2013美赛MCMICM 官方版翻译

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2013年美赛MCM题目A评委点评中文翻译

介绍今年的焦点问题是如何实现质量和数量的平衡。

在质量方面，尽可能使热量均匀地分布。

目标是降低或避免矩形烤盘四个边角发生热量聚集的情况。

所以解决热量均匀分布这方面的问题，使用圆形烤盘是最佳的选择。

在数量方面，应该使烤盘充分的占据烤箱的空间。

所以我们的目的是使用尽可能多的烤盘来充分占据烤箱的空间，此时矩形烤盘是最佳选择。

对于这方面的问题的解决，就要考虑烤盘在烤箱水平截面上所占的比率。

在这个评论中，我们首先描述判断步骤，然后再讨论队伍对于三个问题的求解。

下一个话题就是论文的灵敏度和假设，紧随其后讨论确定一个给定方法的优势和劣势。

最后，我们简短的讨论一下参考和引用之间的区别。

过程第一轮的判别被称为“分流轮”。

这些初始轮的主要思想是确定论文应被给予更详细的考虑。

每篇论文应该至少阅读两次。

在阅读一篇论文的时候，评审的主要问题是论文是否包含所有必要的成分,使它成为一个候选人最详细的阅读。

在这些初始轮中，评审的时间是有限制的，所以我们要尽量让每一篇论文得到一个好的评判。

如果一篇论文解决了所有的问题，就会让评审觉得你的模型建立是合理的。

然后评审可能会认为你的论文是值得注意的。

有些论文在初轮评审中可能会得到不太理想的评论。

特别值得注意的是，一篇好的摘要应该要对问题进行简要概述，另外，论文的概述和方法，队员之间应该互相讨论，并且具体的结果应该在某种程度上被阐述或者表达出来。

在早期的几轮中，一些小细节能够有突出的表现，包括目录，它更便于评委看论文，同时在看论文的时候可能会有更高的期待。

问题求解也很重要。

最后，方法和结果要清晰简明的表达是至关重要的。

另外，在每个部分的开始，应该对那个部分进行一个概述。

在竞赛中，建模的过程是很重要的，同时也包括结论的表达。

如果结果没有确切和充分的表达，那么再好的模型和再大努力也是没有用的。

最后的回合最后一轮阅读的第一轮开始于评委会会议。

在这个会议中，评委将进行讨论，他们会分享他们各自认为的问题的关键方面。

2013美国赛 MCM-ICM 英语原文+翻译

2013 MCM ProblemsPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular（矩形的）pan heat is concentrated（集中）in the 4 corners and the product gets overcooked（焙烧过度）at the corners (and to a lesser extent(较小程度上) at the edges). In a round（圆）pan the heat is distributed evenly（均匀的）over the entire outer edge and the product is not overcooked at the edges. However, since most ovens（烤箱）are rectangular in shape using round pans is not efficient（高效）with respect to（关于）using the space in an oven. Develop a model to show the distribution（分布规律）of heat across the outer edge of a pan for pans of different shapes - rectangular to circular（圆形）and other shapes in between.Assume1. A width to length ratio（···比）of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced（均匀分布）.Develop a model that can be used to select the best type of pan (shape) under the following conditions（条件）:1. Maximize number of pans（平底锅）that can fit in the oven (N)2. Maximize even distribution （均匀分布）of heat (H) for the pan3. Optimize（最优化）a combination of （···的综合）conditions (1) and (2) where weights p and (1- p) are assigned to（被分配···）illustrate（阐明）how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting（使··突显出来）your design and results.在矩形烤盘烘焙的时候，热量会被集中到4个角，食物会被烘焙过度（热量较小程度上在边缘）。

美国数学建模竞赛参赛帮助中英文

MCM: The Mathematical Contest in ModelingICM: The Interdisciplinary Contest in ModelingMCM：数学建模竞赛ICM：交叉学科建模竞赛Contest Registration and Instructions竞赛注册和指导(All instructions and rules apply to ICM as well as to MCM, except where otherwise noted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in MCM a team must be sponsored by a faculty advisor f rom their institution. The registration process must be completed by the advisor.每个MCM的参赛队需有一名所在单位的指导教师负责。

整个注册报名过程需由该指导教师完成。

IMPORTANT CHANGE TO CONTEST RULES FOR MCM/ICM 2009:2009年MCM/ICM规则的重要改变：Teams (Student or Advisor) are now required to submit an electronic copy of their solution paper by email to solutions@. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 9, 2009.要求参赛队（由学生或者指导教师）通过Email提交一份解决方案的电子版拷贝，发到solutions@。

Email邮件必须在美国东部时间2009年2月9日上午8点前发到COMAP。

2013年美国大学生数学建模竞赛(MCMICM)参赛规则中英文对照

2013年美国大学生数学建模竞赛（MCMICM）参赛规则中英文对照2 ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions比赛规则，报名注册和指导(All rules and instructions apply to both ICM and MCM contests, except where otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）To participate in a contest, each team must be sponsored by a faculty advisor fromits institution.参加MCM的每个队伍需有一名在职的高校老师负责指导。

TeamAdvisors: Please read these instructions carefully. It isyour responsibility to make sure that teams are correctly registered and thatall of the following steps required for participation in the contest arecompleted:Pleaseprint a copy of these contest instructions for reference before, during, andafter the contest. Click here for the printer friendly version.指导老师：请认真阅读这些说明事项，确保完成了所有相关的项。

每位指导教师的责任包括确保每个参赛队正确注册并正确完成参加MCM/ICM所要求的相关步骤。

MCM(MCM Mathematical Contest i

MCM/ICM是 Mathematical Contest in Modeling和 Interdisciplinary Contest in Modeling的缩写，即“数学建模竞赛”和“交叉学科建模竞赛”。MCM始于 1985年，ICM始于 2000年，由 COMAP（the Consortium for Mathematics and Its Application，美国数学及其应用联合会）主办，得到了 SIAM，NSA， INFORMS等多个组织的赞助。MCM/ICM着重强调研究问题、解决方案的原创性、团队合作、交流以及结果的合理性。
奖项
美国大学生数学建模竞赛共设置四个奖项，分别为 Outstanding Winner， Finalist， Meritorious Winner， Honorable Mentions， Successfully Participation。在国内，约定俗成地将这四个奖项分别对应为特等奖、特等候选奖、一等奖、二等奖、成功参赛。
MCM（MCM Mathematical Contest i
MCM-Mathematical Contest in Modeling
01 简介
03 奖项
目录
02 历史背景 04 其他
《MCM》是MCM-Mathematical ContCM/ICM），是一项国际级的竞赛项目，为现今各类数学建模竞赛之鼻祖。
感谢观看
竞赛以三人（本科生）为一组，在四天时间内，就指定的问题完成从建立模型、求解、验证到论文撰写的全部工作。竞赛每年都吸引大量著名高校参赛。2008年 MCM/ICM有超过 2000个队伍参加，遍及五大洲。MCM/ICM 已经成为最著名的国际大学生竞赛之一。
历史背景
1985年，在美国科学基金会的资助下，创办了一个名为“数学建模竞赛”（Mathematical Competition in Modeling后改名Mathematical Contest in Modeling，简称MCM）一年一度的大学水平的竞赛，MCM的宗旨是鼓励大学师生对范围并不固定的各种实际问题予以阐明、分析并提出解法，通过这样一种结构鼓励师生积极参与并强调实现完整的模型构造的过程。它是一种彻底公开的竞赛，每年只有若干个来自不受限制的任何领域的实际问题，学生以三人组成一队的形式参赛，在三天（72小时）（近年改为四天，即96小时）内任选一题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。由专家组成的评阅组进行评阅，评出优秀论文，并给予某种奖励，它只有唯一的禁律，就是在竞赛期间不得与队外任何人（包括指导教师）讨论赛题，但可以利用任何图书资料、互联网上的资料、任何类型的计算机和软件等，为充分发挥参赛学生的创造性提供了广阔的空间。第一届MCM时，就有美国70所大学90个队参加，到1992年已经有美国及其它一些国家的189所大学292个队参加，在某种意义下，已经成为一种国际性的竞赛，影响极其广泛。

2013数学建模美赛题目(中文版)[1]

