2013年美赛B题原文及翻译

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2013 美国数学建模竞赛题目中文 MCM

2013 竞赛题目
MCM
问题A：
当在矩形平底锅上烘烤食物时，热量集中在四个角，因此食物在四个角上容易烤焦（边上焦的程度较轻一点）。

在圆形平底锅内烘烤时，热量均与地分布于整个外部边缘，食物的边缘部分不会烤焦。

然而，由于大部分烤炉形状为矩形，就利用烤炉中的空间而言，使用圆形平底锅并不是最有效率的做法。

开发一个模型来展现平底锅外边缘热量分布，该平底锅的形状可为矩形或圆形，也可能是其它形状。

假设
1．矩形烤炉长宽比W/L
2．每个平底锅面积为A
3．初始烤炉中的两个架子在空间上平均分布。

开发一模型可用于在下列条件下挑选最佳类型的平底锅（形状）：
1．最大限度提高放入烤炉中的平底锅数量（N）
2．最大限度均匀分布在平底锅上的热量分布（H）
3．最优组合条件（1）和（2），其中指定权值p和（1-p）来解释这些结果如何随W/L和p 的不同值变动。

除了MCM格式化的解决方案，为新的《布朗尼美食家杂志》准备一至两页的广告，表达你的思路。

问题B：水，水，到处都是水
新鲜的水对于世界各地的发展是一个限制性因素。

建立一个数学模型用于决定一个有效、可行且成本效益最大的2013水战略来应对投射出来的2025年水需求[从下列国家中挑选一个国家]，并确认最佳水资源战略。

尤其要注意的是，你的模型必须强调存储量和水的运动；去盐渍及保水。

如果可能的话，使用你的模型来讨论你拟定战略的经济、物理和环境影响。

向政府官员提供一个非技术性意见书，阐述你的方法、可行性和成本，以及你的战略之所以为“最佳水资源战略选择”的原因。

国家：美国，中国，俄国，埃及或沙特阿拉伯。

2013 全国大学生英语竞赛B类真题答案

2013 National English Contestfor College Students(Level B - Preliminary)参考答案及评分标准Part I. Listening Comprehension（30 points）1—5CBCBA 6—10 AABBC 11—15 BACAB 16—20 BABAC21. a dictation 22. keep pace. 23. An active listener 24. the topic 25. heading26. paraphrasing 27. summarising 28. rewrite 29. thoughts and comments 30. useful study aid Part II援Multiple Choice (15 points)Section A (10 points)31—35 ACBBC 36—40 DACBASection B (5 points)41—45 ABCBDPart III援Cloze (10 points)46. popular 47. adopted 48. available 49. longer 50. nervous51. space 52. sufficiently 53. but 54. affectionate 55. retiredPart IV. Reading Comprehension (40 points)Section A (10 points)56. D 57. C58. ordering a hamburger 59. ignorant and inexperienced 60. primary source materialsSection B (10 points)61. For sport or because it蒺s part of a traditional culture.62. Stuff and mount the dead animals.63. Overpopulation of certain species.64. Outbreaks of fowl cholera.65. They kill a limited number of bowheads a year.Section C (10 points)66. a smaller firm 67. promotion prospects 68. morale69. his/her life miserable 70. got on withSection D (10 points)71. N 72. Y 73. Y74. 在我们的竞争对手感到拮据的时候出现这种情况，让人感到非常振奋。

