一类量子Koszul代数的${\mathbb{Z}}_{2}$-Galois 覆盖的 Hochschild上同调

考虑一类量子Koszul代数的 ${\mathbb{Z}}_{2}$-Galois覆盖$\Lambda_{\q}$, 并计算 这类代数的各阶Hochschild上同调群的维数, 进而利用道路的语言, 刻画了 Hochschild上同调环的cup积. 作为应用, 给出了这类代数的Hochschild上同调环模掉幂零理想的 代数结构.     

$U({\mathfrak {so}}(7,{\mathbb C}))$的向量表示的范畴化

The aim of this paper is to categorify the n-th tensor power of the vector representation of U (so(7, C)). The main tools are certain singular blocks and projective functors of the BGG category of the complex Lie algebra gl n .     

相应于Borcherds-Cartan矩阵的双参数弱Hopf代数

In this paper a class of two-parameter weak Hopf algebras wrτ,s（g） corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras wUq（g）.     

Young表与Uq（osp（1｜2n））的晶体基

设Uq（osp（1｜2n））是对应Lie超代数osp（1｜2n）的量子包络超代数．利用满足一定条件的半标准Young表,给出有限维既约Uq（osp（1｜2n））模晶体图的实现．建立晶体图张量积分解的广义Littlewood—Richardson法则．     

Young表与$\textrm{U}_{q}(\mathrm{osp}(1|2n))$的晶体基

设 $U_q(\mathrm{osp}(1|2n))$是对应Lie超代数$\mathrm{osp}(1|2n)$的量子包络超代数. 利用满足一定条件的半标准Young表, 给出有限维既约$U_q(\mathrm{osp}(1|2n))$模晶体图的实现 . 建立晶体图张量积分解的广义Littlewood-Richardson法则.     

Sweedler 4维Hopf代数的Rota-Baxter代数结构

设H_4是Sweedler4维Hopf代数.本文根据Rota-Baxter算子的定义和性质,建立H_4的权为λ的Rota-Baxter算子在选定基下的矩阵元素满足的二次方程组.通过求解权λ=0时的二次齐次方程组和权λ=1时的二次非齐次方程组,给出了Rota-Baxter算子相应的矩阵形式.     

二重积分定义的函数求导

讨论二重积分定义的函数的求导问题     

用乙酰氯淬灭法测定Ziegler-Natta催化剂的活性中心数

The reactions of Solvay TiCl₃-AlR₃ (R=C₂H₅,i-C₄H₉) catalysts with acetyl chloride were studied. The main reaction, which is much faster than the reactions between A1R₃ and CH₃COC₁, is as follows:It is found that when CH₃COC₁ was introduced into 1-octene polymerization systems catalyzed by TiCl₃-AlR₃ for 5-15min, it reacted selectively and completely with the active centers to produce acetyl-ended polymer chains.With CH₃COC₁ as a quenching agent, the number of active centers in .these polymerization systems were determined by measuring the content of carbonyl in the polymer,and the results consist with those obtained by kinetics-molecular-weight method.     

接枝共聚物聚苯乙烯－g－聚氧乙烯的微相分离形态研究

本文利用透射电子显微镜技术，以两性接校共聚物聚苯乙烯－ｇ－聚氧乙烯为研究对象，研究了接枝共聚物的微相分离形态结构，发现聚苯乙烯－ｇ－聚氧乙烯能形成微相分离结构，微区的形状和尺寸与共聚物的组成和侧链长度有关．文中还讨论了嵌段共聚物和接枝共聚物在形成微相分离结构时的共性和个性．