Some Limit Theorems in Geometric Processes

Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n = 1, 2,…} for which there exists a real number a > 0, such that {an-1 Xn, n = 1,2, …} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.     

Technically optimal inspection policy with arithmetical adaption

A process is considered whose quality deteriorates accordingto a constant failure intensity . As in practice it can be difficultto estimate the true value of the purpose of this paper isto present a strategy which can be applied without knowing .In order to maximize the number of conforming items per timeunit perfect inspections and renewals are performed. The lengthof the inspection interval is described by an arithmetical sequenceand changes by the time depending on perceived assignable causes.Optimal adaptive control plans provide nearly the same performanceas in the case when is known.     

Adaptive Smoothing Method,Deterministically Computable Generalized Jacobians,and the Newton Method

In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations.     

Local Rules and Fitness Landscapes: A Catastrophe Model

This paper examines the imposition of local rules in five mail delivery centres of Australia Post. Local rules are patterns of behaviour used by subunits of an organization to optimise their payoff. These local rules may ultimately benefit the total organization. Fitness landscapes are used to examine the emergence of local rules in this workplace. This research examined the relationship between the time taken to sort the mail and the volume of this mail. Work rates show a clear catastrophe shift; that is, work rates suddenly drop when the volume of mail exceeds a certain level, as Postal Delivery Officers apply local rules to maximise gains inherent in the pay structures. Such behaviour is close to that predicted by Kauffman (1995) in computer simulations of lattices and may be indicative of the application of local rules in organizations. The implications of the use of local rules are that behaviour in social systems may be dictated by systemic and emergent processes which are outside immediate management control. A further implication is that organizations may be structured to a significant extent by such local rules.     

Integral representation of linear functionals on spaces of unbounded functions

Let be a vector lattice of real functions on a set with , and let be a linear positive functional on . Conditions are given which imply the representation , , for some bounded charge . As an application, for any bounded charge on a field , the dual of is shown to be isometrically isomorphic to a suitable space of bounded charges on . In addition, it is proved that, under one more assumption on , is the integral with respect to a -additive bounded charge.

     

用于白天自适应光学的波前探测方法分析

提出了两种视场偏移哈特曼波前传感器，用于探测白天条件下强背景中目标信号的波前信息.给出了哈特曼波前传感器子孔径中焦面上天光背景非均匀性分布特征的实验结果，详细分析了基于分光棱镜的双焦面视场偏移哈特曼波前传感器的探测误差，并通过基于倾斜镜的单焦面视场偏移哈特曼波前传感器实验给出了波前测量的结果，证明视场偏移哈特曼波前传感器能够精确、稳定的测量白天条件下目标信号的畸变波前信息，同时给出了其在白天条件下探测能力的估算结果及其受限因素，估算结果表明云南天文台的自适应光学系统在10 W/m²·sr天光背景条件下应用视场偏移哈特曼波前传感器能对5等星(可视星等值)目标进行准确的波前探测. 关键词： 自适应光学 波前传感器 白天工作 误差分析     

度量算符对Gauss编织态的本征作用及自旋几何

对圈量子引力中标架度量矩阵算符对Gauss编织态的作用为本征作用，提供了完整的证明.求得了全部标架度量矩阵算符的表示矩阵，及其期望值.利用自旋几何定理，在内腿颜色k=0和k=2两种情况下，算得了Gauss编织态顶角毗邻的4条腿(P=1)的相位位形切方向间的全部夹角，以及切矢量的长度. 关键词： 度量算符的表示矩阵 度量期望值 切方向间夹角 切矢量长度     

基于液晶光调制器的夏克-哈特曼波前探测技术

微透镜阵列是夏克-哈特曼波前探测器的关键器件。利用液晶器件的空间相位调制特性,可实现微透镜阵列功能,且具有孔径和焦距可变的优点。论述了基于液晶光调制的夏克-哈特曼波前探测校正技术的特征、技术进展、及应用前景。     

内腔自适应光学系统校正激光器畸变

固体激光器中,增益介质由于热沉积产生的热畸变严重影响了激光器的稳定性、输出功率和光束质量。研究了一种内腔自适应光学系统校正激光器腔内畸变的方法,利用微机电变形反射镜作为固体激光器的内腔全反射镜,通过控制变形镜的面型改善激光器输出光束的模式及功率。从腔外引入的一束信标光通过激光器内腔后反射出腔外,用波前探测器可测得激光器工作时腔内畸变对此信标光的影响,并通过搭建的自适应光学系统平台可闭环校正此畸变。实验结果表明,闭环校正后,激光器的输出功率提高了近3倍,且激光光束质量得到了明显的改善。     

基于微光机电系统的微光学自适应微镜的研究

提出了一种利用热应力改变镜面曲率的可调焦微光学自适应微镜。与传统自适应微镜相比,采用该原理制作的微镜具有驱动电压低和驱动力较大的优点,而且制作简单。以硅为基底进行了表面热氧化、光刻显影、HF酸刻蚀、KOH湿法刻蚀,溅射铝膜等微加工工艺的研究,获得硅铝双金属可调焦微反射镜4×4阵列,单元尺寸3 mm×3 mm,单晶硅基底厚60μm,硅表面溅射的铝膜厚150 nm。该微镜的镜面填充率为100%,可变形镜面占总镜面面积的79%。利用激光波面干涉仪对可调焦微反射镜的动态性能进行了测试。实验表明,该微镜可产生单向连续变形,最大变形量15.8μm,非线性滞后27%,工作电压0~2.5V,可调焦范围∞~0.036 m。