闭子模的酉等价与遗传C*-子代数的稳定同构问题

在Hilbert C~*-模框架下,给出了闭子模之间的酉等价与相应的遗传C~*-子代数的*同构,及对应的开投影的等价性的关系定理.     

Regiospecific cationic polymerization of spiroorthoesters with different cyclic ether ring sizes

Spiroorthoesters (SOEs), cis‐2,3‐tetramethylene‐1,4,6‐trioxaspiro[4,5]decane ( I ) and cis‐2,3‐tetramethylene‐1,4,6‐trioxaspiro[4,6]undecane ( II ), with different cyclic ether ring sizes were synthesized, and their stereostructure and steric energy were determined. With steric‐hindrance‐sensitized 9‐phenyl‐9,10‐dihydro‐anthracen‐10‐ylium cation as an initiator, I and II underwent regiospecific polymerization to yield trans form of stereoregular poly(ether esters)—poly(trans‐2‐oxycyclohexyl pentanoate) (? [trans‐2‐OCHP]_n? ) ( III ) and poly(trans‐2‐oxycyclohexyl hexanoate) (? [trans‐2‐OCHH]_n? ) ( V ), respectively. With SnCl₄ as another initiator, I and II underwent regiospecific polymerization through different mechanisms to afford cis form poly(cis‐2‐oxycyclohexyl pentanoate) (? [cis‐2‐OCHP]_n? ) ( IV ) and trans form (? [trans‐2‐OCHH]_n? ) ( VI ) stereoregular poly(ether esters). The polymerization mechanisms of SOEs proceeded in the regiospecific manner were determined by the relationship among the sterostructures of SOEs and its subsequently formed polymers, the steric energy of monomers, and the free energy difference in the transition state of reaction. Owing to the conversion of cis substitution at C‐2 and C‐3 in I or II to the trans form during polymerization, polymers III , V , and VI exhibited a higher volume of expansion during polymerization than IV , which showed high volume shrinkage. Group contributions of divalent trans‐ and cis‐1.2‐cyclohexyl groups were derived and confirmed by measuring the densities of the corresponding stereoregular polymers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Analysis of the laser performance of Tm3+: ZBLAN glass at 1.47μm wavelength

A formula for the threshold energy of a four-level-system laser in Tm^{3+} doped fluoride glass is derived. The formula contains the parameters of the interaction between the ions and the up-conversion rate of the pump-light. It is discussed that the Tb^{3+} ions and the up-conversion pump-light have an influence on the laser performance of Tm^{3+} ions around 1.47μm wavelength. We draw the following two conclusions. (1) The laser threshold descends obviously due to the doping of Tb^{3+} ions, but the descending gradually flattens out with the increase of the content of Tb^{3+} ions. Its suitable content is (1－2)×10^{20}cm^{-3}. (2) When pump-lights both from the up-conversion and from the ground state excite simultaneously the single-doped Tm^{3+} ions, the threshold energy can reduce and the output energy can increase. In this paper, the energy conversion efficiency from the up-conversion pump-light to the output energy of laser is estimated.     

量子群上同调群的合成因子

A＝Z[v]Ω，Ω是Z[v]的由v-1和奇素数p生成的理想，U是A上的量子群，设k是特征为零的代数闭域，A→k(v|→ξ）是代数同态，ζ是p次本原根，命Uk=U与Ak的集,W是weyl群，X^ 是支配权集，本文的主要结果是如下的定理。