环上的广义导子与Von Neumann代数上的P-核值保持映射

设Ａ是Ｂ（Ｈ）的子代数，ψ是Ａ到Ａ的线性映射，且对Ａ中的每个正交投影算子ｐ，有ψ（ｐ）（ｋｅｒｐ）ｒａｎｐ，则称ψ是Ａ到Ａ的Ｐ－核值保持映射，本文主要得到如下结果：每个２－非绕的半素环上的广义Ｊｏｒｄａｎ导子都是广义导子；每个ＶｏｎＮｅｕｍａｎｎ代数上的范数拓扑连续的Ｐ－核值保持映射是广义内导子．     

一种生成对称群S9所有Sylow-p子群的算法

根据对称群的基本性质以及第二同构定理，给出了通过添加生成元到P群来构造对称群的一个Sylow-p子群的定理，添加的生成元保证能够快速得到对称群的一个Sylow—p子群．根据第二西洛定理求出了所有共轭子群，即所有Sylow-p子群．针对求所有共轭子群过程中面临共轭子群出现重复的问题，利用正规化子的性质，找到使得两个Sylow-p子群共轭的元，保证每次求的Sylow-P子群不重复．将此算法应用于S1，实验表明该算法可操作性强，耗费时间少．     

特征为2的素环的Lie理想上中心化自同构

Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4.     

有限局部环Z/q~kZ上矩阵广义逆的几个计数结果

设 R =Z/ qk Z是模整数 qk的有限局部环 ,其中 q是素数 ,k>1 .对 R上给定的 n阶矩阵 A,设 W1={X∈ Mn( R) |PAXP- 1=Q- 1XAQ, 1 P,Q∈ GLn( R) },W2 ={X∈ Mn( R) |AX =XA},W3={X∈ Mn( R) |AXA =A},W4 ={X∈ Mn( R) |XAX =X}.若 Wi≠Φ( i=1 ,2 ,3 ,4) ,用 n( Wi)表示 Wi中所有元素的个数 ,主要计算出 n( Wi) ( i =1 ,2 ,3 ,4)     

A vanishing theorem for modular symbols on locally symmetric spaces

A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV. Received: December 8, 1996     

Strontium‐based initiator system for ring‐opening polymerization of cyclic esters

An amino isopropoxyl strontium (Sr‐PO) initiator, which was prepared by the reaction of propylene oxide with liquid strontium ammoniate solution, was used to carry out the ring‐opening polymerization (ROP) of cyclic esters to obtain aliphatic polyesters, such as poly(ε‐caprolactone) (PCL) and poly(L ‐lactide) (PLLA). The Sr‐PO initiator demonstrated an effective initiating activity for the ROP of ε‐caprolactone (ε‐CL) and L‐lactide (LLA) under mild conditions and adjusted the molecular weight by the ratio of monomer to Sr‐PO initiator. Block copolymer PCL‐b‐PLLA was prepared by sequential polymerization of ε‐CL and LLA, which was demonstrated by ¹H NMR, ¹³C NMR, and gel permeation chromatography. The chemical structure of Sr‐PO initiator was confirmed by elemental analysis of Sr and N, ¹H NMR analysis of the end groups in ε‐CL oligomer, and Fourier transform infrared (FTIR) spectroscopy. The end groups of PCL were hydroxyl and isopropoxycarbonyl, and FTIR spectroscopy showed the coordination between Sr‐PO initiator and model monomer γ‐butyrolactone. These experimental facts indicated that the ROP of cyclic esters followed a coordination‐insertion mechanism, and cyclic esters exclusively inserted into the Sr–O bond. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1934–1941, 2003     

关于结合环和半群的二个定理

讨论了关于结合环和半群的二个定理。并且由结合环的这二个定理推出了如下准则：结合环R是Abel-正则的，当且仅当R的每个拟理想是正则环。     

Synthesis,characterization, and mechanism studies on novel rare‐earth calixarene complexes initiating ring‐opening polymerization of 2,2‐dimethyltrimethylene carbonate

Rare‐earth (Nd, Y) p‐tert‐butylcalix[n]arene (n = 4, 6, and 8) complexes without coligands were synthesized from rare‐earth isopropoxides in toluene. The products were characterized as the following structures: [C4(OH)O₃ · CH₃C₆H₅]Nd ( 4 ), [C6(OH)₂O₄ · CH₃C₆H₅]₃Ln₄ [Ln = Nd ( 5 ), Y ( 6 )], and [C8(OH)₂O₆ · CH₃C₆H₅]Nd₂ ( 7 ). 2,2‐Dimethyl trimethylene carbonate (DTC) can be polymerized with complexes 4 – 7 alone as the initiator. PolyDTC (weight‐average molecular weight: 5700, polydispersity index: 1.11, measured by gel permeation chromatography) initiated by complex 5 was obtained with a conversion of 69.1% within 6 h in toluene at 80 °C. The thermal behavior of polyDTC has been compared with the published data. The DTC ring is opened via acyl‐oxygen bond cleavage with end‐group examination. NMR analyses of the polymerization reaction mixture indicated that the polymerization proceeds via a coordination‐insertion mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1390–1399, 2003     

形式三角矩阵环的可分性和稳定度

In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.