关于带宽极值问题的一些结果

本文研究的问题是确定f(p,B）的值，也就是给定顶点数p和带宽B，求满足最大度不超过B的连通图的最小边数，本文给出了一些f(p,B）的值及相应极图。     

Submanifolds associated with graphs

In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

     

A new fluorescent chemosensor for transition metal cations and on/off molecular switch controlled by pH

A new fluorescent chemosensor with imidazole as ionophore was synthesized by the selective derivation of calixarene, which can effectively recognize Cu²⁺ and Zn²⁺ leading to different fluoroscopic behaviors in CH₃OH-H₂O. This system could be considered as a molecular switch. By modulating the pH of the solution, on-off-on fluorescent switching is carried out upon combinatory addition of acid, base and Cu²⁺.     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

单圈图的最大特征值序

主要讨论了单圈图按其最大特征值进行排序的问题，确定了该序的前六个图。     

最大2-正则诱导子图的长度

设G是2-连通图，c(G)是图G的最长诱导圈的长度，c′(G)是图G的最长诱导2-正则子图的长度。本文我们用图的特征值给出了c(G)和c′(G)的几个上界。     

Silane photoabsorption spectra mear the Si 2p thresholds：the geometry of Si 2p excited SiH4

Based on the multiple-scattering self-consistent-field method, we have studied the photoabsorption spectra near the Si 2p thresholds of silane. According to our calculations, the clear assignments of the inner-shell photoabsorption spectra are provided. In comparison with the high-resolution experimental spectra, the geometric structure of the Si 2p-excited SiH_{4}^{**} is recommended to be of a C_{2v} symmetry. More specifically, the Si 2p-excited SiH_{4}^{**} have two bond lengths of 2.50 a.u. and another two bond lengths of 2.77 a.u., and the corresponding two bond angles are 104.0° and 112.5° respectively.     

强色指数的一个新的上界

给出了图的强色指数的一个新的上界，并指出几类恰好达到该上界的图，从而改进了Erodoes和Nesetri的强色指数猜想，在某种意义上证明了这个猜想。     

Molecular flow and wall collision age distributions

The use of storage cells has become a standard technique for internal gas targets in conjunction with high energy storage rings. In case of spin-polarized hydrogen and deuterium gas targets the interaction of the injected atoms with the walls of the storage cell can lead to depolarization and recombination. Thus the number of wall collisions of the atoms in the target gas is important for modeling the processes of spin relaxation and recombination. It is shown in this article that the diffusion process of rarefied gases in long tubes or storage cells can be described with the help of the one-dimensional diffusion equation. Mathematical methods are presented that allow one to calculate collision age distributions (CAD) and their moments analytically. These methods provide a better understanding of the different aspects of diffusion than Monte Carlo calculations. Additionally it is shown that measurements of the atomic density or polarization of a gas sample taken from the center of the tube allow one to determine the possible range of the corresponding density weighted average values along the tube. The calculations are applied to the storage cell geometry of the HERMES internal polarized hydrogen and deuterium gas target. Received 9 July 2001 and Received in final form 18 September 2001     

Fully-angular polyhex chains with minimal total π-electron energy

By Hückel molecular orbital (HMO) theory, the calculation of the total energy of all π-electrons in conjugated hydrocarbons can be reduced to that of E(G)=|λ₁|+|λ₂|+?+|λn|, where λi are the eigenvalues of the corresponding graph G. Denote by Ψn the set of all fully-angular polyhex chains with n hexagons. In this paper, we show that Hn has the minimum total π-electron energy among chains in Ψn, where Hn is the helicene chain.