数学建模美赛题目及翻译
1989美国数学建模数学竞赛试题及翻译
1989 MCM A: The Midge Classification ProblemTwo species of midges, Af and Apf, have been identified by biologists Grogan and Wirth on the basis of antenna and wing length (see Figure 1). It is important to be able to classify a specimen as Af of Apf, given the antenna and wing length. Given a midge that you know is species Af or Apf, how would you go about classifying it?Apply your method to three specimens with (antenna, wing) lengths(1.24,1.80),(1.28,1.84),(1.40,2.04).Assume that the species is a valuable pollinator and species Apf is a carrier of a debilitating disease. Would you modify your classification scheme and if so, how? 两种蠓Af和Apf已由生物学家W.L.Grongan和W.W.Wirth（1981年）根据他们的触角长和翼长加以区分。
根据触角的长和翼长将标本分类是很重要的。
1、给你一只Af或者Apf的蝶，你怎样对它进行分类呢?2、用你的方法将翅膀、触角的长度分别为（1.24，1.80）（1.28，1.84）（1.40，2.04）的三个标本分类。
3、假设Af这个种类的是宝贵的传粉益虫，Apf确是传递令人衰弱的疾病的载体。
美国数学建模题目至翻译
美国数学建模题目2017至2017翻译篇一：2017年建模美赛C题带翻译Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads.For example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks. This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads. The behavior of these cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (Seethe provided map and Excel spreadsheet).In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage traffic volume, and percentage of vehicles using self-driving, cooperating systems. Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles. Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: Theappendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours. ? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from south to north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。
历年美国大学生数学建模竞赛试题MCM.翻译版doc
1985 年美国大学生数学建模竞赛MCM 试题1985年MCM:动物种群选择适宜的鱼类和哺乳动物数据准确模型。
模型动物的自然表达人口水平与环境相互作用的不同群体的环境的重要参数,然后调整账户获取表单模型符合实际的动物提取的方法。
包括任何食物或限制以外的空间限制,得到数据的支持。
考虑所涉及的各种数量的价值,收获数量和人口规模本身,为了设计一个数字量代表的整体价值收获。
找到一个收集政策的人口规模和时间优化的价值收获在很长一段时间。
检查政策优化价值在现实的环境条件。
1985年MCM B:战略储藏管理钴、不产生在美国,许多行业至关重要。
(国防占17%的钴生产。
1979年)钴大局部来自非洲中部,一个政治上不稳定的地区。
1946年的战略和关键材料储藏法案需要钴储藏,将美国政府通过一项为期三年的战争。
建立了库存在1950年代,出售大局部在1970年代初,然后决定在1970年代末建立起来,与8540万磅。
大约一半的库存目标的储藏已经在1982年收购了。
建立一个数学模型来管理储藏的战略金属钴。
你需要考虑这样的问题:库存应该有多大?以什么速度应该被收购?一个合理的代价是什么金属?你也要考虑这样的问题:什么时候库存应该画下来吗?以什么速度应该是画下来吗?在金属价格是合理出售什么?它应该如何分配?有用的信息在钴政府方案在2500万年需要2500万磅的钴。
美国大约有1亿磅的钴矿床。
生产变得经济可行当价格到达22美元/磅(如发生在1981年)。
要花四年滚动操作,和thsn六百万英镑每年可以生产。
1980年,120万磅的钴回收,总消费的7%。
1986 年美国大学生数学建模竞赛MCM 试题1986年MCM A:水文数据下表给出了Z的水深度尺外表点的直角坐标X,Y在码(14数据点表省略)。
深度测量在退潮。
你的船有一个五英尺的草案。
你应该防止什么地区的矩形(75200)X(-50、150)?1986年MCM B:Emergency-Facilities位置迄今为止,力拓的乡牧场没有自己的应急设施。
(完整)数学建模美赛试题
地球资源的消耗速度快,越来越多的人关注人类社会的未来。
自1960年以来，已经有许多专家研究可持续发展。
然而大多数人的研究对象是整个世界，一个国家或一个地区。
几乎没有人选择48个最不发达国家(LDC)在联合国为研究对象列表。
然而，LDC国家集团共享许多相同的点.他们的发展道路也有法律的内涵。
本文选择这些国家为研究对象针对发现常规的可持续发展道路。
本文组织如下。
第二部分介绍研究的背景和本研究的意义。
第三节描述了我们对可持续发展的理解细节和显示我们的评估系统的建立过程和原理，那么我们估计每一个国家的LDC和获得可持续发展的能力和等级。
第四节提供了一个最糟糕的国家毛里塔尼亚计划指数在第三节。
第五节演示了在第四节的合理性和可用性计划。
最后在第六节总结本文的主要结论和讨论的力量和潜在的弱点。
地球上的资源是有限的。
三大能源石油、天然气和煤炭可再生。
如何避免人类的发展了资源枯竭和实现可持续发展目标是现在的一个热门话题。
在过去的两个世纪，发达国家已经路上,先污染,再控制和达到高水平的可持续发展。
发展中国家希望发展和丰富。
然而,因为他们的技术力量和低水平的经济基础薄弱，浪费和低效率的发展在这些国家是正常的.所以本文主要关注如何帮助发展中国家特别是48在联合国最不发达国家实现可持续发展是列表可持续发展的理解是解决问题的关键。
可持续发展的定义经历了一个长期发展的过程.在这里,布伦特兰可持续发展委员会的简短定义的”能力发展可持续- - — - - -以确保它既满足现代人的需求又不损害未来的能力代来满足自己的需求”[1]无疑是最被广泛接受的一个在各种内吗定义。
这个定义方面发挥了重要作用在很多国家的政策制定的过程。
然而,为了证明一个国家的现状是否可持续不可持续的,更具体的定义是必要的更具体的概念，我们认为,如果一个国家的发展是可持续的，它应该有一个基本的目前的发展水平，一个平衡的国家结构和一个光明的未来.基本的发展水平反映了国家的基础和潜力。
2013年数学建模美赛题目中文翻译_共4页
Problem c:背景：社会正致力于运用和开发模型来预测地球的生物和环境情况。
很多科学研究总结了逐渐增长的地球环境和生物系统压力，但很少有人用全球范围的模型来检测这些观点。
联合国发表的千年生态系统评估综合报告发现：近三分之二的地球生命支持生态系统——包括净水，洁净的空气，稳定的气候——正在因非可持续性使用而逐渐衰减。
其中大部分破坏归咎于人类行为。
暴增的对于食物，淡水，燃料，木材的需求导致了剧烈的环境变化；从森林砍伐到空气，土壤和水污染。
尽管已存在大量关于局部习惯和地区因素的研究，目前的模型还不能告知决定人他们的局部策略是如何影响整个地球的健康的。
许多模型忽略了复杂的全球因素，这些模型无法判断重大政策的长期影响。
尽管科学家们意识到巨大环境和生物系统中存在的复杂关系和交叉作用，当前的模型通常忽略这些管理或限定了系统间的影响。
系统的复杂性体现在多元交互（多个元素的相关性），反馈，突发行为，即将发生的状态变化或触发点。
最近的自然杂志中一篇由22位国际知名科学家撰写的题为“迫近地球生物圈的状态变化”的文章讨论了许多有关科学模型对于预测行星健康系统潜在状态变化的重要性与必需性。
文章提供了两种具体定性的模型，并寻求更好的预测模型：1）通过在全球模型中加入相关系统的复杂性（包括局部情况对全球系统的影响，反之亦然）来优化生物状态预测。
2）辨别不同因素在产生非健康全球状态变化中的作用并展示如何运用有效的生态系统管理来预防或限制这些即将发生的状态变化。
研究最终归结于问题：我们是否能利用全球健康的局部或地区性组成部分预测潜在状态变化来帮助决策者制定基于对全球健康状况潜在影响的，有效的策略。
尽管有越来越多的警示信号出现，没人知道地球是否确实在接近全球性的转折点（极端状态），这种极端的状态是否是不可避免的。
自然杂志等研究指出了地球生态系统中的一些重要工作元素。
（例如：局部因素，全球变化，多维元素与关系，变化的时间与空间范围）。
建模美赛C题带翻译
Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads. For example, in the Greater Seattle area drivers experience long delays during peak traffic hours because the volume of traffic exceeds the designed capacity of the road networks. This is particularly pronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interest for this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highways without increasing number of lanes or roads. The behavior of these cars interacting with the existing traffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving, cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (See the provided map and Excel spreadsheet). In particular, how do the effects change as the percentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there a tipping point where performance changes markedly? Under what conditions, if any, should lanes be dedicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/or average traffic volume, and percentage of vehicles using self-driving, cooperating systems. Your model should address cooperation between self-driving cars as well as the interaction between self- driving and non-self-driving vehicles. Your model should then be applied to the data for the roads of interest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the Governor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours.•The nominal speed limit for all these roads is 60 miles per hour.•Mileposts are numbered from south to north, and west to east.•Lane widths are the standard 12 feet.•Highway 90 is classified as a state route until it intersects Interstate 5.•In case of any conflict between the data provided in this problem and any other source, use the data provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。
数学建模美赛题目及翻译
PROBLEM A: The Keep-Right-Except-To-Pass Rule The Keep-Right-Except-To-Pass RuleIn countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirementsbe needed.Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part ofthe road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results ofyour earlier analysis?问题A ：除非超车否则靠右行驶的交通规则在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。
美国(MCM)(ICM)试题(96年-09年)(英文版)
美国大学生数学建模竞赛试题1996 American MCM Problems Problem AThe world's oceans contain an ambient noise field. Seismic disturbances, surface shipping, and marine mammals are sources that, in different frequency ranges,contribute to this field. We wish to consider how this ambient noise might be used to detect large moving objects, e.g., submarines located below the ocean surface. Assuming that a submarine makes no intrinsic noise, developa method for detecting the presence of a moving submarine, its size, and its direction of travel, using only information obtained by measuring changes to the ambient noise field. Begin with noise at one fixed frequency and amplitude.Problem BWhen determining the winner of a competition like the Mathematical Contest inModeling, there are generally a large number of papers to judge. Let's saythere are P=100 papers.A group of J judges is collected to accomplish thejudging. Funding for the contest constains both the number of judges that canbe obtained and amount of time that they can judge. For eample if P=100, thenJ=8 is typical.Ideally, each judge would read paper and rank-order them, but there are toomany papers for this. Instead, there will be a number of screening rounds inwhich each judge will read some number of papers and give them scores. Thensome selection scheme is used to reduce the number of papers under consideration: If the papers are rank-ordered, then the bottom 30% that eachjudge rank-orders could be rejected. Alternatively, if the judges do not rank-order, but instead give them numerical score (say, from 1 to 100),then all papers below some cut-off level could be rejected.The new pool of papers is then passed back to the judges, and the process is repeated.A concern is then the total number of papers that judge reads must besubstantially less than P. The process is stopped when there are only W papersleft. There are the winners. Typically for P=100, W=3.Your task is to determine a selection scheme, using a combination of rank-ordering, numerical scoring, and other methods, by which the final Wpapers will include only papers from among the "best" 2W papers. (By "best",we assume that there is an absolute rank-ordering to which all judges wouldagree.) For example, the top three papers. Among all such methods, the one thatrequired each judge to read the least number of papers is desired.Note the possibility of systematic bias in a numerical scoring scheme. For example, for a specific collection of papers, one judge could average 70points, while another could average 80 points. How would you scale your schemeto accommodate for changes in the contest parameters (P, J, and W)?1997 American MCM ProblemsProblem A The Velociraptor ProblemThe velociraptor,Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter, and may have hunted in pairs or largerpacks .Unfortunately, there is no way to observe its hunting behavior in the wild as can be done with modern mammalian predators. A group of paleontologists has approached your team and asked for help in modeling the hunting behavior of the velociraptor. They hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals.The average adult velociraptor was 3 meters long with a hip height of 0.5 meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast at speed of 60 km/hr for about 15 seconds. After the initial burst of speed ,the animal needed to stop and recover from a buildup of lactic acid in its muscles.Suppose that velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the