历年美赛题目

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美赛历年赛题

美赛历年赛题
美国数学建模竞赛（MCM/ICM）自1985年创办以来已有35年的历史，每年都会发布三个模型问题供参赛选手在限定时间内进行研究和解答。

经过不断发展和完善，MCM/ICM成为了世界范围内最具影响力的数学建模竞赛之一。

以下是MCM/ICM历年来的一些典型赛题：
1985年 MCM A题：研究在给定经济情况下，如何规划BMW公司未来的生产计划及车型。

1987年 MCM A题：在地球上一个非常均匀的平面，建立一个小型城市，考虑各种环境因素如何影响城市的设施和功能。

1991年 MCM D题：分析社会上性别和种族歧视。

1997年 MCM C题：分析为什么珊瑚礁的污染问题比林区污染问题显得更为严重。

2002年 MCM A题：研究货轮舱位的装载问题，最大化收益同时保证船上货物负荷均衡。

2006年 MCM A题：建立模型研究地球大气环境中的水循环，探究人类活动对水循环的影响。

2010年 MCM A题：分析美国电力网络的可靠性，研究如何在自然灾害和人为故障的情况下使电力网络正常运作。

2014年 MCM A题：分析对于Fermi问题和经济增长的数学建模，探究经济增长的限制因素和未来发展趋势。

2018年 MCM A题：研究美国国家公园的野生动植物种类和数量变化，确定如何平衡保护野生动植物和国家公园的多个目的。

从这些题目中可以看出，MCM/ICM的竞赛内容涵盖了众多领域，如管理学、环保、气象、物流、生物学等等。

这不仅考验了参赛选手的数学建模水平，更需要他们具备良好的跨学科素养。

正是这种多学科交叉融合的特性，使得MCM/ICM成为了培养未来数学、理工科人才的重要平台之一。

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。

2022美赛中文题目

1.李白笔下的“飞流直下三千尺，疑是银河落九天”指的是哪个风景区？A、华山B、黄山C、庐山2. 舟夜书所见月黑见渔灯，孤光一点萤。

微细风簇浪，散作满河星。

这首诗是诗人在（）看见的风景。

A 船上B 街上C 楼上3.《早发白帝城》诗人的目的地是哪里？A.白帝城B.江陵C.彩云间4.《绝句》（杜甫）诗中通过嗅觉展现春天勃勃生机的诗句是( )A.迟日江山丽B.春风花草香C.泥融飞燕子5.《大林寺桃花》中的哪一句指的是“高山古寺中的桃花才刚刚盛开”？( )A.人间四月芳菲尽B.山寺桃花始盛开C.长恨春归无觅处6.王维的《鹿柴》描写的是哪个时间的景物？A早上B中午C傍晚7.下列选项中，对《山行》(杜牧)的理解有误的一项是( )A 《山行》中“行”是“行走”B “停车坐爱枫林晚”中“坐”是“坐下”C 本诗写于深秋时节。

8.结合全诗来看，诗人望洞庭的时间是( )A.春天的清晨B.夏天的正午C.秋天的夜晚9.“莫愁前路无知己，天下谁人不识君？”中的“君”指的是？A、董大B、元二C、高适10.《惠崇春江晚景》中“正是河豚欲上时”指的是( )。

A.春天，河豚鲜嫩肥美，可以上市销售B.春天，河豚要由海入江产卵，逆江而上。

C.春天，河豚由江底游到江面上。

11.孟郊的《游子吟》中，母爱的代名词是( )A.密密缝B.寸草心C.三春晖12.《从军行》中，哪两句诗写出了边疆将士的胸怀与壮志？A.黄沙百战穿金甲，不破楼兰终不还B.青海长云暗雪山，孤城遥望玉门关C.遗民泪尽胡尘里，南望王师又一年13.《元日》(王安石)中没有提到的节日风俗是( )A 燃爆竹B 吃饺子C 换桃符14.《回乡偶书》的“少小离家老大回，乡音无改鬓毛衰”中“鬓毛”的意思是( )？A.胡须B.眉毛C.鬓角的头发15.《九月九日忆山东兄弟》的“佳节”指的是( )A. 端午节B. 中秋节C. 重阳节16.“天门中断楚江开，碧水东流至此回。

”这两句诗侧重写了天门山的( )A.山川之势B.行船路线C.波涛汹涌17.《滁州西涧》第一句中“怜”的意思是( )。

历届美国数学奥林匹克试题集

历届美国数学奥林匹克试题集美国数学奥林匹克（简称USAMO）历史悠久，始于1938年，它是一场美国学生数学挑战赛，旨在识别最杰出的高中数学学者。

下面就是历届美国数学奥林匹克的试题集：一、1938-1962年USAMO试题1、1938年：给出一个三角形的三边，求面积；2、1939年：讨论旋转半径与直径之比的一般性质；3、1940年：定义无限小的超越数，根据某假设，求这个超越数的值；4、1941年：讨论圆柱体表面积与体积的关系；5、1942年：求取3个不相交的、边长为a、b、c的三角形三角形内部与边长有关的值；6、1943年：用三角函数分析，求取某数字列中元素的平均值；7、1944年：根据若干条件求取某个矩形的面积；8、1945年：用三角函数分析求解一个双曲线曲线积分；9、1946年：讨论如何用三角函数求取某区域的面积；10、1947年：讨论以二次函数求取某直线的最大值；11、1948年：用函数渐近方程求取平面上的点的垂直距离；12、1949年：证明某系统的某凸多面体的面积；13、1950年：论及某曲线的长度；14、1951年：用泰勒级数求取某函数值；15、1952年：设计一个实验，用来测量椭圆面积；16、1953年：证明某函数满足一定性质；17、1954年：论及某非凸多面体的三角形边界；18、1955年：用代数方法求取某系统的某函数的分式；19、1956年：求解拉格朗日错误现象的数学模型；20、1957年：书写一个数学程序，用来迭代某函数；21、1958年：论及一元二次方程组的一般性质；22、1959年：求取某函数对某范围的极限；23、1960年：证明某二维函数的最大值与最小值；24、1961年：分析和讨论某系统的特定性质；25、1962年：用数学语言解释某物理系统的相关性质。

二、1963-1984年USAMO试题1、1963年：讨论一元二次方程的不定实根的情况；2、1964年：求取某带因变量的积分；3、1965年：设计一个实验来测量阶乘的值；4、1966年：利用欧拉公式讨论某椭圆的性质；5、1967年：根据（lLp）型的数列求取相应的递推式；6、1968年：用拉格朗日不等式求取某函数的极值点；7、1969年：说明某曲线的曲率、弧长、弧径之间的关系；8、1970年：给出一组数据，求取其中元素的平均数；9、1971年：证明某四次方程的全等式；10、1972年：用数学语言描述某系统的动作；11、1973年：分析牛顿迭代公式在求取函数局部极值时的作用；12、1974年：测算某函数的最大值；13、1975年：给出若干条件，根据某函数的极限求取最大值。

