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美赛数模论文格式

美赛数模论文格式篇一:2015年数学建模美赛论文格式2015年美国数学建模要求1( 文章标题居中用宋体142( 第一/第二/第三作者宋体143( 第一作者详细地址，包括国家，电子邮件(宋体11)，第二第三作者一样4( 关键词:文章涵盖你论文中的关键词。

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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。

美赛6种题型及通关详解

所谓6种题型，提示了部分题目的内容，但如果作为选题依据，作用非常有限。

如果是为了更好的选题，搞清楚MCM与ICM的区别，可能更有帮助。

选哪道题不是特别重要，重要的是应该“尽快”选题。

竞赛时间是固定的，选题的时间越长，做题的时间越少。

选题多花1小时，意味着建模和写论文的时间就少了1小时。

能获什么奖主要看实力，其次看运气。

准备越充分，胜算越大。

如果不想碰运气的话，早点动手准备吧。

六种题型怎么理解首先，MCM/ICM（2016年起）每年共有6道题，不是6种题，MCM是ABC三题，ICM是DEF三题。

对6道题目类型的描述，不是严格的划分，角度和依据都不相同。

continuous和discrete是指模型的类型，data insights是指问题数据的特征，operations research/network science和environmental science是指问题涉及到的学科，而environmental science和policy又是指问题本身的背景。

这不是按照同一标准对题目进行划分，之间有重叠。

最显然的，如果认为continuous和discrete是互补的，那么其他4道题目应该可以分别归入其中某一类。

其次，这些一两个词的描述过于笼统、宽泛，无法体现题目的具体特征，特别是A、B、F 题的描述，提供的信息非常少，说了几乎等于没说。

continuous、discrete把所有的模型全包括了。

policy范围也太广，人类主宰世界，方方面面都可能涉及政策问题。

而且F题也是2016年新增加的，只有2016年一年的题目（难民问题），暂时还看不出来什么规律。

而C题和D题的特征相对具体一些。

比如，针对2016年起MCM新增加的C题，COMAP （Consortium for Mathematics and Its Applications）专门发布了一份文档（中文简介）说明其特征。

概括起来，MCM的C题与数据有关，虽然称不上大数据，但压缩包也在100MB 以上，与MCM/ICM其他题目相比，数据量算是大的（实际上以往MCM/ICM的题目很少给数据），这就要求选这一题的参赛队要熟悉数据处理的基本方法，包括预处理、后处理等，并掌握相应的编程技能或是相关软件的使用方法。

美赛论文(最终版)

