Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives

N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics R^a based on power divergence. All R^a have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of R^a under local alternatives. We obtain an expression of approximation for the distribution of R^a under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of R^a. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of R^a. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance.     

Bestness of the parabola theorem for continued fractions

We show that the simple conditional convergence set

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fixed is maximal in the sense that if b is an arbitrary point in , then P{b} is not conditional convergence set.     

带电粒子束传输中横向发散的类ABCD定律

 傍轴近似下带电粒子束传输可完全类比于近轴光线椭圆高斯光束的传输。基于这种类比，建立了带电粒子束传输中横向发散的复曲率半径的类ABCD定律，引入了带电粒子在横向的复曲率半径的概念，并以复曲率半径的实部表征带电粒子束的敛散特性，虚部表征带电粒子束的束斑大小。由此提出：带电粒子束整体可被看作类椭圆高斯光束，其发射度与光束波长的作用相同。通过这种类比可知，在适宜的加速器环境下，理论上可能产生相干带电粒子束。     

有限温度下胶子场三圈真空图中的红外发散

用热传播子的实时形式对有限温度下胶子场的三圈真空图进行了详细的计算，在维数正规化方案下把真空图中的红外发散全部孤立出来了.     

Guiding Properties of a Tapered Photonic Crystal Fiber Compared with Those of a Tapered Single-Mode Fiber

We have fabricated tapered photonic crystal fibers using a fusion splicer and experimentally observed the near-field mode distribution and the beam divergence of it. We have also compared characteristics of the tapered photonic crystal fiber with those of a tapered standard single-mode fiber. Unlike a tapered standard single-mode fiber, the mode field profile of a tapered photonic crystal fiber shows a good confinement of its field within the core region. The numerical apertures of tapered photonic crystal fibers are increased as the diameter of the fiber is decreased.     

介质平面波导TE0模衍射场的光束参量

对于傍轴光束，提出了介质平面波导衍射场的近场模场半宽度、远场发散角半宽度和光束传输因子M^2等光束参量之间满足简单的关系式，三个光束参量均可直接由波导模式场分布精确计算，或由可实际精确测量的远场衍射频谱分布精确计算。M^2因子的计算公式可表述为以二阶矩和微分算子定义的近场模场半宽度的比值，或以二阶矩和微分算子定义的远场发散角半宽度的比值。最后推导出介质平面波导TE0模衍射场光束参量的解析函数和光束参量的范围。     

受激布里渊散射光束发散性的研究

利用耦合波方程分析了相位共轭效应和受激散射阈值效应对受激散射光发散角的影响.在甲醇、乙醇和丙酮的受激布里渊散射实验中,分别获得受激布里渊散射光发散角减小3.2、3.0和2.4倍,脉宽压缩4.3、4.3和2.6倍,并获得散射光束发散角随泵浦能量的变化关系.     

Tunneling resistivity of a one-dimensional random lattice and the petersburg problem

The resistivity of a one-dimensional lattice consisting of randomly distributed conducting and insulating sites is considered. Tunneling resistance of the form ₀ ne ^bn is assumed for a cluster ofn adjacent insulating sites. In the thermodynamic limit, the mean resistance per site diverges at the critical filling fractionp _c =e^–b, while the mean square resistivity fluctuations diverge at the lower filling fraction =p _c ² . Computer simulations of large but finite systems, however, show only a very weak divergence of resistivity atp _c and no divergence of the fluctuations at . For finite lattices, calculation of the resistivity at the critical filling is shown to be simply related to the Petersburg problem. Analytic expressions for the resistivity and resistivity fluctuations are obtained in agreement with the results of computer simulations.     

普通X—射线荧光光谱仪分辨率的改善

作为改善普通Ｘ－射线荧光光谱仪的分辨率和谱线的低能拖尾现象，于ＰＷ１４０４谱仪上加了可拆卸的限制垂直发散准直器（６．５×２０×５０ｍｍ，片间距０．６５ｍｍ）。实验结果表明，加了限制垂直发散准直器后，谱仪相对分辨率提高１０％，谱仪非对称因子由１．４－１．５改善为１．０－１．１８。为普通Ｘ－射线谱仪用于化学态分析提供了更为有利的条件。     

2μm InGaAsSb/AlGaAsSb双波导半导体激光器的结构设计

为了提高2μm InGaAsSb/AlGaAsSb半导体激光器的最大输出功率,减小远场垂直发散角并实现单模稳定输出,在非对称波导结构的基础上设计了具有双波导结构的2μm InGaAsSb/AlGaAsSb半导体激光器.同时,利用相关的物理模型及SimLastip程序语言构建了InGaAsSb/AlGaAsSb Macro文件,利用SimLastip软件对具有不同结构的2μm InGaAsSb/AlGaAsSb半导体激光器进行了数值模拟分析.研究结果表明,双波导结构可以将半导体激光器的有源区限制因子由0.019 2减小至0.011 3,器件的最大输出功率提高了1.7倍,远场垂直发散角由57°减小到48°,器件性能得到了改善.