Infinite Hamilton cycles in squares of locally finite graphs

We prove Diestel's conjecture that the square G² of a 2-connected locally finite graph G has a Hamilton circle, a homeomorphic copy of the complex unit circle S¹ in the Freudenthal compactification of G².     

An update on the middle levels problem

The middle levels problem is to find a Hamilton cycle in the middle levels, M_2k+1, of the Hasse diagram of (the partially-ordered set of subsets of a 2k+1-element set ordered by inclusion). Previously, the best known, from [I. Shields, C.D. Savage, A Hamilton path heuristic with applications to the middle two levels problem, in: Proceedings of the Thirtieth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1999), vol. 140, 1999], was that M_2k+1 is Hamiltonian for all positive k through k=15. In this note we announce that M₃₃ and M₃₅ have Hamilton cycles. The result was achieved by an algorithmic improvement that made it possible to find a Hamilton path in a reduced graph (of complementary necklace pairs) having 129,644,790 vertices, using a 64-bit personal computer.     

Hamilton cycles in circulant digraphs with prescribed number of distinct jumps

Let G be a digraph that consists of a finite set of vertices V(G). G is called a circulant digraph if its automorphism group contains a |V(G)|-cycle. A circulant digraph G has arcs incident to each vertex i, where integers a_ks satisfy 0<a₁<a₂<a_j≤|V(G)|−1 and are called jumps. It is well known that not every G is Hamiltonian. In this paper we give sufficient conditions for a G to have a Hamilton cycle with prescribed distinct jumps, and prove that such conditions are also necessary for every G with two distinct jumps. Finally, we derive several results for obtaining G^′ with k, k≥2 distinct jumps if the corresponding G contains a Hamilton cycle with two distinct jumps.     

极值Beltrami系数的Hamilton序列

考虑了Strebel点与Hamilton序列之间的关系.这个问题是Gardiner F.P.最早研究的(见[Approximation of infinite-dimensional Tcichmiiller spaces,Trans.Amer.Math.Soc.,1984,282(1):367-383]).在无限小Teichmiiller空间中,证明了范金华在[On infinitesimal Teichmüller space,Bull.Austral Math.Soc.,2008,78:293-300]中得到的使{φ_n}成为Hamilton序列的充分条件不是必要的.     

层合板问题几种求解方法的比较

为比较Lagrange 体系和Hamilton 体系的有限元法在求解层合板问题时的优劣,以寻求此类问题较合适的数值方法,本文在已有研究的基础上,将几种有限元法应用到层合板问题的计算中,编程并对相关算例进行计算和分析. 数值结果表明：Hamilton 体系常规有限元和改进有限元,Lagrange 体系理性有限元在计算此类问题时各有其优势,而Lagrange 体系常规有限元在求解此类问题时的精度较差.     

Hamilton–Jacobi equation,reaction action surface and the emergence of the force concept in chemical reaction dynamics

A combination of Hamilton–Jacobi equation and fast marching algorithm can be used to study reaction dynamics by converting the potential energy surface to a reaction action surface. The reaction action surface has been found to be an important tool in theoretical chemistry, allowing us to provide a different force-based perspective of chemical reactions. Several properties such as reaction force, reaction force surface, reaction path force and reaction path force constant have been defined and calculated by using the reaction action surface. This paper investigates these newly defined properties in order to understand the role they play in chemical reaction with reference to a model 4-well potential energy surface.     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H₃C) to hydroxymethylene radical (H₂?OH).     

Love–Bishop rod solution based on strain gradient elasticity theory

In the present work, the propagation of longitudinal stress waves is investigated with a strain gradient elasticity theory given by Lam et al. In principle, the analysis of wave motion is based on the Love rod model including the lateral deformation effects, but in the same time is also taken into account the shear strain effects with Bishop?s correction. By applying Hamilton?s principle, a general explicit strain gradient elasticity solution is developed for the longitudinal stress waves, and it is compared with the special solutions based on the modified couple stress and classical theories. This work gives useful information with regard to the meaning of the three scale parameters in the strain gradient elasticity theory used here.     

图的度和与扩路

本文讨论了两顶点的度和与路可扩之间的关系,得到了如下结果:设G是n阶图,如果G中任意一对不相邻的顶点u,v满足d(u)+d(v)≥n+n/k(2≤k≤n-2),则G中任意一个满足k+1≤|P|相似文献