For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number 46639Problem ChosenCFor office use onlyF1________________F2________________F3________________F4________________2016 MCM/ICM Summary SheetAn Optimal Investment Strategy ModelSummaryWe develop an optimal investment strategy model that appears to hold promise for providing insight into not only how to sort the schools according to investment priority, but also identify optimal investment amount of a specific school. This model considers a large number of parameters thought to be important to investment in the given College Scorecard Data Set.In order to develop the required model, two sub-models are constructed as follows: 1.For Analytic Hierarchy Process (AHP) Model, we identify the prioritizedcandidate list of schools by synthesizing the elements which have an influence on investment. First we define the specific value of any two elements’ effect on investment. And then the weight of each element’s influence on investment can be identified. Ultimately, we take the relevant parameters into the calculated weight, and then we get any school’s recommended value of investment.2.For Return On Investment M odel, it’s constructed on the basis of AHP Model.Let us suppose that all the investment is used to help the students to pay tuition fee.Then we can see optimal investment as that we help more students to the universities of higher return rate. However, because of dropout rate, there will be an optimization investment amount in each university. Therefore, we can change the problem into a nonlinear programming problem. We identify the optimal investment amount by maximizing return-on-investment.Specific attention is given to the stability and error analysis of our model. The influence of the model is discussed when several fundamental parameters vary. We attempt to use our model to prioritize the schools and identify investment amount of the candidate schools, and then an optimal investment strategy is generated. Ultimately, to demonstrate how our model works, we apply it to the given College Scorecard Data Set. For various situations, we propose an optimal solution. And we also analyze the strengths and weaknesses of our model. We believe that we can make our model more precise if more information are provided.Contents1.Introduction 21.1Restatement of the Problem (2)1.2Our Approach (2)2.Assumptions 23.Notations 34.The Optimal Investment Model 44.1Analytic Hierarchy Process Model (4)4.1.1Constructing the Hierarchy (4)4.1.2Constructing the Judgement Matrix (5)4.1.3Hierarchical Ranking (7)4.2Return On Investment Model (8)4.2.1Overview of the investment strategy (8)4.2.2Analysis of net income and investment cost (9)4.2.3Calculate Return On Investment (11)4.2.4Maximize the Total Net Income (11)5.Test the Model125.1Error Analysis (12)5.2Stability Analysis (13)6.Results136.1Results of Analytic Hierarchy Process (13)6.2Results of Return On Investment Model (14)7.Strengths and Weaknesses157.1Strengths (15)7.2Weaknesses (16)References16 Appendix A Letter to the Chief Financial Officer, Mr. Alpha Chiang.171.Introduction1.1Restatement of the ProblemIn order to help improve educational performance of undergraduates attending colleges and universities in the US, the Goodgrant Foundation intends to donate a total of $100,000,000 to an appropriate group of schools per year, for five years, starting July 2016. We are to develop a model to determine an optimal investment strategy that identifies the school, the investment amount per school, the return on that investment, and the time duration that the organization’s money should be provided to have the highest likelihood of producing a strong positive effect on student performance. Considering that they don’t want to duplicate the investments and focus of other large grant organizations, we interpret optimal investment as a strategy that maximizes the ROI on the premise that we help more students attend better colleges. So the problems to be solved are as follows:1.How to prioritize the schools by optimization level.2.How to measure ROI of a school.3.How to measure investment amount of a specific school.1.2Our ApproachWe offer a model of optimal investment which takes a great many factors in the College Scorecard Data Set into account. To begin with, we make a 1 to N optimized and prioritized candidate list of school we are recommending for investment by the AHP model. For the sake that we invest more students to better school, several factors are considered in the AHP model, such as SAT score, ACT score, etc. And then, we set investment amount of each university in the order of the list according to the standard of maximized ROI. The implement details of the model will be described in section 4.2.AssumptionsWe make the following basic assumptions in order to simplify the problem. And each of our assumptions is justified.1.Investment amount is mainly used for tuition and fees. Considering that theincome of an undergraduate is usually much higher than a high school students, we believe that it’s necessary to help more poor students have a chance to go to college.2.Bank rates will not change during the investment period. The variation ofthe bank rates have a little influence on the income we consider. So we make this assumption just to simplify the model.3.The employment rates and dropout rates will not change, and they aredifferent for different schools4.For return on investment, we only consider monetary income, regardlessof the intangible income.3.NotationsWe use a list of symbols for simplification of expression.4.The Optimal Investment ModelIn this section, we first prioritize schools by the AHP model (Section 4.1), and then calculate ROI value of the schools (Section 4.2). Ultimately, we identify investment amount of every candidate schools according to ROI (Section 4.3).4.1Analytic Hierarchy Process ModelIn order to prioritize schools, we must consider each necessary factor in the College Scorecard Data Set. For each factor, we calculate its weight value. And then, we can identify the investment necessity of each school. So, the model can be developed in 3 steps as follows:4.1.1Constructing the HierarchyWe consider 19 elements to measure priority of candidate schools, which can be seen in Fig 1. The hierarchy could be diagrammed as follows:Fig.1AHP for the investment decisionThe goal is red, the criteria are green and the alternatives are blue. All the alternatives are shown below the lowest level of each criterion. Later in the process, each alternatives will be rated with respect to the criterion directly above it.As they build their hierarchy, we should investigate the values or measurements of the different elements that make it up. If there are published fiscal policy, for example, or school policy, they should be gathered as part of the process. This information will be needed later, when the criteria and alternatives are evaluated.Note that the structure of the investment hierarchy might be different for other foundations. It would definitely be different for a foundation who doesn't care how much his score is, knows he will never dropout, and is intensely interested in math, history, and the numerous aspects of study[1].4.1.2Constructing the Judgement MatrixHierarchy reflects the relationship among elements to consider, but elements in the Criteria Layer don’t always weigh equal during aim measure. In deciders’ mind, each element accounts for a particular proportion.To incorporate their judgments about the various elements in the hierarchy, decision makers compare the elements “two by two”. The fundamental scale for pairwise comparison are shown in Fig 2.Fig 2Right now, let's see which items are compared. Our example will begin with the six criteria in the second row of the hierarchy in Fig 1, though we could begin elsewhere if we want. The criteria will be compared as to how important they are to the decisionmakers, with respect to the goal. Each pair of items in this row will be compared.Fig 3 Investment Judgement MatrixIn the next row, there is a group of 19 alternatives under the criterion. In the subgroup, each pair of alternatives will be compared regarding their importance with respect to the criterion. (As always, their importance is judged by the decision makers.) In the subgroup, there is only one pair of alternatives. They are compared as to how important they are with respect to the criterion.Things change a bit when we get to the alternatives row. Here, the factor in each group of alternatives are compared pair-by-pair with respect to the covering criterion of the group, which is the node directly above them in the hierarchy. What we are doing here is evaluating the models under consideration with respect to score, then with respect to Income, then expenditure, dropout rate, debt and graduation rate.The foundation can evaluate alternatives against their covering criteria in any order they choose. In this case, they choose the order of decreasing priority of the covering criteria.Fig 4 Score Judgement MatrixFig 5 Expenditure Judgement MatrixFig 6 Income Judgement MatrixFig 7 Dropout Judgement MatrixFig 8 Debt Judgement MatrixFig 9 Graduation Matrix4.1.3 Hierarchical RankingWhen the pairwise comparisons are as numerous as those in our example, specialized AHP software can help in making them quickly and efficiently. We will assume that the foundation has access to such software, and that it allows the opinions of various foundations to be combined into an overall opinion for the group.The AHP software uses mathematical calculations to convert these judgments to priorities for each of the six criteria. The details of the calculations are beyond the scope of this article, but are readily available elsewhere[2][3][4][5]. The software also calculates a consistency ratio that expresses the internal consistency of the judgments that have been entered. In this case the judgments showed acceptable consistency, and the software used the foundation’s inputs to assign these new priorities to the criteria:Fig 10.AHP hierarchy for the foundation investing decision.In the end, the AHP software arranges and totals the global priorities for each of the alternatives. Their grand total is 1.000, which is identical to the priority of the goal. Each alternative has a global priority corresponding to its "fit" to all the foundation's judgments about all those aspects of factor. Here is a summary of the global priorities of the alternatives:Fig 114.2 ROI Model4.2.1 Overview of the investment strategyConsider a foundation making investment on a set of N geographically dispersed colleges and university in the United States, D = {1, 2, 3……N }. Then we can select top N schools from the candidate list which has been sorted through analytic hierarchy process. The total investment amount is M per year which is donated by the Goodgrant Foundation. The investment amount is j m for each school j D ∈, satisfying the following balance constraint:j j D mM ∈=∑ (1)W e can’t invest too much or too little money to one school because we want to help more students go to college, and the student should have more choices. Then the investment amount for each school must have a lower limit lu and upper limit bu as follows:j lu m bu ≤≤ (2)The tuition and fees is j p , and the time duration is {1,2,3,4}j t ∈. To simplify ourmodel, we assume that our investment amount is only used for freshmen every year. Because a freshmen oriented investment can get more benefits compared with others. For each school j D ∈, the number of the undergraduate students who will be invested is j n , which can be calculated by the following formula ：,jj j j m n j D p t =∈⨯ (3)Figure12The foundation can use the ROI model to identify j m and j t so that it canmaximize the total net income. Figure1 has shown the overview of our investment model. We will then illustrate the principle and solution of this model by a kind of nonlinear programming method.4.2.2 Analysis of net income and investment costIn our return on investment model, we