2013年数学建模美赛题目中文翻译_共4页

Problem c:背景：社会正致力于运用和开发模型来预测地球的生物和环境情况。

很多科学研究总结了逐渐增长的地球环境和生物系统压力，但很少有人用全球范围的模型来检测这些观点。

联合国发表的千年生态系统评估综合报告发现：近三分之二的地球生命支持生态系统——包括净水，洁净的空气，稳定的气候——正在因非可持续性使用而逐渐衰减。

其中大部分破坏归咎于人类行为。

暴增的对于食物，淡水，燃料，木材的需求导致了剧烈的环境变化；从森林砍伐到空气，土壤和水污染。

尽管已存在大量关于局部习惯和地区因素的研究，目前的模型还不能告知决定人他们的局部策略是如何影响整个地球的健康的。

许多模型忽略了复杂的全球因素，这些模型无法判断重大政策的长期影响。

尽管科学家们意识到巨大环境和生物系统中存在的复杂关系和交叉作用，当前的模型通常忽略这些管理或限定了系统间的影响。

系统的复杂性体现在多元交互（多个元素的相关性），反馈，突发行为，即将发生的状态变化或触发点。

最近的自然杂志中一篇由22位国际知名科学家撰写的题为“迫近地球生物圈的状态变化”的文章讨论了许多有关科学模型对于预测行星健康系统潜在状态变化的重要性与必需性。

文章提供了两种具体定性的模型，并寻求更好的预测模型：1）通过在全球模型中加入相关系统的复杂性（包括局部情况对全球系统的影响，反之亦然）来优化生物状态预测。

2）辨别不同因素在产生非健康全球状态变化中的作用并展示如何运用有效的生态系统管理来预防或限制这些即将发生的状态变化。

研究最终归结于问题：我们是否能利用全球健康的局部或地区性组成部分预测潜在状态变化来帮助决策者制定基于对全球健康状况潜在影响的，有效的策略。

尽管有越来越多的警示信号出现，没人知道地球是否确实在接近全球性的转折点（极端状态），这种极端的状态是否是不可避免的。

自然杂志等研究指出了地球生态系统中的一些重要工作元素。

（例如：局部因素，全球变化，多维元素与关系，变化的时间与空间范围）。

美赛14B题翻译

问题B：大学教练传奇Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports.体育画报（一个体育爱好者喜爱的杂志）正在评选不限男女上世纪‘最好的全职教练’建立一个数学模型去评选在曲棍球，橄榄球，篮球，垒球，篮球，足球领域里最好的教练（过去或现在）。

2013年美国数学建模竞赛B题

水资源计划摘要本文是要设计一个有效的，可行的，低成本的用水计划，来满足某国2025年的用水需求。

我们选择中国为研究对象，根据中国各地区历年的水资源总量并求出其均值，参考各地区历年用水总量来预测2025年的用水总量，将两者相减得出差值，并以此为依据将中国各地区分为缺水地区，不缺水地区，水资源丰富地区三类。

经研究分析有两种可行性高的方案。

第一种，由水资源丰富地区向缺水地区提供水。

第二种，是由沿海缺水城市进行海水淡化并运往其他缺水城市。

我们主要考虑经济因素对两种方案进行分析研究，最终得出结论由水资源丰富地区铺设管道向缺水地区提供水为最优方案。

并以各省的省会作为核心城市，说明全省的需水和调水情况，并以省会城市或直辖市为顶点构成一个赋权图，即把问题转换为求水资源丰富地区到缺水地区的最短路问题，并用图论的知识来解决问题。

在此基础上考虑到此方案会改变就业，生产力，水资源利用等因素，从而对经济，物理，环境产生不同程度的影响，并用层次分析加以研究，最终以报告的方式向政府反映。

关键词：回归分析最小生成树层次分析法一、问题重述淡水是世界大部分地区的发展限制。

试建立一个数学模型，用来确定一个有效的、可行的和低成本的水资源战略，以满足2025年预计的用水需求，特别是，您的数学模型必须解决存储和输送，去盐碱化和环境保护等问题。

如果可能的话，用你的模型探讨此战略在经济，物理和环境等方面的影响。

试提供一个非技术性的文件，向政府相关部门介绍你的方法以及其可行性和成本，并说明为什么它是“最好的水战略”。

二、符号说明ˆy：预测得出的2025年用水量；S：输水的造价；1S：海水淡化的造价；2d1: 输水工程的单位造价；d2：海水淡化的单位造价；2R：拟合度.三、模型假设1.从2013年到2025年各外部因素对水资源总量无影响，例如：雪灾、地震、洪水、战争等对环境的影响；2.各地区海水淡化单位费用相同；3.不同地区淡水转移的单位费用相同；4.人们的消费水平及劳动力费用不会随意外事故发生明显改变。

美赛B题翻译

寻找失联飞机
回想失恋的马航MH370.建立一个通用的数学模型协助计划利用可行搜索手段的搜寻人员，来搜索在从A点飞向B点过程中坠入公开水域例如大西洋、太平洋、印度洋、南极洋或者北冰洋的飞机。

