2015美赛D题H奖论文

2015美赛D题H奖论文
2015美赛D题H奖论文

美赛一等奖经验总结

当我谈数学建模时我谈些什么——美赛一等奖经验总结 作者:彭子未 前言:2012 年3月28号晚,我知道了美赛成绩,一等奖(Meritorus Winner),没有太多的喜悦,只是感觉释怀,一年以来的努力总算有了回报。从国赛遗憾丢掉国奖,到美赛一等,这一路走来太多的不易,感谢我的家人、队友以及朋友的支持,没有你们,我无以为继。 这篇文章在美赛结束后就已经写好了,算是对自己建模心得体会的一个总结。现在成绩尘埃落定,我也有足够的自信把它贴出来,希望能够帮到各位对数模感兴趣的同学。 欢迎大家批评指正,欢迎与我交流,这样我们才都能进步。 个人背景:我2010年入学,所在的学校是广东省一所普通大学,今年大二,学工商管理专业,没学过编程。 学校组织参加过几届美赛,之前唯一的一个一等奖是三年前拿到的,那一队的主力师兄凭借这一奖项去了北卡罗来纳大学教堂山分校,学运筹学。今年再次拿到一等奖,我创了两个校记录:一是第一个在大二拿到数模美赛一等奖,二是第一个在文科专业拿数模美赛一等奖。我的数模历程如下: 2011.4 校内赛三等奖 2011.8 通过选拔参加暑期国赛培训(学校之前不允许大一学生参加) 2011.9 国赛广东省二等奖 2011.11 电工杯三等奖 2012.2 美赛一等奖(Meritorious Winner) 动机:我参加数学建模的动机比较单纯,完全是出于兴趣。我的专业是工商管理,没有学过编程,觉得没必要学。我所感兴趣的是模型本身,它的思想,它的内涵,它的发展过程、它的适用问题等等。我希望通过学习模型,能够更好的去理解一些现象,了解其中蕴含的数学机理。数学模型中包含着一种简洁的哲学,深刻而迷人。 当然获得荣誉方面的动机可定也有,谁不想拿奖呢? 模型:数学模型的功能大致有三种:评价、优化、预测。几乎所有模型都是围绕这三种功能来做的。比如,今年美赛A题树叶分类属于评价模型,B题漂流露营安排则属于优化模型。 对于不同功能的模型有不同的方法,例如评价模型方法有层次分析、模糊综合评价、熵值法等;优化模型方法有启发式算法(模拟退火、遗传算法等)、仿真方法(蒙特卡洛、元胞自动机等);预测模型方法有灰色预测、神经网络、马尔科夫链等。在数学中国网站上有许多关于这些方法的相关介绍与文献。

美赛优秀论文

The Design of Snowboard Halfpipe Abstract: Based on the snowboard movement theory, the flight height depends on the out- velocity. We take the technical parameters of four sites and five excellent snowboarders for statistical analysis. As results show that the size of halfpipe (length, width and depth, halfpipe slope) influence the in- velocity and out- velocity. Help ramp, the angle between the snowboard’s direction and speed affect velocity ’s loss. For the halfpipe, we established the differential equation model, based on weight, friction, air density, resistance coefficient, the area of resistance, and other factors and the law of energy conservation. the model’s results show that the snowboarders’ energy lose from four aspects (1) the angle between the direction of snowboard and the speed, which formed because of the existing halfpipe (2) The friction between snowboard and the surface (3) the air barrier (4) the collision with the wall for getting vertical speed before sliping out of halfpipe. Therefore, we put forward an improving model called L-halfpipe,so as to eliminate or reduce the angle between the snowboard and the speed .Smaller radius can also reduce the energy absorption by the wall. At last, we put forward some conception to optimize the design of the halfpipe in the perspective of safety and producing torsion. Key words:snowboard; halfpipe; differential equation model;L-halfpipe