Velociraptor. A biomachanical analysis of a fossilized Thescelosaurus indicates that it could run at a speed of about 50 km/hr. for long period of time.Part1Assuming the velociraptor is a solitary hunter, design a mathematical model that describe a hunting strategy for a single velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Assume that the Thescelosaurus can always detect the velociraptor when it comes within 15 meters .but may detect the predator at even greater ranges (up to 50 meters depending upon the habitat and weather conditions. Additionally ,due to its physical structure and strength, the velociraptorhas a limited turning radius when running at full speed. This radius is estimated to be three times the animal's hip height. On the other hand, the Thescelosaurus is extremely agile and has a turning radius of 0.5 meters.Part2Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Use the other assumptions and limitations given in Part 1.Problem B Mix Well For Fruitful DiscussionsSmall group meeting for the discussions of important issues, particular long-range planning ,are gaining popularity. It is believed that large groups discourage productive discussion and that a dominant personality will usually control and direct the discussion. Thus ,in corporate board meetings the board will meet in small groups to discuss issues before meeting as a whole, these smaller groups still tun the risk of control by a dominant personality. In an attempt to reduce this danger it is common to schedule several sessions with a different mix of people in each group.A meeting of An Tostal Corporation will be attended by 29 Board Members of which nine are in-house members(i.e., corporate employees).The meeting is to be an all-day affair with three sessions scheduled for the morning and four for the afternoon. Each session will take 45 minutes, beginning on the hour from 9:00 A.M. to 4:00 P.M., with lunch scheduled at noon. Each morning session will consist of six discussion groups with each discussion group led by one of the corporation's six senior officers. None of these officers are board members. Thus each senior officers will not be involved in the afternoon sessions and each of these sessions will consist of only four different discussion groups.The president of the corporation wants a list of board-member assignment to discussion groups for each of the seven sessions. The assignments should achieve as much of a mix of the members as much as possible. The ideal assignment would have each board member in a discussion group the same number of times while minimizing common membership of groups for the different sessions.The assignment should also satisfy the following criteria:1.For the morning sessions ,no board member should be in the same senior officer's discussion group twice.2.No discussion group should contain a disproportionate number of in-house members.Give a list of assignments for members 1-9 and 10-29 and officers 1-6.Indicate how well the criteria in the previous paragraphs are met. Since it is possible that some board members will cancel at the last minute or that some not scheduled will show up, an algorithm that the secretary could use to adjust the assignments with an hour's notice would be appreciated. It would be ideal if the algorithm could also be used to make assignments for future meetings involving different levels of participation for each type of attendee.1998 American MCM ProblemsProblem A MRI ScannersIntroductionIndustrial medical diagnostic machines known as Magnetic Resonance Imager (MRI) scan a three-dimensional object such as a brain, and deliver their results in the form of a three-dimensional array of pixel. Each pixel consists of one number indicating a color or a shade of gray that encodes a measure of water concentration in a small region of the scanned object at the location of the pixel .For instance,0 can picture high water concentration in black (ventricles, blood vessels),128 can picture a medium water concentration in gray(brain nuclei and gray matter),and 255 can picture a low water density in white (liquid-rich white matter consisting of myelinated axons).Such MRI scanners also include facilities to picture on a screen any horizontal or vertical slice through the three-dimensional array (slices are parallel to any of the three Cartesian coordinate axes ).Algorithms for picturing slices through oblique planes ,however ,are proprietary .Current algorithms are limited in terms of the angles and parameter options available ;are implemented only on heavily used dedicated workstations ;lack input capabilities for marking points in the picture before slicing; and tend to blur and "feather out" sharp boundaries between the original pixels.A more faithful, flexible algorithm implemented on a personal computer would be useful.