On the identification of Wiener-Hopf factors

This note is concerned with the identification of the Wiener-Hopf factors of a function 1–f, wheref generates an aperiodic distribution on the integers with a negative mean. The general and rational cases are addressed. We give a concise summary of the main practical facts needed for calculations involving the Wiener-Hopf factors. The basic facts are cited from the literature, but a few aspects are briefly proven here.Supported by the European grant BRA-QMIPS of CEC DG XIII.     

弱吸收基底上弱吸收薄膜的光学常数计算方法

采用一种相对简单而又精确的光度法来计算弱吸收基底上弱吸收薄膜的光学常数,为低损耗紫外薄膜的设计与实现提供了理论基础。采用JGS1型熔融石英基底,制备了MgF2与LaF3材料的单层膜,获得了JGS1型熔融石英基底及MgF2与LaF3薄膜的光学常数色散曲线。结果显示:在200 nm左右处,JGS1型熔融石英基底的吸收已经比较明显,消光系数在10-8量级,因此,应考虑基底的弱吸收,以提高薄膜光学常数的计算精度。     

预处理对355nm激光作用下熔石英损伤增长的影响

测试了经化学蚀刻、紫外激光预处理及其共同处理后的熔石英355 nm激光损伤阈值;研究了处理前后其损伤斑面积随激光辐照脉冲数的增长情况。结果表明,处理后熔石英355 nm激光损伤阈值得到了提高,且损伤斑面积增长变慢。利用CO2激光对熔石英表面损伤点进行了修复处理,修复后的损伤点R-on-1抗损伤阈值和基底阈值相当,损伤增长得到有效抑制。     

纳米TiO_2薄膜的低温等离子体制备技术

以四氯化钛为源物质,氩气为载气,氧气为反应气体,利用低温等离子体增强化学气相沉积在硅基表面制备出了TiO2薄膜。使用场发射扫描电子显微镜、X射线衍射仪等检测分析表征TiO2薄膜的性能与性质,并探讨了工艺条件如基片材料、沉积时间和基片温度对薄膜性能的影响。结果表明:制备的薄膜表面光滑均匀,结构致密,最小晶粒尺寸约15 nm;薄膜的晶型主要依赖于沉积温度,低于300℃沉积的薄膜是无定形的,300℃之上沉积的薄膜是锐钛矿结构。     

Lorentz-Minkowski空间中旋转W超曲面

1841年,D elaunay获得如下定理:如果在一平面上沿定直线滚动一条二次圆锥直线,然后将其焦点的轨迹绕定直线旋转,则所得到的曲面具有常数平均曲率,反之,所有旋转常数平均曲率曲面(除球面外)都有如此构造.本文将以上的D elaunay定理推广到Lorentz-M inkow sk i空间Rn1 1中类空的Sm型旋转W超曲面.     

A combinatorial problem from sooner waiting time problems with run and frequency quotas

In this paper, we study the problem of finding the number of integer solutions solving

     

Toeplitz-Bezout矩阵的若干性质

从定义出发,利用矩阵生成函数的方法来研究Toeplitz-Bezout若干基本性质,同时利用极限的思想将其对角约化.     

基于多重工作休假的成批到达离散时间排队的性能分析

研究了一个成批到达的离散时间 Geom$^{[X]}$/Geom/1 多重工作休假排队. 首先,建立了模型的二维马尔可夫链,利用矩阵分析的方法, 导出了稳态队长复杂的概率母函数. 其次, 为了展示此模型与经典无休假Geom$^{[X]}$/Geom/1排队的联系, 给出稳态队长的随机分解结果. 尤其重要的是,发现了条件负二项分布的双参数加法定理, 利用这些结论,得到了矩母函数序下的稳态等待时间的上下界. 进一步,求出了平均队长和平均等待时间的上下界. 最后,提出一些数值例子以验证结论.     

Vertices of given degree in series‐parallel graphs

We show that the numbers of vertices of a given degree k ≥ 1 in several kinds of series‐parallel labeled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labeled planar graphs. The proof method is based on generating functions and singularity analysis. In particular, we need systems of equations for multivariate generating functions and transfer results for singular representations of analytic functions. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

一类限制m元over-分拆同余式

We discuss a family of restricted m-ary overpartition functions bm,j （n）, which is the number of m-ary overpartitions of n with at most i ＋ j copies of the non-overlined part m^i allowed, and obtain a family of congruences for bm,lm-1 （n）.