Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

Clustering Effect on the Statistical Estimation Accuracy of Distribution Density

The paper is devoted to statistical nonparametric estimation of multivariate distribution density. The influence of data pre-clustering on the estimation accuracy of multimodal density is analyzed by means of the Monte Carlo method. It is shown that the soft clustering is more advantageous than the hard one. While a moderate increase in the number of clusters also increases the calculation time, it considerably reduces the estimation error.     

Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.     

总延误问题顺时安排法的性能比

给定一组工件的加工时间与工期，要求确定这些工件在一台机器上的加．工排列，使相应的总延误达到最小，这就是总延误问题．该问题在近年已被证明是NP困难的．由Wilkermn和Irwin（1971），林勋（1983）等所研究的顺时安排法能得到相邻交换意义下的局部解．在本文中，我们进一步证明该算法能得到前移邻域意义下的局部解，并确定了该算法的性能比．     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

Reactions of mercury salts with benzo- and tetrafluorobenzobarrelenes

Regiochemistry and stereochemistry of the addition of mercury salts to benzobarrelene and tetrafluorobenzobarrelene have been studied in acetic acid and methanol. The effect of the substrate structure on the regiochemistry of the reaction is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1105–1108, June, 1994.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

光双二进制传输系统的性能研究

光双二进制信号的谱宽是传统二进制信号的一半,采用双二进制传输比二进制传输色散限制的中继距离可增加一倍.本文对采用传统光接收机的光双二进制传输系统用MATLAB进行了通信仿真.结果表明:在完全消光条件下,10 Gb/s双二进制信号在常规单模光纤上传输可达160 km,40 Gb/s双二进制信号在非零色散光纤上为30 km,均比二进制增加了一倍;详细考察了消光比对传输的影响,只有消光比大于25 dB时,双二进制相对于二进制传输的优越性才呈现出来.     

用不变速度推导卢瑟福散射公式

通过横向速度变换得到两种不变速度，由此推出卢瑟福散射公式。     

硅色敏器件对复色光色差辨识能力的数值分析

对复色光的光谱功率分布和色敏器件光谱响应的实验曲线进行了函数拟合，采用Mathematica 4．2计算了具有不同峰值波长和半高宽的高斯分布的复色光在色敏器件中产生的电流比．计算结果表明，待测复色光的峰值波长和半高宽变化对两种典型的色敏器件的输出信号影响的权重比分别为100：1和10：1。权重比说明色敏器件的输出电流比随峰值波长和半高宽的变化非常灵敏，但两者权重不同，其中峰值波长的变化影响更为显著，是影响复色光颜色变化的主要因素．数值分析的结果表明，硅双结色敏器件对复色光色差有良好的辨识能力．两种器件权重比的差异说明了器件制作工艺与其辨识能力的关系，为器件合理设计提供了理论依据．