美赛-数学建模-写作模版(最为详细的)
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。
美赛：全国大学生数学建模竞赛论文格式规范---论文写作规范
全国大学生数学建模竞赛论文格式规范●本科组参赛队从A、B题中任选一题，专科组参赛队从C、D题中任选一题。
（全国评奖时，每个组别一、二等奖的总名额按每道题参赛队数的比例分配；但全国一等奖名额的一半将平均分配给本组别的每道题，另一半按每题论文数的比例分配。
）●论文用白色A4纸打印；上下左右各留出至少2.5厘米的页边距；从左侧装订。
●论文第一页为承诺书，具体内容和格式见本规范第二页。
●论文第二页为编号专用页，用于赛区和全国评阅前后对论文进行编号，具体内容和格式见本规范第三页。
●论文题目、摘要和关键词写在论文第三页上（无需译成英文），并从此页开始编写页码；页码必须位于每页页脚中部，用阿拉伯数字从“1”开始连续编号。
注意：摘要应该是一份简明扼要的详细摘要，请认真书写（但篇幅不能超过一页）。
●从第四页开始是论文正文（不要目录）。
论文不能有页眉或任何可能显示答题人身份和所在学校等的信息。
●论文应该思路清晰，表达简洁（正文尽量控制在20页以内，附录页数不限）。
●引用别人的成果或其他公开的资料(包括网上查到的资料) 必须按照规定的参考文献的表述方式在正文引用处和参考文献中均明确列出。
正文引用处用方括号标示参考文献的编号，如[1][3]等；引用书籍还必须指出页码。
参考文献按正文中的引用次序列出，其中书籍的表述方式为：[编号] 作者，书名，出版地：出版社，出版年。
参考文献中期刊杂志论文的表述方式为：[编号] 作者，论文名，杂志名，卷期号：起止页码，出版年。
参考文献中网上资源的表述方式为：[编号] 作者，资源标题，网址，访问时间（年月日）。
●在论文纸质版附录中，应给出参赛者实际使用的软件名称、命令和编写的全部计算机源程序（若有的话）。
同时，所有源程序文件必须放入论文电子版中备查。
论文及源程序电子版压缩在一个文件中，一般不要超过20MB，且应与纸质版同时提交。
（如果发现程序不能运行，或者运行结果与论文中报告的不一致，该论文可能会被认定为弄虚作假而被取消评奖资格。
建模美赛获奖范文
建模美赛获奖范文全文共四篇示例，供读者参考第一篇示例：近日，我校数学建模团队在全国大学生数学建模竞赛中荣获一等奖的喜讯传来，这是我校首次在该比赛中获得如此优异的成绩。
本文将从建模过程、团队合作、参赛经验等方面进行详细介绍，希望能为更多热爱数学建模的同学提供一些借鉴和参考。
让我们来了解一下比赛的背景和要求。
全国大学生数学建模竞赛是由中国工程院主办，旨在促进大学生对数学建模的兴趣和掌握数学建模的基本方法和技巧。
比赛通常会设置一些实际问题，参赛队伍需要在规定时间内通过建立数学模型、分析问题、提出解决方案等步骤来完成任务。
最终评选出的优胜队伍将获得一等奖、二等奖等不同级别的奖项。
在本次比赛中，我们团队选择了一道关于城市交通拥堵研究的题目，并从交通流理论、路网优化等角度进行建模和分析。
通过对城市交通流量、拥堵原因、路段限制等方面的研究，我们提出了一种基于智能交通系统的解决方案，有效缓解了城市交通拥堵问题。
在展示环节，我们通过图表、数据分析等方式清晰地呈现了我们的建模过程和成果，最终赢得了评委的认可。
在整个建模过程中，团队合作起着至关重要的作用。
每个成员都发挥了自己的专长和优势，在分析问题、建模求解、撰写报告等方面各司其职。
团队内部的沟通和协作非常顺畅，大家都能积极提出自己的想法和看法，达成共识后再进行实际操作。
通过团队合作，我们不仅完成了比赛的任务，也培养了团队精神和合作能力，这对我们日后的学习和工作都具有重要意义。
参加数学建模竞赛是一次非常宝贵的经历，不仅能提升自己的数学建模能力，也能锻炼自己的解决问题的能力和团队协作能力。
在比赛的过程中，我们学会了如何快速建立数学模型、如何分析和解决实际问题、如何展示自己的成果等，这些能力对我们未来的学习和工作都将大有裨益。
在未来，我们将继续努力，在数学建模领域不断学习和提升自己的能力，为更多的实际问题提供有效的数学解决方案。
我们也希望通过自己的经验和教训，为更多热爱数学建模的同学提供一些指导和帮助，共同进步，共同成长。
数学建模美赛论文格式中文版Word版
你的论文需要从此开始请居中使用Arial14字体第一作者，第二作者和其他（使用Arial14字体）1.第一作者的详细地址，包括国籍和email(使用Arial11)2.第二作者的详细地址，包括国籍和email(使用Arial11)3.将所有的详细信息标记为相同格式关键词列出文章的关键词。
这些关键词会被出版方用作关键词索引(使用Arial11字体）论文正文使用Times New Roman12字体摘要这一部分阐述说明了如何为TransTechPublications.准备手稿。
最好阅读这些用法说明并且整篇论文都是遵照这个提纲。
手稿的正文部分应该是17cm*25cm（宽*高）的格式（或者是6.7*9.8英尺）。
请不要在这个区域以外书写。
请使用21*29厘米或8*11英尺的质量较好的白纸。
你的手稿可能会被出版商缩减20%。
在制图和绘表格时候请特别注意这些准则。
引言所有的语言都应该是英语。
请备份你的手稿（以防在邮寄过程中丢失）我们收到手稿即默认为原作者允许我们在期刊和书报出版。
如果作者在论文中使用了其他刊物中的图表，他们需要联系原作者，获取使用权。
将单词或词组倾斜以示强调。
除了每一部分的标题（标记部分的标题），不要加粗正文或大写首字母。
使用激光打印机，而不是点阵打印机正文的组织：小标题小标题应该加粗并注意字母的大小写。
第二等级的小标题被视为后面段落的一部分（就像这一大段的一小部分的开头）页码不要打印页码。
请用淡蓝色铅笔在每一张纸的左下角（在打印区域以外）标注数字。
脚注脚注应该单独放置并且和正文分开理想地情况下，脚注应该出现在参考文献页，并且放在文章的末尾，和正文用分割线分开。
表格表格（如表一，表二，...）应该放在正文当中，是正文的一部分，但是，要避免文本混乱。
一个描述性的表格标题要放在图表的下方。
标题应该独立的放在表格的下方或旁边。
表中的单位应放在中括号中[兆伏]如果中括号不可用，需使用大括号{兆}或小括号（兆)。
美国大学生数学建模大赛英文写作
写作要求 ： 1. 简短 论文标题一般在10个字内，最多不超 过15个词。
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 。
关键词（Keywords)
基本功能：顾名思义；便于检索 语言特点：多用名词；字数有限（4-6）； 出处明确 写作要求 :论文的关键字一般列在作者与单 位之下，论文摘要之上。也有列在论文摘 要之下的。关键词除第一个字母大写外， 一般不要求大写。关键词间用逗号、分号 或大间隔隔开。最末一个关键词一般不加 用逗号、分号或句号。
美赛格式要求范文
美赛格式要求范文美赛（MCM/ICM）是美国大学生数学建模竞赛的英文缩写，是一项面向全球大学生的数学建模竞赛。
MCM/ICM每年提供若干个实际问题供参赛者选择，并规定参赛者提交一份由三人组成的队伍作品，要求队伍在规定的时间内解答问题并撰写一篇报告。
以下是美赛格式的一般要求：1.报告页数要求：参赛队伍通常需要撰写一篇1200字以上的报告。
具体的页数要求可以根据不同的问题和竞赛要求略有变化，但一般不超过20页。
尽管有页数限制，但在撰写报告时需要全面、清晰地阐述问题、解决方法和结论。
2.章节结构：一篇标准的美赛报告通常包括以下几个部分：-引言：介绍问题的背景和目的，明确解决问题的方法和目标。
-问题分析：对问题进行深入的分析和理解，包括重新表述问题、提出假设和限制条件，展开问题讨论。
-模型建立：建立一个或多个数学模型，以解决问题。
需要解释模型背后的理论基础和假设，并给出模型的描述和方程。
-模型求解：详细描述解决模型的方法、步骤和计算过程。
需要标注具体的计算公式、算法、图表和详细的计算结果。
-结果分析：对所得结果进行详细的解释和分析，包括结果的合理性和局限性，对模型的优缺点进行评价。
-结论与建议：总结所得结论，并提出可能的进一步研究方向和改进建议。
3.图表和数学符号的使用：美赛报告通常需要使用多个图表和数学符号，以支持和解释问题的分析和解决方法。
图表应该清晰、简洁，并配有必要的标注和说明。
数学符号应该统一、准确地使用，避免造成混淆。
5.语言表达：报告应使用准确、简练、清晰的语言表达问题、论证思路和解决方案。
语法、拼写和标点符号应正确无误。
尽管以上是一般的美赛报告要求，但具体的格式要求可能会因竞赛规则和题目的特殊性而有所不同。
建议参赛队伍在参赛前详细了解官方提供的竞赛规则和报告要求，并遵循官方给出的指导进行撰写报告。
同时，可以参考以往的优秀报告和获奖队伍的经验，借鉴其写作技巧和结构。
数学建模美赛写作各部分模板
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 small farms, 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：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 the engineering parameters of sprinklers available in the market.数学建模美赛论文例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。
美赛-数学建模-写作模板课件-摘要
使用专业术语
摘要中应使用与论文主题 相关的专业术语，以体现 论文的专业性和深度。
突出关键词
摘要中应突出关键词，以 便读者快速了解论文的主 题和主要内容。
突出重点
强调研究目的
摘要应明确指出研究的目 的和目标，以及研究的重 要性和意义。
突出主要发现
摘要中应突出论文的主要 发现或结论，以引起读者 的兴趣和好奇心。
强调研究方法
对于实验或实证研究，摘 要中应简要介绍研究方法， 以增加论文的可信度和说 服力。
保持连贯性
逻辑清晰
使用过渡句
摘要的逻辑应清晰，各部分内容之间 应相互衔接，形成一个完整的整体。
在摘要的不同部分之间，应使用过渡 句来连接，以增强摘要的连贯性和流 畅性。
结构完整
摘要应包含引言、方法、结果和结论 等部分，以确保内容的完整性和连贯 性。
帮助编辑和审稿人评估文章
总结和概括整篇文章
摘要也是编辑和审稿人在评估文章是否适 合发表或是否值得审稿时的重要依据。
摘要需要对整篇文章或报告的内容进行总 结和概括，因此需要作者对文章或报告有 深入的理解和把握。
02 摘要的写作技巧
精炼语言
01
02
03
避免冗余和重复
摘要应简洁明了，避免使 用过多的修饰语和重复的 表述。
精炼内容
删除不必要的描述，突出重点， 使摘要更加紧凑。
调整结构
合理安排摘要的逻辑结构，使其 条理清晰、层次分明。
05 摘要的示例与点评
优秀摘要示例
摘要应简明扼要地概括整个论文 的主要内容和结论，包括问题定 义、模型建立、求解方法和主要
结果。
优秀摘要应具有清晰的结构，使 用简洁明了的语言，避免冗长和
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。
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。
美赛数学建模比赛论文资料材料模板
The Keep-Right-Except-To-Pass RuleSummaryAs for the first question, it provides a traffic rule of keep right except to pass, requiring us to verify its effectiveness. Firstly, we define one kind of traffic rule different from the rule of the keep right in order to solve the problem clearly; then, we build a Cellular automaton model and a Nasch model by collecting massive data; next, we make full use of the numerical simulation according to several influence factors of traffic flow; At last, by lots of analysis of graph we obtain, we indicate a conclusion as follow: when vehicle density is lower than 0.15, the rule of lane speed control is more effective in terms of the factor of safe in the light traffic; when vehicle density is greater than 0.15, so the rule of keep right except passing is more effective In the heavy traffic.As for the second question, it requires us to testify that whether the conclusion we obtain in the first question is the same apply to the keep