PATHS AND CYCLES EMBEDDING ON FAULTY ENHANCED HYPERCUBE NETWORKS

Let Qn,k(n≥3,1≤k≤n-1) be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges,fv and fe be the numbers of faulty vertices and faulty edges,respectively.In this paper,we give three main results.First,a fault-free path P [u,v] of length at least 2n-2fv-1(respectively,2n-2fv-2) can be embedded on Qn,k with fv+fe≤n-1 when d Qn,k(u,v) is odd(respectively,d Qn,k(u,v) is even).Secondly,an Qn,k is(n-2) edgefault-free hyper Hamiltonian-laceable when n(≥3) and k have the same parity.Lastly,a fault-free cycle of length at least 2n-2fv can be embedded on Qn,k with fe≤n-1 and fv+fe≤2n-4.     

含故障点的加强超立方体中路和圈的嵌入

本文研究了含故障点的n-维加强超立方体Q_n,k中的路和圈嵌入的问题.充分分析了加强超立方体网络的潜在特性,利用了构造的方法.得到了含2n-4个故障点的加强超立方体Q_n,k中含长为2ⁿ-2f的容错圈的结论,推广了折叠超立方体网络中1-点容错圈嵌入的结果.其中折叠超立方体网络为加强超立方体网络的一种特殊情况.     

故障加强超立方体中的路和圈

本论文研究了含故障点的加强超立方体中路和圈的嵌入问题.利用数学归纳法,获得了故障加强超立方体中的路和圈,推广了超立方体中点容错路和圈嵌入的结果.     

故障折叠超立方体中的路和圈

本文研究了含故障点的n-维折叠超立方体FQn中的路和圈嵌入的问题,分析了折叠超立方体网络的潜在特性.利用了构造的方法,得到了含2n-3个故障点的折叠超立方体FQn中含长为2n-2f的圈的结论,推广了折叠超立方体网络中1-点容错圈嵌入的结果.     

ON THE CONDITIONAL EDGE CONNECTIVITY OF ENHANCED HYPERCUBE NETWORKS

Let G =(V, E) be a connected graph and m be a positive integer, the conditional edge connectivity λ_δ~m is the minimum cardinality of a set of edges,if it exists, whose deletion disconnects G and leaves each remaining component with minimum degree δ no less than m. This study shows that λ_δ~1(Q_(n,k)) = 2 n,λ_δ~2(Q_(n,k)) = 4 n-4(2 ≤ k ≤ n-1, n ≥ 3) for n-dimensional enhanced hypercube Q_(n,k). Meanwhile, another easy proof about λ_δ~2(Q_n) = 4 n-8, for n ≥ 3 is proposed. The results of enhanced hypercube include the cases of folded hypercube.     

CYCLES EMBEDDING ON FOLDED HYPERCUBES WITH FAULTY NODES

Let FF_v be the set of faulty nodes in an n-dimensional folded hypercube FQ_n with |FF_v| ≤ n-1 and all faulty vertices are not adjacent to the same vertex. In this paper, we show that if n ≥ 4, then every edge of FQn-FF_v lies on a fault-free cycle of every even length from 6 to 2~n-2|FF_v|.     

超方体(d,m)的控制数

This paper shows that the (d,m)-dominating number of the m-dimensional hypercube Qm(m≥4)is 2 for any integer d.([m/2] ≤d≤m).     

EMBEDDING FLOWS OF DIFFEOMORPHISMS

In this paper we first survey the results on the embedding flow problem of dif-feomorphisms in higher dimensional spaces. Next we present some new results on the characterization of semi-unipotent diffeomorphisms in R3, which have a formal embedding flows.     

立方体网络路由选择算法

本文利用图论理论 ,基于路由选择能力的概念 ,建立了一个有效的路由选择算法 ,该算法可以在含有节点故障和边故障的容错超立方体上使用 ,且具有较强的容错性 .     

ON THE NUMBER OF LIMIT CYCLES OF A POLYNOMIAL DIFFERENTIAL SYSTEM

In this paper, we employ qualitative analysis and methods of bifurcation theory to study the maximum number of limit cycles for a polynomial system with center in global bifurcation.     

A Ramsey‐type result for the hypercube

We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Q_n contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006     

具有财政赤字的OLG竞争商业周期

讨论平面上ＯＬＧ模型的均衡解的稳定性，并利用一个类似稳定流形定理的结论，把二维动力系统化为一维动力系统，从而在整体上研究带有国家财政赤字的ＯＬＧ模型．     

DARBOUXEQUATIONS AND ISOMETRIC EMBEDDING OF RIEMANNIAN MANIFOLDS WITHNONNEGATIVE CURVATURE INR

50.IntroductionAsDarbouxpointedout,theisometricembeddingoftwodimensionalRiemannianmanifoldsinR3leadstosolveanonlinearpartialdifferentialequationofMongeAmperetypewhereVZz=(iii--r;zk)denotestheHessianofzwithrespecttothegivensmoothmetricg=gijdu'duidefinedonfi,g'Jtheinverseofthemetrictensorandkthecurvatureofthemetricg.Indeed,fromtheGaussequationsoftherequiredisometricembedding/~(x,igz),wherefitjarethecoefficientsofitssecondfundamentalformandacisitsnormal,computingtheinnerproductsofthelastexpre…     

NUMERICALLY SOLVING PERIODICALLY PERTURBED CONSERVATIVE SYSTEMS BY PARAMETER EMBEDDING METHODS

1　IntroductionConsider the system of differential equationsTu≡ u"+ F( t,u) =0 ( 1 )where F:R×Rn→Rnis a continuos function of2 π-period with respect to tand F( t,· )∈ C1( Rn,Rn) has a symmetric derivative for all t∈R and allξ∈Rn.When the system is of the formu"+ grad G( u) =e( t) ( 2 )where G∈C2 ( Rn,R) ,e:R→Rncontinuousand2 π-periodic.Equation( 2 ) can be interpreted asthe Newtonian equation ofmotion ofa mechanicalsystem subjectto conservative internal forcesand periodic e…     

二维非线性动力系统的多极限环分叉的参数控制

本文研究了一类具有Z2-等变性质的5次扰动平面Hamilton向量场，利用动力系统的分叉理论和判定函数法，通过控制其参数，得到系统在两组不同的参数条件下分别存在20和23个极限环，以及它们之间相对位置的不同构型.这一结果对机械振动中相应的控制问题有理论指导意义。     

SAME DISTRIBUTION OF LIMIT CYCLES TO PERTURBED CUBIC HAMILTONIAN SYSTEMS WITH DIFFERENT PERTURBATIONS

Using qualitative analysis, we study perturbed Hamiltonian systems with different n-th order polynomial as perturbation terms. By numerical simulation, we show that these perturbed systems have the same distribution of limit cycles. Our results imply that these perturbed systems are equivalent in the sense of distribution of limit cycles. This is useful for studying limit cycles of perturbed systems.     

LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new.     

一类三次系统的极限环

本文讨论了一类三次系统 x=-y(1-αx~2)+δx-ιx~3,y=x(1-βx~2)和 x=-y(1-ax)(1-bx)+δx-ιx~3,y=x(1-cx)(1-bx)的极限环问题。     

解非光滑方程组的广义数值延拓算法(Ⅱ)──算法与应用

We present a generalized numerical embedding algorthm for solving nonsmooth equations based on the results in [1],COnvergence of the algorithm is proved carefully and implementation is discussed.Application of the algorithm to the complementartity problem,Variational inequalities and nonlinear optimization problemis discussed.