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.     

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％。     

校正峰电位漂移偏最小二乘极谱催化波同时测定轻稀土

应用Ｍ２７３．Ａ电化学系统中的线性扫描技术，确定了８．０×１０－５ｍｏｌ／Ｌ二甲酚橙及ｐＨ４．０ＨＡｃ－ＮａＡｃ缓冲体系为偏最小二乘极谱法同时测定Ｌａ、Ｃｅ、Ｐｒ、Ｎｄ、Ｓｍ、Ｅｕ的最佳极谱体系。６种稀土元素的线性范围均在１．０× １０－７～１．２ × １０－５ｍｏｌ／Ｌ。并对极谱峰电位随浓度漂移进行了校正，提高了方法的准确度。     

偏最小二乘-速差动力学分光光度法同时测定杀虫剂残杀威和异丙威两组分

采用速差动力学分光光度法对氨基甲酸脂类杀虫剂残杀威和异丙威进行同时测定，这两种化 的能在碱性条件下水解生成酚盐，进而与对氨基苯酚及高碘酸钾的反应产物醌亚胺发生偶联反应，生成蓝色化合物。反应的速率适中，可用于动力学分析。实验采集了多个时间点下538－700nm间的动力学－吸光度数据，构成量测矩阵，并采用偏最小二乘（PLS）法对量测数据进行解析。本文还对合成样品和环境水样中的残杀威和异丙威含量进行测定，获较好的结果。     

Classifying Structural Characteristics to Enhance Computation of Enthalpy of Formation of Halohydrocarbons

Density functional theory (DFT) calculations are made and least squares calibration performed for various halohydrocabons, which were 27 straight‐chain alkyl halides, 20 branch‐chain alkyl halides and 19 aromatic halides, to determine their enthalpies of formation (ΔH_f). The mean absolute error (M. |A.E.|) in ΔH_f across 66 molecular computations was only 7.8 kJ/mol (1.9 kcal/mol). Grouping the molecules by their structural characteristics improved M. |A.E.| of ΔH_f by 0.2–2.2 kJ/mol over that obtained using corresponding modified data for the same 66 unclassified molecules.     

偏最小二乘光度法同时测定多种酚的研究及应用

利用Ｃｕ（Ⅱ）吡啶能与酚形成稳定的三元配合物的特点，研究了Ｃｕ（Ⅱ）－吡啶－酚三元显色新体系，并以偏最小二乘法建立模型预测，同时测定了模拟水样和环境水样中的对苯二酚、间苯二酚、邻苯三酚和对硝基苯酚，取得满意效果。     

傅里叶变换近红外光谱法测定大麦中蛋白质、淀粉和赖氨酸含量

采用傅里叶变换近红外光谱法测定大麦中蛋白质、淀粉、赖氨酸的含量，并用光谱影响值法(leverage)对异常值进行判断和处理。蛋白质、淀粉和赖氨酸含量近红外光谱分析模型的测定系数R。分别为0．985、0．973和0．978；检验集的化学值与模型预测值的相关系数r分别为0．9853、0．9644和0．9172，分析模型的预测相对标准偏差RSD分别为4．0％、2．4％和5．4％，该结果可替代经典分析方法，满足农产品快速分析的需要。     

声光可调-近红外光谱技术分析烟草主要化学成分

建立了声光可调-近红外光谱方法(AOTF-NIR)检测烟草主要化学成分的方法。应用AOTF-NIR光谱仪测定了不同地区、不同等级烟草样品的近红外光谱,用Unscrambler(定量分析软件将光谱与对应的化学成分值相关联,建立了烟草中总糖、还原糖、总烟碱和钾的回归模型。用这些模型对未知样品进行了预测。总糖、还原糖、总烟碱和钾模型预测的平均相对标准偏差分别为2.71%、3.13%、4.04%和6.42%。     

主成份分析-偏最小二乘法分光光度法同时测定钴、镍、铜、锌四组份体系

用 PCA 及 PLS 分步处理分光光度数据,有效降低了计算的维数。以该法对不同酸度体系的5-Br-PADAP-钴、镍、铜、锌分光光度数据进行了处理,定量分析结果良好。