left rule. First of all, we build a stochastic multi-lane traffic model; from the view of the vehicle flow stress, we propose that the probability of moving to the right is 0.7and to the left otherwise by making full use of the Bernoulli process from the view of the ping-pong effect, the conclusion is that the choice of the changing lane is random. On the whole, the fundamental reason is the formation of the driving habit, so the conclusion is effective under the rule of keep left.As for the third question, it requires us to demonstrate the effectiveness of the result advised in the first question under the intelligent vehicle control system. Firstly, taking the speed limits into consideration, we build a microscopic traffic simulator model for traffic simulation purposes. Then, we implement a METANET model for prediction state with the use of the MPC traffic controller. Afterwards, we certify that the dynamic speed control measure can improve the traffic flow .Lastly neglecting the safe factor, combining the rule of keep right with the rule of dynamical speed control is the best solution to accelerate the traffic flow overall.Key words：Cellular automaton model Bernoulli process Microscopic traffic simulator model The MPC traffic controlContentContent (2)1. Introduction (3)2. Analysis of the problem (3)3. Assumption (3)4. Symbol Definition (3)5. Models (3)5.1 Building of the Cellular automaton model (3)5.1.1 Verify the effectiveness of the keep right except to pass rule (4)5.1.2 Numerical simulation results and discussion (5)5.1.3 Conclusion (8)5.2 The solving of second question (8)5.2.1 The building of the stochastic multi-lane traffic model (8)5.2.2 Conclusion (8)5.3 Taking the an intelligent vehicle system into a account (8)5.3.1 Introduction of the Intelligent Vehicle Highway Systems (9)5.3.2 Control problem (9)5.3.3 Results and analysis (9)5.3.4 The comprehensive analysis of the result (9)6. Improvement of the model (10)6.1 strength and weakness (10)6.1.1 Strength (10)6.1.2 Weakness (10)6.2 Improvement of the model (10)7. Reference (12)1. IntroductionAs is known to all, it ’s essential for us to drive automobiles, thus the driving rules is crucial important. In many countries like USA, China, drivers obey the rules which called “The Keep-Right-Except-To-Pass (that is, when driving automobiles, the rule requires drivers to drive in the right-most unless they are passing another vehicle)”.2. Analysis of the problemFor the first question, we decide to use the Cellular automaton to build models, then analyze the performance of this rule in light and heavy traffic. Firstly, we mainly use the vehicle density to distinguish the light and heavy traffic; secondly, we consider the traffic flow and safe as the represent variable which denotes the light or heavy traffic; thirdly, we build and analyze a Cellular automaton model; finally, we judge the rule through two different driving rules, and then draw conclusions.3. AssumptionIn order to streamline our model we have made several key assumptions● The highway of double row three lanes that we study can representmulti-lane freeways.● The data that we refer to has certain representativeness and descriptive● Operation condition of the highway not be influenced by blizzard or accidental factors ● Ignore the driver's own abnormal factors, such as drunk driving and fatigue driving ● The operation form of highway intelligent system that our analysis can reflectintelligent system● In the intelligent vehicle system, the result of the sampling data has high accuracy.4. Symbol Definitioni The number of vehiclest The time5. ModelsBy analyzing the problem, we decided to propose a solution with building a cellular automaton model.5.1 Building of the Cellular automaton modelThanks to its simple rules and convenience for computer simulation, cellular automaton model has been widely used in the study of traffic flow in recent years.Let )(t x i be the position of vehicle i at time t , )(t v i be the speed of vehicle i at time t ,p be the random slowing down probability, and R be the proportion of trucks and buses, the distance between vehicle i and the front vehicle at time t is:1)()(1--=-t x t x gap i i i , if the front vehicle is a small vehicle.3)()(1--=-t x t x gap i i i , if the front vehicle is a truck or bus.5.1.1 Verify the effectiveness of the keep right except to pass ruleIn addition, according to the keep right except to pass rule, we define a new rule called: Control rules based on lane speed. The concrete explanation of the new rule as follow:There is no special passing lane under this rule. The speed of the first lane (the far left lane) is 120–100km/h (including 100 km/h)；the speed of the second lane (the middle lane) is 100–80km8/h (including80km/h)；the speed of the third lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from left to right.● Lane changing rules based lane speed controlIf vehicle on the high-speed lane meets control v v <, ),1)(min()(max v t v t gap i f i +≥, safe b i gap t gap ≥)(, the vehicle will turn into the adjacent right lane, and the speed of the vehicle after lane changing remains unchanged, where control v is the minimum speed of the corresponding lane.● The application of the Nasch model evolutionLet d P be the lane changing probability (taking into account the actual situation that some drivers like driving in a certain lane, and will not take the initiative to change lanes), )(t gap f i indicates the distance between the vehicle and the nearest front vehicle, )(t gap b i indicates the distance between the vehicle and the nearest following vehicle. In this article, we assume that the minimum safe distance gap safe of lane changing equals to the maximum speed of the following vehicle in the adjacent lanes.