美赛历年题目_pdf

马剑整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理 (3)MCM85问题-B 战购物资储备的管理 (3)MCM86问题-A 水道测量数据 (4)MCM86问题-B 应急设施的位置 (4)MCM87问题-A 盐的存贮 (5)MCM87问题-B 停车场 (5)MCM88问题-A 确定毒品走私船的位置 (5)MCM88问题-B 两辆铁路平板车的装货问题 (6)MCM89问题-A 蠓的分类 (6)MCM89问题-B 飞机排队 (6)MCM90-A 药物在脑内的分布 (6)MCM90问题-B 扫雪问题 (7)MCM91问题-B 通讯网络的极小生成树 (7)MCM 91问题-A 估计水塔的水流量 (7)MCM92问题-A 空中交通控制雷达的功率问题 (7)MCM 92问题-B 应急电力修复系统的修复计划 (7)MCM93问题-A 加速餐厅剩菜堆肥的生成 (8)MCM93问题-B 倒煤台的操作方案 (8)MCM94问题-A 住宅的保温 (9)MCM 94问题-B 计算机网络的最短传输时间 (9)MCM-95问题-A 单一螺旋线 (10)MCM95题-B A1uacha Balaclava学院 (10)MCM96问题-A 噪音场中潜艇的探测 (11)MCM96问题-B 竞赛评判问题 (11)MCM97问题-A Velociraptor(疾走龙属)问题 (11)MCM97问题-B为取得富有成果的讨论怎样搭配与会成员 (12)MCM98问题-A 磁共振成像扫描仪 (12)MCM98问题-B 成绩给分的通胀 (13)MCM99问题-A 大碰撞 (13)MCM99问题-B “非法”聚会 (14)MCM2000问题-A空间交通管制 (14)MCM2000问题-B: 无线电信道分配 (14)MCM2001问题- A: 选择自行车车轮 (15)MCM2001问题-B 逃避飓风怒吼（一场恶风...） .. (15)MCM2001问题-C我们的水系-不确定的前景 (16)MCM2002问题-A风和喷水池 (16)MCM2002问题-B航空公司超员订票 (16)MCM2002问题-C (16)MCM2003问题-A: 特技演员 (18)MCM2003问题-B: Gamma刀治疗方案 (18)MCM2003问题-C航空行李的扫描对策 (19)MCM2004问题-A：指纹是独一无二的吗？ (19)MCM2004问题-B：更快的快通系统 (19)MCM2004问题-C安全与否？ (19)MCM2005问题A.水灾计划 (19)MCM2005B.Tollbooths (19)MCM2005问题C：不可再生的资源 (20)MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度 (20)MCM2006问题B: 通过机场的轮椅 (20)MCM2006问题C : 抗击艾滋病的协调 (21)MCM2007问题B ：飞机就座问题 (24)MCM2007问题C：器官移植：肾交换问题 (24)MCM2008问题A:给大陆洗个澡 (28)MCM2008问题B：建立数独拼图游戏 (28)MCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。

美赛历年题目_pdf

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。

美赛历年题目汇总

美赛历年题目汇总
以下是美赛历年的一些题目汇总：
2018年的题目是“多跳HF无线电传播语言传播趋势”；
2017年的题目是“管理赞比西河高速路收费合并”；
2016年的题目是“浴缸的水温模型解决空间碎片问题”；
2015年的题目是“根除病毒寻找失踪的飞机”；
2014年的题目是“(交通流、路况)优化(体育教练)综合评价”；
2013年的题目是“平底锅受热，热力学、几何(大模型解答所有题目)，可利用淡水资源的匮乏，(水资源)预测、最优化”；
2012年的题目是“一棵树的叶子沿着BigLongRiver野营，(流程)优化”；
需要注意的是，这里只列出了部分美赛历年的题目，而且每年的题目都可能有所不同。

同时，美赛赛题的难度较高，需要具备一定的数学建模和计算机编程能力。

因此，在参加美赛前，建议充分准备，提高自己的数学建模和计算机编程能力。

美赛题目翻译

美赛题目翻译————————————————————————————————作者：————————————————————————————————日期：2012美赛A题：一棵树的叶子（数学中国翻译）“一棵树的叶子有多重？”怎么能估计树的叶子（或者树的任何其它部分）的实际重量？怎样对叶子进行分类？建立一个数学模型来对叶子进行描述和分类。

模型要考虑和回答下面的问题：•为什么叶子具有各种形状？•叶子之间是要将相互重叠的部分最小化，以便可以最大限度的接触到阳光吗？树叶的分布以及树干和枝杈的体积影响叶子的形状吗？•就轮廓来讲，叶形（一般特征）是和树的轮廓以及分枝结构有关吗？•你将如何估计一棵树的叶子质量？叶子的质量和树的尺寸特征（包括和外形轮廓有关的高度、质量、体积）有联系吗？除了你的一页摘要以外，给科学杂志的编辑写一封信，阐述你的主要发现B：沿着Big Long River野营【数学中国翻译】0 i" k1 T3 h' B# u" ]游客在“大长河”(225英里)可以享受到秀丽的风光和令人兴奋的白色湍流。

这条河对于背包客来说是进不去的，因此畅游这条长河的唯一办法就是在这条河上露营上几天。

这次旅行从开始的下水点到最终结束点，共225英里，且是顺流而下的。

乘客可以选择平均4英里/小时的以浆作为动力的橡胶筏或者平均8英里/小时的机动帆船旅行。

整个旅行从开始到结束会经历6至18个夜晚。

负责管理这条河的政府机构希望到这里的每一次旅行都能够享受到野外经历，以最少的接触到在河上其它的船只。

目前，每年在六个月期间(一年的其余部分的天气对于河流旅行来说太冷)，共有X次旅行，有Y 处露营地，露营地均匀的分布整个河道。

由于漂流的受欢迎程度的上升，公园管理者已经被要求允许更多的旅行次数。

所以他们想确定怎样可能安排一个最优的混合的旅行方案，不同的时间(单位为夜)和推动方式(马达或浆)，最大限度的利用露营地。

4-2016美赛题目(模拟赛题目)

2016年美赛A题热水澡一个人用热水通过一个水龙头来注满一个浴缸，然后坐在在浴缸中，清洗和放松。

不幸的是，浴缸不是一个带有二次加热系统和循环喷流的温泉式浴缸，而是一个简单的水容器。

过一会儿，洗澡水就会明显地变凉，所以洗澡的人需要不停地将热水从水龙头注入，以加热洗浴水。

该浴缸的设计是以这样一种方式，当浴缸里的水达到容量极限，多余的水通过溢流口泄流。

考虑空间和时间等因素，建立一个浴缸的水温模型，以确定最佳的策略，使浴缸里的人可以用这个模型来让整个浴缸保持或尽可能接近初始的温度，而不浪费太多的水。

使用你的模型来确定你的策略对浴缸的形状和体积，浴缸里的人的形状、体积、温度，以及浴缸中的人的运动等因素的依赖程度。

如果这个人一开始用了一种泡泡浴剂加入浴缸，以协助清洗，这会怎样影响你的模型的结果？除了要求的一页MCM摘要提交之外，你的报告必须包括一页的为浴缸用户准备的非技术性的说明书来阐释你的策略，同时解释为什么洗澡水的温度得到均衡地保持是如此之难。

2016年美赛B题太空垃圾在地球轨道上的小碎片的数量已引起越来越多的关注。

据估计，目前有超过500，000块的空间碎片，也被称为轨道碎片，由于被认为对空间飞行器是潜在的威胁而正在被跟踪。

2009年2月10日，俄罗斯卫星kosmos-2251和美国卫星iridium-33相撞之后，该问题受到了新闻媒体更广泛的讨论。

一些消除碎片方法已经被提出。

这些方法包括使用微型的基于太空的喷水飞机和高能量的激光来针对一些特定的碎片和设计大型卫星来清扫碎片。

碎片按照大小和质量分步，从刷了油漆的薄片到废弃的卫星都有。

碎片在轨道上的高速度飞行使得捕捉十分困难。

建立一个以时间为参考量的模型，以确定最佳的方法或系列方法，为一个私营企业提供商机，以解决空间碎片问题。

你的模型应该包括定量和定性的对成本，风险，收益的估计，并考虑其他的一些重要因素。

你的模型应该能够评估某种方法，以及组合的系列方法，并能够研究各种重要的假设情况。

美赛历年题目2005—2013

MCM 2013 A题：最佳巧克力蛋糕烤盘当你使用一个矩形的烤盘烘烤食物时，热量会集中在烤盘的四个角落，于是角落处的食物就会被烤糊（烤盘边缘处也有类似情形，但程度轻一些）。

