正确写作美国大学生数学建模竞赛论文

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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

Team#31552
Page 1 of 25
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

所需结论由此模型产生
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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。

2020年美赛a题m奖范文

2020年美赛a题m奖范文2020年美国大学生数学建模竞赛（MCM/ICM）已经落下帷幕，各奖项结果也逐一揭晓。

在这其中，A题作为赛事的经典题型，每年都吸引了大量参赛者。

本文将为您呈现一篇获得2020年美赛A题M奖的范文，供大家参考学习。

一、问题分析2020年美赛A题主要围绕一个现实问题展开，要求参赛者运用数学建模方法进行求解。

在分析问题时，我们首先要明确以下几点：1.了解问题的背景和实际意义，以便更好地理解问题的本质。

2.确定问题的关键参数和变量，为建模提供依据。

3.分析问题中的约束条件和目标函数，为后续求解奠定基础。

二、模型建立在明确问题后，我们根据实际情况，选择合适的数学方法建立模型。

以下是本篇范文中采用的主要模型：1.确定变量和参数：根据问题，我们选取了以下变量和参数进行建模。

2.建立关系式：通过分析问题，我们找到了变量和参数之间的关系，并建立了相应的数学表达式。

3.构建目标函数：根据问题中的要求，我们确定了目标函数，并对其进行优化。

三、模型求解在建立模型后，我们需要运用数学软件或编程语言对模型进行求解。

以下是本篇范文中采用的方法：1.选择合适的算法：根据模型的类型和特点，我们选择了合适的算法进行求解。

2.编写程序：利用编程语言，如MATLAB、Python等，编写求解程序。

3.调整参数：在求解过程中，不断调整参数，以获得更优的解。

四、结果分析通过求解，我们得到了以下结果：1.结果展示：将求解结果以图表或文字形式展示，便于分析。

2.结果分析：对求解结果进行分析，探讨其优缺点和适用范围。

3.对比分析：与其他方法或模型进行对比，验证本方法的优越性。

五、结论本篇范文通过以上步骤，成功解决了2020年美赛A题。

以下是我们的主要结论：1.模型有效性：所建立的模型具有较高的准确性和可靠性，能够较好地解决实际问题。

2.方法优越性：采用的方法具有较高的计算效率和稳定性，适用于类似问题的求解。

3.实际意义：本模型为解决实际问题提供了有力支持，具有较高的应用价值。

怎样写作数学建模竞赛论文

怎样写作数学建模竞赛论文在讲怎样写作数学建模竞赛论文之前先对全国大学生数学建模竞赛作个简要介绍,了解数学建模的特点，这对我们的问题还是有帮助的。

1. 竞赛的由来及现状数学建模竞赛源于美国，为了培养应用型数学人才，从1983年起，美国一些有识之士开始探讨组织一项应用数学方面的竞赛。

经过论证、争论、争取资助的过程，终于在1985年开始了美国的第一届大学生数学建模竞赛，简称MCM(1987年以前的全称是Mathematical Competition in Modeling,1987年改为Mathematical Contest in Modeling,其缩写均为MCM). 竞赛由美国工业与应用数学学会和美国运筹学会联合主办。

从1985年起每年举行一届，在每年的二月下旬或三月初的某个星期五到星期日举行。

这项竞赛的宗旨是鼓励大学生运用所学的知识去参与解决实际问题的全过程。

这些实际问题并不限于某个特定领域，可以涉及非常广泛的、并不固定的范围。

这样来促进应用人才的培养。

比赛的形式是：真正的团体赛，每个参赛队由三人组成，在规定的三天时间内共同完成一份答卷，每个参赛队有一个指导老师，在比赛前负责培训并接受考题，将考题在规定的时间发给学生，然后由学生自行做题，教师不得参赛。

每次的考题只有两个题，都是来自实际的问题或有强烈实际背景的问题，没有固定的范围，可能涉及各个非常不同的学科、领域。

每个参赛队从这两道题中任意选做一道题。

参赛队员可以相互讨论，可以查阅资料，可以使用计算机和计算机软件。

一言以蔽之，可以使用任何非生命的资源，但不允许三人以外的其他人(包括指导老师)帮助做题。

参赛队的答卷应是一篇完整的论文，包括对所选问题的重新阐述、对问题的条件和假设的阐明和必要补充、甚至修改、对为什么要用所述模型的分析、模型的设计、对模型的测试检验的讨论、模型的优缺点等，还要有一个一般不超过一页的论文摘要。

