Edge-connectivity and edge-disjoint spanning trees

Given a graph G, for an integer c∈{2,…,|V(G)|}, define λ_c(G)=min{|X|:X⊆E(G),ω(G−X)≥c}. For a graph G and for an integer c=1,2,…,|V(G)|−1, define,

     

Study on UV-light-induced absorption in LiNbO3:Fe, Co crystal

##正##In this paper,the temporary UV-light-induced absorption in LiNbO_3:Fe,Co crystal is investigated for different UV intensities.It is found that the sensitizing process in LiNbO_3:Fe,Co can be considered as a combination of two sub-processes with different time constants.Based on the lattice structure and the photochromic mechanism of the material,the two sub-processes are suggested to arise from electron transfer from O~(2-) to Fe~(3+) through two paths with different distances.The two-colour recording experiment in LiNbO_3:Fe,Co is also preformed by using UV and green light as gating and writing beams respectively.High sensitivity is obtained in the recording,which is considered as the consequence of direct charge transfer from O~(2-) to Fe~(3+).     

Soft supersymmetry breaking, scalar top-charm mixing and Higgs signatures

The squark mass-matrix from the soft supersymmetry (SUSY) breaking sector contains a rich flavor-mixing structure that allows O(1) mixings among top- and charm-squarks while being consistent with all the existing theoretical and experimental bounds. We formulate a minimal flavor-changing-neutral current scheme in which the squark mixings arise from the non-diagonal scalar trilinear interactions. This feature can be realized in a class of new models with a horizontal U(1)_H symmetry which generates realistic quark-mass matrices and provides a solution to the SUSY μ-problem. Finally, without using the mass-insertion approximation, we analyze SUSY radiative corrections to the H^±bc and h⁰tc couplings, and show that these couplings can reveal exciting new discovery channels for the Higgs boson signals at the Tevatron and the LHC.     

Graphs without spanning closed trails

Jaeger (1979) proved that if a graph has two edge-disjoint spanning trees, then it is supereulerian, i.e., that it has a spanning closed trail. Catlin (1988) showed that if G is one edge short of having two edge-disjoint spanning trees, then G has a cut edge or G is supereulerian. Catlin conjectured that if a connected graph G is at most two edges short of having two edge-disjoint spanning trees, then either G is supereulerian or G can be contracted to a K₂ or a K_2,t for some odd integer t 1. We prove Catlin's conjecture in a more general context. Applications to spanning trails are discussed.     

Cycle Cover Ratio of Regular Matroids

A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroidM without coloops has a set S of cycles whose union is E(M) such that every element is in at most three of the cycles in S. It follows immediately from this that, on average, each element of M is in at most three members of the cycle cover S. This improves on a 1989 result of Jamshy and Tarsi who proved that there is a cycle cover for which this average is at most 4, and conjectured that a cycle cover exists for which the average is at most 2.     

Group connectivity and group colorings of graphs — A survey

In 1950s, Tutte introduced the theory of nowhere-zero flows as a tool to investigate the coloring problem of maps, together with his most fascinating conjectures on nowhere-zero flows. These have been extended by Jaeger et al. in 1992 to group connectivity, the nonhomogeneous form of nowhere-zero flows. Let G be a 2-edge-connected undirected graph, A be an (additive) abelian group and A* = A − {0}. The graph G is A-connected if G has an orientation D(G) such that for every map b: V (G) ↦ A satisfying Σ _v∈V(G) b(v) = 0, there is a function f: E(G) ↦ A* such that for each vertex v ∈ V (G), the total amount of f-values on the edges directed out from v minus the total amount of f-values on the edges directed into v is equal to b(v). The group coloring of a graph arises from the dual concept of group connectivity. There have been lots of investigations on these subjects. This survey provides a summary of researches on group connectivity and group colorings of graphs. It contains the following sections.

分子动力学模拟飞秒激光对C60光裂解反应机理的影响

基于半经典分子动力学方法模拟超快激光诱导的C60光裂解反应.选择能量为2.0eV,半峰全宽(FWHM)分别为40和500fs的激光作用于C60分子,调节脉冲强度使其发生裂解反应,比较长短脉宽飞秒激光对C60裂解反应机理的影响.通过分析产物分布、原子平衡指数、温度以及吸收能量(包括动能、势能和电子能量),证实飞秒激光脉冲下C60的光裂解主要由电子激发态控制,非热力学效应在该反应中起重要作用.激光场的作用时间和强度均影响光裂解反应过程,而电子吸收能量饱和后光场强度的作用则变得不明显.     

炸药条加载圆柱壳的数值模拟（Ⅱ）：解耦分析与实验验证

 根据已报道的二维流固耦合数值模拟结果,建立了经缓冲橡胶整形后的单炸药条载荷模型。将炸药条载荷叠加后直接施加在圆柱壳表面,进行二维解耦模拟,得到了与流固耦合模拟基本吻合的应力结果。在此基础上,对19条炸药条加载Φ265 mm×380 mm圆柱壳进行了三维解耦模拟,并采用相同状态的实验予以验证。结果表明,特征点应变响应吻合较好,验证了炸药条加载圆柱壳解耦数值模拟的有效性,为大量工况数值分析、提高建模和计算效率奠定了基础。