三维麦克斯韦方程的对称分裂时域有限差分方法能量守恒性分析

考虑三维电导率为零的麦克斯韦方程的对称分裂时域有限差分(SS-FDTD)方法的能量守恒性.通过新的能量方法与差分算子δx,δy,δz,笔者首次给出了数值逼近格式SS-FDTD在离散的H1模下的能量守恒式,并证明了格式在离散的H1模下的守恒性.数值算例验证了格式解的能量守恒性.     

A gas chromatography/mass spectrometry method for the simultaneous analysis of 50 phenols in wastewater using deconvolution technology

Phenolic compounds exist widely in the influents and effluents of sewage treatment plants (STPs) and most are un-regulated. In this study, a gas chromatography-mass spectrometry (GC-MS) method for the simultaneous analysis of 50 phenolic compounds in wastewater was developed. Deconvolution technology was used to identify contaminants that are covered by co-extracted materials. A mass spectral library containing all 50 silylated phenolic compounds was first established and used for deconvolution. Twelve typical phenolic compounds were selected to optimize the sample preparation procedures. Solid-phase extraction using a C18 cartridge coupled with an HLB cartridge was used for pre-concentration and dichloromethane was used for elution. The solutes were derivatized and analyzed by GC-MS. The blank and matrix spike recoveries ranged from 57.46% to 136.4% and 47.87% to 114.8%, respectively. Method detection limits ranged from 3.64 to 97.64 ng L⁻¹. The relative standard deviations of all the recovery experiments were lower than 13.6%. The instrument limits of quantification ranged from 0.7 to 87.7 pg. The method has been applied to analyze the influents and effluents of 5 Chinese STPs. Except for regulated phenolic compounds (phenol and 2,4,6-trichlorophenol), three un-regulated phenolic compounds, including 2-chlorophenol, 2,5-dichlorophenol and 2,4-dichloro-3-ethyl-6-nitrophenol were identified in the effluent wastewater. The detected concentrations of un-regulated phenolic compounds could possibly cause environmental effects, indicating that immediate attention is required to prevent complications.     

半B-(E,F)-凸约束单目标规划的对偶性

利用半B-(E,F)-凸函数的有关性质讨论了半B-(E,F).凸函数单目标规划的弱对偶定理,强对偶定理和逆对偶定理.     

对称环扩张的一些性质

讨论了对称环的Trivial,Dorroh和Nagata扩张,得出一些结论:(1)若R是一个可除环,则T(R,R)是一个对称环;(2)R是交换环S上的代数,D是R关于S的Dorroh扩张,若环R是对称的 D也是对称的;(3)R是一个交换整环,σ是R的一个内射自同态,则由R,σ形成的R的Nagata扩张也是对称的.     

一类时滞递归神经网络模型的周期振动性

利用线性矩阵不等式方法,研究一类5个神经元时滞递归神经网络模型的周期振动性,得出保证系统存在周期振动性的一组充分条件,理论分析和数值仿真显示,所得结果为一类5个神经元时滞递归神经网络模型提供了新的振动性判定准则.     

一类偏微分方程的有限元解法

推导了一类带复合边界条件的有限元解法,给出了一种快速计算其刚度矩阵的方法.     

平面(kN+1)体问题正多边形解的简明数值方法

讨论平面kN或(kN+1)体问题正多边形解的数值方法.依照力学原理,建立正多边形解的条件方程组,把解微分方程组的问题,转化为解非线性方程组的问题.当质点的质量给定时,用牛顿迭代法解条件方程组.如果给定正多边形的外接圆半径,直接解线性的条件方程组就可以获得答案.     

广义对称正则长波方程的新型守恒差分逼近

作者对一类广义对称正则长波方程的初边值问题进行了数值研究,提出了一个带有加权系数θ的平均隐式差分格式,格式模拟了初值问题的守恒性质,得到了差分解的存在唯一性,并利用离散泛函分析方法分析了该格式的二阶收敛性与稳定性.数值结果表明,该格式是可信的,且适当地调整加权系数θ,可以使计算结果具有更高的精度.     

含非线性色散项的Kadomtsev Petrishvili方程的破缺行波解

 应用平面动力系统分支理论的方法,在参数平面上给出了含非线性色散项的Kadomtsev Petrishvili方程的行波解的分支相图,从而揭示了其行波解与参数的依赖关系,并获得了该方程的破缺行波解的参数表示。     

一维p-Biharmonic方程非零解的存在性

利用一维p-Biharmonic方程在Navier边值条件下特征值问题的相关结果,Leray-Schauder度理论以及标准分支定理讨论了一维p-Biharmonic方程在Navier边值条件下非零解的存在性问题.