关于极限理论的学习经验

分析极限理论在数学分析学习中的重要性，介绍学习极限理论的三点经验与体会，即充分理解基本内容；加强基本功训练；试着多问自己一些问题，学会举出各种各样的例子。     

Results from solvophobic theory applied to methylene selectivity in reversed-phase HPLC

A significant amount of work has been previously dedicated to the understanding of methylene selectivity parameter. The conventional theory applied for this understanding was mostly based on the assumption that the difference in the Gibbs free energy of transfer from the mobile phase to the stationary phase is a constant for any two compounds in a homologous series that differ by a CH₂ group. In the present study, it is shown based on solvophobic theory that this assumption is indeed correct, but it provides a theoretical justification for it. Exemplification of the results of theory was obtained using the values for methylene selectivity (α(CH₂)) measured experimentally for seven different C18 chromatographic columns including two core–shell columns and using water and either methanol or acetonitrile as an organic component. Four different homologous series of compounds were used for evaluation. The study proved the theoretical prediction that the values for α(CH₂) obtained using different homologous series of compounds are only slightly different from those obtained using the toluene–butylbenzene series. Even using different homologous series, the same type of information regarding the columns comparison, and the changes in log α(CH₂) with the solvent composition was obtained.     

基于不同条件的旅游路线规划问题研究

运用2015年全国研究生数学建模竞赛F题的数据资料,针对旅游路线合理规划问题的第一问展开研究.以F题的问题一为起点进行了分析研究,是因为第一问的完成是解决后续问题的关键.首先通过地图搜集并补全了缺失数据并对数据进行合理的处理,然后采用将旅游年数最少目标转化为该最小生成树的"最少圈覆盖"方法来进行对问题一的求解,也可以理解为一个广义的多旅行商问题,以旅行商的人数(即年数)最少为目标.采用Dijkstra算法、最少圈覆盖法、智能算法和图论聚类等方法,通过这些方法建立了单目标优化模型,并运用旅行商问题和模型之间的转换来对问题进行分析与求解.     

Analytical layer-element solutions of Biot’s consolidation with anisotropic permeability and incompressible fluid and solid constituents

Based on the governing equations of 2D plane-strain Biot’s consolidation, the relationship between generalized displacements and stresses of a single soil layer with anisotropic permeability and incompressible fluid and solid constituents is described by an analytical layer-element, which is deduced in the Laplace–Fourier transform domain by using the eigenvalue approach. Taking the boundary conditions and the continuity of the soil layers into consideration, a global stiffness matrix is subsequently assembled and solved. As to the 3D case, the same derivation is employed after the application of a decoupling transformation. The actual solutions in the physical domain can further be acquired by inverting the Laplace–Fourier transform. Finally, numerical examples are carried out to verify the presented theory and discuss the influence of the anisotropic permeability on the consolidation behavior.     

Monitoring of the stability of cocaine and some metabolites in water and oral fluid by a newly developed CE method

A new CE method was here developed, in order to study the stability of cocaine and some of its metabolites in water and in oral fluid. At first, standard mixtures of cocaine (COC), benzoylecgonine (BE) and cocaethylene (COET) in water were used to study the optimal CE parameters to separate the three compounds. Voltage, sample temperature and pH were investigated, and 25 kV, 25°C and a pH of 4.7 were selected to achieve the best separation. The stability of the three compounds in water and oral fluid was then monitored by applying the previously developed method. Three different storage temperatures (8, 25 and 37°C) were selected and analyses during a week were performed. A decrease of COC and COET peak areas and an increase of BE peak area were observed over time at 25 and 37°C. In addition, in oral fluid, the presence of enzymes and other proteins, and the differences in the molecular structures between COC and COET, caused a stronger degradation of the first compound. Instead, when samples were stored at a low temperature (8°C), the peak areas of the compounds did not vary. Thus, the use of this storage temperature is recommended, above all when sample must be analyzed after a relatively long time.     

Dynamical mean‐field theory for correlated electrons

Electronic correlations strongly influence the properties of matter. For example, they can induce a discontinuous transition from conducting to insulating behavior. In this paper basic terms of the physics of correlated electrons are explained. In particular, I describe some of the steps that led to the formulation of a comprehensive, non‐perturbative many‐body approach to correlated quantum many‐body systems, the dynamical mean‐field theory (DMFT). The DMFT becomes exact in the limit of high lattice dimensions (d → ∞) and allows one to go beyond the investigation of simple correlation models and thereby better understand, and even predict, the properties of electronically correlated materials.     

Unsteady hydromagnetic flow of a reactive variable viscosity third‐grade fluid in a channel with convective cooling

This paper examines the combined effects of a transverse magnetic field and variable viscosity on unsteady flow of a reactive third‐grade electrically conducting fluid and heat transfer in a channel with convective cooling at the surface. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi‐implicit finite‐difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system. It is in general noted that those parameters that increase/decrase one flow quantity (velocity or temperature) also lead to the increase/decrease respectively of the other quantity. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of topological degree theory to semi-definite complementarity problem

The topological degree theory is applied to study the problem of existence of solutions to the semi-definite complementarity problem (SDCP). A notion of an exceptional family of matrices is introduced, and assertions of a non-strict alternative type are obtained. Namely, for a continuous mapping, there exists at least one of the following two items: either a solution to the SDCP, or an exceptional family of matrices. Hence, if there is no exceptional family, then at least one solution exists     

First-principles study of structural stability and elastic property of pre-perovskite PbTiO3

The structural stability and the elastic properties of a novel structure of lead titanate,which is named preperovskite PbTiO₃ （PP-PTO） and is constructed with TiO₆ octahedral columns arranged in a one-dimensional manner,are investigated by using first-principles calculations.PP-PTO is energetically unstable compared with conventional perovskite phases,however it is mechanically stable.The equilibrium transition pressures for changing from preperovskite to cubic and tetragonal phases are 0.5 GPa and 1.4 GPa,respectively,with first-order characteristics.Further,the differences in elastic properties between pre-perovskite and conventional perovskite phases are discussed for the covalent bonding network,which shows a highly anisotropic character in PP-PTO.This study provides a crucial insight into the structural stabilities of PP-PTO and conventional perovskite.