正确写作美国大学生数学建模竞赛论文
美国大学生数学建模竞赛优秀论文
For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number7018Problem ChosencFor office use onlyF1________________F2________________F3________________F4________________ SummaryThe article is aimed to research the potential impact of the marine garbage debris on marine ecosystem and human beings，and how we can deal with the substantial problems caused by the aggregation of marine wastes.In task one，we give a definition of the potential long-term and short-term impact of marine plastic garbage. Regard the toxin concentration effect caused by marine garbage as long-term impact and to track and monitor it. We etablish the composite indicator model on density of plastic toxin，and the content of toxin absorbed by plastic fragment in the ocean to express the impact of marine garbage on ecosystem. Take Japan sea as example to examine our model.In ask two, we designe an algorithm, using the density value of marine plastic of each year in discrete measure point given by reference，and we plot plastic density of the whole area in varies locations. Based on the changes in marine plastic density in different years， we determine generally that the center of the plastic vortex is East—West140°W—150°W, South—North30°N—40°N. According to our algorithm, we can monitor a sea area reasonably only by regular observation of part of the specified measuring pointIn task three，we classify the plastic into three types，which is surface layer plastic，deep layer plastic and interlayer between the two. Then we analysis the the degradation mechanism of plastic in each layer. Finally，we get the reason why those plastic fragments come to a similar size.In task four， we classify the source of the marine plastic into three types，the land accounting for 80%，fishing gears accounting for 10%，boating accounting for 10%，and estimate the optimization model according to the duel-target principle of emissions reduction and management. Finally, we arrive at a more reasonable optimization strategy.In task five，we first analyze the mechanism of the formation of the Pacific ocean trash vortex， and thus conclude that the marine garbage swirl will also emerge in south Pacific，south Atlantic and the India ocean. According to the Concentration of diffusion theory, we establish the differential prediction model of the future marine garbage density，and predict the density of the garbage in south Atlantic ocean. Then we get the stable density in eight measuring point .In task six, we get the results by the data of the annual national consumption ofpolypropylene plastic packaging and the data fitting method, and predict the environmental benefit generated by the prohibition of polypropylene take-away food packaging in the next decade. By means of this model and our prediction，each nation will reduce releasing 1.31 million tons of plastic garbage in next decade.Finally, we submit a report to expediction leader，summarize our work and make some feasible suggestions to the policy- makers.Task 1:Definition:●Potential short-term effects of the plastic: the hazardeffects will be shown in the short term.●Potential long-term effects of the plastic: thepotential effects, of which hazards are great, willappear after a long time.The short- and long-term effects of the plastic on the ocean environment:In our definition, the short-term and long-term effects of the plastic on the ocean environment are as follows.Short-term effects:1）The plastic is eaten by marine animals or birds.2） Animals are wrapped by plastics, such as fishing nets, which hurt or even kill them.3）Deaden the way of the passing vessels.Long-term effects:1）Enrichment of toxins through the food chain: the waste plastic in the ocean has no natural degradation in theshort-term, which will first be broken down into tinyfragments through the role of light, waves,micro-organisms, while the molecular structure has notchanged. These "plastic sands", easy to be eaten byplankton, fish and other, are Seemingly very similar tomarine life’s food,causing the enrichment and delivery of toxins.2）Accelerate the greenhouse effect: after a long-term accumulation and pollution of plastics, the waterbecame turbid, which will seriously affect the marineplants (such as phytoplankton and algae) inphotosynthesis. A large number of plankton’s deathswould also lower the ability of the ocean to absorbcarbon dioxide, intensifying the greenhouse effect tosome extent.To monitor the impact of plastic rubbish on the marine ecosystem:According to the relevant literature, we know that plastic resin pellets accumulate toxic chemicals , such as PCBs、DDE , and nonylphenols , and may serve as a transport medium and soure of toxins to marine organisms that ingest them[]2. As it is difficult for the plastic garbage in the ocean to complete degradation in the short term, the plastic resin pellets in the water will increase over time and thus absorb more toxins, resulting in the enrichment of toxins and causing serious impact on the marine ecosystem.Therefore, we track the monitoring of the