER "ON THE CONNECTIVITY OF CAYLEY COLOR GRAPHS

ＡＮＯＴＥＯＮＴＨＥＰＡＰＥＲ＂ＯＮＴＨＥＣＯＮＮＥＣＴＩＶＩＴＹＯＦＣＡＹＬＥＹＣＯＬＯＲＧＲＡＰＨＳ＂￥ＭＥＮＧＪｉｘｉａｎｇ；ＨＵＡＮＧＱｉｏｎｇｘｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｉｉａｎｇＵｎｉｖｅｒｓｉｔｙ，...     

A NEW FAMILY OF TRIVALENT CAYLEY NETWORKS ON WREATH PRODUCT Zm ～ Sn

We propose a new family of interconnection networks （WGn^m） with regular degree three. When the generator set is chosen properly, they are isomorphic to Cayley graphs on the wreath product Zm ～ Sn. In the case of m ≥ 3 and n ≥3, we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by [m/2]（3n^2- 8n ＋ 4） - 2n ＋ 1. The connectivity and the optimal fault tolerance of the proposed networks are also derived. In conclusion, we present comparisons of some familiar networks with constant degree 3.     

ON SUBALGEBRAS OF CHEVALLEY ALGEBRAS CONCERNING SUBFIELDS

ＯＮＳＵＢＡＬＧＥＢＲＡＳＯＦＣＨＥＶＡＬＬＥＹＡＬＧＥＢＲＡＳＣＯＮＣＥＲＮＩＮＧＳＵＢＦＩＥＬＤＳ￥ＺＨＡＪｉａｎｇｕｏ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｏｎｇｊｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２０００９２...     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉ...     

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…     

Traceability of Subsets in Cubic Graphs

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｃｙｃｌａｂｉｌｉｔｙｏｆｒｅｇｕｌａｒｇｒａｐｈｓｉｓａｎａｃｔｉｖｅａｒｅａｏｆｒｅｓｅａｒｃｈｉｎｔｈｅｄｉｒｅｃｔｉｏｎｏｆＤｉｒａｃ’ｓＴｈｅｏｒｅｍ（ｅｖｅｒｙｋｃｏｎｎｅｃｔｅｄｇｒａｐｈ...     

EXACT VALUE OF THE HARMONIOUS CHROMATIC NUMBER OF A COMPLETE TRINARY TREE

1.IntroductionLetG={VE}beafinite,undirected,simplegraPh,TheharmoniouschromaticnumberofagraPhG,denotedbyh(G),istheleastnumber0fcolorsneededtocol0rtheverticesofGinsuchawaythatanytwoadacelitverticesarec0loredbydmerelltcol0rsandanytwodistinctedgeshavedtherentcolorpairs(Here,ac0lorpairforedgee=uvisthepairofcol0rsusedt0coloruandv).Theharmoniouscol0ringshavebeenstudiedinpaPersl1-10].J.Mitchem[10]0btainedtheexactvalue0ftheharm0ni0uschr0maticnUInber0fthepath,cycleandc0mpleten-nytreewith3or4levels…     

Dynamics in small worlds of tree topologies of wireless sensor networks

Tree topologies, which construct spatial graphs with large characteristic path lengths and small clustering coefficients,are ubiquitous in deployments of wireless sensor networks. Small worlds are investigated in tree-based networks. Due to link additions, characteristic path lengths reduce rapidly and clustering coefficients increase greatly. A tree abstract, Cayley tree, is considered for the study of the navigation algorithm, which runs automatically in the small worlds of tree-based networks. In the further study, epidemics in the small worlds of tree-based wireless sen-sor networks on the large scale are studied, and the percolation threshold is calculated, at which the outbreak of the epidemictakes place. Compared with Cayley tree, there is a smaller percolation threshold suffering from the epidemic.     

PACKING A TREE OF ORDER p WITH A （p,p＋1）—GRAPH

Let G1 and G2 be two graphs of the same order,If G1 is isomorphic to a spanning subgraph of the complement of G2,then we say that G1 and G2 are packable.A graph G is called a (p,m)-graph if G has p vertices and m edges.The main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p 1)-graph to be packable.     

