基金评审中的归一化分析方法与应用

本以国家自然科学基金评审为主要研究对象，提出平均非共识度和最大非共识度的概念，针对项目评分的最大非共识度分布不一致的问题，应用优化理论、归一化方法等，建立了确定平均非共识度和最大非共识度的优化模型与算法，克服了因最大非共识度的不同影响项目评审公正性的弊端，经国家自然科学基金委员会部分学科的应用，收到很好效果。     

矩阵非中心Г－分布

本文定义了矩阵形式的非中心－分布。它将常见的一元Ｇａｍｍａ分布，非中心Ｘ２－分布，和多元分析中的中心则Ｗｉｓｈａｒｔ分布，非中心Ｆ－分布等纳入一个整体，进而推导了它的特征函数与特征根的分布密度函数，为一些检验奠定了基础．     

Hilbert空间中渐近殆非扩张曲线的强遍历收敛定理

设C为Hilbert空间H的非空子集，G为一个交换半群．文中定义了G上渐近殆非扩张曲线“（·）：G→C，证明了渐近殆非扩张曲线的强遍历收敛定理．应用于半群，得到了在失去凸性的情况下，渐近非扩张型半群的殆轨道的强遍历收敛定理．推广和改进了以前所有的结果。     

非负性最小方差集的选择理论与实现

本文首先给出了最小方差集的运算模型，在此基础上指出了非负解的重要意义，并给出了非负解的枚举算法，最后给出了一个实例     

非齐次马尔科夫链遍历性的一些结果

本文利用两个非齐次马尔科夫链的转移矩阵列的比较，讨论了两个链启遍历性的关系，得到一个非齐次马尔科夫链是强遍历的一些充分条件．本文还分析了非齐次马尔科夫链的一致强、弱遍历性的关系，得到一个非齐次马尔科夫链是一致强遍历的一些充分条件．     

变质量高阶非Четаев型非完整约束系统动力学

本文给出了高阶非型约束加在广义虚位移上的限制条件，建立了变质量高阶非型非线性非完整系统的Ｒｏｕｔｈ方程、方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌｌ方程；给出了高阶非型约束系统“ｄ”与“δ”之间的交换关系，建立了其积分变分原理；并得到了变质量高阶非型约束系统的广义Ｎｏｅｔｈｅｒ守恒律．     

变质量高阶非ЧeTaeB型非完整约束系统动力学

本文给出了高了阶非ЧｅＴａｅＢ约束加在广义虚位移上的限制条件，建立了变质量高阶非ЧｅＴａｅＢ型非线性非完整系统的Ｒｏｕｔｈ方程，ЧａПЛЫГИН方程、Ｎｉｅｌｓｅｎ方程，给出了高阶非ЧｅＴａｅＢ型约束系统“ｄ”与“δ”之间的产换关系，建立了其积分变分原理，并得到了变质量高阶非ЧｅＴａｅＢ型约束系统的广义Ｎｏｅｔｈｅｒ守恒律。     

基于非单调线搜索非拟牛顿法的全局收敛性

本文就非拟牛顿法在无约束最优化问题上，对采用非单调线搜索的情况下是否具有全局收敛性进行了研究，在目标函数满足一致凸的条件下，证明了非拟牛顿族是全局收敛的．     

奇异半线性热方程初值问题解的存在性与Blow-up问题

本文讨论如下奇异半线性热方程的初值问题其中γ＞1，σ＞O，f（x）连续有界非负但不恒为零．我们讨论了问题（1），（2）非负局部经典解的存在性和非负整体解的不存在问题，得到当0＜σ＜1且时，（1），（2）没有非负整体解．当σ＝1且时，（1），（2）没有非负整体解，当σ＞1时（1），（2）没有非负整体解．     

振荡器链的非成对交联

本文考虑振荡链的非成对交联，包括单向交联和非成对双向交联，给出了锁相解的存在定理，并对其解的渐近性质作了分析。最后，用数值例子对非成对交联和成对交联作了一些比较分析。     

Using the Tower of Hanoi puzzle to infuse your mathematics classroom with computer science concepts