比赛的结果：专家们在评卷时并不对论文给出分数，也不采用“通过”、“失败”这种记分方式,而是将论文分成儿个等级：特等奖(Qutstanding)、一等奖(Meritorious)、二等奖(Honorable Mention)、成功参赛奖(Successful Participation)。

建模美赛获奖范文

建模美赛获奖范文标题：《探索与创新：建模美赛获奖作品范文解析》建模美赛（MCM/ICM）是全球大学生数学建模竞赛的盛事，每年都吸引了众多优秀的学生参与。

在这个舞台上，获奖作品往往展现了卓越的数学建模能力、创新思维和问题解决技巧。

本文将解析一份获奖范文，带您领略建模美赛获奖作品的风采。

一、背景与问题阐述（此处详细描述范文所针对的问题背景、研究目的和意义，以及问题的具体阐述。

）二、模型建立与假设1.模型分类与选择：根据问题特点，范文选择了适当的模型进行研究和分析。

2.假设条件：明确列出建模过程中所做的主要假设，并解释其合理性。

三、模型求解与结果分析1.数据收集与处理：介绍范文中所用数据来源、处理方法及有效性验证。

2.模型求解：详细阐述模型的求解过程，包括算法选择、计算步骤等。

3.结果分析：对求解结果进行详细分析，包括图表展示、敏感性分析等。

四、模型优化与拓展1.模型优化：针对原模型存在的问题，范文提出了相应的优化方案。

2.拓展研究：对模型进行拓展，探讨其在其他领域的应用和推广价值。

五、结论与建议1.结论总结：概括范文的研究成果，强调其创新点和贡献。

2.实践意义：分析建模结果在实际问题中的应用价值和意义。

3.建议：针对问题解决，提出具体的建议和措施。

六、获奖亮点与启示1.创新思维：范文在模型选择、求解方法等方面展现出创新性。

2.严谨论证：文章结构清晰，逻辑严密，数据充分，论证有力。

3.团队合作：建模美赛强调团队协作，范文体现了成员间的紧密配合和分工合作。

总结：通过分析这份建模美赛获奖范文，我们可以学到如何从问题背景出发，建立合理的模型，进行严谨的求解和分析，以及如何优化和拓展模型。

同时，也要注重创新思维和团队合作，才能在建模美赛中脱颖而出。

美国大学生数学建模竞赛美赛--论文

Each team member must sign the statement below: (Failure to obtain signatures from each team member will result in disqualification of the entire team.)
2015 Mathematical Contest in Modeling (MCM/ICM) Control Sheet Please review this page before submitting your solution to ensure that all of the information is correct Do not make changes by hand to the information on this control sheet. If you need to change any of the information on this sheet, login via the Advisor Login link on the MCM web site, make the changes online, and print a new sheet. You may NOT photocopy this control sheet to give to a new team, nor may you assign any team a control number. Each team must have its own control number, obtained by registering via the MCM web site. Advisor Jinpeng Yu Name: Department: Control Engineering Institution: Qingdao University Address: 308 Ningxia Road,Shinan District,Qingdao,Shandong,China Qingdao, Shandong 266000 Phone: 18653250086 Fax: 053285953064 Email: zhanghaoran06@ Home Phone: 053285953064 The names of the team members will appear on your team's certificate exactly as they appear on this page, including all capitalization and punctuation, if any. Gender data is optional and will be used for statistical purposes only; it will not appear on the certificate. Team Member Haoran Zhang Yu Ma Guiying Dong Gender M M F Your team's control number is: 40906 (Place this control number on all pages of your solution paper and on any support material.) Problem Chosen: B

美国大学生数学建模大赛优秀论文一等奖摘要

SummaryChina is the biggest developing country. Whether water is sufficient or not will have a direct impact on the economic development of our country. China's water resources are unevenly distributed. Water resource will critically restrict the sustainable development of China if it can not be properly solved.First, we consider a greater number of Chinese cities so that China is divided into 6 areas. The first model is to predict through division and classification. We predict the total amount of available water resources and actual water usage for each area. And we conclude that risk of water shortage will exist in North China, Northwest China, East China, Northeast China, whereas Southwest China, South China region will be abundant in water resources in 2025.Secondly, we take four measures to solve water scarcity: cross-regional water transfer, desalination, storage, and recycling. The second model mainly uses the multi-objective planning strategy. For inter-regional water strategy, we have made reference to the the strategy of South-to-North Water Transfer[5]and other related strategies, and estimate that the lowest cost of laying the pipeline is about 33.14 billion yuan. The program can transport about 69.723 billion cubic meters water to the North China from the Southwest China region per year. South China to East China water transfer is about 31 billion cubic meters. In addition, we can also build desalination mechanism program in East China and Northeast China, and the program cost about 700 million and can provide 10 billion cubic meters a year.Finally, we enumerate the east China as an example to show model to improve. Other area also can use the same method for water resources management, and deployment. So all regions in the whole China can realize the water resources allocation.In a word, the strong theoretical basis and suitable assumption make our model estimable for further study of China's water resources. Combining this model with more information from the China Statistical Yearbook will maximize the accuracy of our model.。