● Lane changing rules based on keeping right except to passIn general, traffic flow going through a passing zone (Fig. 5.1.1) involves three processes: the diverging process (one traffic flow diverging into two flows), interacting process (interacting between the two flows), and merging process (the two flows merging into one)[4].Fig.5.1.1 Control plan of overtaking process(1) If vehicle on the first lane (passing lane) meets ),1)(min()(max v t v t gap i f i +≥ and safe b i gap t gap ≥)(, the vehicle will turn into the second lane, the speed of the vehicle after lane changing remains unchanged.5.1.2 Numerical simulation results and discussionIn order to facilitate the subsequent discussions, we define the space occupation rate as L N N p truck CAR ⨯⨯+=3/)3(, where CAR N indicates the number of small vehicles on the driveway,truck N indicates the number of trucks and buses on the driveway, and L indicates the total length of the road. The vehicle flow volume Q is the number of vehicles passing a fixed point per unit time,T N Q T /=, where T N is the number of vehicles observed in time duration T .The average speed ∑∑⨯=T it i a v T N V 11)/1(, t i v is the speed of vehicle i at time t . Take overtaking ratio f p as the evaluation indicator of the safety of traffic flow, which is the ratio of the total number of overtaking and the number of vehicles observed. After 20,000 evolution steps, and averaging the last 2000 steps based on time, we have obtained the following experimental results. In order to eliminate the effect of randomicity, we take the systemic average of 20 samples [5].Overtaking ratio of different control rule conditionsBecause different control conditions of road will produce different overtaking ratio, so we first observe relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.(a) Based on passing lane control (b) Based on speed controlFig.5.1.3Fig.5.1.3Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions.It can be seen from Fig. 5.1.3:(1) when the vehicle density is less than 0.05, the overtaking ratio will continue to rise with the increase of vehicle density; when the vehicle density is larger than 0.05, the overtaking ratio will decrease with the increase of vehicle density; when density is greater than 0.12, due to the crowding, it will become difficult to overtake, so the overtaking ratio is almost 0.(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with the increase of large vehicles; when the proportion of large vehicles is about 0.5, the overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than 0.5, the overtaking ratio will decrease with the increase of large vehicles, especially under lane-based control condition s the decline is very clear.Concrete impact of under different control rules on overtaking ratioFig.5.1.4Fig.5.1.4 Relationships among vehicle density, proportion of large vehicles and overtaking ratio under different control conditions. (Figures in left-hand indicate the passing lane control, figures in right-hand indicate thespeed control. 1f P is the overtaking ratio of small vehicles over large vehicles, 2f P is the overtaking ratio ofsmall vehicles over small vehicles, 3f P is the overtaking ratio of large vehicles over small vehicles, 4f P is the overtaking ratio of large vehicles over large vehicles.).It can be seen from Fig. 5.1.4:(1) The overtaking ratio of small vehicles over large vehicles under passing lane control is much higher than that under speed control condition, which is because, under passing lane control condition, high-speed small vehicles have to surpass low-speed large vehicles by the passing lane, while under speed control condition, small vehicles are designed to travel on the high-speed lane, there is no low- speed vehicle in front, thus there is no need to overtake. ● Impact of different control rules on vehicle speedFig. 5.1.5 Relationships among vehicle density, proportion of large vehicles and average speed under different control conditions. (Figures in left-hand indicates passing lane control, figures in right-hand indicates speed control. a X is the average speed of all the vehicles, 1a X is the average speed of all the small vehicles, 2a X is the average speed of all the buses and trucks.).It can be seen from Fig. 5.1.5:(1) The average speed will reduce with the increase of vehicle density and proportion of large vehicles.(2) When vehicle density is less than 0.15,a X ,1a X and 2a X are almost the same under both control conditions.● Effect of different control conditions on traffic flowFig.5.1.6Fig. 5.1.6Relationships among vehicle density, proportion of large vehicles and traffic flow under different control conditions. (Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b indicates the traffic flow difference between the two conditions.It can be seen from Fig. 5.1.6：(1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0.4 to 1, the traffic flow of the two control conditions are basically the same.(2) Except that, the traffic flow under passing lane control condition is slightly larger than that of speed control condition.5.1.3 ConclusionIn this paper, we have established three-lane model of different control conditions, studied the overtaking ratio, speed and traffic flow under different control conditions, vehicle density and proportion of large vehicles.5.2 The solving of second question5.2.1 The building of the stochastic multi-lane traffic model5.2.2 ConclusionOn one hand, from the analysis of the model, in the case the stress is positive, we also consider the jam situation while making the decision. More specifically, if a driver is in a jam BP(situation, applying ))results with a tendency of moving to the right lane for this,2(xRdriver. However in reality, drivers tend to find an emptier lane in a jam situation. For this reason, we apply a Bernoulli process )7.0,2(B where the probability of moving to the right is 0.7and to the left otherwise, and the conclusion is under the rule of keep left