Constructions for cyclic Moebius ladder systems

J.A. Gallian has proved [J.A. Gallian, Labeling prisms and prism related graphs, Congr. Numer. 59 (1987) 89-100] that every cubic graph M_2k obtainable from a 2k-cycle by adding its k diameters (the so-called Moebius Ladder of order 2k) is graceful. Here, in the case of k even, we propose a new graceful labeling that besides being simpler than Gallian’s one is able to give, at the same time, a graceful labeling of the prism of order 2k. Most importantly in the case of k odd, namely in the bipartite case, we prove that M_2k also admits an α-labeling. This implies that there exists a cyclic decomposition of the complete graph K_6kt+1 into copies of M_2k for every pair of positive integers k and t with k odd.In some cases we are able to give such decompositions also when k is even. Apart from the case of t=1 that is an obvious consequence of the gracefulness of M_2k, this happens, for instance, when k≡2 (mod 4) and 6kt+1 is a prime.     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.     

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r ^?2〉, 〈r ²〉, 〈T〉, 〈V〉, 〈H〉, 〈p ²〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.     

H-bonding template-directed synthesis of a complete m-PDA-bridged ladder polyhydrosiloxane （OLPHS）

A highly ordered m-phenylenediimino-bridged ladder polyhydrosiloxane (abbr. OLPHS) with Mn = 1.24 104 was synthesized under assistance of H-bonding template constructed from imino H-bonding, N(Si)-H N(Si)-H, via a modified process of stoichiometric hydrolysis and dehydrochlorination condensation reaction between Si–Cl and Si–OH bonds. The complete ladder structure of OLPHS has been confirmed by the following three data. Two characteristic Bragg’s peaks representing the ladder width (w =0:94 nm) and ladder thickness (t = 0.42 nm) were observed in XRD analysis, which are consistent with those cal- culated by molecular simulation. The very sharp absorption with a small half-peak width ew1=2=0:5 ppmT for [(–HN)HSiO2/2]n moiety of OLPHS in 29Si NMR spectrum indicated presence of the complete ladder structure. As collateral evidence, a higher glass transition temperature (Tg = 105 8C) is also recorded in the DSC measurement, implying the high stiffness of ladder chain of OLPHS.     

梯形高聚物PTL导电机理的研究

本文采用EHMO/CO半经验计算方法,以准一维体系对梯形高聚物聚吩噻嗪(简称PTL)本征态及掺杂态电子能带进行了计算,讨论了PTL的导电机理,提出了当掺杂剂为质子酸时的荷电孤子或极化子导电模型及p-型掺杂时的极化子导电模型。     

A ladder type structure: Rubidium diphenylacetate diphenylacetic acid

A new rubidium complex, rubidium diphenylacetate diphenylacetic acid has been synthesised and characterised by single-crystal X-ray diffraction: triclinic, P with a=7.437(3) ?, b=12.377(4) ?, c=14.384(3) ?, α=107.08(2)°, β=103.67(2)°, γ=96.95(3)°, Mr=508.93, V=1203.6(6) ?³, Z=2. The diphenylacetic molecules bridge the metallic ions forming an infinite ladder structure. Two strong hydrogen bonds link the organic moieties. Supplementary materials Crystallographic data for structural analysis have been deposited with the Cambridge Crystallographic Data Center, CCDC No. 602647. Copies of this information may be obtained free of charge on application to CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (fax: +44 1223 336 033; e-mail: deposit@ccdc.cam.ac.uk or http://www.ccdc.cam.ac.uk).     

用升降算符法计算多原子分子振动-转动能级

自70年代起,Handy^[1]等,用变分法计算了H₂、SO₂等分子的振动-转动光谱,所得结果与实验吻合。但因在于计算久期行列式元素的积分,其计算方法不易推广。     

随机游动的阶梯高度和最大值及其在风险理论中的应用

该文研究了均值为负的实值随机游动的阶梯高度及最大值, 在指数估计的条件不满足的情况下,得到了它们分布的局部渐近估计和尾渐近估计, 并将这些结果应用到风险理论中的Sparre Andersen 风险模型上, 得到了一些关于破产概率的新结果.