分形与量子世界

此文立意新颖且有挑战性,是融合玻尔及爱因斯坦争论的突破口之一.     

n模耦合谐振子量子系统的精确波函数

利用不变本征算符法研究了n模耦合谐振子量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出坐标表象中系统的精确波函数的解析解.并对不同情形的耦合系数进行了讨论,认识到n模动量耦合谐振子体系和n模坐标耦合谐振子体系是本文所研究的体系的特例.     

通电螺线管2维磁场有限元计算

 通过对通电螺线管磁系统理论分析,实现了通电螺线管2维磁场计算。该算法是采用一次、二次插值函数计算螺线管模型磁场的有限元算法,用于求解螺线管内外任意位置处的磁感应强度分布。实现了螺线管及周期结构的计算,并将结果与Ansoft Maxwell 2-D的计算结果进行了对比。结果表明：较一次插值函数有限元算法相比,二次插值函数算法在对称轴上轴向磁感应强度的分布更准确,体现了该算法的优越性,具有显著的工程应用价值。     

用于观测细胞培养罐的显微系统设计

由于现有实验室显微镜物距较小,且光源发散角较大,无法实时对培养罐中细胞进行观测,设计了一款用于不同容量细胞培养罐外部观测的显微系统,系统工作距离45mm,NA=0.19,像方分辨率δ=10.8μm,实现在细胞培养罐外部进行检测。设计结果表明子午线与胡矢线重合较好,与理论衍射极限接近,在空间频率88lp/mm下,各视场MTF均在0.05以上,具有较高的分辨力,各视场的弥散斑均小于艾里斑半径,成像质量良好。     

樽海鞘群算法在可见光通信调制器的应用

针对可见光多载波通信系统传输速率低、帧间干扰大的问题,采用改进的樽海鞘群算法对可见光多载波通信系统的调制器算法进行优化,以提高可见光通信的数据传输速率。该文详细分析了可见光通信系统的多载波调制器,全面考虑了相关调制系统的重要参数集,并给出合理的质量评价函数。将布谷鸟搜索算子引入樽海鞘群算法以增强其全局搜索能力,最终利用改进的樽海鞘群算法对可见光通信多载波调制器做优化。仿真实验结果表明,运用樽海鞘群算法能够对可见光通信多载波调制系统的参数进行优化,提高可见光通信的传输速率。     

近紫外-可见三倍率筒镜系统设计

紫外显微检测系统在生命科学及半导体工业等领域具有越来越广泛的应用,筒镜是无限共轭显微系统的重要组成部分。针对目前紫外显微筒镜系统对变倍性能的要求与变倍精确性之间存在的矛盾,设计了一款工作波段为355～500nm,具有三倍率、高分辨率、大视场及低畸变特性的近紫外-可见筒镜系统。其结构特殊之处在于由共用前固定组和齐焦后更换组构成,可通过更换后组实现筒镜放大倍率的准确切换。使用Zemax软件对筒镜系统进行优化设计,并分析了系统的像差和调制传递函数。设计结果表明:系统在三种倍率模式下,空间频率70lp/mm处系统各视场的MTF均接近衍射极限;畸变均小于0.5%,具有高相对像面照度,在合理的公差参数下能较好地满足设计指标,可适配多种紫外显微物镜进行准确的显微检测成像。     

Z 2-equivariant cubic system which yields 13 limit cycles

For the planar Z_2-equivariant cubic systems having two elementary focuses,the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved.The necessary and sufficient conditions for the existence of the bi-center are obtained.On the basis of this work,in this paper,we show that under small Z_2-equivariant cubic perturbations,this cubic system has at least 13 limit cycles with the scheme 16∪6.     

Banach Algebra Dynamical Systems

This paper generalizes the C*-dynamical system to the Banach algebra dynamical system(A,G,α)and define the crossed product A α G of a given Banach algebra dynamical system(A,G,α).Then the representation of A α G is described when A admits a bounded left approximate identity.In a natural way,the authors define the reduced crossed product A α,r G and discuss the question when A α G coincides with A α,r G.     

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS INVOLVING m CRITICAL HARDY-SOBOLEV EXPONENTS AND m SIGN-CHANGING WEIGHT FUNCTION

In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign- changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.     

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.