文章主要构建了置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数的胞腔基,从而说明置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数是胞腔代数。文章的证明根据章节分成三部分内容,第一部分给出了胞腔代...文章主要构建了置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数的胞腔基,从而说明置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数是胞腔代数。文章的证明根据章节分成三部分内容,第一部分给出了胞腔代数的定义,中心化子代数的定义,以及一些符号的意义。然后第二部分根据循环群在复数域上的群代数和某些置换矩阵的中心化子代数的联系,证明了循环群在复数域上的群代数是胞腔的。文章的第三部分是根据置换群的群元素可以表示成不相交轮换的乘积,通过其置换矩阵的分块乘积,发现该中心化子的结构和循环群在复数域上的基的联系,最后根据循环群在复数域上的胞腔基构造了一般的置换矩阵在复数域上全矩阵代数的中心化子代数的胞腔基。The article mainly constructs the cellular basis of the centralizer of the permutation matrix corresponding to the elements of the permutation group in the full matrix algebra over the complex field, thus showing that the centralizer of the permutation matrix corresponding to the elements of the permutation group in the full matrix algebra over the complex field is a cellular algebra. The proof of the article is divided into three parts according to the sections. The first part gives the definition of cellular algebra, the definition of centralizer algebra, and the meaning of some symbols. Then, the second part proves that the group algebra of the cyclic group over the complex field is cellular based on the connection between the group algebra of the cyclic group over the complex field and the centralizer algebra of some permutation matrices. The third part of the article discovers the connection between the structure of the centralizer and the basis of the cyclic group over the complex field through the block product of the permutation matrix according to the fact that the group elements of the permutation group can be expressed as the product of disjoint cycles, and then constructs the cellular basis of the centralizer of the general permutation matrix in the full matrix algebra over the complex field based on the cellular basis of the cyclic group over the complex field.展开更多
文章首先从四个方面提出了新工科背景下线性代数课程思政的挖掘方式与教学目的,即教师在传授知识的过程中通过线性代数包含的数学文化故事、与之相关的生活案例、科学实践以及课程本身所蕴含的传统文化和哲学道理来培养学生的家国情怀...文章首先从四个方面提出了新工科背景下线性代数课程思政的挖掘方式与教学目的,即教师在传授知识的过程中通过线性代数包含的数学文化故事、与之相关的生活案例、科学实践以及课程本身所蕴含的传统文化和哲学道理来培养学生的家国情怀、爱国主义、科研精神以及唯物主义辩证思想。其次,探索并给出了线性代数教学中课程思政的实践路径,从而为教师在新工科背景下线性代数教学中融入课程思政提供一定的参考。This paper first proposes the exploration methods and teaching objectives of courses ideological and political education from four aspects in linear algebra under the background of new engineering, that is, during the process of imparting knowledge, teachers should cultivate students’ patriotism, scientific research spirit, and materialistic and dialectic philosophy through traditional culture and philosophical principles contained in mathematical cultural stories, related life cases, scientific practices, and the curriculum itself of linear algebra. Secondly, the practical paths of integrating ideological and political education into linear algebra teaching have been explored and provided, thus it provides some reference for teachers to integrate ideological and political education into linear algebra teaching in the context of new engineering.展开更多
本文以一元Birkhoff插值研究结果为基础,对二元Birkhoff插值泛函组的适定性问题进行了研究。通过提出弱Gröbner基的概念及其发现其性质,提出了一种利用两条不同次数代数曲线相交的点,构造出二元Birkhoff插值问题适定泛函组的新方法...本文以一元Birkhoff插值研究结果为基础,对二元Birkhoff插值泛函组的适定性问题进行了研究。通过提出弱Gröbner基的概念及其发现其性质,提出了一种利用两条不同次数代数曲线相交的点,构造出二元Birkhoff插值问题适定泛函组的新方法,从而将该方法所得到的结果推广到一般情形。并得到了构造平面代数曲线二元Birkhoff插值适定泛函组的一般性方法和实用性较强的理论,最后给出了具体实验算例,对所得研究结论给予了验证。This paper takes the research results of univariate Birkhoff interpolation as its foundation to study the stability problem of two-dimensional Birkhoff interpolation generalized function sets. By introducing the concept and properties of weak Gröbner bases, a new method is obtained which utilizes the intersection of any two arbitrary algebraic curves to construct the two-dimensional Birkhoff well-posed interpolation functional systems. This method extends the research direction’s findings to general cases, providing a general approach and practical theory for constructing planar algebraic curve well-posed interpolation functional systems. Finally, specific experimental examples are provided to validate the research conclusions obtained.展开更多
近日,河北师范大学数学科学学院房军生团队以“On Finite Sums of Projections and Dixmier's Averaging Theorem for Type Ⅱ1 Factors”和“A Stronger Version of Dixmier's Averaging Theorem and Some Applications”为题...近日,河北师范大学数学科学学院房军生团队以“On Finite Sums of Projections and Dixmier's Averaging Theorem for Type Ⅱ1 Factors”和“A Stronger Version of Dixmier's Averaging Theorem and Some Applications”为题在泛函分析领域Top期刊《Journal of Functional Analysis》上发表2篇论文,给出Ⅱ1型因子von Neumann代数的一个加强版本Dixmier平均值定理,并借助此定理解决了4个算子代数中的公开问题.展开更多