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi puzzle. These concepts include, but are not limited to, conditionals, iteration, and recursion. Lessons, such as the one proposed in this article, are easily implementable in mathematics classrooms and extracurricular programmes as they are good candidates for ‘drop in’ lessons that do not need to fit into any particular place in the typical curriculum sequence. As an example for readers, the author describes how she used the puzzle in her own Number Sense and Logic course during the federally funded Upward Bound Math/Science summer programme for college-intending low-income high school students. The article explains each computer science term with real-life and mathematical examples, applies each term to the Tower of Hanoi puzzle solution, and describes how students connected the terms to their own solutions of the puzzle. It is timely and important to expose mathematics students to computer science concepts. Given the rate at which technology is currently advancing, and our increased dependence on technology in our daily lives, it has become more important than ever for children to be exposed to computer science. Yet, despite the importance of exposing today's children to computer science, many children are not given adequate opportunity to learn computer science in schools. In the United States, for example, most students finish high school without ever taking a computing course. Mathematics lessons, such as the one described in this article, can help to make computer science more accessible to students who may have otherwise had little opportunity to be introduced to these increasingly important concepts.     

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.     

考虑网络外部性的生鲜企业渠道选择策略研究

考虑到生鲜产品容易变质而且线上配送时间较长,并且线上销售可为消费者带来额外网络外部性,传统生鲜企业在电商冲击的背景下需要考虑是否入驻电商平台开拓线上业务。为解决此类企业所面临渠道选择问题,本文考虑一个传统生鲜企业和一个主导电商市场的电商平台,并通过构建理论模型研究企业最优生鲜产品定价和渠道选择策略。研究结果表明,若平台所收取年服务费较低,则企业应入驻平台;反之,企业不应入驻平台。此外,消费者网络外部性敏感程度对企业入驻平台行为具有正影响。在拓展模型,本文考虑分散式供应链情形下企业最优渠道选择,结果表明相较于集中式决策,分散式供应链情形下零售商更不愿意入驻平台。此外,本文通过设计收益共享契约以协调生鲜企业与电商平台,并发现通过契约协调,零售商更愿意入驻电商平台。     

非常规油气资源开发投资决策优化模型研究

非常规油气资源作为最现实的可替代能源,对其进行勘探和开发对于降低日益加大的石油供需矛盾缺口和确保国家能源安全均具有重要的战略意义。然而,非常规油气资源勘探开发十分复杂,开发投资决策好坏已经成为制约其能否实现规模化和产业化的关键问题,科学投资决策问题已逐步成为石油企业高层管理者的主要职责。针对非常规油气资源开发投资的多阶段多目标决策优化难题,以可供开发区块的资源分配为重点研究对象,从解决不同区块投资规模入手,运用多阶段决策、多目标决策和不确定多属性方案优选的方法理论,通过剖析非常规油气开发投资决策过程及其复杂性特征,将开发投资决策过程进行形式化描述并在计算机中加以实现,从而得以实现开发投资决策方案的动态性调整。本项研究不仅有助于深化多目标动态优化决策理论的研究,还为解决非常规油气资源开发投资决策难题提供一种新的思路和方法。     

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.     

带有常数返回率的动态易逝品供应链协调模型

以动态易逝品为研究对象,探讨了由单个制造商单个零售商所组成的两层供应链生产订购协调问题.在假定零售商所售产品存在返回的前提下,分别建立了集中决策和分散决策模型,并证明了这两个模型解的存在唯一性.提出了一个两阶段的收益共享契约,该契约不仅能达到供应链协调,而且还能实现供应链两成员的"双赢".最后,通过数值实例来验证模型的结论并得出相关管理启示.     

基于集对分析的地区经济发展水平综合评价研究——以环渤海地区为例

地区经济发展水平问题是一个复杂的系统问题,运用集对分析同一度概念的综合评价方法,以环渤海地区为例,对其五个省市经济发展情况进行了综合评价、排序及分析,为环渤海地区经济发展提供借鉴和参考.     

在位企业适应突破性创新的投资策略研究

突破性技术创新的出现对企业的生存环境和技术基础产生巨大的冲击,在位企业应对突破性创新时一般有被动适应和主动适应两种策略。当突破性创新已经发生,在位企业只能根据企业自身条件和特点被动地适应技术变革。当突破性创新有可能发生时,在位企业会从战略视角作出预期,采取灵活性的投资策略,主动地适应突破性创新的冲击。本文通过一个简单的投资模型,对在位企业适应突破性创新的两种不同策略进行了分析,并给出相应的算例。     

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。     

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.