(1)for planning minimally invasive treatments,(2)for calibrating the MRI machines,(3)for investigating structures oriented obliquely in space, such as post-mortem tissue sections in a animal research,(4)for enabling cross-sections at any angle through a brain atlas consisting (4)for enabling cross-sections at any angle through a brain atlas consistingof black-and-white line drawingTo design such an algorithm, one can access the value and locations of the pixels, but not the initial data gathered by the scanners.ProblemDesign and test an algorithm that produces sections of three-dimensional arrays by planes in any orientation in space, preserving the original gray-scale value as closely as possible.Data SetsThe typical data set consists of a three-dimensional array A of numbers A(i,j,k) which indicates the density A(i,j,k) of the object at the location (x,y,z)i,j,k. Typically A(i,j,k) can range from 0 to 255.In most applications the data set is quite large.Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely to be of diagnostic interest. Teams should also characterize data sets the limit the effectiveness of their algorithms.SummaryThe algorithm must produce a picture of the slice of the three-dimensional array by a plane in space. The plane can have any orientation and any location in space.(The plane can miss some or all data points.)The result of the algorithm should be a model of the density of the scanned object over the selected plane.Problem B Grade InflationBackgroundSome college administrators are concerned about the grading at A Better Class(ABC) college. On average, the faculty at ABC have been giving out high grades(the average grade now given out is an A-),and it is impossible to distinguish between the good and mediocre students .The terms of a very generous scholarship only allow the top 10% of the students to be funded, so a class ranking is required.The dean had the thought of comparing each student to the other students in each class ,and using this information to build up a ranking. For example, if a student obtains an A in a class in which all students obtain an A, then this student is only "average" in this class. On the other hand, if a student obtain the only A in a class, then that student is clearly "above average". Combining information from several classes might allow students to be placed in deciles (top 10%,next 10%,ect.)across the college.ProblemAssuming that the grades given out are(A+,A-,B+,B-,...)can the dean's idea be made to work?Assuming that the grades given out are only (A,B,C,...)can the dean's idea be made to work?Can any other schemes produce a desired ranking?A concern is that the grade in a single class could change many student's deciles. Is this possible?Data SetsTeams should design data sets to test and demonstrate their algorithms. Teams should characterize data sets that limit the effectiveness of their algorithms.Mathematical Contest in Modeling 1999 ProblemsProblem A - Deep ImpactFor some time, the National Aeronautics and Space Administration (NASA) has been considering the consequences of a large asteroid impact on the earth.As part of this effort, your team has been asked to consider the effects of such an impact were the asteroid to land in Antarctica. There are concerns that an impact there could have considerably different consequences than one striking elsewhere on the planet.You are to assume that an asteroid is on the order of 1000 m in diameter, and that it strikes the Antarctic continent directly at the South Pole.Your team has been asked to provide an assessment of the impact of such an asteroid. In particular, NASA would like an estimate of the amount and location of likely human casualties from this impact, an estimate of the damage done to the food production regions in the oceans of the southern hemisphere, and an estimate of possible coastal flooding caused by large-scale melting of the Antarctic polar ice sheet.Problem B - Unlawful AssemblyMany public facilities have signs in rooms used for public gatherings which state that it is "unlawful" for the rooms to be occupied by more than a specified number of people. Presumably, this number is based on the speed with which people in the room could be evacuated from the room's exits in case of an emergency. Similarly, elevators and other facilities often have "maximum capacities" posted.Develop a mathematical model for deciding what number to post on such a sign as being the "lawful capacity". As part of your solution discuss criteria, other than public safety in the case of a fire or other emergency, that might govern the number of people considered "unlawful" to occupy the room (or space). Also, for the model that you construct, consider the differences between a room with movable furniture such as a cafeteria (with tables and chairs), a gymnasium, a public swimming pool, and a lecture hall with a pattern of rows and aisles. You may wish to compare and contrast what might be done for a variety of different environments: elevator, lecture hall, swimming pool, cafeteria, or gymnasium. Gatherings