【完整解析】美赛-数学建模-写作模版(各部分)

Summary：clearly describe your approach to the problem and,most prominently,your most important conclusions.●Restatement and clarification of the problem:State in your own words what you aregoing to do.●Explain assumptions and rationale（principle）/justification:Emphasize the assumptionsthat bear on the problem.Clearly list all variables used in your model.●Include your model design and justification for type model used or developed.●Describe model testing and sensitivity analysis,including error analysis,etc.●Discuss the strengths and weaknesses of your model or approach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.我们找到了在给定XX的情况下最佳的……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.XX需要具有B性能的C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.我们通过分析参数B确定A，并且检验了现实情况C例4:After mathematically analyzing the……problem,our modeling group would like to present our conclusions,strategies,(and recommendations)to the…….在数学分析B后，我们的模型组将呈现了我们的结论和建议We begin by considering only the rigid recoil effects of the bat–ball col-LisionOur main goal is to understand the sweet spot.A secondary goal is tounderstand the differences between the sweet spots of different bat types.Because the collision happens on such a short time-scale(around1ms),we treat the bat as a free body.That is to say,we are not concerned with the batter’s hands exerting force on the bat that may be transferred to the ball....Our paper is organized as follows....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。

美国大学生数学建模竞赛二等奖论文

The P roblem of R epeater C oordination SummaryThis paper mainly focuses on exploring an optimization scheme to serve all the users in a certain area with the least repeaters.The model is optimized better through changing the power of a repeater and distributing PL tones,frequency pairs ing symmetry principle of Graph Theory and maximum coverage principle,we get the most reasonable scheme.This scheme can help us solve the problem that where we should put the repeaters in general cases.It can be suitable for the problem of irrigation,the location of lights in a square and so on.We construct two mathematical models(a basic model and an improve model)to get the scheme based on the relationship between variables.In the basic model,we set a function model to solve the problem under a condition that assumed.There are two variables:‘p’(standing for the power of the signals that a repeater transmits)and‘μ’(standing for the density of users of the area)in the function model.Assume‘p’fixed in the basic one.And in this situation,we change the function model to a geometric one to solve this problem.Based on the basic model,considering the two variables in the improve model is more reasonable to most situations.Then the conclusion can be drawn through calculation and MATLAB programming.We analysis and discuss what we can do if we build repeaters in mountainous areas further.Finally,we discuss strengths and weaknesses of our models and make necessary recommendations.Key words:repeater maximum coverage density PL tones MATLABContents1.Introduction (3)2.The Description of the Problem (3)2.1What problems we are confronting (3)2.2What we do to solve these problems (3)3.Models (4)3.1Basic model (4)3.1.1Terms,Definitions,and Symbols (4)3.1.2Assumptions (4)3.1.3The Foundation of Model (4)3.1.4Solution and Result (5)3.1.5Analysis of the Result (8)3.1.6Strength and Weakness (8)3.1.7Some Improvement (9)3.2Improve Model (9)3.2.1Extra Symbols (10)Assumptions (10)3.2.2AdditionalAdditionalAssumptions3.2.3The Foundation of Model (10)3.2.4Solution and Result (10)3.2.5Analysis of the Result (13)3.2.6Strength and Weakness (14)4.Conclusions (14)4.1Conclusions of the problem (14)4.2Methods used in our models (14)4.3Application of our models (14)5.Future Work (14)6.References (17)7.Appendix (17)Ⅰ.IntroductionIn order to indicate the origin of the repeater coordination problem,the following background is worth mentioning.With the development of technology and society,communications technology has become much more important,more and more people are involved in this.In order to ensure the quality of the signals of communication,we need to build repeaters which pick up weak signals,amplify them,and retransmit them on a different frequency.But the price of a repeater is very high.And the unnecessary repeaters will cause not only the waste of money and resources,but also the difficulty of maintenance.So there comes a problem that how to reduce the number of unnecessary repeaters in a region.We try to explore an optimized model in this paper.