concentration of PCBs, DDE, and nonylphenols containing in the plastic resin pellets in the sea water, as an indicator to compare the extent of pollution in different regions of the sea, thus reflecting the impact of plastic rubbish on ecosystem.To establish pollution index evaluation model: For purposes of comparison, we unify the concentration indexes of PCBs, DDE, and nonylphenols in a comprehensive index.Preparations:1）Data Standardization2）Determination of the index weightBecause Japan has done researches on the contents of PCBs,DDE, and nonylphenols in the plastic resin pellets, we illustrate the survey conducted in Japanese waters by the University of Tokyo between 1997 and 1998.To standardize the concentration indexes of PCBs, DDE,and nonylphenols. We assume Kasai Sesside Park, KeihinCanal, Kugenuma Beach, Shioda Beach in the survey arethe first, second, third, fourth region; PCBs, DDE, andnonylphenols are the first, second, third indicators.Then to establish the standardized model:j j jij ij V V V V V min max min --= （1,2,3,4;1,2,3i j ==）wherej V max is the maximum of the measurement of j indicator in the four regions.j V min is the minimum of the measurement of j indicatorstandardized value of j indicator in i region.According to the literature [2], Japanese observationaldata is shown in Table 1.Table 1. PCBs, DDE, and, nonylphenols Contents in Marine PolypropyleneTable 1 Using the established standardized model to standardize, we have Table 2.In Table 2，the three indicators of Shioda Beach area are all 0, because the contents of PCBs, DDE, and nonylphenols in Polypropylene Plastic Resin Pellets in this area are the least, while 0 only relatively represents the smallest. Similarly, 1 indicates that in some area the value of a indicator is the largest.To determine the index weight of PCBs, DDE, and nonylphenolsWe use Analytic Hierarchy Process (AHP) to determine the weight of the three indicators in the general pollution indicator. AHP is an effective method which transforms semi-qualitative and semi-quantitative problems into quantitative calculation. It uses ideas of analysis and synthesis in decision-making, ideally suited for multi-index comprehensive evaluation.Hierarchy are shown in figure 1.Fig.1 Hierarchy of index factorsThen we determine the weight of each concentrationindicator in the generall pollution indicator, and the process are described as follows:To analyze the role of each concentration indicator, we haveestablished a matrix P to study the relative proportion.⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=111323123211312P P P P P P P Where mn P represents the relative importance of theconcentration indicators m B and n B . Usually we use 1，2，…，9 and their reciprocals to represent different importance. The greater the number is, the more important it is. Similarly, the relative importance of m B and n B is mn P /1（3,2,1,=n m ）.Suppose the maximum eigenvalue of P is m ax λ, then theconsistency index is1max --=n nCI λThe average consistency index is RI , then the consistencyratio isRICI CR = For the matrix P of 3≥n , if 1.0<CR the consistency isthougt to be better, of which eigenvector can be used as the weight vector.We get the comparison matrix accoding to the harmful levelsof PCBs, DDE, and nonylphenols and the requirments ofEPA on the maximum concentration of the three toxins inseawater as follows:⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=165416131431P We get the maximum eigenvalue of P by MATLAB calculation0012.3max =λand the corresponding eigenvector of it is()2393.02975.09243.0，，=W1.0042.012.1047.0<===RI CI CR Therefore,we determine the degree of inconsistency formatrix P within the permissible range. With the eigenvectors of p as weights vector, we get thefinal weight vector by normalization ()1638.02036.06326.0'，，=W . Defining the overall target of pollution for the No i oceanis i Q , among other things the standardized value of threeindicators for the No i ocean is ()321,,i i i i V V V V = and the weightvector is 'W ,Then we form the model for the overall target of marine pollution assessment, （3,2,1=i ）By the model above, we obtained the Value of the totalpollution index for four regions in Japanese ocean in Table 3T B W Q '=In Table3, the value of the total pollution index is the hightest that means the concentration of toxins in Polypropylene Plastic Resin Pellets is the hightest, whereas the value of the total pollution index in Shioda Beach is the lowest(we point up 0 is only a relative value that’s not in the name of free of plastics pollution)Getting through the assessment method above, we can monitor the concentration of PCBs, DDE and nonylphenols in the plastic debris for the sake of reflecting the influence to ocean ecosystem.The highter the the concentration of toxins,the bigger influence of the marine organism which lead to the inrichment of food chain is more and more dramatic.Above all, the variation of toxins’ concentration simultaneously reflects the distribution and time-varying of marine litter. We can predict