Polyhydroxy pregnanes from Dregea volubilis

Three new polyhydroxy pregnanes named dregealol (1), volubilogenone (2) and volubilol (3) were isolated from the flowers of Dregea volubilis, and their structures elucidated from extensive 2D NMR analysis. The structure of volubilol (3) was confirmed by X-ray crystallographic studies. The known pregnane derivatives drevogenin D, iso-drevogenin P and 17α-marsdenin were also isolated.     

卡尔曼滤波紫外光度法同时测定饮料中苯甲酸及糖精的研究

在酸性条件下，用乙醚萃取、蒸干乙醚后，用ＮａＨＣＯ３溶解残渣，从复杂的样品中分离出苯甲酸和糖精，测定它们在２４５～２８１ｎｍ之间的紫外吸收，运用卡尔曼滤波算法计算两者的浓度，用新息序列监测干扰物质分离的程度。此法简化了许多分离手续，用于饮料分析，结果满意。     

Automated at-line solid-phase extraction-gas chromatographic analysis of micropollutants in water using the PrepStation

A fully automated at-line solid-phase extraction-gas chromatography procedure has been developed for the analysis of aqueous samples using the PrepStation. The sample extract is transferred from the sample preparation module to the gas chromatograph via an autosampler vial. With flame-ionization detection, limits of determination (S/N=10) of 0.05–0.13 μg/l were obtained for the analysis of HPLC-grade water when modifying the PrepStation by: (i) increasing the sample volume to 50 ml, (ii) increasing the injection volume up to 50 μl, and (iii) decreasing the desorption volume to 300 μl. The HP autosampler had to be modified to enable the automated “at-once” on-column injection of up to 50 μl of sample extract. The amount of packing material in the original cartridge had to be reduced to effect the decrease of the desorption volume. The total set-up did not require any further optimization after having set up the method once. The analytical characteristics of the organonitrogen and organophosphorus test analytes, i.e. recoveries (typically 75–105%), repeatability (2–8%) and linearity (0.09–3.0 μg/l) were satisfactory. The potential of the system was demonstrated by determining triazines and organophosphorus pesticides in river Rhine water at the 0.6 μg/l level using flame-ionization and mass-selective detection. No practical problems were observed during the analysis of more than 100 river water samples.     

Fluorinated nitroxides as ESR probes of solvation

Some newly synthesized fluorinated nitroxides, such as t-butyl perfluoroalkyl nitroxides Bu^tN(O) R_f (R_f=CF₃, 5; C₂F₅, 6; n-C₃F₇, 7) and s-butyl perfluoroacyl nitroxides Bu^sN(O) COR_f (R_f=CF₃, 9; n-C₃F₇, 10) have been employed as ESR probes of solvation in different common organic solvents. In aprotic solvents, the measured a_N values for each of the nitroxyl probes show a linear correlation with the cybotactic polar solvent parameters E_T (Dimroth) and Z (Kosowar), i.e. a_N=bE_T+c, and a_N=b′Z+c′. The physical significance for the slope (b or b′), the slope×E_T or slope×Z, the extrapolated intercept on a_N axis, c or c′, are linked, respectively, to the sensitivity of a specific nitroxide toward solvation, the magnitude of the overall solvation effect on the a_N value, and the intrinsic a_N value of each nitroxide in the ideal gaseous state. The intercept on the a_N axis may also serve as a new measure of electronegativity for perfluoroalkyl groups, CF₃, C₂F₅, n-C₃F₇, and perfluoroacyl groups, CF₃CO, n-C₃F₇CO. In protic solvents, i.e. alcohols and carboxylic acids, however, a_N values of all the probes, kept almost no change with the increase in E_T and Z. Furthermore, the plots of a_N versus non-cybotactic solvent constants, such as dipolar moment (μ) and dielectric constant (ε), all show random variations.     

New results on multi-dimensional linear discriminant analysis

Fisher linear discriminant analysis is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. In this paper we concentrate on three different formulations of the multi-dimensional problem. We provide a mathematical explanation why two of the formulations are equivalent and prove that this equivalency can be extended to a broader class of objective functions. The second contribution is a rate of convergence of a fixed point method for solving the third model.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

高维稳健主成分聚类方法及其应用研究

随着信息技术的高速发展,每条数据所包含的信息越来越丰富,使得数据不可避免地含有异常值,且随着维数的增加,异常值出现的可能性更大。传统的主成分聚类分析对异常值特別敏感,基于MCD估计的主成分聚类方法虽然对异常值具有防御作用,但是在高维数据下MCD估计的偏差过大,其稳健性显著降低,而且当维数大于观测值个数时MCD估计失效。为此本文提出了基于MRCD估计的稳健主成分聚类方法,数值模拟和实证分析表明,基于MRCD估计的主成分聚类分析的效果优于传统的主成分聚类分析和基于MCD估计的主成分聚类分析,尤其是在维数大于样本观测值的情况下,MRCD估计更为有效。     

考虑偏差值的中立型区间交叉效率研究

在不确定性环境下,当决策单元(DMU)的投入产出数据为区间数形式时,为解决决策单元之间既不是合作也不是竞争关系时的交叉评价问题,本文提出一种中立型区间交叉效率模型。从所有被评价者的角度出发解决评价权重的选取问题,以决策单元投入得分的平均偏差与产出得分的平均偏差之和最小化为目标,建立决策单元在最佳和最差两种生产状态下的中立型区间交叉效率模型。在本文提出的中立型模型视角下,DMU的投入得分平均偏差和产出得分平均偏差之和达到最小。算例结果表明该中立型区间交叉效率模型的有效性,解决了不确定性环境下的交叉评价问题,保证评价的客观公正,更加符合现实。     

含有偏好的DEA-BWM评价方法研究

针对传统的DEA模型在评估过程中并未考虑决策者对相关指标权重的偏好,将最优最差方法(BWM)嵌入到传统DEA模型中,基于决策者偏好排序的判断矩阵,构建一种含有偏好的DEA-BWM评价方法。首先在保持传统DEA方法的优势基础上,构建了CCR-BWM评价模型对各DMU进行评价。同时考虑为了便于各决策单元在统一权重基础上相互比较,构建了CSW-BWM公共权重模型。另外考虑决策单元自评和互评,构建了NCE-BWM中立型交叉效率。然后采用min-max方法分别将上述三种多目标评价模型转换为单目标线性规划进行求解。最后,选择一组算例对三种模型的有效性与合理性进行验证。