多元弱酸(碱)溶液pH的简易通用计算方法

提出了计算多元弱酸(或碱)溶液pH的新方法.该计算方法具有以下特点:限制条件简单,即多项式中某一项小于最大项的5％即可忽略该项贡献;计算过程和步骤清晰易记;通用性好,一元或多元弱酸(碱)溶液pH计算均可适用.     

多元弱酸(碱)平衡体系中平衡型体浓度的精确数值解法

提出了在多元弱酸(碱)平衡体系中各种平衡型体浓度精确求解的新处理方法。抽象出一般性精确浓度数值解法的数学模型和算法框图。计算过程实用、新颖。     

CTMAB存在下钪多元络合物的研究

本文系统研究了在阳离子表面活性剂存在下钪与溴邻苯三酚红及三乙烯四胺形成多元络合物的条件，测定了络合物的最大吸收波长和摩尔吸光系数，确定了络合物的组成。并初步探讨了反应机理。     

改进的CPA法及其在多元稀土分析中的应用

本文基于吸光度矩阵的奇值分解，并利用广义逆代替ＣＰＡ法的通常求逆过程，改建了改进的ＣＰＡ法。算法中通过用样本的预测误差平方和（ＰＲＥＳＳ）合理地去吸光度中的实验误差，从而使系数矩阵Ｐ中元素的数值大为减小，提高了预测精度。本方法用于测定二元或三元混合稀土中单一稀土元素，结果满意。     

分析化学计量学的若干新进展

对分析化学计量学的若干新进展进行了讨论, 侧重从作者实验室所进行的研究工作的视角论述了高维数据的分辨、用于化学信号处理的形态学理论和方法、解决复杂化学问题的多元校正和化学模式识别以及联用色谱仪二维数据的分辨新方法的发展.     

构建法治主导下的中国社会秩序结构：多元规范和多元秩序的共存共治

构建一个适合于当代中国社会的社会秩序结构,是法学、政治学、社会学等诸多学科关注的重大理论和实践问题。一个国家和社会中的规范形态和社会秩序状态是相互照应的关系,有什么样的规范形态,便会有什么样的社会秩序状态。规范是社会秩序形成的必要要素,而社会秩序则是规范产生的结果,它们互为一体,互相照应,由此而形成一个色彩斑斓的规范和秩序的世界,主导着人们的生产和生活方式及其样态。在当代中国社会,存在着多元的规范形态,由此形成多元的社会秩序状态,针对这一客观现状,应当构建一个法治主导下的多元规范和多元秩序共存共治的中国社会秩序结构。     

多元统计描述中随机误差与变量空间角的关系

多元分析的误差传递需要一种简单、准确、数值化的表达方法.向量空间中,线性多元混合信号的随机误差可表述成真值子空间中随机向量的表现;由体系多元变量对应的向量构成的真值子空间中,被关注向量和其他向量子空间的空间角θ是描述多元体系的重要参数.如果被关注向量和其他向量子空间关系确定,体系总体误差呈正态分布,那么,被关注向量上误差也是正态分布,其多元统计分析结果的标准差与体系误差标准差的比值为1/(2·sin(θ/2),结论在构造算例和邻、间、对苯二酚混合体系的紫外光度分析中得到验证.     

叠加多元校正分析

基于多模型(模型融合)建模的思想,开发了两种新的叠加多元校正分析算法:叠加PCR(PLS)多元校正分析和叠加移动窗口PCR(PLS)多元校正分析。与一般的多模型建模方法不同的是其通过赋予光谱数据中的不同部分不同权重叠加子多元校正模型。因此,其可以通过权重调节或选择变量。在消除光谱数据中常见的冗余信息的同时,避免信息遗漏的缺点,并最终提高模型的稳健性,简化了模型。对于这两个新的算法,尽管其具体步骤不同,但仍取得了相似的预测结果。本文通过两套近红外光谱文献数据计算验证了这两个新方法的优越性。     

Evaluation of climatic factors on the yield and chemical composition of the essential oil of Myrocarpus frondosus

The species Myrocarpus frondosus is native to southern Brazil, and it is known as cabreúva. It is a large tree, and its wood is used as a reservoir for distilled spirits, especially Cachaça. In this pioneering work, the essential oil was extracted monthly from the leaves of M. frondosus, for a period of 1 year. The essential oil was extracted by using hydrodistillation and the determination of the chemical composition of essential oil was performed by using the chromatographic techniques GC-FID and GC–MS. Thirty-three compounds were identified in the essential oil and bicyclogermacrene was the major compound. Through multivariate analysis, it was determined that β-caryophyllene, limonene and terpinen-4-ol were directly proportional to climatic factors. The yield of the oil was directly proportional to temperature and radiation.     