except to pass, So, the fundamental reason is the formation of the driving habit.5.3 Taking the an intelligent vehicle system into a accountFor the third question, if vehicle transportation on the same roadway was fully under the control of an intelligent system, we make some improvements for the solution proposed by usto perfect the performance of the freeway by lots of analysis.5.3.1 Introduction of the Intelligent Vehicle Highway SystemsWe will use the microscopic traffic simulator model for traffic simulation purposes. The MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the states when the speed limits are applied in Fig.5.3.1. We implement a METANET model for prediction purpose[14].5.3.2 Control problemAs a constraint, the dynamic speed limits are given a maximum and minimum allowed value. The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For the calculation of the optimal control values, all speed limits are constrained to this range. When the optimal values are found, they are rounded to a multiplicity of 10 km/h, since this is more clear for human drivers, and also technically feasible without large investments.5.3.3 Results and analysisWhen the density is high, it is more difficult to control the traffic, since the mean speed might already be below the control speed. Therefore, simulations are done using densities at which the shock wave can dissolve without using control, and at densities where the shock wave remains. For each scenario, five simulations for three different cases are done, each with a duration of one hour. The results of the simulations are reported in Table5.1, 5.2, 5.3.●Enforced speed limits●Intelligent speed adaptationFor the ISA scenario, the desired free-flow speed is about 100% of the speed limit. The desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100% of the speed limit, and a standard deviation of 5% of the speed limit. Based on this percentage, the influence of the dynamic speed limits is expected to be good[19].5.3.4 The comprehensive analysis of the resultFrom the analysis above, we indicate that adopting the intelligent speed control system can effectively decrease the travel times under the control of an intelligent system, in other words, the measures of dynamic speed control can improve the traffic flow.Evidently, under the intelligent speed control system, the effect of the dynamic speed control measure is better than that under the lane speed control mentioned in the first problem. Becauseof the application of the intelligent speed control system, it can provide the optimal speed limit in time. In addition, it can guarantee the safe condition with all kinds of detection device and the sensor under the intelligent speed system.On the whole, taking all the analysis from the first problem to the end into a account, when it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed control system.Thus, under the state of the light traffic, we propose a new conclusion different from that in the first problem: the rule of keep right except to pass is more effective than that of lane speed control.And when it is in the heavy traffic, for sparing no effort to improve the operation efficiency of the freeway, we combine the dynamical speed control measure with the rule of keep right except to pass, drawing a conclusion that the application of the dynamical speed control can improve the performance of the freeway.What we should highlight is that we can make some different speed limit as for different section of road or different size of vehicle with the application of the Intelligent Vehicle Highway Systems.In fact, that how the freeway traffic operate is extremely complex, thereby, with the application of the Intelligent Vehicle Highway Systems, by adjusting our solution originally, we make it still effective to freeway traffic.6. Improvement of the model6.1 strength and weakness6.1.1 Strength●it is easy for computer simulating and can be modified flexibly to consider actual trafficconditions ,moreover a large number of images make the model more visual.●The result is effectively achieved all of the goals we set initially, meantime the conclusion ismore persuasive because of we used the Bernoulli equation.●We can get more accurate result as we apply Matlab.6.1.2 Weakness●The relationship between traffic flow and safety is not comprehensively analysis.●Due to there are many traffic factors, we are only studied some of the factors, thus ourmodel need further improved.6.2 Improvement of the modelWhile we compare models under two kinds of traffic rules, thereby we come to the efficiency of driving on the right to improve traffic flow in some circumstance. Due to the rules of comparing is too less, the conclusion is inadequate. In order to improve the accuracy, Wefurther put forward a kinds of traffic rules: speed limit on different type of cars.The possibility of happening traffic accident for some vehicles is larger, and it also brings hidden safe troubles. So we need to consider separately about different or specific vehicle types from the angle of the speed limiting in order to reduce the occurrence of traffic accidents, the highway speed limit signs is in Fig.6.1.Fig.6.1Advantages of the improving model are that it is useful to improve the running condition safety of specific type of vehicle while considering the difference of different types of vehicles. However, we found that the rules may be reduce the road traffic flow through the analysis. In the implementation it should be at the85V speed of each model as the main reference basis. Inrecent years, the85V of some researchers for the typical countries from Table 6.1[ 21]:Author Country ModelOttesen andKrammes2000America LCDCLDCVC⨯---=01.0012.057.144.10285Andueza2000 Venezuela].[308.9486.7)/894()/2795(25.9885curvehorizontalLDCRaRVT++--=].