美赛论文优秀模版

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________ Team Control Number 11111 Problem Chosen ABCD For office use only F1 ________________ F2 ________________ F3 ________________ F4 ________________ 2015 Mathematical Contest in Modeling (MCM/ICM) Summary Sheet In order to evaluate the performance of a coach, we describe metrics in five aspects:historical record, game gold content, playoff performance, honors and contribution to the sports. Moreover, each aspect is subdivided into several secondary metrics. Take playoff performance as example, we collect postseason result (Sweet Sixteen, Final Four, etc.) per year from NCAA official website, Wikimedia and so on. First, ****grade. To eval*** , in turn, are John Wooden, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Knight. Time line horizon does make a difference. According to turning points in NCAA history, we divide the previous century into six periods with different time weights which lead to the change of ranking. We conduct sensitivity analysis on FSE to find best membership function and calculation rule. Sensitivity analysis on aggregation weight is also performed. It proves AM performs better than single model. As a creative use, top 3 presidents(U.S.) are picked out: Abraham Lincoln, George Washington, Franklin D. Roosevelt. At last, the strength and weakness of our mode are discussed, non-technical explanation is presented and the future work is pointed as well. Key words: Ebola virus disease; Epidemiology; West Africa; ******

美赛一等奖论文-中文翻译版

目录 问题回顾 (3) 问题分析: (4) 模型假设: (6) 符号定义 (7) 4.1---------- (8) 4.2 有热水输入的温度变化模型 (17) 4.2.1模型假设与定义 (17) 4.2.2 模型的建立The establishment of the model (18) 4.2.3 模型求解 (19) 4.3 有人存在的温度变化模型Temperature model of human presence (21) 4.3.1 模型影响因素的讨论Discussion influencing factors of the model (21) 4.3.2模型的建立 (25) 4.3.3 Solving model (29) 5.1 优化目标的确定 (29) 5.2 约束条件的确定 (31) 5.3模型的求解 (32) 5.4 泡泡剂的影响 (35) 5.5 灵敏度的分析 (35) 8 non-technical explanation of the bathtub (37)

Summary 人们经常在充满热水的浴缸里得到清洁和放松。本文针对只有一个简单的热水龙头的浴缸,建立一个多目标优化模型,通过调整水龙头流量大小和流入水的温度来使整个泡澡过程浴缸内水温维持基本恒定且不会浪费太多水。 首先分析浴缸中水温度变化的具体情况。根据能量转移的特点将浴缸中的热量损失分为两类情况:沿浴缸四壁和底面向空气中丧失的热量根据傅里叶导热定律求出;沿水面丧失的热量根据水由液态变为气态的焓变求出。因涉及的参数过多,将系数进行回归分析的得到一个一元二次函数。结合两类热量建立了温度关于时间的微分方程。加入阻滞因子考虑环境温湿度升高对水温的影响,最后得到水温度随时间的变化规律(见图**)。优化模型考虑保持水龙头匀速流入热水的情况。将过程分为浴缸未加满和浴缸加满而水从排水口溢出的两种情况,根据能量守恒定律优化上述微分方程,建立一个有热源的情况下水的温度随时间变化的分段模型,(见图**) 接下来考虑人在浴缸中对水温的影响。我们从各个方面进行分析:人的体温恒定在37℃左右,能量仅因人的生理代谢而丧失,这一部分数量过小可以不考虑;而人在水中人的体积和运动都将引起浴缸中水散热面积和总质量的变化,从而改变了热量的损失情况。因人的运动是连续且随机的,利用MATLAB生成随机数表示人进入水中的体积变化量,将运动过程离散化。为体现其振荡的特点,我们利用三角函数拟合后离散的数据,以频率和振幅的变化来反映实际现象。将得到的函数与上述模型相结合,作图分析其变化规律(见图**)。 利用以上温度变化的优化模型,结合用水量建立多目标优化模型。将热水浴与缸中水温差、浴缸水温偏离最适温度最值进行正向化和归一化再加权求和定义为舒适度。在流量维持稳定的情况下,要求舒适度越大而用水量越小。因该优化模型中的约束条件中含有微分方程,难以求解,则对其进行离散仿真,采用模拟退火算法求解全局最优解。最后讨论了加入泡泡剂后对模型的影响,求得矩形浴缸尺寸为长*宽*高=1.5m*0.6m*0.5m时,最优的热水温度、热水输入速率为T1= 63.4℃,f=0.33L/s。然后对浴缸形状体积和人的形状体积等影响因素进行灵敏性分析,发现结果受浴缸体积的影响最大。 ?