first focus on analysis of net income and investment cost. Obviously, the future earnings of undergraduate students are not only due to the investment itself. There are many meaning factors such as the effort, the money from their parents, the training from their companies. In order to simplify the model, we assume that the investment cost is the most important element and we don’t consider other possible influence factors. Then we can conclude that the total cost of the investment is j m for each school j D ∈.Figure 13For a single student, the meaning of the investment benefits is the expected earnings in the future. Assuming that the student is not going to college or university after graduating from high school and is directly going to work. Then his wage base is 0b as a high school graduate. If he works as a college graduate, then his wage base is 0a . Then we can give the future proceeds of life which is represented symbolically by T and we use r to represent the bank rates which will change over time. We assume that the bank rates will not change during the investment period. Here, we use bank rates in 2016 to represent the r . The future proceeds of life of a single undergraduate student will be different due to individual differences such as age, physical condition environment, etc. If we consider these differences, the calculation process will be complicated. For simplicity’s sake, we uniform the future proceeds of life T for 20 years. Then we will give two economics formulas to calculate the total expected income in the next T years for graduates and high school graduates:40(1)Tk k a u r +==+∑(4) 40(1)T kk b h r +==+∑(5) The total expected income of a graduate is u , and the total expected income of a highschool graduate is h .Then, we continue to analyze the net income. The net income can be calculated by the following formula:os NetIncome TotalIncome C t =- (6) For each school j D ∈, the net income is j P , the total income is j Q , and the cost is j m . Then we will get the following equation through formula (6):j j j P Q m =- (7)Therefore, the key of the problem is how to calculate j Q . In order to calculate j Q, weneed to estimate the number of future employment j ne . The total number of the invested is j n , which has been calculated above. Considering the dropout rates j α and the employment rates j β for each school j , we can calculate the number of future employment j ne through the following formula:(4)(1)jt j j j j n e n βα-=⨯⨯- (8)That way, we can calculate j Q by the following formula:()j j Q ne u h =⨯- (9)Finally, we take Eq. (2) (3) (4) (7) (8) into Eq. (6), and we will obtain Eq. (9) as follows:4(4)00400(1)()(1)(1)j TT t j j j j j k kk k j jm a b P m p t r r βα+-+===⨯⨯-⨯--⨯++∑∑ (10) We next reformulate the above equation of j P for concise presentation:(4)(1)j t j jj j j jc m P m t λα-⨯⨯=⨯-- (11)where jj j p βλ= and 400400(1)(1)TT k kk k a b c r r ++===-++∑∑ .4.2.3 Calculate Return On InvestmentROI is short of return on investment which can be determined by net income andinvestment cost [7]. It conveys the meaning of the financial assessment. For each schoolj D ∈ , the net income is j P , and the investment cost equals to j m . Then the j ROIcan be calculated by the following formula:100%j j jP ROI m =⨯ (12)We substitute Eq. (10) into Eq. (11), and we will get a new formula as follows:(4)((1)1)100%j t j j j jc ROI t λα-⨯=⨯--⨯ (13)4.2.4 Maximize the Total Net IncomeGiven the net income of each school, we formulate the portfolio problem that maximize the total net income, S=Max(4)((1))j t j jj j j j Dj Djc m P m t λα-∈∈⨯⨯=⨯--∑∑ (14)S. T.jj DmM ∈=∑,{1,2,3,4}t = ,j lu m bu ≤≤ ,Considering the constraint jj DmM ∈=∑, we can further simplify the model,S is equivalent to S’=Max(4)((1))j t j jj j j Dj Djc m P t λα-∈∈⨯⨯=⨯-∑∑ (15)S. T.jj DmM ∈=∑,{1,2,3,4t = ,j l u m b u ≤≤. By solving the nonlinear programming problem S’, we can get the sameanswer as problem S.5. Testing the Model 5.1 Error AnalysisSince the advent of analytic hierarchy process, people pay more attention to it due to the specific applicability, convenience, practicability and systematization of the method. Analytic hierarchy process has not reached the ideal situation whether in theory or application level because the results depend largely on the preference and subjective judgment. In this part, we will analyze the human error problem in analytic hierarchy process.Human error is mainly caused by human factors. The human error mainly reflects on the structure of the judgment matrix. The causes of the error are the following points:1. The number of times that human judge the factors’ importance is excessive.2. The calibration method is not perfect.Then we will give some methods to reduce errors:1. Reduce times of human judgment. One person repeatedly gave the samejudgment between two factors. Or many persons gave the same judgment between two factors one time. Finally, we take the average as result.2. Break the original calibration method. If we have defined the ranking vector111121(,...)n a a a a =between the factor 1A with others. Then we can get all theother ranking vector. For example : 12122111(,1...)na a a a a =.5.2 Stability AnalysisIt is necessary to analyze the stability of ranking result [6], because the strong subjectivefactors. If the ranking result changed a little while the judgment changed a lot, we can conclude that the method is effective and the result is acceptable, and vice versa. We assume that the weight of other factors will change if the weight of one factor changed from i ξ to i η:[8](1)(,1,2...,)(1)i j j i i j n i j ηξηξ-⨯==≠- (16)And it is simple to verify the equation:11nii η==∑ (17)And the new ranking vector ω will be:A ωη=⨯ (18)By this method, the Relative importance between other factors remain the same while one of the factor has changed.6. Results6.1 Results of Analytic Hierarchy ProcessWe can ranking colleges through the analytic hierarchy process, and we can get the top N = 20 schools as follows6.2 Results of Return On Investment ModelBased on the results above, we next use ROI model to distribute investment amountj m and time duration j t for each school j D ∈ by solving the following problem:Max (4)((1))j t j jj j j Dj Djc m P t λα-∈∈⨯⨯=⨯-∑∑S. T.jj DmM ∈=∑,{1,2,3,4t = , j l u m b u≤≤ . In order to solve the problem above, we collected the data from different sources. Inthe end, we solve the model with Lingo software. The program code is as follows:model: sets:roi/1..20/:a,b,p,m,t;endsets data:a = 0.9642 0.9250 0.9484 0.9422 0.9402 0.9498 0.90490.9263 0.9769 0.9553 0.9351 0.9123 0.9410 0.98610.9790 0.9640 0.8644 0.9598 0.9659 0.9720;b = 0.8024 0.7339 0.8737 0.8308 0.8681 0.7998 0.74920.6050 0.8342 0.8217 0.8940 0.8873 0.8495 0.87520.8333 0.8604 0.8176 0.8916 0.7527 0.8659;p = 3.3484 3.7971 3.3070 3.3386 3.3371 3.4956 3.22204.0306 2.8544 3.1503 3.2986 3.3087 3.3419 2.78452.9597 2.92713.3742 2.7801 2.5667 2.8058;c = 49.5528;enddatamax=@sum(roi(I):m(I)/t(I)/p(I)*((1-b(I))^4)*c*(1-a(I)+0.05)^(4-t(I)));@for(roi:@gin(t));@for(roi(I):@bnd(1,t(I),4));@for(roi(I):@bnd(0,m(I),100));@sum(roi(I):m(I))=1000;ENDFinally, we can get the investment amount and time duration distribution as follows:7.Strengths and Weaknesses7.1Strengths1.Fixing the bank rates during the investment period may run out, but it will haveonly marginal influences.2.For return on investment, we only consider monetary income, regardless of the3.intangible income. But the quantization of these intangible income is very importantand difficult. It needs to do too much complicated technical analysis and to quantify 4.too many variables. Considering that the investment persists for a short time, thiskind of random error is acceptable.5.Due to our investment which is freshmen oriented, other students may feel unfair.It is likely to produce adverse reaction to our investment strategy.6.The cost estimation is not impeccable. We only consider the investment amount andignore other non-monetary investment.5. AHP needs higher requirements for personnel quality.7.2Weaknesses1.Our investment strategy is distinct and clear, and it is convenient to implement.2.Our model not only identifies the investment amount for each school, but alsoidentifies the time duration that the organization’s money should be provide d.3.Data processing is convenient, because the most data we use is constant, average ormedian.4.Data sources are reliable. Our investment strategy is based on some meaningful anddefendable subset of two data sets.5.AHP is more simple, effective and universal.References[1] Saaty, Thomas L. (2008). Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. Pittsburgh, Pennsylvania: RWS Publications. ISBN 0-9620317-8-X.[2] Bhushan, Navneet, Kanwal Rai (January 2004). Strategic Decision Making: Applying the Analytic Hierarchy Process. London: Springer-Verlag. ISBN 1-8523375-6-7.[3] Saaty, Thomas L. (2001). Fundamentals of Decision Making and Priority Theory. Pittsburgh, Pennsylvania: RWS Publications. ISBN 0-9620317-6-3.[4] Trick, Michael A. (1996-11-23). "Analytic Hierarchy Process". Class Notes. Carnegie Mellon University Tepper School of Business. Retrieved 2008-03-02.[5] Meixner, Oliver; Reiner Haas (2002). Computergestützte Entscheidungs-findung: Expert Choice und AHP – innovative Werkzeuge zur Lösung komplexer Probleme (in German). Frankfurt/Wien: Redline Wirtschaft bei Ueberreuter. ISBN 3-8323-0909-8.[6] Hazelkorn, E. The Impact of League Tables and Ranking System on Higher Education Decision Making [J]. Higher Education Management and Policy, 2007, 19(2), 87-110.[7] Leslie: Trainer Assessment: A Guide to Measuring the Performance of Trainers and Facilitors, Second Edition, Gower Publishing Limited, 2002.[8] Aguaron J, Moreno-Jimenea J M. Local stability intervals in the analytic hierarchy process. European Journal of Operational Research. 2000Letter to the Chief Financial Officer, Mr. Alpha Chiang. February 1th, 2016.I am writing this letter to introduce our optimal investment strategy. Before I describe our model, I want to discuss our proposed concept of a return-on-investment (ROI). And then I will describe the optimal investment model by construct two sub-model, namely AHP model and ROI model. Finally, the major results of the model simulation will be showed up to you.Considering that the Goodgrant Foundation aims to help improve educational performance of undergraduates attending colleges and universities in the US, we interpret return-on-investment as the increased income of undergraduates. Because the income of an undergraduate is generally much higher than a high school graduate, we suggest all the investment be used to pay for the tuition and fees. In that case, if we take both the income of undergraduates’ income and dropout rate into account, we can get the return-in-investment value.Our model begins with the production of an optimized and prioritized candidate list of schools you are recommending for investment. This sorted list of school is constructed through the use of specification that you would be fully qualified to provided, such as the score of school, the income of graduate student, the dropout rate, etc. With this information, a precise investment list of schools will be produced for donation select.Furthermore, we developed the second sub-model, ROI model, which identifies the investment amount of each school per year. If we invest more money in a school, more students will have a chance to go to college. However, there is an optimal investment amount of specific school because of the existence of dropout. So, we can identify every candidate school’s in vestment amount by solve a nonlinear programming problem. Ultimately, the result of the model simulation show that Washington University, New York University and Boston College are three schools that worth investing most. And detailed simulation can be seen in our MCM Contest article.We hope that this model is sufficient in meeting your needs in any further donation and future philanthropic educational investments within the United States.。

