蕴含W5可图序列的最小度和

Gould,Jacobson和Lehel考虑了下述经典Tur偄n型极值问题的变形:对于给定的图H,确定最小的正偶数σ(H,n),使得对于每一个n项可图序列π=(d1,d2,…,dn),当σ(π)=d1+d2+…+dn≥σ(H,n)时,π有一个实现G包含H作为可图的.本文确定了当n≥11时,σ(W5,n)之值,其中Wr是r个顶点的轮图.     

不饱和烃同系物凝聚型物理性质递变规律的数学描述

以H-(CH2)n-CH=CH2和H-(CH2)n-C≡CH型同系物结构重复单元数值连续变化为模型,获得了描述该同系物凝聚型物理性质递变规律的数学表达式:P=(a0+a1n+a2n2)/(1+b2n2),式中a0、a1、a2、b2均为常数,n为结构重复单元数值,P为同系物的凝聚型物理性质。通过非线性回归分析,得到回归方程,结果表明同系物的凝聚型物理性质与重复结构单元数值之间满足上述关系式,并显示优良的相关性。     

关于图的第二特征标R2(G)

对任意图G，h(G，x)表示图G的伴随多项式，R2(G)表示图G的第二特征标，本文刻画了R2(G)=-2，-1，0，1，2的全部连通图。     

Research on a New-style Pipeline Inspection Robot System

IntroductionRecently pipe is used widely on the industry,agriculture and daily life. Natural gas and oil supplybecomes one of the fundamental public services and itsimpact on the urban infrastructure is getting larger. Theurban oil/gas pipelines, as they are buried under theground, are prone to external corrosion usually derived bymoisture and chemical agent in soil, which causes materiallosses of the pipe wall. Also, cracks in the welded regionand the da…     

Activation of peroxyl and molecular oxygen using bis -benzimidazole diamide copper (II) compounds

New tetradentatebis-benzimidazole ligands have been synthesized and utilized to prepare copper (II) complexes. Some of these copper (II) complexes have been characterized structurally. The copper (II) in these complexes is found to possess varying geometries. A distorted octahedral geometry is found with a highly unsymmetrical bidentate nitrate group. An unusual polymeric one-dimensional structure is observed where copper (II) is in a distorted square pyramidal geometry with a monodentate nitrate ion, having long Cu-O bond, while a distorted triagonal bipyramidal geometry is found with two carbonyl O atoms and a Cl atom in the equatorial plane, and two benzimidazole imine N atoms occupy the axial position. These compounds are found to activate the cumylperoxyl group, and this has been utilized in the facile oxidation of aromatic alcohols to aldehydes, where they act as catalysts with large turnovers. The yields of the respective products vary from 32 to 65%. The role of molecular oxygen has been studied and an attempt has been made to identify the “active copper species”. Activation of molecular oxygen has also been observed and has been used for oxidative dealkylation of a hindered phenol, producing di-butyl quinones with yields of 20–25% and 10–12 fold catalytic turnover. Dihydroxybenzenes and substituted catechols are also readily oxidized to the corresponding quinones, in oxygen-saturated solvents. Yields of 84% have been observed with 34-fold catalyst turnover, with di-t-butylcatechol. The activity of these copper (II) —bis-benzmidazolediamide compounds is reminiscent of the functioning of copper centres in galactose oxidase, tyrosinase and catechol oxidase.     

Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

On universal subsets of Banach spaces

We prove that to most of the known hypercyclic operators A on separable Banach spaces there exist compact (compact convex, compact connected) subsets K of E such that each compact (compact convex, compact connected) subset of E can be approximated with respect to Hausdorff's distance by for suitable . Received July 8, 1997, in final form October 17, 1997     

Boundedness of commutators on homogeneous Herz spaces

The boundedness on homogeneous Herz spaces is established for a large class of linear commutators generated by BMO(R ⁿ ) functions and linear operators of rough kernels which include the Calderón-Zygmund operators and the Ricci-Stein oRfiUatory singular integrals with rough kernels. Project supponed in pan by the National h’atural Science Foundation of China (Grant No. 19131080) and the NEDF of China.     

Hamilton线图中的泛圈性

对于图Ｇ的边ｅ＝ｕｖ，定义ｄ（ｅ）－ｄ（ｕ）＋ｄ（ｖ），这里ｄ（ｕ）和ｄ（ｖ）分分别表示ｕ和ｖ的度，该文的主要结果是：对阶为ｎ（ｎ≥４０）的简单连通图Ｇ，如果对Ｇ中任意两条边距离为２的边ｅ１，ｅ２都有ｄ（ｅ１）＋ｄ（ｅ２）≥ｎ，并且线图Ｌ（Ｇ）是Ｈａｍｉｌｔｏｎ的，则Ｌ（Ｇ）是泛圈的，并且条件Ｌ（Ｇ）是Ｈａｍｉｌｔｏｎ是必要的。