2011年美赛真题优秀论文

中继站的协调方案 摘要(Abstract ) 中继站是将信号进行再生、放大处理后,再转发给下一个中继站,以确保传输信号的质量。低功耗的用户,例如移动电话用户,在不能直接与其他用户联系的地方可以通过中继站来保持联系。然而,中继站之间会互相影响,除非彼此之间有足够远的距离或通过充分分离的频率来传送。为了排除信号间的干扰,实现某一区域内(题中以40英里为半径的圆形区域)通信设备正常的发射和接收信号,需要利用PL 技术对中继站作合理的协调和分配。 首先本文结合香农理论的相关算法,考虑了信号供给系统的损耗、天线增益、信号的传播损耗、辐射效率因素的影响,得到中继站的辐射范围半径公式为: ,10,10log ( )37.2328 20 10 r out r in p P d -= 在供给对象为低功率消耗设备,查资料一般发射功率为3.2W ,中继站能接收到的最弱的信号1W μ,代入数据得到每个中继站的辐射半径为15.28m iles 。同时本文在不考虑其他因素(包括:地形、大雾、山川、建筑物等)对辐射范围和辐射强度的影响下,结合相关知识和题目中给出的条件,在不引入PL 技术时得出每个中继站所服务的用户数量为39个。 对于问题一, 我们首先定义了均衡覆盖、覆盖效率,在均衡覆盖中即用圆覆盖圆形区域,我们根据式子 2(2)n k n ππ -= ,得出(,)k n 的可能值有 (3,6),(4,4),三种,即等效三角形、正方形、正六边形覆盖,并通过覆盖效率的比较,最终得出正六边形覆盖是最好的覆盖方法,即蜂窝拓扑网络。在这种覆 盖情况下我们,我结合中继站覆盖半径15.28m iles ,根据式子 m i n 3(1)1,0,1,2,3,N K K K =++= ……,求出最少需要19个中继站,并在满足单位 面积覆盖同时在线人数的情况下引入PL 技术,得出此时中继站在该区域可同时 服务在限人数为1292人。 对于问题二,我们在问题一模型基础上从提高中继站服务人数和减少中继站半径两方面考虑,得出在将PL 分为18层,即中继站同时在线服务人数为702的情况下,结合单位面积同时在线服务人数,得出在中继站最少的情况下,中继站半径在[]11.094,,11.68范围内都可,我们为了让同时在线服务人数最大,取11.094英里,得出服务人数为11305。 问题三:对于山区地形,信号在传播过程中会有绕射和绕射损耗情况的出现,我们通过解析几何法寻找到发生绕射的山峰,通过菲涅尔积分和信号损耗理论 ,把山峰的损耗累加,最终算出信号由于绕射山峰而发生的功率损耗 。 关键词(Key Words):蜂窝拓扑网络,香农理论,容量和辐射半径,亚音频率层, 解析几何