the future development of marine litter by regularly monitoring the content of these substances, to provide data for the sea expedition of the detection of marine litter and reference for government departments to make the policies for ocean governance.Task 2:In the North Pacific, the clockwise flow formed a never-ending maelstrom which rotates the plastic garbage. Over the years, the subtropical eddy current in North Pacific gathered together the garbage from the coast or the fleet, entrapped them in the whirlpool, and brought them to the center under the action of the centripetal force, forming an area of 3.43 million square kilometers (more than one-third of Europe) .As time goes by, the garbage in the whirlpool has the trend of increasing year by year in terms of breadth, density, and distribution. In order to clearly describe the variability of the increases over time and space, according to “Count Densities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999—2008”, we analyze the data, exclude them with a great dispersion, and retain them with concentrated distribution, while the longitude values of the garbage locations in sampled regions of years serve as the x-coordinate value of a three-dimensional coordinates, latitude values as the y-coordinate value, the Plastic Count per cubic Meter of water of the position as the z-coordinate value. Further, we establish an irregular grid in the yx plane according to obtained data, and draw a grid line through all the data points. Using the inverse distance squared method with a factor, which can not only estimate the Plastic Count per cubic Meter of water of any position, but also calculate the trends of the Plastic Counts per cubic Meter of water between two original data points, we can obtain the unknown grid points approximately. When the data of all the irregular grid points are known (or approximately known, or obtained from the original data), we can draw the three-dimensional image with the Matlab software, which can fully reflect the variability of the increases in the garbage density over time and space.Preparations:First, to determine the coordinates of each year’s sampled garbage.The distribution range of garbage is about the East - West 120W-170W, South - North 18N-41N shown in the “Count Densities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”, we divide a square in the picture into 100 grids in Figure (1) as follows:According to the position of the grid where the measuring point’s center is, we can identify the latitude and longitude for each point, which respectively serve as the x- and y- coordinate value of the three-dimensional coordinates.To determine the Plastic Count per cubic Meter of water. As the “Plastic Count per cubic Meter of water” provided by “Count Densities of P lastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”are 5 density interval, to identify the exact values of the garbage density of one year’s different measuring points, we assume that the density is a random variable which obeys uniform distribution in each interval.Uniform distribution can be described as below:()⎪⎩⎪⎨⎧-=01a b x f ()others b a x ,∈We use the uniform function in Matlab to generatecontinuous uniformly distributed random numbers in each interval, which approximately serve as the exact values of the garbage density andz-coordinate values of the three-dimensional coordinates of the year’s measuring points.Assumptions(1)The data we get is accurate and reasonable.(2)Plastic Count per cubic Meter of waterIn the oceanarea isa continuous change.(3)Density of the plastic in the gyre is a variable by region.Density of the plastic in the gyre and its surrounding area is interdependent , However, this dependence decreases with increasing distance . For our discussion issue, Each data point influences the point of each unknown around and the point of each unknown around is influenced by a given data point. The nearer a given data point from the unknown point, the larger the role.Establishing the modelFor the method described by the previous,we serve the distributions of garbage density in the “Count Pensities of Plastic Debris from Ocean Surface Samples North Pacific Gyre 1999--2008”as coordinates ()z y,, As Table 1:x,Through analysis and comparison, We excluded a number of data which has very large dispersion and retained the data that is under the more concentrated the distribution which, can be seen on Table 2.In this way, this is conducive for us to get more accurate density distribution map.Then we have a segmentation that is according to the arrangement of the composition of X direction and Y direction from small to large by using x co-ordinate value and y co-ordinate value of known data points n, in order to form a non-equidistant Segmentation which has n nodes. For the Segmentation we get above,we only know the density of the plastic known n nodes, therefore, we must find other density of the plastic garbage of n nodes.We only do the sampling survey of garbage density of the north pacificvortex,so only understand