A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems

In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.     

Multiple comparisons with a control in direction-mixed families of hypothesis under heteroscedasticity

For general inferential families with a mixture of one- and two-sided inferences two procedures are proposed to compare several treatments with a control under heteroscedasticity. Critical constants required for the proposed procedures are tabulated, and a numerical example is given.     

基于BCR和HG-ICP-AES的矿区土壤重金属污染特征分析

建立了基于BCR法(连续提取法)和HG-ICP-AES技术的土壤重金属形态含量的检测方法。在选定的实验条件下,HG-ICP-AES对Hg, Pb和As的检测限分别达到0.6,1.5和0.8 ng·mL-1。对国家标准沉积物样品中Hg,Pb和As的含量进行对照测定,检测结果与推荐值一致,标准物质中Hg, Pb和As多次重复测定的RSD均<8%。应用本法实测了湘西某有色金属矿区土壤中Hg, Pb和As各形态的含量,发现矿区土壤中Hg, Pb和As均以残渣态为主,有机态和Fe-Mn氧化态次之,酸交换态含量较少;与对照区相比,矿区土壤中酸交换态、Fe-Mn氧化态、有机态、残渣态Hg, Pb和As的含量分别增加1.2, 3.0, 47, 272倍(Hg); 1.2, 4.6, 8.1, 4.5倍(Pb); 1.5, 2.9, 3.3, 2.2倍(As); 表明湘西矿区土壤同时存在Hg, Pb和As的复合污染。     

岩土材料应变局部化的有限元分析方法

采用有限单元法分析岩土材料的应变局部化时经常会遇到单元尺寸敏感性问题和网格锁定问题。自适应网格技术能够有效地解决网格锁定问题,但仍然无法克服计算结果对单元尺寸的依赖性,尽管在一维情况下被证明是可行的。复合体理论(均匀化理论)和弱非连续有限元方法可以成功地解决岩土材料的单元尺寸敏感性问题,在一维情况下两类方法实际上是一致的。本文针对岩土材料应变局部化的有限元新技术所存在的若干问题进行了详细的讨论,并给出了有关算例。     

The Influence of Synthesis Conditions on the Antioxidant Activity of Selenium Nanoparticles

Selenium nanoparticles (SeNPs) have attracted great attention in recent years due to their unique properties and potential bioactivities. While the production of SeNPs has been long reported, there is little news about the influence of reaction conditions and clean-up procedure on their physical properties (e.g., shape, size) as well as their antioxidant activity. This study takes up this issue. SeNPs were synthesized by two methods using cysteine and ascorbic acid as selenium reductants. The reactions were performed with and without the use of polyvinyl alcohol as a stabilizer. After the synthesis, SeNPs were cleaned using various procedures. The antioxidant properties of the obtained SeNPs were investigated using DPPH and hydroxyl radical scavenging assays. It was found that their antioxidant activity does not always depend only on the nanoparticles size but also on their homogeneity. Moreover, the size and morphology of selenium nanoparticles are controlled by the clean-up step.     

A note on simultaneous preconditioning and symmetrization of non‐symmetric linear systems

Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd.     

On the Vector ε-Algorithm for Solving Linear Systems of Equations

The four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation and the topological epsilon algorithm, when applied to linearly generated vector sequences are Krylov subspace methods and it is known that they are equivalent to some well-known conjugate gradient type methods. However, the vector -algorithm is an extrapolation method, older than the four extrapolation methods above, and no similar results are known for it. In this paper, a determinantal formula for the vector -algorithm is given. Then it is shown that, when applied to a linearly generated vector sequence, the algorithm is also a Krylov subspace method and for a class of matrices the method is equivalent to a preconditioned Lanczos method. A new determinantal formula for the CGS is given, and an algebraic comparison between the vector -algorithm for linear systems and CGS is also given.     

Production and Application of the Langmuir Aggregates of Eosine with Cetyl Trimethyl Ammonium Bromide

The procedure of microphase adsorption–spectral correction is applied to the interaction of eosine Y (EO) to the micelles of cetyl trimethyl ammonium bromide (CTAB). The Langmuir aggregation of EO on CTAB occurs owing to microelectrostatic attraction. The results have shown that at pH 3.8, monomeric and micellar aggregates have the structure EO₅·CTAB₂ and (EO₅·CTAB₂)₃₉. The adsorption constant of an aggregate is 7.01·10⁵, its molar absorption coefficient is = 8.8·10⁴ liters·mole^–1·cm^–1 at 550 nm. Application of the aggregation of EO on CTAB gives satisfactory results for quantitative determination of cation surfaceactive agents (surfactants).     

On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

Measuring the Polarization Parameters of Rain by Inverse Scattering

The theory is presented for one method of determining the effective polarization parameters of the rain medium in the problem of polarization information processing of detecting target. The determination of the effective polarization parameters of the propagation medium is from the data of propagation measurements over a line-of-sight link. The polarization parameters the effective average value, the effective standard deviation and F the effective shape parameter of the propagation medium are obtained by means of the method of inverse scattering, showing a good agreement with the data from direct measurements.