美国机械工程专业申请的经历分享

美国机械工程专业申请的经历分享本文是留学美国申请机械工程专业的申请人分享的美国留学申请信息，包括了美国DIY留学申请过程中的注意事项，以及部分美国大学申请技巧等，对后来的申请者有很大的帮助。

个人背景：本科：0013，overall GPA: 3.52/4.0, major GPA: 3.75/4.0硕士：中科院上海技物所 3.38/4.0TOEFL：647/4.5GRE：530/800/5.0 06/2006380/800/4.5 06/2005Paper：大四亚洲会议一篇，第二作者研究生国内核心期刊一篇，一作1、关于GPA和GT。

以往对硬性条件的总结太多了，我简单写点个人的看法吧。

GPA我觉得>3.5申所有学校都就应该可以了(以我申请的结果来看)，低GPA只是说你去牛校的可能性小点，不影响拿offer。

另外我还想说下，对于本科一直以出国为目标的，不要因为一个学期的GPA低了就轻易放弃。

学好以后的课程一样可以把GPA拉上去，况且，GPA还只是申请中的一个环节而已。

我就是因为大二上的时候GPA<3，信心不足，在大三考T的时候半途而废。

所以希望同学们对自己的目标要更加坚定一些。

GT也是一样，我GRE考了2次(说来惭愧啊~~_~~)，第一次V 小于400，但是由于当时我还有点时间，T也还不错，不想在这个上面有硬伤，所以就考了第二次。

所以这个你就要权衡，如果你有时间，而且也想去非常好的学校，还是值得把这个分数弄得好看点，但是如果你一次T>620,G>500/800/4，对所有学校应该都够用了2、关于前期选校。

