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2005年美赛B题

MCM2005B.Tollbooths

收费亭

Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided highways that are interrupted at intervals by toll plazas.

像Garden State Parkway,Interstate 95等等这样的长途收费公路,通常是多行道的,被分成几条高速公路,在这些高速公路上每隔一定的间隔会设立一个通行税收费广场。Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas.

因为征收通行税通常不受欢迎,所以应该尽量减少通过通行税收费广场引起的交通混乱给汽车司机带来的烦恼。

Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza.

通常,收费亭的数量要多于进入收费广场的道路的数量。

Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza.

进入通行税收费广场的时候,流到大量收费亭的车辆呈扇形展开,当离开通行税收费广场的时候,车流将只能按照收费广场前行车道路的数量排队按次序通过!

Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza.

从而,当交通是拥挤的时,拥挤在违背通行税广场上增加。

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.

当交通非常拥挤的时候,因为每车辆付通行费的时间要求,阻塞也会出现在通行税收费广场的入口处。

Make a model to help you determine the optimal number of tollbooths to deploy in a barrier-toll plaza.

建立一个模型来确定在一个容易造成阻塞的通行税收费广场中应该部署的最优的收费亭的数量。

Explicitly consider the scenario where there is exactly one tollbooth per incoming travel lane.

需要保证每一个进入收费广场的交通线路上都仅有一个收费亭。

Under what conditions is this more or less effective than the current practice?

与当今的实践相比较,在什么条件下这或多或少有效?

Note that the definition of "optimal" is up to you to determine.

注意:"最佳"的定义由你自己决定。

09年美赛A题优秀论文翻译

A题设计一个交通环岛 在许多城市和社区都建立有交通环岛,既有多条行车道的大型环岛(例如巴黎的凯旋门和曼谷的胜利纪念碑路口),又有一至两条行车道的小型环岛。有些环岛在进入口设有“停车”标志或者让行标志,其目的是给已驶入环岛的车辆提供行车优先权;而在一些环岛的进入口的逆向一侧设立的让行标志是为了向即将驶入环岛的车辆提供行车优先权;还有一些环岛会在入口处设立交通灯(红灯会禁止车辆右转);也可能会有其他的设计方案。 这一设计的目的在于利用一个模型来决定如何最优地控制环岛内部,周围以及外部的交通流。该设计的目的在于可利用模型做出最佳的方案选择以及分析影响选择的众多因素。解决方案中需要包括一个不超过两页纸,双倍行距打印的技术摘要,它可以指导交通工程师利用你们模型对任何特殊的环岛进行适当的流量控制。该模型可以总结出在何种情况之下运用哪一种交通控制法为最优。当考虑使用红绿灯的时候,给出一个绿灯的时长的控制方法(根据每日具体时间以及其他因素进行协调)。找一些特殊案例,展示你的模型的实用性。 标题:一个环来控制一切:优化交通圈。 安德里亚?利维亚伦 安德烈娅?利维 拉塞尔?梅里克 哈维姆德学院 顾问:苏珊 摘要 我们的目的是利用车辆动力学考虑在圆形交叉路口的道路情况。我们主要根据进入圆形道路的速度决定最好的方式来控制车流量。我们假设在一个车道通过圆形道路循环,这样交通输入量能够被调节。(也就是,不会有优先的交通输入量) 对于我们的模型,可改变的参数是排队等候进入的速率,进入圆形道路的速率(服务速率),这个圆形道路最大的容量和离开这个道路的速率。我们使用带有队列和交通圈的隔室模型作为隔间。来自外界的车辆首先进行排队等候,然后进入圆环交叉路口,最后离开到外界。我们把服务速率和离开速率作为在圆环交叉路口的车辆数量参考。 另外,我们利用计算机来拟态一个可见表示,发生在不同情形下的圆环交叉路口。允许我们检验不同的情况,例如不平等的交通流量由于不同的队列,一些十字路口比其他车辆有一个更高的概率。这个拟态模仿实施栩栩如生,例如如何当前面是空道路时进行加速,而当前面有其他车辆时进行减速。大多数情况下,我们发现:一个高服务效率能够保持交通顺畅的最佳方式,这意味着对于进入交通的效率是最有效的。然而,当交通变得拥堵时,较低的服务率更好的适应了交通,这指示应该使用一个红绿灯。所以,在不同时间段,依靠预测中的交通流量,一个信号灯应该被安装进行循环实现。

