A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Categorical Approach to Horizontal Structuring and Refinement of High-Level Replacement Systems

Based on the well-known theory of high-level replacement systems – a categorical formulation of graph grammars – we present new results concerning refinement of high-level replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. This concept is called Q-transformations and is established within the framework of high-level replacement systems. The main idea is to supply rules with an additional morphism, which belongs to a specific class Q of morphisms. This leads to the new notions of Q-rules and Q-transformations. Moreover, several concepts and results of high-level replacement systems are extended to Q-transformations. These are sequential and parallel transformations, union, and fusion, based on different colimit constructions. The main results concern the compatibility of these constructions with Q-transformations that is the corresponding theorems for usual transformations are extended to Q-transformations. Finally, we demonstrate the application of these techniques for the special case of Petri nets to a case study concerning the requirements engineering of a medical information system.     

Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two

Let be the variety of associative (special Jordan, respectively) algebras over an infinite field of characteristic 2 defined by the identity ((((x ₁,x ₂),x ₃), ((x ₄,x ₅),x ₆)), (x ₇,x ₈)) = 0 (((x ₁ x ₂ · x ₃)(x ₄ x ₅ · x ₆))(x ₇ x ₈) = 0, respectively). In this paper, we construct infinite independent systems of identities in the variety ( , respectively). This implies that the set of distinct nonfinitely based subvarieties of the variety has the cardinality of the continuum and that there are algebras in with undecidable word problem.     

中心代数上的矩阵方程组

设Ω是一个特征非2的具有对合反自同构的有限维中心代数.本文研究Ω上的两个矩阵方程组,分别给出了其有一般解和次(斜)自共轭解的充要条件.     

基于截断δ-冲击模型的不完全维修更换策略

本文在截断δ-冲击模型的基础上,考虑了因系统劣化而导致的冲击失效门限值与维修时间的变化,扩充失效状态,从而提出一种新的截断δ-冲击模型。以最小费用为目标,稳态可用度为约束条件,建立N型更换策略的不完全维修更换策略模型,并给出三种常用冲击到达间隔分布的期望寿命。最后通过算例验证模型的有效性,并对参数进行灵敏度分析。     

一类三次Kolmogorov系统可积性的判断方法

研究了一类系统可积性的判断方法问题,特别地,给出了易于计算的一类任意的1:-q型三次Kolmogorov系统原点的鞍点量的代数递推公式,同时还给出了一个相应的例子.     

On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.     

一阶非线性微分方程组的反周期解

讨论了一阶非线性常微分方程组x′=G(t,x(t)),x(0)=-x(π),x∈R~n的反周期解问题,给出了此类方程组解的存在惟一性的判定定理,并通过实例对所得定理进行了进一步解释说明.     

有首次积分的K型单调系统

本文考察Smith[7]意义上的K型单调系统=F(χ)的渐近性质.在假定系统无闭轨且F有一个具有一定单调性质的首次积分的条件下,我们证明了,这类系统在一定区域内的解或者收敛于某一平衡点,或者对于充分大的(?)离开该区域的任一紧子集.     

Comparison of Sampling Schemes with and without Replacement

An urn contains colored balls, ~balls of each of different colors. The balls are drawn sequentially and equiprobably, one ball at a time, and then each drawn ball drawn is either returned to the urn (sampling with replacement) or left outside the urn (sampling without replacement). The drawing continues until some colors are drawn at least ~times each. Observable statistics are the numbers , , of colors that have appeared precisely ~times each by the stopping time. The asymptotic behavior as of these values for each of the two sampling models is studied; the possibility of their use for identifying the model is discussed.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

On the Automorphism Group of the First Weyl Algebra

Let A ₁: = 𝕜[t, ?] be the first algebra over a field 𝕜 of characteristic zero. Let Aut_𝕜(A ₁) be the automorphism group of the ring A ₁. One can associate to each right ideal I of A ₁ a subgroup of Aut_𝕜(A ₁) called the isomorphism subgroup of I. In this article, we show that each such isomorphism subgroup is equal to its normalizer. For that, we study when the isomorphism subgroup of a right ideal of A ₁ contains a given isomorphism subgroup.     

竞争环境下基于退换货的网购供应链动态均衡研究

研究竞争环境下基于退换货的网购供应链动态均衡模型.此供应链包含多个生产商、电商、快递商及需求市场.将快递商的运输速度作为竞争的一个重要因素进行研究.通过正弦函数说明,网购供应链的市场需求也呈季节性变化.利用纳什均衡及变分不等式得到各层决策者的竞争均衡解.通过分析换货比重得出电商应减少消费者的退货率,以提高整条供应链的利润和竞争能力.并利用数值算例说明模型的正确性与合理性.     

基于两种不同延迟过程的退化系统之最优更换策略

将延迟几何过程进行推广并引入延迟α-幂过程,以用于处理退化过程会发生延迟且延迟发生的概率会随故障次数的增多而减小的系统.以系统的故障次数为更换策略,以平均费用率为目标函数,建立了维修更换模型,证明了最优维修更换策略的存在性.最后,通过一个数值例子验证了方法的有效性.     

带一类第一积分的非完整系统的Szebehely问题

研究非完整系统动力学的一类逆问题·给出非完整系统的运动方程及其显式，考虑一类仅受齐次非完整约束的力学系统的Ｓｚｅｂｅｈｅｌｙ问题，研究已知一类第一积分的一般非完整系统的情形·最后举例说明其应用·     

Factorization of the Loop Algebra and Integrable Toplike Systems

With any Lie algebra of Laurent series with coefficients in a semisimple Lie algebra and its decomposition into a sum of the subalgebra consisting of the Taylor series and a complementary subalgebra, we associate a hierarchy of integrable Hamiltonian nonlinear ODEs. In the case of the so(3) Lie algebra, our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows generating integrable deformations for known integrable models.     

Oscillation and Nonoscillation Criteria for Two-Dimensional Systems of First Order Linear Ordinary Differential Equations

Sufficient conditions are established for the oscillation and nonoscillation of the system     

一致稳定合作系统的全局稳定性

本文讨论了一类合作系统的解的收敛性.其基本假设是Jacobi矩阵在中一致稳定．在这个假设下,我们对这类系统给出了完整的全局性态．本文的主要结果如下：如果系统有一个正平衡点,那么它在Int中全局渐近稳定,并给出了系统的非负平衡点全局渐近稳定的充分必要条件．     

Towards an Automated Reduction Method for Polynomial ODE Models of Biochemical Reaction Systems

This paper presents the first version of an algorithmic scheme dedicated to the model reduction problem, in the context of polynomial ODE models derived from generalized chemical reaction systems. This scheme, which relies on computer algebra, is implemented within a new MAPLE package. It is applied over an example. The qualitative analysis of the reduced model is afterwards completely carried out, proving the practical relevance of our methods. We would like to thank Marc Lefranc and Pierre-Emmanuel Morant. This work was partially supported by the PPF Bioinfo of the University Lille I.