logically each known data point has a certain extent effect on the unknown node and the close-known points of density of the plastic garbage has high-impact than distant known point.In this respect,we use the weighted average format, that means using the adverse which with distance squared to express more important effects in close known points. There're two known points Q1 and Q2 in a line ,that is to say we have already known the plastic litter density in Q1 and Q2, then speculate the plastic litter density's affects between Q1、Q2 and the point G which in the connection of Q1 and Q2. It can be shown by a weighted average algorithm22212221111121GQ GQ GQ Z GQ Z Z Q Q G +*+*=in this formula GQ expresses the distance between the pointG and Q.We know that only use a weighted average close to the unknown point can not reflect the trend of the known points, we assume that any two given point of plastic garbage between the changes in the density of plastic impact the plastic garbage density of the unknown point and reflecting the density of plastic garbage changes in linear trend. So in the weighted average formula what is in order to presume an unknown point of plastic garbage density, we introduce the trend items. And because the greater impact at close range point, and thus the density of plastic wastes trends close points stronger. For the one-dimensional case, the calculation formula G Z in the previous example modify in the following format:2212122212212122211111112121Q Q GQ GQ GQ Q Q GQ Z GQ Z GQ Z Z Q Q Q Q G ++++*+*+*=Among them, 21Q Q known as the separation distance of the known point, 21Q Q Z is the density of plastic garbage which is the plastic waste density of 1Q and 2Q for the linear trend of point G . For the two-dimensional area, point G is not on the line 21Q Q , so we make a vertical from the point G and cross the line connect the point 1Q and 2Q , and get point P , the impact of point P to 1Q and 2Q just like one-dimensional, and the one-dimensional closer of G to P , the distant of G to P become farther, the smaller of the impact, so the weighting factor should also reflect the GP in inversely proportional to a certain way, then we adopt following format:221212222122121222211111112121Q Q GQ GP GQ GQ Q Q GQ GP Z GQ Z GQ Z Z P Q Q Q Q G ++++++*+*+*=Taken together, we speculated following roles:(1) Each known point data are influence the density of plastic garbage of each unknown point in the inversely proportional to the square of the distance;(2) the change of density of plastic garbage between any two known points data, for each unknown point are affected, and the influence to each particular point of their plastic garbage diffuse the straight line along the two known particular point; (3) the change of the density of plastic garbage between any two known data points impact a specific unknown points of the density of plastic litter depends on the three distances: a. the vertical distance to a straight line which is a specific point link to a known point;b. the distance between the latest known point to a specific unknown point;c. the separation distance between two known data points.If we mark 1Q ，2Q ，…，N Q as the location of known data points,G as an unknown node, ijG P is the intersection of the connection of i Q ，j Q and the vertical line from G to i Q ，j Q()G Q Q Z j i ,,is the density trend of i Q ，j Q in the of plasticgarbage points and prescribe ()G Q Q Z j i ,,is the testing point i Q ’ s density of plastic garbage ,so there are calculation formula:()()∑∑∑∑==-==++++*=Ni N ij ji i ijGji i ijG N i Nj j i G Q Q GQ GPQ Q GQ GP G Q Q Z Z 11222222111,,Here we plug each year’s observational data in schedule 1 into our model, and draw the three-dimensional images of the spatial distribution of the marine garbage ’s density with Matlab in Figure (2) as follows:199920002002200520062007－2008(1)It’s observed and analyzed that, from 1999 to 2008, the density of plastic garbage is increasing year by year and significantly in the region of East – West 140W-150W, south - north 30N-40N. Therefore, we can make sure that this region is probably the center of the marine litter whirlpool. Gathering process should be such that the dispersed garbage floating in the ocean move with the ocean currents and gradually close to the whirlpool region. At the beginning, the area close to the vortex will have obviously increasable about plastic litter density, because of this centripetal they keeping move to the center of the vortex ,then with the time accumulates ,the garbage density in the center of the vortex become much bigger and bigger , at last it becomes the Pacific rubbish island we have seen today.It can be seen that through our algorithm, as long as the reference to be able to detect the density in an area which has a number of discrete measuring points,Through tracking these density changes ,we Will be able to value out all the waters of the density measurement through our models to determine,This will reduce the workload of the marine expedition team monitoring marine pollution significantly, and also saving costs .Task 3:The degradation mechanism of marine plasticsWe know that light, mechanical force, heat, oxygen, water, microbes, chemicals, etc. can result in the degradation of plastics . In mechanism ,Factors result in the degradation can be summarized as optical ，biological，and chemical。