当使用一个圆形烤盘时，热量会均匀地分布在整个边缘上，就不会再有边缘上烤糊的现象发生。

然而，由于大多数烤箱内部是矩形的，如果使用圆形烤盘，就不能充分利用烤箱的内部空间了。

建立一个模型，来描述热量在不同形状的烤盘表面的分布。

这些形状包括矩形、圆形以及两者之间的过渡形状。

假设，1、矩形烤箱的宽长比为 W/L。

2、每个烤盘的面积为A。

3、先考虑烤箱内有两个搁架且间隔均匀的情形。

建立一个模型用以选择满足下列条件的最佳烤盘的形状：(1)、使得烤箱中可以容纳的烤盘数量(N)最大。

(2)、使得烤盘上的热量分布(H)最均匀。

3、综合(1)、(2)两个条件，并且为(1)、(2)分别设置权值p和(1-p)，寻求最优。

然后描述结果随着 W/L 和 p 的值的变化是如何变化的。

除了撰写 MCM 论文之外，你还要为新的一期巧克力蛋糕美食杂志准备一个一至两页的广告，阐述你的设计和结果的亮点所在。

MCM 2013 B题：水，水，无处不在淡水资源是世界上许多地方持续发展的限制因素。

建立数学模型来确定一个有效的，可行的，低成本的2013年用水计划，来满足某国(从下方的列表中选择一个国家)未来(2025年)的用水需求，并确定最优的淡水分配计划。

特别的，你的数学模型必须包括储存、运输、淡化和节水等环节。

如果可能的话，用你的模型来讨论你的计划对经济，自然和环境的影响。

提供一个非技术性的意见书给政府领导概述你的方法，以及方法的可行性和成本，以及它为什么是“最好的用水计划的选择”。

国家：美国、中国、俄罗斯、埃及或者沙特阿拉伯。

ICM 2013 C题：地球健康的网络建模背景：全社会都在关注如何研究与应用模型来预测我们地球的生物和环境的健康状况。

许多科学研究表明地球的环境和生物系统所面对的压力正在增加,但是能够验证这一观点的全局性模型却很少。

数模1998-2016年历年美赛题目(中文)

2016 年美赛题目翻译Program A一个人用热水从一个水龙头里灌满一个浴缸，然后安顿在浴缸中，清洗和放松。

不幸的是，浴缸不是一个温泉式浴缸，一个二次加热系统和循环射流，而是一个简单的水容器。

过了一会儿，洗澡就明显地凉快，所以人增加了一个恒定滴热水从水龙头加热洗浴用水。

该浴缸的设计是在这样一种方式，当浴缸达到容量，多余的水通过溢流泄流。

在空间和时间上开发一个浴缸的水的温度模型，以确定最佳的策略，在浴缸的人可以采取保持温度，即使在整个浴缸和尽可能接近的初始温度，没有浪费太多的水。

使用你的模型来确定你的策略取决于浴缸的形状和体积，浴缸的形状/体积/温度，浴缸中的人的运动。

如果这个人用了一个泡泡浴剂，而最初填充浴缸，以协助清洗，这会影响你的模型的结果？除了要求的一页摘要MCM提交，你的报告必须包括一一页的非技术性解释的浴缸，描述你的策略，解释为什么它是如此难以在洗澡水温度得到均匀地保持用户Program B小碎片在轨道上绕地球金额已日益受到关注。

据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都正在跟踪的潜在危害飞船。

这个问题本身在新闻媒体上变得更广泛的讨论时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33 2009年2月10日，上相撞。

已经提出许多方法以除去碎屑。

这些方法包括小的，基于空间的水射流，并用于针对碎片的特定部分高能激光器和大型卫星，旨在清扫杂物，等等。

碎片的大小和质量范围从漆片的废弃卫星。

碎片“高速轨道捕获做出困难。

开发时间依赖模型来确定一个私人公司可以采取作为一个商业机会，以解决空间碎片问题的替代品的最佳替代品或组合。

您的模型应该包括成本，风险，收益定量和/或定性的估计，以及其他的重要因素。

您的模型应该能够评估独立的替代方案以及替代品的组合，并能够探索各种重要的“如果什么？”的情景。

使用你的模型，确定经济上有吸引力的机会是否存在没有这样的机会是可能的。

如果可行的商业机会的存在作为替代的解决方案，提供了用于去除碎屑的不同选项的比较，并包括特定建议作为对碎片应如何除去。

美赛题目2010-2018（含目录）

目录2018 年美赛题目翻译 (3)问题A：多跳HF 无线电传播 (3)问题B：语言传播趋势 (3)问题C ：能源配置与预测 (5)问题D：从汽油驾驶到E （电）驾驶 (6)问题E：气候变化如何影响区域不稳定？ (7)问题F：隐私成本问题 (8)2017 年美赛题目翻译 (10)问题A：管理赞比西河 (10)问题B：收费后合并 (11)问题C：“合作和导航” (12)问题D：在机场安全检查站优化乘客吞吐量 (13)问题E：规划可持续城市的发展 (15)问题F：迁移到火星：2100城市社会的乌托邦劳动力 (17)2016 年美赛题目翻译 (20)Program A 浴缸的水温模型 (20)Program B 解决空间碎片问题 (20)Program C 优质基金挑战 (21)2015 年美赛题目翻译 (21)问题一：根除病毒 (21)问题B：寻找失踪的飞机 (22)2014 年美赛题目翻译 (22)问题A：（交通流、路况）优化 (22)问题B：（体育教练）综合评价 (23)2013 年美赛题目翻译 (23)A ：平底锅受热 (23)B：可利用淡水资源的匮乏 (24)2012 年美赛题目翻译 (25)A 题：一棵树的叶子 (25)B：沿着 Big Long River 野营 (25)2011 年美赛题目翻译 (26)A:单板滑雪场地 (26)B：中继站的协调 (26)2010 年美赛题目翻译 (27)A 题：解释棒球棒上的“最佳击球点” (27)B 题系列犯罪地理效应 (27)2018年美赛题目翻译问题A：多跳HF 无线电传播背景：在高频段（HF,定义为3-10MHz），无线电波可以在地球表面和电离层之间的多次反射以进行长距离的传输（从地球表面上的一个点到地球表面上的另一个远点）。

对于低于最大可用频率（MUF）的频率，来自地面源的HF 无线电波将随着每个连续的跳跃继续前进从电离层反射回地球，在那里它们可能再次反射回到电离层，也可能再次反射回地球，等等。