THE EXISTENCE OF JENSEN BOUNDARY POINTS IN COMPLEX BANACH SPACES

Inthelasttenyears,severalremarkableresultswereestablishedinthegeometricaltheoryofinfinitelydimensionalcomplexBanachspaces.In[1],A.V.BukhvalovandA.A.DanilevichhaveintroducedtheanalyticRadon--NikodympropertyincomplexBanachspaces,whichcanbeseenastheanalyticanalogueofthewell-knownRadon-NikodympropertyconcerningtherealstructuresofBanachspaces.TheanalyticRadon-Nikodympropertyhasbeenextensivelystudied(see[2--6]),onecancharacterizetheanalyticRadon-Nikodympropertyintermsoftheconvergenceofplurisub…     

A NEW ROUTING ALGORITHM FOR THE SHUFFLE-EXCHANGE PERMUTATION NETWORK

In this paper, a new routing algorithm is given for the shuffle-exchange permutation network （SEPn）. The length of the path between any two nodes given by our algorithm is not more than 11/16n^2＋O（n）, i.e., the diameter of SEPn is at most 11/16n^2＋ O（n）. This improves on a 1/8（9n^2- 22n＋24） routing algorithm described earlier by S. Latifi and P. K. Srimani. We also show that the diameter of SEPn is more than 1/2n^2-n.     

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

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

A PROPERTY OF PRODUCTS OF NEW GENERALIZED FUNCTIONS

ＡＰＲＯＰＥＲＴＹＯＦＰＲＯＤＵＣＴＳＯＦＮＥＷＧＥＮＥＲＡＬＩＺＥＤＦＵＮＣＴＩＯＮＳＬＩＹａｑｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＡＰＲＯＰＥＲＴＹＯＦ...     

ON EVALUATING THE RUN LENGTH PROPERTIES OF  CHARTS WITH ESTIMATED CONTROL LIMITS

(?) charts with estimated control limits are commonly used in practice and treated as if the in-control process parameters were known. However, the former can behave quite differently from the latter. To understand the differences, it is necessary to study the run length distribution (RLD), its mean (ARL) and standard deviation (SDRL) of the (?) charts when the control limits are estimated. However, ARL and SDRL are integrals over an infinite region with a boundless integrand, the finiteness has not been proved in literature. In this paper, we show the finiteness and uniform integrability of ARL and SDRL. Furthermore, we numerically evaluate the ARL, SDRL and the RLD using number theory method. A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.     

APPLICATIONS OF INTEGRATED SEMIGROUPS TO HIGHER ORDER ABSTRACT CAUCHY PROBLEMS

This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:(ACP_n) x~(n)(t)=sum from i=0 to n-1 B_ix~(i)(t),x~(i)(0)=x_i,0(?)i(?)n-1where B_i (0(?)i(?)n-1) are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B_(n-1) is bounded andD(B_(n-2))(?)D(B_i)(0(?)i(?)n-3) are obtained.     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＭＥＲＯＭＯＲＰＨＩＣＳＯＬＵＴＩＯＮＳＯＦＡＬＧＥＢＲＡＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＹＵＡＮＷｅｎｊｕｎ（ＤｅｐａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｏｒｍａｌＵｎｉｖｅｒｓ...     

某型无人机降落伞回收系统动力学分析

针对我国某型无人机降落伞回收系统,建立了无人机降落伞回收过程中各阶段的动力学模型,分析降落伞-无人机组合体在整个回收过程中的运动特性。并将将计算结果与试验结果中无人机俯仰角的变化进行比较,以验证数值仿真的可靠性。研究结果表明:(1)减速伞开伞动载第一峰值约为1G,第二峰值约为1.3G。主伞开伞动载第一个峰值约为2G;第二个峰值约为2.3G。减速伞和主伞的两个动载峰值相差均不大,说明降落伞设计比较成功;(2)在回收开始后第4秒至第5秒之间,无人机出现了较为强烈的抬头。为了使无人机姿态进一步稳定在期望值,需要在控制律设计中着重解决无人机在回收各个阶段受伞系统影响而产生抬头的问题;(3)当回收高度在2000-10000m之间时,从回收系统在有控和无控状态下的工作包线可知,有控状态时回收系统的正常工作范围比无控状态要广。     

ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES

ＯＮＡＦＩＮＩＴＥＮＥＳＳＴＨＥＯＲＥＭＡＢＯＵＴＰＲＯＢＬＥＭＳＩＮＶＯＬＶＩＮＧＩＮＥＱＵＡＬＩＴＩＥＳ￥ＷＵＷｅｎｉｎｎ（ＷＵＷｅｎ－ｔｓｕｎ）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１...