秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix

A non-linear structure preserving matrix method for the computation of a structured low rank approximation of the Sylvester resultant matrix S(f,g) of two inexact polynomials f=f(y) and g=g(y) is considered in this paper. It is shown that considerably improved results are obtained when f(y) and g(y) are processed prior to the computation of , and that these preprocessing operations introduce two parameters. These parameters can either be held constant during the computation of , which leads to a linear structure preserving matrix method, or they can be incremented during the computation of , which leads to a non-linear structure preserving matrix method. It is shown that the non-linear method yields a better structured low rank approximation of S(f,g) and that the assignment of f(y) and g(y) is important because may be a good structured low rank approximation of S(f,g), but may be a poor structured low rank approximation of S(g,f) because its numerical rank is not defined. Examples that illustrate the differences between the linear and non-linear structure preserving matrix methods, and the importance of the assignment of f(y) and g(y), are shown.     

秩函数在研究独立空间拥有一对互斥基的特征上之作用

利用秩函数,本文给出如何判定一个独立空间拥有一对互斥基的一些充要条件.其目的是回答这样一个公开问题:在什么条件下,一个独立空间可以拥有一对互斥基.该问题是Welsh于1976年提出的.     

中国海洋经济可持续发展能力省际空间差异研究——基于组合综合评价方法

海洋经济可持续发展是实现海洋经济强国发展战略的重要手段,定量评价海洋经济可持续发展水平及其特征是合理开发海洋资源、发展海洋经济的重要保证.在构建我国海洋经济可持续发展能力评价指标体系基础上,运用组合综合评价方法定量分析我国11个沿海地区海洋经济可持续发展类型及其发展对策.     

非参数秩检验在宿舍因素对学风影响中的应用

学风建设是大学教育教学管理中的重要环节,对学生的学习成绩、顺利毕业和就业等都有至关重要的影响。宿舍是学生学习和生活的重要场所,本文应用非参数统计秩检验和中位数检验研究了宿舍对学生学业成绩的影响,得到目前大学宿舍因素对学生学业成绩的影响高度显著,进而建议高等学校应加强学生宿舍管理,把宿舍作为学风建设的重要环节。     

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Median absolute deviation (MAD) is a well‐established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F‐tests, extensive calibration tables, time‐consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

Rank annihilation factor analysis for multicomponent kinetic‐spectrophotometric determination using difference spectra

In this work rank annihilation factor analysis (RAFA) is used to analyze difference spectra of kinetic‐spectrophotometric data. Annihilation of the contribution of one chemical component from the original data matrix is a general method in RAFA. However, sometimes RAFA is not suitable for studying rank deficient data such as kinetic‐spectrophotometric measurements. On the other hand, in order to apply RAFA for the determination of an analyte in an unknown sample, a standard two‐way matrix of the analyte with rank one should generally be available. This is not usually attainable for kinetic‐spectrophotometric monitoring of complexation reactions. Processes monitored by difference spectroscopy always have the spectrum of the initial stage subtracted from each spectrum in the data matrix. In this work we show that, for kinetic‐spectrophotometric data of complexation reactions, the spectrum of ligand (reactant) itself can be used as initial spectrum for subtraction. The obtained difference matrix of sample and that of analyte of interest will be full‐rank and rank 1, respectively. Therefore the system can be analyzed by RAFA. The proposed method was investigated with simulated data at the first stage. The method was then applied in the analysis of experimental kinetic‐spectrophotometric data of a complexation reactions of Co(II) and Ni(II) with chromogenic reagent 1‐(2‐pyridylazo) 2‐naphthol in order to do multi‐component determination of these ions in various real samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Non-trivially graded self-dual fusion categories of rank 4

Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K(C) of C; that is, we prove that K(C)≌Fib■Z[Z_2],where Fib is the Fibonacci fusion ring and Z[Z_2] is the group ring on Z_2. In particular, if C is braided,then it is equivalent to Fib Ve■cω_(Z_2) as fusion categories, where Fib is a Fibonacci category and VecωZ_2 is a rank 2 pointed fusion category.     

Differentiation of 18O‐ and 16O‐rich layers in anodic alumina films by glow discharge time‐of‐flight mass spectroscopy

The performance of glow discharge time‐of‐flight mass spectrometry in isotopic differentiation is revealed using the distribution of oxygen isotopes ¹⁶O and ¹⁸O in barrier‐type anodic alumina films as a focus. Anodic alumina films comprising ¹⁸O‐rich layers of controlled thickness were formed by the appropriate combination of anodising of superpure aluminium in electrolytes enriched with ¹⁸O isotopes and of natural abundance of ¹⁸O isotopes. Analysis of the elemental depth profiles of selected ionic species, i.e. ¹⁶O¹⁸O, allowed determination of the locations of the ¹⁸O‐rich layers and the ¹⁸O/¹⁶O interface. Copyright © 2010 John Wiley & Sons, Ltd.     

First approach based on direct ultrasonic assisted enzymatic digestion and capillary-high performance liquid chromatography for the peptide mapping of soybean proteins

This work proposes, for the first time, the use of a high intensity ultrasonic probe to accelerate the tryptic digestion of soybean proteins. Different digestion parameters were optimized: protein extracting solution, reduction, and alkylation conditions (time, concentration, and temperature), trypsin:protein ratio, and ultrasonic conditions (sonication amplitude and time). Separation of peptide profiles was carried out by capillary-HPLC. The effect of the variation of chromatographic conditions (elution gradient, column temperature, and injection volume) on peptide separation was also studied using two capillary-HPLC columns with different column diameters and particle sizes. Moreover, samples were focused at the top of the column in order to obtain an increasing sensitivity without loss of efficiency. This method was successfully applied to the profiling of soybean peptides from transgenic and non-transgenic soybeans and from different pigmented beans commercialized as soybeans.