Vertex reconstruction in Cayley graphs

In this survey paper we review recent results on the vertex reconstruction problem (which is not related to Ulam’s problem) in Cayley graphs. The problem of reconstructing an arbitrary vertex x from its r-neighbors, that are, vertices at distance at most r from x, consists of finding the minimum restrictions on the number of r-neighbors when such a reconstruction is possible. We discuss general results for simple, regular and Cayley graphs. To solve this problem for given Cayley graphs, it is essential to investigate their structural and combinatorial properties. We present such properties for Cayley graphs on the symmetric group and the hyperoctahedral group (the group of signed permutations) and overview the main results for them. The choice of generating sets for these graphs is motivated by applications in coding theory, computer science, molecular biology and physics.     

Partitioning a graph into alliance free sets

A strong defensive alliance in a graph G=(V,E) is a set of vertices A⊆V, for which every vertex v∈A has at least as many neighbors in A as in V−A. We call a partition A,B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is other than an odd clique or an odd cycle.     

Effect of composition and forming parameters on the conductance of amorphous chalcogenide threshold switches

The effect on the conductance of formed STAG threshold switches of changing both the composition of the virgin films and the ON time of the switching pulse during the forming process has been studied. It was found that the silicon content of the glass has a large effect on the activation energy and conductivity parameters of virgin devices. After forming, the conductance of the device is much higher than in the unformed state; however, silicon no longer controls the conductivity parameters. When switching STAG threshold switches it was found that increasing the ON time of each switching cycle causes a decrease in the conductance of the formed device from its value when formed with very short ON times. For low pulse repetition frequencies the conductance saturates for ON times typically greater than 100 μs. The rate at which the conductance decreases is dependent upon the silicon content of the virgin glass. For high pulse repetition frequencies the conductance initially falls, following the low pulse repetition frequency case, and then rises, finally locking on to a memory state. The observations have been explained in terms of an initial large structural change of the glass, caused through adiabatic heating during switching. Relaxation of this structure back to more stable glass phases is possible during the ON time if the ON state temperature is sufficiently high. For high pulse repetition frequencies the temperature of the device is much higher, allowing for the possibility of crystalline growth. This leads to an increase in conductance and eventual lock on.     

Molecular mechanics analysis of restricted rotation about pivot bond in substituted bicyclohexyls and phenylcyclohexanes. Importance of successive gauche and progauche sequences in conformational dynamics

Rotation of pivot bond in bicyclohexyls and phenylcyclohexanes carrying methyl groups vicinal to the rotating bond have been simulated by the second derivative molecular mechanics calculations. Barriers are characterized by long-range nonbonded interaction types occurring across the pivot bond such as gg, gp (p=progauche), po (o=ortho), ge (e=eclipse), ggg and gpo with alternating signs regarding gauche and progauche. Very high barriers are expected to appear when at least one 1,b interaction type, ggg or gpo, occurs simultaneously with another interaction type. Experimental examples including known atropisomers have been interpreted in the light of the present results.     

An XPS study of carbon monoxide and nitric oxide adsorption on platinum (410): Unusual dissociation activity

The adsorption of NO and CO on platinum (410) is studied by X-ray photoemission spectroscopy (XPS). It is found that the (410) surface shows unusual activity for NO and CO bond breaking. CO is found to adsorb molecularly on Pt (410) at 300 K, but it partially dissociates upon heating to 500 K. NO is found to adsorb dissociatively under all conditions studied. By comparison, the low index faces of platinum and stepped surfaces considered previously give negligible dissociation of CO and negligible dissociation of NO up to 450 K. The (410) surface is also unusual from an orbital symmetry standpoint; in fact, it was predicted to be unusually active for NO and CO bond breaking based on Woodward-Hoffman ideas. The present results show, then, that Woodward-Hoffman (i.e., orbital symmetry conservation) methods could yield valuable insights into the nature of active sites on single crystal catalysts.     

关于单形k级顶点角的一类几何不等式

本文获得关于单形ｋ级顶点角的一类几何不等式，它包含并推广了［３］、［４］、［５］中的一些重要结果。     

Nonadiabatic superconductivity in K3C60 and Rb3C60

We discuss the validity of Migdal–Eliashberg theory applied to the superconductor fullerides K₃C₆₀ and Rb₃C₆₀. Recently, the relevant superconductor properties have been measured, like the isotope coefficient, the energy gap and critical temperatures for these compounds and compared with their optical properties. They all present a very disperse band of phonon frequencies, running from very small to very large energies, the latter being close to the Fermi edge. Therefore, these materials exceed the limit of validity of the adiabatic Migdal theorem, measured with a nonadiabatic parameter m=w₀/E_F, where w₀ is a characteristic phonon frequency and E_F=250 meV, the Fermi level. We examine previous theories incorporating vertex corrections into the Eliashberg equations to deal with such a situation. We compare these approaches by calculating the critical temperatures using a multimodal Eliashberg spectral function ²F(w) to study the contribution of the various phononic modes. We arrive at the conclusion that the optical modes, not the intramolecular ones, are among those which maximize T_c independently of including vertex corrections or not. This result goes in the direction to understand why doped fullerides A₃C₆₀ are superconductors.     

我国各地区城乡居民人均收入的对应分析

利用SAS软件 ,对我国 1999年度的城乡居民人均收入的统计资料进行了对应分析 ,又对城乡、东西部地区居民的收入进行了均值差异检验 ,得到了许多有意义的结果。     

Inversion of band matrices

In this paper, a formula for inverting general band matrices is established. It takes a simple form when the matrices are tridiagonal, and as a special case it includes the Bukhberger-Emel'yanenko algorithm for symmetric tridiagonal matrices.