A_2(F)在G_2(F)中的扩群及其泛正规性

域Ｆ上Ａ２型Ｃｈｅｖａｌｌｅｙ群Ａ２（Ｆ）可视为Ｆ上Ｇ２型Ｃｈｅｖａｌｌｅｙ群Ｇ２（Ｆ）的子群．当 Ｆ是特征不为 ２，３的域且 Ｆ＝Ｆ３时，本文给出了 Ａ２（Ｆ）在 Ｇ２（Ｆ）中的所有扩群及其泛正规性．     

Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see http://www.sciencedirect.com/science/journal/03770427, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.     

A Parameterization of the Canonical Bases of Affine Modified Quantized Enveloping Algebras

For a symmetrizable Kac-Moody Lie algebra g, Lusztig introduced the corresponding modified quantized enveloping algebra˙U and its canonical basis˙B given by Lusztig in 1992. In this paper, in the case that g is a symmetric Kac-Moody Lie algebra of finite or affine type, the authors define a set M which depends only on the root category R and prove that there is a bijection between M and ˙B, where R is the T~2-orbit category of the bounded derived category of the corresponding Dynkin or tame quiver. The method in this paper is based on a result of Lin, Xiao and Zhang in 2011, which gives a PBW-type basis of U~+.     

The Square Root Problem and Aluthge transforms of weighted shifts

In this paper we consider the following question. When does there exist a square root of a probability measure supported on ? This question is naturally related to subnormality of weighted shifts. The main result of this paper is that if μ is a finitely atomic probability measure having at most 4 atoms, then μ has a square root, i.e., there exists a measure ν such that (* means the convolution) if and only if the Aluthge transform of a subnormal weighted shift with Berger measure μ is subnormal. As an application of them, we give non‐trivial, large classes of probability measures having a square root. We also prove that there are 6 and 7‐atomic probability measures which don't have any square root. Our results have a connection to the following long‐open problem in Operator Theory: characterize the subnormal operators having a square root.     

On the similarity of some three-point methods for solving nonlinear equations

In this short note we discuss certain similarities between some three-point methods for solving nonlinear equations. In particular, we show that the recent three-point method published in [R. Thukral, A new eighth-order iterative method for solving nonlinear equations, Appl. Math. Comput. 217 (2010) 222-229] is a special case of the family of three-point methods proposed previously in [R. Thukral, M.S. Petkovi?, Family of three-point methods of optimal order for solving nonlinear equations, J. Comput. Appl. Math. 233 (2010) 2278-2284].     

Solving cubics by polynomial fitting

A top-performance algorithm for solving cubic equations is introduced. This algorithm uses polynomial fitting for a decomposition of the given cubic into a product of a quadratic and a linear factor. This factorization can be computed extremely accurately and efficiently using a fixed-point iteration of the linearized fitting error. The polynomial fitting concept performs orders of magnitude better in terms of numerical accuracy and precision than any of the currently known and available algorithms for solving cubic equations. A special exception handler is presented for a reliable operation in the event of double, triple and tightly clustered roots.     

甘草中金属元素与总黄酮含量测定与抗氧化研究

对中草药甘草中金属元素与总黄酮含量进行测定,并对其清除超氧自由基进行研究.测定结果显示,甘草中含有丰富的金属元素和黄酮类化合物,其中总黄酮为16.42%,金属元素含量为铁>锌>锰>铜,对超氧自由基具有一定的清除作用.实验结果为研究甘草治疗呼吸系统疾病及清除自由基提供了有用的数据.     

疏水缔合聚丙烯酸与蠕虫状胶束的协同作用

从宏观流变性和介观尺度方面, 研究了疏水缔合聚丙烯酸(HMPA)与油酸钠(NaOA)构筑的蠕虫状胶束的协同作用. 考察HMPA对蠕虫状胶束溶液流变性和表观粘度的影响, 结果表明, 极少量HMPA的引入导致蠕虫状胶束溶液体系动态模量明显增加; 其表观粘度随HMPA浓度的增加先增强后减弱. 另一方面, 通过耗散颗粒动力学(DPD)分子模拟方法研究了混合体系中溶液组成对HMPA分子链的均方根末端距的影响. 结果表明,随着NaOA浓度增加, HMPA的均方根末端距会出现峰值; HMPA的伸展程度受其自身浓度变化制约, 相对于纯HMPA体系, NaOA胶束的存在对高浓度区的HMPA伸展程度影响更明显. 结合流变实验和分子模拟结果,初步解释了聚合物与蠕虫状胶束的协同作用机制.     

气相色谱-串联质谱法测定人参和黄芪中7种毒杀芬残留量

建立了人参和黄芪中毒杀芬代表性单体残留量的检测方法。选择7种指示性毒杀芬单体为检测品种,样品用环己烷-丙酮(9:1,v/v)加速溶剂萃取法提取,经弗罗里硅土固相萃取柱净化后,以气相色谱-电子轰击离子源串联质谱(GC-EI-MS/MS)在多反应监测(MRM)模式下进行测定。在人参和黄芪两种中药材样品基质,0.005、0.01和0.1 mg/kg 3个加标水平条件下,7种毒杀芬单体的回收率为72.4%～105%,相对标准偏差为0.96%～10.4%;方法的检出限(S/N=3)为0.2～1.7 μg/kg,均符合农药残留检测要求。该方法提取效果好,检测灵敏度高,适用于人参和黄芪中7种毒杀芬残留量的检测。     

On Rank 2 Complex Reflection Groups

We describe a class of groups with the property that the finite ones among them are precisely the complex reflection groups of rank 2. This situation is reminiscent of Coxeter groups, among which the finite ones are precisely the real reflection groups. We also study braid relations between complex reflections and indicate connections to an axiomatic study of root systems and to the Shephard–Todd “collineation groups.”