2014年美国大学生数学建模竞赛A题论文综述
数学建模综述2014年美国大学生数学建模竞赛A题论文综述我们小组精读两篇14年美赛A题论文，选择了其中一篇来进行学习，总结。
1、问题分析The Keep-Right-Except-To-Pass Rule除非超车否则靠右行驶的交通规则问题：建立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的表现。
这条规则在提升车流量的方面是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替代品（包括完全没有这种规律）并加以分析。
在一些国家，汽车靠左形式是常态，探讨你的解决方案是否稍作修改即可适用，或者需要一些额外的需要。
最后，以上规则依赖于人的判断，如果相同规则的交通运输完全在智能系统的控制下，无论是部分网络还是嵌入使用的车辆的设计，在何种程度上会修改你前面的结果论文：基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。
首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆，我们建立一个跟随模型,和超车模型。
然后我们设计规则来模拟车辆的运动模型。
我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。
我们也设计一个道路的危险指数评价公式。
我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道（总共6车道)。
通过计算机和分析数据。
我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。
我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。
左手交通也进行了讨论。
根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。
该论文在一开始并没有作过多分析，而是一针见血的提出了自己对于这个问题的做法。
由于题目给出的背景只有一条交通规则，而且是题目很明确的提出让我们建立模型分析。
美国大学生数学建模论文及其翻译31552
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Best all time college coach Summary
In order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical Hierarchy Process. The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly ， Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the selecting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball com
美国大学生数学建模比赛的论文格式
ContentsⅠIntroduction (1)1.1Problem Background (1)1.2Previous Research (2)1.3Our Work (2)ⅡGeneral Assumptions (3)ⅢNotations and Symbol Description (3)3.1 Notations (4)3.2 Symbol Description (4)ⅣSpread of Ebola (5)4.1 Traditional Epidemic Model (5)4.1.1.The SEIR Model (5)4.1.2 (6)4.1.3 (6)4.2 Improved Model (7)4.2.1.The SEIHCR Model (8)4.2.2 (9)ⅤPharmaceutical Intervention (9)5.1 Total Quantity of the Medicine (10)5.1.1.Results from WHO Statistics (10)5.1.2.Results from SEIHCR Model (11)5.2 Delivery System (12)5.2.1.Locations of Delivery (13)5.2.2 (14)5.3 Speed of Manufacturing (15)ⅥOther Important Interventions (16)6.1 Safer Treatment of Corpses (17)6.2 Conclusion (18)ⅦControl and Eradication of Ebola (19)7.1 How Ebola Can Be Controlled (20)7.2 When Ebola Will Be Eradicated (21)ⅧSensitivity Analysis (22)8.1 Impact of Transmission Rate (23)8.2 Impact of the Incubation Priod (24)ⅨStrengths and Weaknesses (25)9.1 Strengths (26)9.2 Weaknesses (27)9.3 Future Work (28)Letter to the World Medical Association (30)References (31)ⅠIntroduction1.1.Promblem Background1.2.Previous Research1.3.Our WorkⅡGeneral Assumptions●●ⅢNotations and Symbol Description3.1. Notataions3.2. Symbol DescriptionSymbol DescriptionⅣSpread of Ebola4.1. Traditional Epidemic Model4.1.1. The SEIR Model4.1.2. Outbreak Data4.1.3. Reslts of the SEIR Model4.2. Improved Model4.2.1. The SEIHCR Model4.2.2. Choosing paametersⅤPharmaceutical Intervention 5.1. Total Quantity of the Medicine 5.1.1. Results from WHO Statistics5.2. Delivery System5.2.1. Locations of Delivery5.2.2. Amount of Delivery5.3. Speed of Manufacturong5.4. Medicine EfficacyⅥOther Important Interventions 6.1. Safer Treatment of Corpses6.2. ConclusionⅦControl and Eradication of Ebola 7.1. How Ebola Can Be Controlled7.2. When Ebola Will Be EradicatedⅧSensitivity Analysis8.1. Impact of Transmission Rate8.2. Impact of Incubation PeriodⅨStrengths and Weaknesses 9.1. Strengths●●●9.2. Weaknesses●●●9.3.Future WorkLetter to the World Medical AssociationTo whom it may concern,Best regards,Team #32150References ［1］［2］［3］［4］。
美国大学生数学建模大赛英文写作
多用名词群
如: data transmission systems; high precision instrument;
句式结构(Sentence Structure)
陈述句多 科学论文中,在描述实验、说明现象、明确 定义、表达定理、定律和原理时，多用陈 述句，很少使用疑问句，几乎不用感叹句 如：Gathering facts, confirming them,
多用复合词
如：self-design, cross-sectional, dust-free, water-proof, input-orientation, piece-wiselinear 利用缩略词 如：e.g., i.e., vs.（与…相对), ibid.(出处相同）， etc., cit.(在上述引文中), et al.(等人), viz.(即,就是), DEA (data envelopment analysis), OLS(Ordinary least-squares)
“Investigation on …”, “Observation on …”, “The Method of …”, “Some thought on…”, “A research on…”等冗余套语 。
4. 少用问题性标题 5. 避免名词与动名词混杂使用 如:标题是 “The Treatment of Heating and Eutechticum of Steel” 宜改为 “Heating and Eutechticuming of Steel” 6. 避免使用非标准化的缩略语 论文标题要 求简洁,但一般不使用缩略语 ,更不能使用 非标准化的缩略语 。
主题句= what 指出论文主要是什么内容 展开句= how 进一步阐明主题句的具体内 容，指出研究方法、分析过程及论证的要 点等。 结尾句= what 是全文作出的结论或补充交 代等，即得出何种结论、结果或其意义。 4. 内容完整 完整的内容主要包括四个方面: ①研究的目的和范围；② 研究的方法；③ 研究的结果；④ 作者对研究的主要结论等。
美国数学建模竞赛论文写作
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三、写作规范
4. 写简单的句子
差：The value of the parameter a, which was used in the previous section to determine the height of the building, can also be used to determine its width. 好：In the previous section, we use the value of the parameter a to determine the height of the building. We can also use a to determine the width of the building.
