LU分解的增长因子

In this article, we derive upper bounds of different growth factors for the LU factorization, which are dominated by A11(k)-1A12(k),A21(k)A11(k)-1, where A11(k), A12(k), A21(k), A22(k) are sub-matrices of A. We also derive upper bounds of growth factors for the Cholesky factorization. Numerical examples are presented to verify our findings.     

Best constants in the Hardy-Rellich type inequalities on the Heisenberg group

We prove some sharp Hardy-Rellich inequalities on the Heisenberg group, using the method given by D.G. Costa in [D.G. Costa, Some new and short proofs for a class of Caffarelli-Kohn-Nirenberg type inequalities, J. Math. Anal. Appl. 337 (2008) 311-317].     

H型群上的非线性Liouville定理

对H型群上的次线性方程ΔGu up=0进行了研究,其中ΔG是对应的sublaplace算子．通过将移动平面方法推广到H型群上,证明了在一定条件下的p和函数u,次线性方程ΔGu up=0的唯一解是u≡0．     

浅水湖泊中介质吸收系数的反演

基于在太湖、天目湖观测的水下光场资料,假定在水体中无内光源及无非弹性散射的情况下,通过水体中向上、向下的辐照度廓线分布,及由此确定的漫射反射率、漫射衰减系数,较为成功地反演了水体中介质的固有光学参数--吸收系数,且在较大程度上降低了由波浪及船舶阴影所带来的误差.同时将该反演结果与通过定量滤膜技术测定的结果进行了比较,二者吻合得较好.该方法有利于研究进入水体的太阳辐射能在各介质之间的分配及水生生态系统对水下光场的响应、大型浅水湖泊中蓝藻水华的暴发机理、提高二类水体水质定量遥感精度.     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G=SU(2.2).K=S(U(2)×U(2)),and for l∈Z.let{τ_l}_(leZ) be a one- dimensional K-type and let E_l be the line bundle over G/K associated toτ_l .It is shown thal theτ_l-spher cal function on G is given by the hypergeometric functions of several variables.By applying this result,a central limit theorem for the space G/K is obtained.     

Hyperbranched ferrocenyl polymer film with high charge transport efficiency

The electrochemical behaviors of hyperbranched poly(ferrocenyl-methylsilane) (HPFMS) and linear oligo(ferrocenyldimethylsilane) (LOFS) films were studied systematically by cyclic voltammetry and chronocoulometry under different polymer coverage and solvents. Both poly(ferrocenylsilanes) show stable cyclic voltammographs in LiClO 4 solutions. Compared with LOFS films, HPFMS films exhibit higher charge transport efficiency because of their hyperbranched structure: peak current ( i p) and apparent diffusion coefficient ( D app) for HPFMS films are larger than those for LOFS films, especially at high polymer coverage (3.8 x 10 (-11) vs 3.9 x 10 (-12) cm (2)/s for HPFMS and LOFS film at the coverage of 2.1 x 10 (-6) mol Fc/cm (2)). The conceptual models of electrode processes for HPFMS and LOFS films were proposed to account for higher charge transport efficiency of HPFMS films. It is also found that a solvent with the appropriate solubility parameter and polarity, lower viscosity, and higher dielectric constant is in favor of charge transport through polymer films, which is consistent with the proposed model of electrode process for HPFMS films. These results imply that hyperbranched ferrocenyl polymers have the potential to be excellent chemical sensor materials with convenient synthesis and high sensitivity.     

第11届全国大学生化学实验邀请赛无机及分析化学实验试题评析与思考

介绍了第11届全国大学生化学实验邀请赛无机及分析化学实验操作试题的命题思路,并对实验中存在的问题及成绩进行了总结分析。     

电化学测定谷胱甘肽方法的研究

采用循环伏安扫描的方法, 促进谷胱甘肽与邻苯醌亲核加成产物在玻碳电极表面的生成和富集. 在此后的差分脉冲分析中, 邻苯醌的还原峰与谷胱甘肽-邻苯醌加合物的还原峰完全分开, 实现了谷胱甘肽的单独测定. 研究了溶液pH值, 邻苯二酚浓度及循环伏安扫描条件对谷胱甘肽测定的影响. 在优化的条件下, 测定谷胱甘肽的检测限为0.05 µmol/L, 线性范围是0.1 µmol/L～1.7 µmol/L, 同时抗坏血酸, 甘氨酸, L-酪氨酸, L-赖氨酸和半胱氨酸对测定没有干扰. 此电化学测定谷胱甘肽方法选择性好、灵敏度高.