基于傅里叶变换的高精度条纹细分方法

针对传统傅里叶变换法在提取条纹图相位中存在的能量泄漏问题,提出了条纹图整周期裁剪的方法,可有效抑制能量泄漏对检相精度的影响,提高傅里叶变换法相位计算的精度。在此基础上,提出了一种基于傅里叶变换时移特性的叠栅条纹细分新方法。与传统傅里叶变换法相比,该方法求取相邻两帧条纹图间的相移,只需经过两次傅里叶变换,不需要截取条纹图的基频再逆变换回空域,因此计算量至少减少了一倍,计算速度大大提高。数值计算结果表明,对两束单色平面波形成的条纹,理想条件下细分精度高达10-12量级;对高斯包络调制的条纹,细分精度至少可达10-3量级。     

双δ掺杂In0.65Ga0.35As/In0.52Al0.48As赝型高迁移率晶体管材料子带电子特性研究

研究了基于InP基的In0.65Ga0.35As/In0.52Al0.48As赝型高迁移率晶体管材料中纵向磁电阻的Shubnikov-deHaas(SdH)振荡效应和霍耳效应,通过对纵向磁电阻SdH振荡的快速傅里叶变换分析,获得了各子带电子的浓度,并因此求得了各子带能级相对于费米能级的位置.联立求解Schrdinger方程和Poisson方程,自洽计算了样品的导带形状、载流子浓度分布以及各子带能级和费米能级位置.理论计算和实验结果很好符合.实验和理论计算均表明,势垒层的掺杂电子几乎全部转移到了量子阱中,转移率在95%以上.     

A-单调映象的广义隐拟变分包含

本文引入了一类A-单调映象的广义隐拟变分包含问题,利用A-单调映象的预解算子技巧研究了这类变分包含解的迭代算法逼近,证明了其解的存在性以及由算法生成的迭代序列的收敛性。     

透射型亚波长二元闪耀光栅的数值模拟与分析

使用OptiFDTD对透射型亚波长二元闪耀光栅的透射场进行了数值模拟;使用FFT方法对电磁场分量进行分析,得到其各个级次的能量分布,进而分析了亚波长结构二元光栅的各个参数对衍射性能的影响。分析结果证实:透射型亚波长二元闪耀光栅可将正入射的TE波闪耀到 1级,且等分数对衍射角影响很小。给定波长,其设计主要由光栅周期、光栅材料折射率和等分数这3个参数决定。     

Small divisor problem for an analytic q-difference equation

Similar to the problem of linearization, the “small divisor problem” also arises in the discussion of invertible analytic solutions of a class of q-difference equations. In this paper we give the existence of such solutions under the Brjuno condition and prove that the equation may not have a nontrivial analytic solution when the Brjuno condition is violated. These results are applied to discussing a nonlinear iterative equation.     

A cubically convergent Newton-type method under weak conditions

Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f^′(x)=0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method.     

含弛豫项的广义光学Bloch方程的近似解

本文用叠代法求得了含弛豫项的广义光学Bloch方程的近似解。与计算机给出的数值积分解的比较表明,一阶叠代解具有足够好的精度。由此得出了上能级占有几率随时间变化的解析表达式及多光子吸收、Bloch-Siegert频移等有用结果。     

A note on iterative roots of PM functions

In this paper we study iterative roots of PM functions, a special class of non-monotone functions. Problem 2 in [W. Zhang, PM functions, their characteristic intervals and iterative roots, Ann. Polon. Math. LXV (1997) 119-128] is solved partly and Theorem 4 in that paper is generalized.     

A weak Kantorovich existence theorem for the solution of nonlinear equations

The Kantorovich theorem is a fundamental tool in nonlinear analysis for proving the existence and uniqueness of solutions of nonlinear equations arising in various fields. This theorem was weakened recently by Argyros who used a combination of Lipschitz and center-Lipschitz conditions in place of the Lipschitz conditions of the Kantorovich theorem. In the present paper we prove a weak Kantorovich-type theorem that gives the same conclusions as the previous two results under weaker conditions. Illustrative examples are provided in the paper.     

On new third-order convergent iterative formulas

In this paper, we present new iteration methods with cubic convergence for solving nonlinear equations. The main advantage of the new methods are free from second derivatives and it permit that the first derivative is zero in some points. Analysis of efficiency shows that the new methods can compete with Newton’s method and the classical third-order methods. Numerical results indicate that the new methods are effective and have definite practical utility.