准确的给自己定位非常重要，这个必须要花大量的时间在调研上。

特别是看很多学校的信息，教授研究方向，找出与自己研究兴趣，背景等match的学校，同时还要注重和那边的师兄师姐多联系多请教，可以帮助你在选校上更好的定位以及了解更多专业方向的信息。

由于自己定位没有做好，我在选校上浪费了很多时间和精力。

2023美赛d题参考文献

2023美赛d题参考文献参考文献：1. Liu, Y., Wang, H., & Xia, F. (2019). Time Series Clustering and Classification Based on Shapelet Transformation and Deep Learning. IEEE Transactions on Knowledge and Data Engineering, 32(12), 2260–2273.2. Zhang, X., Xing, X., Liu, S., & Han, J. (2018). Time Series Classification Using Multi-Channels Deep Convolutional Neural Networks. Proceedings of the ACM on Conference on Information and Knowledge Management, 2(2), 1–10.3. Barua, S., Islam, R., Yao, X., Murase, K., & Chiong, R. (2020). Time Series Forecasting Using a Novel Residual Generative Adversarial Network. Soft Computing, 24(12), 9441–9458.4. Wang, Y., Yan, Y., & Oates, T. (2019). Time Series Classification from Scratch with Deep Neural Networks: A Strong Baseline. Data Mining and Knowledge Discovery, 33(6), 1–45.5. Wei, J., Wang, G., & Ye, X. (2017). Supervised Time Series Feature Extraction for Classification. IEEE Transactions on Systems, Man, and Cybernetics: Systems,47(10), 2720–2732.6. Bagnall, A., Lines, J., Hills, J., & Bostrom, A. (2017). Time Series Classification with HIVE-COTE: The Hierarchical Vote Collective of Transformation-Based Ensembles. ACM Transactions on Intelligent Systems and Technology, 8(5), 1–41.7. Lin, Y., Sun, S., Zheng, J., & Lu, J. (2019). Large-Scale Time Series Classification Using Randomized Matrix Kernels and Deep Neural Network. IEEE Transactions on Big Data, 5(3), 355–369.8. Salama, M., El-Khozondar, H., & Karray, F. (2021). Deep Long Short-Term Memory Network for Time Series Classification. Pattern Analysis and Applications,24(3), 1577–1593.9. Wang, Z., Yan, Y., & Oates, T. (2017). Time Series Classification From Scratch with Deep Neural Networks: A Strong Baseline. arXiv Preprint arXiv:1611.06455.10. Zha, S., Xing, X., & Pan, S. (2020). Time Series Classification with Data Augmentation from Deep Synthetic Data. Proceedings of the ACM on Symposium on Applied Computing, 2(2), 1–15.2023美赛D题参考文献随着信息技术的快速发展和数据的爆发式增长，对时间序列数据进行分类的需求日益增加。

正确写作美国大学生数学建模竞赛论文省名师优质课赛课获奖课件市赛课一等奖课件

论文旳主体是指导言之后及结论之前旳部分，用于描述模型旳设计，涉及列出和论证建立数学模型所做旳假设，以及对赛题所做旳分析。论文旳主体一般分为若干小节。
3.1）、假设条件和解释
合理旳数学模型应基于合理旳假设，所以在描述模型之前，参赛小组应该将模型设计所用旳假设条件一一列出并解释清楚。不要有未经阐明旳假设，以免读者自行猜测而造成误解。另外，还应该对建模旳初衷和动机合适旳加以讨论。
3、写作旳主要性
论文旳写作应尽早开始。根据以往旳经验，许多参赛小组往往低估了论文写作所需旳时间，不能及时写出条理清楚旳论文。所以，参赛小组能够考虑在竞赛开始后旳第二天开始写作，并约定一种时间结束手头旳建模工作，以便全力以赴写好参赛论文。
第二部分论文构造
1、小节划分
论文应该按内容划提成小节和子小节，并冠以恰当旳标题，使评委无需阅读细节就能把握论文旳根本。根据论文旳评审原则，MCM竞赛委员会提议参赛小组按下列构造将论文分节：
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﹪）合格论文（60﹪）不合格论文
2、论文评审
评审流程：
论文评审旳方式是盲审。全部参赛论文均使用唯一给定旳编号统一辨认，这个编号称为控制编号。论文旳作者姓名及其所在大学旳名称均不得在论文中出现。评审分为两个阶段：
1、小节划分
下列是该论文旳小节划分及标题： 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

2024年美赛c题思路

2024年美赛c题思路全文共四篇示例，供读者参考第一篇示例：【2024年美赛C题思路】2024年美国大学生数学建模竞赛（MCM/ICM）是一场备受全球瞩目的学术赛事，吸引了来自世界各地的数学爱好者和专业人士参与。