国际数学建模竞赛 论文写作
参 考 书 目
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说明：
※ 这不是灵丹妙药 ※ 这不是英语课程
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一、写作的重要性 二、论文结构 三、写作规范 四、英语用法 五、符号与图标 六、数学表达式和句子
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一、写作的重要性
1. 摘要是论文最重要的部分； 2. 写作是国际建模竞赛的难点.
差：We will now find the solutions of the following equation. 好：We will now solve the following equation.
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三、写作规范
8. 使用并列短语强调相似性
美国大学生数学建模竞赛MCM写作模板（各个部分）
美国⼤学⽣数学建模竞赛MCM写作模板（各个部分）摘要：第⼀段：写论⽂解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the ……problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goal is... that (minimizes the time )……….2．解决这个问题的伟⼤意义反⾯说明。
92年美国数学建模竞赛优秀论文介绍
由华盛顿大学三名学生(简称华队)完成的92年美国大学党建是竞赛B题的一篇优秀论文1．题目与背景题目：研究室紧急电力修复系统的修复计划背景：沿海地区由于经常受风暴袭击，电力公司必须有相应的修复系统。
过去电力公司(HECO)由于缺少优先排序受到媒体批评，故欲聘请顾问提出合理修复计划。
风暴修复申请报告如表所列。
(略)表上提供了报告时间(即申请提出时间)、申请单位类型、估计修复所需时间以及单位位置。
2．基本假设与条件公司对于修复工作，给出下述假设与条件：(1)有两个修复中心，其位置为(0,0)、(40,40)、修复区域为6565,5050-<<-<<；x y(2)道路系统良好，修理工只需在交接班时返回修理中心；(3)除了交通枢纽及医院需立即修理外，其余的修理工作必须在风暴过后(6：00以后)开始进行；(4)每个中心有三名熟练工人全天轮流值班，每人工作8小时，紧急修理时每个点有6名工人可启用，每个工人在一个工作日里可加班8小时，加班报酬为正常报酬的1.5倍。
此外命题者允许参赛者作必要的简化或假设。
除上述假设外华队又增加了一些假设，可概括为：(1)街道为东西---南北向，两点间路程公式为||||ab a b a b d x x y y =-++道路状况良好，均匀，路途时间只取决于距离。
车辆路途运行费用与工资相比可忽略不计。
(2) 每个正常班工资为$10/小时，加班费为$15/小时。
工人在未完成一项任务时不得移动地点，每个工人可以加班8小时，但已超过时不得开始新工作。
各工人联系充公，保证工作指派不合冲突。
(3) 同一作业不因指派多于1 人而加速。
所有工作人员均有相同的能力与效率。
(4) 车辆行驶速度规定为60哩/小时。
(5) 在未发生风暴前每点有1 人值班，风暴后每点有6人安排在3班上(午夜12点，早8点，下午4点)。
3． 对问题的分析华队认为问题的关键是将修复单位合理排序并合理指派工人。
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1、小节划分
以下是该论文的小节划分及标题： Summary
1 Restatement of the Problem
2 Assumptions 3 Justification of Our Approach
4 The Model
4.1 Dissatisfaction of a passenger needing a connection 4.2 Dissatisfaction of a passenger not needing a connection 4.3 Total dissatisfaction on an aircraft 5 Testing the Model 6 Results 7 Strengths and Weaknesses References
