亚双曲型广义Cartan矩阵的分类

本文解决了一类非双曲型的不定型（亚双曲型）广义Ｃａｒｔａｎ矩阵的分类问题．证明了亚双曲型矩阵的阶数范围，并做出了阶数为３，５，６的亚双曲型广义Ｃａｒｔａｎ矩阵的Ｄｙｎｋｉｎ图．     

广义Kac-Moody代数的根系

本文描述了在一定条件下带有虚单根的广义Kac—Moody代数的根系,证明了其实根系就是某个与其相关的kac-Moody代数的实根系;解决了其虚根系的构造并确定了其生成元的最小个数;此外还确定了只含有一个实单根和一个虚单根的广义Kac-Moody代数的所有根。     

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.     

浅谈不定积分教学过程中“美”的体现

探讨了不定积分教学过程中，如何体现数学的美。     

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.     

东海某区块致密砂岩钻井液侵入深度实验研究

针对东海区块在钻井作业中钻井液对储层造成严重伤害的问题,开展了东海某区块致密砂岩钻井液侵入深度实验研究,研究中采用了电阻测试法和体积法两种方法,通过测量钻井液侵入过程中岩样电阻和钻井液滤液最大侵入量,并根据电阻、侵入量与时间的关系拟合出侵入深度和时间的关系从而计算钻井液侵入深度。获得了花港组下段致密砂岩基块岩样钻井液侵入深度,电阻测试法计算的钻井液侵入深度主要分布在34~49 cm,体积法计算结果为30~56 cm,钻井液侵入储层后伤害程度为78.2%~97.9%,伤害程度均为强。实验研究为东海区块在钻井和完井作业中控制滤失,减小损害程度提供了依据。     

映射的应用

探计了在教学过程中如何运用映射概念解决具体问题。     

Eisenstein判别法的推广

本文给出了Eisenstein判别法的两个推广。     

矩阵标准形的应用

探讨了矩阵标准形在高等代数理论中的若干应用 .