美国数学建模型A题
2024美赛数学建模题目
2024美赛数学建模题目
2024年美国大学生数学建模竞赛（MCM/ICM）赛题包括以下六道题目：
MCM A（环境类）题目：遭受旱灾的植物群落。
题目要求建立预测模型，预测植物群落未来随时间的变化。
MCM B（环境类、政策类）题目：重新想象马赛马拉。
题目难度主要在数据不好找，预测动物和人们相互作用的模型。
MCM C（数图、图论优化类知识）题目：预测单词结果。
可以采用神经网络模型，利用隶属度函数进行分类，用聚类模型转换为不同的类，再用神经网络作为输出。
ICM D 题目：联合国可持续发展目标的优先顺序。
关键在数据层面，构建
各个指标之间的关系网络，各个指标之间存在限制。
ICM E（环境类）题目：光污染。
难度系数主要还是在获取光污染的数据上。
ICM F 题目：绿色GDP。
择某个标准来计算绿色GDP，基于水资源安全的模型来构建它对全球气候变化的影响。
以上就是2024年美国大学生数学建模竞赛的六道赛题，每道题目的主题和要求均已给出。
如需更多信息，可以登录美赛官网进行查询。
(完整)数学建模美赛试题
地球资源的消耗速度快,越来越多的人关注人类社会的未来。
自1960年以来，已经有许多专家研究可持续发展。
然而大多数人的研究对象是整个世界，一个国家或一个地区。
几乎没有人选择48个最不发达国家(LDC)在联合国为研究对象列表。
然而，LDC国家集团共享许多相同的点.他们的发展道路也有法律的内涵。
本文选择这些国家为研究对象针对发现常规的可持续发展道路。
本文组织如下。
第二部分介绍研究的背景和本研究的意义。
第三节描述了我们对可持续发展的理解细节和显示我们的评估系统的建立过程和原理，那么我们估计每一个国家的LDC和获得可持续发展的能力和等级。
第四节提供了一个最糟糕的国家毛里塔尼亚计划指数在第三节。
第五节演示了在第四节的合理性和可用性计划。
最后在第六节总结本文的主要结论和讨论的力量和潜在的弱点。
地球上的资源是有限的。
三大能源石油、天然气和煤炭可再生。
如何避免人类的发展了资源枯竭和实现可持续发展目标是现在的一个热门话题。
在过去的两个世纪，发达国家已经路上,先污染,再控制和达到高水平的可持续发展。
发展中国家希望发展和丰富。
然而,因为他们的技术力量和低水平的经济基础薄弱，浪费和低效率的发展在这些国家是正常的.所以本文主要关注如何帮助发展中国家特别是48在联合国最不发达国家实现可持续发展是列表可持续发展的理解是解决问题的关键。
可持续发展的定义经历了一个长期发展的过程.在这里,布伦特兰可持续发展委员会的简短定义的”能力发展可持续- - — - - -以确保它既满足现代人的需求又不损害未来的能力代来满足自己的需求”[1]无疑是最被广泛接受的一个在各种内吗定义。
这个定义方面发挥了重要作用在很多国家的政策制定的过程。
然而,为了证明一个国家的现状是否可持续不可持续的,更具体的定义是必要的更具体的概念，我们认为,如果一个国家的发展是可持续的，它应该有一个基本的目前的发展水平，一个平衡的国家结构和一个光明的未来.基本的发展水平反映了国家的基础和潜力。
2022年MathorCup高校数学建模挑战赛A题
2022年第十二届MathorCup 高校数学建模挑战赛题目A 题 大规模指纹图像检索的模型与实现在生物特征识别领域，指纹作为最具独特性与持久性的生物特征之一，被广泛应用于身份识别。
指纹识别过程分为特征提取和比对两个环节。
其中特征提取环节会提取用于指纹识别的指纹特征，一般国际上最为常见的指纹特征为“细节点”特征，其可视化展示形式如图1中的浅蓝色小圆圈及对外伸出的浅蓝色短线段，短线段用于指示细节点处纹线方向。
细节点一般采用三元存储格式： ，分别表示x 轴像素坐标、y 轴像素坐标及细节点方向。
一般而言：（1）指纹图像坐标体系：左上角为坐标原点，且x 轴方向向右，y 轴方向向下；（2）细节点表达约定：细节点x , y 的位置采用指纹图像坐标系表达，其方向规定：零度方向为x 轴正方向（向右），90度方向为y 轴负方向（向上），180度方向为x 轴负方向（向左），270度方向为y 轴正方向（向下），最大角度为359度。