2013 ICM问题problem A:当用矩形平底锅高温加热物品时，热量一般集中于4个角落，因而在角落的物品会被焙烧过度（较小程度在角落的物品一部分会被焙烧过度）。

当用一个圆锅加热物品时，热量是均匀分布在整个外缘，因而物品不会在边缘被焙烧过度。

然而，大多数烤箱是长方形的，而圆型的锅被认为效率低的。

建立一个模型以显示不同形状如矩形圆形或者其他介于两者之间的形状的锅在整个外缘的热量分布。

假设1长方形烤箱的宽/长=W/L ；2 每个锅的面积是确定的常熟A；3 最初，烤箱里的烤架两两之间间隔均匀。

建立一个模型，该模型可用于在下列条件之下选择最佳形状的锅：1烤箱中，锅数量（N）最大；2均匀分布的热量（H）最大的锅；3 优化组合条件1和条件2，以比重p和（1-p）的不同分配来说明结果与W/L 和p的不同值的关系。

problem B :对世界来说，新鲜的水资源是限制发展的制约因素。

对2013年建立一个确实有效的，可行的和具有成本效益的水资源战略数学模型，以满足2025年[从下面的列表选择一个国家]预计的用水需求,并确定最佳水资源战略。

尤其是，你的数学模型必须解决水的存储，运动，盐碱化和保护等问题。

如果可能的话，用你的模型，探讨经济，物理和环境对于你的战略的影响。

提供一个非技术性的文件，向政府领导介绍你的方法，介绍其可行性和成本，以及为什么它是“最好的的水战略选择。

”国家有：美国，中国，俄罗斯，埃及，沙特阿拉伯3.网络建模的地球的健康背景:社会是感兴趣的发展和使用模型来预测生物和环境卫生条件我们的星球。

许多科学研究认为越来越多的压力在地球的环境和生物吗系统,但是有很少的全球模型来测试这些索赔。

由联合国支持的年生态系统评估综合报告》显示,近三分之二的地球的维持生命的生态系统——包括干净的水,纯净的空气,和稳定的气候-正在退化,被不可持续的使用。

人类是归咎于很多这次的损坏。

不断飙升的要求食品、新鲜水、燃料和木材有贡献到戏剧性的环境变化,从森林砍伐,空气,土地和水的污染。

2013ICM中文翻译

2013年ICM问题地球的健康的网络建模背景：社会是有兴趣在开发和使用模型来预测我们这个星球的生物和环境的健康状况。

许多科学研究得出的结论是，有越来越大的压力对地球环境和生物系统，但也有极少数的全球模型，以测试这些要求。

联合国支持千年生态系统评估综合报告发现，近三分之二的地球的生命支持生态系统，包括干净的水，纯净的空气，稳定气候是降低不可持续的利用。

人类被指责为许多这种损伤。

飙升的食品，淡水，燃料和木材的需求作出了贡献剧烈的环境变化，滥伐森林，空气，土地和水的污染。

尽管当地的栖息地和区域进行了大量的研究因素的影响，目前的模式不充分告知决策者如何省政策可能会影响到整个地球健康的。

许多模型忽略了复杂的全球因素，是无法确定的远射潜在的政策的影响。

而科学家们认识到在无数的复杂关系和交叉效应环境和生物系统产生影响地球的生物圈，目前的模型往往忽略这些关系，或限制系统的连接。

该系统的复杂性体现在多个交互，反馈回路，紧急行为，和即将到来的状态的变化或临界点。

最近22国际自然写的文章知名科学家题为“走近地球的生物圈”的状态转变列出了很多相关的问题需要科学模型的重要性预测潜在的行星卫生系统状态的变化。

本文提供两个具体的量化建模的挑战，他们要求更好的预测模型：1）为了提高生物通过全球性的拥抱复杂的模型，预测地球上的相互关联的系统，包括当地条件的影响全球性的系统，反之亦然。

2 ）确定因素，可能会产生不健康的全局状态变化，并显示如何使用有效的生态系统管理，以防止或限制这些即将发生的状态的变化。

研究的问题是，我们是否可以建立的全球车型使用本地或地球的健康状况，预测潜在状态的变化，并帮助区域组成部分决策者设计有效的政策，根据他们的潜在影响地球上的健康。

虽然许多警告标志出现，没有人知道地球是真正接近全球的临界点，如果这种极端的状态是不可避免的。

2013美赛MCM A题标准翻译

PROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.Develop a model that can be used to select the best type of pan (shape) under the following conditions:1. Maximize number of pans that can fit in the oven (N)2. Maximize even distribution of heat (H) for the pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.Problem A: 终极布朗尼锅当在一个矩形的锅里烹煮食物时，受热集中在锅的4个角落里，因此食品在这4个拐角处被过度烹饪（在边缘程度会稍微轻点）。

2013年美国数学建模大赛B题

For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number2222463463Problem ChosenBFor office use onlyF1________________F2________________F3________________F4________________ 2013Mathematical Contest in Modeling(MCM/ICM)Summary Sheet(Attach a copy of this page to your solution paper.)AbstractRecently,more and more information about freshwater resource comes into people’s view.Actually,the freshwater resource,which is originally small in reserve,becomes more and more precious with the pollution of wastewater discharged by lawbreakers. So it’s not surprising that many areas in China is short of freshwater.This paper aims at formulating a comprehensive planning of freshwater use.Initially,we make a prediction in model1to find which provinces are short of water by applying polynomial fitting toolbox of MATLAB.Eventually,our results indicate that10provinces in China are short of freshwater,which are as follows:Jiangsu, Shandong,Ningxia,Hebei,Henan,Tianjin,Beijing,Inner Mongolia and Anhui.Then,in our model2,employing the Principal Component Analysis method and the statistical software SPSS,we finally conclude that the major factors influence the sustainable use of freshwater are rainfall,polluted water treatment ratio,GDP growth ratio and direct discharge quantity.Finally,according to the results and conclusions draw in the former analysis,we construct an optimization model,in which we provide the detailed water useplannings from2013to2025to the governments of every area.Key words:freshwater resource,polluted water treatment,desalination,sustainable developmentWater,Water everywhereMathematic Models of National Water Strategy in China1.IntroductionIn recent years,with the dramatic growth of the world’s population and the development of industry,more and more challenges emerge in the process of people dealing with the world,of which,water shortage is a serious problem threatens humanity.As we all know,water is indispensable in guaranteeing life and health. However,the freshwater,which can be directly used by human,is extremely limited though the fact that water covers70.8percent of the earth’s surface,in which,97.5 percent is undrinkable salt water while the rest2.5percent is polar ice caps,mountain glaciers and the snow and ice of the permafrost zone that are difficult to exploit.In fact,only0.26percent of the water reserved in the earth can be accessible,which are mainly rivers,lakes and a part of the groundwater(See,fig.1).Given the current situation of freshwater on the earth showed previously,it is not surprising that more than1billion people have no access to safe water to meet their basic need for life[1].Fig.1.Distribution of water resources in worldAs the country with the most population but less abundant water resource,China will be more nervous in dealing with water problems.The total water reserve of China in 20th,October,2009is2800billion cubic meters,of which surface water reserve is 2700billion cubic meters and underground water reserve is830billion cubic meters. Considering the mutual interconversion and supply between surface water and groundwater,we deduct the double-counting amount730billion cubic meters and then the underground water reserve is about100billion cubic meters.According to the international criterion,water reserve per capita(WRPC)is classified into four grades:(1)the WRPC lower than3000cubic meters is defined as mild water shortage;(2)the WRPC lower than2000cubic meters is defined as moderate water shortage;(3)the WRPC lower than1000cubic meters is defined as severe water shortage;(4)the WRPC lower than500cubic meters is defined as extreme water shortage. (1)-(4)will be the criterion to evaluate the grade of water shortage.In this paper,first,we make a prediction in model1to find which provinces are short of water by applying polynomial fitting toolbox of MATLAB.Second,employing the Principal Component Analysis method and the statistical software SPSS,we finally conclude that the major factors influence the sustainable use of freshwater are rainfall, polluted water treatment ratio,GDP growth ratio and direct discharge quantity. Finally,according to the results and conclusions draw in the former analysis,we construct an optimization model,in which we provide the detailed water use plannings from2013to2025to the governments of every area.2.Assumptions(1)The influence of the thaw of glaciers caused by climate change and global warming on freshwater use and storage is not considered.(2)Sweeping reforms will not be implemented in terms of water use,industry, economy and environment-protection.(3)The population change follows the current demographic trends and the water use situation will not change dramatically with mutations in the population.(4)The natural purification of water is neglected in the model.3.MODEL1(1)Prediction of the water shortage in every province of China in2025After experimenting and comparing various predicting methods like Grey Forecasting Model and Gaussian Interpolation Fitting Forecast,we finally choose Linear Fit, which is proved to show the best effect,to complete our prediction model.The predicting result of water storage and water need of every province in China in 2025is showed in the Table1(the calculating results are from MATLAB).Table1.The predicting result of water storage and water need of every province in China in2025[2]In the sheet,Water Shortage=Water Need-Water Storage;Water Utilization=Water Need/Water Storage.From the sheet,we can conclude that Jiangsu,Shandong,Ningxia,Hebei,Henan, Tianjin,Beijing,Inner Mongolia and Anhui will be seriously shortage of water in 2025.Because the water storage can not be totally used every year,shortage of water is routinely defined as the water need is less than75percent of the water storage.Validation of the M odel1(2)Validation(2)Fig.2.The freshwater distribution map of ChinaCompared with the freshwater distribution map of China displayed in the following picture,our conclusion of prediction is matches with the actual situation[3](See,fig.2).MODEL2：Sustainable Water Use Plans For The Provinces Which Are 4.4.MODELShort of Water Based on Principal Component AnalysisBefore making a sustainable and efficient planning for the provinces that are short of water,we must know which kinds of factors influences the water use system most.And then our planning can be mainly concentrated on the key factor,which will greatly simplify the evaluation model.Take into consideration that the evaluation to the utilization of water resource system is a complex process,which involves the mutual coordination relationship among water reserve,water distribution,water use, water environment protection and polluted water treatment,we are supposed to apply a variety of indexes to construct a comprehensive evaluation system to describe the water use situation.Additionally,diffident indexes,being dimensioned in variable criteria,may lead to different evaluation results which may even conflict.Principal component analysis is appropriate when you have obtained measures on a number of observed variables and wish to develop a smaller number of artificial variables(called principal components)that will account for most of the variance in the observed variables.The principal components may then be used as predictor or criterion variables in subsequent analyses.So PCA has great superiority in constructing a comprehensive evaluating system,in which water use evaluation indexes are observed variables while our task is to develop some principal unobserved components and find the relationship between the components and evaluation system.(1)Principal Component AnalysisPrincipal component analysis is a variable reduction procedure.It is useful when you have obtained data on a number of variables(possibly a large number of variables), and believe that there is some redundancy in those variables.In this case,redundancy means that some of the variables are correlated with one another,possibly because they are measuring the same construct.Because of this redundancy,you believe that it should be possible to reduce the observed variables into a smaller number of principal components(artificial variables)that will account for most of the variance in the observed variables.The mathematical technique used in PCA is called eigen analysis:we solve for the eigenvalues and eigenvectors of a square symmetric matrix with sums of squares and cross products.The eigenvector associated with the largest eigenvalue has the same direction as the first principal component.The eigenvector associated with the second largest eigenvalue determines the direction of the second principal component.The sum of the eigenvalues equals the trace of the square matrix and the maximum number of eigenvectors equals the number of rows (or columns)of this matrix.PCA is mathematically defined as an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component),the second greatest variance on the second coordinate,and so on.When the analysis is complete,the resulting components will display varying degrees of correlation with the observed variables,but are completely uncorrelated with one another [4].(2)Procedure of PCA StandardizationStandardizing the original data is inevitable because of their different dimension and criteria.Given n samples and p indexes,we can get the data matrix:X =()ij n p x ×.Then standardize the data by:*()/ij ij i i x x x σ=−，whereij X :the value of index j in sample i;ij x :the original data of index j in sample i;i x :the mean of the original data of one index in sample i;i σ:the standard deviation of the original data of one index in sample i.(3)(3)CalculateCalculate the correlation coefficient matrix Calculate the correlation coefficient matrix R=()ij n n r ×according to the standardizeddata matrix *()ij n p x ×.11()()/.nij ki i kj j i j k r X X x x n σσ==−−∑(4)(4)CalculateCalculate the eigenvalues and eigenvectors On the basis of characteristic equation 0I R λ−=,we can get the eigenvalues i λand eigenvectors i e .(1i e =)(5)(5)CalculateCalculate the contribution rate of the principal component The contribution rate of the principal component i z is 1/pi k k λλ=∑,the cumulativecontribution rate is11ikk pkk λλ==∑∑.Generally,we choose the principal components 1,2,.....mcorresponds to the eigenvalues of 12,,...m λλλwhich make up the cumulative contribution rate of 85%(or higher than 85%).(6)Calculating Principal C omponent L oadingsThe principal component loading is calculatedby following formula ：(,)ij i i ija p z x ==（i,j=1,2,3,...p ）With the former analyzing process,we can make a rational simplification to the numerous variables under the principle of guaranteeing the least loss of infor mation.(7)PCA Applied To The Evaluation SystemTo apply the PCA to our water use evaluation model,we divide the final evaluation target into three subsystems:water utilization system,economic system and water environment system.Then we determine a variety of indexes(as follows)to indicate and quantify these three abstract subsystems.Fig.3.Water utilization systemFig.4.Economic systemFig.5.Water environment systemAn comprehensive water use evaluation system is showed in the follow picture:prehensive water use evaluation systemBecause of the heavy calculating tasks caused by numerous indexes and data,we use SPSS,an accurate and popular statistical analysis software,to simplify the complex computing task.Enter the data and we get the result as follow:urate and popular statistical analysis resultAfter several rounds of PCA experiments and then,from the data and sheets showed in the analysis results,we can conclude that the most-influenced factors are as follows:RainfallPolluted Water Treatment RatioGDP Growth RatioDirect Discharge QuantityConsidering that the unstable economic development environment leads to the change of GDP growth ratio undulates dramatically in the recent years,we find it difficult to evaluate the influence of GDP Growth Ratio on the Water Use Evaluation System.So the GDP Growth Ratio factor may need more data,assumptions and professional knowledge to deal with,which may be out of our capacity.We decide to focus more on the other3factors.According to the statistics，the drainage area of Yangtze River and its southernregions possess36.5percent of the land area but81percent of the freshwater while the drainage area of Huaihe River and its northern regions possess63.5percent of the land area but19percent of the freshwater.The Yellow River drainage,the Huaihe River drainage and the Haihe River drainage are most shortage of freshwater,with only7.7percent of freshwater.Currently,16provinces in China are under the line of severe water shortage(1000cubic meter per capita),and6provinces Ningxia,Hebei, Shandong,Henan,Shanxi and Jiangsu are under the line of extreme water shortage (500cubic meter).Though the shortage of water mainly highlights in the northern areas in the term of water reserve per capita,water pollution is a nationwide problem.Moreover,the more water an area possesses and the more intensive the population is,the more serious the pollution is.As a result,the water of the areas which are abundant of water is in poor quality,which is a more serious problem.Based on the survey,about90percent of city freshwater reserve is polluted to some extent,and the water pollution has been spreading from the rivers and tributaries to the main stream,penetrating from surface to underground,stretching from the land to the sea,spreading from urban to rural areas.Recently,the polluted water emissions are increasing by1.8billion tons,and the industrial wastewater and domestic sewage emissions have reached