图P^3n的奇优美标号算法

本文讨论了图P^3n的奇优美性,给出了图只奇优美标号算法．     

Asymptotics in percolation on high‐girth expanders

We consider supercritical bond percolation on a family of high‐girth ‐regular expanders. The previous study of Alon, Benjamini and Stacey established that its critical probability for the appearance of a linear‐sized (“giant”) component is . Our main result recovers the sharp asymptotics of the size and degree distribution of the vertices in the giant and its 2‐core at any . It was further shown in the previous study that the second largest component, at any , has size at most for some . We show that, unlike the situation in the classical Erd?s‐Rényi random graph, the second largest component in bond percolation on a regular expander, even with an arbitrarily large girth, can have size for arbitrarily close to 1. Moreover, as a by‐product of that construction, we answer negatively a question of Benjamini on the relation between the diameter of a component in percolation on expanders and the existence of a giant component. Finally, we establish other typical features of the giant component, for example, the existence of a linear path.     

A note on the -th power mean of character sums over the quarter interval

We obtain an asymptotic formula for the -th power mean of odd primitive character sums over the interval .

     

奇数阶中立型差分方程的线性化振动性定理

本文得到了奇数阶中立型差分方程的一个线性化振动性定理,是Ｇｙ氹ｒｉ和Ｌａｄａｓ在文［２］中所提公开问题的一个离散结果     

Synthesis and fluoride-induced chemiluminescent decomposition of bicyclic dioxetanes substituted with a 2-hydroxynaphthyl group

Five bicyclic dioxetanes bearing a 2-hydroxynaphthyl group, 1aA-1eA, were synthesized and their chemiluminescent decomposition was examined by the use of tetrabutylammonium fluoride (TBAF) as a base in DMSO. It was found that these dioxetanes hold completely the ‘odd/even’ relationship between the substitution pattern of hydroxy as a trigger on the naphthalene ring and their chemiluminescent efficiency, and that dioxetane 1aA exhibited chemiluminescence with the highest efficiency among those for the oxynaphthyl-substituted dioxetanes hitherto known. The significant change in chemiluminescent efficiency depending on the substitution pattern was clarified to be attributed to the marked change in singlet-chemiexcitation efficiency for charge-transfer-induced chemiluminescence (CTICL) of 1aA-1eA. In respect of the rate of CTICL-decomposition, ‘odd/even’ relationship was observed for 1aA-1dA.