一类三参数混沌动力学系统模型及其在经济增长研究中的应用

从非线性自回归模型Xt+1=-αXtλ+1+βXt+γ出发,通过变量替换Xt=aYt,推出三参数混沌动力学系统模型Yt+1=kYt(1-Ytλ)+c;采用线性回归与非线性回归相结合的改进的混合法,对模型参数作了估计;实际研究表明,该模型可以用于对国内生产总值GDP增长的研究.     

Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.     

Design of recursive least-squares fixed-lag smoother using covariance information in linear continuous stochastic systems

This paper newly designs the recursive least-squares (RLS) fixed-lag smoother and filter using the covariance information in linear continuous-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The estimators require the covariance information of the signal and the variance of the observation noise. The auto-covariance function of the signal is expressed in the semi-degenerate kernel form.     

重整汽油近红外光谱的稳健偏最小二乘解析

近红外光谱(ＮＩＲ)光谱复杂,组分间光谱重叠严重,目前,多元线性回归(ＭｕｌｔｉｐｌｅＬｉｎｅａｒＲｅ ｇｒｅｓｓｉｏｎ,ＭＬＲ)和偏最小二乘法(ＰａｒｔｉａｌＬｅａｓｔ ｓｑｕａｒｅｓ,ＰＬＳ)是近红外光谱分析中使用最多和效果较好的方法[1]。稳健偏最小二乘(ＲｏｂｕｓｔＰａｒｔｉａｌＬｅａｓｔ Ｓｑｕａｒｅｓ,ＲＰＬＳ)是由稳健统计学构造的具有稳健性能的多元校正方法。当化学测量中引入随机异常点或误差的内在分布偏离正态分布时,它仍能给予接近最优性能的校正,确保分析结果的准确性,是消除奇异点的非常有效的方法[2-4],…     

Direct and simultaneous spectrofluorometric determination of naproxen and salicylate in human serum assisted by chemometric analysis

A direct method for the simultaneous determination of naproxen and salicylate in human serum is reported, based on a combination of spectrofluorometric measurements with two multivariate calibration techniques: partial least-squares (PLS-1) and the novel net analyte preprocessing (NAP). The method is rapid, selective and sensitive, and is based on the measurement of the fluorescence spectra of NH₃ alkalinized whole human sera at the excitation wavelength of 315 nm. It can be applied within the ranges of concentrations 50-200 ng ml⁻¹ for naproxen and 100-300 ng ml⁻¹ for salicylate. The employed chemometric techniques have been compared on the basis of the statistical indicators for calibration and validation. Reproducibility and interference studies in abnormal sera have also been carried out.     

胶束增溶光度法同时测定铂、铑、钯和金的研究

本文研究了贵金属Pt、Rh、Pd和Au在SnCl_2-BRB-AG-乳化剂OP离子缔合物体系中显色反应的条件,采用偏最小二乘回归法对上述体系重迭光谱进行解析及数据处理。结果表明,该体系灵敏度高,表观摩尔吸光系数可达1.74×10～6～2.47×10～6L·mol～-1·cm～-1;体系稳定性较好。应用本文方法对混合试样中Pt、Rh、Pd、Au进行同时测定,取得较满意的结果。     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

Multivariate calibration techniques applied to the spectrophotometric analysis of one-to-four component systems

The UV spectrophotometric analysis of a multicomponent mixture containing paracetamol, caffeine, tripelenamine and salicylamide by using multivariate calibration methods, such as principal component regression (PCR) and partial least-squares regression (PLS), was described. The calibration set was based on 47 reference samples, consisting of quaternary, ternary, binary and single-component mixtures, with the aim to develop models able to predict the concentrations of unknown samples containing as many as one-to-four components. The calibration models were optimized by an appropriate selection of the number of factors as well as wavelength ranges to be used for building up the data matrix and excluding any information about the interfering excipients included in pharmaceutics. The PCR and PLS models were compared and their predictive performance was inferred by a successful application to the assays of synthetic mixtures and pharmaceutical formulations.     

Measurement of lactate in whole human blood with near-infrared transmission spectroscopy

We have evaluated the potential of near-infrared spectroscopy (NIRS) as a technique for rapid analysis of lactate in whole blood. To test the NIRS technique, a comparison was made with a standard clinical method using whole blood samples taken from five exercising human subjects at three different stage of exercise. To expand lactate concentration within the physiological range, standard additions method was used to generate 45 unique data points. Spectra were collected over the 2050-2400 nm spectral range with a 1 mm optical path length quartz cell. Reference lactate concentrations in the samples were determined by enzymatic measurements. Estimates and calibration of the lactate concentration with NIRS was made using partial least squares (PLS) regression analysis and leave-N-out cross validation on second derivative spectra. Separate calibrations were determined from each of the subject samples and cumulative PRESS was used to determine the number of PLS factors in the final model. The results from the PLS model presented are generated from the five individual calibration coefficient vectors and provided a correlation coefficient of 0.978 and a standard error of cross validation of 0.65 mmol l⁻¹ between the enzymatic assay and the NIRS technique. To study the parameters that impact the spectra baseline and the correlation between the calculated model and the data, referenced measurements of lactate against baseline spectrum were made for each individual. A correlation coefficient of 0.992 and a standard error of cross validation of 0.21 mmol l⁻¹ were found. The results suggest that NIRS may provide a valuable tool to assess physiological status for both research and clinical needs.