1、小节划分
例如，在1989年的MCM竞赛中，有一篇题为“How to Please Most of the People Most of the Time”的优胜论文， 便是一篇结构出众的范文。
这篇论文研究飞机起飞时的排队问题。因为机场跑道 通常只有一条或两条起飞跑道，所以在相近时间内起飞的 飞机通常需要排队等候，如果等候时间太长，中途需要转 机的乘客便有可能会耽误转机。所以需要找出最佳的调度 方案，使机内大多数乘客不会因为延迟到达目的地而不满。
例如，2010年MCM竞赛中有一道赛题，要求参赛小 组根据以往的作案地点预测连环犯罪的位置。
3.1）、假设条件和解释 解答这道赛题的重点是犯罪活动方式。在一篇题为 “Centroids, Clusters, and Crime: Anchoring the Geographic Profiles of Serial Criminals”的论文中，有一条假设是“罪犯 的活动不受限制”，但罪犯是在市区的活动，实际上会受 到街道的布局及街道两旁建筑物的限制。由于街道布局通 常类似于网格，所以参赛小组对这个假设做了如下解释： Criminal’s movement is unconstrained. Because of the difficulty of finding real-world distance data, we invoke the „Manhattan assumption‟: There are enough streets and sidewalks in a sufficiently grid-like pattern that movements along real-world movement routes is the same as „straight-line‟ movement in a space discretized into city blocks…
1、简史
Ben Fusaro曾经说过，“三名都很优秀的学生不一定 能组成最好的参赛小组；最好的参赛小组是由三名配合 默契的优秀队员组成。”
换句话说，在组间参赛小组时，应该挑选能够相互 配合并且取长补短的小组成员。
2、论文评审
MCM赛题不设标准答案，解答论文没有及格分数线， 也不打分。参赛论文将按评审标准划分等级。
摘要是论文最重要的部分！
2、论文评审
2）、评审阶段： （15—30分钟） 通过第一阶段评审后，参赛论文按题型分类，分别进 入第二阶段的评审。 第二阶段的评审又分成若干轮，通过评审的轮数越多， 论文的评定级别也将越高。
论文的写作必须结构严谨、条理清晰、 简单易读，同时将主要结果以最明显的方 式表达出来。
评审标准： 评委关心的是参赛小组的解题思路和建模过程，以及是否给出了清晰的描述， 并着重检查一下内容： 1）、是否给出了令人满意的赛题解读，以及对赛题中可能出现的模糊概念是 否给予了必要的澄清； 2）、是否明确列出了建模需要用到的所有前提条件及假设，对其合理性是否 给出了满意的解释或论证； 3）、是否通过对赛题的分析给出了建模的动机或论证了建模的合理性； 4）、是否设计出了能有效地解答赛题的模型； 5）、是否对模型给出了稳定性测试； 6）、是否讨论了模型的优缺点，并给出了清晰的结论； 7）、是否给出了符合要求的摘要。
1）、鉴别阶段： （10分钟）
所有论文在此阶段按其质量分别归入一下三类：第一类 是可以进入下一评审阶段的论文（略少于二分之一）；第二类 是满足竞赛要求，但不足以进入下一评审阶段的论文（这一类 就被定为合格论文）；第三类是不符合竞赛要求的论文（不合 格论文）。 由于在第一阶段中，评委只有10分钟左右的时间评审一 篇论文，因此评委常常只能通过阅读摘要来判断论文水平的高 低。
2）、应避免在小节中出现大段的文字叙述。重要的句子， 包括首次定义的概念，应该用黑体或斜体书写。（当然，黑体 或斜体过多，又会使论文看上去杂乱，影响阅读，因此在突出 重点的前提下应该尽可能少用。）
3）、重要的数学公式应另起新行单独列出； 4）、建模所用的假设条件以及所有可以列表方式表述的 内容，为了方便阅读，都应该用符号列表（或编号列表）的方 式逐条陈列出来，不要将它们淹没在段落里。 5）、图表也是很好的表现形式，在使用图表时要给图表 加上简单明确的文字说明，使读者很快知道图表所要表达的内 容。
没有全部完成解答的论文是可以被接受的，而且如果再某些 方面有创意，仍然有可能获得较好的评审结果。
2、论文评审
等级划分：