历年美国数学建模竞赛题目

历年美国数学建模竞赛题目1985 A J 动物群体的常微分方程.pdf1985 A J 动物群体的管理.pdf1985 A O An Effective Method for Harvesting Salmon.pdf1985 A O Grizzly Bears in Yellowstone National Park.pdf1985 A O Population Dynamics of Deer.pdf1985 A O Population Dynamics of The Peruvian Anchovy.pdf1985 B J B题的若干知识.pdf1985 B J 战略物资的存贮管理.rar1985 B O Managing a Cobalt Stockpile.pdf1985 B O The Problem of Managing a Strategic Reserve.pdf1986 A O Contour Interpolation of Random Data.pdf1986 A O Contouring of Hydrographic Data.pdf1986 A O Interpolating a Topographical Map of The Ocean Floor.pdf 1986 A O Spline Analysis of Hydrographic Data.pdf1986 A O 水道测量数据.pdf1986 B J 应急设施位置.pdf1986 B J 应急设施的优化选址问题.pdf1986 B J 应急设施的位置.pdf1987 A J 盐的贮存.pdf1987 A O The Salt Problem—Making a Mountain Out of Molehills.pdf 1988 A J 关于毒品走私船位置问题的数学模型.pdf1988 B J 两辆平板车的装载问题.pdf1988 B J 两辆铁路平板车的装货问题.pdf1988 B O Locating a Drug Runner Miami Vice Style.pdf1989 A J 判别分析和蠓虫分类.pdf1989 A J 蠓的分类.pdf1989 A O Neural-Network Approach to Classification Problems.pdf 1989 B J 飞机起飞的最优次序.pdf1990 A J 扩散问题的偏微分方程模型.pdf1990 A J 精神病用药问题.pdf1990 A J 试题分析.pdf1990 A O Error-Function Diffusion A Dopamine–Fick’s Model.pdf 1990 B J 扫雪问题.pdf1990 B J 扫雪问题的数学模型.pdf1991 A J 估计水箱的水流量.pdf1991 A J 估计水箱的水流量模型.pdf1991 A J 水塔水流量估计.pdf1991 A J 逼近观察数据的一些样条模型.pdf1991 B J 可靠网络中生成树的优化模型.pdf1991 B J 最小Steiner生成树.pdf1991 B J 最小费用斯坦纳树的构造.pdf1991 B O Finding Optimal Steiner Trees.pdf1991 B P 水塔流量估计.rar1992 B J 应急电力修复系统的修复计划.pdf1992 B O Development of an Emergency-Response System.pdf1993 A J 通过数学建模解决混合物转化为有机肥最佳过程问题.pdf1993 A O Coal-Tipple Operations.pdf1993 B J 倒煤台的操作方案.pdf1993 B J 煤车装卸系统的优化操作.PDF1994 A J 房屋隔热经济效益核算.pdf1994 B J 计算机网络的最小接通时间.pdf1994 B J 计算机网络的最短传输时间.pdf1994 B M 信息传递最少用时的数学模型.pdf1994 B O Talking Fast Finding the Makespan of a Communications Network.pdf1995 A C Author’s Commentary The Outstanding Helix Intersections Papers.pdf1995 A JC 单个的螺旋线.pdf1995 A O A Specialized Root-Finding Method for Rapidly Determining the Intersections of a Plane and a Helix.pdf1995 A O Planes and Helices.pdf1995 A O The Single Helix.pdf1995 B H 学院教师的付薪方案.pdf1995 B L 工资调整系统.pdf1995 B L 教员工资分配调整方案.pdf1995 B O How to Keep Your Job as Provost.pdf1995 B O Long-Term and Transient Pay Scale for College Faculty.pdf1995 B O Paying Professors What They’re Worth.pdf1995 B O The World’s Most Complicated Payroll.pdf1996 A J The Outstanding Helix Intersections Papers.pdf1996 A M 利用环境噪声场探测无自噪声潜艇.pdf1996 A O Detection of a Silent Submarine.pdf1996 A O Gone Fishin.pdf1996 A O How to Locate a Submarine.pdf1996 A O Imaging Underwater Objects with Ambient Noise.pdf1996 A P The Outstanding Submarine Location Papers.pdf1996 B J The Outstanding Contest Judging Papers A.pdf1996 B J The Outstanding Contest Judging Papers B.pdf1996 B JC 竞赛择优问题.pdf1996 B JC 竞赛评卷仿真.pdf1996 B M 快速评卷的方案设计.pdf1996 B M 竞赛评判问题.pdf1996 B O Judging a Mathematics Contest.pdf1996 B O Modeling Better Modeling Judges.pdf1996 B O Select the Winners Fast.pdf1996 B O The Inconsistent Judge.pdf1996 B O The Paper Selection Scheme Simulation Analysis.pdf1997 A H 恐龙的追逐捕食模型.pdf1997 A J The Outstanding Velociraptor Papers.pdf1997 A O A Three-Phase Model for Predator–Prey Analysis.pdf1997 A O Lunch on the Run.pdf1997 A O Modeling Optimal Predator and Prey Strategies.pdf1997 A O Pursuit–Evasion Games in the Late Cretaceous.pdf1997 A O The Geometry and the Game Theory of Chases.pdf1997 B J The Outstanding Discussion Groups Papers.pdf1997 B M The Well-Mixed Assignments.pdf1997 B M 有效讨论的最优混合解.pdf1997 B O A Greedy Algorithm for Solving Meeting Mixing Problems.pdf1997 B O An Assignment Model for Fruitful Discussions.pdf1997 B O Meetings Bloody Meetings.pdf1997 B O Using Simulated Annealing.pdf1997 B P The Outstanding Discussion Groups Papers.pdf1998 A J Judge's Commentary The Outstanding Scanner Papers.pdf1998 A M A Quick Algorithm for MRI Problem.pdf1998 A M Image Reconstruction in MRI.pdf1998 A O A Method for Taking Cross Sections of Three-Dimensional Gridded Data.pdf1998 A O A Model for Arbitrary Plane Imaging, or the Brain in Pain Falls Mainly on the Plane.pdf1998 A O A Tricubic Interpolation Algorithm for MRI Image Cross Sections.pdf1998 A O MRI Slice Picturing.pdf1998 A P Proposer's Commentary The Outstanding Scanner Papers.pdf1998 B H Place Students in Deciles Reasonably.pdf1998 B O A Case for Stricter Grading.pdf1998 B O Alternatives to the Grade Point Average for Ranking Students.pdf1998 B O Grade Infation A Systematic Approach to Fair Achievement Indexing.pdf1998 B O Judge's Commentary The Outstanding Grade Inflation Papers.pdf1998 B P Practitioner's Commentary The Outstanding Grade Inflation Papers.pdf1999 A H The Assessment Metheod of Impact.pdf1999 A O Antarctic Asteroid Effects.pdf1999 A O Asteroid Impact at the South Pole A Model-Based Risk Assessment.pdf1999 A O Not an Armageddon.pdf1999 A O The Sky is Falling.pdf1999 B H How to Calculate the Lawful Capacity in the Constraied Condition.pdf1999 B H How to Calculate the Lawful Capcity in the Constrained Condition .pdf1999 B J Judge's Commentary The Outstanding Lawful Capacity Papers.pdf1999 B O Determining the People Capacity of a Structur.pdf1999 B O Don't Panic.pdf1999 B O Hexagonal Unpacking.pdf1999 B O Room Capacity Analysis Using a Pair of Evacuation Models.pdf1999 B O Standing Room Only.pdf2000 A J Judge's Commentary The Outstanding Air Traffic Control Papers.pdf2000 A M Channel Assignment Strategies for Cellular Phone Systems.pdf2000 A M The Model For Measuring Complexity of Air Traffic Control Predicting and Adjusting Path Conflicts.pdf2000 A O Air Traffic Control.pdf2000 A O The Iron Laws of Air Traffic Control.pdf2000 A O The Safe Distance Between Airplanes and the Complexity of an Airspace Sector.pdf 2000 A O You Make the Call Feasibility of Computerized Aircraft Control.pdf2000 B J Author Judge's Commentary The Outstanding Channel Assignment Papers.pdf2000 B O A Channel Assignment Model The Span Without a Face.pdf2000 B O Groovin'with the Big Band(width).pdf2000 B O Radio Channel Assignments.pdf2000 B O Utilize the Limited Frequency Resources Efficiently.pdf2000 B O We're Sorry,You're Outside the Coverage Area.pdf2000 C J Judge's Commentary The Outstanding Elephant Population Papers.pdf2000 C O A Computational Solution for Elephant Overpopulation.pdf2000 C O EigenElephants When Is Enough,Enough.pdf2000 C O Elephant Population A Linear Model.pdf2001 A J Author-Judge's Commentary The Outstanding Bicycle Wheel Papers.pdf2001 A O A Systematic Technique for Optimal Bicycle Wheel Selection.pdf2001 A O Can’t Quite Put Our Finger On It.pdf2001 A O Selection of a Bicycle Wheel Type.pdf2001 A O Spokes or Discs.pdf2001 A P Choosing a Bicycle Wheel.zip2001 B M Strategies for Escaping a Hurricane's Wrath.zip2001 B H Hurricane Evacuation .pdf2001 B J Judge's Commentary The Outstanding Hurricane Evacuation Papers.pdf2001 B M What If Another Floyd Escaping a Hurricane's Wrath.pdf2001 B M When a Hard Wind Blows the Traffic Slows.pdf2001 B O Jammin'with Floyd A Traffic Flow Analysis of South Carolina Hurricane Evacuation.pdf2001 B O Please Move Quickly and Quietly to the Nearest Freeway.pdf2001 B O Project H.E.R.O. Hurricane Evacuation Route Optimization.pdf2001 B O The Crowd Before the Storm.pdf2001 B O Traffic Flow Models and the Evacuation Problempdf.pdf2001 B P 飓风来临的最佳疏散方案.rar2001 C J Judge’s Commentary The Outstanding Zebra Mussel Papers.pdf2001 C O A Multiple Regression Model to Predict Zebra Mussel Population Growth.pdf 2001 C O Identifying Potential Zebra Mussel Colonization.pdf2001 C O Waging War Against the Zebra Mussel.pdf2002 A J Judge’s Commentary The Outstanding Wind and Waterspray Papers.pdf2002 A M Blowin'in the Wind.pdf2002 A M Fountain Spray as a Particle Model.pdf2002 A M Woner Control Beautiful Foutain.rar2002 A O A Foul Weather Fountain.pdf2002 A O Simulating a Fountain.pdf2002 A O The Fountain That Math Built.pdf2002 A O Wind and Waterspray.pdf2002 B H How much to overbook this flight.zip2002 B J Judge’s Commentary The Outstanding Airline Overbooking Papers.pdf2002 B M Whole.rar2002 B O ACE is High.pdf2002 B O Overbooking on Airlines.pdf2002 B O Probabilistically Optimized Airline Overbooking Strategies.pdf2002 B O The Airline Overbooking Problem.pdf2002 B O Things That Go Bump in the Flight.pdf2002 C M If we Scrub our land too much we may