Fourier-inversion and wavelet-transform methods applied to X-ray reflectometry and HRXRD profiles from complex thin-layered heterostructures

We show that X-ray scattering techniques can be used for the assessment of individual layer thicknesses inside complicated semi-conductor heterostructures dedicated to the opto-electronic domain. To this end, we propose methods to overcome two main drawbacks coming from: (1) the complexity of the X-ray profiles and, hence the difficulty to use model-dependent tools such as fitting procedures and (2) large dynamics in intensity due to numerous high diffraction superlattice peaks from superlattices which limit the use of the model-independent Fourier-inversion method.We demonstrate first the reliability of the Fourier-inversion method applied to high-resolution X-ray diffraction profiles curve from quantum well infrared photodetectors heterostructures, complementary to the model-dependent fitting tools. Then, a wavelet-transform-based procedure has been successfully used on X-ray reflectometry profiles containing intense SL Bragg peaks.     

方差分量模型参数的广义岭估计

本文先将方差分量模型的方差分量化为派生模型的均值参数，分别作出其相对于ＬＳＥ和ＢＬＵＥ的广义岭估计，再根据二步估计法作出原模型均值参数的广义二乘估计及其进行一步的岭估计。证明了这样不仅使方差分量估计的均方误差减少，而且使原模型均值参数估计的均方误差也不均加和地一步减少。本文还找到了岭参数仅仅依据于样本的估计，这样既将岭估计方法推进至方差分量模型，也改进了方差分量模型参数的离差均值对应方法。     

岭回归中确定K值方法的推广

给出了一种新的逐步改进岭参数 k的方法 .这种方法能够通过调整岭参数来进一步减少岭估计的均方误差 ,并改进了 Hoerl和 Kennard的结果 .     

Linear Discrimination with Adaptive Ridge Classification Rules

This article considers the use of adaptive ridge classification rules for classifying an observation as coming from one of two multivariate normal distributionsN(μ⁽¹⁾, Σ) andN(μ⁽²⁾, Σ). In particular, the asymptotic expected error rates for a general class of these rules are obtained and are compared with that of the usual linear discriminant rule.     

Entropy,Universal Coding,Approximation, and Bases Properties

We shall present here results concerning the metric entropy of spaces of linear and nonlinear approximation under very general conditions. Our first result computes the metric entropy of the linear and m-terms approximation classes according to a quasi-greedy basis verifying the Temlyakov property. This theorem shows that the second index r is not visible throughout the behavior of the metric entropy. However, metric entropy does discriminate between linear and nonlinear approximation. Our second result extends and refines a result obtained in a Hilbertian framework by Donoho, proving that under orthosymmetry conditions, m-terms approximation classes are characterized by the metric entropy. Since these theorems are given under the general context of quasi-greedy bases verifying the Temlyakov property, they have a large spectrum of applications. For instance, it is proved in the last section that they can be applied in the case of L _p norms for R ^d for 1 < p < \infty. We show that the lower bounds needed for this paper in fact follow from quite simple large deviation inequalities concerning hypergeometric or binomial distributions. To prove the upper bounds, we provide a very simple universal coding based on a thresholding-quantizing constructive procedure.     

小波变换用于植物激素重叠色谱峰中组分的定量分析

根据小波变换将信号按频率大小分解的性质，作者提出了一种用小波变换直接提取重叠色谱峰中单一组分信息的方法，并将其应用于植物激素混和体系重叠峰的解析与定量分析。结果表明：单组分的色谱信号经小波变换分解后仍能保持原有的线性关系，用小波变换从重叠信号中提取的单一组分信息也具有良好的线性关系。     

红外光谱数据的小波压缩和重建

介绍了小波变换及多分辨分析理论，并利用Ｄａｕｂｅｃｈｉｅｓ的正交紧支集小波基和Ｍａｌｌａｔ算法实现了对红外光谱数据的压缩和重建。计算表明，即使对原始数据压缩５倍，仍能很好地重建原有图谱，重建光谱数据与原始光谱数据之间的均方差为０．２６０。这为光谱数据的存储、检索和处理带来了方便。     

Wavelet Derivative: Application in Multicomponent Analysis of Electrochemical Signals

The wavelet derivative was developed for resolving overlapped signals in electrochemical analysis. It has been shown that the wavelet derivative could be used as an effective tool in resolution enhancement of the electrochemical signals. Since signal‐to‐noise ratio (SNR) does not degrade significantly at high order derivatives, the wavelet derivative is much better than the conventional numerical derivative in resolving practical signals with low SNR, particularly in the case when the overlapped degree of complex is high and high order derivatives are required for the further resolution enhancement. In this article, applications of the wavelet derivative in the voltammetric determination of small mounts of substances in the presence of large mounts of potentially interfering species are presented, and the advantages of this technique are discussed as well.     

Extracting robust and physically meaningful pitzer parameters for thermodynamic properties of electrolytes from experimental data. Ridge regression as an aid to the problem of intercorrelation

The Pitzer interaction model for thermodynamic properties of electrolytes is reevaluated in view of available regression techniques for the statistical inference of Pitzer parameters from experimental data. It is concluded that ordinary least squares regression is not generally suited, because of the intrinsic correlations among the various predictor variables in the Pitzer model. The predictor variables all are some function of the concentration of the electrolyte considered. Ridge regression, a mathematically only slightly different procedure designed to overcome the problem of intercorrelations, often yields more robust estimates for the Pitzer parameters. The potential of RR is demonstrated by some examples for the system GaCl₃–HCl. The ridge estimates are expected to be closer to the physically true parameter values.     

小波变换用于色谱重叠峰的解析

利用小波变换的时频局部化性质，通过对色谱重叠峰信号小波变换后的某些频率段进行放大，使重叠谱峰得到了分离，并将此方法用于苯和甲苯二组分色谱体系的定量分析，重叠峰中各组分均得到了良好的线性关系及令人满意的定量分析。本文还讨论了不同小波基、分解的次数及放大系数在解析结果的影响。