Development of a new dioid algebraic model for manufacturing with the scheduling decision making capability

The dioid algebraic model, which is developed in this paper, captures the discontinuous nature of Discrete-Event Dynamic Systems and has widespread applicational capabilities. As a further improvement over existing dioid algebraic models, decision making capability is introduced to the developed dioid algebraic model. With this new capability, sequencing decisions at each machine can be represented in the model. Furthermore, the developed algebraic model is capable of representing job and resource unavailability, technological constraints, alternative process plans, and is easily modifiable to include new jobs and exclude finished jobs. In a possible application, the model can be used in representing dynamic scheduling problems and can be used as an important part of a real-time control and scheduling scheme of a manufacturing system.     

基于Rough集的牛顿迭代法求方程近似解算法

Rough集理论作为一种新型的数学工具已广泛应用于各个领域。提出一种基于Rough集的牛顿迭代法求方程近似解算法，该算法将Rough理论中的下近似和上近似与牛顿迭代法有机地结合起来，寻找方程的近似解，其优点在于所求方程的根是一个精确的区间，该区间中任意实数都可作为所求方程的近似解，避免了一般方法求方程的近似解，把求得的近似数作为近似解，算法计算简单，易推广到其它的近似计算中，同时，有助于人们深刻理解Rough集理论本质。     

Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple

Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as more geometric topics of invariant theory, e.g., the Graßmann-Cayley bracket algebra, are all covered by the Hopf algebraic framework. The new branch of experimental mathematics allows one to easily enter these fields through direct calculations using symbolic manipulation and computer algebra system (CAS). We discuss problems which were solved when building the BIGEBRA package for Maple and CLIFFORD to handle tensor products, Graßmann and Clifford algebras, coalgebras and Hopf algebras. Recent results showing the usefulness of CAS for investigating new and involved mathematics provide us with examples. An outlook on further developments is given.     

Recursive operations in image algebra

The image algebra, developed by Ritter et al. at the University of Florida, is an algebraic structure for image processing. The three commonly used high-level image-template operations provided by the image algebra are the generalized convolution , the additive maximum or generalized lattice convolution {ie23-1}, and the multiplicative maximum {ie23-2}. These are used to realize various nonrecursive image transformations, including morphological transformations. Along with nonrecursive transformations, a class of recursive transformations, such as IIR filters, adaptive dithering, and predictive coding, are also widely used in signal and image processing. In this paper the notions of recursive templates and recursive template operations are introduced; these allow the image algebra to express a set of linear and nonlinear recursive transformations. Algebraic properties of these recursive operations are given, providing a mathematical basis for recursive template composition and decomposition. Finally, applications of recursive template operations in specifying some image processing algorithms are presented.     

抽象函数的Riemann—Stieltjes积分

本文给出了从闭区间[a,b]到局部凸拓扑代数的抽象函数的Riemann—Stieltijes积分的定义。讨论了这种积分的性质及存在条件,并给出了一类连续线性算子的表达式。     

用极小代数方法求解最短路径问题的进一步探讨

用极小代数方法求由n个节点组成的有向连接图的最短路径公式是:A~*=sum from k=0 to n-1 (?)A~k。本文在此基础上给出了求最短路径的充要条件:A~(l+1)=A~l。举出最短运输网络实例加以说明,并和动态规划法作了比较,指出了极小代数法的优越之处。     

动载荷反演分析技术研究综述

介绍了动载荷反演分析技术工程应用背景,综述了动载荷反演分析理论研究的最新进展.从动载荷反演分析理论、工程应用等方面回顾了动载荷反演分析技术的发展历程,探讨了动载荷反演分析研究中存在的关键科学问题,对动载荷反演分析技术应用于实际工程,后续需要进一步开展的研究方向进行了展望.     

分析动力学三个问题的研究进展

分析力学的发展涉及理论的和应用的诸多方面.本文在分析力学与数学交缘的三个问题上综述分析力学的近代发展.第一是利用Lie群和Lie代数的一些成果来研究分析动力学方程的积分问题.第二是将分析力学的经典和近代积分方法应用于一般微分方程的积分问题.第三是将分析动力学方程在一定条件下化成梯度系统的方程,再用梯度系统的性质来研究力学系统的动力学行为.     

代数图论方法在并行处理中的应用研究

并行处理提高了计算机解决问题的运算速度,在当代计算机科学技术占有重要的地位。代数图论方法对于并行处理的研究起着重要作用。就并行互连网结构与负载平衡中使用的代数图论方法进行了阐述,说明了代数图论方法为更深一步地研究并行处理指明了方向。     

一种结合时间区间代数建模的主动系统的故障诊断方法

研究了在全局时钟、线性观测、串行事件触发的主动系统的故障诊断,在原有主动系统的自动机建模的基础上,引入时间区间代数表达更为详细的时间约束信息,构成带有时间的自动机对系统组件建模;同样在所得观测中也加入相应的更为详细的时间信息.由于加上了时间的约束,可使得诊断的解释空间进一步缩小,从而在一定情况下可提高诊断效率.最后讨论了非线性不确定观测或并发等一般情形下的处理方法.