Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.     

基于变芯径光纤的光学系统在光造型中的应用

光学系统采用变芯径光纤，可大幅度提高光的传输效率，增加光学子系统柔性。描述了光造型工作原理及其理论依据，在介绍所研制的光的成型系统光学子系统的基础上，阐述了紫外光源的选择与设计，及变芯径光纤的设计、传输、耦合与聚焦等技术。该套基于变芯径光纤的光学子系统成本低、体积小、效率高，巳成功应用于所研制的台式低成本快速成型系统中，为该系统的进一步推广奠定了技术基础。     

Second-order relativistic electron capture

Starting with the impulse approximation, we analyse second-order effects in relativistic electron capture. The relation of this model with relativistic distorted-wave approximations is clarified. In particular it is shown that the second-order spin-coupling terms in the RCDW theory are consistent with the correct form given by perturbation theory. In the semirelativistic limit, the RCDW results are shown to accord with the formulae of Moiseiwitsch for flip and nonflip transitions in the ultra-relativistic limit. This confirms that the continuum-distorted-wave model generalises to relativistic spinors, and highlights the defects of scalar models. We also present a new symmetric eikonal theory which gives reliable results for capture without change of spin, but leads to a divergent total cross section for spin-flip transitions in the second-order term. This effect, which is quite distinct from the spurious spin-flip amplitudes of the scalar symmetric eikonal theory, is taken as further evidence that the eikonal approximation is not valid for magnetic transitions.     

Perfectly alternating segmented polyimide-polydimethyl siloxane copolymers via transimidization

New strategies for the synthesis of perfectly alternating segmented polyimide-polydimethyl siloxane copolymers were developed by utilizing a transimidization method. Imide oligomers endcapped with 2-aminopyrimidine were reacted with aminopropyl terminated (dimethyl siloxane) oligomers to afford perfectly alternating segmented imide siloxane copolymers. The polymerization was conducted in solvents such as chlorobenzene and chlorofrom. High molecular weight, fully imidized perfectly alternating segmented imide siloxane copolymers were obtained within 2 h at temperatures of 60-110°C. The mechanism of the reaction was further elucidated via model compounds and NMR characterization. The block copolymers exhibited two T_gs due to the microphase separation of the polyimide and polysiloxane phases. The T_g of the polyimide phase was a function of the length of the polyimide block. However, partial phase mixing was also evident from the DSC results on the imide siloxane copolymers prepared with low molecular weight polyimide segments. Thermooxidative stability and tensile properties of the perfectly alternating segmented imide siloxane copolymers were found to be principally dependent on the amount of poly (dimethyl siloxane) incorporated in the copolymer and did not correlate with the poly (dimethyl siloxane) or polyimide block lengths. The stress-strain behavior of both solvent cast films or molded films is also reported. © 1994 John Wiley & Sons, Inc.