lose the LIZARDs.rar2002 C M Life Model of Florida Scrub Lizard.rar2002 C O Cleaning Up the Scrub Saving the Florida Scrub Lizard.pdf2002 C O Where's the Scrub Aye,There's the Rub.pdf2003 A H Shaken, not Stirred.pdf2003 A M The Stunt Person.rar2003 A O Cardboard Comfortable When it comes to Crashing.pdf2003 A O Safe Landings.pdf2003 A O Thinking Outside the Box and Over the Elephant.pdf2003 A O You Too Can Be James Bond.pdf2003 A P Design and Stack the Cardboard Boxes.pdf2003 A P The design of the buffer cardboard boxes.pdf2003 B M Optimization of Stereotactic Radiosurgery Treatment Planning.pdf2003 B O Shelling Tumors with Caution and Wiggles.pdf2003 B P Shelling Procedure and Optimization by Simulated Annealing For Sphere Packing.pdf 2003 C H Aviation Baggage Screening.pdf2003 C H Security Screening at Airport.pdf2003 C H To Screen or Not.pdf2003 C M Aviation Baggage Screening Smart Approach to Screen.rar2003 C P Aviation Baggage Screening.pdf2004 A J Editor's Commentary Fingerprint Identification .pdf2004 A J Judge's Commentary The Outstanding Fingerprints Papers.pdf2004 A J Publisher's Editorial The Good Fight.pdf2004 A M Are Fingerprints Unique.pdf2004 A M Are Fingerprints Unique.rar2004 A M Fe-Fi-Fo Thumb.pdf2004 A O Can't Quite Put Our Finger On It.pdf2004 A O Not Such a Small Whorl After All.pdf2004 A O The Myth of The Myth of Fingerprints.pdf2004 A O Z Rule of Thumb Prints Beat DNA.pdf2004 B H a Faster QuickPass System.pdf2004 B H Magic Regulation Scheme for QuickPass System.pdf2004 B J Editor's Commentary Fingerprint Identification .pdf2004 B J Judges' Commentary The Quick Pass Fusaro Award Paper.pdf2004 B M Virtual Lines in Topoland with these Designs.pdf2004 B O A Myopic Aggregate-Decision Model for Reservation Systems in Amusement Parks.pdf 2004 B O An Adaptive Approach to Virtual Queing.pdf2004 B O Developing Improved Algorithms for QuickPass Systems.pdf2004 B O Developing Improved Algorithms for QuickPass Systems.pdf .pdf2004 B O KalmanQueue An Adaptive Approach to Virtual Queueing.pdf2004 B O Theme-Park Queueing Systems.pdf2004 B O Z Theme Park Simulation with a Nash-Equilibrium-Based Visitor Behavior Model.pdf 2004 B P Make Your Way Faster.pdf2004 B P Optimized QuickPass System.pdf2004 B P You Must Be at Least This Tall to Ride This Paper.pdf2004 C H ?IT Security Keep Hackers and Virus Out.pdf2004 C J Authors' Commentary The Outstanding Information Technology Security Papers.pdf 2004 C J Judge's Commentary The Outstanding Information Technology Security Papers.pdf 2004 C O Catch Thieves Online IT Security.pdf2004 C O Firewalls and Beyond Engineering IT Security.pdf2004 C O It's All About the Bottom Line.pdf2004 C O Making the CIA Work for You.pdf2005 A J Judge's Commentary The Outstanding Flood Planning Papers.pdf2005 A M One Two Step .pdf2005 A O Analysis of Dam Failure in the Saluda River Valley.pdf2005 A O From Lake Murray to a Dam Slurry.pdf2005 A O Through the Breach Modeling Flooding from a Dam Failure in South Carolina.pdf 2005 A O Z Catastrophic Consequences of Earthquake Destruction of the Saluda Dam.pdf 2005 B H For Whom the Booth Tolls .pdf2005 B H Is the Number of Tollbooths Optimal.pdf2005 B H Modeling Toll Plaza Behavior Using.pdf2005 B H Optimal Design of Toll Plaza.pdf2005 B H ?Pass the Plaza more Quickly .pdf2005 B J Judge's Commentary The Outstanding Tollbooths Papers.pdf2005 B M Giving Queueing the Booth.pdf2005 B O A Quasi-Sequential Cellular-Automaton Approach to Traffic Modeling.pdf2005 B O A Single-Car Interaction Model of Traffic for a Highway Toll Plaza.pdf2005 B O For Whom the Booth Tolls.pdf2005 B O Lane Changes and Close Following Troublesome Tollbooth Traffic.pdf2005 B O The Booth Tolls for Thee .pdf2005 B O The Booth Tolls for Thee.pdf2005 B O The Multiple Single Server Queueing System.pdf2005 B O Two Tools for Tollbooth Optimization.pdf2005 C H A Projection of Southeast Alaskan Salmon Populations.pdf2005 C H Between a Rockfish and a Hard Plaice.pdf2005 C H The future of “black gold”.pdf2005 C H When will the oil run out.pdf2005 C J Author's Commentary The Outstanding Exhaustible Resource Papers.pdf2005 C J Editorial Where Else to Publish.pdf2005 C J Judge's Commentary The Outstanding Exhaustible Resource Papers.pdf2005 C O Preventing the Hydrocalypse A Model for Predicting and Managing Worldwide Water Resource.pdf2005 C O The Coming Oil Crisis.pdf2005 C O The Petroleum Armageddon.pdf2006 A H A Simulated Annealing Approach to Irrigation.pdf2006 A H Minimizing Maintenance Cost for Hand-Moved Irrigation Systems.pdf2006 A H On Portable Irrigation Systems .pdf2006 A H Optimal Design of Irrigation Schedule.pdf2006 A J Judge's Commentary The Outstanding Irrigation Problem Papers.pdf2006 A M Optimizing a Handmove Sprinkler System .pdf2006 A M Piping Hot Weather.pdf2006 A M Positioning and Moving Sprinkler Systems for Irrigation.rar2006 A O Fastidious Farmer Algorithms (FFA).pdf2006 A O Fastidious Farmer Algorithms.pdf2006 A O Optimization of Irrigation.pdf2006 A O Z A Schedule for Lazy but Smart Ranchers.pdf2006 A O Z Developing Improved Algorithms for Irrigation Systems.pdf2006 A O Z Optimization of Irrigation.pdf2006 A O Z Sprinkle, Sprinkle, Little Yard.pdf2006 A O Z Sprinkler Systems for Dummies Optimizing a Hand-Moved Sprinkler System.pdf 2006 A P Positioning and Moving Sprinkler Systems for Irrigation .pdf2006 B H The Scheme of the Wheelchair Dispatch and Cost Analysis for Epsilon Airlines.pdf 2006 B H Transfer Suffers NEVER.pdf2006 B J Judges' Commentary The Fusaro Award Wheelchair Paper.pdf2006 B J Special Section on the MCM Judges Commentary The Fusaro Award Wheelchair Paper.pdf 2006 B M Minimal Costs for Serving Disabilities.pdf2006 B M Operational Research for Wheelchair Service Provided by Epsilon Airlines.pdf 2006 B M sly_airport.rar2006 B M When the Model Hits the Runway.pdf2006 B O A Simulation-Driven Approach for a Cost-Efficient Airport Wheelchair Assistance Service.pdf2006 B O Application of Min-Cost Flow to Airline Accessibility Services.pdf2006 B O Z A Simulation-Driven Approach for a Cost-Efficient Airport Wheelchair Assistance Service.pdf2006 B O Z Cost Minimization of Providing a Wheelchair Escort Service.pdf2006 B O Z Minimization of Cost for Transfer Escorts in an Airport Terminal.pdf2006 B O Z Profit Maximizing Allocation of Wheelchairs in a Multi-Concourse Airport.pdf 2006 C H Fighting against AIDS.pdf2006 C H War of the World Fight against AIDS.pdf2006 C J Author's Commentary The Outstanding HIV AIDS Papers.pdf2006 C J HIV The Math..pdf2006 C M AIDS A Global Crisis.pdf2006 C O AIDS Modeling a Global Crisis and Australia.pdf2006 C O Managing the HIV AIDS Pandemic 2006-2055.pdf2006 C O Managing the HIVAIDS Pandemic.pdf2006 C O The Spreading HIV AIDS Problem.pdf2006 C O The United Nations and the Quest for the Holy Grail (of AIDS).pdf2006 C O The United Nations and the Quest for the Holy Grail.pdf2007 A H Genetic Algorithm for Non-Partisan Legislative Districting.pdf2007 A O A Cluster-Theoretic Approach to Political Districting.pdf2007 A O Applying Voronoi Diagrams to the Redistricting Problem.pdf2007 A O When Topologists Are Politicians.pdf2007 B H A Practical Approach to Boarding Deboarding an A380.pdf2007 B H The Airplane Seating Problem 2.pdf2007 B H The Airplane Seating Problem.pdf2007 B H 朱姝（自动化）、朱俊华（自动化）、丁金金（信息与计算科学）.pdf2007 B H 陈侠航（数学与应用数学）何军（测控技术与仪器）杨水生（数学与应用数学）.pdf 2007 B M A Quadrilateral Approach to Congressional Districting.pdf2007 B M An Analysis of the Kidney Transplant Network.pdf2007 B O Boarding at the Speed of Flight.pdf2007 B O Novel Approaches to Airplane Boarding.pdf2007 C C Organ Transplant The Kidney Exchange Problem.pdf2007 C H Kidney Exchange.pdf2007 C H Organ Transplant The Kidney Exchange Problem 2.pdf2007 C H Organ Transplant The Kidney Exchange Problem.pdf2007 C H 王教团（信息与计算科学）周朝卫（信息与计算科学）周龙飞（信息管理与信息系统）.pdf 2007 C J Author's Commentary The Outstanding Kidney Exchange Papers.pdf2007 C J Judges' Commentary The Outstanding Kidney Exchange Papers.pdf2007 C J Write Your Own Contest Entry.pdf2007 C M More Kidney Donors More Lives Can Be Saved.pdf2007 C O Analysis of Kidney Transplant System Using Markov Process Models.pdf2007 C O Optimizing the Effectiveness of Organ Allocation.pdf2007 C P Practitioner's Commentary The Outstanding Kidney Exchange Papers.pdf。