[tan819.27)/3032(69.10085gentLRVT+-=Jessen2001 America][00239.0614.0279.080.86185LSDADTGVVP--+=][00212.0432.010.7285NLSDADTVVP-+=Donnell2001 America22)2(8500724.040.10140.04.78TLGRV--+=22)3(85008369.048.10176.01.75TLGRV--+=22)4(8500810.069.10176.05.74TLGRV--+=22)5(8500934.008.21.83TLGV--=BucchiA.BiasuzziK.And SimoneA.2005 ItalyDCV124.0164.6685-=DCEV4.046.3366.5585--=Meanwhile, there are other vehicles driving rules such as speed limit in adverse weather conditions. This rule can improve the safety factor of the vehicle to some extent. At the same time, it limits the speed at the different levels.7. Reference[1] M. Rickert, K. Nagel, M. Schreckenberg, A. Latour, Two lane traffic simulations usingcellular automata, Physica A 231 (1996) 534–550.[20] J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffic Management and Control inIntelligent Vehicle Highway Systems,18(2009).[21] Yang Li, New Variable Speed Control Approach for Freeway. (2011) 1-66。
【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。
美赛-数学建模-写作模版(各部分)讲课稿
美赛-数学建模-写作模版(各部分)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。
数学建模美赛写作模版(包含摘要、格式、总结、表格、公式、图表、假设)
论文reference 格式中文解说版总体要求1 正文中引用的文献与文后的文献列表要完全一致.ν文中引用的文献可以在正文后的文献列表中找到；文献列表的文献必须在正文中引用。
2 文献列表中的文献著录必须准确和完备。
3 文献列表的顺序文献列表按著者姓氏字母顺序排列；姓相同,按名的字母顺序排列；著者姓和名相同，按出版年排列。
νν相同著者，相同出版年的不同文献，需在出版年后面加a、b、c、d……来区分，按文题的字母顺序排列。
如: Wang, M. Y。
（2008a). Emotional……Wang, M。
Y。
(2008b). Monitor……Wang，M。
Y. (2008c). Weakness……4 缩写chap. chapter 章ed。
edition 版Rev. ed。
revised edition 修订版2nd ed. second edition 第2版Ed. (Eds。
）Editor （Editors）编Trans. Translator（s) 译n.d. No date 无日期p。
(pp。
）page （pages）页Vol. Volume (as in Vol。
4) 卷vols。
volumes （as in 4 vols.）卷No。
Number 第Pt。
Part 部分Tech. Rep. Technical Report 技术报告Suppl. Supplement 增刊5 元分析报告中的文献引用ν元分析中用到的研究报告直接放在文献列表中，但要在文献前面加星号＊。
并在文献列表的开头就注明*表示元分析用到的的文献。
正文中的文献引用标志在著者—出版年制中，文献引用的标志就是“著者”和“出版年”，主要有两种形式：（1）正文中的文献引用标志可以作为句子的一个成分，如：Dell（1986）基于语误分析的结果提出了音韵编码模型，…….汉语词汇研究有庄捷和周晓林（2001）的研究。
（2)也可放在引用句尾的括号中，如:在语言学上，音节是语音结构的基本单位，也是人们自然感到的最小语音片段。
数模美赛论文模板
内容格式：AbstractIntroductionAssumptionsAnalysis of the problemTask 1 : predicting survivorshipTask2 : achieving stability….Sensitivity analysisStrengthsWeaknessesConclusionReferencesTitle(use Arial 14)First author , second author , the other (use Arial 14)Full address of first author . Including country and mail(use Arial 11)Full address of second author . Including country and mailList all distinct addresses in the same wayKeywords(use Arial 11)Abstract1985:模型概述-考虑因素-使用理由We modelled …. Since … – we used …. We included …which were to be chosen in order to …假设条件-数据处理方法We assumed that…We used actual data to estimate realistic ranges on the parameters in the model.评估标准-衡量方法-得到结论-结论的可靠性We defined…We then used …we found …We examined the results for different values of the mortality parameters and found them to be the same . Therefore ,our solution appears to be stable with respect to environmental conditions.2000:背景设置-模型引入…in order to determine …, we develop models using…解决问题-模型解决（层次排比）For the solution of …, we develop… model based … to … . For the solution of … , we employ … What is more , a self-adaptive traffic light is employed to … according to …模型检验-模型修正By comparison of … simulation results , the models are evaluated . …is formulated to judge which solution is effective .2002:The task is to … we begin by constructing a model of … base on … Using this model we can … Using… , we model … through … and obtain … we compare the performance of our model in … simulations show that …2001:We examine the … . Such evacuations been required due to … . in order to … , we begin with an analysis of … . For a more realistic estimate , including the effects of … , we formulate models of … . The model we construct is based on … .This model leads to a … and it further show that … what’ more , it agrees with …2004:（修正递进式模型摘要模板）The purpose of this paper is to propose … . We propose that … . To build a solid foundation , we define and test a simple model for … . We then develop … system , but we find it would be far from optimal in practice . We then propose that the best model is one that adapts to … . We implement … . We simulate the … with … and we find this system quickly converges to a nearly optimal solution subject to our constraints . It is , however , sensitive to some parameters . We discuss the effects of these findings on the expected effectiveness of the system in a real environment . We conclude that … is a good solution .问题分析句式：… is a real-life common phenomenon with many complexities .For a better view of … , we …To give a clear expression, we will introduce the method presented by …模型引入句式：In this paper , we present … model to simulate efficient methods for …We also apply … methods to solve …We address the problem of …. through ….We formulate the problem as …We formulate a … model to account for …Base on … , we establish a model ….We build a model to determine …We modify the model to reflect …To provide a more complete account for … , ... model has been employed .In this paper , in order to … , we design a … model based on …We propose a solution that …We have come up with an … for … andStrong evidence of ... , and powerful models have been created to estimate ...