2015年美赛B题论文

Where is the MH 370? Abstract Where is the crashed MH 370? This is an issue of global concern. In this article, the search work for the crashed aircraft is divided into three stages:determining the fall area, select the search location, arrange rescue equipment.To solve problems, we have set up three mathematical models. According to physics equations,we have established a differential equations model that can describe the crashed procedure of the aircraft.By combined maritime related cases,we have calculated the theoretical appeared area of the aircraft. Because of the large area of theory, it will be split into many small regions of equal area. With the limited search capability,we need to find a small piece where the aircraft is most likely to exist in.Then we use the conditional probability to establish a maritime search model and have got the actual search area and search paths. Each time a search is completed.We use a Bayesian probability formula to update the appearing probability of the aircraft in each small area if the crashed aircraft is not found.Besides,we resolve the model to acquire the actual search area and search paths. From an economic point of view, we have created a scheduling model of the search appliances with the existed search equipment. Then we made reasonable arrangements for personnel and equipment based on the results of the model. Keywords:Differential Equations Conditional Probability Bayesian Methods Nonlinear Programming

2015年美赛O奖论文A题Problem_A_35532.pdf

Team Control Number For office use only 35532 For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ Problem Chosen F3 ________________ T4 ________________ F4 ________________ A 2015 Mathematical Contest in Modeling (MCM) Summary Sheet Summary The complex epidemic of Zaire ebolavirus has been affecting West Africa. A series of realistic, sensible, and useful mathematical model about Ebola of spreading and medication delivery are developed to eradicating Ebola. 这个复杂的传染病,埃博拉,已经影响西非好久。一系列真实可信的关于抑制埃博拉传播和医药相关的数学模型正在建立。 First, we divide the spreading of disease into three periods: naturally spreading period, spreading period with isolation but without effective medications and spreading period with effective medications. We develop a SEIR (susceptible-exposed-infectious-recovered) model to simulate the spread of the disease in the primary period. Then the model are improved to a SEIQR (susceptible-exposed-infectious-quarantined-recovered) model to adapt to the second and third period and to predict the future trends in 第一,我们把这个疾病划分为三个部分:自然传播过程,没有有效药物控制的独立传播过程和有有效控制的传播过程。我们建立了一个SEIR (易受暴露的感染性恢复)模型来模拟早期疾病的传播。接着我们又把模型升级为一个SEIQR (易受暴露性感染后的隔离恢复)来适应第二和第三阶段的传播同时也用来预测在Guinea, Sierra Leone and Liberia.的传播情况。 According to our plan, drugs are delivered to countries in need separately by air, then to medical centers by highway and be used for therapy of patients there. To solve the problem of location decision of medical centers , which belongs to a set covering problem , we developed a multi-objective optimization model . The model’s goal is minimizing the numbers of medical centers and total patients’ time cost on the road on the condition that all of patients can be sent a medical center in time. We solved the model with genetic algorithm, and get an approximate optimal solution with 7 medical centers. 根据我们的计划,运送药物的国家个别的需要空中运输,然后疾病中心通过高速公路将药物运送到患者手中。为了决定当地医疗中心位置的一个覆盖问题,我们建立了一个多元线性规划的选择模型。这个模型的目的是最小化医疗中心与主要患者之间在路上的距离使得所有患者能够被及时得送去医疗中心。我们用一个演变的算法解决了这个模型并得出一个最优化的结果----7个医疗中心。 Then we built a logistic block growth model to describe the changing speed of drugs manufacturing. Comparing it with the SEIIR model, we considered the two situations: one is in severe shortage of drugs, the other is relatively sufficient in drugs. We built two optimization models for the two situations. The optimization goal is minimizing the number of the infectious and minimizing of death cases and the number of infectious individuals, respectively. The decision variables is the drug allocation for every country, and the constraint conditions is drug production.

