逆步李代数g(A)的导子代数

本文对逆步李代数g(A)的导子代数进行了研究.这里A是任意一个n×n阶的复矩阵,而g(A)是和其相关联的逆步李代数.特别地,当A是广义Caftan矩阵时, g(A)则为Kac-Moody代数.在这里,我们得到了g(A)的导子代数的结构.     

一类李代数的结构

本文给出了复数域Ｃ上具有有限多个理想的有限维非可解李代数的结构为Ｌ＝Ｃｒ○＋Ｎ○＋Ｓ，其中Ｓ是Ｌ的Ｌｅｖｉ因子，Ｎ是Ｌ的幂零根基，Ｃｒ○＋Ｎ是Ｌ的根基，ａｄｒ是Ｎ的半单纯线性变换，［ｒ，Ｓ］＝０；还给出了这类李代数的一些重要性质．     

Influence of mixed common solvent on the co-assembled morphology of PS-<Emphasis Type="Italic">b</Emphasis>-PEO and CdS quantum dots

The hybrid structures of polystyrene-b-poly(ethylene oxide) (PS-b-PEO) block copolymer and inorganic nanoparticles with good stability and biocompatibility have potential applications in drug delivery and bioimaging. Spherical co-assemblies of PS₁₂₀-b-PEO₃₁₈ and oleylamine-capped CdS quantum dots (QDs) are produced successfully in this work by adding water to a mixed common solvent, such as N,N-dimethylmethanamide (DMF)/chloroform, DMF/tetrahydrofuran (THF), or DMF/toluene. The energy dispersive X-ray (EDX) spectrum indicates that QDs are located at the interface between the core and shell of the spherical co-assemblies. The co-assembly process during water addition is traced by transmission electron microscopy (TEM) and turbidity measurement. Spherical co-assemblies are formed through budding from bilayers of the block copolymer and QDs. The morphology of the co-assemblies is related to the miscibility of the QD-dispersing solvents with water and the morphology changes from a spherical to a vesicle-like structure with DMF/toluene. Increasing THF content in the mixed solvent causes morphological transitions from spherical co-assemblies to multi-branched cylinders and micelles where QDs are located in the central core. Increasing chloroform content yields vesicle-like structures with protruding rods on the surface. The mechanism of the morphological transitions is also discussed in detail.     

二硫化四甲基秋兰姆的表面增强拉曼光谱研究

制备了两种简单常用的具有表面增强拉曼(SERS)活性的银基底—银镜和硝酸刻蚀银箔,并应用于二硫化四甲基秋兰姆(福美双)的检测及其结构变化的分析。SERS技术提供了不同浓度下的二硫化四甲基秋兰姆分子的振动信息,发现当其与金属银基底作用后,二硫键断裂,并且通过化学作用吸附在银基底表面。通过分析不同浓度福美双分子吸附在银表面的拉曼光谱,证明其在金属表面存在两种吸附方式即表现为单齿形和双齿形两种几何形状。这些光谱及结构信息有助于理解和检测自然环境中二硫化四甲基秋兰姆及其分解产物。同时也对二硫代氨基甲酸盐类化合物的研究有一定的借鉴意义。     

Weyl代数的表示

设Ｋ是一个域．证明了，若ｃｈＫ＝０，那么ｎ－ｔｈＷｅｙｌ代数Ａ_ｎ（ｋ）没有有限维表示．还给出了Ａ_ｎ（ｋ）的不可约Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模的分类．当Ｋ是一个特征非零的代数闭域时，给出了有限维不可约Ａ_ｎ（Ｋ）－模的分类．     

Double emulsion droplets as microreactors for synthesis of magnetic macroporous polymer beads

An easy method is presented to fabricate monodisperse magnetic macroporous polymer beads（MMPBs）. Waterin-oil high internal phase emulsion（HIPE） is prepared by emulsifying aqueous iron ions solution in an oil phase containing monomers. The HIPE is introduced into a simple microfluidic device to fabricate monodisperse（water-in-oil）-in-water double emulsion droplets. The droplets serve as microreactors to synthesize Fe3O4 nanoparticles and are on-line polymerized to form MMPBs. The prepared MMPBs display uniform size, interconnected porous structure, superparamagnetic behavior and uniform distribution of Fe3O4 in polymer matrix. The MMPBs are characterized by scanning electron microscopy（SEM）, Fourier transform infrared spectroscopy（FTIR）, X-ray diffraction（XRD）, transmission electron microscopy（TEM）, vibrating sample magnetometry（VSM）. We believe that this method is a universal technique in preparing macroporous nanocomposite beads.