本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能...本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能的顶点算子代数结构。In this paper, we mainly study the vertex operator algebra generated by two pairs of Ising vectors in the moonshine type vertex operator algebra. These two pairs of Ising vectors each generate one 3A algebra, and the intersection of the two generated 3A algebras contains a subvertex operator subalgebra that is isomorphic to L(4/5, 0)⊕L(4/5, 3). We have shown that there are three possible structures of vertex operators algebraic.展开更多
文摘文章主要构建了置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数的胞腔基,从而说明置换群群元素对应的置换矩阵在复数域上全矩阵代数的中心化子代数是胞腔代数。文章的证明根据章节分成三部分内容,第一部分给出了胞腔代数的定义,中心化子代数的定义,以及一些符号的意义。然后第二部分根据循环群在复数域上的群代数和某些置换矩阵的中心化子代数的联系,证明了循环群在复数域上的群代数是胞腔的。文章的第三部分是根据置换群的群元素可以表示成不相交轮换的乘积,通过其置换矩阵的分块乘积,发现该中心化子的结构和循环群在复数域上的基的联系,最后根据循环群在复数域上的胞腔基构造了一般的置换矩阵在复数域上全矩阵代数的中心化子代数的胞腔基。The article mainly constructs the cellular basis of the centralizer of the permutation matrix corresponding to the elements of the permutation group in the full matrix algebra over the complex field, thus showing that the centralizer of the permutation matrix corresponding to the elements of the permutation group in the full matrix algebra over the complex field is a cellular algebra. The proof of the article is divided into three parts according to the sections. The first part gives the definition of cellular algebra, the definition of centralizer algebra, and the meaning of some symbols. Then, the second part proves that the group algebra of the cyclic group over the complex field is cellular based on the connection between the group algebra of the cyclic group over the complex field and the centralizer algebra of some permutation matrices. The third part of the article discovers the connection between the structure of the centralizer and the basis of the cyclic group over the complex field through the block product of the permutation matrix according to the fact that the group elements of the permutation group can be expressed as the product of disjoint cycles, and then constructs the cellular basis of the centralizer of the general permutation matrix in the full matrix algebra over the complex field based on the cellular basis of the cyclic group over the complex field.
文摘文章首先从四个方面提出了新工科背景下线性代数课程思政的挖掘方式与教学目的,即教师在传授知识的过程中通过线性代数包含的数学文化故事、与之相关的生活案例、科学实践以及课程本身所蕴含的传统文化和哲学道理来培养学生的家国情怀、爱国主义、科研精神以及唯物主义辩证思想。其次,探索并给出了线性代数教学中课程思政的实践路径,从而为教师在新工科背景下线性代数教学中融入课程思政提供一定的参考。This paper first proposes the exploration methods and teaching objectives of courses ideological and political education from four aspects in linear algebra under the background of new engineering, that is, during the process of imparting knowledge, teachers should cultivate students’ patriotism, scientific research spirit, and materialistic and dialectic philosophy through traditional culture and philosophical principles contained in mathematical cultural stories, related life cases, scientific practices, and the curriculum itself of linear algebra. Secondly, the practical paths of integrating ideological and political education into linear algebra teaching have been explored and provided, thus it provides some reference for teachers to integrate ideological and political education into linear algebra teaching in the context of new engineering.
文摘本文以一元Birkhoff插值研究结果为基础,对二元Birkhoff插值泛函组的适定性问题进行了研究。通过提出弱Gröbner基的概念及其发现其性质,提出了一种利用两条不同次数代数曲线相交的点,构造出二元Birkhoff插值问题适定泛函组的新方法,从而将该方法所得到的结果推广到一般情形。并得到了构造平面代数曲线二元Birkhoff插值适定泛函组的一般性方法和实用性较强的理论,最后给出了具体实验算例,对所得研究结论给予了验证。This paper takes the research results of univariate Birkhoff interpolation as its foundation to study the stability problem of two-dimensional Birkhoff interpolation generalized function sets. By introducing the concept and properties of weak Gröbner bases, a new method is obtained which utilizes the intersection of any two arbitrary algebraic curves to construct the two-dimensional Birkhoff well-posed interpolation functional systems. This method extends the research direction’s findings to general cases, providing a general approach and practical theory for constructing planar algebraic curve well-posed interpolation functional systems. Finally, specific experimental examples are provided to validate the research conclusions obtained.
文摘近日,河北师范大学数学科学学院房军生团队以“On Finite Sums of Projections and Dixmier's Averaging Theorem for Type Ⅱ1 Factors”和“A Stronger Version of Dixmier's Averaging Theorem and Some Applications”为题在泛函分析领域Top期刊《Journal of Functional Analysis》上发表2篇论文,给出Ⅱ1型因子von Neumann代数的一个加强版本Dixmier平均值定理,并借助此定理解决了4个算子代数中的公开问题.
文摘本文主要研究在月光型顶点算子代数中满足一定条件的2对Ising向量生成的顶点算子代数的结构,这2对Ising向量分别生成1个3A代数,并且生成的2个3A代数的交包含一个同构于L(4/5, 0)⊕L(4/5, 3)的子顶点算子代数,本文证明了其一共有3种可能的顶点算子代数结构。In this paper, we mainly study the vertex operator algebra generated by two pairs of Ising vectors in the moonshine type vertex operator algebra. These two pairs of Ising vectors each generate one 3A algebra, and the intersection of the two generated 3A algebras contains a subvertex operator subalgebra that is isomorphic to L(4/5, 0)⊕L(4/5, 3). We have shown that there are three possible structures of vertex operators algebraic.