Ⅱ.The Description of the Problem2.1What problems we are confrontingThe signals transmit in the way of line-of-sight as a result of reducing the loss of the energy. As a result of the obstacles they meet and the natural attenuation itself,the signals will become unavailable.So a repeater which just picks up weak signals,amplifies them,and retransmits them on a different frequency is needed.However,repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.In addition to geographical separation,the“continuous tone-coded squelch system”(CTCSS),sometimes nicknamed“private line”(PL),technology can be used to mitigate interference.This system associates to each repeater a separate PL tone that is transmitted by all users who wish to communicate through that repeater. The PL tone is like a kind of password.Then determine a user according to the so called password and the specific frequency,in other words a user corresponds a PL tone(password)and a specific frequency.Defects in line-of-sight propagation caused by mountainous areas can also influence the radius.2.2What we do to solve these problemsConsidering the problem we are confronting,the spectrum available is145to148MHz,the transmitter frequency in a repeater is either600kHz above or600kHz below the receiver frequency.That is only5users can communicate with others without interferences when there’s noPL.The situation will be much better once we have PL.However the number of users that a repeater can serve is limited.In addition,in a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.Taking the natural attenuation itself is reasonable.Now the most important is the radius that the signals transmit.Reducing the radius is a good way once there are more users.With MATLAB and the method of the coverage in Graph Theory,we solve this problem as follows in this paper.Ⅲ.Models3.1Basic model3.1.1Terms,Definitions,and Symbols3.1.2Assumptions●A user corresponds a PLz tone (password)and a specific frequency.●The users in the area are fixed and they are uniform distribution.●The area that a repeater covers is a regular hexagon.The repeater is in the center of the regular hexagon.●In a flat area ,the obstacles such as mountains ,buildings don’t need to be taken into account.We just take the natural attenuation itself into account.●The power of a repeater is fixed.3.1.3The Foundation of ModelAs the number of PLz tones (password)and frequencies is fixed,and a user corresponds a PLz tone (password)and a specific frequency,we can draw the conclusion that a repeater can serve the limited number of users.Thus it is clear that the number of repeaters we need relates to the density symboldescriptionLfsdfminrpμloss of transmission the distance of transmission operating frequency the number of repeaters that we need the power of the signals that a repeater transmits the density of users of the areaof users of the area.The radius of the area that a repeater covers is also related to the ratio of d and the radius of the circular area.And d is related to the power of a repeater.So we get the model of function()min ,r f p µ=If we ignore the density of users,we can get a Geometric model as follows:In a plane which is extended by regular hexagons whose side length are determined,we move a circle until it covers the least regular hexagons.3.1.4Solution and ResultCalculating the relationship between the radius of the circle and the side length of the regular hexagon.[]()()32.4420lg ()20lg Lfs dB d km f MHz =++In the above formula the unit of ’’is .Lfs dB The unit of ’’is .d Km The unit of ‘‘is .f MHz We can conclude that the loss of transmission of radio is decided by operating frequency and the distance of transmission.When or is as times as its former data,will increase f d 2[]Lfs .6dB Then we will solve the problem by using the formula mentioned above.We have already known the operating frequency is to .According to the 145MHz 148MHz actual situation and some authority material ,we assume a system whose transmit power is and receiver sensitivity is .Thus we can conclude that ()1010dBm mW +106.85dBm −=.Substituting and to the above formula,we can get the Lfs 106.85dBm −145MHz 148MHz average distance of transmission .()6.4d km =4mile We can learn the radius of the circle is 40mile .So we can conclude the relationship between the circle and the side length of regular hexagon isR=10d.1)The solution of the modelIn order to cover a certain plane with the least regular hexagons,we connect each regular hexagon as the honeycomb.We use A(standing for a figure)covers B(standing for another figure), only when As don’t overlap each other,the number of As we use is the smallest.Figure1According to the Principle of maximum flow of Graph Theory,the better of the symmetry ofthe honeycomb,the bigger area that it covers(Fig1).When the geometric centers of the circle andthe honeycomb which can extend are at one point,extend the honeycomb.Then we can get Fig2,Fig4:Figure2Fig3demos the evenly distribution of users.Figure4Now prove the circle covers the least regular hexagons.Look at Fig5.If we move the circle slightly as the picture,you can see three more regularhexagons are needed.Figure 52)ResultsThe average distance of transmission of the signals that a repeater transmit is 4miles.1000users can be satisfied with 37repeaters founded.3.1.5Analysis of the Result1)The largest number of users that a repeater can serveA user corresponds a PL and a specific frequency.There are 5wave bands and 54different PL tones available.If we call a code include a PL and a specific frequency,there