Linear maps leaving the alternating group invariant

Let A_n be the group of n×n even permutation matrices, and let V_n be the real linear space spanned by A_n. The purpose of this note is to characterize those linear operators φ on V_n satisfying φ(A_n)=A_n. This answers a question raised by C.K. Li, B.S. Tam, N.K. Tsing [Linear Algebra Appl., to appear].     

交替光谱辐照对叶用莴苣营养元素水平的影响

在人工光型植物工厂中采用深液流水培法栽培叶用莴苣,依托光谱时空分布可精准调控的智能LED光源系统,应用电感耦合等离子体原子发射光谱技术（ICP-AES）,研究了5 min,10 min,15 min,30 min,60 min,2 h,4 h和8 h等不同间隔的红、蓝光谱交替照射对叶用莴苣中K,P,Ca,Mg,Fe,Mn,Zn和Cu等8种营养元素吸收和累积的影响。结果表明：(1) 与同时照射模式相比,所有的交替光谱处理均显著提高了叶用莴苣地上部生物量,其中鲜重提高幅度约为18.6%~67.4%,干重提高幅度约为5.1%~88.0%;所有的交替红蓝光谱照射下叶用莴苣体内Mg,Fe和Zn元素的植株累积量均得到显著（p＜0.05）地提高;所有的红蓝交替光谱辐射处理均不同程度地降低了叶用莴苣植株中Ca元素含量。(2) 间隔为5 min的红蓝交替光谱辐射下莴苣植株Fe元素含量显著高于其他任意处理,较其他处理增加了38.87%~85.37%,高频次的红蓝光切换照射刺激了叶用莴苣植株对Fe元素的吸收。(3) 红蓝交替光谱辐射有利于提高叶用莴苣的能量利用效率,与红蓝同时供光的RB处理相比,所有交替处理均显著提高了叶用莴苣的光、电能利用率,提高幅度分别约为34.3%~87.5%和34.6%~87.9%;其中,间隔为4 h的红蓝交替光谱辐射下叶用莴苣植株的光、电能利用率均最大,分别为6.13%和2.01%,除间隔为5和10 min的红蓝交替光谱辐射处理外的其他交替光谱处理下的植株光、电能利用率均与处理间最大值无显著性差异。(4) 叶用莴苣对K和Mg两种元素的吸收在红蓝光交替间隔为10 min,15 min,60 min及4 h等多个处理下呈现拮抗现象。(5) R/B(30 m)处理下叶用莴苣中P,Ca,Fe和Mn等四种元素的含量水平均呈现处理间最低水平,其中P和Ca元素含量水平显著低于对照。     

三维荧光结合化学多维校正快速灵敏测定环境水样中的噻菌灵和双酚A

随着经济的高速发展,环境问题正在日益引起人们的广泛关注。在实际生产中,农药和塑化剂长期存在滥用的问题,使其成为最为广泛的环境污染源并对生态环境、食品、人畜等造成严重的危害。针对环境中农药和塑化剂的残留问题,开发一种灵敏、快速的高效检测分析方法,采用三维荧光结合化学计量学方法用于环境水样中噻菌灵（TBZ）与双酚A（BPA）的快速灵敏分析。兼顾了三维荧光分析的灵敏度高、信息丰富及化学多维校正方法“数学分离”的显著优势,仅需要简单的预处理过程即可实现TBZ和BPA的痕量检测。即使分析物之间以及分析物和水样中未知背景干扰之间的光谱存在严重的重叠,基于交替三线性分解（ATLD）算法的二阶校正方法仍能借助其显著的“二阶优势”对其进行解析,并获得可靠的定性定量结果。其中,TBZ在20~200 ng·mL-1范围内线性关系良好（r=0.9999）,而BPA在40~280 ng·mL-1范围内线性关系良好（r=0.999 1）。TBZ和BPA在两种水样中的平均加标回收率分别为96.3%~99.1%和90.0%~90.8%,且标准偏差均低于7.2%。另外,计算品质因子,如灵敏度（SEN）、选择性（SEL）、检测限（LOD）和定量限（LOQ）,评估了该方法的准确性。所得结果均令人满意,表明所提出的方法能够用于环境水样中TBZ和BPA的准确、快速定量分析,为环境中农药和塑化剂的残留问题提供了一种科学有效的监测手段。     

Robust canonical correlations: A comparative study

Summary  Several approaches for robust canonical correlation analysis will be presented and discussed. A first method is based on the definition of canonical correlation analysis as looking for linear combinations of two sets of variables having maximal (robust) correlation. A second method is based on alternating robust regressions. These methods are discussed in detail and compared with the more traditional approach to robust canonical correlation via covariance matrix estimates. A simulation study compares the performance of the different estimators under several kinds of sampling schemes. Robustness is studied as well by breakdown plots.     

二维变系数扩散方程交替分组显格式的稳定性分析

1.引言 由于高性能并行计算机的出现和并行计算的推动,十多年来,抛物型方程有限差分并行算法设计与分析一直受到关注. D.J.Evalns和A.R.B.Abdullah(1983,[1,2]利用Saul’yev非对称格式对常系数抛物方程设计了AGE(交替分组显格式)算法,并用矩阵分析的方法证明了该算法的无条件稳定性.该算法有明显的并行性,倍受推崇,且计算的实践([8],[9])表明它对变系数的抛物方程也是可行的,但稳定性的分析成为一个难点.张宝琳([3])在一维情     

Variations on the Theorem of Birkhoff – von Neumann and Extensions

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory. Received: October 10, 2000 Final version received: April 11, 2002     

A Modified Alternating Direction Method for Variational Inequality Problems

The alternating direction method is an attractive method for solving large-scale variational inequality problems whenever the subproblems can be solved efficiently. However, the subproblems are still variational inequality problems, which are as structurally difficult to solve as the original one. To overcome this disadvantage, in this paper we propose a new alternating direction method for solving a class of nonlinear monotone variational inequality problems. In each iteration the method just makes an orthogonal projection to a simple set and some function evaluations. We report some preliminary computational results to illustrate the efficiency of the method. Accepted 4 May 2001. Online publication 19 October, 2001.     

The one-dimensional 1/4-filled Hubbard model with alternating interactions

The one-dimensional Hubbard model with different on-site interaction on the even (U_a) and odd (U_b) sites is considered within the framework of the weak coupling approach. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for U_a ≠ U_b and U_a>0 or U_b>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next-nearest neighbour sites is also considered.     

Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra

The multiexponential analysis problem of fitting kinetic models to time-resolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard error estimates. A new derivation of the Fisher information matrix under the full Golub-Pereyra gradient allows a numerical comparison of parameter precision under variable projection variants. Under the criteria of efficiency, quality of standard error estimates and parameter precision, we conclude that the Kaufman variable projection technique performs well, while techniques based on alternating least squares have significant disadvantages for application in the problem domain.