to0.16billion tons,of which80percent is directly eliminated without treatment.The third point is that both low efficient water use and over-exploit exist.Firstly,it is low efficient water use.And the more it lacks water,the lower efficiency it is.For example,reaches of yellow river lack water severely but agricultural irrigation still adopts large area flooding.In Ningxia,Inner Mongolia irrigated areas,each unit of land uses water of over1,000m³on average,several times and even over ten times higher than water-efficient irrigated area;water use ratio of agriculture is lower generally.At present,water use amount for producing one unit of food is2~2.5times as much as that in developed countries.Water use for agriculture is like that,and water use for industry is also like that. Presently water recycling use ratio for industry of china is much lower than75%of that in developed countries.GDP water use amount per unit is as over10times todozens of tiimes as that in developed countries.Water deprivation per unit for some important products is also several times,even dozens of times higher than that in devloped countries.Secondly,it is more severe to exploit water source excessively.take haihe river drainage basin for an example.It is one of the densest populations in china,including most areas in Beijing,Tianjin,Hebei and some parts in Shandong,Shanxi,Neimeng and Henan.Social economics here change a lot in recent pared to1950s, the population increases as much as before;the irrigated areas increase6times as much as before;gdp increases over30times as much as before;and these make total water use amount increase4times as much as before which exceed bearing capacity of water source.In result,surface water and ground water are over exploited for long time.The exploitation ratio reaches98%and it is much higher than40%of warning line.As the data from ministry of water resources shows,the ground water over-exploitation extends from56areas in1980s to present164areas,from87,000 square km to180,000square km and is more than10billion m³each year on average. The ground of over60,000square km descend to some extend.(China Ministry of Water Resources)According to these situations,we plan to take the following measures.(1)No flooding irritation for agriculture irritation;try little sprairritation;it is best to the best practical irritation method like drip irritation etc.(2)Take more invest in swage treatment to get100%of industrial and life swage treatment ratio;no discharging without life swage treatment in order for recycling use.(3)Increase management of contaminated river;reorganize severely contaminated factories and mines;the state offers some finance and subsidy to those who are not able to deal with pollution.(4)Try to use river fresh water;reduce exploiting the ground water.(5)For investment of seawater desalting,build seawater desalting factories;midland builds disposal factories for salt and soda water.In the PCA method,we know what affect more for water resource recycling use arerainfall,swage treatment ratio,swage direct discharging amount and water use amount per unit of farmland.(1)RainfallThe data and conclusions from China Meteorological Research Institute reveals that precipitation in China varies with locations and the precipitation change is cyclical(with a fixed period).In other words,the precipitation trends to be stable.So we believe that in a long period(until2025in this model),the influence of rainfall on the freshwater stabilizes and can be out of our consideration in the sustainable water use planning.(2)(2)TheThe A nalysis On The Conservation Of Farmland IrrigationAgricultural water consumption of the ten provinces which are shortage of water[5]: Table2.Agricultural water consumption of the ten provinces which are shortage of waterRegions 201120102009200820072006200520042003 Agricultural Water Consumption(0.1billion cubic meter)nation37433689.137233663.53599.53664.453580.3585.73432.8Beijing1010.811.411.411.712.0512.713.012.9 Tianjin1211.012.813.013.813.4313.612.011.2 Hebei140143.8143.9143.2151.6152.57150.2147.1149.6 InnerMongolia136134.5138.7134.1141.8142.18143.9149.4146.1Shanghai1616.816.816.716.218.3718.518.816.3Jiangsu308304.2300.1287.3268.5270.69263.8288.5223.1 Anhui168166.7167.2151.9120.6136.44113.6121.793.8 Shandong149154.8156.4157.6159.7169.40156.3154.3157.0Henan125125.6138.1133.5120.1140.15114.5124.5113.3 Ningxi6665.165.368.064.871.7372.368.658.4aThe following is the nationwide agricultural water consumption per mu from2006to 2007,Table3.The nationwide agricultural water consumption per mu from2006to20072006449m32007434m32008435m32009431m32010421m32011415m3mean430.8m3According to the calculation,we can conclude that we will save about40billion cubic meters water every year if the agricultural water consumption make a10%reduction. Agricultural water consumption accounts for about10percent of the total water consumption in the ten provinces.Assume that the national agricultural water consumption reduces by half in2025,then the amount of water saved will be surprising(show in the following sheet):Table4.Regions Mean Water Consumption Saving WaterNation3631.291102.536518Beijing11.77 3.57362117Tianjin12.54 3.807409471Hebei146.8944.59891365 Inner Mongolia140.7442.73164345 Shanghai17.16 5.210139276Jiangsu279.3584.81657382Anhui137.7741.82988858Shandong157.1747.72013928Henan126.0838.2805571Ningxia66.6920.24849582 Analysis and planning of polluted water treatment(3)Analysis(3)Polluted water emissions are very large in China every year,we make a prediction onthe industrial polluted water emissions in2025with the data from2003to2010by linear fitting toolbox in MATLAB.The results are as follows:Table5.YearIndustrial Polluted WaterEmissions(ten thousand cubic meter)Polluted Water TreatmentRatio200322440600.93917200422732100.9397200523023600.94023200623315000.94076200723606500.941289200823898000.941819200924189400.942349201024480900.942879201124772400.943409201225063800.943939201325355300.944468201425646800.944998201525938200.945528201626229700.946058201726521200.946588201826812600.947118201927104100.947648202027395500.948177202127687000.948707202227978500.949237202328269900.949767202428561400.950297202528852900.950827The results of domestic wastewater emissions are as follows:Table6.The results of domestic wastewater emissionsYear domestic wastewater emissions2003242793020042613170200527984202006298366020073168900200833541402009353939020103724630201139098702012409511020134280360201444656002015465084020164836090201750213302018520657020195391810202055770602021576230020225947540202361327802024631803020256503270From the results,it’s not difficult to find that the polluted water emissions are increasing sharply,reaching933888.17million cubic meters.Polluted water recycling can greatly alleviate the circumstance of water shortage,make contribution to environment protection and sustainable water use.The sheet also shows that the polluted water treatment ratio exceeds95%in2025 while the rest5%polluted water is difficult to purify.This rest part seriously harms the environment.So proposals of dealing with refractory polluted water are expected to implement before dry season in2025approaches to guarantee abundant freshwater. Constructing polluted water treatment factories to purify the polluted water eliminated by factories is executable in the process.Domestic wastewater emissions are not strictly limited by legislation,which leads tothe wastewater emissions without treatment.Our preliminary plans to deal with domestic wastewater emissions are constructing small-scale purifying factories which are capable of dealing with the99%domestic wastewater produced by the cities where the factories locate.This planning aims at dealing with the domestic wastewater of which the emissions are not strict and recycling the freshwater.We can know from the previous data that the expense of treating one cubic meter polluted water is0.6yuan.Assume that the polluted water emissions are900cubic meters a year,and we can get the expense a year54billion pared to the GDP(39798.3billion yuan in2010)and revenue(8308billion yuan),the investment on dealing with the polluted water is acceptable.However,the investment on the polluted water treating factories is high,1500yuan a square meter,so investment can be accomplished year by year.The polluted water treatment ratio is above94percent, so the late investment is810billion yuan(dealing with0.54billion cubic meters). Though the investment is high but the benefit is low,it is inevitable for recycling freshwater and protecting environment.In summary,the polluted water treatment quantity will reach90billion cubic meters until2025while the saving quantity of water in agriculture reaching110.25billion cubic meters.5.Analysis of the water diversionIt’s exactly the greatest characteristic of the distribution of the freshwater in China, seriously unbalanced in south and north,that mainly leads to the water shortage in the northern areas.The total freshwater resources is relatively stable in China every year.The south-to-north water diversion project dramatically improves the unbalanced situation.The project eventually will achieve a44.8billions cubic meters water diversion,in which the eastern route contributes an amount of14.8billion cubic meters while the central route13billion and the western route17billion.Now that this project is so important,we will devote to analyzing the project in detail and working out a rational water transfer planning to deal with the current water use situation.(1)Eastern routeThe Eastern route is the most advanced in terms of construction.It consists of an upgrade of the Grand Canal.Water from the Yangtze River will be drawn into the canal in Jiangdu,where a giant400m³/s.(12.6Billion m3/year if operated continuously)pumping station was built already in the1980s,and is then fed uphill by pumping stations along the Grand Canal and through a tunnel under the Yellow River,from where it can flow downhill to reservoirs near Tianjin.Construction on the Eastern Route officially began on December27,2002,and water was supposed to reach Tianjin by2012.However,water pollution has affected the viability of this project.The completed line will be slightly over716miles(1,152km)long,equipped with23pumping stations with a power capacity of454megawatts.It includes two 9.3m diameter horizontal tunnels70m under the riverbed of the Yellow River.(2)Central routeThe central route is from Danjiangkou Reservoir on the Han river,a tributary of the Yangtse River,to Beijing.This route is built on the North China Plainand,once the Yellow River has been crossed,water can flow all the way to Beijing by gravity.The main engineering challenge is to build a tunnel under theYellow River.Construction on the central route began in2004.In2008the307km-long Northern stretch of the central route was completed at a cost of US$2billion.Water in that stretch of the canal does not yet come from the Han River,but from various reservoirs in Hebei Province south of Beijing.Farmers and industries in Hebei had to cut back water consumption to allow for water to be transferred to Beijing.The whole project was expected to be completed around2010.This has recently been set back to2014to allow for more environmental protections to be built.A problem is the influence on the Han River,where~1/3of the water is diverted.One long-term consideration is to build another canal to divert water from the Three Gorges Dam to Danjiangkou Reservoir.Another major difficulty is the resettlement of~330,000 persons around Danjiangkou Reservoir and along the route.On October18,2009, Chinese officials began to relocate residents from the areas of the Hubei and Henan provinces that will be affected by the reservoir.The completed line will be approximately1,264km long,initially providing9.5billion m3of water annually.By 2030,it is expected to increase its water transfer to12to13billion m3annually. Industries are prohibited to locate in the watershed of the reservoir in order to keep its water drinkable.(3)Western routeThe western route,called the Big Western Line,is still at the planning stage.It aims to divert water from the headwaters of the Yangtze River(the Tontian,Yalong and Dadu Rivers)into the headwaters of the Yellow River.In order to move the water through the drainage divide between these rivers,huge dams and long tunnels are needed to be built to cross the Qinghai-Tibetan Plateau and Western Yunnan Plateaus. This route is designed to bring3.8billion m3of water from three tributaries of the Yangtze River about450km across the Bayankala Mountains to northwest China.The Tongtian diversion line would be289km in length,the Yalong131km,and the Dadu 30km.The feasibility of this route is still under study and this project won't start in the near future.Environmentalists have raised concerns about potential flooding that could result.[5]The respective rivers are entirely within China.In addition,there are long-standing plans to divert about200billion cubic metres of water annually from the upstream sections of six rivers in southwesternChina, including the Mekong(Lancang River),the Yarlung Zangbo(called Brahmaputra further downstream)and the Salween(Nu River),to the Yangtze River,the Yellow River and ultimately to the dry areas of northern China through a system of reservoirs, tunnels and natural rivers.The project was considered too immense and costly to be undertaken at the time.The respective rivers are transboundary and a diversion would affect India,Bangladesh,Myanmar,Laos,Thailand,Cambodia and Vietnam.The diversion map is showed in the following picture:Fig.8.The diversion map。

