An extended Jacobi elliptic function rational expansion method and its application to ()-dimensional dispersive long wave equation

With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.     

探地雷达技术在古城墙修缮中的应用

平遥古城墙是我国珍贵的文化遗产。由于古城墙经历年代久远以及近代人为破坏,其内部结构发生了很大改变,目前已有部分马面和墙体出现裂缝,甚至发生了严重的跨塌事故。本文以探地雷达技术的应用为基础,简述了探地雷达在古城墙修缮中的基本原理及应用。通过讨论探地雷达技术对目标体的检测,分析古城墙雷达剖面,得出了城墙内部存在松软土体、孔洞、裂缝等结构缺陷,并给出危险等级,为制定修缮计划提供了可靠的依据。     

Symbolic computation and a uniform direct ansätze method for constructing travelling wave solutions of nonlinear evolution equations

On the basis of the computer symbolic system Maple and the tanh method, the Riccati equation method as well as all kinds of improved versions of these methods, we present a further uniform direct ansätze method for constructing travelling wave solutions of nonlinear evolution equations. Compared with the existing methods, the presented method can be used to construct more new general solutions. And we give some examples to illustrate the key step of our method.     

一类带弱奇异核偏积分微分方程二阶差分空间半离散格式的全局稳定性

本文给出了数值求解一类带弱奇异核偏积分微分方程的二阶差分空间半离散格式;借助于Laplace变换及Parseval等式,得到了全局稳定性的证明.     

Exact Solutions for a Family of Variable-Coefficient “Reaction–Duffing” Equations via the Bäcklund Transformation

The homogeneous balance method is extended and applied to a class of variable-coefficient reaction–duffing equations, and a Bäcklund transformation (BT) is obtained. Based on the BT, a nonlocal symmetry and several families of exact solutions of this equation are obtained, including soliton solutions that have important physical significance. The Fitzhugh–Nagumo and Chaffee–Infante equations are also considered as special cases.     

MgO对La2O3-TiO2系陶瓷性能的影响

研究了MgO的加入对La2O3-TiO2陶瓷的烧结和介电性能的影响, 并对影响机制作了初步探讨. 结果表明添加MgO的La2O3-TiO2陶瓷能在1200～1280 ℃之间烧结. 随着MgO量的增加, 材料的介电常数下降, 介电常数的温度系数增加. 在1～40 MHz频率下没有添加MgO和添加2.4%的试样的介电常数分别为41和36, 介电损耗都在10-4数量级上, 在10 kHz下介电常数的温度系数分别为-24×10-6/℃和82×10-6/℃, 是一种性能良好的介质材料.     

Theoretical study on the hydrogen abstraction reaction of CH3CH2F (HFC-161) with Cl atom

A direct dynamics method is employed to study the hydrogen abstraction reaction of CH₃CH₂F+Cl. Three distinct transition states are located, one for -H abstraction and two for β-H abstraction. The potential energy surface (PES) information is obtained at the QCISD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p), CCSD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p) and G2//MP2/6-311G(d,p) level. Based on the QCISD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p) results, the rate constants of the three reaction channels are evaluated by using the canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) contributions over the temperature range of 220–2800 K. The calculated results indicate that -H abstraction dominates the total reaction almost over the whole temperature range.     

求解非线性方程的双函数法

基于齐次平衡法和李志斌的tanh函数法,得到简单有效的求解非线性发展方程的双函数法,这种方法利用非线性发展方程孤立波的局部性特点,把非线性方程的孤波解表示为函数f和g的多项式,并用这种方法求出了非线性波理论中的基本模型KdV方程的多组孤波解。     

灭多威的超声降解研究

研究了灭多威模拟废水在超声作用下的降解反应动力学、降解产物、降解途径、以及影响降解速率的因素等问题.结果表明,灭多威经超声作用35min,可被完全转换为无机物,其降解过程为假一级反应;浓度增加时,降解减慢;Fe     

关于构造数学物理中非线性发展方程组孤波解的一种新算法

根据改进的sine-cosine法和吴文俊消元法,给出了一种构造非线性发展方程组孤波解的新算法。这种算法比已知的双曲函数法有更好的结论,并且在使用的过程中更简单。借助于MATH-EMATICA软件,这一算法能够在计算机上实现。