A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

具有导子的李三系的中心扩张与形变

考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配.     

基于颜色模型和稀疏表示的图像型火焰探测

常用的图像型火焰探测算法是提取火焰在图像上表现出的单个特征信息或其有效组合作为识别的依据,需要大量的训练样本进行学习与参量优化,且识别率对特征选择的要求也很高.本文从火焰的整体特征考虑,提出了基于颜色模型和稀疏表示模型相结合的图像型火灾探测方法.首先在HIS空间建立颜色模型对火灾图像进行预处理提取出疑似区域,建立稀疏表...     

单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类. 利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数, 推广了现有文献中的相关结果.     

一对四元数矩阵方程的共轭延拓解

定义广义四元数共轭延拓矩阵的概念,利用矩阵分块和四元数矩阵的实表示方法,分别给出四元数矩阵方程AX=C和XB=D存在列共轭延拓解和行共轭延拓解的必要充分条件及解的表达式.     

EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

The classical risk process that is perturbed by diffusion is studied .The explicit expressions for the runi probability and the surplus distribution of the risk process at the time of runi are obtained when the claim amount distribution is a finite mixture of exponential distributions of a Gamma (2,α） distribution.     

REPRESENTATIONS OF THE TWO PARAMETER DEFORMATION OF THE VIRASORO ALGEBRA

This paper constructs a class of Harish-Chandra modules with multiplicity ≤1 of the two parameter deformation of Virasoro algebra and proves a classification theorem.     

Lax表示的变形与Hamilton方程族的Lax表示

本文首先给出了构造演化方程族的Ｌａｘ表示的马文秀方法的一种变形，后对这一方法作了改进，使之适用于Ｈａｍｉｌｔｏｎ形式的方程族．作为应用，得到了具有非等谱Ｌａｘ表示的杨方程族．     

浅议抽象函数周期性的表达方式

我们知道,周期函数的表达方法是多式多样的,有的表示方法容易发现、理解和应用,有的表示方法却是非常隐蔽、不易被发现的,而这样的表示方法却常常出现在各式各类的考试中,因此,我们有必要全面认识函数周期性的表示方法.下面是本人在学习中所遇到的周期函数的一些表示方法,现总结如下,有不到之处,敬请各位读者批评指正.     

Gel＇fand三元组上分式Levy过程的新息表示

借助于分式积分-微分算子和关于Gel＇fand三元组上分式Levy过程的随机积分，本文给出分式Levy过程的新息表示公式，此公式可将Gel＇land三元组上分式Levy过程转换成更简单的Levy过程，并且可以应用在信号识别和行为金融学中．