<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.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.     

光学工程分析中的镜面面形处理新方法

光学系统在载荷的作用下会发生变形。基于干涉检验理论,提出了一种先调整后再拟合的处理方法。首先利用下山法计算光学镜面在法线方向的变形;然后利用Zernike多项式拟合变形曲面得到Zernike系数;最后去除刚体位移,作等高线图。新的数据处理方法可以更好的与干涉检验保持一致。对某相机的主镜进行仿真试验,结果表明,下山法计算效率较高,先调整后再拟合的处理结果与干涉检验结果的一致性较好。     

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.     

“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

光学系统光阑应用的实例

介绍了一种光学组合系统，通过构造光学系统虚拟的视场光阑实现人眼屈光度测量，它是光学系统光阑应用的生动实例.     

Studies on recoil proton tracks in NTA films with the T(d,n)He reaction

Recoil proton tracks in nuclear emulsion are counted by scanning them using strip, square or circular field of view of optical microscope. In this paper, the overestimate due to the edge effects in counting recoil proton tracks at different neutron energies produced from the T(d,n)⁴He reaction has been determined by measuring the true track density in NTA film. The overestimate has also been calculated using the measured value of the mean projected track length (L) in the film. The percentage of measured overestimates has been compared with those obtained by calculation and the results agree reasonably well. Fading effect in NTA film has been studied and found to be 22% more in the summer than in the winter season. A great reduction in fading rate could be achieved if the films are desiccated and sealed in highly pure dry nitrogen maintained at an over-pressure of 1000 Pa to reduce water vapour ingress. After the edge effect correction, the sensitivity of NTA film has been calculated from (1.72±0.08)×10⁻³ tracksn⁻¹ to (1.97±0.16)×10⁻³ tracksn⁻¹ in the neutron energy ranges from 15.91 to 18.88 MeV. The response was found to be from 0.24±0.02 trackscm⁻² permSv to 0.26±0.01 trackscm⁻² permSv in the same energy range.     

杨氏模量的不确定度评定

本文介绍杨氏模量的不确定度计算方法。