假设坠落飞机没有信号。

你的模型应该认识到，我们可能搜索各种各样的飞机，也应该意识到，携带各种不同电子设备或传感器的搜寻飞机也有很多种。

另外，为航空公司准备1-2页的非技术性文章，以为其在关于未来飞机搜寻计划的新闻发布会上使用。

2013年美赛B中文翻译

PROBLEM B: Water, Water, EverywhereFresh 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 onecountry from the list below] in 2025, and identify the best water strategy. Inparticular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss theeconomic, physical, and environmental implications of your strategy. Provide anon-technical position paper to governmental leadership outlining yourapproach, its feasibility and costs, and why it is the “best water strategychoice.”Countries: United States, China, Russia, Egypt, or Saudi Arabia问题B：可利用淡水资源的匮乏淡水资源匮乏已经成了世界很多国家发展的瓶颈。

数学建模美赛B题论文

2013建模美赛B题思路数学建模美赛B题论文摘要水资源是极为重要生活资料，同时与政治经济文化的发展密切相关，北京市是世界上水资源严重缺乏的大都市之一。

本文以北京为例，针对影响水资源短缺的因素，通过查找权威数据建立数学模型揭示相关因素与水资源短缺的关系，评价水资源短缺风险并运用模型对水资源短缺问题进行有效调控。

首先，分析水资源量的组成得出影响因素。

主要从水资源总量（供水量）和总用水量（需水量）两方面进行讨论。

影响水资源总量的因素从地表水量，地下水量和污水处理量入手。

影响总用水量的因素从农业用水，工业用水，第三产业及生活用水量入手进行具体分析。

其次，利用查得得北京市2001-2008年水量数据，采用多元线性回归，建立水资源总量与地表水量，地下水量和污水处理量的线性回归方程yˆ=-4.732+2.138x1+0.498x2+0.274x3根据各个因数前的系数的大小，得到风险因子的显著性为rx1>rx2>rx3(x1, x2，x3分别为地表水、地下水、污水处理量)。

再次，利用灰色关联确定农业用水、工业用水、第三产业及生活用水量与总用水量的关联程度ra =0.369852，rb= 0.369167，rc=0.260981。

从而确定其风险显著性为r a>r b>r c。

再再次，由数据利用曲线拟合得到农业、工业及第三产业及生活用水量与年份之间的函数关系，a=0.0019（t-1994）3-0.0383（t-1994）2-0.4332（t-1994）+20.2598;b=0.014（t-1994）2-0.8261t+14.1337;c=0.0383（t-1994）2-0.097（t-1994）+11.2116;D=a+b+c；预测出2009-2012年用水总量。

最后，通过定义缺水程度S=（D-y）/D=1-y/D，计算出1994-2008的缺水程度，绘制出柱状图，划分风险等级。

我们取多年数据进行比较，推测未来四年地表水量和地下水量维持在前八年的平均水平，污水处理量为近三年的平均水平，得出2009-2012年的预测值，并利用回归方程yˆ=-4.732+2.138x1+0.4982x2+0.274x3计算出对应的水资源总量。

2013年数学建模美赛B题论文

2013建模美赛B题思路摘要水资源是极为重要生活资料，同时与政治经济文化的发展密切相关，北京市是世界上水资源严重缺乏的大都市之一。

首先，分析水资源量的组成得出影响因素。

主要从水资源总量（供水量）和总用水量（需水量）两方面进行讨论。

影响水资源总量的因素从地表水量，地下水量和污水处理量入手。

影响总用水量的因素从农业用水，工业用水，第三产业及生活用水量入手进行具体分析。

其次，利用查得得北京市2001-2008年水量数据，采用多元线性回归，建立水资源总量与地表水量，地下水量和污水处理量的线性回归方程yˆ=-4.732+2.138x1+0.498x2+0.274x3根据各个因数前的系数的大小，得到风险因子的显著性为r x1>r x2>r x3(x1, x2，x3分别为地表水、地下水、污水处理量)。

再次，利用灰色关联确定农业用水、工业用水、第三产业及生活用水量与总用水量的关联程度r a=0.369852，r b= 0.369167，r c=0.260981。