such as rock concerts and soccer tournaments may present special conditions.Apply your model to one or more public facilities at your institution (or neighboring town). Compare your results with the stated capacity, if one is posted. If used, your model is likely to be challenged by parties with interests in increasing the capacity. Write an article for the local newspaper defending your analysis.2000 Mathematical Contest in ModelingProblem A Air traffic ControlDedicated to the memory of Dr. Robert Machol, former chief scientist of the Federal Aviation Agency To improve safety and reduce air traffic controller workload, the Federal Aviation Agency (FAA) is considering adding software to the air traffic control system that would automatically detect potential aircraft flight path conflicts and alert the controller. To that end, an analyst at the FAA has posed the following problems.Requirement A: Given two airplanes flying in space, when should the air traffic controller consider the objects to be too close and to require intervention?Requirement B: An airspace sector is the section of three-dimensional airspace that one air traffic controller controls. Given any airspace sector, how do we measure how complex it is from an air traffic workload perspective? To what extent is complexity determined by the number of aircraft simultaneously passing through that sector (1) at any one instant?(2) during any given interval of time?(3) during a particular time of day? How does the number of potential conflicts arising during those periods affect complexity?Does the presence of additional software tools to automatically predict conflicts and alert the controller reduce or add to this complexity?In addition to the guidelines for your report, write a summary (no more than two pages) that the FAA analyst can present to Jane Garvey, the FAA Administrator, to defend your conclusions.Problem B Radio Channel AssignmentsWe seek to model the assignment of radio channels to a symmetric network of transmitter locations over a large planar area, so as to avoid interference. One basic approach is to partition the region into regular hexagons in a grid (honeycomb-style), as shown in Figure 1, where a transmitter is located at the center of each hexagon.Figure 1An interval of the frequency spectrum is to be allotted for transmitter frequencies. The interval will be divided into regularly spaced channels, which we represent by integers 1, 2, 3, ... . Each transmitter will be assigned one positive integer channel. The same channel can be used at many locations, provided that interference from nearby transmitters is avoided. Our goal is to minimize the width of the interval in the frequency spectrum that is needed to assign channels subject to some constraints. This is achieved with the concept of a span. The span is the minimum, over all assignments satisfying the constraints, of the largest channel used at any location. It is not required that every channel smallerthan the span be used in an assignment that attains the span.Let s be the length of a side of one of the hexagons. We concentrate on the case that there are two levels of interference.Requirement A: There are several constraints on frequency assignments. First, no two transmitters within distance of each other can be given the same channel. Second, due to spectral spreading, transmitters within distance 2s of each other must not be given the same or adjacent channels: Their channels must differ by at least 2. Under these constraints, what can we say about the span in,Requirement B: Repeat Requirement A, assuming the grid in the example spreads arbitrarily far in all directions.Requirement C: Repeat Requirements A and B, except assume now more generally that channels for transmitters within distance differ by at least some given integer k, while those at distance at most must still differ by at least one. What can we say about the span and about efficient strategies for designing assignments, as a function of k?Requirement D: Consider generalizations of the problem, such as several levels of interference or irregular transmitter placements. What other factors may be important to consider?Requirement E: Write an article (no more than 2 pages) for the local newspaper explaining your findings.2001 Mathematical Contest in Modeling (MCM)Problem A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic typesof wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic.A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition,and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used fora given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right. The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front butthere is a choice of wheels for the rear.Task 1. Provide a table iving the wind peed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments. (Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.A rider will lose about 8 kph for a five percent grade over 100 meters.Task 2. Provide an example of how the table could be used for a specific time trial courseTask 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.Problem B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfallof Hurricane Floydin 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way.Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversalof traffic onI-26, so that both sides, including the coastal-bound lanes,have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web)by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data,if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther northby other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastal region was ordered. Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?3.Several smaller highways besides I-26 extend inland from the coast. Under what conditions would it improve evacuation flow to turn around traffic on these?4.What effect would it have on evacuation flow to establish more temporary shelters in Columbia, to reduce the traffic leaving Columbia?5.In 1999, many families leaving the coast brought along their boats, campers, and motor homes. Many drove all of their cars. Under what conditions should there be restrictionson vehicle types or numbers of vehicles brought in order to guarantee timely evacuation? 6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida, who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south, came upI-95 and compounded the traffic problems. How big an impact can they have on the evacuation traffic flow? Clearly identify what measures of performance are used to compare strategies. Required: Prepare a short newspaper article, not to exceed two pages,explaining the results and conclusions of your study to the public.问题 A: 选择自行车车轮骑自行车的人有几种不同类型的车轮可以用在他们的自行车上。
2020年数学建模美赛题目
2020年数学建模美赛题目
1. 题目A，关于空中交通的问题，要求参赛者利用数学建模方法对航班的轨迹进行优化，以减少飞行时间和燃料消耗。
2. 题目B，关于林业管理的问题，要求参赛者利用数学建模方法对森林资源的管理和可持续利用进行分析和优化。
3. 题目C，关于自然灾害的问题，要求参赛者利用数学建模方法对地震后的救援物资调度进行优化，以提高救援效率。
每个题目都提供了大量的背景资料和数据，参赛者需要根据所提供的信息，结合数学建模理论和方法，进行问题分析、模型建立和求解，最终撰写一份完整的数学建模报告。
这些题目涉及到了航空、林业和灾害管理等不同领域，要求参赛者具备跨学科的综合能力和创新思维。
每个题目都有其独特的挑战和难点，参赛者需要全面理解问题背景，合理假设模型，运用数学工具进行分析，并给出切实可行的解决方案。
这些题目不仅考察了参赛者的数学建模能力，还要求他们具备对实际问题的深刻理解和解决问题的能力。
MCM_2009_翻译
2009年美国数学建模竞赛MCM试题翻译A题设计一个交通环岛在许多城市和社区都建立有交通环岛，既有多条行车道的大型环岛（例如巴黎的凯旋门和曼谷的胜利纪念碑路口），又有一至两条行车道的小型环岛。
有些环岛在进入口设有“停车”标志或者让行标志，其目的是给已驶入环岛的车辆提供行车优先权；而在一些环岛的进入口的逆向一侧设立的让行标志是为了向即将驶入环岛的车辆提供行车优先权；还有一些环岛会在入口处设立交通灯（红灯会禁止车辆右转）；也可能会有其他的设计方案。
这一设计的目的在于利用一个模型来决定如何最优地控制环岛内部，周围以及外部的交通流。
该设计的目的在于可利用模型做出最佳的方案选择以及分析影响选择的众多因素。
解决方案中需要包括一个不超过两页纸，双倍行距打印的技术摘要，它可以指导交通工程师利用你们模型对任何特殊的环岛进行适当的流量控制。
该模型可以总结出在何种情况之下运用哪一种交通控制法为最优。
当考虑使用红绿灯的时候，给出一个绿灯的时长的控制方法（根据每日具体时间以及其他因素进行协调）。
找一些特殊案例，展示你的模型的实用性。
B题能源和手机能源和手机这个问题涉及到手机革命的能源问题。
手机使用率迅速增加，许多人使用手机并放弃了固定电话。
这方面的电能使用会带来什么后果？每个手机都配备了电池和充电器。
要求1考虑现在的美国，人口约为3亿，从现有数据估计美国有H个家庭，每个家庭有M个成员，以前是使用固定电话的。
现在，假设所有的座机被手机取代，也就是说每个家庭成员都有一部手机。
建立当前美国在手机使用的过渡和稳定两个阶段用电改变的模型，分析应该考虑到对移动电话充电的需要，同时移动电话不能像固定电话那样长期使用也是一个现实问题（比如说移动电话可能会丢失或者损坏）要求2考虑“伪美国”--一个约3亿人口，跟当前美国具有相同的经济状况的国家。
然而，这个新兴国家既没有固定电话也没有移动电话，从能源角度看，为这个国家提供电话服务的最佳方式是什么？当然，手机有很多固定电话所不具有的用途和社会影响。
1992美国数学建模数学竞赛试题及翻译
1992 MCM A: Air-Traffic-Control Radar Power 空中交通雷达控制问题你将决定雷达在一个大型综合城市机场辐射的能量。
机场当局希望在减少雷达辐射能的情况下，保持安全与降低成本一致。
机场当局希望利用原有的高塔和接收电路系统。
为加大雷达使用度，唯一的选择就是：提升发送电路系统。
你所要回答的问题是：雷达必须释放多少能量以保证在离地100千米的高空飞行的普通客运机的检测。
1992 MCM B: Emergency Power Restoration紧急电力修复问题由于暴风雨的侵袭，沿海一带的电力公司必须有防控断电的应急系统。
这种系统要求：一输入数据，系统估算出修复所需的时间和成本，以及客观估算出由断电造成的损失。
在过去，夏威夷电力公司曾因为缺少这样一个优化项目被媒体抨击。
现在你是夏威夷电力公司的一名顾问。
HECO拥有一个电脑化的数据库和实时访问服务需要,目前需要以下的信息：报告的时间，报告者类型，受影响者人数估量，位置（x,y）.电力公司位于坐标轴的（0，0）和（40，40）之间，其中x,y的单位为米。
夏威夷电力公司的服务范围为-65 < x < 60 and -50 < y < 50。
该区域拥有优良的网络系统。
公司明确规定：在暴风雨离开之前，任何工作不得开始，除非求助区域是医院和铁路单位，这些区域需要立即处理如果工作人员可得到。
夏威夷电力公司聘用你制定客观评判标准并安排暴风雨后的修复工作。
要求见表1，人力资源见表2.注意：最早客户热线为4:20 A.M.暴风雨离开时间为6:00 A.M。
还要注意很多停电用户总是推迟才保修的。
夏威夷电力公司出自自身目的需要一份技术报告和一份用外行术语写的“执行简要“提交给新闻媒介。
另外，他们希望公众能为将来提供些建议。
为制定出你的优先计划安排系统，你还需做一些附加假设，并详细陈述这些假设。
数学建模美赛试题原文及翻译2009b
美赛试题2009b试题B：This question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones. What is the consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.这个问题涉及到“能量”影响的手机革命，手机的使用量迅速增长，许多人正在使用手机来代替固定电话。
这方面的电力使用的结果是什么？每个手机配有一个电池和一个充电器。
Requirement 1Consider the current US, a country of about 300 million people. Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that all the landlines are replaced by cell phones; that is, each of the m members of the household has a cell phone. Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones (for example, the cell phones get lost and break).要求一目前认为美国是一个人口约有3亿人的国家，从现有数据估计家庭数为h，每个家庭有M个成员，以前是使用座机电话的。
美赛历年赛题及其翻译-推荐下载
2015年：A题一个国际性组织声称他们研发出了一种能够阻止埃博拉，并治愈隐性病毒携带者的新药。
建立一个实际、敏捷、有效的模型，不仅考虑到疾病的传播、药物的需求量、可能的给药措施、给药地点、疫苗或药物的生产速度，而且考虑你们队伍认为重要的、作为模型一部分的其他因素，用于优化埃博拉的根除，或至少缓解目前（治疗）的紧张压力。
除了竞赛需要的建模方案以外，为世界医学协会撰写一封1-2页的非技术性的发言稿，以便其公告使用。
B题回顾马航MH370失事事件。
建立一个通用的数学模型，用以帮助失联飞机的搜救者们规划一个有效的搜索方案。
失联飞机从A地飞往B地，可能坠毁在了大片水域（如大西洋、太平洋、印度洋、南印度洋、北冰洋）中。
假设被淹没的飞机无法发出信号。
你们的模型需要考虑到，有很多种不同型号的可选的飞机，并且有很多种搜救飞机，这些搜救飞机通常使用不同的电子设备和传感器。
