双圈图的零度与其匹配数之间的关系

Let G be a graph with n(G) vertices and m(G) be its matching number.The nullity of G,denoted by η(G),is the multiplicity of the eigenvalue zero of adjacency matrix of G.It is well known that if G is a tree,then η(G) = n(G)-2m(G).Guo et al.[Jiming GUO,Weigen YAN,Yeongnan YEH.On the nullity and the matching number of unicyclic graphs.Linear Alg.Appl.,2009,431:1293 1301]proved that if G is a unicyclic graph,then η(G)equals n(G)-2m(G)-1,n(G)-2m(G),or n(G)-2m(G) +2.In this paper,we prove that if G is a bicyclic graph,then η(G) equals n(G)-2m(G),n(G)-2m(G)±1,n(G)-2m(G)±2or n(G)-2m(G) + 4.We also give a characterization of these six types of bicyclic graphs corresponding to each nullity.     

A phenomenological theory for polarization flop in spiral multiferroic TbMnO<Subscript>3</Subscript>

A phenomenological Landau theory has been used to explain magnetic field-driven polarization flop in TbMnO ₃. The Néel wall-like magnetic structure in spiral multiferroics induces a space-dependent internal magnetic field which exerts a torque on spins to rotate bc-spiral to ab-spiral. The external magnetic field is argued to be competing with easy axis anisotropy and the system stabilizes when anisotropy is minimum. With the help of Landau free energy with DM magnetoelectric coupling and a general ansatz for magnetization, the phenomenon of polarization flop has been explained. Relation between T_flop and critical magnetic field has been established and found to be in good agreement with the experiment. This could be an indication that anisotropy of the system is temperature- and magnetic field-dependent.     

Could the New Absorption Cross Section of J/ψ Change the Aspect of Nuclear Absorption Mechanism

The enlarged new absorption cross sections of J/ψ by π and ρ were put into the hadron and string cascade model, JPCIAE, and the J/ψ suppression factors in P-A, O-U, S-U and Pb-Pb minimum bias collisions at 200A GeV/c were calculated with nuclear absorption mechanism only. The results seem to indicate that, with new enlarged cross section it is still hard to change the aspect that nuclear absorption mechanism itself could not easily account for the J/ψ anomalous suppression in Pb-Pb collisions.     

尿素分子团簇线性和一阶非线性光学极化率的理论计算

检验分子晶体非线性光学极化率的可加性,对于确认有向气体模型(Oriented-Gas Model) 具有重要的科学意义,对探索新型实用的分子非线性光学材料也有实际的意义。本文对尿素晶体中分子簇非线性光学极化率的可加性做了详尽的理论研究。首次做到了尿素分子最近邻排布团簇的非线性光学极化率的从头算,从而扩展了前人的工作。研究结果有效地确认了有向气体模型。同时,我们还提出了壳层结构模型 (Shell-Structure Model),用以解决有向气体模型中的缺陷,可实现更为有效可靠地计算晶体宏观非线性光学系数。     

核形变对J/ψ压低的效应

用强子和弦级联模型,JPCIAE,研究(200A GeV)U+U中心碰撞中核形变对J/ψ压低的效应.结果表明:在两形变核的长轴都沿束流方向的碰撞中,J/ψ压低因子约为两长轴都垂直于束流方向碰撞时的二分之一.     

Zirconium-substituted isopolytungstates: structural models for zirconia-supported tungsten catalysts

The synthesis and characterization of a series of mixed W-Zr polynuclear Lindqvist-type complexes, deriving from hexatungstate [W6O19]2-, are described in this work. This family of compounds is built from {W5O18Zr}2- moieties as shown by the X-ray structures of the monomeric [W5O18Zr(H2O)(3-n)(DMSO)n]2- (n = 1 and 2) and dimeric [{W5O18Zr(mu-OH)}2]6- anions. A comprehensive spectroscopic study (183W NMR, FTIR, Raman, EXAFS, and EPR) of these compounds is presented. The goal of incorporating Zr(IV) cations into an oxotungstic core is to obtain spectroscopic models that could mimic the interactions that develop in supported catalysts between the active phase and the supporting oxide. This work tends to show that these molecular compounds can be regarded as soluble structural analogues of WOx/ZrO2 catalysts, which are interesting candidates for the skeletal isomerization of light n-alkanes.     

Synthesis and characterization of tetrahedral and square planar Bis(iminopyrrolyl) complexes of cobalt(II)

A series of 2-iminopyrrole ligand precursors with increasing bulkiness [HNC4H3C(R)=N-2,6-R'2C6H3] (R = R' = H, 1a; R = Me, R'= H, 1b; R = H, R' = Me, 1c; R = R' = Me, 1d; R = H, R' = iPr, 1e; R = Me, R' = iPr, 1f) were synthesized and deprotonated with NaH to give the corresponding iminopyrrolyl sodium salts 2a-f. A set of homoleptic bis-ligand Co(II) complexes of the type [Co(kappa2N,N'-NC4H3C(R)=N-2,6-R'2C6H3)2] (R = R'= H, 3a; R = Me, R'= H, 3b; R = H, R' = Me, 3c; R = R' = Me, 3d; R = H, R' = iPr, 3e; R = Me, R' = iPr, 3f) was prepared by reaction of CoCl2 with the corresponding iminopyrrolyl sodium salts 2a-f. The new complexes were characterized by elemental analysis, magnetic susceptibility measurements, in powder and in solution, UV/vis/NIR, and, in some cases, X-ray crystallography. According to X-ray diffraction and magnetic measurements, the Co complexes 3a-e proved to be tetrahedral, which is the preferred geometry for Co(II) compounds. However, a square planar geometry is observed in the case of 3f, as determined by several characterization techniques. In this case, DFT calculations suggest the square planar geometry is slightly more stable than the tetrahedral one probably due to a combination of steric and electronic reasons.     

相对论重离子碰撞的温度涨落与热容

使用LUCIAE3.0模型模拟了SPS能区Pb+Pb和C+C在不同能量(E_lab=20—200A GeV)和不同中心度下的重离子碰撞.并通过逐个事件的粒子温度涨落提取出了相应粒子的热容,发现对于同一碰撞系统,单位发射粒子的热容随碰撞能量的升高而下降直至饱和,随着碰撞参数b的增大而减小,而且发现单位发射粒子的热容具有随粒子质量的变大而变大的关系.同时还发现不同碰撞系统中同一种粒子具有相同的单位发射粒子热容,并给出了相应的解释.     

158A GeV的相对论重离子碰撞的强子快度分布及温度拟合

针对最近NA49在158A GeV的实验(C+C,Si+Si,Pb+Pb)数据,应用LUCIAE3.0模型进行模拟,得到了强子的快度分布和横向动量分布,并与实验数据进行比较,发现基本与实验数据相吻合。并对横向动量分布进行温度拟合,给出了和实验数据吻合很好的结果,但是对于重系统或重强子LUCIAE3.0给出的结果与实验符合相对较差.     

Reactions of Podophyllotoxin with DDQ

Introduction 2, 3-Dichloro-5, 6-dicyanobenzoquinone (DDQ) can react with lignans of the mono- arylidene-butyrolactone1, aryltetralin2, dibenzylbutane3 and aryltetralin-butyrolactone4,5 series. We have studied the reactions of this reagent with podophyllotoxin 1, which is a well-known natural product on account of its long history of use in folk medicine and the biological activity of its many derivatives6. In particular, derivatives of 4-demethyl epipodophyllotoxin are used in cancer chemo…