理学类大学生竞赛

美国大学生数学建模竞赛（MCM/ICM）关键词：MCM简介MCM参赛方式MCM流程MCM作品汇MCM网址一．简介美国大学生数学建模竞赛（MCM/ICM），是一项国际级的竞赛项目，为现今各类数学建模竞赛之鼻祖。

MCM/ICM 是Mathematical Contest in Modeling 和Interdisciplinary Contest in Modeling 的缩写，即“数学建模竞赛”和“交叉学科建模竞赛”。

MCM 始于1985 年，ICM 始于2000 年，由COMAP（the Consortium for Mathematics and Its Application，美国数学及其应用联合会）主办，得到了SIAM，NSA，INFORMS 等多个组织的赞助。

MCM/ICM 着重强调研究问题、解决方案的原创性、团队合作、交流以及结果的合理性。

二．参赛方式所有的参赛队必须在美国东部时间2013年1月31号（星期四）下午2点前完成注册如果您刚刚开始注册竞赛的第一个参赛队，请点击网页左边的Register for 2013 Contest 。

输入所有需要的信息，包括邮箱地址和联系方式。

如果您已经注册过一个参赛队而想为另外一个参赛队注册，请点击Advisor Login，打开页面后请您使用在注册第一支参赛队时使用的E-mail地址和密码进行登入。

虽然每个指导老师只能注册两个队，但是对指导老师或者是总的队数是没有限制的。

1．您必须在在美国东部时间2013年1月31日（星期四）晚上8点大赛开始以前选择好您的参赛队的队员。

一旦比赛开始，您将不能增加或是改变任何一个参赛队队员（但是如果参赛队员本人决定不参加比赛，您可以取消他/她的参赛资格）。

2．每个参赛队最多都只能由3名学生组成。

3．一个学生最多只能参加一个参赛队。

4．在比赛时间内，参赛队成员必须是在校学生，但可以不是全日制学生。

参赛队成员和指导教师必须来自同一所学校。

2013年美赛c题生态系统评价英文版.

For office use onlyT1________________ T2________________ T3________________T4________________Team Control Number15879Problem ChosenAFor office use onlyF1 ________________F2 ________________F3 ________________F4 ________________ Small Leaf, Big WorldAbstract地球的生态状况越来越受到人们的关注,但评价地球这个大生态系统的健康状况一直是个难题。

本文我们主要通过主成分分析分析各国家(节点的健康状况,利用有向复杂网络构建了一个可以联系各节点的网络,并对地球健康状况进行GM(1,1预测来分析复杂的地球生态系统。

地球是一个庞大而复杂的生态系统,就像一个网络。

对此,我们选取国家作为我们分析地球这个复杂网络的节点,因为地球上的国家较多,我们通过考虑地理位置和国家发展状况选取典型的国家,最终确定21个国家作为我们分析的节点。

对于各个节点健康状况,我们根据生态学的相关知识确定了社会、经济、环境和人这四个因素范围内的11个地球健康指标,并在世界银行数据库查得21个国家的11个指标在1991年到2010年这20年的数据,以及世界总的相关数据。

我们分析这个复杂的地球生态系统主要有以下三个方面:(1对每个节点的健康指数求解。

我们采用主成分分析法对21个节点以及世界的11个指标进行综合分析,把11个指标抽象成5个主成分进行健康指数的求解,我们以2000年的数据用MATLAB进行编程求解,结果显示五个主成分的累积贡献率高达92%,结果可靠。

我们同时对各个节点的综合值Z(健康指数进行排名,排名靠前的是美国、澳大利亚、加拿大等发达国家,排名靠后的是Morocco、Egypt Arab Rep. China、Kenya等发展中国家且生态保护较差的国家。

2013年武汉大学美赛选拔题翻译

应对飓风背景介绍最近发生的桑迪飓风对于美国西北部沿海沿海地区来说是一场空前的灾难.桑迪和之前发生的艾琳飓风都是百年一遇的飓风.他们两者都在纽约造成了百年一遇的洪灾并造成了巨大的人员伤亡和上亿美元的财产损失.为了保护纽约市免于洪水的侵扰,一组科学家和工程师建议建立巨大的”海门”作为应对措施.所谓”海门”是指一种能够在飓风来临时关闭从而阻止飓风造成的风暴潮将海水倒灌入哈德森河和东河造成洪灾的工程.建立像”海门”这样浩大的工程是非常昂贵的.根据目前粗略的估算,建立这样工程需要花费一百亿美元.从实际层面考虑,假设划拨给你一次性的200亿美元的建设资金以及工程建成之后的每年5亿美元的后续维护资金.其中维护资金包括工程维护、安全性以及工业、贸易和生态影响。

问题1.假设桑迪飓风从未发生，而像艾琳这样的飓风每年发生的概率是P1=0.01.那么海门的建立是否在经济上是合理的？2.很多研究人员发现气候变化造成的海平面上升会极大的增加飓风之类的事件在未来发生的概率，从而让海门这样的虽然造价昂贵的工程变得较具有吸引力。