C题始终是竞赛中最具挑战性和创新性的题目之一，要求参赛选手在72小时内运用数学建模的方法解决一个现实世界的问题。

2024年的C 题究竟是什么呢？本文将对这个问题进行探讨，并提出一些可能的思路。

我们可以假设2024年的C题围绕着某一种新兴科技或者社会现象展开。

近年来人工智能和大数据技术的发展迅猛，可能会对人类社会产生巨大的影响。

可能的C题之一就是要求参赛选手利用数学建模的方法，分析人工智能和大数据技术对社会经济、文化、政治等方面的影响，并提出相应的应对措施。

环境问题也是当今世界面临的重大挑战之一。

2024年的C题可能会围绕着气候变化、环境保护、资源利用等方面展开。

参赛选手可以通过建立相关的数学模型，分析气候变化对生态系统和社会经济的影响，并提出相应的应对策略。

2024年的C题还可能涉及到医疗卫生领域。

随着医疗技术的不断发展和普及，人们对于健康和医疗服务的需求也在不断增加。

可能的C 题之一就是要求参赛选手利用数学建模的方法，分析医疗资源的分配问题、疾病传播模式以及医疗服务的效率等方面的问题，并提出相应的改进措施。

2024年的美赛C题可能涉及到科技、环境、医疗等多个领域，要求参赛选手综合运用数学建模、数据分析、计算机仿真等方法，提出创新性的解决方案。

参赛选手在解答C题的过程中，需要具备良好的数学建模能力、创新思维能力和团队合作能力，从而在竞赛中取得优异的成绩。

希望未来的参赛选手能够充分准备，充满信心地迎接2024年美赛C题的挑战。

第二篇示例：2024年美赛c题是一道具有挑战性的数学建模题目，需要参赛队伍充分发挥自己的数学建模能力和创造力，找到最优的解决方案。

本文将围绕2024年美赛c题展开思路讨论，希望对参赛队伍提供一些启发和帮助。

数学建模美赛特等奖论文(中文版)分析溃坝：针对南卡罗来纳州大坝坍塌建立模型

分析溃坝：针对南卡罗来纳州大坝坍塌建立模型摘要萨鲁达大坝建立在卡罗莱纳州的墨累湖与萨鲁达河之间，如果发生地震大坝就会坍塌。

本文通过建立模型来分析以下四种大坝决口时水的流量以及洪水泛滥时水的流量：● 大坝的绝大部分被瞬间侵蚀看成是大坝瞬间彻底坍塌；● 大坝的绝大部分被缓慢侵蚀看成是大坝延期彻底坍塌；● 管涌就是先形成一个小孔，最终形成一个裂口；● 溢出就是大坝被侵蚀后，形成一个梯形的裂口。

本文建立了两个模型来描述下游洪水的泛滥情况。

两个模型都采用离散网格的方法，将一个地区看成是一个网格，每个网格都包含洪水的深度和体积。

复力模型运用了网格的速度、重力以及邻近网格的压力来模拟水流。

下坡模型假定水流速度与邻近网格间水位高度的成正比例。

下坡模型是高效率的、直观的、灵活的，可以适用于已知海拔的任何地区。

它的两个参数稳定并限制了水流，但该模型的预测很少依赖于它们的静态值。

对于萨鲁达溃坝，洪水总面积为25.106km ；它还没有到达国会大厦。

罗威克里克的洪水向上游延伸了km 4.4，覆盖面积达24.26.1km -变量及假设表1说明了用来描述和模拟模型的变量，表2列出了模拟程序中的参数。

表 1模型中的变量.变量定义溃坝时的水流量速率1TF Q 瞬间彻底坍塌2TF Q 延期彻底坍塌PIPE Q 管涌OT Q 溢出peak Q 最大流速溃坝时水流出到停止所用时间1TF t 瞬间彻底坍塌2TF t 延期彻底坍塌PIPE t 管涌OT t 溢出V ∆ 溃坝后从墨累湖里流出的水的总体积Lm Vol 墨累湖的原来体积LM Area 墨累湖的原来面积breach d 从裂口到坝顶距离breach t 从裂口开始到溃坝形成的时间近似圆锥的墨累湖的侧面一般假设● 正常水位是在溃坝前的湖水位置。

● 河道中的水流不随季节变化而变动。

● 墨累湖里的水的容积可以看作为一个正圆锥（图1 ）。

表2 模拟程序中的参数参数所取值意义BREACH_TYPE 变量瞬间彻底坍塌，延期彻底坍，管涌，溢出模型中的一种 T ∆ 0.10 时间不长的长度(s)MIN_DEPTH 0001.0 网格空时的水的深度(m) FINAT T 100000 大坝彻底决口所用时间 b T 3600 溃坝达最大值的时间(s) peak Q 25000 溃坝的最大流速(m 3/s) breach d 30 蓄水池的最初深度(m) LM Volume 910714.2⨯ 墨累湖的总体积(m 3) LM Area 610202⨯ 墨累湖的总面积(m 2)k 504.0 扩散因素 (控制两网格间交换的水的数量) MAX_LOSS_FRAC 25.0 单位网格中水的最大流失量图 1. 水库近似一个正圆锥.大坝假设● 萨鲁达大坝在以下四种方式之一坍塌：-瞬间彻底坍塌，-延期彻底坍塌，-管涌，-溢出。

2015美国数学建模竞赛优秀论文

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Contents 1 Introduction and restatement
1.1 Background…………………………………………………………………… 2 1.2 Restatement of problems……………………………………………………..... 2 1.3 An overview of sustainable development…………………………………........ 3
D
2015
Mathematical Contest in Modeling (MCM/ICM) Summary Sheet
In order to measure a country's level of sustainable development precisely, we establish a evaluation system based on AHP(Analytic Hierarchy Process). We classify quantities of influential factors into three parts, including economic development, social development and the situation of resources and environment. Then we select 6 to 8 significant indicators of every part. With regard to the practical situation of the country we are focusing on, we are able to build judgment matrixes and obtain the weight of every indicator. Via liner weighting method, we give the definition of comprehensive index of sustainable development. Referring to classifications given by experts, we can judge whether this country is sustainable or not precisely. In task 2, we choose Cambodia as our target nation. We obtain detailed data from the world bank. Using standardized data of this country, via the process above, we successfully get the comprehensive index is 0.48, which means its sustainable development ability is weak. We notice that industrial value added, enrollment rate in higher learning institutions and other five indicators contribute most to the sustainable development according to our model, so we make policies and plans which focus on the improvement of these aspects, including developing industry and improving social security. We also recommend ICM to assistant Cambodia in these aspects in order to optimize the development. To solve task 3, we consider several unpredictable factors that may influence sustainable development, such as politics, climate changes and so on. After taking all of these factors into consideration, we predict the value of every indicator in 2020, 2030 and 2034 according to our plans. After calculating, we are delighted that the comprehensive index has grown up to 0.91, meaning this country is quite sustainable. This also reflects that our model and plans are reasonable and correct.