2013美赛A题一等奖论文

Team #17999 2013美赛A题一等奖论文 哈尔滨工业大学 杨宜蒙 李春柳 姜子木 【注:此页非正式论文页】

Contest 1.Introduction (1) 2.General assumption for all models (1) 3.What is the distribution of heat across the outer edge of a pan? (1) 3.1Model establishment (1) 3.1.1Model Ⅰ: Micro-point model (1) 3.1.2Model Ⅱ:Thermodynamics conduction model (3) 3.2Model solution and analysis (5) 3.2.1Model Ⅰ: Micro-point model (5) 3.2.2Model Ⅱ: Thermodynamics conduction model (6) 3.3Sensitivity analysis (11) 4.How to choose an optimal pan? (14) 4.1Model assumption (14) 4.2Model requirement (14) 4.3Model establishment (14) 4.4Model solution and analysis (20) 4.5Sensitivity analysis (21) 5.Superiority and weakness (22) 6.Further research (22) 7.Practical suggestions (23) 8.References (23) 9.ADS (24) 10.Appendix ...................................................................................................... 错误!未定义书签。

15年美赛B题一等奖论文

For office use only T1________________ T2________________ T3________________ T4________________ Team Control Number 32642 Problem Chosen B For office use only F1________________ F2________________ F3________________ F4________________ 2015 Mathematical Contest in Modeling (MCM/ICM) Summary Sheet (Attach a copy of this page to your solution paper.) Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page. Searching a crashed plane in the sea is a hard job, while searching a lost plane presumed crashed in the open sea is much harder. To help find a lost plane, we restore the whole process, divide it into three periods and construct models respectively. The first model is a Stochastic Particle Simulation Model(SPSM), which describes the process that the plane loses contact with the ground and falls into the sea. Then we treat debris of the plane as separate particles and build a Drift Model based on Stochastic Particle Migration Model, which helps us to describe the motion of the debris of the plane and find the possible area containing the lost plane. Finally, we use BP-Artificial Neural Network Algorithm to choose the most suitable type of search planes and try to plan the optimal routine based on Time Homogeneous Markov Chain Model. In the first period, we break it down into two models: Fly Model and Fall Model. In the Fly Model, considering the great uncertainty on the plane crash, we use SPSM to find the distributions of the position where the plane lost power. Also, we get the distributions of flight speed, fight course and flight duration in that position. Then we divided the crashed plane into two types: with gliding function and without gliding function. Each type of the plane falls down in different way. In the second period, our goal is to simulate the motion of the debris in the water. We assume that the debris of the plane float on the surface, and it is small enough to ignore the affection of wave force. Based on the Leeway Model, we analyze its acceleration while considering the disturbance of environment at the same time. Then we check the model with data from National Oceanographic Data Center (NOAA) and get a good result. In the third period, we should choose the most suitable type of search plane and plan the optimal search routine. Using BP-ANNs Model, we determine the input layer as some factors on sea states and the output layer as several factors on the performance of a search plane. The outputs we get are the criterion by which we choose the most suitable plane. Then we try to find the optimal routine based on Time Homogeneous Markov Chain Model. We conduct Sensitive Analysis on the BP-ANNs and find that the model is robust. We also analyze our strengths and weaknesses and give a brief conclusion.

数模美赛论文常用词汇

exclusively专门 undobtedly毫无疑问的 notable 值得注意的 tremedous/significant极大的 notion概念 definition定义——define Interpret……as…… 理解……为 invoke(+模型援引,引用 equation方程式,等式 function因变量——提示符号的含义 matrix矩阵,模型 constant 常数,常量It requires I t o be a constant for …to be true algorithm演算方法——a general algorithm 通用算法simplify the algorithm 简化算法we have produced a general algrrithm to solve this tpye of problems. derivative微分,倒数antiderivative 不定积分 optimal results 最优结果 invesgate the problem from different point of view调查问题——investgation调查survey 调查 subproblem 子问题,次要问题——major problem 主要问题 metric 度量标准,指标 digit 数字delete some digits element /component 元素

解题思路seek/explore—— explore different ideas探索不同的想法 we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations. 解决方案design/device ——develop/establish/conduct Based on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm to produce near optimal https://www.360docs.net/doc/cf1176364.html,ing integral linear programming.We then device a polynominal-time approximation to We conduct sensitivity analysis on…to find…xxx analysis is also performed. 解决结果tackle/solve We tackle the problem using the new technique we developed in the previous section.While it is difficult to solve the problem completely, we are able to solve a major subproblem. 计划与打算approach/propose We approach the problem using the proposed method. We propose a new approach to tackling the problem. 词组 Basedon…以……为基础 According to根据 Devide …into…——subdivide into细分 …is applied to…使用了……模型来……——we apply our model into将我们的模型运用于 Model proves to be efficient in other sports.模型被证明在其他方面有效 ….,which indicates that………反映了