请你找到一个P1的最小值,使建立海门工程来保护纽约市是有意义的3.假设艾琳飓风和桑迪飓风发生的年概率分别是P1P2。

请你找到最小的（P1,P2）组合使得建立海门工程是合理的。

4.高额的花费并非是海门工程的唯一问题所在。

当海门工程在保护曼哈顿和其他的一些区(类似布鲁克林这样的区)时，反而会增加其他未受其保护的区域的洪灾，诸如布鲁克林、皇后区和新泽西。

试为皇后区和曼哈顿海滩未来五十到一百年的房地产价格和人口密度变化建立一个模型。

你的模型需要同时预测在建立和未建立海门工程两种情况下的变化。

5.假设现在你的论文的初稿因为某种原因交到了一个急于发表一篇类似的模拟结果来使民众恐慌并打击科研人员的记者手上。

请用通俗易懂的文字给编辑写一封半页长的信来阐述你的模型在实际应用中的局限性。

建模建议1.从简单模型开始，再逐渐考虑其他的现实因素2.你需要的大多数据都能在网上很容易发现3.如果你觉得问题太长，你可以从问题3和问题4中选一个解决。

2012美赛ICM C题题目翻译

星际犯罪塑型（ICM）正在调查串谋犯犯罪行为。

调查是非常有信心，他们知道的几名成员的阴谋，但他们进行逮捕之前，希望能找出其他成员和领导人。

阴谋和所有可能涉嫌同谋为同一家公司在一个大办公室复杂的工作。

“公司一直快速增长，并为自己的名称，开发和销售计算机银行和信用卡公司的软件。

ICM最近发现了一个消息从一个小集组82个工人，他们认为在公司将帮助他们找到最有可能的候选人身份不明的同谋者和未知的领导人。

由于信息流量是所有的办公在该公司的工人，它很可能是一些（或许很多）在确定的传播者消息流量不涉及阴谋。

事实上，他们是一定的，他们知道有些人谁是不是在阴谋。

建模工作的目标将是确定人们在办公室复杂谁是最有可能的同谋。

一个优先列表将是理想的，因此ICM可以调查，监视之下的地方，和/或询问最有可能的候选人。

一个判别线分离从非同谋的同谋也将是有益的，以明显的分类，在每个人组。

这也将是有用的模型，如果提名的阴谋领导人检察官办公室。

在当前情况下的数据是给你的犯罪建模团队，你的上司给你以下情形（称为调查的EZ），她曾在几年前在另一座城市。

甚至虽然她是她对简易案件的工作感到非常自豪，她说，这是一个非常小的，简单的例子，但它可以帮助你了解自己的任务。

她的数据如下：她考虑为同谋的十人分别为：安妮＃，鲍勃，卡罗尔，大卫*，艾伦，弗雷德，乔治·哈利，伊内兹和JAYE＃的。

（*表示已知的同谋者，＃表示事先已知nonconspirators）28消息，她为她的案件有编号为每个主题年表的消息，她分配的基础上分析她的消息：安妮对鲍勃：你为什么今天迟到了吗？（1）鲍勃对卡罗尔：这该死的安妮总是看着我。

我是不是晚了。

（1）卡罗尔对戴夫：安娜和鲍勃再次战斗是鲍勃的迟到。

（1）戴夫对艾伦：我要看看你今天早晨。

当你能来吗？带来的预算文件。

（2）戴夫对弗雷德：我能来，随时随地今天看到你。

让我知道什么时候是一个好时机。

我应该带来的预算文件吗？（2）戴夫对乔治：我会看到你以后---说不完的话。

2010MCMandICM题目翻译

2010年美赛MCM/ICM题目翻译【转自数学中国】问题A：最佳击球点解释一下棒球棒的“最佳击球点”。

每个击球者都知道，在棒球棒的大头部分有一个点，当用这一点击球时转移的能量会达到最大。

这一点为什么不在棒球棒的顶端呢？一个基于扭矩的简单解释似乎可以确定“最佳点”应该出现在球棒的顶端，但是这与实际的经验不符。

建立一个模型，解释这一经验结论。

一些球员认为，给球棒“软木化”（在球棒头部掏出一个圆柱空腔，在里面塞入软木或橡胶，然后盖上木帽）能够增加“最佳点”的效果。

补充你的模型，以证实或否认这种效果。

这是否能解释为什么美国职棒大联盟禁止“软木化”？球棒的构造问题是否会涉及材料的选择？也就是说，是否这个模型能预测木质（通常是岑木）或金属（通常是铝）球棒的不同特性？为什么美国职棒大联盟要禁止使用金属球棒？问题B：犯罪学在1981年，彼得萨克利夫被判犯有十三起谋杀罪和一系列的恶意伤害罪。

在该案中，一种用来缩小搜索萨克利夫先生所在范围的方法是找到这些犯罪地点发生的“重心”。

最后,这个嫌疑犯恰好生活在用这种技术所预测的那个城镇里。

从那时起,许多更复杂的技术被发展起来，用来确定系列犯罪的嫌疑人位置的“地理轮廓”。

一个当地的**机构要求你的团队开发一种方法来帮助他们调查连环犯罪。

你开发的这种方法,应至少使用两种不同的方案来产生一个地理轮廓。

你需要发展一种技术，能综合不同方案的结果为执法人员产生一种有用的预测。

这种预测应基于过去的系列犯罪现场的时间和地点，提供下次犯罪发生的可能位置。

如果在你们的模型中，使用了除时间和地点之外的证据,你必须提供具体的细节,说明你是如何纳入额外信息的。

你的方法还应提供，在某一特定情况下方法可靠度的某种形式的估计,包括适当的警告。

除了要求的一页摘要以外，你的报告应该包括一个额外的2页纸的实施概要。

这个概要应该对潜在问题进行综述。

它要概述你的方法,描述你的方法适合以及不适合的情况。

概要将会被呈给**局长阅读，所以概要中应包括适当的技术细节以适合其读者。

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2000-2013美国数学建模竞赛(MCM、ICM)历年试题汇总