模型推进：… will scale up to an effective model for …模型求解：We employ … , one based on … and the other … , whose results agree closely.To combat this , we impose …结合数据：Using data from … , we determine …To ground this model in reality , we incorporate extensive demographic data ….We use data assembled by …Using a wide scale regression , we found that …We extrapolate from longevity data and explore the long-term behavior of …The base we developed was based off real-life data that gathered by …We estimate these characteristic numbers for a representative sample of …We fit the modified model to data , we conclude that …By statistical processing to results of …By analyzing the … on the basis of historic data in the same way mentioned in …结果给出句式：Results of this computation are presented , and ….We elicit that a conclusion …We conclude with a series of recommendations for …Given a … deviation in the value of the parameter , we calculate the percentage change in the value that the system converges to …As we can find out , in the situation of …. , …. is subject to the logistic regression .We conclude through analyzing that ….it is apparent that …Through comparing the … , we conclude that …According to the laws of … , we draw a conclusion of …From the formula , we know that …Thus we arrive at the conclusion :We elicit that a conclusion …As a consequence , we can get …模型可行性：Our suggested solution , which is easy to ….Since our model is based on … it can be applied to …Importantly , we use some practical data to test our model and analysis its stability , we simulate this model and receive a well effect .Therefore , we trust this model as an accurate testing ground for …Our algorithm is broad enough to accommodate various …定理可靠说明：That is the theoretical basis for … in many application areas .模型简化With further simplification, utilizing … we can reach …承上启下：In addition to the model , we also discuss …Because the movement of … operates by the same laws and equations as the movement of … , we can ….Based on the above discussion, considering …., let’s …误差句式：… does not deviate more than … from the target value .Theoretically , error due to … should not play a tremendous role under our model .Up to this point , we have made many approximations , not all of which are justified theoretically , but the results of algorithm are quite reasonable .This is a naïve approach which may mot ensure the …. , however if we … , the error is negligible .Context:方程给出：We derive the equation expressing the … as a function of… we haveA simple formula determined by the … is given by the equation :… can be written as the following system of equations :In particular , the … is defined in terms of … ,It is convenient to rewrite equations into the vector form:The expression of … can be expanded as …Equation (1) is reduced to ..Substitute the values into equation (1) ,we get …So its expression can be derived from equation (1) with small changes .Our results are summarized in the formula for …Plugging (1) into the equation for (2) , we obtain …Therefore , from (1)(2)(3) , we have the junction that …We use the following initial conditions to determine …When computing , we suppose … ,so this suppose doesn’t … ,then by … , we can get :According to equation (1)(2) , we can eliminate … ,then we can acquire :By connecting equation (6)(7) , we get the conclusion that …Then we can acquire … through the following equation :Its solution is the following …, in which … is …客观条件引入：A commonly accepted fact is that …A lot of research has been done to explain and find …In our model , we prefer to follow the conclusion used by …Here , we cite the model constructed by …There is one paper from … ,which concluded that …We get performance of … by citing the experimental results of …Here, we will introduce some terms used to address the problem, and we …方法给出句式：We construct … intelligent algorithms , a conservative approach , and an enthusiastic system to ..We formulate a simplified differential equation governing …This equation will be based on …The above considerations lead us to formulate the … asGiven this , it is easy to determine …To analyze the accuracy of our model , and determine a reasonable value for …We will evaluate the performance of our … by …We tabulate the … as a function of …Analysis for the … can be carried out exactly in the same fashion as …The main goal in attempting to model … is to determine … and … should be considered .The first requirement that the model reproduce is to determine if the model is reasonable .We begin our analysis of the phenomenon of congestion with the question of …In modeling this behavior , we begin with …In laying down the mathematics of this model , we begin with …When … is not taken into account ,it is …We give the criterion that …We fix A and examine the change of B with respect to CAttention has been draw to determine …To reveal the trend of … in a long horizonTo deal with the problem, we need figure out …图表句式：We can graph … with …,and such a plot is shown in …According to the above data , we can see that … . This phenomenon shows that … . Hence, we can safely arrive the conclusion that …Table 7 reports the general statistics under …文献句式：There is rather substantial literature on models for evaluating regional health condition, and most models fall into one of two categories: microscopic and macroscopic. Nevertheless, to get a more accurate understanding, we need to conduct quantitative modeling in our call for a better evaluation and predictive model.假设句式：In order to present our solution , we have made numerous simplifications to the given problem . we made several assumptions regarding either the problem domain itself , or …For the sake of simplicity , we will generally assume in our discussions that …… are assumed to have …We assume … are …Due to the symmetry of the image we can assume that …We came up with a few different hypotheses that …For simplicity we consider …We will use the following symbols and definitions in the description of the model:To get the general picture of the … , we rely on the assumption that …Hence we are bale to …This assumption makes sense , because we expect …Assumption … is valid , since if it was not the case , the … would …Make the following assumptions to approximate and simplify the problem …As a sweet spot , there is no doubt that … ,if not , …For the purpose of reaching a conclusion conveniently , we assume …We adopt a set of assumptions as follows …模型验证：To test our model , we developed a … simulator based on … , and the simulator was written in … and can