are 54*5=270codes.However each code in two adjacent regular hexagons shouldn’t be the same in case of interfering with each other.In order to have more code available ,we can distribute every 3adjacent regular hexagons 90codes each.And that’s the most optimized,because once any of the three regular hexagons have more codes,it will interfere another one in other regular hexagon.2)Identify the rationality of the basic modelNow we considering the influence of the density of users,according to 1),90*37=3330>1000,so here the number of users have no influence on our model.Our model is rationality.3.1.6Strength and Weakness●Strength:In this paper,we use the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.It is much more intuitive once we change the function model to the geometric model.●Weakness:Since each hexagon get too close to another one.Once there are somebuildingsor terrain fluctuations between two repeaters,it can lead to the phenomenon that certain areas will have no signals.In addition,users are distributed evenly is not reasonable.The users are moving,for example some people may get a party.3.1.7Some ImprovementAs we all know,the absolute evenly distribution is not exist.So it is necessary to say something about the normal distribution model.The maximum accommodate number of a repeater is 5*54=270.As for the first model,it is impossible that 270users are communicating in a same repeater.Look at Fig 6.If there are N people in the area 1,the maximum number of the area 2to area 7is 3*(270-N).As 37*90=3330is much larger than 1000,our solution is still reasonable to this model.Figure 63.2Improve Model3.2.1Extra SymbolsSigns and definitions indicated above are still valid.Here are some extra signs and definitions.symboldescription Ra the radius of the circular flat area the side length of a regular hexagon3.2.2Additional AdditionalAssumptionsAssumptions ●The radius that of a repeater covers is adjustable here.●In some limited situations,curved shape is equal to straight line.●Assumptions concerning the anterior process are the same as the Basic Model3.2.3The Foundation of ModelThe same as the Basic Model except that:We only consider one variable(p)in the function model of the basic model ;In this model,we consider two varibles(p and μ)of the function model.3.2.4Solution and Result1)SolutionIf there are 10,000users,the number of regular hexagons that we need is at least ,thus according to the the Principle of maximum flow of Graph Theory,the 10000111.1190=result that we draw needed to be extended further.When the side length of the figure is equal to 7Figure 7regular hexagons,there are 127regular hexagons (Fig 7).Assuming the side length of a regular hexagon is ,then the area of a regular hexagon is a .The area of regular hexagons is equal to a circlewhose radiusis 22a =1000090R.Then according to the formula below:.221000090a R π=We can get.9.5858R a =Mapping with MATLAB as below (Fig 8):Figure 82）Improve the model appropriatelyEnlarge two part of the figure above,we can get two figures below (Fig 9and Fig 10):Figure 9AREAFigure 10Look at the figure above,approximatingAREA a rectangle,then obtaining its area to getthe number of users..The length of the rectangle is approximately equal to the side length of the regular hexagon ,athe width of the rectangle is ,thus the area of AREA is ,then R −*R a ⎛⎞−⎜⎟⎜⎟⎝⎠we can get the number of users in AREA is()，2**10000 2.06R a R π⎡⎤⎛⎞−⎢⎥⎜⎟⎢⎥⎝⎠=⎢⎥⎢⎥⎢⎥⎣⎦9.5858R a =As 2.06<<10,000,2.06can be ignored ,so there is no need to set up a repeater in.There are 6such areas(92,98,104,110,116,122)that can be ignored.At last,the number of repeaters we should set up is,1276121−=2)Get the side length of the regular hexagon of the improved modelThus we can getmile=km 40 4.1729.5858a == 1.6* 6.675a =3)Calculate the power of a repeaterAccording to the formula[]()()32.4420lg ()20lg Lfs dB d km f MHz =++We get32.4420lg 6.67520lg14592.156Los =++=32.4420lg 6.67520lg14892.334Los =++=So we get106.85-92.156=14.694106.85-92.334=14.516As the result in the basic model,we can get the conclusion the power of a repeater is from 14.694mW to 14.516mW.3.2.5Analysis of the ResultAs 10,000users are much more than 1000users,the distribution of the users is more close toevenly distribution.Thus the model is more reasonable than the basic one.More repeaters are built,the utilization of the outside regular hexagon are higher than the former one.3.2.6Strength and Weakness●Strength:The model is more reasonable than the basic one.●Weakness:Repeaters don’t cover all the area,some places may not receive signals.And thefoundation of this model is based on the evenly distribution of the users in the area,if the situation couldn’t be satisfied,the interference of signals will come out.Ⅳ.Conclusions4.1Conclusions of the problem●Generally speaking,the radius of the area that a repeater covers is4miles in our basic model.●Using the model of honeycomb-hexagon structure can maximize the use of resources,avoiding some unnecessary interference effectively.