“军事行动避空侦察的时机和路线选择”评注

简述2016年全国研究生数学建模竞赛D题"军事行动避空侦察的时机和路线选择"的命题背景、数据来源和设计思路,并对参赛论文所涉及的有关问题进行评注.     

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.     

2015年全国研究生数学建模竞赛C题综述

对2015年全国研究生数学建模竞赛C题"移动通信中的无线信道指纹特征建模"进行综述,包括:命题背景和目的,可能的求解思路,以及评阅中发现的问题.     

变循环发动机部件法建模及优化述评

叙述了2013年全国研究生数学建模竞赛A题"变循环发动机部件法建模及优化"的命题背景和目的,分析了本赛题的建模及求解思路,总结了参赛队的一些好的做法和评阅过程中发现的一些问题,最后叙述了本赛题还需要继续思考的问题.     

2016年研究生数学建模竞赛B题综述

对2016年全国研究生数学建模B题"具有遗传性疾病和性状的遗传位点分析"进行综述,包括命题的背景和目的,解题的方法和思路,研究生竞赛中的答题情况及问题分析.     

与封堵溃口有关的重物落水后运动过程的分析

针对2010年全国研究生数学建模竞赛B题一"与封堵溃口有关的重物落水后运动过程"中的命题背景,建立了重物在水中的运动的数学模型,并处理了小型试验获取的相关数据.     

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.     

城市道路交通信号实时控制问题的评述

对2008年全国研究生数学建模竞赛B题"城市道路交通信号实时控制问题"的命题背景,问题要求,建模方法,模型算法,结果分析,模型应用、模型评价等相关问题进行了分析和评述.结果表明,该问题的选择具有重要理论和实际应用价值,对研究生创新能力的培养具有重要作用.     

High school students' use of representations in physics problem solving

Findings from physics education research strongly point to the critical need for teachers’ use of multiple representations in their instructional practices such as pictures, diagrams, written explanations, and mathematical expressions to enhance students' problem‐solving ability. In this study, we explored use of problem‐solving tasks for generating multiple representations as a scaffolding strategy in a high school modeling physics class. Through problem‐solving cognitive interviews with students, we investigated how a group of students responded to the tasks and how their use of such strategies affected their problem‐solving performance and use of representations as compared to students who did not receive explicit, scaffolded guidance to generate representations in solving similar problems. Aggregated data on students' problem‐solving performance and use of representations were collected from a set of 14 mechanics problems and triangulated with cognitive interviews. A higher percentage of students from the scaffolding group constructed visual representations in their problem‐solving solutions, while their use of other representations and problem‐solving performance did not differ with that of the comparison group. In addition, interviews revealed that students did not think that writing down physics concepts was necessary despite being encouraged to do so as a support strategy.     

Developing a statistical modeling framework to characterize Year 7 students’ reasoning

Some researchers advocate a statistical modeling approach to inference that draws on students’ intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of TinkerPlots Sampler technology. However, little is known about what statistical modeling reasoning students need to acquire. Drawing and building on previous research, this study aims to uncover the statistical modeling reasoning students need to develop. A design-based research methodology employing Model Eliciting Activities was used. The focus of this paper is on two 11-year-old students as they engaged with a bag weight task using TinkerPlots. Findings indicate that these students seem to be developing the ability to build models, investigate and posit factors, consider variation and make decisions based on simulated data. From the analysis an initial statistical modeling framework is proposed. Implications of the findings are discussed.     

太阳能小屋设计的问题解析

就2012年“高教社杯”全国大学生数学建模竞赛B题“太阳能小屋的设计”的背景作了介绍,针对该问题提出一种启发式算法的求解方法,虽然不能保证得到的结果是最优解,但至少还是比较好的可行解。在分析和求解过程中,针对学生在赛题试卷中出现的问题作了简要的说明。     

The next generation of UK military satellite communication systems

UK military satellite communications systems are currently provided by the Skynet programme. The current generation is collectively known as Skynet 4, and is due to be replaced from 2003 by the next generation. CDA has been asked to conduct an operational research study to review the potential communications requirements of the Ministry of Defence (MoD) in the period 2003–2013, and assess what contribution could be made to them by the proposed future military satellite communications system. This paper discusses some of the political and technical issues surrounding the work carried out. Technically, the study looked at the dynamic loading of five different satellite options in three scenarios set in 2010. Each combination of scenario and satellite was modelled, and the results produced in terms of the chosen measures of effectiveness. The sensitivity of these results to various assumptions was tested to determine the robustness of the results. The scenarios included land, air and maritime operations. In an area where little or no analysis had previously been attempted (at least in the military context) in the UK, this ‘intervention’ succeeded in clarifying the main issues, and setting a course for future work.     

A Markov Chain Application to Manpower Supply Planning

Markov chains have been suggested since the early sixties for modeling manpower supply, mostly in military, governmental and public agencies. An actual industrial application is presented. This will be of interest to managers as well as practitioners and students of operational research. The approach, use and validation of the Markov model are discussed, along with some limitations and extensions.     

An efficient approximate solution for stochastic Lanchester models

Combat modeling is one of the essential topics for military decision making. The Lanchester equation is a classic method for modeling warfare, and many variations have extended its limitations and relaxed its assumptions. As a model becomes more complex, solving it analytically becomes intractable or computationally expensive. Hence, we propose two approximation methods: moment-matching scheme and a supporting method called battle-end approximation. These methods give an approximate solution in a short amount of time, while maintaining a high level of accuracy in simulation results in terms of hypothesis testing and numerical verification. They can be applied to computationally intensive problems, such as optimal resource allocation and analysis with asymmetric power like snipers or stealth aircrafts.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

A reduced FE formulation based on POD method for hyperbolic equations

A proper orthogonal decomposition (POD) method was successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, namely, apply POD method to a classical finite element (FE) formulation for second-order hyperbolic equations with real practical applied background, establish a reduced FE formulation with lower dimensions and high enough accuracy, and provide the error estimates between the reduced FE solutions and the classical FE solutions and the implementation of algorithm for solving reduced FE formulation so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced FE formulation based on POD method is feasible and efficient for solving FE formulation for second-order hyperbolic equations.     

A Modeling Perspective on the Teaching and Learning of Mathematical Problem Solving

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving.