Moderate Deviations for M-estimators in Linear Models with φ-mixing Errors

In this paper, the moderate deviations for the M-estimators of regression parameter in a linear model are obtained when the errors form a strictly stationary φ-mixing sequence. The results are applied to study many different types of M-estimators such as Huber's estimator, Lp-regression estimator, least squares estimator and least absolute deviation estimator.     

基于飞秒光学频率梳的大尺寸精密测距综述

飞秒光学频率梳的出现对时间频率技术和光谱学技术产生了深远重大的影响,由此衍生的飞秒光学频率梳绝对测距技术以其快速、大尺寸、高精度等优点已成为国际研究热点,并有望直接应用于大装备制造、激光雷达和卫星编队飞行等大尺寸精密测距。在简要阐述飞秒光学频率梳的原理特性及主要应用的基础上,围绕光梳测距的发展历程及前沿方向,着重介绍了飞秒光梳精密测距近两年来的最新研究进展,并对该技术进行了总结和展望。     

Synthesis of Four Enantiomers of (1-Amino-3-Hydroxypropane-1,3-Diyl)Diphosphonic Acid as Diphosphonate Analogues of 4-Hydroxyglutamic Acid

All the enantiomers of (1-amino-3-hydroxypropane-1,3-diyl)diphosphonic acid, newly design phosphonate analogues of 4-hydroxyglutamic acids, were obtained. The synthetic strategy involved Abramov reactions of diethyl (R)- and (S)-1-(N-Boc-amino)-3-oxopropylphosphonates with diethyl phosphite, separation of diastereoisomeric [1-(N-Boc-amino)-3-hydroxypropane-1,3-diyl]diphosphonates as O-protected esters, followed by their hydrolysis to the enantiomeric phosphonic acids. The absolute configuration of the enantiomeric phosphonates was established by comparing the ³¹P NMR chemical shifts of respective (S)-O-methylmandelic acid esters obtained from respective pairs of syn- and anti-[1-(N-Boc-amino)-3-hydroxypropane-1,3-diyl]diphosphonates according to the Spilling rule.     

柯西分布的参数估计

研究了柯西分布的参数估计问题,给出了位置参数的最小一乘估计和尺度参数的低阶矩估计.证明了柯西分布位置参数的最小一乘估计具有渐近无偏性与强相合性;尺度参数的低阶矩估计具有强相合性.     

一种新型多波长绝对距离干涉测量系统的研究

介绍了一种新型多波长绝对距离干涉测量系统。系统采用633nm的双纵模He-Ne激光器和629nm的He-Ne激光器,组成三级合成波长链对较大距离进行精密测量,并作了误差分析。系统采用高稳定度的声光晶体对各波长分别进行偏频,再用外差探测法测量出光束通过参考光路和测量光路后的位相差。简要介绍了629nm的He-Ne激光器的设计方案。     

椭圆形平面镜的高精度面形重构技术

为了实现大口径椭圆形光学平面镜的高精度面形测量,提升大口径望远镜系统的像质,本文对椭圆形平面反射镜面形的绝对检测算法进行了研究。首先,对椭圆形镜面进行了多项式正交化拟合研究。接着,对绝对检测算法进行了理论研究,利用正交化绝对检测算法可以有效分离参考镜与待测镜的面形误差,从而实现待测椭圆形平面镜面的高精度面形重构。为了证明上述方法的实际检测精度,本文对250 mm×300 mm的椭圆形镜面进行了绝对检测模拟与检测实验。对参考镜面形精度不高的情况进行了仿真计算,实验中利用光阑在Zygo300 mm口径标准平面镜头中选取250 mm×300 mm椭圆形检测区域,采用150 mm口径Zygo干涉仪对上述椭圆形区域完成绝对检测,并基于上述正交化绝对检测算法对椭圆形平面镜实现了面形重构。实验结果表明,利用本文所述方法可以实现参考镜与椭圆形待测镜面的面形误差分离,绝对检测结果的残差图RMS(Root-mean square)值为0.29 nm,证明了本文所述方法的可行性。利用上述方法可以实现椭圆形平面反射镜的高精度面形重构。     

On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations

This paper continues to study the explicit two-stage fourth-order accurate time discretizations [5-7]. By introducing variable weights, we propose a class of more general explicit one-step two-stage time discretizations, which are different from the existing methods, e.g. the Euler methods, Runge-Kutta methods, and multistage multiderivative methods etc. We study the absolute stability, the stability interval, and the intersection between the imaginary axis and the absolute stability region. Our results show that our two-stage time discretizations can be fourth-order accurate conditionally, the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth- or fifth-order Runge-Kutta method, and the interval of absolute stability can be almost twice as much as the latter. Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.