A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.     

On the generalized Hermite-based lattice Boltzmann construction,lattice sets,weights, moments,distribution functions and high-order models

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Bofiz- mann （LB） construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function （EDF） are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly inatch some first hydrodynamic inoments thermally i） on-Cartesian lattice, ii） with thermal weights in the EDF, iii） whilst the highest possible hydrodynamic moments that are exactly reatched are obtained with the shortest on-Cartesian lattiee sets with some fixed real-valued temperatures, is also analyzed.     

近地面层大气非Kolmogorov湍流特征参数测量

分析了2011年1月13日至17日超声气温时间序列数据,不仅采用结构函数和谱分析方法得到了Kolmogorov结构常数C2n,而且提出了非Kolmogorov湍流特征参数测量方法,获得了非Kolmogorov谱幂率α、广义折射率结构常数珟C2n以及等效折射率结构常数珚C2n等测量结果。结论如下:1)实验期间一维温度谱幂率在-1.9-α1-1.5范围内的频数为77.9%,弱湍流时谱幂率与Kolmogorov-5/3谱相比偏平;2)单点温度结构函数法和单点温度频谱法测量C2n差别不大;3)C2n和珟C2n量级和变化趋势基本一致,差别主要体现在弱湍流时C2n比珟C2n小,往往发生在谱幂率偏平的时段;4)珟C2n与珚C2n量级和变化趋势基本一致,差别主要体现在珚C2n有一些起伏,且与给定波长λ和传输路径长度L的选取有关。     

Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

Optoelectronic Properties,Elastic Moduli and Thermoelectricity of SrAlGa： An Ab Initio Study

Half-Heusler compounds are an impressive class of materials with a huge potential for different applications such as in future energy, especially in the fields of thermoelectrics and solar cells. We present ab fnitio total energy calculations within the modified Becke-Johnson generalized gradient approximation （mBJ-GGA） to obtain the physical properties of SrAlGa compounds. The structural, elastic, acoustic, electronic, chemical bonding, optical, and thermoelectric properties are calculated and compared with the available calculation data. The SrAlGa is found to be a small-band-gap （0.125-0.175 eV） material, suitable for thermoelectric applications with a relatively high Seebeck coefficient. Also, SrAIGa has the potential in the optoelectronic applications due to high optical conductivity and reflectivity in the infrared and visible region of electromagnetic spectra.     

基于粒子群算法进行参数自我调整的广义预测控制算法在汽包液位控制中的应用

PID控制算法的学习性能及泛化性能取决于参数设置;在常规方法中,这些参数以固定值形式参与运算,而当面对复杂分布的数据集时,可能无法挑选出一组能够胜任各种分布情况的参数;因此,提出一种基于粒子群算法(particle swarm optimization, PSO)进行参数自我调整的广义预测控制算法(generalized predictive control, GPC);该算法根据工业锅炉现场环境的复杂性,机组参数的时变性,有效地解决了PID控制的控制精度受到限制的问题;着重讲述了汽包液位控制方案的设计,可看出PSO-GPC控制在汽包液位控制中的重要应用,其次,通过粒子群算法对参数进行辨识,并给出了仿真算例,参数辨识准确,最后用PID控制算法在液位控制中的仿真曲线与广义预测控制算法对锅炉汽包液位进行了仿真曲线进行了对比分析,可见广义预测控制增强了系统的快速性,稳定性好且抗干扰性强。     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

基于广义极值的混沌电场峰值分布研究

通过分析峰值分布及广义极值分布理论关于混沌电场峰值分布的特点,获得一种混沌电场峰值分布的计算方法,结合Bootstrap重采样技术,提出了混沌电场峰值分布参数估计方法,该方法吸取了重采样技术估计的优点,对分布参数置信区间的估计更为准确、实用。以蒙特卡罗仿真和某机械搅拌混响室内电场数据为实例,结果表明,与传统的正态近似法、百分位法、BC-t等方法相比,其计算结果与实际结果更为吻合,证明了该方法具有更高的准确度。     

广义矩阵代数上的k-斜中心映射(英文)北大核心CSCD

本文给出了广义矩阵代数上k-斜中心映射(k>2)的一般形式,并给出了一些使得所有k-斜中心映射都为0的充分条件.