2013美赛MCMICM 官方版翻译
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
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数学建模美赛题目(中文版)[1]](https://img.taocdn.com/s3/m/2a43be292f60ddccda38a018.png)
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。
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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）。
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参赛队成员和指导教师必须来自同一所学校。
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Teams (Student or Advisor) are now required to submit an electronic copy (summary sheet and solution) of their solution paper by email too solutions@ as a Word or PDF attachment. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 4, 2013.
Subject line
COMAP your control number
Example: COMAP 11111
Click here to download a PDF of the complete contest instructions.
Click here to download a copy of the Summary Sheet in Microsoft Word format. *Be sure to change the control number and problem selected before printing out the page.
Teams are free to choose between MCM Problem A, MCM Problem B or ICM Problem C.
COMAP Mirror Site: For more in:
/undergraduate/contests/mcm/
MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling
2013 Contest Problems
MCM PROBLEMS
PROBLEM A: The Ultimate Brownie Pan
When 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.
Assume
1. 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 pan
3. 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.
当用矩形锅烘烤时，热集中在4个角落，食物就会在角落里被过度烘焙。
而在边缘受热则弱一些。
在圆形锅中，温度均匀地分布在整个外部边缘上，食物就不会在边缘上被过度烘焙。
但是，大多数的炉子都是矩形的，使用圆形盘子在空间上不能很好利用。
建立一个模型展示热在平底锅边缘的分布，从矩形到圆形和在这之间的任一形状。
假设：
1.矩形炉子的长宽比
2.每个平底锅必须有一个固定的面积
3.最初，炉子的两个架间隔均匀分布
建立一个模型，选择一个平底锅最好的形状，在以下的条件下。
1.最大化可以用于炉子中的平底锅数量（N）
2.最大化热（H）在锅上的分布
3.根据条件1和2得到一个最优化的结合，其中权重p和1-p已被赋值，阐明结果随长宽比W/L和p值的不同的变化
PROBLEM B: Water, Water, Everywhere
Fresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the “best water strategy choice.”
Countries: United States, China, Russia, Egypt, or Saudi Arabia
建立一个数学模型，决定一个在年有效的，可行的，合算的关于水的策略，满足目标水量的需要，从以下选择一个国家，确定最好的水策略。
特别地，你的模型必须处理存储和运输，淡化，保护。
如果可能的话，使用你的模型讨论经济的，符合自然规律的，环保的策略。
给政府的领导提供一个非技术职位的论文来概述你的方法，它的可行性和费用，而且为什么它是最好的水策略。