Variability in the Chemical Composition of Myrcia sylvatica (G. Mey) DC. Essential Oils Growing in the Brazilian Amazon

Myrcia sylvatica (G. Mey) DC. is known as “insulin plant” because local communities use the infusions of various organs empirically to treat diabetes. The leaves of seven specimens of Myrcia sylvatica (Msy-01 to Msy-07) were collected in the Brazilian Amazon. Furthermore, the essential oils were extracted by hydrodistillation and analyzed by gas chromatography coupled to mass spectrometry, and their chemical compositions were submitted to multivariate analysis (Principal Component Analysis and Hierarchical Cluster Analysis). The multivariate analysis displayed the formation of four chemical profiles (chemotypes), described for the first time as follows: chemotype I (specimen Msy-01) was characterized by germacrene B (24.5%), γ-elemene (12.5%), and β-caryophyllene (10.0%); chemotype II (specimens Msy-03, -06 and -07) by spathulenol (11.1–16.0%), germacrene B (7.8–20.7%), and γ-elemene (2.9–7.6%); chemotype III (Msy-04 and -05) by spathulenol (9.8–10.1%), β-caryophyllene (2.5–10.1%), and δ-cadinene (4.8-5.6%); and chemotype IV, (Msy-02) by spathulenol (13.4%), caryophyllene oxide (15.0%), and α-cadinol (8.9%). There is a chemical variability in the essential oils of Myrcia sylvatica occurring in the Amazon region.     

Automated establishment and plotting of multivariate functions

The earlier package for univariate functions is extended to multivariate functions in the QQN series software, which contains millions of models. The models are characterized by numbered basic and compound functions which are selected by the user. Plots for a selected model are displayed in rotatablethree-dimensional coordinates. The package can be run on an IBM-PC or compatible computer.     

The differentiation and identification of pathogenic bacteria using FT-IR and multivariate statistical analysis

Correspondence analysis was used to classify the pattern-like FT-IR spectra of intact bacteria. The analysis was performed on a data set of approximately 80 normalized spectral derivatives of a selection of pathogenic bacteria. The correspondence analysis proved that the various different bacterial species were clustering in distinct regions of the correspondence maps suggesting that there do exist correlations between spectral data and biochemical/microbiological classification.     

Interpretation of geochemical data by the use of multivariate data analysis

Different strategies of multivariate data analysis are used to interpret a data base from geological samples. Cluster and correspondence analysis are applied to classify properly 34 chemical elements from 10 representative rock samples (volcanic series from Borovitsa, Rhodopa mountains, Bulgaria). Principal components analysis is also used as display method to visualize the relation between the variables and objects of interest. The multivariate data analysis applied makes it possible to interpret the origin and orogenesis of the samples.     

Multivariate analysis of a data matrix containing A-DNA and B-DNA dinucleoside monophosphate steps: Multidimensional Ramachandran plots for nucleic acids

A method to construct the equivalent of multidimensional Ramachandran plots for nucleic acids on the basis of singular value decomposition (SVD) is presented. For this purpose, a data matrix containing 244 DNA dinucleoside monophosphate steps, represented by nine torsion angles, was decomposed into a score and loading matrix. It is shown that biplots, containing both score points and loading vectors, provide a simple tool to interpret the principles of DNA class separation. Scores separate the data matrix into one A-DNA class, two different B-DNA classes, and one so-called crankshaft class. Loading vectors correlate torsion angles. The projections of scores on loading vectors indicate which torsion angles play a dominant role in DNA class separation. The results of the biplots are supported by (simple) physical interpretations. From a three-dimensional score space the nine original torsion angles can be reconstructed. Hence, the potential to create the multidimensional equivalent of a Ramachandran plot is available; that is, forbidden and accessible regions in the reduced space reflect these same regions in the nine-dimensional original space. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 695–715, 1998     

Quantification and methodology issues in multivariate analysis of ToF‐SIMS data for mixed organic systems

Multivariate methods, such as principal component analysis (PCA) and multivariate curve resolution (MCR), are often employed to aid the analysis of large complex data sets such as time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) images. There is, however, much confusion over the most appropriate choice of method for any given application and the effects of data preprocessing, which is exacerbated by the confusing terminologies and the use of jargon in this field. In the present study, a simple model system consisting of a ToF‐SIMS image of an immiscible polymer blend is used to evaluate PCA and MCR in the accurate identification, localisation and quantification of the phase‐separated polymer domains, using four data preprocessing methods (no scaling, normalisation, variance scaling and Poisson scaling). This highlights significant issues and challenges in the quantitative multivariate analysis of mixed organic systems, including the discrimination of chemically significant features from experimental noise, the resolution of weak chemical contributions and potential bias introduced by data preprocessing. Multivariate analysis using Poisson scaling, identified as the most suitable data preprocessing method for both PCA and MCR, demonstrates a marked improvement upon traditional (manual) analysis and provides valuable additional information that is difficult to detect using traditional analysis. Using these results, we present recommendations for the optimum use of multivariate analysis by analysts and provide guidance on selecting the most appropriate methods. Confusing terminology is also clarified. © Crown copyright 2008. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.     

N‐way modeling for wavelet filter determination in multivariate image analysis

When trying to analyze spatial relationships in image analysis, wavelets appear as one of the state‐of‐the‐art tools. However, image analysis is a problem‐dependent issue, and different applications might require different wavelets in order to gather the main sources of variation in the acquired images with respect to the specific task to be performed. This paper provides a methodology based on N‐way modeling for properly selecting the best wavelet choice to use or at least to provide a range of possible wavelet choices (in terms of families, filters, and decomposition levels), for each image and problem at hand. The methodology has been applied on two different data sets with exploratory and monitoring objectives. Copyright © 2015 John Wiley & Sons, Ltd.