目录2000 年美国大学生数学建模竞赛MCM、ICM 试题 (3)2000 MCM A: Air Traffic Control (3)2000 MCM B: Radio Channel Assignments (3)2000 ICM: Elephants: When is Enough, Enough? (5)2001 年美国大学生数学建模竞赛MCM、ICM 试题 (7)2001 MCM A: Choosing a Bicycle Wheel (7)2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...). (8)2001 ICM: Our Waterways - An Uncertain Future (10)2002 年美国大学生数学建模竞赛MCM、ICM 试题 (14)2002 MCM A: Wind and Waterspray (14)2002 MCM B: Airline Overbooking (14)2002 ICM: Scrub Lizards (15)2003 年美国大学生数学建模竞赛MCM、ICM 试题 (19)2003 MCM A: The Stunt Person (19)2003 MCM B: Gamma Knife Treatment Planning (19)2003 ICM: Aviation Baggage Screening Strategies: To Screen or Not to Screen, that is the Question (20)2004 年美国大学生数学建模竞赛MCM、ICM 试题 (24)2004 MCM A: Are Fingerprints Unique? (24)2004 MCM B: A Faster QuickPass System (24)2004 ICM: To Be Secure or Not to Be? (24)2005 年美国大学生数学建模竞赛MCM、ICM 试题 (25)2005 MCM A: Flood Planning (25)2005 MCM B: Tollbooths (25)2005 ICM: Nonrenewable Resources (25)2006 年美国大学生数学建模竞赛MCM、ICM 试题 (27)2006 MCM A: Positioning and Moving Sprinkler Systems for Irrigation (27)2006 MCM B: Wheel Chair Access at Airports (27)2006 ICM: Trade-offs in the fight against HIV/AIDS (28)2007 年美国大学生数学建模竞赛MCM、ICM 试题 (32)2007 MCM A: Gerrymandering (32)2007 MCM B: The Airplane Seating Problem (32)2007 ICM: Organ Transplant: The Kidney Exchange Problem (33)2008 年美国大学生数学建模竞赛MCM、ICM 试题 (38)2008 MCM A: Take a Bath (38)2008 MCM B: Creating Sudoku Puzzles (38)2008 ICM: Finding the Good in Health Care Systems (38)2009 年美国大学生数学建模竞赛MCM、ICM 试题 (40)2009 MCM A: Designing a Traffic Circle (40)2009 MCM B: Energy and the Cell Phone (40)2009 ICM: Creating Food Systems: Re-Balancing Human-Influenced Ecosystems41 2010年美国大学生数学建模竞赛 MCM、ICM 试题 (42)2010 MCM A: The Sweet Spot (42)2010 MCM B: Criminology (43)2010 ICM: The Great Pacific Ocean Garbage Patch (44)2011年美国大学生数学建模竞赛 MCM、ICM 试题 (45)2011 MCM A: Snowboard Course (45)2011 MCM B: Repeater Coordination (45)2011 ICM: Environmentally and Economically Sound (46)2012年美国大学生数学建模竞赛 MCM、ICM 试题 (48)2012 MCM A: The Leaves of a Tree (48)2012 MCM B: Camping along the Big Long River (50)2012 ICM: Modeling for Crime Busting (51)2013年美国大学生数学建模竞赛 MCM、ICM 试题 (59)2013 MCM A: The Ultimate Brownie Pan (59)2013 MCM B: Water, Water, Everywhere (61)2013 ICM: NetworkModeling of Earth's Health (62)2000 年美国大学生数学建模竞赛MCM、ICM 试题2000 MCM A: Air Traffic ControlTo improve safety and reduce air traffic controller workload, the Federal Aviation Agency (FAA) is considering adding software to the air traffic control system that would automatically detect potential aircraft flight path conflicts and alert the controller. To that end, an analysit at the FAA has posed the following problems.Requirement A: Given two airplanes flying in space, when should the air traffic controller consider the objects to be too close and to require intervention? Requirement B: And airspace sector is the section of three-dimensional airspace that one air traffic controller controls. Given any airspace sector, how do we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of aircraft simultaneously passing through that sector1.at any one instant?2.during any given interval of time?3.during a particular time of day?How does the number of potential conflicts arising during those periods affect complexity? Does the presence of additional software tools to automatically predict conflicts and alert the controller reduce or add to this complexity? In addition to the guidelines for your report, write a summary (no more than two pages) that the FAA analyst can present to Jane Garvey, the FAA Administrator, to defend your conclusions.2000 MCM B: Radio Channel AssignmentsWe seek to model the assignment of radio channels to a symmetric network of transmitter locations over a large planar area, so as to avoid interference. One basic approach is to partition the region into regular hexagons in a grix (honeycomb-style), as shown in Figure 1, where a transmitter is located at the center of each hexagon.An interval of the frequency spectrum is to be alloted for transmitter frequencies. The interval will be divided into regularly spaced channels, which we represent by integers 1,2,3, … . Each transmitter wil be assigned one positive integer channel. The same channel can be used at many locations, provided that interference from nearby transmitters is avoided.Our goal is to minimize the width of the interval in the frequency spectrum that is needed to assugn channels subject to some constraints. This is achieved with the concept of a span. The span is the minimum, over all assignments satisfying the constraints, of the largest channel used at any location. It is not required that every channel smaller than the span be used in an assignment that attains the span.Let s be the length of a side of one of the hexagons. We concentrate on the case that there are two levels of interference.Requirement A: There are several contrainsts on the frequency assignments. First, no two transmitters within distance 4s of each other can be given the same channel. Second, due to spectral spreading, transmitters within distance 2s of each other must not be given the same or adjacent channels: Their channels must differ by at least 2. Under these contraints, what can we say about the span in Figure 1?Requirement B: Repeat Requirement A, assuming the grid in the example spreads arbitrarily far in all directions.Requirement C: Repeat Requirements A and B, except assume now more generally that channels for transmitters within distance 2s differ by at least some given integer k, while those at distance at most 4s must still differ by at least one. What cna we say about the span and about efficient strategies for designing assignments, as a function of k?Requirement D: Consider generalizations of the problem, such as several levels of interference or irregular transmitter placements. What other factors may be important to consider?Requirement E: Write an article (no more than 2 pages) for the local newspaper explaining your findings.2000 ICM: Elephants: When is Enough, Enough?“Ultimately, if a habitat is undesirably changed by elephants, then their removal should be considered -even by culling.”National Geographic (Earth Almanac) –December 1999 A large National Park in South Africa contains approximately 11,000 elephants. Management policy requires a healthy environment that can maintain a stable herf of 11,000 elephants. Each year park rangers count the elephant population. During the past 20 years whole herds have been removed to keep the population as close to 11,000 as possible. The process involved shooting (for the most part) and occasionally relocating approximately 600 to 800 elephants per year.Recently, there has been a public outcry against the shooting of these elephants. In addition, it is no longer feasible to relocate even a small population of elephants each year. A contraceptive dart, however, has been developed that can prevent a mature elephant cow from conceiving for a period of two years.Here is some information about eh elephants in the Park:∙There is very little emigration of immigration of elephants.∙The gender ratio is very close to 1:1 and control measures have endeavored to maintain parity.∙The gender ratio of newborn calves is also about 1:1. Twins are born about 1.35% of the time.∙Cows first conceive between the ages of 10 and 12 and produce, on average, a calf every 3.5 years until they reach an age of about 60.Gestation is approximately 22 months.∙The contraceptive dart causes an elephant cow to come into oestrus every month (but not conceiving). Elephants usually have courtship only once in 3.5 years, so the monthly cycle can cause additional stress.∙ A cow can be darted every year without additional detrimental effects. A mature elephant cow will not be able to conceive for 2 years after thelast darting.∙Between 70% and 80% of newborn calves survive to age 1 year.Thereafter, the survival rate is uniform across all ages and is very high(over 95%), until about age 60; it is a good assumption that elephantsdie before reading age 70.There is no hunting and negligible poaching in the Park.The park management has a rough data file of the approximate ages and gender of the elephants they have transported out of the region during the past 2 years. This data is available on website: icm2000data.xls. Unfortunately no data is available for the elephants that have been shot or remain in the Park.Your overall task is to develop and use models to investigate how the contraceptive dart might be used for population control. Specifically:Task 1: Develop and use a model to speculate about the likely survival rate for elephants aged 2 to 60. Also speculate about the current age structure of the elephant population.Task 2: Estimate how many cows would need to be darted each year to keep the population fixed at approximately 11,000 elephants. Show how the uncertainty in the data at your disposal affects your estimate. Comment on any changes in the age structure of the population and how this might affect tourists. (You may want to look ahead about 30-60 years.)Task 3: If it were feasible to relocate between 50 and 300 elephants per year, how would this reduce the number of elephants to be darted? Comment on the trade-off between darting and relocation.Task 4: Some opponents of darting argue that if there were a sudden loss of a large number of elephants (due to disease or uncontrolled poaching), even if darting stopped immediately, the ability of the population to grow again would be seriously impeded. Investigate and respond to this concer.Task 5: The management in the Park is skeptical about modeling. In particular, they argue that a lack of complete data makes a mockery of any attempt to use models to guide their decision. In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the park management that responds to their concerns and provides advice. Also suggest ways to increase the park managers confidence in your model and your conclusions.Task 6: If your model works, other elephant parks in Africa would be interested in using it. Prepare a darting plan for parks of various sizes (300-25,000 elephants), with slightly different survival rates and transportation possibilities.2001 年美国大学生数学建模竞赛MCM、ICM 试题2001 MCM A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades startingfrom zero percent to ten percent in one percent increments. (Roadgrade is defined to be the ratio of the total rise of a hill divided by thelength of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportionalto the road grade. A rider will lose about 8 kph for a five percent grade over 100 meters.∙Task 2. Provide an example of how the table could be used for a specific time trial course.∙Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the two coastal-boundlanes of I-26 into two lanes of Columbia-bound traffic, essentiallyturning the entire I-26 into one-way traffic, significantly improveevacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastal regionwas ordered. Would the evacuation traffic flow improve under analternative strategy that staggers the evacuation, perhapscounty-by-county over some time period consistent with the pattern of how hurricanes affect the coast?3.Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these?4.What effect would it have on evacuation flow to establish moretemporary shelters in Columbia, to reduce the traffic leaving Columbia?5.In 1999, many families leaving the coast brought along their boats,campers, and motor homes. Many drove all of their cars. Under whatconditions should there be restrictions on vehicle types or numbers ofvehicles brought in order to guarantee timely evacuation?6.It has been suggested that in 1999 some of the coastal residents ofGeorgia and Florida, who were fleeing the earlier predicted landfalls ofHurricane Floyd to the south, came up I-95 and compounded the traffic problems. How big an impact can they have on the evacuation trafficflow? Clearly identify what measures of performance are used tocompare strategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.Clearly identify what measures of performance are used to compare strategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.2001 ICM: Our Waterways - An Uncertain FutureZebra mussels, Dreissena polymorpha, are small, fingernail-sized, freshwater mollusks unintentionally introduced to North America via ballast water from a transoceanic vessel. Since their introduction in the mid 1980s, they have spread through all of the Great Lakes and to an increasing number of inland waterways in the United States and Canada. Zebra mussels colonize on various surfaces,such as docks, boat hulls, commercial fishing nets, water intake pipes and valves, native mollusks and other zebra mussels. Their only known predators, some diving ducks, freshwater drum, carp, and sturgeon, are not numerous enough to have a significant effect on them. Zebra mussels have significantly impacted the Great Lakes ecosystem and economy. Many communities are trying to control or eliminate these aquatic pests. SOURCE: Great Lakes Sea Grant Network /.Researchers are attempting to identify the environmental variables related to the zebra mussel infestation in North American waterways. The relevant factors that may limit or prevent the spread of the zebra mussel are uncertain. You will have access to some reference data to include listings of several chemicals and substances in the water system that may affect the spread of the zebra mussel throughout waterways. Additionally, you can assume individual zebra mussels grow at a rate of 15 millimeters per year with a life span between 4 - 6 years. The typical mussel can filter 1 liter of water each day.Requirement A: Discuss environmental factors that could influence the spread of zebra mussels.Requirement B: Utilizing the chemical data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAChem1.xls, and the mussel population data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAPopulation 1.xls model the population growth of zebra mussels in Lake A. Be sure to review the Information about the collection of the zebra mussel data. Requirement C: Utilizing additional data on Lake A from another scientist provided at :ap/undergraduate/contests/icm/imagesdata/LakeAChem2.xls and additional mussel population data provided at:ap/undergraduate/contests/icm/imagesdata/LakeAPopulation 2.xls corroborate the reasonableness of your model from Requirement B. As a result of this additional data, adjust your earlier model. Analyze the performance of your model. Discuss the sensitivity of your model. Requirement D: Utilizing the Chemical data from two lakes (Lake B and Lake C) in the United States provided atap/undergraduate/contests/icm/imagesdata/LakeB.xls and ap/undergraduate/contests/icm/imagesdata/LakeC.xls determine if these lakes are vulnerable to the spread of zebra mussels. Discuss your prediction.Requirement E: The community in the vicinity of Lake B (in requirement D) is considering specific policies for the de-icing of roadways near the lake duringthe winter season. Provide guidance to the local government officials regarding a policy on “de-icing agents.”In your guidance include predictions on the long-term impact of de-icing on the zebra mussel population. Requirement F: It has been recommended by a local community in the United States to introduce round goby fish. Zebra mussels are not often eaten by native fish species so they represent a dead end ecologically. However, round gobies greater than 100 mm feed almost exclusively on zebra mussels. Ironically, because of habitat destruction, the goby is endangered in its native habitat of the Black and Caspian Seas in Russia. In addition to your technical report, include a carefully crafted report (3-page maximum) written explicitly for the local community leaders that responds to their recommendation to introduce the round goby. Also suggest ways to help reduce the growth of the mussel within and among waterways.Information about the collection of the zebra mussel dataThe developmental state of the Zebra mussel is categorized by three stages: veligers (larvae), settling juveniles, and adults. Veligers (microscopic zebra mussel larvae) are free-swimming, suspended in the water for one to three weeks, after which they begin searching for a hard surface to attach to and begin their adult life. Looking for zebra mussel veligers is difficult because they are not easily visible by the naked eye. Settled juvenile zebra mussels can be felt on smooth surfaces like boats and motors. An advanced zebra mussel infestation can cover a surface, even forming thick mats sometimes reaching very high densities. The density of juveniles was determined along the lake using three 15×15 cm settling plates. The top plate remained in the water for the entire sampling season (S - seasonal) to estimate seasonal accumulation. The middle and bottom plates are collected after specific periods (A –alternating ) of time denoted by “Lake Days”in the data files.The settling plates are placed under the microscope and all juveniles on the undersides of the plate are counted and densities are reported as juveniles/m^2.2002 年美国大学生数学建模竞赛MCM、ICM 试题2002 MCM A: Wind and WatersprayAn ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area. Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.2002 MCM B: Airline OverbookingYou're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations. Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.Consider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B Heightened security at and around airports Passengers' fear Loss of billions of dollars in revenue by airlines to dateBuild a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, andconsider alternatives for handling “bumped”passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.2002 ICM: Scrub LizardsThe Florida scrub lizard is a small, gray or gray-brown lizard that lives throughout upland sandy areas in the Central and Atlantic coast regions of Florida. The Florida Committee on Rare and Endangered Plants classified the scrub lizard as endangered.You will find a fact sheet on the Florida Scrub Lizard at/undergraduate/contests/mcm/contests/2002/problem s/icm2002data/scrublizard.pdfThe long-term survival of the Florida scrub lizard is dependent upon preservation of the proper spatial configuration and size of scrub habitat patches.Task 1: Discuss factors that may contribute to the loss of appropriate habitat for scrub lizards in Florida. What recommendations would you make to the state of Florida to preserve these habitats and discuss obstacles to the implementation of your recommendations?Task 2: Utilize the data provided in Table 1 to estimate the value for Fa (the average fecundity of adult lizards); Sj (the survivorship of juvenile lizards- between birth and the first reproductive season); and Sa (the average adult survivorship).Table 1Summary data for a cohort of scrub lizards captured and followed for 4 consecutive years. Hatchling lizards (age 0) do not produce eggs during the summer they are born. Average clutch size for all other females is proportional to body size according to the function y = 0.21*(SVL)-7.5, where y is the clutch size and SVL is the snout-to-vent length in mm.Year Age Total NumberLivingNumber of LivingFemalesAvg. Female Size(mm)1 0 972 495 30.32 1 180 92 45.83 2 20 11 55.84 3 2 2 56.0Task 3: It has been conjectured that the parameters Fa , Sj , and Sa , are related to the size and amount of open sandy area of a scrub patch. Utilize the data provided in Table 2 to develop functions that estimate Fa, Sj , and Sa for different patches. In addition, develop a function that estimates C, the carrying capacity of scrub lizards for a given patch.Table 2Summary data for 8 scrub patches including vital rate data for scrub lizards. Annual female fecundity (Fa), juvenile survivorship (Sj), and adult survivorship (Sa) are presented for each patch along with patch size and the amount of open sandy habitat.Patch Patch Size (ha) Sandy Habitat (ha) Fa Sj Sa Density (lizards/ha)a 11.31 4.80 5.6 0.12 0.06 58b 35.54 11.31 6.6 0.16 0.10 60c 141.76 51.55 9.5 0.17 0.13 75d 14.65 7.55 4.8 0.15 0.09 55e 63.24 20.12 9.7 0.17 0.11 80f 132.35 54.14 9.9 0.18 0.14 82g 8.46 1.67 5.5 0.11 0.05 40h 278.26 84.32 11.0 0.19 0.15 115Task 4: There are many animal studies that indicate that food, space, shelter, or even reproductive partners may be limited within a habitat patch causing individuals to migrate between patches. There is no conclusive evidence on why scrub lizards migrate. However, about 10 percent of juvenile lizards do migrate between patches and this immigration can influence the size of the population within a patch. Adult lizards apparently do not migrate. Utilizing the data provided in the histogram below estimate the probability of lizards surviving the migration between any two patches i and patch j.Table 3HistogramMigration data for juvenile lizards marked, released, and recaptured up to 6 months later. Surveys for recapture were conducted up to 750m from release sites.Task 5: Develop a model to estimate the overall population size of scrub lizards for the landscape given in Table 3. Also, determine which patches are suitable for occupation by scrub lizards and which patches would not support a viable population.Patch size and amount of open sandy habitat for a landscape of 29 patches located on the Avon Park Air Force Range. See:/undergraduate/contests/icm/2002problem/map.jpg for a map of the landscape.Patch Identification Patch Size (ha) Sandy Habitat (ha)1 13.66 5.382 32.74 11.913 1.39 0.234 2.28 0.765 7.03 3.626 14.47 4.387 2.52 1.998 5.87 2.499 22.27 8.44。

