多元线性回归应用于近代物理实验

本文介绍非线性方程转化直线性方程和多元线性回归法来分析近代物理实验中塞曼效应分裂干涉圆环多处选点测量的处理过程。     

Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

多指标区间决策的理想点贴近法

研究了指标的权重不能完全确定但知道其所在区域的条件下的多指标决策问题 ,给出了方案与理想解的贴近度及其算法 ,按贴近度的大小可以对方案进行排序 .它同传统的决策方法相比较 ,具有需要信息量少 ,简单可靠等特点 .最后用该决策方法分析了一个实际问题 .     

A Generalized Markov Sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis–Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.     

Quantitative assessment of solid oxide electrochemical doping

Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al₂O₃ (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al₂O₃ and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi₂Sr₂CaCu₂O_y (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm⁻²). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm⁻²). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount.     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

指数型寿命数据中异常值的检验

本文讨论了在指数型寿命数据中,对同时存在的异常大数据和异常小数据的检验方法,给出了一个明确的判别标准,并以一例说明其应用。     

一些新的数论函数及其均值公式

对于给定的自然数m,我们利用最大公约数和最小公倍数定义数论函数(m,n)和[m,n]/m.本文主要目的是研究这两个新的函数的渐近性质,利用解析方法得到这两个函数的几个渐近公式.     

Energy levels in doped SiGe quantum well studied by admittance spectroscopy

SiGe/Si quantum wells (QWs) with different Boron doping concentrations were grown by molecular beam epitaxy (MBE) on p-type Si(1 0 0) substrate. The activation energies of the heavily holes in ground states of QWs, which correspond to the energy differences between the heavy hole ground states and Si valence band, were measured by admittance spectroscopy. It is found that the activation energy in a heavily doped QW increases with doping concentration, which can be understood by the band alignment changes due to the doping in the QWs. Also, it is found that the activation energy in a QW with a doping concentration of 2 × 10²⁰ cm⁻³ becomes larger after annealing at a temperature of 685 °C, which is attributed to more Boron atoms activation in the QW by annealing.