从而确定其风险显著性为r a>r b>r c。

最后，通过定义缺水程度S=（D-y）/D=1-y/D，计算出1994-2008的缺水程度，绘制出柱状图，划分风险等级。

2013年美赛数学建模b题的分析

Байду номын сангаас
美国2025年可提供的实际淡水量怎样预测？
（可以先预测不同地区不同领域供水量，再相加）
如果实际淡水量小于需求量，可通过那些方法提供不足的淡水？（例如：海水淡化、不同地区淡水转移）
这些方法那个更好？（比较的依据是什么？例如费用，环境）需要做出那些假设？
1. 从现在到2025年之前不会有战争，自然灾害等影响因素 2.同一个地区的居民年用水量相同 3.同一个地区的居民量的年增长率为常数 4.不同地区海水淡化的单位费用相同 5.不同地区淡水转移的单位费用相同
注：模型假设一般是在问题分析中根据需要提出的，所以可以先提出基本假设，以后再补充
Vx pre S
1.预测2025年供水量的模型（以一个州的降水量为例）
其中，表示州i 的可用降水量，表示该州的单位面积平均年降水量， Si 表示该州的淡水地表面积
Vx pre S
2.预测2025年需水量的模型（以一个州的居民用水量为例）
若 V大于0，则说明2025年美国的淡水量是足够的，然后再看每个州需要补充的淡水量，即 V V ，
si ri
若每个州需要补充的淡水量均大于0，则不需要采取任何措施，
否则，需要在不通州之间进行淡水调度。
若 V小于0，则说明2025年美国的淡水量是不足的，需要采取海水淡化等措施
注：为使表达更清晰，可以在论文中采用图、表等形式
其中，表示州i 在2025年人口数量，表示该州在2010年人口数量，表示该州的人口平均年增长率则该州在2025年的居民用水量为
i Vri w N 2 0 0 5
其中，w 表示该州居民的平均年用水量
3. 2025年美国需要补充的淡水量

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。

2013全美数学建模题目

2013 Contest ProblemsMCM PROBLEMSPROBLEM 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 B: Water, Water, EverywhereFresh 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, useyour 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 ArabiaICM PROBLEMPROBLEM C: Network Modeling of Earth's HealthClick the title below to download a PDF of the 2013 ICM Problem. Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.Network Modeling of Earth's Health© 2013 COMAP, The Consortium for Mathematics and Its Applications May be reproduced for academic/research purposesFor More information on COMAP and this projectvisit 。

2013美赛ICM题目翻译

Using Networks to Measure Influence and Impact利用网络来衡量影响和冲击One of the techniques to determine influence of academic research is to build and measure properties of citation or co-author networks.一种确定科学研究的影响力的技术是通过建立和衡量引用属性或合著网络Co-authoring a manuscript usually connotes a strong influential connection between researchers.合著一份手稿通常意味着研究者之间存在很强的影响力的关系。

One of the most famous academic co-authors was the 20th-century mathematician Paul Erdös who had over 500 co-authors and published over 1400 technical research papers.最著名的学术和作者之一是20世纪的数学家“Paul Erdös”。

他曾经有超过500个的共著者并且发表了超过1400份的技术研究报告。

It is ironic, or perhaps not, that Erdös is also one of the influencers in building the foundation for the emerging interdisciplinary science of networks, particularly, through his publication with Alfred Rényi of the paper “On Random Graphs” in 1959.不知否是带有讽刺的意味，Erdös还是为新兴的跨学科网络奠定基础影响者之一，特别是1959年，他与“Alfred Rényi”合著的论文《随机图像》的发表。

2013年大学生英语竞赛(NECCS)B类初赛真题试卷(题后含答案及解析)

2013年大学生英语竞赛（NECCS）B类初赛真题试卷(题后含答案及解析)题型有：1. Listening Comperhension 2. Multiple Choice 3. Cloze 4. Reading Comperhension 5. Translation 6. IQ Test 7. Writing 8. Error CorrectionPart I Listening ComperhensionSection A听力原文：W: Sue’s ideas for her research project sound great, don’t you agree? M: I think they’re somewhat overambitious.Q: What does the man imply?1．What does the man imply?A．He’s heard about Sue’s great ideas.B．He finds some of Sue’s ideas acceptable.C．He thinks Sue’s ideas are impractical.正确答案：C解析：录音中女士对男士说“Sue对研究项目提出的想法很好，你认为呢”，男士回答道“我认为，这些想法都过于宏大”。

由此可知男士认为Sue的想法不现实，所以选C。

听力原文：M: We need to replace the glass in that picture frame before we can hang these pictures in the dormitory lobby. W: We can go to the framing shop and have it done now. Q: What are the speakers talking about?2．What are the speakers talking about?A．Hanging a picture.B．Framing a painting.C．Buying new glasses.正确答案：B解析：录音中男士提到他们需要把相框里的玻璃替换掉，才能把这些图画挂在宿舍大厅里。

