On ＂Problems on von Neumann Algebras by R. Kadison, 1967＂

A brief summary of the development on Kadison‘s famous problems (1967) is given. A new set of problems in von Neumann algebras is listed.     

流体力学中少变量的量纲分析法

量纲和谐原理指出,要正确反映一个物理现象所代表之客观规律,其所遵循的物理方程式各项的量纲必须一致.这是量纲分析法的基础,因此也以用这一原理来校核物理方程和经验公式的正确性和完整性.     

Five-Dimensional Cosmological Model with Variable G and A

Einstein＇s field equations with C and A both varying with time are considered in the presence of a perfect fluid for five-dimensional cosmological model in a way which conserves the energy momentum tensor of the matter content. Several sets of explicit solutions in the five-dimensional Kaluza-Klein type cosmological models with variable G and A are obtained. The diminishment of extra dimension with the evolution of the universe for the five-dimensional model is exhibited. The physical properties of the models are examined.     

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

狭义相对论的数学问题（三）—洛伦兹协变量

在郭硕鸿《电动力学》教材中狭义相对论部分的基础上对洛伦兹协变量作了较详细的讨论．     

平行导体板与带电直导线电场的保角变换分析

平行导体板间点电荷的静电场问题,由于其物理图像清晰,已经得到解决．平行导体平板问线电荷的静电场,可用分离变量法求解其问的电场,但比较繁琐、不直观．本文采用保角变换法分析了平行导体板和线电荷形成的静电场问题,采用指数变换与镜像法联合使用的方法,求解其间的电场分布．通过电势表达式,得到电场的解析形式,并结合Maflab画出电场线图形,最后将结果引申到平行导体板带电情况下的电势分布．     

模糊合作博弈局中人参与水平间相互作用度量

本文基于经典合作博弈局中人间相互作用现象的有关度量方法,针对具有模糊联盟的合作博弈问题,给出了模糊联盟中各局中人参与水平间相互作用的度量方法,定义了水平间相互独立性概念,建立了反映局中人各参与水平间相互作用平均程度的两指标:Shapley相互作用指标及Banzhaf相互作用指标.同时对于具有k-单调性的模糊合作博弈局中人参与水平间的边缘相互作用的有关性质作了进一步研究,得出了一些新的结论.     

双阱结构含时量子输运的微扰论及输运方程

利用Lewis-Riesenfeld不变量理论和与不变量有关的幺正变换方法研究了双阱结构含时量子 输运的微扰论.获得了双阱内含时薛定谔方程的精确解的完备集，在此基础上，把双阱与左 右热库的相互作用作为微挠，获得了双阱结构一阶近似下的输运方程，并在绝热近似下提供 了一种用于研究量子输运过程中几何相因子(Berry相因子)的方法. 关键词： 含时量子输运 输运方程 不变量 几何相因子     

Interaction between two folded solitary waves for a modified Broer--Kaup system

By means of a Painlevé-Baicklund transformation and a multi-linear separation-of-variable approach, abundant localized coherent excitations of a modified Broer-Kaup system are derived. There appear possible phase shifts for the interactions of the （2＋1）-dimensional novel localized structures, which are discussed in this paper.     

Modelling of chaotic systems based on modified weighted recurrent least squares support vector machines

Positive Lyapunov exponents cause the errors in modelling of the chaotic time series to grow exponentially. In this paper, we propose the modified version of the support vector machines (SVM) to deal with this problem. Based on recurrent least squares support vector machines (RLS-SVM), we introduce a weighted term to the cost function tocompensate the prediction errors resulting from the positive global Lyapunov exponents. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to the Santa Fe competition time series. The simulation results shows that the proposed method can capture the dynamics of the chaotic time series effectively.