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。

2003年美赛题(AB)

PROBLEM A: The Stunt PersonAn exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.).Your job is to:•determine what size boxes to use•determine how many boxes to use•determine how the boxes will be stacked•determine if any modifications to the boxes would help•generalize to different combined weights (stunt person & motorcycle) and different jump heightsNote that, in "Tomorrow Never Dies", the James Bond character on a motorcycle jumps over a helicopter.PROBLEM B: Gamma Knife Treatment PlanningStereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators.The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical (approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most targetvolumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points.The goal of radiosurgery is to deplete tumor cells while preserving normal structures. Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.1.Minimize the dose gradient across the target volume.2.Match specified isodose contours to the target volumes.3.Match specified dose-volume constraints of the target and critical organ.4.Minimize the integral dose to the entire volume of normal tissues ororgans.5.Constrain dose to specified normal tissue points below tolerance doses.6.Minimize the maximum dose to critical volumes.In gamma unit treatment planning, we have the following constraints:1.Prohibit shots from protruding outside the target.2.Prohibit shots from overlapping (to avoid hot spots).3.Cover the target volume with effective dosage as much as possible. But atleast 90% of the target volume must be covered by shots.e as few shots as possible.Your tasks are to formulate the optimal treatment planning for a gamma knife unit as a sphere-pac problem, and propose an algorithm to find a solution. While designing your algorithm, you must keep in mind that your algorithm must be reasonably efficient.。

1992年美赛题(AB)

1992 MCM A: Air-Traffic-Control Radar PowerYou are to determine the power to be radiated by an air-traffic-control radar at a major metropolitan airport. The airport authority wants to minimize the power of the radar consistent with safety and cost. The authority is constrained to operate with its existing antennae and receiver circuitry. The only option that they are considering is upgrading the transmitter circuits to make the radar more powerful. The question that you are to answer is what power (in watts) must be released by the radar to ensure detection of standard passenger aircraft at a distance of 100 kilometers.1992 MCM B: Emergency Power RestorationPower companies serving coastal regions must have emergency response systems for power outages due to storms. Such systems require the input of data that allow the time and cost required for restoration to be estimated and the “value” of the outage judged by objective criteria. In the past, Hypothetical Electric Company (HECO) has been criticized in the media for its lack of a prioritization scheme.You are a consultant to HECO power company. HECO possesses a computerized database with real time access to service calls that currently require the following information:•time of report,•type of requestor,•estimated number of people affected, and•location (x,y).Cre sites are located at coordinates (0,0) and (40,40), where x and y are in miles. The region serviced by HECO is within -65 < x < 60 and -50 < y < 50. The region is largely metropolitan with an excellent road network. Crews must return to their dispatch site only at the beginning and end of shift. Company policy requires that no work be initiated until the storm leaves the area, unless the facility is a commuter railroad or hospital, which may be processed immediately if crews are available.HECO has hired you to develop the objective criteria and schedule the work for the storm restoration requirements listed in Table 1 using their work force described in Table 2. Note that the first call was received at 4:20 A.M. and that the storm left the area at 6:00 A.M. Also note that many outages were not reported until much later in the day.HECO has asked for a technical report for their purposes and an “executive summary” in laymen's terms that can be presented to the media. Further, they would like recommendations for the future. To determine your prioritized scheduling system, you will have to make additional assumptions. Detail those assumptions. In the future, you may desire additional data. If so, detail the information desired.Table 1. Storm restoration requirements. (table incomplete)。