2018年数学建模论文写作技巧 论文自评(美赛一等奖获得者从获奖论文评述中总结的经验)word版本 (4页)

本文部分内容来自网络整理,本司不为其真实性负责,如有异议或侵权请及时联系,本司将立即删除! == 本文为word格式,下载后可方便编辑和修改! == 数学建模论文写作技巧论文自评(美赛一等奖获得者从获奖论文评述中总结的经验) 论文自评 Successful teams would have to combine existing models, data, and new ideas in creative and original ways. (成功的队伍会把现有的模型、数据和新的思想创造性地组合起来) Here are some of the issues that kept papers from the final rounds: (以下问题会使得论文无法进入最后一轮评审) ?Errors in mathematics, which quickly took them out of further consideration. (数学上的错误,使他们无法进行更深层次的思考) ?Including mathematics that didn’t fit the flow of the presentation. In a few cases, mathematics appears to have been inserted to make a paper look more credible or to take the place of other work that had led to a dead end. (数学方法被插入论文中是为了使论文看起来更可信或 是取代某些其他的工作将会使论文被淘汰) ?Changing notation, sometimes even within a single section. (改变符号,有时甚至在同一个章节中) ?Using undefined or poorly defined symbols, or using symbols before defining them. (用没有定义过的符号,或者在定义之前使用它 们) ?Incomplete expressions, either because the team made an error or because the expression did not survive the word-processor. (One of the Outstanding papers addressed in this commentary had a few incomplete, probably because they didn’t survive the word-processor, but the coherence of its model and the strength of its presentation overcame that defect.) (不完整的表述)

2019年美赛C题特等奖论文

Random Walks and Rehab: Analyzing the Spread of the Opioid Crisis Ellen Considine Suyog Soti Emily Webb University of Colorado Boulder Boulder,Colorado USA ellen.considine@https://www.360docs.net/doc/cf1176364.html, Advisor:Anne Dougherty Summary We classify69types of opioid substances into four categories based on synthesis and availability.Plotting use rates of each category over time re-veals that use of mild painkillers and natural alkaloids has stayed relatively constant over time,semi-synthetic drugs have declined slightly,and syn-thetic drugs such as fentanyl and heroin have increased dramatically.These ?ndings align with reports from the CDC.We select54of149socioeconomic variables based on their variance in?ation factor score(a common measure of multicollinearity)as well as on their relevance based on the public health literature. To model the spread of the opioid crisis across Kentucky,Ohio,Penn-sylvania,West Virginia,and Virginia,we develop two completely different models and then compare them. Our?rst model is founded on common modeling approaches in epidemi-ology:SIR/SIS models and stochastic simulation.We design an algorithm that simulates a random walk between six discrete classes,each of which represents a different stage of the opioid crisis,using thresholds for opioid abuse prevalence and rate of change.We penalize transitions between cer-tain classes differentially based on realistic expectations.Optimization of parameters and coef?cients for the model is guided by an error function in-spired by the global spatial autocorrelation statistic Moran’s I.Testing our model via both error calculation and visual mapping illustrates high accu-racy over many hundreds of trials.However,this model does not provide much insight into the in?uence of socioeconomic factors on opioid abuse The UMAP Journal40(4)(2018)353–380.c Copyright2019by COMAP,Inc.All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for pro?t or commercial advantage and that copies bear this notice.Abstracting with credit is permitted,but copyrights for components of this work owned by others than COMAP must be honored.To copy otherwise, to republish,to post on servers,or to redistribute to lists requires prior permission from COMAP.

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