2017美赛A题中文翻译

A题中文翻译: 问题A:管理赞比西河 赞比西河上的卡里巴水坝是非洲较大的水坝之一。它的建设是有争议的,南非风险管理研究所的2015年报告包括一个警告,大坝是急需维护。赞比西河管理局(ZRA)可提供若干选择,以解决这一问题。ZRA特别感兴趣的有三个选项: (选项1)修复现有的Kariba水坝(选项2)重建现有的Kariba水坝,或(选项3)拆除Kariba 水坝,并更换为沿赞比西河的一系列十到二十个较小的水坝。 这个问题有两个主要要求: 要求1 ZRA管理要求对所列出的三个选项进行简要评估,并提供足够的详细信息,以提供与每个选项相关的潜在成本和收益的概述。此要求的长度不应超过两页,除了主要报告之外,还必须提供此页面。 要求2对选项(3)进行详细分析- 删除Kariba水坝,并用赞比西河沿岸一系列十至二十个较小的水坝替代。这个新的水坝系统应该与现有的Kariba水坝具有相同的整体水管理能力,同时为现有的水坝提供与卡里巴湖相同或更高水平的保护和水管理选择。您的分析必须支持关于沿赞比西河新坝的数量和位置的建议。 在您的要求2报告中,您应该包括一个策略,用于调节通过您的新多坝系统的水流,从而在安全和成本之间提供合理的平衡。除了解决已知或预测的正常水循环,您的战略应为ZRA 经理提供指导,解释和证明应当采取的行动,以正确处理应急水流情况(即洪水和/或长期低水位状况)。您的策略应为从最大预期排放到最小预期排放的极端水流提供具体指导。最后,您的建议战略应包括解决对赞比西河不同地区暴露于极端条件最有害影响的位置和时间长度的任何限制的信息。 您的MCM提交应包括三个要素:标准的1页MCM摘要表,1-2页简要评估报告(要求1)和您的主要MCM解决方案(要求2)不超过20页,最多提交23页面。注意:您加入的任何附录或参考页面不会计入23页的上限。

2019美赛建模A题

2019MCM Problem A:A Hot Youbot Background:Thermal Analysis,using finite element techniques,is carried out as a steady-state or transient analysis.Conductive heat transfer is handled directly by finite element techniques; conduction occurs in a solid due to temperature differences.However,radiation heat transfer analysis may require additional particle-tracking or ray-tracing techniques to approximate the radiant energy arriving at a given surface. The material is assumed to be a magnesium alloy and to have a thermal conductivity of52W/m?K. Material properties were taken from"Thermal Conductivity of Magnesium Alloys".Since the model is in inches you can use symunit to rewrite the value in inches.Now you need remove the units to obtain the value for the thermal properties.Unless overwritten,all of the side faces are set to have a natural convection coefficient of25W/m2?K representing heat transfer to an ambient air temperature of288.15K(25℃).Convert and calculate the convection coefficient to W/inch2?K to be consistent with the model dimensions. Explore different material selections for the robotic https://www.sodocs.net/doc/5419217338.html,pute the change in max body temperature as a function of increasing thermal conductivity.Before begining calculate the expected run time from the previous run time.Run the models using a parfor loop to speed up the simulation by parallelizing the iterations across Parallel Computing Toolbox workers.If you do not have the Parallel Toolbox change parfor to for. Problem: Part I:Develop a mathematical model for the heat transfer among the gripper pivot.In the youBot,the gripper pivot sits underneath the electronics board and is exposed to the heat coming off the circut board.Here you will create the pde model,import the STL file of the gripper pivot, and plot it.Create and visualize a tetrahedral mesh of the component with a maximum value of 0.09inches.Measure the x,y and z dimensions of the mesh. Part II:The bottom face is given a fixed temperature assuming that the rest of the robotic arm acts as a heat sink.The top face and inner hole is arbitrarily given a heat flux to represent the heat off the circuit board.Solve the model and calculate the max and bulk body temperatures and time how long the solve https://www.sodocs.net/doc/5419217338.html,pute the max temperature in K and rewrite that to℃and F,then plot the distribution of temperature of the gripper pivot in3D. Part III:Develop a mathematical model for predicting the relationship between thermal conductivity and max temperature for this geometry and material.Assume the robotic arm shuts off at a max temperature of311K,find the associated allowable heat transfer coefficient for the alloy.Which materials are appropriate for being made into the the gripper pivot? Part IV:Prepare a short(1to2pages)synopsis of your results suitable for publication as a short note in IEEE Communications Magazine. Your submission should consist of: ●One-page Summary Sheet, ●Two-page synopsis,