2012年美国国际大学生数学建模竞赛(MCM+ICM)题目+翻译

2012 Contest ProblemsPROBLEM A: The Leaves of a Tree"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.2012美赛A题：一棵树的叶子（数学中国翻译）“一棵树的叶子有多重？”怎么能估计树的叶子（或者树的任何其它部分）的实际重量？怎样对叶子进行分类？建立一个数学模型来对叶子进行描述和分类。

2015年美国大学生数学建模竞赛赛题翻译

2015年美国大学生数学建模竞赛赛题翻译2015年美国大学生数学竞赛正在进行，比赛时间为北京时间：2015年2月6日（星期五）上午9点-2月10日上午9点。

竞赛以三人（本科生）为一组，在四天时间内，就指定的问题，完成该实际问题的数学建模的全过程，并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解（及软件）、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。

2015 MCM/ICM Problems总计4题，参赛者可从MCM Problem A, MCM Problem B, ICM Problem C or ICM Problem D等四道赛题中自由选择。

2015 Contest ProblemsMCM PROBLEMSPROBLEM A: Eradicating EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems (sending the medicine to where it is needed), (geographical) locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 pagenon-technical letter for the world medical association to use in their announcement.中文翻译：问题一：根除埃博拉病毒世界医学协会已经宣布他们的新药物能阻止埃博拉病毒并且可以治愈一些处于非晚期疾病患者。