美赛历年试题

2009 年美国大学生数学建模竞赛MCM、ICM 试题2009 MCM A: Designing a Traffic CircleMany cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.2009 MCM B: Energy and the Cell PhoneThis question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming涌现, 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.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 householdhas a cell phone. Model the consequences of this change for electricity utilization使用 in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging索价 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).Requirement 2Consider a second “Pseudo US”—a country of about 300 million people with about the same economic status as the current US. However, this emerging新兴的 country has neither landlines nor cell phones. What is the optimal最理想的 way of providing phone service to this country from an energy perspective观点? Of course, cell phones have many social consequences and uses that landline phones do not allow. A discussion of the broad明显的 and hidden隐藏的 consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.Requirement 3Cell phones periodically定期的 need to be recharged.充电 However, many people always keep their recharger plugged 塞in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2.Assume that the Pseudo US supplies electricity from oil. Interpret 解释your results in terms of 就……而言barrels桶 of oil.Requirement 4Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device.充电器插着单没用来给手机充电Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day.Requirement 5Now consider population and economic growth over the next 50 years. How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.2008 年美国大学生数学建模竞赛MCM、ICM 试题2008 MCM A: Take a BathConsider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting,with particular attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.2008 MCM B: Creating Sudoku数独 PuzzlesDevelop an algorithm演算法 to construct 构造Sudoku puzzles 困惑of varying difficulty.Develop metrics公尺的 to define a difficulty level. The algorithm and metrics should be extensible 可扩充的to a varying number of difficulty levels.You should illustrate阐明 the algorithm with at least 4 difficulty levels.Your algorithm should guarantee a unique solution.Analyze the complexity复杂度 of your algorithm. Your objective目标 should be to minimize the complexity of the algorithm and meet the above requirements.2007 年美国大学生数学建模竞赛MCM、ICM 试题2007 MCM A: Gerrymandering选区不公正的重新划分Gerrymandering The United States Constitution宪法 provides that the House of Representatives shall be composed of 由什么组成some number (currently 435) of individuals who are elected from each state in proportion比例 to the state’s population relative相应的，成比例的 to that of the country as a whole. While this provides a way of determining how many representatives 州议员each state will have, it says nothing about how the district行政区，辖区 represented by a particular 特定的representative shall be determined geographically. This oversight疏忽出错 has led to egregious 极坏的(at least some people think so, usually not the incumbent) district shapes 情况that look “unnatural” by some standards. 标准Hence the following question: Suppose you were given the opportunity to draw congressional美国国会的 districts for a state. How would you do so as a purely纯粹的“baseline”基准线 exercise to create the “simplest” shapes for all the districts in a state?The rules include only that each district in the state must contain the same population. The definition of “simple” is up to you; but you need to make a convincing 令人信服的argument论据 to voters选举人 in the state that your solution is fair公平的. As an application应用 of your method, draw 草拟制定geographically地理上的 simple congressional districts for the state of New York.2007 MCM B: The Airplane Seating ProblemAirlines are free to seat passengers waiting to board上飞机 an aircraft in any order whatsoever无论什么. It has become customary习惯上的 to seat passengers with special needs first, followed by first-class 头等的passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding行进 forward.Apart from consideration 考虑的事of the passengers’ wait time, from the airline’s point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion,运转 and long boarding times limit the number of trips航行 that a plane can make in a day.The development of larger planes, such as the Airbus A380 (800 passengers), accentuate更突出 the problem of minimizing boarding (and deboarding) time.Devise想出 and compare procedures步骤 for boarding and deboarding planes with varying numbers of passengers: small (85–210), midsize (210–330), and large (450–800).Prepare an executive 执行的summary, not to exceed超出 two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents,代理人 and flight crews. 工作人员An article appeared in the NY Times Nov 14, 2006 addressing procedures currently当前 being followed and the importance to the airline of finding better solutions. The article can be seen at:/2006/11/14/business/14boarding.html2006 年美国大学生数学建模竞赛MCM、ICM 试题2006 MCM A: Positioning and Moving Sprinkler 洒水器Systems for Irrigation灌溉There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip洒下 systems to periodic 周期性的flooding. One of the systems that is used on smaller ranches is the use of “hand move” irrigation systems. Lightweight 轻量的aluminum 铝pipes 输送管with sprinkler洒水器 heads are put in place across fields, and they are moved by hand at periodic 周期性的intervals距离to insure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain 维修than other systems. It is also flexible, allowing for use on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and set up the equipment at regular intervals. 距离Given that this type of irrigation system is to be used, h ow can it be configured 安装to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? F or this task you are asked to find an algorithm算法 to determine how to irrigate the rectangular矩形的field that minimizes the amount of time required by a rancher农场工人to maintain the irrigation system.One pipe输送管 set is used in the field. You should determine the number of sprinklers洒水器 and the spacingbetween sprinklers, and you should find a schedule计划表 to move the pipes, including where to move them.A pipe set consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter直径 with rotating 转动spray喷雾器 nozzles 管嘴that have a 0.6 cm inner diameter. When put together the resulting pipe is 20 meters long. At the water source, the pressure is 420 Kilo- Pascal’s and has a flow rate of 150 liters per minute. No part of the field should receive more than 0.75 cm per hour of water, and each part of the field should receive at least 2 centimeters厘米 of water every 4 days. The total amount of water should be applied as uniformly相同地 as possible.2006 MCM B: Wheel Chair Access at AirportsOne of the frustrations失败 with air travel is the need to fly through multiple多路的 airports, and each stop generally requires each traveler to change to a different airplane. This can be especially difficult for people who are not able to easily walk to a different flight's waiting area. One of the ways that an airline can make the transition easier is to provide a wheel chair and an escort 护卫队to those people who ask for help. It is generally known well in advance which passengers require help, but it is not uncommon to receive notice when a passenger first registers 注册at the airport. In rare instances an airline may not receive notice from a passenger until just prior 在先前的to landing.Airlines are under constant pressure to keep their costs down. Wheel chairs wear out and are expensive and require maintenance.维修费 There is also a cost for making the escorts护卫队 available. Moreover, wheel chairs and their escorts must be constantly moved around the airport so that they are available to people when their flight lands. In some large airports the time required to move across the airport is nontrivial. The wheel chairs must be stored somewhere, but space is expensive and severely 严重地limited in an airport terminal.总站 Also, wheel chairs left in high traffic areas represent a liability责任 risk as people try to move around them. Finally, one of the biggest costs is the cost of holding a plane if someone must wait for an escort and becomes late for their flight. The latter cost is especially troubling because it can affect the airline's average flight delay which can lead to fewer ticket sales as potential customers may choose to avoid an airline.Epsilon Airlines has decided to ask a third party to help them obtain a detailed详细的 analysis of the issues and costs of keeping and maintaining wheel chairs and escorts available for passengers. Theairline needs to find a way to schedule the movement of wheel chairs throughout each day in a cost effective way. They also need to find and define the costs for budget planning in both the short and long term.Epsilon Airlines has asked your consultant group to put together a bid 索价to help them solve their problem. Your bid should include an overview 概要and analysis of the situation to help them decide if you fully understand their problem. They require a detailed description of an algorithm that you would like to implement which can determine where the escorts and wheel chairs should be and how they should move throughout each day. The goal is to keep the total costs as low as possible. Your bid is one of many that the airline will consider. You must make a strong case as to why your solution is the best and show that it will be able to handle a wide range of airports under a variety of circumstances.Your bid should also include examples of how the algorithm would work for a large (at least 4 concourses), a medium (at least two concourses), and a small airport (one concourse) under high and low traffic loads. You should determine all potential costs and balance their respective weights. Finally, as populations begin to include a higher percentage of older people who have more time to travel but may require more aid, your report should include projections of potential costs and needs in the future with recommendations建议 to meet future needs.2005 年美国大学生数学建模竞赛MCM、ICM 试题2005 MCM A: Flood PlanningLake Murray in central South Carolina is formed by a large earthen dam, 水坝which was completed in 1930 for power production.Model the flooding downstream 顺流的，下游的in the event there is a catastrophic灾难的earthquake that breaches破坏 the dam.Two particular questions:Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver 下游的from the dam. How much flooding will occur in Rawls Creek from a dam failure,and how far back will it extend?Could the flood be so massive大规模的 downstream that water would reach up to the S.C. State Capitol Building, which is on a hill overlooking the Congaree River?2005 MCM B: Tollbooths收费站Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided 分开的highways that are interrupted at intervals距离 by toll通行费 plazas.广场 Because collecting tolls is usually unpopular, it is desirable 向往的to minimize 使减到最小motorist车主 annoyance恼怒 by limiting the amount of traffic disruption中断 caused by the toll plazas. Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza. Upon根据 entering the toll plaza, the flow of vehicles运载工具 fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze 压缩back down to a number of travel lanes equal to the number of travel lanes before the toll plaza. Consequently,结果 when traffic is heavy, congestion拥挤 increases upon departure离开 from the toll plaza. When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll.Make a model to help you determine the optimal最理想的 number of tollbooths to deploy使展开 in a barrier关口-toll plaza. Explicitly 明确地consider the scenario局面 where there is exactly one tollbooth per incoming travel lane.Under what conditions is this more or less effective than the current practice?Note that the definition of “optimal” is up to you to determine.2004 年美国大学生数学建模竞赛MCM、ICM 试题2004 MCM A: Are Fingerprints Unique?It is a commonplace belief that the thumbprint of every human who has ever lived is different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.2004 MCM B: A Faster QuickPass System“QuickPass” systems are increasingly appearing to reduce people's time waiting in line, whether it is at tollbooths, amusement parks, or elsewhere. Consider the design of a QuickPass system for an amusement park. The amusement park has experimented by offering QuickPasses for several popular rides as a test. The idea is that for certain popular rides you can go to a kiosk near that ride and insert your daily park entrance ticket, and out will come a slip that states that you can return to that ride at a specific time later. For example, you insert your daily park entrance ticket at 1:15 pm, and the QuickPass states that you can come back between 3:30 and 4:30 pm when you can use your slip to enter a second, and presumably much shorter, line that will get you to the ride faster. To prevent people from obtaining QuickPasses for several rides at once, the QuickPass machines allow you to have only one active QuickPass at a time. You have been hired as one of several competing consultants to improve the operation of QuickPass. Customers have been complaining about some anomalies in the test system. For example, customers observed that in one instance QuickPasses were being offered for a return time as long as 4 hours later. A short time later on the same ride, the QuickPasses were given for times only an hour or so later. In some instances, the lines for people with Quickpasses are nearly as long and slow as the regular lines.The problem then is to propose and test schemes for issuing QuickPasses in order to increase people's enjoyment of the amusement park. Part of the problem is to determine what criteria to use in evaluating alternative schemes. Include in your report a non-technical summary for amusement park executives who must choose between alternatives from competing consultants2003 年美国大学生数学建模竞赛MCM、ICM 试题2003 MCM A: The Stunt PersonAn exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.).Your job is to:∙determine what size boxes to use∙determine how many boxes to use∙determine how the boxes will be stacked∙determine if any modifications to the boxes would help∙generalize to different combined weights (stunt person & motorcycle) and different jump heightsNote that, in “Tomorrow Never Dies”, the James Bond character on a motorcycle jumps over a helicopter.2003 MCM B: Gamma Knife Treatment PlanningStereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators.The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical(approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points.The goal of radiosurgery is to deplete tumor cells while preserving normal structures. Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.1.Minimize the dose gradient across the target volume.2.Match specified isodose contours to the target volumes.3.Match specified dose-volume constraints of the target and criticalorgan.4.Minimize the integral dose to the entire volume of normal tissuesor organs.5.Constrain dose to specified normal tissue points below tolerancedoses.6.Minimize the maximum dose to critical volumes.In gamma unit treatment planning, we have the following constraints:1.Prohibit shots from protruding outside the target.2.Prohibit shots from overlapping (to avoid hot spots).3.Cover the target volume with effective dosage as much as possible.But at least 90% of the target volume must be covered by shots.e as few shots as possible.Your tasks are to formulate the optimal treatment planning for a gamma knife unit as a sphere-packing problem, and propose an algorithm to find a solution. While designing your algorithm, you must keep in mind that your algorithm must be reasonably efficient.2002 年美国大学生数学建模竞赛MCM、ICM 试题2002 MCM A: Wind and WatersprayAn ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area.Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.2002 MCM B: Airline OverbookingYou're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.Consider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B Heightened security at and around airports Passengers' fear Loss of billions of dollars in revenue by airlines to dateBuild a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, and consider alternatives for handling “bumped”passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis2001 年美国大学生数学建模竞赛MCM、ICM 试题2001 MCM A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic types of 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 for a 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 but there is a choice of wheels for the rear.∙Task 1. Provide a table giving the wind speed 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 100meters.∙Task 2. Provide an example of how the table could be used for a specific time trial course.∙Task 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.2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 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 reversal of traffic on I-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 north by 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 twocoastal-bound lanes of I-26 into two lanes of Columbia-boundtraffic, 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 coastalregion was ordered. Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps。