be executed on several platforms .To demonstrate how our model works , we apply it to …跨段内容：For a further discussion of this model , please see Appendix A .The underlying idea is fairly simple内容引导：What we are really interested in is …With this consideration in mind , we now …Our goal is to … , one that would …We must restate the problem mathematically by narrowing our focus and defining our goals in order to obtain a good model .Given this idea , it is clear that we cannot compromise the …This immediately leads to useful conclusions . For example , …Given these assumptions , the following results can be quickly derived …We will pursue this goal …We turn our attention to …We restrict our attention to …In addition to the model , we also discuss policies for …In our paper , we take … factors into consideration to …… is not as simple a task as it might seem , because …For the … , we only take … into account .As the next step , we will introduce our advanced method to …Under the premise of this , …On the basis of previous analyses , we find the …效果评价:This is a good indication that our simulations are producing reasonable results .The results of our simulations ,shown in … indicate that the performance of …This is no surprise the distinguishing features of …This would appear very encouraging indeed , were it not …We therefore regard this model as reasonable .Here very little congestion occurs …As we will see when we apply our model to … ,this model works well . It should be noted ,though that this is not the only way to define the location of generator points , but it is a very good firs approach .//数据缺乏的理论化模型Of course , only theoretical explanations are not completely convincing . But mass of data relevant to our calculation can be obtained through experiments . Owing to our limit conditions , we only quote some experimental results from other literatures to assist and analyze our derived theoretical conclusion .变量指定句式：Let … denote … , and … to be …The … is … , where … is , W stands for , and … stands for bucks .For better description we assign …Note for brief description of the model , we will denote …解释句式：In fact , this assumption is reasonable not only because … but also that …In other word , …The key feature of this algorithm is …It is important to note that … can no longer be ignored when considering …If … , we can gain more insight into the nature of …The reason we care about … is that … ,the problem is determining …, if … so we ..Our approach weighs heavily on …To show that … are negligible , we vary …This is likely due to …修正：We modify … according to …We modify the model to reflect … and generalize the model to …影响：Because the effect of … and omit the resistance of …As the effect of …The model also incorporates the …At other impact points , the impact may …... has been implicated as the major component of ...图表用语：However , from this figure it is clear that the …From this figure one can see that …,one also notices that …This graph can be compared to the results of the symbolic model to see how well the model agrees with our simulated …The two plots at above which show … .According to …, there exists the fact that …According to …, it is no doubt that…拟合近似,模拟：Given the above assumptions , we may approximate …In simulations over a suitably long time period , we find …For each run of the simulation we fire enough blobs so that results are …An appropriate estimate for the … can be obtain as follows .In assessing the accuracy of a mathematical model , …We now propose a way to extend our model using a computer simulation of …It is obvious , however , that this is a highly subjective value that must be determined through experiment for each … that our model is applied to .This model leads to a computer simulation of …主要因素:Analyzing what parameters have the greatest effect on the simulation results indicates the things that we should focus on in order to produce a more effective evacuation scheme .Sensitivity analysisWe use the sensitivity analysis to defend our model . The sensitivity of a model is a measure of how sensitive the result changes at small changes of parameters . A good model is corresponding to low sensitiveness .Considering the parameters used in our solutions , here we provide following discussion .The above models we have built is based on … ,which has well solved … . To the final issue , we have take … into account in order to …Strength:On the whole , we have hound our model to be quite natural and easy to apply . Here , we list some of the advantages of our approach to the problem .The most distinct advantage of our model is that …Our methods can incorporate various scenarios : ….This model is simple enough for … to understand .Our method is robust (健壮), so that other variables or situations can be easily introduced .Our model … and is not overly sensitive to small changes in …Additionally , we avoided harsh assumptions that would constrain the possible …Most of the assumptions we did make could be accounted for as well in a more general model .We use random events to simulate the chaos of real world .The key insight to our model is that ….Our model also takes into account the …The model allows … which is more close to reality .The model is able to handle a range of …Besides rigorous theoretical derivation , we also citing the research results of numerous experts and scholars to test the result of our method .Weakness:Of course , there are many ways to attack a problem such as this one , In this section , we discuss some of the drawbacks of our approach to the problem , and some things that could have been done to deal with these issues .Some special data can’t be found , and it makes that we have to do some proper assumption before the solution of our models . A more abundant data resource can guarantee a better result in our model .The model responds slowly to dramatic changes in …The method does not allow … , which might be possible with a more radicalmodel .However , … constraints arise when pursuing this methodology .Additionally , this method would have required … , which would …However , the algorithms do have unique strengths and weaknesses when …Our model does take into account the complicated effects that …Factors considered in our method is relatively unitary , we only take the important factor into consideration .Lacking brief numerical calculation in our method , though we display rigorous theoretical derivation .。
