广义卷积代数与Hun半群及（，＊_α）的半群结构

利用Ｈｕｎ半群理论，证明了任一正则广义卷积代数，按广义卷积运算和弱收敛拓扑构成一个可度量化，稳定，可模的Ｈｕｎ半群，且无除么元以外的幂等元，并研究了（，＊α）的半群结构．     

国家精品课程《线性代数与空间解析几何》建设

简述了我校在进行国家级精品课程《线性代数与空间解析几何》建设方面的认识、理念和所进行的教学改革取得的成绩。论述了进一步深化这门课程改革的构想。     

A Systematic Approach to Determining the Identifiability of Multistage Carcinogenesis Models

Multistage clonal expansion (MSCE) models of carcinogenesis are continuous‐time Markov process models often used to relate cancer incidence to biological mechanism. Identifiability analysis determines what model parameter combinations can, theoretically, be estimated from given data. We use a systematic approach, based on differential algebra methods traditionally used for deterministic ordinary differential equation (ODE) models, to determine identifiable combinations for a generalized subclass of MSCE models with any number of preinitation stages and one clonal expansion. Additionally, we determine the identifiable combinations of the generalized MSCE model with up to four clonal expansion stages, and conjecture the results for any number of clonal expansion stages. The results improve upon previous work in a number of ways and provide a framework to find the identifiable combinations for further variations on the MSCE models. Finally, our approach, which takes advantage of the Kolmogorov backward equations for the probability generating functions of the Markov process, demonstrates that identifiability methods used in engineering and mathematics for systems of ODEs can be applied to continuous‐time Markov processes.     

Existence conditions for balanced fractional 3m factorial designs of resolution R({00, 10, 01, 20, 11})

We consider a fractional 3^m factorial design derived from a simple array (SA) such that the non negligible factorial effects are the general mean, the linear and the quadratic components of the main effect, and the linear-by-linear and the linear-by-quadratic components of the two-factor interaction. If these effects are estimable, then a design is said to be of resolution R({00, 10, 01, 20, 11}). In this paper, we give a necessary and sufficient condition for an SA to be a balanced fractional 3^m factorial design of resolution R({00, 10, 01, 20, 11}). Such a design is concretely characterized by the suffixes of the indices of an SA.     

Analysis of variance of balanced fractional 2n factorial designs of resolution 2l+1

By use of the algebraic structure of the triangular multidimensional partially balanced association scheme, we present the analysis of variance and the hypotheses testing of a balanced fractional 2ⁿfactorial design of resolution 2l+1, which is derived from a balanced array of strength 2l.     

线性代数精品课程的教学改革与实践

线性代数作为讨论代数学中线性关系经典理论的课程,它具有较强的抽象性与逻辑性,是培养学生的基本数学素养的经典课程。线性代数课程的教学改革与建设是一项长期且重要的工作,并且随着时代的发展需要赋予其新的内涵。文章从线性代数课程体系、教学内容、教学方法和教学手段的改革以及教材建设等多个方面,研究、探索如何进一步进行线性代数精品课程的建设。     

探讨线性代数的一个定理在射影几何中的应用

探讨了含有n个未知量n个方程的齐次线性方程组有非零解的充分必要条件在射影几何中的应用.     

用辩证思想方法指导高等代数教学刍议

分析了高等代数中的辩证思维的思想方法 ,探讨了在该课程教学中如何利用这些素材来培养学生分析、认识、解决问题的能力     

电磁波极化状态的计算机展示

介绍了借助计算机代数系统Maple实现电磁波极化状态的动态展示的做法，讨论了它在基础物理教学中的作用。     

BCI-代数的拟结合部分的性质

在BCI-代数X中，把Q（X）={x∈X｜0＊（0＊x）=0＊x}叫做X的拟结合部分．讨论了它与X的G-部分和p-半单部分的关系，给出了Q（x）的其它性质．