Some remarks on multivariate stable distributions

This paper deals with multivariate stable distributions. Press has given an explicit algebraic representation of characteristic functions of such distributions [J. Multivariate Analysis2 (1972), 444–462]. We present counter-examples and correct proofs of some of the statements of Press. The properties of multivariate stable distributions, connected with the spectral measure Γ, present in the expression of the characteristic function, are studied.     

正相薄层色谱中常见人参皂甙结构与保留值之间关系的初步研究(英文)

 在硅胶薄层板上用氯仿-乙酸乙酯-甲醇-水(体积比为15∶40∶22∶10)作展开剂,测定了常见人参皂甙的Rf值。为了研究它们的结构与保留值之间的关系,对它们的17种结构参数进行了计算。除了拓扑指数和理化参数外,引入了代表构成人参皂甙的母体化合物种类并反映它们分子极性特征的新参数“E”。通过相关分析优化选出范德华分子表面积AW、拓扑指数0B和参数E,建立了多参数线性回归方程,较好地描述了在正相薄层色谱中常见人参皂甙结构与保留值之间的关系,并与人工神经网络方法进行了比较。     

Multivariate calibration: What is in chemometrics for the analytical chemist?

Chemometrics has been used for some 30 years but there is still need for disseminating the potential benefits to a wider audience. In this paper, we claim that proper analytical chemistry (1) must in fact incorporate a chemometric approach and (2) that there are several significant advantages of doing so. In order to explain this, an indirect route will be taken, where the most important benefits of chemometric methods are discussed using small illustrative examples. Emphasis will be on multivariate data analysis (for example calibration), whereas other parts of chemometrics such as experimental design will not be treated here. Four distinct aspects are treated in detail: noise reduction; handling of interferents; the exploratory aspect and the possible outlier control. Additionally, some new developments in chemometrics are described.     

Determination of carbendazim, thiabendazole and fuberidazole using a net analyte signal-based method

The net analyte signal (NAS)-based method HLA/GO, modification of the original hybrid linear analysis (HLA) method, has been used to determine carbendazim, fuberidazole and thiabendazole in water samples. This approach was used after a solid-phase extraction (SPE) step, using the native fluorescence emission spectra of real samples, previously standardized by piecewise direct standardization (PDS). The results obtained show that the modification of HLA performs in a similar way that partial least-squares method (PLS-1). The NAS concept was also used to calculate multivariate analytical figures of merit such as limit of detection, selectivity, sensitivity and analytical sensitivity (γ⁻¹). With this purpose, blanks of methanol and ternary mixtures, with the target analyte at low concentration and the other two ranging according to the calibration matrix, were used, with different results. Detection limits calculated in the last way are more realistic and show the influence of the other components in the sample. Selectivity for carbendazim is higher than the corresponding values for fuberidazole and thiabendazole, whereas sensitivity, as well as the values obtained for their detection limits, are lower for carbendazim, followed by thiabendazole and fuberidazole. Results obtained by modification of HLA vary in the same way that the ones obtained by PLS-1.     

Characterization and discrimination of pollen by Raman microscopy

The chemical characterization and discrimination of allergy-relevant pollen (common ragweed (Ambrosia artemisiifolia), white birch (Betula pendula), English oak (Quercus robur), and European linden (Tilia cordata)) has been studied by Raman microscopy. Spectra were obtained at different excitation wavelengths (514, 633, and 780 nm) and various methods were examined to minimize the strong fluorescence background. The use of a He–Ne laser (633 nm) for excitation yields high-quality single pollen Raman spectra, which contain multiple bands due to pollen components such as carotenoids, proteins, nucleic acids, carbohydrates, and lipids. Multivariate classification, i.e. principal component analysis (PCA) and hierarchical cluster analysis, demonstrated the validity of the approach for discrimination between different pollen species.     

Force field calculation for inplane vibrations of ethylene usingcndo/Force method

cndo/Force method is used to evaluate redundancy-free internal valence force field (rfivff) for inplane vibrations of ethylene. The bending force constants, the stretch-band and bend-bend interaction force constants are predicted reasonably well in magnitude and sign by this method; whereas stretching force constants and stretch-stretch interactions are overestimated. Initial force field is set up by transferring stretching force constants from structurally-related molecules and including the rest of the force constants fromcndo force field. The field so constructed is subjected to refinement by the least square method. A total of 64 vibrational frequencies of C₂H₄, C₂D₄, C₂H₂D₂ and their¹³C isotopic modifications are used to determine force field containing 15 parameters. The final force field is found to be reasonable on the basis of frequency fits, potential energy distribution and band assignments.     

Differential pulse voltammetric study of the complexation of Cd(II) by the phytochelatin (γ-Glu---Cys)2Gly assisted by multivariate curve resolution

A multivariate curve resolution method by alternating least-squares (MCR-ALS) is applied to differential pulse voltammograms measured on the Cd(II)+(γ-Glu---Cys)₂Gly system as a model of metal–phytochelatin interactions at concentrations of both components in the range 10⁻⁷–10⁻⁵ mol l⁻¹. The course of complexation is different when peptide is titrated with metal from that when metal is titrated with peptide. The combined analysis of both matrices from titrations of peptide with metal and of metal with peptide allowed the resolution of the system. The analysis of the resulting pure voltammograms and concentration profiles of the resolved components suggested the presence of four different types of bound Cd(II) and made possible the formulation of a complexation model.     

Molecular mechanics force field parameterization of the fluorescent probe rhodamine 6G using automated frequency matching

Novel single-molecule fluorescence experimental techniques have prompted a growing need to develop refined computational models of dye-tagged biomolecules. As a necessary first step towards useful molecular simulations of fluorescence-labeled biomolecules, we have derived a force field for the commonly used dye, rhodamine 6G (R6G). A novel automated method is used that includes fitting the molecular mechanics potential to both vibrational frequencies and eigenvector projections derived from quantum chemical calculations. The method is benchmarked on a series of aromatic molecules then applied to derive new parameters for R6G. The force field derived reproduces well the crystal structure of R6G.