行波前置短磁聚焦飞秒条纹管设计

设计了一款长度为265 mm的飞秒条纹管。采用短磁聚焦透镜和行波偏转板,并将行波偏转板置于磁透镜之前以提高偏转灵敏度。采用蒙特卡罗方法对阴极表面理想点和阴极狭缝发射的光电子初始参量进行了模拟抽样,用CST软件的Particle Tracking模块模拟跟踪了光电子的运行轨迹,统计分析了光电子在最佳像面上的位置分布和渡越时间,给出了光电子在最佳像面上的点扩展函数和调制传递函数。计算结果显示,所设计的条纹管阴极有效尺寸达到6 mm,放大率为2.4~2.5,动态空间分辨力大于55 lp/mm。经保守估算,条纹管的时间分辨力有望达到245 fs。     

复迭代映射z_(n 1)= c的 广义Mandelbrot集研究

研究了复迭代映射ｚ（ｎ＋１）＝／ｚｎｍ＋ｃ的广义Ｍａｎｄｅｌｂｒｏｔ集,指出其关于实轴是对称的,并且具有ｍ＋１次的旋转对称性,得出周期轨道的稳定性条件及一周期轨道的稳定区域的边界方程．利用逃逸时间算法和周期点查找的算法构造Ｍａｎｄｅｌｂｒｏｔ集,可以更清楚地了解Ｍａｎｄｅｌｂｒｏｔ集的结构．     

Almost Combinatorial Selector Sets

Classes of subsets of positive integers based on the notion of selector functions similar to the Jockusch selector of a semirecursive set are studied.     

Absolute fixed point sets for continuum-valued maps

The notion of an absolute fixed point set in the setting of continuum-valued maps will be defined and characterized.

     

Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

On two-coefficient identification in elliptic variational inequalities

Abstract

This paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation.     

Domination number in graphs with minimum degree two

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.     

利用GM(1,1)模型预测曲线波形

针对给出的函数y=f(x),x∈[a,b],将其值域进行n等分,设yi为其中任一分点,对应x=xi(i=1,2,…,m),用GM(1,1)模型对序列{x1,x2,…,xm}进行预测,得到曲线y=f(x)在下一段时间与直线y=yi的交点位置.当GM(1,1)模型的误差较大时,可利用带有残差修正的GM(1,1)模型进行残差修正,以提高GM(1,1)模型预测值的精确度.     

Ends,tangles and critical vertex sets

We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph is critical if its deletion leaves some infinitely many components each with neighbourhood precisely equal to X. We further provide a concrete separation system whose ?₀‐tangles are precisely the ends plus critical vertex sets. Our tangle compactification is a quotient of Diestel's (denoted by ), and both use tangles to compactify a graph in much the same way as the ends of a locally finite and connected graph compactify it in its Freudenthal compactification. Finally, generalising both Diestel's construction of and our construction of , we show that G can be compactified by every inverse limit of compactifications of the sets of components obtained by deleting a finite set of vertices. Diestel's is the finest such compactification, and our is the coarsest one. Both coincide if and only if all tangles are ends. This answers two questions of Diestel.     

New Exact Travelling Wave Solutions to Kundu Equation

Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.