●The minimum number of repeaters necessary to accommodate1,000simultaneous users is37.The minimum number of repeaters necessary to accommodate10,000simultaneoususers is121.●A repeater's coverage radius relates to external environment such as the density of users andobstacles,and it is also determined by the power of the repeater.4.2Methods used in our models●Analysis the problem with MATLAB●the method of the coverage in Graph Theory4.3Application of our models●Choose the ideal address where we set repeater of the mobile phones.●How to irrigate reasonably in agriculture.●How to distribute the lights and the speakers in squares more reasonably.Ⅴ.Future WorkHow we will do if the area is mountainous?5.1The best position of a repeater is the top of the mountain.As the signals are line-of-sight transmission and reception.We must find a place where the signals can transmit from the repeater to users directly.So the top of the mountain is a good place.5.2In mountainous areas,we must increase the number of repeaters.There are three reasons for this problem.One reason is that there will be more obstacles in the mountainous areas. The signals will be attenuated much more quickly than they transmit in flat area.Another reason is that the signals are line-of-sight transmission and reception,we need more repeaters to satisfy this condition.Then look at Fig11and Fig12,and you will know the third reason.It can be clearly seen that hypotenuse is larger than right-angleFig11edge(R>r).Thus the radius will become smaller.In this case more repeaters are needed.Fig125.3In mountainous areas,people may mainly settle in the flat area,so the distribution of users isn’t uniform.5.4There are different altitudes in the mountainous areas.So in order to increase the rate of resources utilization,we can set up the repeaters in different altitudes.5.5However,if there are more repeaters,and some of them are on mountains,more money will be munication companies will need a lot of money to build them,repair them when they don’t work well and so on.As a result,the communication costs will be high.What’s worse,there are places where there are many mountains but few persons. Communication companies reluctant to build repeaters there.But unexpected things often happen in these places.When people are in trouble,they couldn’t communicate well with the outside.So in my opinion,the government should take some measures to solve this problem.5.6Another new method is described as follows(Fig13):since the repeater on high mountains can beFig13Seen easily by people,so the tower which used to transmit and receive signals can be shorter.That is to say,the tower on flat areas can be a little taller..Ⅵ.References[1]YU Fei,YANG Lv-xi,"Effective cooperative scheme based on relay selection",SoutheastUniversity,Nanjing,210096,China[2]YANG Ming,ZHAO Xiao-bo,DI Wei-guo,NAN Bing-xin,"Call Admission Control Policy based on Microcellular",College of Electical and Electronic Engineering,Shijiazhuang Railway Institute,Shijiazhuang Heibei050043,China[3]TIAN Zhisheng,"Analysis of Mechanism of CTCSS Modulation",Shenzhen HYT Co,Shenzhen,518057,China[4]SHANGGUAN Shi-qing,XIN Hao-ran,"Mathematical Modeling in Bass Station Site Selectionwith Lingo Software",China University of Mining And Technology SRES,Xuzhou;Shandong Finance Institute,Jinan Shandon,250014[5]Leif J.Harcke,Kenneth S.Dueker,and David B.Leeson,"Frequency Coordination in the AmateurRadio Emergency ServiceⅦ.AppendixWe use MATLAB to get these pictures,the code is as follows:1-clc;clear all;2-r=1;3-rc=0.7;4-figure;5-axis square6-hold on;7-A=pi/3*[0:6];8-aa=linspace(0,pi*2,80);9-plot(r*exp(i*A),'k','linewidth',2);10-g1=fill(real(r*exp(i*A)),imag(r*exp(i*A)),'k');11-set(g1,'FaceColor',[1,0.5,0])12-g2=fill(real(rc*exp(i*aa)),imag(rc*exp(i*aa)),'k');13-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode','x0r')14-text(0,0,'1','fontsize',10);15-Z=0;16-At=pi/6;17-RA=-pi/2;18-N=1;At=-pi/2-pi/3*[0:6];19-for k=1:2;20-Z=Z+sqrt(3)*r*exp(i*pi/6);21-for pp=1:6;22-for p=1:k;23-N=N+1;24-zp=Z+r*exp(i*A);25-zr=Z+rc*exp(i*aa);26-g1=fill(real(zp),imag(zp),'k');27-set(g1,'FaceColor',[1,0.5,0],'edgecolor',[1,0,0]);28-g2=fill(real(zr),imag(zr),'k');29-set(g2,'FaceColor',[1,0.5,0],'edgecolor',[1,0.5,0],'EraseMode',xor';30-text(real(Z),imag(Z),num2str(N),'fontsize',10);31-Z=Z+sqrt(3)*r*exp(i*At(pp));32-end33-end34-end35-ezplot('x^2+y^2=25',[-5,5]);%This is the circular flat area of radius40miles radius 36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)38-axis off;Then change number19”for k=1:2;”to“for k=1:3;”,then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:4;”,then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:1;”,and delete number 35“ezplot('x^2+y^2=25',[-5,5]);”then we get another picture:Change the original programme number19“for k=1:2;”to“for k=1:6;”,and change number 35“ezplot('x^2+y^2=25',[-5,5]);”to”ezplot('x^2+y^2=6*sqrt(3)*10000/360/pi',[-20,20]);”Change number36,37“36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)”To“xlim([-20,20]*r)ylim([-20.1,20.1]*r)”,then we getTeam#8921Page21of21Delete“36-xlim([-6,6]*r)37-ylim([-6.1,6.1]*r)”We get。

