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     

n阶全矩阵环(代数)的极小生成集

证明了下面的结论：１．若Ｒ是有单位元１的环，则Ｍｎ（Ｒ）作为环与Ｒ－模可由两个元生成；２．设Ｆ是域，Ｍｎ（Ｆ）作为Ｆ－代数可由两个元生成，且Ｍｎ（Ｆ）的任意非中心元皆可作为极小生成集中的一员；３．设Ｆ是特征为零的域，则Ｍｎ（Ｆ）的上三角矩阵子代数可由两个元生成     

Formation of 4-arylpyridines from pyridinium salts under the action of methylammonium sulfite

Reactions of pyridinium salts or nonquaternized pyridine with 4-methylpyridinium salts in the presence of methylammonium sulfite in aqueous methylamine afford 4-phenylpyridine in 29—57% yields. The probable mechanism of ring transformation in simplest pyridine derivatives under the action of nucleophiles is discussed.     

Photoinduced and thermally induced cationic polymerizations using S,S‐dialkyl‐S‐(3,5‐dimethylhydroxyphenyl)sulfonium salts

A study of the photoinitiated and thermally initiated cationic polymerizations of several monomer systems with S,S‐dialkyl‐S‐(3,5‐dimethylhydroxyphenyl)sulfonium salt (HPS) photoinitiators bearing different lengths of alkyl chains on the positively charged sulfur atom has been conducted. HPS photoinitiators are capable of photoinitiating the cationic polymerization of a wide variety of epoxy and vinyl ether monomers directly on irradiation with short‐wavelength UV light. Aryl ketone photosensitizers are effective in extending the spectral response of these photoinitiators into the long‐wavelength UV region. Kinetic studies with real‐time infrared spectroscopy show that HPS photoinitiators exhibit good efficiency in the polymerization of epoxide and vinyl ether monomers. Comparative studies also demonstrate that S,S‐dimethyl‐S‐(3,5‐dimethyl‐2‐hydroxyphenyl)sulfonium salts are more active photoinitiators than their isomeric S,S‐dimethyl‐S‐(3,5‐dimethyl‐4‐hydroxyphenyl)sulfonium salt counterparts. Both types of HPS photoinitiators display reversible photolysis as a result of facile termination reactions that take place between the growing chains ends with the photogenerated sulfur ylides. Preliminary studies have shown that HPS photoinitiators can also be employed as thermal initiators for the cationic ring‐opening polymerization of epoxides at moderate temperatures. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2570–2587, 2003     

Zpe上本原序列的元素分布

文研究了Zpe上本原序列的元素分布.利用Ga,lois环上的指数和估计和本原序列的迹表示,得到了Zpe中各元素在本原序列的一个周期中出现频率的一个估计.当n＞4e时(n为本原序列生成多项式的次数).我们的估计优于Kuzmin的结果[1].     

The Becker-Döring equations at large times and their connection with the LSW theory of coarsening

A systematic procedure is given for obtaining the asymptotic late-time behavior of the Becker-Döring equations describing the time evolution of a population of clusters of particles. In lowest order of approximation, the distribution of the sizes of the largest clusters satisfies the equations of the Lifshitz-Slyozov-Wagner theory of coarsening.     

Ring opening cross-metathesis on solid support: a combinatorial library synthesis of highly functionalized cyclopentanes

Ruthenium catalyzed ring opening cross-metathesis of resin-bound bicyclic alkenes with terminal aryl olefins was utilized for the construction of a combinatorial library containing highly functionalized cyclopentane derivatives. The technology described herein represents a convergent method for the diastereospecific synthesis of unique cyclopentane molecular scaffolds useful for exploratory medicinal chemistry. This revised version was published online in August 2006 with corrections to the Cover Date.     

Some equivalents of AC in algebra II

We show that the axiom of choice AC is equivalent to the statement Any quotient group of any abelian group has a selector. We also show that the multiple choice axiom MC is equivalent to the assertion: Any filter in any Boolean ring has a well ordered filterbase. Received October 3, 1996; accepted in final form May 1, 1998.