Highly edge-connected factors using given lists on degrees

Let G be a 2k-edge-connected graph with and let for every . A spanning subgraph F of G is called an L-factor, if for every . In this article, we show that if for every , then G has a k-edge-connected L-factor. We also show that if and for every , then G has a k-edge-connected L-factor.     

基于低场核磁共振的抚顺油页岩孔隙连通性演化研究

油页岩原位注热开采过程中，储层内部孔隙结构的连通性直接影响载热介质的流动行为和传热效率，同时对油气产物的扩散和流动行为起控制作用.本文利用低场核磁共振（LF NMR）技术，考察了不同热解终温（23~650℃）处理时，饱和水及束缚水状态下抚顺油页岩的T₂谱，分析了可动流体T₂截止值、束缚流体孔隙度、饱和流体孔隙度、渗透率等NMR孔隙参数，定量研究了随热解终温升高，抚顺油页岩孔隙结构的连通性演化规律.研究结果表明热解终温对抚顺油页岩孔隙连通性及渗透率的变化起控制作用，且可动流体孔隙度对总孔隙度的增加起主要促进作用，这说明热解终温升高加大了渗透率及油气产物的输运能力.本文为深入认识油页岩原位热解过程中孔隙结构的演化提供了依据.     

Hamiltonian graphs of given order and minimum algebraic connectivity

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs on n vertices.     

静息态脑功能连接在不同认知状态老年人中的应用

目的探讨不同认知状态老年人静息态脑功能连接情况。方法收集阿尔茨海默病患者（AD组）13例、轻度认知功能障碍患者（MCI组）12例、认知正常老年人（对照组）13例，进行磁共振扫描，应用局部一致性（ReHo）方法确定种子点，并进行静息态功能连接分析。结果在静息状态下，AD组和MCI组患者的后扣带回区域、额叶内侧、前额叶背外侧和顶叶部分区域的ReHo均较高。与对照组相比，MCI患者左侧颞叶（颞下回及颞中回）、海马旁回及右侧枕叶舌回、皮层下的部分脑区ReHo显著降低；而右侧额叶（额上回、额中回及中央前回）、顶上小叶及左侧梭状回、颞上回、额下回的部分脑区ReHo显著增高。AD患者变化更加明显，额叶-顶叶，颞叶-脑岛，颞叶-枕叶之间的长距离连接降低，但是额叶内部和枕颞间、丘脑及颞叶间的功能连接增高，3组间差异有统计学意义（P＜0.05）。结论3组不同认知状态老年人的功能连接不同，有助于AD、MCI患者及正常老年人的鉴别诊断。     

On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.     

The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

Prediction of the vaporization enthalpy based on modified Randi? indices. I. Monohydric alcohols

The vaporization enthalpy of monohydric alcohols with different structures under normal conditions is calculated using a modified Randič method with an error comparable to the experimental one. The energy of hydrogen bonds in alcohols is determined and shown to be constant and independent on the alcohol structure. Original Russian Text Copyright ? 2009 by E. L. Krasnykh __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 50, No. 3, pp. 577–581, May–June, 2009.     

两个修正的分子连接性指数用于有机物反磁磁化率的改进QSPR研究

为了预测有机物的摩尔反磁磁化率,基于分子图的连接矩阵和可变的原子价连接性指数δi’提出了一种可变的分子连接性指数mχ’ 及其逆指数mχ”。包含在δi’、 mχ’ 和mχ”定义式中的三个可变参数x、 a和y的最佳值可通过优化方法得到。当x=2.9、a=1.10、y=0.36时, 通过最佳子变量集合法可以构建一个良好的5参数模型。对721个有机物（训练集）,该模型的相关系数r、标准偏差s和平均绝对偏差分别是0.9930、4.96 cgs和3.74cgs。交叉验证说明,从统计学角度该模型具有良好的稳定性。另外该模型对另外360个有机物（测试集）摩尔反磁磁化率预测结果的平均绝对偏差为4.37cgs。结果表明本文的方法在预测有机物摩尔反磁磁化率方面比文献方法更有效。多元线性方法能得到比较理想的预测有机物摩尔反磁磁化率的模型。     

带弦圈的最小2宽直径

设k为正整数,G是简单k连通图.图G的k宽直径,dk(G),是指最小的整数ι使得对任意两不同顶点x,y∈V(G),都存在k条长至多为ι的内部不交的连接x和y的路.用C(n,t)表示在圈Gn上增加t条边所得的图.定义h(n,t):min{d2(C(n,t))}.本文给出了h(n,2)=[n/2].而且,给出了当t较大时h(n,t)的界.