怎样写好数学建模竞赛论文

00:26:11
13
数学建模论文的一般结构
摘要问题重述模型假设符号说明问题分析模型建立模型求解模型检验
假设的合理性是评阅的一个重要指标，如何作假设？（1）从题目所给条件中作假设（2）从题目的要求中作假设注： 1、作假设要切合题意， 2、关键性假设不可缺， 3、不要罗列一大堆无用的假设。
00:26:11 10ቤተ መጻሕፍቲ ባይዱ
论文评卷标准
假设的合理性
表达清晰程度
建模的创造性
结果的正确性
11
00:26:11
数学建模论文的一般结构
摘要问题重述模型假设符号说明问题分析模型建立模型求解模型检验
模型评价、推广
参考文献、附录
摘要是整个论文核心思想的浓缩，读者通过阅读摘要了解论文的基本情况，决定是否阅读正文。简要论述本文所要解决的问题及意义，解决问摘要要求语言精炼、准确，介绍针对什么问题、题的思路与方法，主要结果（数值结果或结论），作了哪些重要假设、采用了什么方法、建立了什么模型，获得了什么结论，主要创新是什么。摘要要建模的创新之处与特色等。摘要欲想吸引评委的眼反映所作工作的闪光点。球，必须能表达全文的概貌、要点、特色，要回答题目要求的全部问题。以下五个内容不可缺少：问摘要用字准确，尽量达到少一字不行，多一字题、模型、算法、结论和特色。文中最好能出现浪费的程度。不用修饰词、感叹句。 “问题”“模型”“算法”等字眼，让评委一目了然。禁忌：表格、图表、公式代摘要；摘要主要是文字，可以有个别重要结果，一般不使用表格公式图表。
模型评价、推广
参考文献、附录
00:26:11
15

怎样写作数学建模竞赛论文详解

怎样写作数学建模竞赛论文一如何建立数学模型—建立数学模型的涉骤和方法建立数学模型没有固定的模式，通常它与实际问题的性质、建模的目的等有关。

当然，建模的过程也有共性，一般说来大致可以分以下几个步骤：1. 形成问题要建立现实问题的数学模型，首先要对所要解决的问题有一个十分明晰的提法。

只有明确问题的背景，尽量弄清对象的特征，掌握有关的数据，确切地了解建立数学模型要达到的目的，才能形成一个比较明晰的“问题”。

2. 假设和简化根据对象的特征和建模的目的，对问题进行必要的、合理的假设和简化。

现实问题通常是纷繁复杂的，我们必须紧紧抓住本质的因素(起支配作用的因素)，忽略次要的因素。

此外，一般地说，一个现实问题不经过假设和简化，很难归结为数学问题。

因此，有必要对现实问题作一些简化，有时甚至是理想化3 .模型的构建根据所作的假设，分析对象的因果关系，用适当的数学语言刻画对象的内在规律，构建现实问题中各个量之间的数学结构，得到相应的数学模型。

