The convergence rate of a three-term HS method with restart strategy for unconstrained optimization problems

Although the Hesteness and Stiefel (HS) method is a well-known method, if an inexact line search is used, researches about its convergence rate are very rare. Recently, Zhang, Zhou and Li [Some descent three-term conjugate gradient methods and their global convergence, Optim. Method Softw. 22 (2007), pp. 697–711] proposed a three-term Hestenes–Stiefel method for unconstrained optimization problems. In this article, we investigate the convergence rate of this method. We show that the three-term HS method with the Wolfe line search will be n-step superlinearly and even quadratically convergent if some restart technique is used under reasonable conditions. Some numerical results are also reported to verify the theoretical results. Moreover, it is more efficient than the previous ones.     

GLn(k)和SLn(k)的阶

本文利用矩阵行的初等变换 ,采用递推的方法 ,求出了有限域 k上 n次一般线性群 GLn(k)和 n次特殊线性群 SLn(k)的阶 .     

Simple and automatic determination of aldehydes and acetone in water by headspace solid-phase microextraction and gas chromatography-mass spectrometry

We describe a simple and automatic method to determine nine aldehydes and acetone simultaneously in water. This method is based on derivatization with 2,2,2-trifluoroethylhydrazine (TFEH) and consecutive headspace-solid-phase microextraction and gas chromatography-mass spectrometry. Acetone-d(6) was used as the internal standard. Aldehydes and acetone in water reacted for 30 min at 40°C with TFEH in a headspace vial and the formed TFEH derivatives were simultaneously vaporized and adsorbed on polydimethylsiloxane-divinylbenzene. Under the established condition, the method detection limit was 0.1-0.5 μg/L in 4 mL water and the relative standard deviation was less than 13% at concentrations of 0.25 and 0.05 mg/L. This method was applied to determine aldehydes and acetone in 5 mineral water and 114 surface water samples. All mineral water samples had detectable levels of methanal (24.0-61.8 μg/L), ethanal (57.7-110.9 μg/L), propanal (11.5-11.7 μg/L), butanal, pentanal (3.3-3.4 μg/L) and nonanal (0.3-0.4 μg/L). Methanal and ethanal were also detected in concentration range of 2.7-117.2 and 1.2-11.9 μg/L, respectively, in surface water of 114 monitoring sites in Korea.     

A volatolomic approach using cerumen as biofluid to diagnose bovine intoxication by Stryphnodendron rotundifolium

An innovative volatolomic approach employs the detection of biomarkers present in cerumen (earwax) to identify cattle intoxication by Stryphnodendron rotundifolium Mart., Fabaceae (popularly known as barbatimão). S. rotundifolium is a poisonous plant with the toxic compound undefined and widely distributed throughout the Brazilian territory. Cerumen samples from cattle of two local Brazilian breeds (‘Curraleiro Pé-Duro’ and ‘Pantaneiro’) were collected during an experimental intoxication protocol and analyzed using headspace (HS)/GC–MS followed by multivariate analysis (genetic algorithm for a partial least squares, cluster analysis, and classification and regression trees). A total of 106 volatile organic metabolites were identified in the cerumen samples of bovines. The intoxication by S. rotundifolium influenced the cerumen volatolomic profile of the bovines throughout the intoxication protocol. In this way, it was possible to detect biomarkers for cattle intoxication. Among the biomarkers, 2-octyldecanol and 9-tetradecen-1-ol were able to discriminate all samples between intoxicated and nonintoxicated bovines. The cattle intoxication diagnosis by S. rotundifolium was accomplished by applying the cerumen analysis using HS/GC–MS, in an easy, accurate, and noninvasive way. Thus, the proposed bioanalytical chromatography protocol is a useful tool in veterinary applications to determine this kind of intoxication.     

A translation plane of order 192 admitting SL(2,5), obtained by 12-nest replacement

The problem of determining two-dimensional translation planes admitting SL(2,5) in the translation complement has been intensively studied. Most examples arise from multiple-derivation of a Desarguesian plane. In this paper, we construct two translation planes of order 19² admitting SL(2,5), one of which is obtained by 12-nest replacement.      

顶空-气质联用法对醋酸纤维滤棒中溶剂残留的测定

利用顶空-气质联用仪(HS/GC-MS)建立了一种同时测定醋酸纤维滤棒中溶剂残留的测定方法.利用顶空气相色谱技术,用选择离子模式对醋酸纤维滤棒中溶剂残留进行了定量分析.分析结果表明,方法线性关系良好,相关系数均大于0.998 0,检出限为0.010 4~0.157 8 mg/kg.9种溶剂残留的平均回收率为90.3%~102.2%,相对平均偏差小于10%.方法适用于醋酸纤维滤棒溶剂残留的测定且高效、准确、简便.     

基于协方差匹配SLO算法的MIMO雷达DOA估计

利用加权平滑l0范数(Smoothed l0, SL0)算法估计MIMO雷达目标DOA时,需要把协方差矩阵进行矢量化来获得相应的稀疏重构模型,并利用信号和噪声子空间的正交性来构造加权向量。然而当存在相干信源时,MIMO雷达协方差矩阵的秩将退化,这会使得稀疏重构模型的误差较大以及无法正确区分信号和噪声子空间,导致加权SL0算法的DOA估计性能恶化。针对上述问题提出了一种基于协方差匹配SL0算法的MIMO雷达DOA估计方法。该方法利用协方差匹配准则重构出一个满秩的协方差矩阵,恢复MIMO雷达协方差矩阵的Toeplitz特性,并利用协方差逆矩阵的高阶幂来近似噪声子空间从而计算加权向量。仿真分析表明,该方法能够在无需预知信源数目的情况下有效地完成对相干信号的DOA估计。     

基于截断修正平滑l0范数的MIMO雷达目标参数估计

在多输入多输出(MIMO)雷达中,针对平滑l0范数(SL0)因感知矩阵的病态性而导致其失效的问题,提出了一种基于截断修正SL0的MIMO雷达目标参数估计方法.该方法在对MIMO雷达感知矩阵进行截断奇异值分解(TSVD)处理的基础上,将保留的奇异值以均值为截断门限,分成较大和较小的两部分,分别采用不同的修正准则进行修正;然后经奇异值分解(SVD)反变换获得非病态感知矩阵,利用该非病态感知矩阵通过SL0算法对MIMO雷达目标参数进行估计,从而显著提高了MIMO雷达目标参数估计的精度和速度.仿真结果验证了该方法的有效性.