美赛A题翻译

2017MCM ProblemA:Managing TheZambeziRiver管理赞比西河 TheKaribaDamontheZambezi River is oneofthelarger dams inAfrica.Its constructionwas controversial, anda2015report bytheInstitute ofRisk Management ofSouth Africaincludedawarningthatthedamis indire need of maintenance.A numberofoptionsareavailabletotheZambezi River Authority(ZRA) thatmight addressthesituation.Threeoptionsinparticular are ofinteresttoZRA: 赞比西河上的卡里巴大坝是非洲的一个大水坝。它的建设是有争议的,南非风险管理研 究所2015年的报告包括警告大坝急需维修。一些由赞比西河管理局(ZRA)所接受的 方案,可能会解决问题。特别是三个ZRA感兴趣的选择: (Option1) Repairingthe existingKaribaDam, 修复现有的卡里巴大坝, (Option2)Rebuildingthe existingKaribaDam,or 改造现有的卡里巴大坝,或者 (Option3) RemovingtheKaribaDam andreplacingitwithaseriesoftento twentysmaller dams alongtheZambezi River. 移除卡里巴大坝并用沿赞比西河一系列的十到二十个小坝取代它。There aretwomainrequirementsfor this problem: 这个问题有两个主要的要求: Requirement1ZRAmanagementrequires a brief assessmentofthethree options listed, withsufficientdetailtoprovide an overviewof potential costsand benefits associatedwith eachoption. This requirementshouldnot exceedtwo pages inlength,and mustbe providedinadditiontoyour mainreport. 要求一:ZRA管理要求对列出的三个选项作简要评价,提供足够的细节,提供与 每个选项相关的潜在成本和效益概述。这一要求长度不超过两页,并且必须提供 您的主要报告.。 Requirement2Providea detailedanalysis ofOption(3) - removingtheKariba Damandreplacingitwithaseries oftentotwentysmaller dams alongthe Zambezi river. This newsystemof dams shouldhave thesame overall water managementcapabilities as theexistingKaribaDamwhile providingthesameor greater levels of protectionandwatermanagementoptionsfor LakeKaribathat are in placewith the existingdam.Your analysis mustsupportarecommendation as tothenumber andplacementofthenewdamsalongtheZambezi River. 要求二:提供方案3的详细分析——去除卡里巴大坝,取而代之的是一系列的十到二十个沿Zambezi河的小坝。这个新的水坝系统应该和现有的卡里巴大坝一样有 相同的综合水管理能力,并且为卡里巴湖提供现有的保护和水管理相同或更高的水平。你的分析必须支持推荐为沿赞比西河修建水坝的数量和位置。 Inyour reportfor Requirement 2, youshouldincludeastrategyformodulatingthewater flowthroughyour newmultipledamsystemthat provides areasonable balance betweensafetyandcosts. Inaddition to addressingknown or predictednormal water cycles,your strategyshould provideguidance totheZRAmanagers thatexplains and

2013年美赛A题

最终的布朗尼锅 摘要 关键字:

目录 引言 题目背景 近年来,电烤箱普遍采用远红外加热技术,使电烤箱的技术含量增加,耗能降低,深受广大用户的欢迎。利用红外线加热物体,就是利用辐射波长与物体接收波长一致时,物体吸收大量的红外能,从而加剧物体内部的分子运动,使之加热升温。加热时间短,能耗低,使用方便。 但是,当我们使用矩形烤盘烘烤食物时,热传导方程,加上一些边界条件,导致方形烤盘热量集中在的四个角上,因此四个角上的物体会因过度受热(以及在较小程度的边缘处)而变焦。如果用圆形烤盘,热量会平均分布在整个外围边缘,在外围的物体就不会过度受热。然而,由于大多数的烤箱都是矩形的,所以用圆形的烤盘就不能较好的利用烤箱的空间。给烘烤食物的朋友带来了很大的不便。为什么角部的食物肉容易烤焦,以及选择哪种形状的烤盘,,这是令人很费解的问题。 电烤箱工作原理 电烤箱利用电热元件所发出的辐射热来烘烤食品,利用它我们可以制作烤鸡、烤鸭、烘烤面包、糕点等。根据烘烤食品的不同需要,电烤箱的温度一般可在50-250℃范围内调节。 电烤箱主要由箱体、电热元件、调温器、定时器和功率调节开关等构成。其箱体主要由外壳、中隔层、内胆组成三层结构,在内胆的前后边上形成卷边,以隔断腔体空气;在外层腔体中充填绝缘的膨胀珍珠岩制品,使外壳温度大大减低;同时在门的下面安装弹簧结构,使门始终压紧在门框上,使之有较好的密封性。电烤箱的加热方式可分为面火(上加热器加热)、底火(下加热器加热)和上下同时加热三种。 电烤箱技术参数 温度范围室温-200℃(300℃) 温度稳定度±0.5℃ 温度分布均匀度±2℃(特佳) 排气烟道叶片式设计可调出风量 符号和定义 l:多边形边长 L: 多边形周长 k: 周长与面积的比 G:单位圆的周长 C: 单位椭圆周长 a: 椭圆的长半轴 b: 椭圆的短半轴 假设 1、烤箱内温度同一层表分布均匀且稳定 2、烤箱内风扇使空气及时流通 3、假设烤盘之间相互不影响 4、假设各层之间相互不影响 5、假设烤盘的深度影响忽略不计 6、假设烤箱内垂直分布的热辐射场为递增

2016年数学建模美赛A题题面及翻译

2016 MCM Problem A A Hot Bath A person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax. 一个人用一个水龙头让浴缸装满了热水,(然后?)睡进去来清洗和放松。 //那就先放到一定的程度,泡进去,然后边加水这样。 Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel. 不幸的是,这个浴缸没有温泉热水模式,就是没有另外的加热系统和循环的喷嘴,而是个简单的水密闭容器。 After a while, the bath gets noticeably cooler, so the person adds a constant trickle of hot water from the faucet to reheat the bathing water. 不一会儿,这个水池明显的变冷了,所以这个人打开水龙头,加入了持续的细细的水,来加热这个浴缸里面的水。 The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain. 这个浴缸设计成一种形式,当这个池子到达了它的容量,多余的水会通过一个溢出排水系统排出。 Develop a model of the temperature of the bathtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water. 设计一个浴缸里面的水温度关于空间和时间上的模型,去决定最好的策略,让这个人在浴缸里能够在不浪费太多的水的前提下,去尽量的靠近初始的温度。 Use your model to determine the extent to which your strategy depends upon the shape and volume of the tub, the shapeolume/temperature of the person in the bathtub, and the motions made by the person in the bathtub. 用你的模型去决定你的策略对以下因素的依赖程度(依赖关系)。因素为:缸的形状和容量,这个浴缸里面的人的形状,体积,温度,还有这个人在浴缸里面的动作。 If the person used a bubble bath additive while initially filling the bathtub to assist in cleansing, how would this affect you r model’s results? 如果这个人在一开始装满这个浴缸的时候,就加入了泡泡添加剂去帮助清洗,这个会如何影响你的模型的结果呢? In addition to the required one-page summary for your MCM submission, your report must include a one-page non-technical explanation for users of the bathtub that describes your strategy while explaining why it is so difficult to get an evenly maintained temperature throughout the bath water. 除了已经要求的一页的总结,你的报告必须含有一页的对浴缸使用者的非技术性的解释,去描述你的策略,同时解释为什么如此难以做到保持整个洗澡水的水温是均匀的。

2014年美赛数学建模A题翻译版论文

数学建模竞赛(MCM / ICM)汇总表 基于细胞的高速公路交通模型 自动机和蒙特卡罗方法 总结 基于元胞自动机和蒙特卡罗方法,我们建立一个模型来讨论“靠右行”规则的影响。首先,我们打破汽车的运动过程和建立相应的子模型car-generation的流入模型,对于匀速行驶车辆,我们建立一个跟随模型,和超车模型。 然后我们设计规则来模拟车辆的运动模型。我们进一步讨论我们的模型规则适应靠右的情况和,不受限制的情况, 和交通情况由智能控制系统的情况。我们也设计一个道路的危险指数评价公式。 我们模拟双车道高速公路上交通(每个方向两个车道,一共四条车道),高速公路双向三车道(总共6车道)。通过计算机和分析数据。我们记录的平均速度,超车取代率、道路密度和危险指数和通过与不受规则限制的比较评估靠右行的性能。我们利用不同的速度限制分析模型的敏感性和看到不同的限速的影响。左手交通也进行了讨论。 根据我们的分析,我们提出一个新规则结合两个现有的规则(靠右的规则和无限制的规则)的智能系统来实现更好的的性能。1介绍 1.1术语 1.2假设 2模型 2.1设计的元胞自动机 2.2流入模型 2.3跟随模型 2.4超车模型 2.4.1超车概率 2.4.2超车条件 2.4.3危险指数 2.5两套规则CA模型 2.5.1靠右行 2.5.2无限制行驶规则 3补充分析模型 3.1加速和减速概率分布的设计 3.2设计来避免碰撞 4模型实现与计算机 5数据分析和模型验证 5.1平均速度 5.2快车的平均速度 5.3密度 5.4超车几率 5.5危险指数 6在不同速度限制下敏感性评价模型 7驾驶在左边 8交通智能系统 8.1智能系统的新规则