这里，有一个应遵循的原则：即尽量采用简单的数学工具。

4. 检验和评价数学模型能否反映厡来的现实问题，必须经受多种途径的检验。

这里包括：(1).数学结构的正确性，即有没有逻辑上自相矛盾的地方；(2).适合求解，即是否有多解或无解的情况出现；(3).数学方法的可行性，即迭代方法是否收敛，以及算法的复杂性等。

而更重要和最困难的问题是检验模型是否真正反映厡来的现实问题。

模型必须反映现实，但又不等同于现实；模型必须简化，但过分的简化则使模型远离现实，无法解决现实问题。

因此，检验模型的合理性和适用性，对于建模的成败是非常重要的。

评价模型的根本标准是看它能否准确地反映现实问题和解决现实问题。

此外，是否容易求解也是评价模型的一个重要标准。

5. 模型的改进模型在不断检验过程中经过不断修正，逐步趋向完善，这是建模必须遵循的重要规律。

一旦在检验中发现问题，人们必须重新审视在建模时所作的假设和简化的合理性，检查是否正确刻画对象内在的量之间的相互关系和服从的客观规律。

美国大学生数学建模大赛模拟1论文

又实际中影响生猪存栏量和猪肉价格的因素复杂多变因此我们的预测模型只能进行短期预成艳聂锐灰色预测模型gm11在江苏省能源消费量预测中的应用中国矿业大学管理学院江苏徐州221116我国生猪生产的波动性研究辽宁农业职业技术学院辽宁营口1150093盛建华程功鹏金喜新任广智高腾云李晓峰河南省猪肉价格变化规律及其预测研究河南农业大学学报1315生猪年末存栏量及猪肉价格周期性波动研究附录
生猪年末存栏量及猪肉价格周期性波动研究
摘要
本文是关于时间序列数据的预测探究的，我们利用灰色系统理论和自己建立的模拟函数对生猪的年末存栏量和 36 个大中城市的猪肉价格进行了模拟和预测。在对第一问生猪年末存栏量的预测中，由于 1997 年以前的统计数据不真实，从而导致可用信息贫乏，据此特点我们采用了灰色系统理论中的 GM(1,1)模型。通过对已知数据和生猪养殖业的分析我们发现生猪养殖随供求关系的变化呈周期性的波动，波动周期为 3 至 4 年，又鉴于我国经济社会和人民生活水平的不断发展，生猪养殖业总体上呈现上升趋势。GM(1,1)并无对周期性变化数据的预测能力，但对单调趋势的小信息量数据有较好的预测能力，据此我们剔除数据中的波动成分，即选取原始序列时每隔 3 年取一点，得出 2010 的生猪存栏量为 44770.6 （万头）。最后对预测结果的检验发现其与原数据的偏差不会超过 3.03%，从而保证了预测结果的可靠性。利用生猪年末存栏量随时间增长但呈现周期性波动的特性，我们还建立了与之适应的模拟函数模型，模拟函数包括由一次函数表征的增长部分、由正弦函数表征的波动部分和由正态函数表征的冲击部分（如 03 年和 06 年生猪养殖业遭到了重大变故，反应在存栏量上有很大波动）。以最小二乘法确定此模拟函数的各项参数，进而预测出 2010 年末的生猪存栏量为 46813 万头。由于模拟函数是在机理分析的基础上建立的，所以很好的吻合了已知数据，从而对未来数据的预测也就有了保证。两种预测模型预测结果还是有较大差异的，但我们认为机理分析在预测中是更有效的方式，所以更倾向于把 46813 万头作为最终预测结果。第二问要求对 36 个大中城市的猪肉价格做出预测。通过对猪肉市场和已有数据的分析研究，我们发现猪肉价格在总体上仍然呈现 3 到 4 年为一个周期的波动，而在每一年中，猪肉价格受节假日、经济波动和病疫等诸多因素的影响，呈现小幅度短周期的波动情况。鉴于此变化规律，我们构造的模拟函数包括表示初始价格的常数、表示总体波动的周期为 4 年的正弦函数和表示众多繁杂因素影响的傅里叶级数（出于计算考虑取级数前 50 项）。通过最小二乘法确定各参数，得出的模拟函数对已知数据完全贴合。在模型检验中，我们只用部分已知数据来确定模拟函数，发现模拟结果与未使用的数据也有很好的吻合程度。为了进一步检验模型我们查阅了新的猪肉价格信息发现其与预测价格有相近的走势。这些都验证了模拟方法的正确性和模拟函数的有效性。