Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Simultaneous quantification of leukotrienes and hydroxyeicosatetraenoic acids in cell culture medium using liquid chromatography/tandem mass spectrometry

Leukotrienes (LTs) and hydroxyeicosatetraenoic acids (HETEs) are important bioactive lipid mediators that participate in various pathophysiological processes. To advance understanding of the mechanisms that regulate these mediators in physiological and pathological processes, an analytical method using liquid chromatography/tandem mass spectrometry for the simultaneous quantification of LTB₄, LTC₄, LTD₄, LTE₄, 5‐HETE_, 8‐HETE, 12‐HETE and 15‐HETE in cell culture media was developed. A Supel?‐Select HLB solid‐phase extraction cartridge was used for sample preparation. The compounds were separated on a C₁₈ column using gradient elution with acetonitrile–water–formic acid (20:80:0.1, v/v/v) and acetonitrile–formic acid (100:0.1, v/v). The calibration curves of LTB₄, LTD₄, LTE₄ and HETEs were linear in the range of 0.025–10 ng/mL, and the calibration curve of LTC₄ was linear in the range of 0.25–10 ng/mL. Validation assessment showed that the method was highly reliable with good accuracy and precision. The stability of LTs and HETEs was also investigated. Using the developed method, we measured LTs and HETEs in the culture supernatant of the human mast cell line HMC‐1. The present method could facilitate investigations of the mechanisms that regulate the production, release and signaling of LTs and HETEs. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

线性双向联想存储器

提出了一个线性双向联想存储器的模型，一组有限个向量对由一线性算子建立起双向联想关系，此线性算于是一个网络的联结权重矩阵。该权矩阵由最小二乘法决定。由权矩阵的解导出一特殊类型的Ｌｙａｐｕｎｏｖ矩阵方程．本文提供了这种Ｌｙａｐｕｎｏｖ矩阵方程的解。     

介质折射率对一维三元光子晶体带隙的影响

利用光学传输矩阵法,数值模拟了一维二元、三元光子晶体的带隙结构,得出:三元光子晶体的主带隙略宽于二元光子晶体的主带隙;三元光子晶体的主带隙主要取决于最高折射率的介质和最低折射率的介质,而与居于两者之间的介质关系不大,并作出了相应的关系曲线。最后推导了三元光子晶体的色散关系。     

Algebra matrix and similarity classification of operators

In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem.     

用Java实现网上结构图实验仿真

基于线性系统仿真的连接矩阵方法，用Java语言开发面向结构图的实验仿真程序，以Applet小应用程序的形式插入网页中运行，实现了信号与系统网上实验教学中的结构图实验仿真。经试用，程序在浏览器中运行正常，可以完成一般线性系统仿真，与以MATLAB，LABView等程序开发的实验仿真程序相比，该程序运行环境简单，几乎所有常用的Web浏览器都支持Java运行，不需另行安装相应组件。对于线性系统结构图，实现了所见即所得的图形化编程环境，具有较好的人机交互性。     

Coxeter Transformation and Quasiquivers

Mathematical Notes -