有理逼近和Pad\'e逼近的高阶紧致型方法

对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述. 这就是: 回顾了方法的发展历史, 指出了方法优点, 分析了方法的基本特征、构造方式和应用现状, 预示了它的近期发展和研究形势. 特别地, 就方法的数学基础------有理逼近和Pad\'e逼近进行了归纳. 在文章中提供了丰富的方法信息和大量的有关公式.      

关于推导反应速率方程中的稳态近似与平衡态假设方法——对2005年全国高中学生化学竞赛的一道试题解法辨析

2005年全国高中学生化学竞赛中有一道试题（试题7—1问）是考查学生由拟设反应机理推导反应速率方程的能力的。在由拟设反应机理推导反应速率方程时,比较简单有效的方法是采用稳态近似和平衡假设。该题的标准答案是用平衡假设处理得到与实验结果相符的速率方程。而在是否可以用稳态近似方法推导结果引起了争议。本文就此发表一点浅见,以供参考。     

A Hybrid Smoothing-Nonsmooth Newton-Type Algorithm Yielding an Exact Solution of the $P_0$-LCP

We propose a hybrid smoothing-nonsmooth Newton-type algorithm for solving the P0 linear complementarity problem (P0-LCP) based on the techniques used in the non-smooth Newton method and smoothing Newton method. Under some assumptions, the proposed algorithm can find an exact solution of P0-LCP in finite steps. Preliminary numerical results indicate that the proposed algorithm is promising.     

Linear entropy dynamics of the field in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation

We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.     

Soliton Solutions and Interaction Between a Line Soliton and a y-Periodic Soliton in Generalized （2W1）-Dimensional Nizhnik-Novikov-Veselov Equation

Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.     

奇异摄动方法在输电线非线性振动问题中的应用

同一系统内部快变量和慢变量的同时存在往往引发相异于一般系统的特殊效应,比如输电线的松弛振荡.本文推导了架空输电线具有初始垂度的非线性动力学模型,发现该模型是具有快慢变量耦合的数学模型,应用求解周期运动的奇异摄动方法,得到系统的近似解析解,考察了快慢变量对系统周期运动的影响规律.结果表明解析解较数值解略微偏小,但仍有很好的吻合度,说明本文结果的有效性和正确性.进一步计算表明,随着摄动方法应用过程中近似次数的增加,两解逐次接近.     

Two-mode squeezed state of nanomechanical resonators

In this paper, we introduce a flexible model for the control and measurement of NAMRs （nanomechanical resonators）. We obtain the free Hamiltonian of the dcSQUID （direct current superconducting quantum interference device） and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.     

C0-半群关于参数的可微性及其应用

考虑了C0-半群关于参数的可 微性,而参数含在半群的无穷小生成元中. 证明了：无穷小生成元关于参数的广义连续 性及强可微性蕴含着该C0-半群关于参数的可微性. 这些结果被应用于证明线性延 滞微分方程的解关于延滞量的可微性质.     

用改进的标量微分耦合模型计算核表面性质与自旋-轨道耦合势

使用相对论Ｔｈｏｍａｓ－Ｆｅｒｍｉ（ＲＴＦ）及相对论Ｈａｒｔｒｅｅ近似方法,在改进的标量微分耦合模型的基础上,计算了半无穷上核物质中张量耦合及ｍ。的变化对核表面性质与自旋－轨道耦合势的影响．结果表明张量耦合改善了标量微分耦合模型的自旋－轨道耦合势,但核表面张力系数及核表面厚度因张量耦合常数的增加而变小。     

用改进的标量微分耦合模型计算核表面性质与自旋–轨道耦合势

使用相对论Thomas-Fermi(RTF)及相对论Hartree近似方法,在改进的标量微分耦合模型的基础上,计算了半无穷上核物质中张量耦合及m_σ的变化对核表面性质与自旋–轨道耦合势的影响.结果表明张量耦合改善了标量微分耦合模型的自旋–轨道耦合势,但核表面张力系数及核表面厚度因张量耦合常数的增加而变小.