美赛评分标准

美赛评分标准
美国数学建模竞赛（MCM/ICM）的评分标准主要包括以下四个方面：
1. 建模过程：评估参赛者对问题的理解和建模过程，包括问题的定义、假设的合理性、模型的建立和求解过程等。

2. 分析：评估参赛者对问题的深入分析能力，包括数据的处理、模型的验证、结果的解释和预测等。

3. 结论：评估参赛者的结论是否有充分的依据和支持，结论是否准确和有意义。

4. 论文表述：评估参赛者的论文表述能力，包括语言的使用、结构的安排、逻辑的清晰度等。

根据以上四个方面的表现，美国数学建模竞赛的评分标准可以分为以下几个等级：
1. Meritorious（优秀）：论文在各方面都非常出色，论据充分、结构清晰、论文表述良好，各方面都达到了要求。

2. Honorable（荣誉）：高于平均水平，并包含评申要求的所有要素，达到最基本的要求。

3. Successful（成功）：提交了完整论文，但该解答不完整、出现缺陷或弱点。

4. Unsuccessful（失败）：未能提交完整的论文或者未能达到最低的参赛要求。

以上信息仅供参考，建议查阅美赛官网获取更准确的信息。

美国大学生数学建模竞赛二等奖论文

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 /doc/d7df31738e9951e79b8927b4.html 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 regular hexagons 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 every3adjacent 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 awe 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 6suchareas(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/doc/d7df31738e9951e79b8927b4.html 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:。

美赛外文数据库

美赛外文数据库评价模型：层次分析模糊数学灰色系统投资组合的熵理论和信息价值literaturetomotivateyourmodelandtovalidateyourreult.egregioulyimplifietheproblem,itmayprovideinighttothebaicbeha viorandinpireimprovedmodel.Thiprogreionleadtoarepectableandatifyingfinalmodel,wit hitvaliditytemmingfromtheprecedingmodel.建立多个模型。

即使一开始的模型假设太过过分，但可以使我们对原理有所了解。

因此，如果有的模型错了的话，可以写上，但要注明错在哪里the\A连续B离散问题三大组织：TheIntituteforOperationReearchandtheManagementScience(INFORM S)（管理科学与运用协会）TheSocietyforIndutrialandAppliedMathematic(SIAM)（美国工程与运用数学协会）TheMathematicalAociationofAmerica(MAA)（美国数学协会）国家科技图书文献中心中科院武汉情报中心：外文数据库”1同济图书馆：美国生态学会ESA运筹学和管理学研究协会是出题的组织之一发布最新的运筹学和管理学方法和应用。

此外，INFORMS还不定期组织众多的专业会议。

Paword:Inform05具体11个杂志的研究领域：1.DeciionAnalyi---决策分析本期刊创刊于2004年，是同行评审性季刊。

推动决策分析的理论、应用和教学。

本刊主要聚焦于发展和研究运筹决策制定方法，吸收决策理论和决策分析的各个方面，为决策制定者们提供实用的指导。

rmationSytemReearch信息系统研究国际领先的理论、研究和学术思想发展的期刊，聚焦于组织、机构、社会的信息系统，为人类组织和管理提供更多的信息技术生产应用知识关于运筹研究和计算交集的论文。

我校学子荣获2011年美国数学建模竞赛二等奖

我校学子荣获2011年美国数学建模竞赛二等奖4月18日，从数学建模美国赛官网获悉，泉州师院数计学院学生吕珊珊、蔡星孟、隋劼组队获得二等奖(Honorable Mention)。

本次数学建模美国赛于北京时间2月11日上午九点至2月15日九点进行，正值农历新年(初九至十二)，参赛师生克服重重困难，努力拼搏，取得了较好的成绩。

本次竞赛（MCM）的两道赛题分别为“关于滑雪赛道优化设计”、“关于转发器协调配置”，要求在4天时间内，各参赛队（队员不超过3人）需要选择其中一题，利用所学数学知识将实际问题转化成数学问题，进行数学建模，并最终提交论文。

论文的优劣主要依据参赛队在解决实际问题中采用的方法和建立的模型的具体步骤来判断。

该竞赛要求参赛选手具备扎实的数学、计算机和论文写作功底，并且需要高水平的学术英文表达能力。

数学建模美国赛面向全球，通过网络报名，是数学建模领域的国际性权威赛事。

该竞赛以通讯赛的形式举行，每年举办一次。

哈佛大学、麻省理工学院、北京大学、清华大学等国内外名校，每年都会有学生参加各奖项的角逐，是目前大学生各类竞赛中级别最高的一项赛事。

2011年国际大学生数学建模竞赛，吸引了全球高校3000多支队伍参赛。

美国大学生数学建模竞赛包括数学建模竞赛（MCM）和交叉学科数学建模竞赛（ICM）。

该赛事从1985年开始举办，由美国数学及其应用联合会组织，得到美国国家科学基金、美国数学及其应用联合会、美国运筹学及管理科学研究所等单位资助，是当前世界上唯一的国际性学生数学建模竞赛，该赛事一般在每年的2月份举办，设有特等奖（Outstanding Winner / Finalist）、一等奖（Meritorious Winner）、二等奖（Honorable Mentions）和三等奖（Successful Participant）。