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。

2013美国数学建B题,模水资源利用论文

承诺书我们仔细阅读了中国大学生数学建模竞赛的竞赛规则.我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。

我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。

如有违反竞赛规则的行为，我们将受到严肃处理。

我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。

我们参赛选择的题号是（从A/B/C/D中选择一项填写）： B我们的参赛报名号为（如果赛区设置报名号的话）：所属学校（请填写完整的全名）河南理工大学参赛队员(打印并签名) 1.2.3.指导教师或指导教师组负责人(打印并签名)：日期： 2013 年 07 月 29 日赛区评阅编号（由赛区组委会评阅前进行编号）：编号专用页赛区评阅编号（由赛区组委会评阅前进行编号）：赛区评阅记录（可供赛区评阅时使用）：评阅人评分备注全国统一编号（由赛区组委会送交全国前编号）：全国评阅编号（由全国组委会评阅前进行编号）：新能源ne-37与pw2u 路线铺设摘要本文通过最小生成树方法、最优化算法、网络规划方法等解决了关于新能源ne-37与pw2u 路线铺设问题。

对于问题一，首先将所给的交通图抽象成一张无向图，以各管道在各边铺设的长度为权值赋给各边。

然后我们运用了两种方法最小生成树算法和Dijkstra 算法求出连接各能源消耗单位之间的最短路径，滤去无用数据，找出我们所需要的满足每个单位至少有一点经过，且尽可能短的路径，其结果分别为24.3公里和23.6公里。

比较后发现两种方法结果相近，都能满足所得结果即为问题1所要求的最优公路交通网数学模型。

2013全国大学生英语竞赛B类决赛答案

2013National English Contestfor College Students(Level B-Final)参考答案及评分标准Part I.Listening Comprehension（30points）1—5CBACA6—10BBACC11—15ABACC16—20ACABB21.significant geopolitical event22.the economic reforms23.10%/ten percent24.Industrial production25.overtake the US26.rural areas27.the backbone28.foreign investment/outside investment29.foreign companies30.skills and trainingPart II.Multiple-choiceSection A(10points)31—35BDAAC36—40CBCADSection B(5points)41—45BDABCPart III.Cloze(10points)46.disappeared47.recorded48.extermination49.forests50.environment 51.purposes52.agricultural53.domestication54.but55.adapt/adjustPart IV.Reading comprehension(40points)Section A(10points)56.B57.B58.global climate change59.deform and move60.electricitySection B(10points)61.For his beliefs./Not believing in the recognizes gods and for corrupting young people.62.The pursuit of truth.63.The recognized gods.64.To encourage independent thinking.65.To show his recognition of the legal system./He is a firm believer in law.Section C(10points)66.Obesity67.lose weight68.putting on weight69.lead to death70.eat sensibly1--Section D(10points)71.N72.Y73.Y74.作为团队的一部分在特定的地点和特定的时间内为同一个目标而努力，工作为我们提供了个人难以加于自己的构架和目标。

2013美赛翻译

当用方形的平底锅烤饼时，热量会集中在四角，食物就在四角（甚至还有边缘）烤焦了。

在一个圆形的平底锅热量会均匀分布在整个外缘，食物就不会被边缘烤焦。

但是，因为大多数烤箱是矩形的，使用圆形的平底锅不那么有效率。

建立一个模型来表现热量在不同形状的平底锅的外缘的分布——包括从矩形到圆形以及中间的形状。

试构建一个模型来显示通过不同锅底的外沿热量的分布情况：方形到圆形极其两者之间的其他形状。

假定：
1. 方形烤箱宽长比为W/L；
2. 所有参考锅的面积必须为A；
3. 最初烤箱的两个支架均衡放置。

构建一个模型用于在如下情境下筛选最佳锅型：
1. 适合该烤炉(N)的最大锅型数；
2. 最大化均匀热度分布(H)的锅型；
3. 最优化条件(1)和(2)，各自占有比率为p 和(1- p)用以描述W/L与p的差异性。

除了提供标准的MCM格式解答之外，为布朗尼美食杂志提供一份1-2页的广告宣传，你需要突出你的设计和结果。