Quasi-monotone mappings on θn-continua

A continuous function f from a continuum X onto a continuum Y is quasi-monotone if, for every subcontinuum M of Y with nonvoid interior, f^-1(M) has a finite number of components each of which is mapped onto M by f. A θ_n-continuum is one that no subcontinuum separates into more than n components. It is known that if f is quasi-monotone and X is a θ₁-continuum, then Y is a θ₁-continuum or a θ₂-continuum that is irreducible between two points. Examples are given to show that this cannot be generalized to a θ_n-continuum and n + 1 points for any n >1, but it is proved that if f is quasi-monotone and X is a θ_n-continuum, then Y is a θ_n-continuum or a θ_n+1-continuum that is the union of n + 2 continua H,S₁,S₂,…,S_n+1, whe for each i, S_i is the closure of a component of Y H, S_i is irreducible from some point P_i to H, and H is irreducible about its boundary. Some theorems and examples are given concerning the preservation of decomposition elements by a quasi-monotone map defined on a θ_n-continuum that admits a monotone, upper-semicontinuous decomposition onto a finite graph.     

二次李超三系的分解及唯一性

研究了二次李超三系的分解及唯一性问题,讨论了二次李超三系的唯一分解,得到了二次李超三系分解为非退化不可约阶化理想的分解定理,从而使李超三系与二次李超三系理论得到了进一步的完善.     

l k,s -Singular values and spectral radius of rectangular tensors

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of l ^k,s -singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of l ^k,s -singular values /vectors, some properties of the related l ^k,s -spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.     

非奇异H-矩阵的一类新判定

本文研究了非奇异H-矩阵的数值判定问题.利用不等式的放缩方法,获得了一类判别非奇异H-矩阵的新判据,推广了相关已有结果,并通过数值实例说明了本文结果判断范围的更广泛性.     

Isotropic polynomial invariants of Hall tensor

The Hall tensor emerges from the study of the Hall effect, an important magnetic effect observed in electric conductors and semiconductors. The Hall tensor is third-order and three-dimensional, whose first two indices are skew-symmetric. This paper investigates the isotropic polynomial invariants of the Hall tensor by connecting it with a second-order tensor via the third-order Levi-Civita tensor. A minimal isotropic integrity basis with 10 invariants for the Hall tensor is proposed. Furthermore, it is proved that this minimal integrity basis is also an irreducible isotropic function basis of the Hall tensor.     

有理数域上的不可约多项式

主要利用Eisenstein判别法及其一些推广来研究一些特殊的有理数域上的不可约多项式结构．通过对研究整系数不可约多项式所得的结果进行总结和归纳,对一些特殊的整系数多项式的不可约性给出了判断,并对文献中的两个定理给出了其他证明方法．     

α-次对角占优矩阵与非奇异次H矩阵的判定

利用α-次对角占优矩阵的一些性质,通过选取正对角因子元素和放缩不等式的技巧,获得了广义严格次对角占优矩阵的几个判定定理,从而将一些已有的结论推广到非奇异次H矩阵中,并用数值例子说明了所得结果的实用性.     

基于代数神经网络的多元多项式不可约判定及学习算法

把感知器作为数学模型,充分利用神经元的运算特性,以二元多项式近似求根神经网络模型为基础,设计一类多元多项式不可约判定的神经网络模型,它是单输入多输出三层前向神经网络,给出神经网络学习算法,这种学习算法在ｐ－ａｄｉｃ意义下,通过调整隐层与输出层的权值Ｃｉ,ｊ完成学习,可确定出多元多项式不可约,通过算例表明,该算法有效,相比传统的判定算法,可操作性强。     

非奇异H-矩阵判定的充分条件

给出了非奇异H-矩阵判定的充分条件,并用数值例子说明了结果的有效性。