Cognitive Mapping: Testing Application of Causal Algebra

This paper takes the basic mathematical operations required to manipulate the cognitive maps. This paper start by presenting all the values that a causal relationship can take. By the using of causal algebra, cognitive map (CC) become not only a graphical representation of a person’s beliefs, an agent or a particular area but also can capture the causal relationships existing between the concepts of a given system in a simple manner. Cognitive maps do not use a conventional algebra;algebra causal is needed to treat.

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.

Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras

A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.

Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals

Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.

Non-linear Invertible Maps that Preserve Staircase Subalgebras

Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.

Haagerup测度下的自由群傅里叶代数上的MAP性质（英文）

令群F_N是自由群且有一个Haagerup测度μ.

POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from {π_1,π_2} is positive. A necessary and sufficient condition is obtained for a pair {π_1,π_2} to have property(C),and an easily checked necessary and sufficient condition for the pairs of the form {π~p,π~q} to have property(C) is given, whereπ is the permutation defined by π(i) = i + 1 mod n and 1≤ p < q≤ n.

APPROXIMATION OF ADJOINT OF A MULTIPLIER ON BANACH ALGEBRAS

For a Banach algebra A, we denote by .A＊ and .A＊＊ the first and the second duals of A respectively. Let T be a mapping from .A＊ to itself. In this article, we will investigate some stability results concerning the equations T（αf ＋ βg） -= αT（f） ＋ βT（g）, T（af） = aT（f） andT（αf ＋βg） ＋ T（αf - βg） =- 2α2T（f） ＋ 2β2T（g） where f, g e .A＊, a ∈ A, and α,β ∈ Q ／ {0}.

基于MAPGIS的西安地裂缝分析应用

地裂缝是西安市区较为严重的地质灾害,其影响因素有构造运动、地下水开采、地形地貌、地层条件等。本文将具有统一地理坐标和空间分析能力的MAPGIS地理信息系统应用于地裂缝活动强度评价,根据对地裂缝影响因素的分析,建立层次分析模型,计算每一影响因素的权重,确定在GIS支持下的地裂缝活动强度评价模型。再通过MAPGIS图形、图像处理等模块对各单因素专题层进行地图代数运算,得出地裂缝影响因素叠加图像并确定分区阈值,以此为依据对西安地裂缝活动强度进行分区,进而实现对地裂缝活动强度的预测。

DISTORTIONAL PROPERTIES OF THE BIJECTIVE PATTERN MAP (PART I: DISTORTION IN LENGTH)

The Bijective Pattern Map maps the 3D surface patch to the 2D flat pattern. The bijection property has been proved. However, since the 3D Algebraic Mannequin is not developeable, meaning that it is not isometric to the 2D plane, the intrinsic geometry of the 3D surface patches is different from their images on the 2D plane. Consequently, distortion exists. The distortional property of the Bijective Pattern Map is discussed in this article.

Distortional Properties of the Bijective Pattern Map (Part II: Change of Reference)

This is the part n of the study of distortion property of the Bijective Pattern Map maps. In part I, the generic distortion was presented. In this article, the distortion using different set of reference points and pre - image is compared with the result in part I. Moreover, the distortion induced by a change of reference is illustrated with examples. The formulation of the relationship between the distortion and the Gaussian curvature will be followed.

Relational Representations of Strongly Algebraic Lattices

In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.

套代数上的一类非线性中心化子

为了推广算子代数中的基本理论,对一类非线性映射成为套代数上的可加中心化子的条件进行了研究。首先,基于Hilbert空间上的非平凡套定义与该套有关的套代数,并定义套代数上的一个非线性映射;其次,采用矩阵分块方法获得关于此映射的几个性质;最后,证明套代数上满足某种条件的非线性映射为可加中心化子,给出刻画该映射的具体形式。结果表明,套代数上满足某种条件的非线性映射为可加中心化子,且可完全刻画。研究结果推广了非线性映射成为套代数上可加中心化子的结论,丰富了算子代数拓扑结构的分类问题,为套代数上其他类型非线性映射问题的刻画提供了借鉴与参考。

An Improvement in Ordered Cone b-metric Spaces Over Banach Algebras

The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations.

课程思政背景下代数学教学的探索与实践

课程思政背景下,代数学教学要求教师在讲授专业知识的过程中,不仅要培养学生的抽象思维能力和逻辑推理能力,更要注重对学生的思政教育。以同态基本定理为例,通过分析教学内容,挖掘事物的内在联系,在专业课的教学过程中实现课程育人的协同效应,同时为教师教学和学生学习提供一定的借鉴和参考。

广义矩阵代数上的一类非线性局部可导映射

设G=G(A,M,N,B)是一个广义矩阵代数,∅:G→G是一个映射(无可加性假设).利用代数分解的方法,证明:如果对任意的X,Y∈G,且X和Y至少有一个是幂等元时,∅(XY)=∅(X)Y+X∅(Y)成立,则∅是G上的可加导子.

一类Heisenberg-Virasoro李代数上的交换线性映射

根据交换线性映射的性质,计算秩为2的Heisenberg-Virasoro李代数上的交换线性映射,以确定此李代数的形心.

超Grassmannian流形上的超Plücker映射

■表示■-维向量空间中的■-维子空间构成的超Grassmannian流形。本文研究超Grassmannian流形上的超Plücker映射,刻画了■和■上的超Plücker映射的齐次坐标矩阵。

论多边形中轴问题和算法

比较了当前国内外GIS中和计算几何中关于多边形中轴的定义,讨论了它们的主要特点,指出多边形中轴应是到两个以上边距离相等点的轨迹,并据此分析了相应的各种算法和实际应用场合,提出了理论上较为严密、能够广泛满足实际应用需要的几何方法———点对序列法和地图代数多边形中轴法。

GIS的基本理论问题——地图代数的空间观

通过分析比较地学各学科的空间概念 ,深入地论述了地球信息系统的空间概念这一基本理论问题 ,指出了地球信息系统的空间数学基础是GIS空间概念的数学定义 ,揭示并论证了地理信息系统的空间数学基础 ,并相应讨论了“无缝空间数据库”技术的若干基本问题 ,认为“无缝”不仅是形式上的“无缝可视” ,更重要在于“无缝量度”、“无缝空间分析”、“规范地无缝集成”的实质性能力上。最后通过对“无缝空间数据库”下的空间分析理论和技术、空间 (数据 )的表达、国家地球空间数据框架和技术路线的论述 ,表明使GIS与各地球科学学科的地球空间完全一致 ,将全面有益于地球信息科学的新发展。