角锥棱镜的直角面面形问题

从一个侧面论述了角锥棱镜直角面面形误差所导致的出射波面像差及两面直角误差之间的定量关系 ,因而可以分别从后两者的精度要求提出对面形误差的要求。对于高精度的角锥棱镜 ,直角面面形问题应如同两面直角误差一样受到重视和关注     

薄透镜焦距测定的改进及误差分析

本文通过对薄透镜距测量的改进，并以薄透镜焦距测量为例进行误差分析及讨论．恰当地运用数学工具对观测数据做出科学的分析处理，获得正确的结论，对提高实验能力和运用误差理论来处理实验数据起到很大作用．     

关于Fejer算子的逼近度

用Ｋｎ记Ｆｅｊｅｒ算子的逼近度．本文证明是单调增加的，而且     

关于Lipschitz强增生算子的迭代程序

本文在一般的Ｂａｎａｃｈ空间中讨论Ｌｉｐｓｃｈｉｔｚ强增生算子方程解和严格伪压缩算子不动点的迭代逼近问题．我们的结果统一和推广了Ｄｅｎｇ，Ｌｉｕ，Ｔａｎ和Ｘｕ的结果，完整地回答了Ｃｈｉｄｕｍｅ提出的公开问题．     

On the longest circuit in an alterable digraph

Analterable digraph is a digraph with a subset of its edges marked alterable and their orientations left undecided. We say that an alterable digraph has an invariant ofk on the length of the longest circuit if it has a circuit of length at leastk regardless of the orientations over its alterable edges. Computing the maximum invariant on the length of the longest circuit in an alterable digraph is aglobal optimization problem. We show that it is hard to approximate the global optimal solution for the maximum invariant problem.Research supported in part by NSF grant CCR 9121472.     

中子与90,91,92,94Zr反应的理论计算和分析

根据中子与天然Zr及其同位素反应的总截面,去弹截面和弹性散射角分布的实验数据,得到一组普适的光学模型势参数;应用得到的光学模型势参数,光学模型,Hauser-Feshbach理论,预平衡反应的激子模型和扭曲波玻恩近似理论,系统计算和分析了中子与^90,91,92,94Zr反应的非弹散射角分布和双微分截面,理论结果与实验很好的一致.     

Unification of basic and composite nondifferentiable optimization

There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages.     

一类抛物型方程初值问题的随机数值算法

本文引入了求解二阶拟线性抛物型微分方程初值问题的一类新的数值算法一分层方法,这种数值方法是通过弱显式欧拉法离散其方程解的概率表示而得到的,相应地给出了该分层方法的收敛性结果.此外,还构造了基于插值的数值算法,最后提供了数值实验,得到的数值结果验证了获得的算法的精确性和有效性.     

On the choice of approximations in direct problems of nozzle design

Two problems are considered: the design of a supersonic nozzle with a uniform exit characteristic and the design of a subsonic nozzle part with a plane (straight) sonic line in the minimum cross section. It is shown how the choice of a nozzle profile approximation affects the direct solutions to variational gas dynamics problems. The nozzle profile is described by polynomials or splines (quadratic, cubic, rational). The varied variables are the profile’s expansion coefficients in terms of basis functions or the parameters to be interpolated. It is shown that a priori information on the monotonicity of the desired profile improves the efficiency of the solution.     

干涉显微镜中相移误差分析

相移误差是影响干涉显微镜测量表面形貌精度的主要因素之一。介绍了四帧算法、五帧算法、四帧免疫算法、五帧免疫算法的原理和计算公式 ,并对其特点进行了分析比较。利用自行研制的带旋转检偏器的干涉显微测量系统 ,分别用四种算法对Ra=0 35μm和Ra=0 .0 9μm粗糙度样块进行了实测。结果表明 ,五帧算法的重复测量精度优于0 5nm ,五帧免疫算法的重复测量精度优于 0 3nm。同时对在普通干涉显微镜上进一步提高其测量精度做了初步探讨