The Lazer-Solimini equation with state-dependent delay

Sufficient criteria are established for the existence of T-periodic solutions of a family of Lazer-Solimini equations with state-dependent delay. The method of proof relies on a combination of Leray-Schauder degree and a priori bounds.     

The bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation

By using methods from dynamical systems theory, this paper researches the bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation. Implicit exact parametric representations of all travelling wave solutions as well as some explicit analytic solutions are given. Specially, breaking wave solutions are obtained, which KdV equation does not include.     

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order derivatives are taken into account, namely, the Caputo, Riemann-Liouville and Grunwald-Letnikov definitions. As a consequence, the non-existence of exact periodic solutions in a wide class of fractional-order dynamical systems is obtained. As an application, it is emphasized that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system.     

大视场光学系统像面照度均匀性优化

为提高大视场光学系统像面照度的均匀性,从理论上分析了光学系统像面照度的影响因素,提出使用中心遮拦产生的轴外斜光束截面积与轴上光束截面积之比对像面照度进行优化的思路。以理想系统建立数学模型,得到了中心圆形遮拦影响下不同视场角光束截面积比值的变化规律,并分析了遮拦对调制传递函数(MTF)的影响。进一步提出采用Zemax与Matlab软件动态数据交换(DDE)进行像面照度自动计算优化的方法。以某焦距56mm,相对孔径=1/5.6,视场角2ω=80°的航测镜头为例进行了优化,通过在光学系统第5表面上增加半径为4.384mm的中心遮拦,像面照度的不均匀性由优化前的22.3%降低至3.5%,均匀性明显改善。在优化实例中讨论了MTF曲线的变化,指出采用中心遮拦后的传函指标仍满足CCD探测器成像使用要求。     

极紫外光刻离轴照明技术研究

离轴照明技术(OAI)是极紫外光刻技术中提高光刻分辨率的关键技术之一。为了实现考虑掩模阴影效应情况下离轴照明的优化选择,构造了一种新型实现OAI曝光的成像模型。将照射到掩模上的非相干光等效为一系列具有连续入射方向的等强度平行光,基于阿贝成像原理分别对掩模进行成像,最终在像面进行强度叠加实现OAI方式下空间成像的计算;并通过向投影系统函数添加离焦像差项实现不同离焦面上空间成像计算。该模型极大地简化了OAI条件下对掩模阴影效应的计算,提高了成像质量计算效率。结合光刻胶特性及投影曝光系统焦深设计要求,以显影后光刻胶轮廓的侧壁倾角为判据,获得了采用数值孔径为0.32的投影系统实现16 nm线宽黑白线条曝光的最优OAI参数。     

与光场依赖强度耦合下运动纠缠双原子的周期量子回声

本文将Tavis-Cummings (T-C)模型推广到同时考虑原子运动及与光场依赖强度耦合的情况.运用全量子理论,研究了与光场依赖强度耦合下运动纠缠双原子量子态保真度演化.采用数值计算的方法,探讨了双原子初始纠缠因子θ、光场平均光子数n以及场模结构参量p对双原子量子态保真度演化的影响,解析分析了双原子周期量子回声的形成规律,揭示了其物理实质.结果表明,在场模结构参量p=1的情况下,无论光强和双原子初始纠缠因子如何取值,双原子均产生周期2π的量子回声;在强相干场n=30条件下,改变P从1到小于800时,Bell态双原子产生2π/P周期量子回声.当p≥800时,无论光场是真空场、弱相干场或强相干场,双原子量子态保真度恒为1,即第一类Bell态原子持续处于保真态;而当双原子初始纠缠因子为3π/4时,无论n、p取何值,双原子量子态保真度保持为1,双原子持续处于第二类Bell态的保真态.其结论表明,该推广模型具有很好的双原子周期量子回声性质,为纠缠双原子信息高保真输出及噪音环境下量子信息处理的实验实现提供了理论参量和物理载体.     

On Graph-realizable Sets of Periods

We characterize sets of periods of cycles which arbitrary continuous graph maps may have. In this investigation, we need the spectral decomposition for graph maps [Blokh, A.M. "On dynamical systems on one-dimensional branched manifolds", Theory Funct. Funct. Anal. Appl. Kharkov 46 (1986) pp. 8-18 (Russian); 47 (1986) pp. 67-77; 48 (1987) pp. 32-46] briefly described in "The Spectral Decomposition" Section.