正确写作美国大学生数学建模竞赛论文
1）、鉴别阶段： （10分钟）
所有论文在此阶段按其质量分别归入一下三类：第一类 是可以进入下一评审阶段的论文（略少于二分之一）；第二类 是满足竞赛要求，但不足以进入下一评审阶段的论文（这一类 就被定为合格论文）；第三类是不符合竞赛要求的论文（不合 格论文）。 由于在第一阶段中，评委只有10分钟左右的时间评审一 篇论文，因此评委常常只能通过阅读摘要来判断论文水平的高 低。
例如，2010年MCM竞赛中有一道赛题，要求参赛小 组根据以往的作案地点预测连环犯罪的位置。
3.1）、假设条件和解释 解答这道赛题的重点是犯罪活动方式。在一篇题为 “Centroids, Clusters, and Crime: Anchoring the Geographic Profiles of Serial Criminals”的论文中，有一条假设是“罪犯 的活动不受限制”，但罪犯是在市区的活动，实际上会受 到街道的布局及街道两旁建筑物的限制。由于街道布局通 常类似于网格，所以参赛小组对这个假设做了如下解释： Criminal’s movement is unconstrained. Because of the difficulty of finding real-world distance data, we invoke the „Manhattan assumption‟: There are enough streets and sidewalks in a sufficiently grid-like pattern that movements along real-world movement routes is the same as „straight-line‟ movement in a space discretized into city blocks…
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
摘要（至关重要）第一段：写论文解决什么问题1．问题的重述其中主要的内容是美国发的题目为主，注意叙述即可！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。
如果没有……Without implementing defensive measure, the university is exposed to an expected loss of $8.9 million per year.3．总的解决概述a．通过什么方法解决什么问题例：We address the problem of optimizing amusement park enjoyment through distributing Quick Passes (QP), reservation slips that ideally allow an individual to spend less time waiting in line.b．实际问题转化为数学模型例1 We formulate the problem as a network flow in which vertices are the locations of escorts and wheelchair passengers.例2 : A naïve strategy would be to employ the minimum number of escorts to guarantee that all passengers reach their gates on time.c.将问题分阶段考虑例3：We divide the jump into three phases: flying through the air, punching through the stack, and landing on the ground.第二、三段：具体分析1．在什么模型中/ 建立了什么模型a. 主流模型例1：We formulate a differential model to account for the rates of change of these uses, and how this change would affect the overall consumption of water within the studied region.例2:We examined the mathematical effects of……. We developed a detailed……(simulation methodology) to test our ideas and to quantify the differences between (among) different ……(strategies).例3：Based on (write your basis .such as the theory of supply and demand), we establish a model (such as differential equation system that includes demand, supply).例4：To (write the aims), we establish a criterion (write the criterion).b. 模型非主流例5：We build a model to determine how to lay out the pipe each time the equipment is moved.例6：We determine…………例7：We build a model to determine……….例8：We formulate a model for………By analyzing…and examining…..2．分析模型（使用什么数据，怎么做，一般三句话）a. 写历史数据例1：Using historical data from the United States, we determine initial conditions for our model.b. 写计算机模拟例1：this model leads to a computer simulation of catch-can tests of the irrigation system and……例2:Software packing reaches………by calculating and comparing………..c. 运用数据模拟例1：to ground this model in reality, we incorporate extensive demographic data and run……例2：We fit the modified model to data (such as 1970-2003.). We conclude that(write the last conclude).d. 讲详细分析例1：We physically characterize the system that…例2：We provide a strategy (write the logical strategy).例3：The …model is (efficient, intuitive, and flexible) and could be applied to…例4：To meet the needs of people today without, we establish a criterion of rational(合理的标准) oil allocation(分配).3．总结该模型的结果/得到什么结论a. 说明不是最优但能产生作用例：We show that this strategy is not optimal but can be improved by assigning different numbers……b. 说明如果用这个模型，结果如何例1：If Delta Airlines were to utilize the naïve strategy at Atlanta International Airport, the cost would be……例2：We modify the model to reflect(some trend such as exponentially increasing……) and generalize the model to (other field).例3：Our results are summarized in the formula for the optimal number Bof tollbooths for c．通过其上情况的列举得到的结论例：For various situations, we propose an optimal solution.d. 得出了结论例1：we elicit that a conclusion.例2：We conclude with a series of recommendations for how best to…e.进一步说明其他因素对模型的影响例：In addition to the model, we also discuss policies for …..f.用真实数据检验模型例:To demonstrate how our model works, we apply it to ………..最后一段：写总的结论a. 说明结论的可行性例：Our suggested solution, which is easy to implement, includes a detailed timetable and the arrangement of pipes.b.说明算法的广泛性例1：Our algorithm is broad enough to accommodate various airport concourses, flight schedules, and flight delays.例2：Our analysis began by determining what factor impact……, Our conclusions are presented……c.说明模型可用于其他领域例：Since our model is based on…… it can be applied to (other domain).其他（承上启下的连接词/常用词组）例:In addition to the model, we also discuss……引言部分（1）回顾研究背景，常用词汇有review, summarize, present, outline, describe等（2）说明写作目的，常用词汇有purpose, attempt, aim等，另外还可以用动词不定式充当目的状语来表达（3）介绍论文的重点内容或研究范围，常用词汇有study, present, include, focus, emphasize, emphasis, attention等方法部分（1）介绍研究或试验过程，常用词汇有test study, investigate, examine, experiment, discuss, consider, analyze, analysis等（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等（3）介绍应用、用途，常用词汇有等结果部分（1）展示研究结果，常用词汇有show, result, present等（2）介绍结论，常用词汇有summary, introduce, conclude等讨论部分（1）陈述论文的论点和作者的观点，常用词汇有suggest, repot, present, expect, describe等（2）说明论证，常用词汇有等support, provide, indicate, identify, find, demonstrate, confirm, clarify（3）推荐和建议，常用词汇有suggest, suggestion, recommend, recommendation, propose, necessity, necessary, expect等。