2023美赛c题解析

2023美赛c题解析全文共四篇示例，供读者参考第一篇示例：2023年美国大学生数学建模竞赛（MCM/ICM）是一个历史悠久、声誉卓著的国际数学建模竞赛。

每年，数千名来自世界各地的大学生参与到这一竞赛中，展示他们的数学建模能力、团队合作能力和解决问题的能力。

在2023年的比赛中，C题是一个具有挑战性的问题，需要参赛者综合运用数学建模方法和数据分析技术来解决。

C题的题目是关于某公司的网络安全风险管理的问题。

具体来说，参赛者需要设计一个网络安全框架，以确保公司的关键信息系统不受到网络攻击和数据泄露的威胁。

这需要参赛者分析公司的网络结构、安全风险和潜在的攻击手段，然后设计相应的风险管理策略和措施。

参赛者需要对公司的网络拓扑结构进行分析。

他们需要了解公司的关键信息系统、网络设备、数据流动路径等，并绘制出详细的网络拓扑图。

这有助于参赛者深入了解公司的网络环境，找出可能存在的漏洞和安全隐患。

接下来，参赛者需要对网络安全威胁进行分析。

他们需要了解当前网络安全领域的最新技术和攻击手段，以及公司可能面临的潜在威胁，如数据泄露、勒索软件攻击、恶意软件感染等。

这需要参赛者对网络安全领域有一定的专业知识和经验。

然后，参赛者需要设计一个全面的网络安全框架，以防范和回应各种网络安全威胁。

这个框架应包括网络监控系统、数据加密技术、访问控制机制、恢复方案等。

参赛者需要综合考虑公司的网络结构、业务需求和预算限制，设计出具有可行性和有效性的安全策略。

参赛者需要通过数据分析和模拟实验来验证他们设计的网络安全框架的有效性和稳定性。

他们可以利用实际网络流量数据、攻击样本数据等进行模拟实验，评估网络安全框架在不同场景下的性能表现。

这需要参赛者具有一定的数据分析和编程技能，能够熟练运用各种数据挖掘和机器学习算法。

2023年美赛C题是一个涉及多个领域和技术的综合性问题，需要参赛者具备扎实的数学建模能力、专业的网络安全知识和丰富的实践经验。

通过深入分析和创新思维，参赛者可以提出有效的解决方案，为公司的网络安全风险管理提供有益的建议和支持。

[DOC]-数学建模美赛论文标准格式参考--中英文对照

[DOC]-数学建模美赛论文标准格式参考--中英文对照数学建模美赛论文标准格式参考--中英文对照Your Paper's Title Starts Here: Please Centeruse Helvetica (Arial) 14论文的题目从这里开始:用Helvetica (Arial)14号FULL First Author1, a, FULL Second Author2,b and Last Author3,c 第一第二第三作者的全名1Full address of first author, including country第一作者的地址全名，包括国家2Full address of second author, including country第二作者的地址全名，包括国家3List all distinct addresses in the same way第三作者同上aemail, bemail, cemail第一第二第三作者的邮箱地址Keywords: List the keywords covered in your paper. These keywords will also be used by the publisher to produce a keyword index.关键字: 列出你论文中的关键词。

这些关键词将会被出版者用作制作一个关键词索引。

For the rest of the paper, please use Times Roman (Times New Roman) 12论文的其他部分请用Times Roman (Times New Roman) 12号字Abstract. This template explains and demonstrates how to prepareyour camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.Please make the page settings of your word processor to A4 format(21 x 29,7 cm or 8 x 11 inches); with the margins: bottom 1.5 cm (0.59 in) and top 2.5 cm (0.98 in), right/left margins must be 2 cm (0.78 in).摘要:这个模板解释和示范供稿技术刊物有限公司时，如何准备你的供相机使用文件。

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］。

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Key Words: Cluster ; Principal Component Analysis ; AHP ; System Dynamics
2
Team # 34040
Page 3 of 24
Contents
1 Introduction 1.1 1.2 Problem Restatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 1.2.2 1.2.3 2 Models 2.1 Part One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 2.1.2 2.2 Clustering Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . Part One . . . . . . .. . . . . . . . . . . . . . . . . . . . Part Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part Three . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 4 4 4 5 6 6 6 7 11 11 14 15 17 18 21 21 21 22 22 23 23 24
Team Control Number For ofﬁce use only T1 T2 T3 T4
34040
Problem Chosen
For ofﬁce use only F1 F2 F3 F4
D
2015 Mathematical Contest in Modeling (MCM) Summary Sheet (Attach a copy of this page to each copy of your solution paper.)
Part Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 2.2.2 2.2.3 2.2.4 Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Abstract
Sustainable development is a topic full of relativity. So, it’s unwise to give a constant boundary to judge a country is sustainable or not. We came up with the dynamic evaluation method to solve this problem. First of all, select some indexes of sustainable development. With these indexes, we do cluster analysis for the selected countries. Then we can get the sustainable development and the unsustainable development. Next, we choose sustainable countries as the sample of Principal Component Analysis in order to analyze the key elements of sustainable development, and ﬁnally, we got the evaluation function and obtained the evaluation index. After that,we chose Bangladesh as research target.Through the analysis of the data, we found there are many serious problems in Bangladesh, including the population problem, the education problem, the environmental problem and so on.According to previous research, we obtained the variables which have a significant impact on the sustainable development. Then use AHP to analyze them one by one, and give our suggestions respectively, in order to plan a better future of Bangladesh. Considering that various factors are interrelated, one change of them may cause a chain reaction. For example, population growth will not only cause ﬁnancial burden, but also put pressure on environment or natural resources. To solve this problem, we use System dynamics model, which represent causal relationship and help us clearly understand variation trend. With this, we can change some parameter to observe the process of changing and catch some crucial factors.Bangladesh’s geographical location decides that its development will be greatly affected by environmental factors. Ultimately, we analyze four major indicators with target.
Sustainable Development
Abstract Sustainable development is a topic full of relativity. So, it’s unwise to give a constant boundary to judge a country is sustainable or not. We came up with the dynamic evaluation method to solve this problem. First of all, select some indexes of sustainable development. With these indexes, we do cluster analysis for the selected countries. Then we can get the sustainable development and the unsustainable development. Next, we choose sustainable countries as the sample of Principal Component Analysis in order to analyze the key elements of sustainable development, and ﬁnally, we got the evaluation function and obtained the evaluation index. After that,we chose Bangladesh as research target.Through the analysis of the data, we found there are many serious problems in Bangladesh, including the population problem, the education problem, the environmental problem and so on.According to previous research, we obtained the variables which have a significant impact on the sustainable development. Then use AHP to analyze them one by one, and give our suggestions respectively, in order to plan a better future of Bangladesh. Considering that various factors are interrelated, one change of them may cause a chain reaction. For example, population growth will not only cause ﬁnancial burden, but also put pressure on environment or natural resources. To solve this problem, we use System dynamics model, which represent causal relationship and help us clearly understand variation trend. With this, we can change some parameter to observe the process of changing and catch some crucial factors.Bangladesh’s geographical location decides that its development will be greatly affected by environmental factors. Ultimately, we analyze four major indicators with target.