一类n维非自治系统的周期解

本文应用Ｓｃｈａｕｄｅｒ和Ｒｏｔｈ不动点定理，给出了周期系统存在周期解的一组充分性条件，推广了文「１」「２」的结果。     

两自由度非线性振动系统周期运动及其稳定性研究

运用Liapunov函数方法，对一类两自由度非线性振动系统周期运动及其稳定性进行了研究，得到了存在唯一渐近稳定的周期解的充分条件。     

有食饵补充的二维捕食食饵模型的周期解与概周期解

对于有食饵补充的非定常二维捕食食饵模型，利用微分不等式，讨论了周期解的存在性及其全局吸收性，概周期解的存在性及其在壳扰动不的稳定性。     

核自旋器动力系统周期轨道的最小周期

核自旋器动力系统周期轨道的最小周期高占海（西北大学数学系，西安７１００６９）１．引言三维动力系统其中，此方程描述了一个典型的核自旋发生器（ｎｕｃｌｅａｒｓｐｉｎｇｅｎｅｒａｔｏｒ）的行为，这种核自旋发生器首先由Ｓｃｌｉｍｅｌｚｅｒ［２］于１９５３年提...     

周期系数Ricatti方程之周期解

本文利用Brouwer不动定理，研究了Ricatti方程的周期解的存在性。     

N种群周期系数非线性关系捕食—竞争系统的定性分析

本文应用比较定理，Ｂｒｏｕｗｅｒ不动点定理和Ｖ函数方法，讨论了Ｎ种群周期系数非线性关系捕食－竞争系统的正解的有界性，正周期解的存在性，正周期解的全局吸引性及唯一性。     

概周期系统概周期解的存在唯一性

应用构造Ляпунов函数的方法，讨论了非线性微分方程系概周期解的存在唯一性.同时给出了Liénard方程存在唯一概周期解的一组充分条件.     

Hénon映射的周期过程

本文研究了Ｈｅｎｏｎ映射Ｈ（ｘ，ｙ）＝（ａ＋ｂｙ－ｘ２，ｘ）的周期过程，给出了Ｈ有某些周期的充分必要条件或充分条件，得到其周期集的一段序结构．     

泛函微分方程的全局稳定周期解

本文综合运用相空间理论，泛函分析方法和李雅普诺夫第二方法，研究具无限时滞的泛函微分方程周期解的存在性，唯一性和稳定性问题，得到了新的结果．     

高维非自治系统非平凡周期解的存在性

本文利用非线性泛函分析中锥的理论，讨论了ｎ维非自治系统ｘ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ）ｘ∈Ｒ＾ｎ产工得到了系统（１）存在非平凡ω周期解的充分条件。     

培养学生科学思维和创新能力的研究与实践——谈大学数学研究型教学

通过从一个导数值等式的证明谈起,探讨教师在课堂教学中如何根据教学内容创设能激起学生新异感的问题情景,启发和引导学生发散思考,类比、联想、猜想,探索和发现新问题并给出解答.使学生思维不断攀升,丰富教学内容,激发学生兴趣,培养学生科学思维方法和创新能力.     

Mexican high school students' social representations of mathematics,its teaching and learning

This paper reports a qualitative research that identifies Mexican high school students’ social representations of mathematics. For this purpose, the social representations of ‘mathematics’, ‘learning mathematics’ and ‘teaching mathematics’ were identified in a group of 50 students. Focus group interviews were carried out in order to obtain the data. The constant comparative style was the strategy used for the data analysis because it allowed the categories to emerge from the data. The students’ social representations are: (A) Mathematics is…(1) important for daily life, (2) important for careers and for life, (3) important because it is in everything that surrounds us, (4) a way to solve problems of daily life, (5) calculations and operations with numbers, (6) complex and difficult, (7) exact and (6) a subject that develops thinking skills; (B) To learn mathematics is…(1) to possess knowledge to solve problems, (2) to be able to solve everyday problems, (3) to be able to make calculations and operations, and (4) to think logically to be able to solve problems; and (C) To teach mathematics is…(1) to transmit knowledge, (2) to know to share it, (3) to transmit the reasoning ability, and (4) to show how to solve problems.     

Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.This revised version was published online in September 2005 with corrections to the Cover Date.     

Dependence Graphs: Dependence Within and Between Groups

This paper applies the two-party dependence theory (Castelfranchi, Cesta and Miceli, 1992, in Y. Demazeau and E. Werner (Eds.) Decentralized AI-3, Elsevier, North Holland) to modelling multiagent and group dependence. These have theoretical potentialities for the study of emerging groups and collective structures, and more generally for understanding social and organisational complexity, and practical utility for both social-organisational and agent systems purposes. In the paper, the dependence theory is extended to describe multiagent links, with a special reference to group and collective phenomena, and is proposed as a framework for the study of emerging social structures, such as groups and collectives. In order to do so, we propose to extend the notion of dependence networks (applied to a single agent) to dependence graphs (applied to an agency). In its present version, the dependence theory is argued to provide (a) a theoretical instrument for the study of social complexity, and (b) a computational system for managing the negotiation process in competitive contexts and for monitoring complexity in organisational and other cooperative contexts.     

Polynomial Approximation of Functions: Historical Perspective and New Tools

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the thinking process of the creators of the theory. They used a Computer Algebra System to manipulate algebraic expressions and generate a wide variety of dynamic graphics; thus21st century technology was applied in order to “walk” with the students from the period of Euler in 1748 to the period of Runge in 1901. We describe some situations in which the combination of dynamic graphics,algorithms, and historical perspective enabled the students to improve their understanding of concepts such as limit, convergence, and the quality of approximation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Degenerate Linear Multicriteria Sensitivity

Sensitivity to perturbations of the vector objective function and/or the constraints is studied for the efficient (or weakly) set associated to a linear multicriteria program whose the feasible polyhedron is not necessarily assumed to be nondegenerate. Namely, the efficient set in the linear case being a connected union of some faces of the polyhedron, then we establish firstly second order necessary and sufficient conditions for the feasibility of a degenerate vertex under small perturbations, and finally, we give necessary and sufficient conditions of Simplex type, for a such vertex, or incident face to it, to be efficient and mostly to preserve this quality after the perturbations.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

Studying the interdependence of contractual and operational flexibilities in the market of specialty chemicals

This paper focuses on the market of specialty chemicals and deals with the joint investigation and valuation of contractual and operational flexibilities from a manufacturers’ point of view. In this market, customized services related to research, development and manufacturing of chemicals, intermediates and active pharmaceutical ingredients are offered to a small number of customers. Traditionally, customers are granted a large degree of freedom with respect to demand quantity and time exposing the manufacturer to high uncertainty and financial risk. Using a model-based approach we quantify the effect of this contractual flexibility and relate it to the manufacturing flexibility concerning capacity allocation. Through the valuation of these flexibilities we provide first insights for the manufacturer on which customer requests to accept, how to set up the associated contracts with the customers and how to allocate capacity for a given portfolio of products.     

研究式教学:初等代数研究教学模式引探

探索初等代数研究教学改革之路是适应时代发展,培养新型师范生的需要,是实现"教育以学生发展为本"新教育观的必由之路.在高师数学系开展研究式教学是一项十分有意义的实践,它是对传统教学模式的反思,对培养学生创新能力,启迪学生走上教育和科研之路具有方法论意义.研究式教学的基本模式有目标探究、过程探究和模型探究等,自由探究为其最高境界.     

基于本体的决策问题智能分析方法及其应用

在决策支持系统(DSS)中,决策问题分析理解的目的是识别决策问题的求解方法,以辅助用户快速求解问题,制定决策方案。为了提高DSS对决策问题分析理解的智能性和准确性,采用本体方法,定义了决策问题知识的本体概念结构,提出了一种基于本体的决策问题类型智能识别方法。最后,通过一个应用实例说明了该方法的具体分析过程,验证了该方法的有效性。