具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．     

同输入M/M/∞排队群的联合队长过程

本提出一个偏微分方程方法，用这一方法研究同输入M/M／∞排队群中的联合队长分布。在任意初始条件下，给出了瞬时联合队长分布的多元母函数，也讨论了稳态队长的联合分布及各排队系统之间的相关性。     

Design and fabrication of fluid controlled dynamic optical lens system

A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.3° could be achieved. The smallest f-number (f_/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35.     

Stability of Markovian structure observed in high frequency foreign exchange data

Contrary to the common sense in economics and financial engineering, price fluctuations at very fine level of motion exhibit various evidences against the efficient market hypothesis. We attempt to investigate this issue by studying extensive amount of foreign currency exchange data for over five years at the finest level of resolution. We specifically focus on the proposed stability in binomial conditional probabilities originally found in much smaller examples of financial time series. In order to handle very large data, we have written an efficient program in C that automatically generates those conditional probabilities. It is found that the stability is maintained for extremely large time duration that covers almost the entire period. Based on the length of conditions for which the conditional probabilities are distinguishable each other, we identify the length of memory being less than 3 movements.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

高灵敏可见／紫外条纹相机的最小可探测能量密度

分析了影响条纹相机最小可探测能量密度的主要因素，通过采用两级增强器级联的方法降低了条纹最小可探测能量密度。利用超短激光脉冲经过标准具后形成一个能量等比衰减的脉冲序列，对ＺＰＴ－３Ｋ紫外／可见皮秒条纹相机的最小可探测能量密度进行了测量。测量表明：相机最小可探测能量密度在可见波段（５３２ｎｍ）达１×１０－１３Ｊ／ｃｍ２。     

L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

第Ⅰ种强度不对称三态叠加多模叠加态光场N次方Y压缩—第一正交相位分量的压缩情况

根据量子力学中的线性叠加原理,构造了由三个强度不等的多模相干态光场|{Z_j^(A)}>_q、|{Z_j^(B)}>_q和|{Z_j^(C)}>_q的线性叠加所组成的第Ⅰ种强度不对称三态叠加多模叠加态光场|ψ_l^(ABC)>_q.利用多模压缩态理论,研究了态|ψ_l^(ABC)>_q的第一正交方分量(即磁场分量)的广义非线性等幂次N次方Y压缩特性.结果发现:①在上述各多模相干态光场中各模的强度和各模的初始相位各不相等的情况下,态|ψ_l^(ABC)>_q的第一正交分量-磁场分量在一定的条件下,总可呈现出周期性变化的、任意等幂次的N次方Y压缩效应;②当上述各多模相干态光场的强度和各模的初始相位相等时,态|ψ_l^(ABC)>_q的磁场分量的N次方Y压缩现象消失,态|ψ_l^(ABC)>_q可恒处于等幂次N-Y最小测不准态.     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

A decomposition result for a class of polling models

Boxma and Groenendijk have shown that the workload in polling models decomposes into two independent variables. This paper demonstrates a different type of decomposition that has an explicit multi-dimensional form. This decomposition does not apply to all polling models, but does, for example, apply to models with constant switch-over times and either exhaustive or gated service disciplines. For such models, we show that the population of customers present in the system (represented by a vector indicating the number of customers at each queue) at key time points breaks into two independent subpopulations: (1) the population of customers present in the related model with zero switch-over times; (2) another population, which is particularly easy to analyze. This result has a number of theoretical and applied implications.