2018美赛数学建模A题

2018MCM Problem A: 多跳短波无线电传播 背景:在高频率(HF,定义为3 - 30兆赫),无线电波可以长途旅行(从地球表面的 一个点到地球表面的另一个遥远的地方)通过电离层和地球以外的多次反射。下面的最高可用频率(MUF),高频无线电波从地面源反映了电离层返回地球,在那里他们可以 再次回到电离层反射,在那里他们可以再次回到地球的反映,等等,旅行还与每个连 续跳。在其他因素中,反射表面的特性决定了反射波的强度,以及信号在保持有用信 号完整性的情况下最终会传播多远。而且,随着季节的变化,白天的时间和太阳的条 件也不同。上面的MUF频率不是反射和折射,但通过电离层进入太空。在这个问题上,重点特别是海面上的反射。经验发现,在汹涌的海洋中,反射比平静的海面上的反射 减弱。海洋湍流将影响海水的电磁梯度,改变海洋的局部介电常数和磁导率,改变反 射面的高度和角度。一个汹涌的海洋,其中浪高、形状和频率变化很快,波的传播方向也可能改变。 问题: 第一部分:建立海洋信号反射的数学模型。一个100瓦的高频恒定载波信号,低于MUF,从陆地上的点源,确定第一反射强度和湍流海洋用了平静的海洋的第一反射强度的比较。(注意,这意味着这个信号在电离层上有一次反射)如果额外的反射(2到n)在平静 的海洋上发生,那么信号在强度低于可用的信噪比(SNR)阈值10分贝之前,可以达到的最大跳数是多少? 第二部分:你如何从第一部分的调查结果与HF反射在山区或崎岖的地形与光滑的地形 比较? 第三部分:穿越海洋的船将使用短波进行通信,并接收天气和交通报告。你的模型如何改变以适应船上的接收器在湍流的海洋上行驶?使用相同的多跳路径,船舶能保持多长时间通信? 第四部分:准备一份简短的(1到2页)你的结果概要,适合作为IEEE通讯杂志中的简短说明发表。 您的提交应包括: ?一页摘要表, ?两页简介, ?你的解决方案不超过20页,最多有23页的摘要和概要。 注:参考清单和任何附录不计入23页的限制,并应在您完成的解决方案之后出现。

美赛2013A题论文(终极布朗尼盘)

For office use only T1________________ T2________________ T3________________ T4________________Team Control Number 18263 Problem Chosen A For office use only F1________________ F2________________ F3________________ F4________________ 2013Mathematical Contest in Modeling(MCM/ICM)Summary Sheet (Attach a copy of this page to your solution paper.) Type a summary of your results on this page.Do not include the name of your school,advisor,or team members on this page. There are plenty of people who are fond of Brownies.Industrial manufacturing of them requires to bake the biggest amount of Brownies in the same batch and also to avoid overcooking of the batter next to the corners of the pan,in order to avoid losses. Overcooking can affect the volumes of batter that are in direct contact with more than one hot surface of the pan,for instance the bottom of it and one of its sides.The corners of the pan are the hottest regions,as three surfaces deliver heat simultaneously(two sides plus the bottom).That’s why overcooking is frequent in the corners. Round pans distribute heat in a more even way,due to the fact that there are never three surfaces delivering heat to a volume of batter(two at most),.The problem with them is that they cause a big loss of oven space as compared to square ones,even to hexagonal ones.As round pans minimize overcooking and rectangular pans minimize oven-space loss,our model posits a compromise between these two shapes,namely modified rectangular pans having a 90°centred-angle arc instead of being standard rectangles. In order to clarify which factor will be advantaged by variations of this type of shape(either space saving or heat evenness),we put weights p and(1-p)on the sum of the line lengths and on the sum of the arc lengths.As we consider that the area of the pan is fixed and its width-to-length ratio W/L is given,we propose3equations expressing the effect of having longer or shorter arcs on the pans performances(the longer the arcs,the evener the heat distribution;the shorter the arcs,the better the space in the oven is filled). We use matlab to solve these equations.Once we give p and W/L two values between0to1, we can get a shape of pan.By changing the weights p by small steps while the ratio W/L is fixed,we can plot the figure in a three-dimentional space layer by layer,so that we can see clearly how the figure changes with weights changing for a given W/L ratio.From these graphs,we can conclude that the space the pan takes increases with increasing weights on the arc factor(we provide some charts to make clear). In general,if the producer wants to increase the quality of the brownies by avoiding overcooking of volumes placed in critical locations,he needs to decrease p.If he wants to increase the production by filling the oven as much as possible,he needs to increase p. Large p values amount to short arcs,small p values mean long arcs.