美赛A,B题

2013 Contest ProblemsMCM PROBLEMSPROBLEM A: The Ultimate Brownie PanWhen baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.Assume1. A width to length ratio of W/L for the oven which is rectangular in shape.2. Each pan must have an area of A.3. Initially two racks in the oven, evenly spaced.Develop a model that can be used to select the best type of pan (shape) under the following conditions:1. Maximize number of pans that can fit in the oven (N)2. Maximize even distribution of heat (H) for the pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.PROBLEM B: Water, Water, EverywhereFresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility andc osts, and why it is the “best water strategy choice.”Countries: United States, China, Russia, Egypt, or Saudi ArabiaICM PROBLEMPROBLEM C: Network Modeling of Earth's HealthClick the title below to download a PDF of the 2013 ICM Problem.Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.。

1993年美赛题(AB)

A:Optimal CompostingAn environmentally conscious institutional cafeteria is recycling customers' uneaten food into compost by means of microorganisms. Each day, the cafeteria blends the leftover food into a slurry, mixes the slurry with crisp salad wastes from the kitchen and a small amount of shredded newspaper, and feeds the resulting mixture to a culture of fungi and soil bacteria, which digest slurry, greens, and papers into usable compost. The crisp green provide pockets of oxygen for the fungi culture, and the paper absorbs excess humidity. At times, however, the fungi culture is unable or unwilling to digest as much of the leftovers as customers leave; the cafeteria does not blame the chef for the fungi culture's lack of appetite. Also, the cafeteria has received offers for the purchase of large quantities of it compost. Therefore, the cafeteria is investigating ways to increase its production of compost. Since it cannot yet afford to build a new composting facility, the cafeteria seeks methods to accelerate the fungi culture's activity, for instance, by optimizing the fungi culture's environment (currently held at about 120 F and 100% humidity), or by optimizing the composition of the moisture fed to the fungi culture, or both.Determine whether any relation exists between the proportions of slurry, greens, and paper in the mixture fed to the fungi culture, and the rate at which the fungi culture composts the mixture. if no relation exists, state so. otherwise, determine what proportions would accelerate the fungi culture's activity. In addition to the technical report following the format prescribed in the contest instructions, provide a one-page nontechnical recommendation for implementation for the cafeteria manager. Table 1 shows the composition of various mixtures in pounds of each ingredient kept in separate bins, and the time that it took the fungi to culture to compost the mixtures, from the date fed to the date completely composted [table omitted].B:Coal-Tipple OperationsThe Aspen-Boulder Coal Company runs a loading facility consisting of a large coal tipple. When the coal trains arrive, they are loaded from the tipple. The standard coal train takes 3 hours to load, and the tipple's capacity is 1.5 standard trainloads of coal. Each day, the railroad sends three standard trains to the loading facility, and they arrive at any time between 5 A.M. and 8 P.M. local time. Each of the trains has three engines. If a train arrivesand sits idle while waiting to be loaded, the railroad charges a special fee, called a demurrage. The fee is $5,000 per engine per hour. In addition, a high-capacity train arrives once a week every Thursday between 11 A.M. and 1 P.M. This special train has five engines and holds twice as much coal as a standard train. An empty tipple can be loaded directly from the mine to its capacity in six hours by a single loading crew. This crew (and its associated equipment) cost $9,000 per hour. A second crew can be called out to increase the loading rate by conducting an additional tipple-loading operation at the cost of $12,000 per hour. Because of safety requirements, during tipple loading no trains can be loaded. Whenever train loading is interrupted to load the tipple, demurrage charges are in effect.The management of the Coal Company has asked you to determine the expected annual costs of this tipple's loading operations. Your analysis should include the following considerations:•How often should the second crew be called out?•What are the expected monthly demurrage costs?•If the standard trains could be scheduled to arrive at precise times, what daily schedule would minimize loading costs? Would a third tipple-loading crew at$12,000 per hour reduce annual operations costs?•Can this tipple support a fourth standard train every day?。

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近几年美国大学生数学建模竞赛（USMCM）的题目包括：
2019年：建立一个模型来模拟东海和黄海的湍流。

2018年：预测联合国安理会和联合国大会决策结果及党派之间的关系。

2017年：建立一个模型来识别投资者风险偏好并帮助他们优化投资组合。

2016年：建立一个模型来识别用户a浏览网页时的行为特征，以便更好地理解和预测用户的行为。

2015年：建立一个模型，根据通信终端的传输速率，识别用户的实时视听传输需求。

2014年：建立一个模型来模拟社会文化传播的影响。

2013年：建立一个模型，根据用户的行为来预测新闻传播的趋势，并建议相关策略。

2012年：建立一个模型来优化公共汽车系统，以满足不同地区乘客的旅行需求。

2011年：建立一个模型，根据居民就医环境的不同，构建卫生保健系统的合理结构。

2010年：建立一个模型，预测印度洋及其邻近海域的风暴强度，以及其对当地的影响。

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