此外，为航空公司撰写一份1-2页的文件，以便在其公布未来搜救进展的新闻发布会上发表。
2014美赛A题翻译问题一:通勤列车的负载问题在中央车站,经常有许多的联系从大城市到郊区的通勤列车“通勤”线到达。
大多数火车很长(也许10个或更多的汽车长)。
乘客走到出口的距离也很长，有整个火车区域。
每个火车车厢只有两个出口,一个靠近终端, 因此可以携带尽可能多的人。
每个火车车厢有一个中心过道和过道两边的座椅，一边每排有两个座椅，另一边每排有三个座椅。
走出这样一个典型车站,乘客必须先出火车车厢,然后走入楼梯再到下一个级别的出站口。
通常情况下这些列车都非常拥挤,有大量的火车上的乘客试图挤向楼梯，而楼梯可以容纳两列人退出。
大多数通勤列车站台有两个相邻的轨道平台。
在最坏的情况下,如果两个满载的列车同时到达,所有的乘客可能需要很长时间才能到达主站台。
建立一个数学模型来估计旅客退出这种复杂的状况到达出站口路上的时间。
假设一列火车有n个汽车那么长,每个汽车的长度为d。
站台的长度是p,每个楼梯间的楼梯数量是q。
MCM2012 数学建模美赛 A题题目及翻译
PROBLEM A: The Leaves of a Tree "How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:• Why do leaves have the various shapes that they have?• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volu me”of the tree and its branches effect the shape?• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.问题A：一棵树的叶子“一棵树上的叶子有多重？”如何估计叶子的实际重量（或树的其他部分）的实际重量？如何对叶子进行分类？建立一个数学模型来描述和分类叶子。
【数学建模】—2021年MCM美赛A题翻译
【数学建模】—2021年MCM美赛A题翻译问题A:真菌碳循环描述了地球地球化学循环中碳的交换过程，是地球上⽣命的重要组成部分。
碳循环的⼀部分包括化合物的分解，使碳得以更新并以其他形式使⽤。
这⼀过程的⼀个关键组成部分是植物材料和⽊质纤维的分解。
真菌是分解⽊质纤维的主要因素。
最近⼀篇关于真菌分解⽊材的研究⽂章的作者鉴定了真菌分解速率的特性，并注意到某些特性[1]之间的联系。
特别是，⽣长缓慢的菌种往往能够更好地在湿度和温度等环境变化中⽣存和⽣长，⽽⽣长较快的菌种往往对相同的变化不那么强健。
这篇⽂章的概要见下⾯第3页。
⽣长缓慢的菌种往往能够更好地在湿度和温度等环境变化中⽣存和⽣长⽣长较快的菌种往往对相同的变化不那么强健这些研究⼈员检查了⼤量与不同真菌相关的性状，以及它们在地⾯凋落物(死植物物质)和⽊质纤维分解中的作⽤。
对于MCM问题，你应该关注真菌的两个特性:真菌的⽣长速度和真菌的耐湿性。
您的主要⽬标是为给定⼟地上的⽊质纤维分解建模，并在存在多种类型的真菌分解同⼀区域中的⽊质纤维的情况下进⾏建模。
两个特性真菌的⽣长速度和真菌的耐湿性主要⽬标为给定⼟地上的⽊质纤维分解建模，并在存在多种类型的真菌分解同⼀区域中的⽊质纤维的情况下进⾏建模。
当您探索感兴趣的两个性状，⽣长速率和耐湿性以及分解速率之间的关系时，可能会出现⼀些问题，包括：利⽤这两个特征，不同的真菌如何相互作⽤和分解不同环境下固定⼟地上的地⾯垃圾? 在这些不同的环境中，随着条件的变化，分解将如何随着时间的推移⽽受到影响？环境如何变化以及环境变化如何，在这些不同的环境中，随着时间的推移条件的变化，分解将如何受到影响?给定⽣长速率，对分解速率的估算如图1所⽰。
给定相对湿度，给出分解速率的估算，如图2所⽰。
利⽤这两个特征，不同的真菌如何相互作⽤和分解不同环境下固定⼟地上的地⾯垃圾?在这些不同的环境中，随着条件的变化，分解将如何随着时间的推移⽽受到影响？环境如何变化以及环境变化如何，在这些不同的环境中，随着时间的推移条件的变化，分解将如何受到影响?图1:在不同温度下，各种真菌的菌丝延伸率(mm/天)与⽊材分解率(122天质量损失%)之间的关系。
2021年数模小美赛C题翻译参考
2021年数模小美赛C题翻译参考C题原文Why people turn to terrorism, and especially suicidal terrorism?What arethe major reasons? It’s typically a combination of big issues and little ones, or what some call “push and pull” factors. The bigger issues include alienation, shared anger or outrage (e.g. at some foreign policy), frustration, disillusionment, a sense of victimization by the actions, or in the case of Syria, inactions, of others.The littler issues, the “lures” include the perceived benefits of turning - e.g. adventure, excitement, camaraderie, a sense of belonging,being part of something far bigger etc. The key to understanding is not just to ask why people turn but how they turn, and what strategies recruiters use in that process. Effective recruiters will use whatever tools in their arsenal to pull someone in, whether it is convincing them of their duty to go fight in defense of others,to convincing them that involvement offers them a way out of the humiliation and victimization the recruiter will remind the young person they are otherwise destined to face at home. Radicalization,and how it relates to recruitment (and how we respond to it) is a constantly changing system. Some extreme traits are not as disadvantageous for fitness, as they appear to be for social adaptation orwell-being, even when severely disordered subjects are examined.In fact, some traits increase in severity, they become more advantageous for attracting more mates and even producing more offspring.This would characterize these traitsas risky shortcuts to fitness,owing less to failures than to the twists and turns made by genes in order to perpetuate themselves. Why someone joins today is different to why someone might have joined even the same group three years ago. The idealism that helps draw someone into terrorism often conflicts with the reality as experienced by the newly minted recruit.Entrapment (in a psychological sense) develops quickly and recruits haveto cope with that disillusionment one way or another.You acquiesce to it and move on, maybe by embracing ideological content or seeking comfort in the camaraderie. Or you struggle with and try to conceal it until you can get out. Some terrorists report being disillusioned long before they have been able to disengage from terrorism. They report a sense of suffocation - being unable to leave for fear of retaliation (either by the terrorists or by the State) and being equally afraid of their disillusionment being detected by those close to them in the movement. We need to do a better job of providing “o ff-ramps”not just for people who are on the road to terrorism in the first place, butalso to those who have gotten themselves in a jam and want to get out beforeit’s too late. We need to know their certain psychologicalcharacteristics.Consider two questions. First: Who are you? What makes you different from your peers, in terms of the things you buy, the clothes you wear, and the car you drive (or refuse to)? What makes you unique in terms of your basic psychological make-up-the part of you that makes you do the things you do, say the things you say, and feel the