On Super Hamiltonian Semigroups

The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.     

无K1,r图中的哈密顿圈（英文）

本文借助对图的本质独立集和图的部分平方图的独立集的研究，对于K1,r图中哈密顿圈的存在性给出了八个充分条件。我们将利用T－插点技术对这八个充分条件给出统一的证明，本文的结果从本质上改进了C－Q.Zhang于1988年利用次形条件给出的k-连通无爪图是哈密顿图的次型充分条件，同时。G.Chen和R.H.Schelp在1995年利用次型条件给出的关于k-连通无K1，4图是哈密顿图的充分条件也被我们的结果改进并推广到无K1,r图。     

邻域并与泛圈图

本文中 ,我们用邻域并对泛圈图进行深入的研究 ,主要取得了“2连通 n( n≥ 3 )阶图 G,满足下列条件之一 ,则 G是泛圈图 : :δ≤ ( n-7) /3 ,N C≥ ( 2 n-3 ) /3 ; :( n-6) /3≤ δ≤ ( n+2 ) /3 ,N C≥ 2 n/3 ; :δ≥ ( n+3 ) /3 ,N C≥ ( 2 n-3 ) /3 .当 3≤ n≤ 14时 ,N C≥ 2 n/3”     

SYMPLECTIC SCHEMES FOR NONAUTONOMOUS HAMILTONIAN SYSTEM

ＳＹＭＰＬＥＣＴＩＣＳＣＨＥＭＥＳＦＯＲＮＯＮＡＵＴＯＮＯＭＯＵＳ　ＨＡＭＩＬＴＯＮＩＡＮ　ＳＹＳＴＥＭＱＩＮＭＥＮＧＺＨＡＯ（秦孟兆）（ＩｎｓｔｉｔａｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃｓａｎｄＳｃｉｅｎｔｉｆｉｃ－Ｅｎｇｉｎｅｅ...     

周期性Hubbard模型密度矩阵函数的研究

在晶格密度泛函理论(LDFT)的框架内研究了哈巴德(Hubbard)模型,当考虑晶格内位置的单粒子密度矩阵γij、自旋S时,这个模型的相互作用能w[γij,S]为密度矩阵γij、总自旋S的函数.且当所有最近邻的γij=γ12时,对环状系统的w[γij,S]可获得精确的数值计算结果;文中同时还讨论了w[γij,S]函数在弱电子关联(γ102)和强电子关联(γi∞j)以及在γ1∞2<γ12<γ012区域限制下的性质.以非关联能w0[γ0ij,S]为单位标度的w[γij,S]表明的赝普适行为与g12=(γ12-γ1∞2)/(γ012-γ1∞2)函数一样.另外,w[γij,S]函数对不同总自旋S有一定的依赖.     

Solutions for subquadratic fractional Hamiltonian systems without coercive conditions

In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems (FHS) where α ∈ (1 ∕ 2,1), , , is a symmetric and positive definite matrix for all , , and ? W is the gradient of W at u. The novelty of this paper is that, assuming L is bounded in the sense that there are constants 0 < τ₁ < τ₂ < + ∞ such that τ₁ | u | ² ≤ (L(t)u,u) ≤ τ₂ | u | ² for all and W is of subquadratic growth as | u | → + ∞ , we show that (FHS) possesses infinitely many solutions via the genus properties in the critical theory. Recent results in [Z. Zhang and R. Yuan, Variational approach to solutions for a class of fractional Hamiltonian systems, Math. Methods Appl. Sci., DOI:10.1002/mma.2941] are generalized and significantly improved. Copyright © 2014 John Wiley & Sons, Ltd.     

Independent dominating sets and hamiltonian cycles

A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r‐regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 233–244, 2007     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

Leaf‐Critical and Leaf‐Stable Graphs

The minimum leaf number ml(G) of a connected graph G is defined as the minimum number of leaves of the spanning trees of G if G is not hamiltonian and 1 if G is hamiltonian. We study nonhamiltonian graphs with the property for each or for each . These graphs will be called ‐leaf‐critical and l‐leaf‐stable, respectively. It is far from obvious whether such graphs exist; for example, the existence of 3‐leaf‐critical graphs (that turn out to be the so‐called hypotraceable graphs) was an open problem until 1975. We show that l‐leaf‐stable and l‐leaf‐critical graphs exist for every integer , moreover for n sufficiently large, planar l‐leaf‐stable and l‐leaf‐critical graphs exist on n vertices. We also characterize 2‐fragments of leaf‐critical graphs generalizing a lemma of Thomassen. As an application of some of the leaf‐critical graphs constructed, we settle an open problem of Gargano et al. concerning spanning spiders. We also explore connections with a family of graphs introduced by Grünbaum in correspondence with the problem of finding graphs without concurrent longest paths.     

Contractibility techniques as a closure concept

We introduce a closure concept in the class of line graphs and claw‐free graphs based on contractibility of certain subgraphs in the line graph preimage. The closure can be considered as a common generalization and strengthening of the reduction techniques of Catlin and Veldman and of the closure concept introduced by the first author. We show that the closure is uniquely determined and the closure operation preserves the circumference of the graph. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 37–48, 2003