一个多元校正的稳健诊断新方法

提出一种新的稳健诊断方法，与最小二乘估计结合进行混合物光谱中非线性点的诊断。文中探讨了该方法的性能，用计算机数字模拟及实际多组分光谱体系夺其进行检验，展示了此诊断方法在分析化学计量学中实际应用的可行性。     

Chemometric analysis of groundwater quality data of alluvial aquifer of Gangetic plain, North India

Water quality data set from the alluvial region in the Gangetic plain in northern India, which is known for high fluoride levels in soil and groundwater, has been analysed by chemometric techniques, such as principal component analysis (PCA), discriminant analysis (DA) and partial least squares (PLS) in order to investigate the compositional differences between surface and groundwater samples, spatial variations in groundwater composition and influence of natural and anthropogenic factors. Trilinear plots of major ions showed that the groundwater in this region is mainly of Na/K-bicarbonate type. PCA performed on complete data matrix yielded six significant PCs explaining 65% of the data variance. Although, PCA rendered considerable data reduction, it could not clearly group and distinguish the sample types (dug well, hand-pump and surface water). However, a visible differentiation between the water samples pertaining to two watersheds (Khar and Loni) was obtained. DA identified six discriminating variables between surface and groundwater and also between different types of samples (dug well, hand pump and surface water). Distinct grouping of the surface and groundwater samples was achieved using the PLS technique. It further showed that the groundwater samples are dominated by variables having origin both in natural and anthropogenic sources in the region, whereas, variables of industrial origin dominate the surface water samples. It also suggested that the groundwater sources are contaminated with various industrial contaminants in the region.     

Determination of BHT in the presence of surfactants using a cellulose acetate coated electrode and square wave voltammetry

A direct voltammetric method for the rapid determination of butylated hydroxytoluene has been developed. The procedure utilizes a hydrolyzed cellulose acetate film in intimate contact with a glassy carbon electrode and square wave voltammetry. The coated electrode prevents passivation due to adsorption of polymeric oxidation products by way of a size exclusion principle. BHT solutions containing lipid-like surfactants can be analyzed without the need for frequent resurfacing of the electrode.     

Fermentation characteristics and the dynamic trend of chemical components during fermentation of Massa Medicata Fermentata

As a representative of traditionally fermented Chinese medicine, Massa Medicata Fermentata (MMF) shows the functions of invigorating the spleen and stomach and promoting digestion, which plays an important role in the treatment of gastrointestinal diseases. The fermentation mechanism and the key factors that affect the quality of MMF have not been revealed yet, which has become an urgent issue that limits its clinical application. This article aims to systematically and comprehensively reveal the transformation of physical properties and the dynamic trend of chemical components including substrate components, volatile components, and lactic acid as anaerobic fermentation product during MMF fermentation. Along with obvious hyphae growth observed for MMF, the weight of MMF decreased, and the moisture and temperature increased. Through the quantified 14 components from substrate, ferulic acid increased from 45.53 ± 6.94 to 141.89 ± 78.40 μg/g, while glycosides and phenolic acids declined except caffeic acid. Also, within the 66 volatile components analyzed, alcohols and acids increased, while aldehydes and ketones decreased. Lactic acid was not detected in the fermentation substrate, but an apparent increase in lactic acid content was observed along with the increased fermentation days, resulting in 2.54 ± 0.15 mg/g on day 8. Based on the tested components, the fermentation process of MMF was discriminated into three distinct stages by principal component analysis, and an optimal fermentation time of four days was proposed. The results of this study will be of great significance to clarify the characteristics of fermentation and conduce to improving quality standards of MMF.     

M-矩阵平方根的一类迭代法

矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.     

A law of the iterated logarithm for processes with independent increments

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A preconditioner for constrained and weighted least squares problems with Toeplitz structure

We study methods for solving the constrained and weighted least squares problem min _x by the preconditioned conjugate gradient (PCG) method. HereW = diag (₁, , _m ) with _{1 m} 0, andA ^T = [T ₁ ^T , ,T _k ^T ] with Toeplitz blocksT _l R ^{n × n} ,l = 1, ,k. It is well-known that this problem can be solved by solving anaugmented linear 2 × 2 block linear systemM +Ax =b, A ^T = 0, whereM =W ^–1. We will use the PCG method with circulant-like preconditioner for solving the system. We show that the spectrum of the preconditioned matrix is clustered around one. When the PCG method is applied to solve the system, we can expect a fast convergence rate.Research supported by HKRGC grants no. CUHK 178/93E and CUHK 316/94E.     

Cellular automata approach to site percolation on ℤ2. A numerical study

We present a cellular automata model as a new approach to Bernoulli site percolation on the square lattice. A new macroscopic quantity is defined and numerically computed at each level step of the automata dynamics. Its limit manifests a critical behavior at a value of the site occupancy probability quite close to those obtained for site percolation on ² with the best-known numerical methods.     

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.     

同时测定水溶液中葡萄糖、果糖和蔗糖的近红外光谱法

通过对27个葡萄糖、果糖和蔗糖水溶液的混合体系进行近红外光谱分析，建立了葡萄糖、果糖和蔗糖含量测定的偏最小二乘法(PLS)模型；葡萄糖、果糖和蔗糖的线性范围分别为0—300g/L、0—200g/L、0—300g/L，模型校正集的标准误差(SEC)分别为1．4、1．8、1．4g/L；用该模型对6个样品进行分析，葡萄糖、果糖和蔗糖含量测定的相对标准偏差(RSD)分别为1．2％、2．6％和1．8％。