things you feel? And the second question: How do you use the internet?Although these questions may seem unrelated, they’re not. Clearly the content of your internet usage cansuggest certain psychological characteristics. Spending a lot of late nights playing high stakes internet poker? Chances are you are1 / 42021年数模小美赛C题翻译参考a risk taker. Like to post videos of yourself doing karaoke on YouTube? Clearly an extravert. Choose to play as a opposite gender character in online games? You want to get attention or kinder treatment from other players.But what about the mechanics of your internet usage - how often you email others, chat online, stream media, play game, or multi-task (switch from one application or website to another)? Can these behaviors - regardless of their content - also predict psychological Why people turn to terrorism, andespecially suicidal terrorism?What are the major reasons? It’s typically a combination of bi g is sues and little ones, or what some call “push and pull” factors. The bigger issues include alienation, shared anger or outrage (e.g.at some foreign policy), frustration, disillusionment, a sense ofvictimization by the actions, or in the case of Syria, inactions, ofothers.The littler issues, the “lures” include the perceived benefits of turning - e.g. adventure, excitement, camaraderie, a sense of belonging,being part of something far bigger etc. The key to understanding is not just to ask why people turn but how they turn, and what strategies recruiters use in that process. Effective recruiters will use whatever tools in their arsenal to pull someone in, whether it is convincing them of their duty to go fight in defenseof others,to convincing them that involvement offers them a way out of the humiliation and victimization the recruiter will remind the young person theyare otherwise destined to face at home. Radicalization,and how it relates to recruitment (and how we respond to it) is a constantly changing system. Some extreme traits are not as disadvantageous for fitness, as they appear to befor social adaptation or well-being, even when severely disordered subjectsare examined.In fact, some traits increase in severity, they become more advantageous for attracting more mates and even producing more offspring.This would characterize these traits as risky shortcuts to fitness, owing less to failures than to the twists and turns made by genes in order to perpetuate themselves.Why someone joins today is different to why someone might have joined even the same group three years ago. The idealism that helps draw someone into terrorism 1characteristics?Assume we can monitor some people’s Internet use. We didn’t know what people were looking at on the internet (for example, depressed person - a dead giveaway), but merely how they were using the internet. None of the data categories gave specific information about what websites people were visiting, the content of their emails or chats, or the types of files being downloaded - they simply indicated the extent to which people used different broad categories of net-based resources, as well as differences in people’s tendency to use many resources at once.Task 1: Build a mathematical model to obtain a risk index, so we can evaluate the situation of each monitored person use it.Task 2: Experts use the expression big data to indicate huge amounts of information. We’ll get a lot of monitoring data, Please develop a series of statistical techniques to categorize them in an effective, fast and automatic manner.Task 3: If President Obama asked for your advice on fighting terrorism, what would you tell him? What should he do about ISIS?2 / 42021年数模小美赛C题翻译参考*Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.C题翻译为什么人们转向恐怖主义，特别是自杀的恐怖主义？主要的原因是什么？它通常是一个大问题和小的组合，或者说什么叫做“推拉”因素。
美赛题目2024年中文题目
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PROBLEM A: The Keep-Right-Except-To-Pass Rule
In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane.
Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important.
In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements
be needed.
Lastly, the rule as stated above relies upon human judgment for compliance. If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?
问题A：除非超车否则靠右行驶的交通规则
在一些汽车靠右行驶的国家（比如美国，中国等等），多车道的高速公路常常遵循以下原则：司机必须在最右侧驾驶，除非他们正在超车，超车时必须先移到左侧车道在超车后再返回。
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。
你不妨考察一下流量和安全的权衡问题,车速过高过低的限制，或者这个问题陈述中可能出现的其他因素。
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？
PROBLEM B: College Coaching Legends
Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your model’s top 5 coaches in each of 3 different sports.
In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.问题B：大学传奇教练
体育画报是一个为运动爱好者服务的杂志，正在寻找在整个上个世纪的“史上最好的大学教练”。
建立数学模型选择大学中在一下体育项目中最好的教练：曲棍球或场地曲棍球，足球，棒球或垒球，篮球，足球。
时间轴在你的分析中是否会有影响？比如1913年的教练和2013年的
教练是否会有所不同？清晰的对你的指标进行评估，讨论一下你的模型应用在跨越性别和所有可能对的体育项目中的效果。
展示你的模型中的在三种不同体育项目中的前五名教练。
除了传统的MCM格式，准备一个1到2页的文章给体育画报，解释你的结果和包括一个体育迷都明白的数学模型的非技术性解释。