谈解析函数级数展开式的一些应用

通过实例给出解析函数的级数展开式在求留数、积分及收敛级数求和中的具体应用.     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

有关常数项级数的几个典型例题

通过实例考察常数项级数收敛和发散时一般项的一些特点,并讨论级数不满足比值判别法、根值判别法或莱布尼茨定理的条件时的收敛性问题.     

一类四进制U-正交函数系

本文给出了一类四进制的分段多项式正交系(简称QU-系统)的构造方法,讨论了该构造算法的可行性,并给出了1至3次QU-系统的一组显式表达式.同时,研究了QU-系统的性质以及与二进制U-系统之间的关系,并推导出了QU-系统的基函数值与Fourier-QU系数的计算公式.由本文的方法可以构造一类L2[0,1]中的完备的正交系...     

与$\zeta(2k 1)$函数有关的两类快速收敛级数

Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.     

混合交通流时间序列的去趋势波动分析

应用去趋势波动分析法研究交通流时间序列的复杂性,探讨了混合交通流时间序列演变行为的标度指数.根据标度指数的变化特征,进而揭示交通流时间序列所具有的长程相关性和短程相关性.通过分析发现,存在一密度ρ,当ρ₁<ρ<ρ₂时,交通流时间序列具有长程相关性;而当ρ<ρ₁或ρ>ρ₂时,交通流时间序列具有短程相关性,即密度的变化影响着标度指数的变化.另外分析了在不同慢车比率条件下时间序列的标度指数,发现慢车比率的变化 关键词： 混合交通流 去趋势波动分析 时间序列 长程相关     

水热法制备注射器样纳米氧化锌场发射特性的研究

应用水热法制备了注射器样纳米结构氧化锌样品,室温下测量其真空场发射特性.根据测量数据,基于Fowler-Nordheim方程,估算了场发射效应增强因子,观察到增强因子随外加电压增加取值的两阶段性;结合样品的光致发光谱和能量散射谱,应用半导体材料中强场效应理论,结合场发射电流密度测量系统的串联电路等效,研究样品中空位对场发射特性影响机理.结果表明,制备过程中形成的锌、氧空位,在样品中产生了相当于杂质态的缺陷能级,缺陷能级与样品形貌共同作用,使样品较大的增强因子随场强增加而阶跃性下降.最后,用电化学沉淀法和气 关键词： 场发射 强场效应 缺陷态 串联等效     

远场模型方程的同伦近似对称约化

以同伦近似对称法为理论依据研究了远场模型方程, 通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解. 各阶相似约化方程均为线性变系数常微分方程, 并且可以从零阶开始依次求解. 同伦模型中的辅助参数影响同伦级数解的收敛性. 关键词： 同伦近似对称法 远场模型方程 同伦级数解     

Influence of sputter power on structural and electrical properties of TiO2 films for Al/TiO2/Si gate capacitors

Titanium dioxide (TiO₂) thin films were deposited onto p‐Si substrates held at room temperature by reactive Direct Current (DC) magnetron sputtering at various sputter powers in the range 80–200 W. The as‐deposited TiO₂ films were annealed at a temperature of 1023 K. The post‐annealed films were characterized for crystallographic structure, chemical binding configuration, surface morphology and optical absorption. The electrical and dielectric properties of Al/TiO₂/p‐Si structure were determined from the capacitance–voltage and current–voltage characteristics. X‐ray diffraction studies confirmed that the as‐deposited films were amorphous in nature. After post‐annealing at 1023 K, the films formed at lower powers exhibited anatase phase, where as those deposited at sputter powers > 160 W showed the mixed anatase and rutile phases of TiO₂. The surface morphology of the films varied significantly with the increase of sputter power. The electrical and dielectric properties on the air‐annealed Al/TiO₂/p‐Si structures were studied. The effect of sputter power on the electrical and dielectric characteristics of the structure of Al/TiO₂/p‐Si (metal‐insulator‐semiconductor) was systematically investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.