A note on cycle spectra of line graphs

We show that line graphs G=L(H) with σ₂(G)≥7 contain cycles of all lengths k, 2rad(H)+1≤k≤c(G). This implies that every line graph of such a graph with 2rad(H)≥Δ(H) is subpancyclic, improving a recent result of Xiong and Li. The bound on σ₂(G) is best possible.     

关于集合的粗相似度量的注记

举例说明文献"集合的粗相似度量"中定理3.1(2)的结论是不严谨的,从而给出一个严谨的结论。     

偏振模色散补偿控制中偏振度技术的性能

基于主偏振态理论，导出了光信号偏振度的解析表达式.并对40 Gb/s光传输系统中的信号偏振度受各种因素的影响进行了数值模拟，包括啁啾、脉冲形状、脉冲宽度、自发辐射噪声以及消光比等.结果表明，偏振度技术能有效地监测和控制40 Gb/s系统中小于37.5 ps的偏振模色散.而且发现就最大化偏振度技术对差分群延时的容许范围而言，脉冲的1/e强度半宽取0.45个位宽（11.25 ps）是最优的.     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.     

Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

Chiral separation abilities of homogeneously synthesized cellulose 3,5-dimethylphenylcarbamates: Influences of degree of substitution and molecular weight

A series of cellulose 3,5-dimethylphenylcarbamates(CDMPCs) with different degrees of substitution(DS) and degrees of polymerization(DP) were homogeneously synthesized in 1-allyl-3-methylimidazolium chloride(Amim Cl). Then, the CDMPCs were coated on silica gel and used as chiral stationary phases(CSPs), and their chiral recognition abilities for seven racemates were evaluated by high performance liquid chromatography. The results showed that DS and DP of CDMPCs had a great influence on chiral recognition abilities of the CSPs. The CSPs with the DS ≈ 1 gives a low chiral recognition to most racemates. On the contrast, the CSPs with the DS ? 2 exhibited high chiral separation abilities. For example, six racemates could be separated on the CSP with CDMPC of DS ≈ 2(CSP-2). Especially, for the enantioseparation of 1-(2-naphthyl) ethanol and Tr?ger's base, CSP-2 gave the highest separation ability in all of CSPs. On the other hand, when the DP of cellulose was in a range from 39 to 220, the chiral separation abilities of CDMPCs increased as the DP increased. This work demonstrates that the structure of cellulose esters such as DS and DP has important effect on their chiral separation ability, and therefore provides a practical method to design and prepare desirable CSPs for different racemates.     

Degree of branching of the hyperbranched polymers resulted from ab<Subscript>2</Subscript> polycondensation with substitution effect

The analytical expressions of the various structural units and the average degree of branching for the hyperbranched polymers resulted from AB₂ polycondensation with substitution effect were derived by the kinetic mechanism.The reactivity difference between the B group in linear unit and that in terminal group has great effect on the molecular parameters of the products obtained.The concentration of terminal units has a maximum with the increase of the conversion of A groups（x）.The higher the reactivity ratio（r） of linear B group to branched one is,the later the maximum appears and the larger it is.The degree of branching of the hyperbranched polymers obtained is controllable by adjusting the parameters of r and x,which increases with increasing both x and r.     

DEGREE OF BRANCHING OF THE HYPERBRANCHED POLYMERS RESULTED FROM AB_2 POLYCONDENSATION WITH SUBSTITUTION EFFECT

The analytical expressions of the various structural units and the average degree of branching for the hyperbranched polymers resulted from AB_2 polycondensation with substitution effect were derived by the kinetic mechanism.The reactivity difference between the B group in linear unit and that in terminal group has great effect on the molecular parameters of the products obtained.The concentration of terminal units has a maximum with the increase of the conversion of A groups(x).The higher the reactivity...     

On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its fourier series

In a recent paper Lal and Yadov [4] obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.