Outstanding Winner， Finalist， Meritorious， Honorable Mentions， 特级论文（0.5﹪） 特级提名论文（0.5﹪） 甲级论文（10﹪—15﹪） 乙级论文（25-30﹪）
3、写作的重要性
论文的写作应尽早开始。根据以往的经验，许 多参赛小组往往低估了论文写作所需的时间，不能 及时写出条理清晰的论文。因此，参赛小组可以考 虑在竞赛开始后的第二天开始写作，并约定一个时 间结束手头的建模工作，以便全力以赴写好参赛论 文。
第二部分 论文结构
1、小节划分
论文应该按内容划分成小节和子小节，并冠以恰当的标 题，使评委无需阅读细节就能把握论文的主线。根据论文的 评审标准，MCM竞赛委员会建议参赛小组按以下结构将论文 分节： 重述并澄清赛题。 列出建模所用的所有前提条件及假设，并给出清晰的解 释。 分析赛题，给出建模动机或论证建模的合理性。 模型设计。 讨论如何检验模型，包括误差分析和稳定性测试（如对 条件、敏感度等因素进行分析和测试）。 讨论模型的优缺点。 书写论文摘要。摘要必须按要求写在特定的摘要页上， 长度不超过一页，提交时作为参赛论文的首页。
2、写好引言（问题重述）
例如，在1988年MCM竞赛中，有一道赛题要求参赛 小组在已知船只当前位置的前提下，设计一个搜索方法定 位其驶离后的位置，位置要求“精确到2°以内”。 在题为“Locating a Drug Runner: Miami Vice Style”的引 言中这样写道：
We interpret the error of ±2°as a normal distribution , … with standard deviation of 1°.
1、简史
1985年举办的第一届MCM竞赛，只有美国的158个 小组参赛（最终只有90个参赛小组提交了解答论文）。 在国际数学界的支持下，2010年共有2254个小组参赛 （美国358个）；2013年有6593个参赛小组（MCM 5636个队，ICM 957个队） 赛题分为两类，一类涉及连续数学，称为A题；另 一类涉及离散数学，称为B题。 COMAP（美国数学及应用联合会）从2000年开始 增设立交叉学科的建模竞赛，称为ICM。ICM竞赛每年 只出一道赛题，称为C题，涉及离散数学、连续数学或 者二者都涉及。
正确写作美国大学生数 学建模竞赛论文
第一部分 简介
1、简史
普特南数学竞赛始于1938年，学生个人参赛，独立解答 赛题。赛题通常是比较深的纯数学问题，满分120分。大约 一半的学生只能拿到1分或2分，甚至不少学生只能得零分。 美国数学建模竞赛的创始人Ben Fusaro对普特南竞赛缺 乏实用性，且难度太大导致学生参赛热情不高而深感忧虑。 于20世纪80年代提出设立一种新的竞赛机制，鼓励学生以 小组的形式参赛，共同解决具有实际应用背景的数学问题。 他的设想是：参赛小组在一天内解答两个实用背景的建模 问题，一个用离散数学的方法，一个用连续数学的方法。
Successfully Participation ，
Unsuccessfully Participation ，
合格论文（60﹪）
不合格论文
2、论文评审
评审流程：
论文评审的方式是盲审。所有参赛论文均使用唯一给定的 编号统一识别，这个编号称为控制编号。论文的作者姓名及其 所在大学的名称均不得在论文中出现。 评审分为两个阶段：
1、小节划分
摘要 1 问题重述
2 假设条件
3 建模方法的合理性论证 4 模型设计
4.1 需要转机乘客的不满意程度
4.2 无需转机乘客的不满意程度 4.3 所有乘客的不满意程度 5 模型测试 6 结论 7 模型的优点与弱点 参考文献
1、小节划分
1）、不是所有的论文都必须与MCM建议的小节划分，但 参赛小组还是应该尽可能的按照所建议的内容划分小节。简单 明了、条理清晰的小节划分有助于评委迅速掌握论文的要点。
2、写好引言（问题重述）
引言应该包括以下内容：对赛题的解读、对现有研究成 果的综述与评论、以及对解题思路和主要方法的简要介绍。 参赛小组应通过引言向评委表明，参赛小组对赛题做了 认真仔细的思考与研究。为了写好引言，参赛小组应该在解 题时就开始思考如何写引言，并在解题过程中反复修改，直 到满意为止。 引言的第一句话是全文最重要的句子，用于激发读者 阅读论文的兴趣。同理引言的第一段也是全文最重要的一个 段落，应该写的浅显易懂，尽量少用或者不用数学表达式， 使得读者对所要解决的数学问题不甚了解，也能看懂第一段 话的内容而产生继续阅读的兴趣。所以，引言的第一句及第 一段要经过反复推敲和修改，不可掉以轻心。