2015年全国研究生数学建模竞赛F题综述

叙述了2015年全国研究生数学建模竞赛F题"旅游路线规划问题"的命题背景和目的,分析了本赛题的建模及求解思路,对评阅中发现的问题进行了综述,最后叙述了本赛题还需继续思考的问题.     

2016年全国研究生数学建模竞赛A题综述

叙述了2016年全国研究生数学建模竞赛A题"多无人机协同任务规划"的命题背景和目的,分析了本赛题的建模及求解思路,对评阅中发现的问题进行了综述,最后叙述了本赛题还需继续思考的问题.     

2018年中国研究生数学建模竞赛E题综述

叙述了2018年中国研究生数学建模竞赛E题"多无人机对组网雷达的协同干扰"的命题背景和目的,分析了本赛题的建模及求解思路,对评阅中发现的问题进行了综述,最后讨论了本赛题还需继续思考的问题.     

2018年中国研究生数学建模竞赛D题综述

介绍了2018年中国研究生数学建模竞赛D题"基于卫星高度计海面高度异常资料获取潮汐调和常数方法及应用"的命题背景和目的,分析了本赛题的建模及求解思路,对评阅中发现的问题进行了综述,最后提出了本赛题还需继续思考的问题.     

军事行动避空侦察的时机和路线选择的评述

建模竞赛D题"军事行动避空侦察的时机和路线选择"来源于国家反卫星侦察的军事背景,其核心是要找出卫星的运行规律并建立相关预测模型,体现了全国研究生数学建模竞赛的特色.阐述了命题背景,分析了本赛题的建模及求解思路.通过赛题的研究,使得研究生们更加关心国防建设,引导学生把数学建模应用到军事领域建模中来,解决实际问题.     

第十届研究生全国研究生数学建模竞赛——赛题“中等收入定位与人口度量模型研究”述评

对第十届全国研究生数学模型竞赛中赛题之一"中等收入定位与人口度量模型研究"的有关情况进行简要述评,认为达到了本赛题的设计目标,对培养参赛研究生思考重大经济、社会问题方面有重要意义.     

2018年中国研究生数模竞赛F题的赛后综述

美国世博国际有限公司(Sabre?)有幸参与了2018年《第十五届中国研究生数学建模竞赛》的命题和赛后评审工作,负责的赛题是F题《机场新增卫星厅对中转旅客影响的评估方法》.介绍命题思路、解题方法和评审感想.本赛题取材于中国东方航空公司和上海浦东国际机场,但对数据进行了适当修改.     

2016年全国研究生数学建模竞赛E题赛题点评

首先阐明了2016年全国研究生数学建模竞赛E题"粮食最低收购价政策问题研究"的研究背景和问题研究的实际意义.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了详细的叙述.最后,对学生论文中出现的问题、难点以及创新性等方面做了点评.     

2014年全国研究生数学建模竞赛D题赛题点评

首先阐明了2014年全国研究生数学建模竞赛D题"人体营养健康角度的中国果蔬发展战略研究"的研究背景.接着,针对每一个问题,从研究思路、研究方法、研究结论等方面均作了叙述.最后,对学生论文出现的问题、难点以及创新性等方面均做了点评.     

2018年中国研究生数学建模竞赛A题评阅综述

为2018年中国研究生数学建模竞赛A题"关于跳台跳水体型系数设置的建模分析"的评阅综述,含评阅要点以及竞赛论文中较普遍存在的一些问题.     

“关灯”游戏的数学建模与求解

对互联网上的一个数学游戏的控制问题,进行了一般性推广,运用数学建模的方法给出了其基于有限域上的线性方程组的数学模型及求解.     

围绕财经特色主题 加强《高等代数》精品课程建设

我校精品课程《高等代数》建设的思路是,围绕财经特色主题,坚持以高等代数理论为基础,以经济、管理类的专业为依托,以数学实验室为训练基地,将数学建模的思想融入到《高等代数》的教学活动中.这种教学模式的改变不仅有利于学生的培养,而且有助于培养出一支有较高水平的师资队伍.使我们的《高等代数》课程真正成为高水平、高质量的示范性课程.     

中国现行财政体制下“买税”行为的博弈分析

博弈论为理论依据,通过对高、低两种任务下买税利益团体和上级监管部门的利益偏好和行为特征进行建模对比分析,考察影响其行为的各种因素,从经济学角度探求引起“买税”行为的根源,并试着给出建议.     

Computing tournament solutions using relation algebra and RelView

We describe a simple computing technique for the tournament choice problem. It rests upon relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView’s labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory.     

Arbres de Markov couplePairwise Markov trees

The Hidden Markov Chain (HMC) models are widely applied in various problems. This succes is mainly due to the fact that the hidden model distribution conditional on observations remains a Markov chain distribution, and thus different processings, like Bayesian restorations, are handleable. These models have been recetly generalized to “Pairwise” Markov chains, which admit the same processing power and a better modeling one. The aim of this Note is to show that the Hidden Markov trees, which can be seen as extensions of the HMC models, can also be generalized to “Pairwise” Markov trees, which present the same processing advantages and better modelling power. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 79–82.     

<Emphasis FontCategory="NonProportional">pyomo.dae</Emphasis>: a modeling and automatic discretization framework for optimization with differential and algebraic equations

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http://www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, predefined forms of differential equations, providing a high degree of modeling flexibility and the ability to express constraints that cannot be easily specified in other modeling frameworks. Other key features of pyomo.dae are the ability to specify optimization problems with high-order differential equations and partial differential equations, defined on restricted domain types, and the ability to automatically transform high-level abstract models into finite-dimensional algebraic problems that can be solved with off-the-shelf solvers. Moreover, pyomo.dae users can leverage existing capabilities of Pyomo to embed differential equation models within stochastic and integer programming models and mathematical programs with equilibrium constraint formulations. Collectively, these features enable the exploration of new modeling concepts, discretization schemes, and the benchmarking of state-of-the-art optimization solvers.     

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using micro-analysis to examine modeling processes. The findings and the MTDs were used to critically question the implications of using modeling cycles as a theory of mathematical modeling processes.     

Every rose has its thorn: secondary teachers’ reasoning about statistical models

Statistical modeling is a core component of statistical thinking and has been identified by several countries as a curricular goal for secondary education. However, many secondary teachers have minimal preparation for teaching this topic. The goal of this research study is to learn about teachers’ perceptions of the role statistical models play in statistical inference and how these perceived purposes affect their reasoning about statistical models and inference. Problem-solving interviews were conducted with four in-service teachers who had recently taught a modeling and simulation-based introductory statistics course. Teachers’ responses suggest they may not see modeling variation as the primary purpose of statistical modeling and instead substitute two other purposes: making a decision and replicating the data collection process. Suggestions for how to build on teachers’ transitional conceptions and refocus attention on modeling variation are discussed.     

Chaı̂nes de Markov TripletTriplet Markov Chains

The Hidden Markov Chains (HMC) are widely applied in various problems. This succes is mainly due to the fact that the hidden process can be recovered even in the case of very large set of data. These models have been recetly generalized to ‘Pairwise Markov Chains’ (PMC) model, which admit the same processing power and a better modeling one. The aim of this note is to propose further generalization called Triplet Markov Chains (TMC), in which the distribution of the couple (hidden process, observed process) is the marginal distribution of a Markov chain. Similarly to HMC, we show that posterior marginals are still calculable in Triplets Markov Chains. We provide a necessary and sufficient condition that a TMC is a PMC, which shows that the new model is strictly more general. Furthermore, a link with the Dempster–Shafer fusion is specified. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 275–278.