关于“序列号”方法的讨论

对于无放回抽样和有放回抽样两种情形,研究了"序列号"方法,给出并讨论了某些相关的估计量的优良性.     

采样窗口对光学系统MTF测量影响的研究

对光学系统MTF测试中采样窗口对其测量影响进行了研究。在对标准镜头MTF测试时,采用离散傅里叶变换计算,线扩散函数扫描方向长度为所选针孔像线扩散函数半高宽的5倍左右时,MTF测试结果与设计值差异极值为0．011;采用快速傅里叶变换计算,线扩散函数扫描方向长度为所选针孔像线扩散函数半高宽的5倍左右时,同时采样点数要满足2^N,测试结果与设计值差异极值为0．010。为了证明此结论的普适性,按所提的采样窗口选取原则,对大像差镜头轴上和轴外的MTF进行了试验,并将测试结果与OPTIKOS的测试结果进行对比,最大极差为0．013。试验结果表明,此结论能够为光学系统MTF测试时采样窗口选择提供依据。     

Efficient rare-event simulation for perpetuities

We consider perpetuities of the form

D=_B1exp(_Y1)+_B2exp(_Y1+_Y2)+?,$D=B_{1}exp\left(Y_1\right)+B_{2}exp(Y_1+Y_2)+?\text{,}$

where the _Yj$Y_j$’s and _Bj$B_j$’s might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the _Yj$Y_j$’s satisfy the so-called Cramér condition with associated root _θ∗∈(0,∞)${\theta }_{\ast }\in (0,\infty )$ and that the tails of the _Bj$B_j$’s are appropriately behaved so that D$D$ is regularly varying with index _θ∗${\theta }_{\ast }$. We illustrate by means of an example that the natural state-independent importance sampling estimator obtained by exponentially tilting the _Yj$Y_j$’s according to _θ∗${\theta }_{\ast }$ fails to provide an efficient estimator (in the sense of appropriately controlling the relative mean squared error as the tail probability of interest gets smaller). Then, we construct estimators based on state-dependent importance sampling that are rigorously shown to be efficient.     

Nonconforming spline collocation methods in irregular domains II: Error analysis

A nonconforming spline collocation method is investigated for elliptic PDEs in an irregular region with a triangular mesh. The existence and uniqueness of the spline collocation system and the optimal H¹ and L² ‐error analysis of the numerical solution are provided. Numerical experiments are presented to confirm the theoretical analysis and show the efficiency of this method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 441–456 2012     

Finite p-Groups with a Cyclic Subgroup of Index p3

We classify up to isomorphism those finite p-groups,for odd primes p,which contain a cyclic subgroup of index p3.     

连续性抽样调查理论研究综述

从国外近60多年来的理论及其应用研究情况来看,连续性抽样调查是一个具有极大理论研究价值的新领域,在我国也具有广阔的应用价值。本文选择连续性抽样调查作为研究对象,对国内外已有的相关研究成果进行理论化、系统化的研究综述,并重点总结了各类连续性抽样设计与抽样估计方法,进一步归纳出存在的问题及未来继续研究的新趋势,另外也为该理论在我国实际调查中的应用研究奠定扎实的理论基础,使我国统计调查工作少走弯路,尽快与国外统计调查工作接轨。     

大功率恒流源取样电阻设计

针对取样电阻在大功率恒流源中的作用和技术要求,在理论和实验上对取样电阻的设计原则、结构形式和材料选择方法进行了系统分析。对水冷式和自冷式两种结构形式的大功率恒流源取样电阻进行了比较研究,实验结果表明:相比于水冷式取样电阻情形,装配自冷式取样电阻的恒流源主要技术指标得到明显改善,输出电流失稳度降低2/3,纹波系数由2.7%降低到2.3%,使用寿命提高10倍以上。     

有源光纤环等效时间脉冲复制研究

对利用半导体光放大器有源光纤环为光等效时间采样提供低失真脉冲序列的方法进行了研究。分析了提高复制精度的辅助直流光非线性增益抑制方法,并给出基于递推方式,可进一步提高采样精度的后处理算法。通过实验验证了辅助直流光注入对复制器非线性增益的抑制作用;以及在不充分辅助直流光注入条件下,利用后处理算法抑制非线性误差的效果。结果显示利用半导体光放大器有源光纤环结合后处理算法可以有效地为光等效时间采样提供特性一致、误差可处理的时序脉冲序列。     

延迟基因开关体系的稳定性及转变动力学

对延迟基因开关体系的稳定性及转变动力学进行了系统的研究．通过前向流采样及延迟随机模拟方法,获得了相空间稳态分布、转变路径和速率以及转变态系综的分布等信息．数值结果表明,基因开关体系中的延迟会减小稳态之间的间距,增大体系在转变态的布居．此外,转变速率也会随着延迟时间的增大单调增加,这些现象都说明延迟会削弱双稳基因开关体系的稳定性．转变路径由两种转录因子蛋白质的总的粒子数的差和操纵子位点的状态来描述,对转变路径的数值分析表明转录和翻译过程导致的延迟会显著影响转变动力学．特别是对于转变态系综而言,操纵子结合两种不同二聚体概率的差异随着延迟时间的增加逐渐加大.     

Stochastic optimal design in multivariate stratified sampling

This work considers the allocation problem for multivariate stratified random sampling as a problem of integer non-linear stochastic multiobjective mathematical programming. With this goal in mind the asymptotic distribution of the vector of sample variances is studied. Two alternative approaches are suggested for solving the allocation problem for multivariate stratified random sampling. An example is presented by applying the different proposed techniques.