n阶不等距常系数线性差分方程的解

利用Mikusinski的算符演算理论和移动算符的幂级数表示,给出了n阶不等距常系数线性差分方程的解法.     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

北京大学分析化学系列小班阅读讨论课的教学实践

简介了北京大学化学与分子工程学院分析化学系列基础课(定量分析化学、仪器分析、中级分析化学)开展小班阅读讨论课教学的实践。     

第一过渡系金属-镝单分子磁体研究进展与展望

第一过渡系中的顺磁性离子Cr^Ⅲ、Mn^Ⅱ/Mn^Ⅲ、Fe^Ⅱ/Fe^Ⅲ、Co^Ⅱ、Ni^Ⅱ和Cu^Ⅱ及抗磁性离子Co^Ⅲ和Zn^Ⅱ均可与Dy^Ⅲ在多齿螯合配体配位下形成单分子磁体配合物。在本文中,我们阐述或汇总了几乎所有的第一过渡系金属-镝单分子磁体。对于由顺磁性第一过渡金属离子和Dy^Ⅲ离子形成的配合物,有2个有趣的现象需要引起人们的注意：一是一些Cr-Dy配合物具有较高的阻塞温度和较大的矫顽场,这可归功于配合物内Cr^Ⅲ离子和Dy^Ⅲ离子之间较强的磁耦合作用（|J|>10 cm^-1）。二是报道的Fe^Ⅱ₂-Dy配合物的能垒可达到319 cm^-1（459 K）,这在第一过渡系金属-镝单分子磁体中也是比较高的。这可能与Fe^Ⅱ₂-Dy中Dy^Ⅲ具有较高的轴向对称性（D_5h）有关,且从头计算表明该配合物中Dy的第一激发态也具有较高的轴向对称性。除了部分Cr-Dy和Fe^Ⅱ-Dy配合物外,其他顺磁性第一过渡金属-Dy的能垒较低,这可能由配合物内顺磁离子间弱的磁耦合造成的。为了消除磁耦合对磁弛豫行为影响,近年来人们关注于使用抗磁性第一过渡金属离子与Dy^Ⅲ构建单分子磁体配合物。相比其他核数的Zn-Dy配合物,三核Zn₂Dy配合物被报道的数目最多且研究得最为深入,这可能与较易调控Zn₂Dy中Dy配位几何对称性有关。最后,我们提出了几点关于进一步提升第一过渡系金属-镝单分子磁体的磁性能的建议,其中最为重要的是控制Dy配位几何的轴向对称性及Dy的基态m_J的电荷分布。对于第一过渡系金属-镝单分子磁体中的Dy^Ⅲ离子,Dy^Ⅲ基态m_J的电荷与配体的电荷之间的静电排斥应该降到最低。     

On the molecular mechanism of ion specific Hofmeister series

Hofmeister series ranks the ability of salt ions in influencing a variety of properties and processes in aqueous solutions.In this review,we reexamine how these ions and some other small molecules affect water structure and thermodynamic properties,such as surface tension and protein backbone solvation.We illustrate the difficulties in interpreting the thermodynamic information based on structural and dynamic arguments.As an alternative,we show that the solvation properties of ions and proteins/small molecules can be used to explain the salt effects on the thermodynamic properties of the solutions.Our analysis shows that the often neglected cation-anion cooperativity plays a very important role in these effects.We also argue that the change of hydrogen donor/acceptor equilibrium by added cosolutes/cosolvents can be used to explain their effects on protein secondary structure denaturation/protection:those increase hydrogen donor concentrations such as urea and salts with strongly solvated cations/weakly hydrated anions tend to dissolve protein backbone acting as secondary structure denaturants,whereas those lack of hydrogen donors but rich in acceptors have the opposite effect.     

Retention behavior of a homologous series and positional isomers of aliphatic amino acids in hydrophilic interaction chromatography

The retention behavior of several series of free α‐ and ω‐amino acids and positional isomers of amino pentanoic acid in the hydrophilic interaction chromatography mode (HILIC) was studied. The study was carried out on three stationary phases followed by post‐column derivatization with fluorescence detection in order to describe the retention mechanism of the tested amino acids. The effect of chromatographic conditions including acetonitrile content in the mobile phase, mobile phase pH (ranging from 3.5 to 6.5) and concentration of buffer in the mobile phase was investigated. The effect of the number of carbon atoms (n_C) in aliphatic chains of the individual homologue of α‐ and ω‐amino acids and the logarithm of the partition coefficient (logD) on retention was also a part of the presented study. A good correlation (r > 0.98) between the logk and logD values of amino acids or n_C, respectively, was observed. The described linear relationships were subsequently applied to predict the retention behavior of individual members of the homologous series of amino acids and to optimize the mobile phase composition in HILIC. The obtained results confirmed that the retention mechanism of α‐amino acids, ω‐amino acids and positional isomers of amino acids was based on the logD values and the number of carbon atoms in the aliphatic chains of amino acids. The elution order of ω‐amino acids and positional isomers of amino pentanoic acid was strongly dependent on the mobile phase pH in the investigated range whereas the retention factors of all α‐amino acids remained essentially unchanged on all tested stationary phases.     

有关常数项级数的几个典型例题

通过实例考察常数项级数收敛和发散时一般项的一些特点,并讨论级数不满足比值判别法、根值判别法或莱布尼茨定理的条件时的收敛性问题.     

根值判别法的两个推广

讨论正项级数的根值判别法．若将判别极限lim↓n→∞ n√an更改为lim↓n→∞或lim↓n→∞^n√am^n＋i,则相应结果在一定条件下将比原判别方法更为精细,且应用范围也有所推广．     

谈解析函数级数展开式的一些应用

通过实例给出解析函数的级数展开式在求留数、积分及收敛级数求和中的具体应用.     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.