EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES

This paper describes a database model based on the original rough sets theory. Its rough relations permit the representation of a rough set of tuples not definable in terms of the elementary classes, except through use of lower and upper approximations. The rough relational database model also incorporates indiscernibility in the representation and in all the operators of the rough relational algebra. This indiscernibility is based strictly on equivalence classes which must be defined for every attribute domain. There are several obvious applications for which the rough relational database model can more accurately model an enterprise than does the standard relational model. These include systems involving ambiguous, imprecise, or uncertain data. Retrieval over mismatched domains caused by the merging of one or more applications can be facilitated by the use of indiscernibility, and naive system users can achieve greater recall with the rough relational database. In addition, applications inherently “rough” could be more easily implemented and maintained in the rough relational database.     

Sparse shape functions for tetrahedral <Emphasis Type="Italic">p</Emphasis>-FEM using integrated Jacobi polynomials

Summary In this paper, we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp-version of the finite element method using a mesh of tetrahedrons. We present several bases based on integrated Jacobi polynomials in which the element stiffness matrix has nonzero entries, where p denotes the polynomial degree. The proof of the sparsity requires the assistance of computer algebra software. Several numerical experiments show the efficiency of the proposed bases for higher polynomial degrees p.      

A 3D GIS spatial data model based on conformal geometric algebra

We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are con...     

电子信息学科中线性代数的教学方法探讨

针对电子信息学科,分析了传统线性代数授课中存在数学与专业课、数学与工程脱节的问题,提出了进行线性代数教学改革的思想,以线性代数课程中”向量空间的基”为例,具体阐述了如何在教学中融入专业知识与工程实例的教学方法。通过近5年的教学实践,验证了此教学方法不仅增强了学生学习数学课程的兴趣,提高了教学质量,而且还促进了相关课程建设。     

网络微积分学研究

网络微积分是最小加代数理论在网络分析中的应用。网络微积分主要用于对网络中流问题的考察．它所形成的体系可以用于对网络中的流问题进行建模和定量分析。网络微积分广泛用于网络中的流量控制协议的分析，调度器分析，以及与网络QoS控制相关的分析。文中主要对网络微积分的基本原理和重要结论做了一个系统的综述。     

工科《线性代数》的课程设计及探讨

文章主要讨论了工科专业线性代数的课程设计,并基于课程设计,对向量组的线性相关性进行了探讨及对矩阵的应用进行了研究.     

(L)集合范畴中的(L)幺半群模

本文引入以完备的Heyting代数为真值集L集合范畴及L幺半群范畴概念,构造了L幺半群模结构与L幺半群T代数结构;讨论了L积函子F与L幺半群单位函子G的伴随性,并证明了与该伴随对应的L比较函子K是一个同构,从而得出L幺半群单位函子G是L可模的。     

三角代数上的n阶导子系

设U=Tri(A,M,B)是三角代数,Dn={δ0,δ1,…,δn}为U上的一组可加映射且δ0=I.若A,B∈U有δm(AB)=∑mk=0Cmkδk(A)δm-k(B)(m=0,1,2,…,n),则称Dn为U上的一个n阶导子系,若A∈U有δm(A2)=∑mk=0Cmkδk(A)δm-k(A)(m=0,1,2,…,n),则称Dn为U上的一个n阶Jordan导子系.利用算子论的方法讨论了三角代数上的n阶导子系,证明了三角代数上的每个n阶Jordan导子系都是n阶导子系.     

矩阵指数计算的广义极分解方法

李群算法是在流形上计算微分方程数值解的方法,其基本思想是把数值解限制在比平直的欧氏空间小而又比解流形大的流形上,这样从整体上会对算法有约束作用,使得数值解不会随着时间的增加而变得面目全非。虽然如此,李群算法有一个重大缺陷,当离散后得到的矩阵规模变大时,矩阵指数计算的计算量会迅速增大,从而严重影响了李群算法的应用。针对这一问题,讨论了提高计算矩阵指数运算速度的广义极分解方法。     

Banach代数上映射的方向导数

设A为一有单位元的复Banach代数，D包含A为非空开集。西方中引入并研究了映射F：D→A的一阶方向导数DF（a）和高阶方向导数D^(n)f(a)。利用Riesz函数演算，证明了它们的一些性质，讨论了它们与内导子δa的关系。特别地，当f∈H（Ω），a∈A且δ(a)包含Ω时，得到了算子δ^(n)F(a)的一个表示。