2019美赛数学建模A题论文

Winter is approaching, may the dragon’s wings grow more abundant Summary In the game of thrones, Daenerys Targaryen depicts the image of a dragon. In eastern and western cultures, the phenomenon of dragons is not uncommon. If dragons live in modern society, how can we raise these war monsters? Research, and applied the cross disciplines of biology, physics, and chemistry to build a mathematical model and solve it to achieve the maximum growth of the dragon. Of course, dragons do not exist in real life, so we likened pterosaurs, modern Aircraft and chemical burner to derive the specific physiological characteristics of the dragon to ensure the rationality and scientificity of the research. First, we studied the flight and fire-spitting models of dragons. Through analogical reasoning, our hypothetical dragon's fire-spitting principle is similar to modern alcohol flamethrowers. For dragon flight, we used fluid mechanics to get the dragon's flight speed. And glucose energy loss. Combining the two to get the energy loss model of the dragon. Second, we studied the basic physical characteristics of the dragon. For the relationship between the body length and body age of the dragon, we established an elastic model of growth. Because the weight and body length of dragons have upper and lower limits, in order to comply with basic ecology, we have defined the dragon's bone saturation value as the cut-off value, and conducted a segmented study. When studying the relationship between weight and body length, We know that the weight of the dragon is proportional to the cube of the body length. Then, because the dragon needs resources to replenish like other animals, we built a dragon's food supply model. Suppose that the three dragons have the same competitiveness and the daily sheep Resources are the same. According to ecology, when the number of sheep in a certain area reaches k / 2, we need to migrate the dragon. Finally, the temperature will affect the living environment of the dragon, so the dragon needs to followMigration was selected for changes in temperature, and we selected three areas of drought, cold, and warmth to study the dragon, and integrated the model of the regional area of the dragon by the appealing model. In addition, we wrote a letter to the author of the Song of Ice and Fire, giving some suggestions on the actual ecological foundation of the dragon, hoping to be adopted. Although the dragon does not exist in our real life, the dragon can be broken down into Part of our modern society. For the dragon's flying spitfire energy loss model, we can further study the aircraft's fluid mechanics and modern flamethrowers. The study of non-existent organisms also prepares us for the arrival of new species .

MCM2012 数学建模美赛 A题题目及翻译

PROBLEM A: The Leaves of a Tree "How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following: ? Why do leaves have the various shapes that they have? ? Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volu me”of the tree and its branches effect the shape? ? Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure? ? How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)? In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings. 问题A:一棵树的叶子“一棵树上的叶子有多重?”如何估计叶子的实际重量(或树的其他部分)的实际重量?如何对叶子进行分类?建立一个数学模型来描述和分类叶子。考虑并回答以下问题: ?为什么叶片有现在的各种形状? 树叶的形状会“最小化”他们之间的阴影重叠,来让他们接受阳光照射达到最大码??叶子在树和分支上“体积”的分布影响叶子的形状吗? 说到轮廓,叶子的形状(一般特征)与树的轮廓和枝干结构有关联吗? ?你将如何估计树的叶重?叶质量和树(由轮廓定义的高度,质量,体积)的大小特征之间有无联系? 除了总结,你还需要准备一篇给科技期刊编辑的信来说明你的主要发现。

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