Homology of Linear Groups with Coefficients in the Adjoint Action and K-Theory

The main purpose of this paper is to compute some homology groups of linear groups with coefficients in the adjoint action which have appeared in different works. Our method uses various weight decompositions in group homology, algebraic K–theory, and Hochschild homology. This paper originated in a question posed by Cathelineau which is related to Hilbert's third problem on the scissors congruence of polyhedra.     

某四阶微分算子的一个正则性定理

本文给出了某带参数λ的四阶微分算子B_λ的一个正则性定理,由此我们分别获得了关于该算子在“非线性情形”的二个同胚类及在“线性情形”的三个线性同构类。这对描述某飞行器在其运行过程中某些类双向稳定性质是有用与方便的。     

Synthesis of polyolefins with unique properties by using metallocene-type catalysts

Copolymerization of ethylene and 1,5-hexadiene (HD) by zirconocene catalysts proceeded via cyclization-addition mechanism to form 1,3-didsubstituted cyclopentane structure in the polyethylene chain. The 1,3-cyclopentane structure was found to be taken in the crystalline structure of polyethylene (isomorphism) by partially chainging the trans zigzag chain into gauche conformation, thereby, inducing a transformation of orthorhombic crystal to pseudohexagonal crystal. Copolymerization of ethylene and cyclopentene (CPE) by zirconocene catalysts yielded copolymers having 1,2-disubstituted cyclopentane structure in the polyethylene chain. The 1,2-cyclopentane structure was not taken into the crystalline structure of polyethylene. The melting point (T_m) and the crystallinity (X_c) of polyethylene decreased by copolymerization of HD or CPE, and the T_m- and X_c-decreasing effect of CPE was stronger than HD. For copolymers of propylene and HD or CPE obtained with isospecific zirconocene catalyst, the isomorphism was not ovserved.