角度的最小区分单位为1度。
图1 指纹识别原理(,,)x y q在指纹匹配环节，需要对两幅指纹图像的“同一性”进行定量评价，通常采用相似度指标。
常见的两枚指纹之间的相似度评价主要依据每枚指纹图像中各个细节点之间的匹配关系。
如图1所示，相互具有匹配关系的细节点之间用一根跨越两幅图像的红线将其互相连接，用于可视化展示。
在指纹图像匹配环节，常需要考虑如下的情况：考虑到在采集指纹图像时，手指按压图像采集设备的角度、轻重及位置各不相同，因此两幅指纹图像需要做图像的旋转、平移后才能相互对准。
由于手指皮肤较为柔软，通过按压方式采集到的指纹图像会发生一定程度的不规则弹性形变，在图1中会发现两幅指纹图像中，某些相互匹配的细节点在对准时，不能完全“重叠”，有一定幅度的位置及角度的偏差。
这一现象也可以从“跨越两幅图像的红线并不是都平行”现象中观察到。
考虑到手指可能存在临时性蜕皮、褶皱等因素，且空气中的湿度及皮肤表面的干燥程度或粘附在皮肤上的异物等都会导致采集到的指纹图像存1中可以观察到并不是所有的细节点都有对应的红线进行关联。
美赛a题思路
美赛a题思路
美赛A题思路
美国大学生数学建模竞赛（USAMO）A题是一道关于四边形的问题，要求给出一个正方形ABCD，以及在正方形边上的4个点P，Q，R，S。
要求在这4个点上分别划出4个三角形，使得这4个三角形的外接圆的半径最小。
该题的解法应用了几何学中的相关定理，如三角形外接圆的半径和内接圆的半径之间的关系。
此外，还要考虑正方形ABCD的对称性，这样可以将原问题简化。
首先，我们可以将正方形ABCD平分成四个三角形，即ACD，ADB，BCS，CSA。
根据这4个三角形的特点可知，它们的外接圆必须通过正方形ABCD的4个顶点。
同时，由于三角形外接圆的半径和内接圆的半径之间的关系，我们可以确定每个三角形的外接圆的半径。
接下来，我们可以利用正方形ABCD的对称性，将原问题简化为另一个问题，即在正方形ABCD的四条边上，找出两个点，使得它们分别在四个三角形的外接圆上，且外接圆的半径最小。
在此基础上，我们可以利用斜率的概念，判断某一点在哪个三角形的外接圆上。
具体来说，我们可以计算正方形ABCD的4条边上的各点的斜率，与之前求出的每个三角
形外接圆的斜率进行比较，从而判断某一点在哪个三角形的外接圆上。
最后，我们可以通过对四条边上的点的排列组合，找出最优解，即得到4个三角形的外接圆的半径最小的情况。
以上就是美赛A题的思路。
解决该题，需要综合运用几何学、代数学中的相关定理，以及斜率的概念，最终求出最优解。
美国数学建模竞赛题目(1985--2009年)
美国数学建模竞赛题目1985年：A题：动物群体的管理B题：战略物资储备的管理问题1986年：A题：海底地型测量问题B题：应急设施的优化选址问题1987年：A题：堆盐问题（盐堆稳定性问题）B题：停车场安排问题1988年：A题：确定毒品走私船位置B题：平板列车车厢的优化装载1989年：A题：蠓虫识别问题；最佳分类与隔离B题：飞机排队模型1990年：A题：脑中多巴胺的分布B题：铲雪车的路径与效率问题1991年：A题：估计水塔的水流量B题：通信网络费用问题1992年：A题：雷达系统的功率与设计式样B题：紧急修复系统的研制1993年：A题：堆肥问题B题：煤炭装卸场的最优操作1994年：A题：保温房屋设计问题B题：计算机网络的最小接通时间1996年：A题：大型水下物体的探测B题：快速遴选优胜者问题1997年：A题：恐龙捕食问题B题：会议混合安排问题1998年：A题：MRI图象处理问题B题：分数贬值问题1999年：A题：小星体撞击地球问题B题：公用设施的合法容量问题C题：确定环境污染的物质、位置、数量和时间的问题2000年：A题：空间交通管制B题：无线电信道分配C题：大象群落的兴衰2001年：A题：选择自行车车轮B题：逃避飓风怒吼C题：我们的水系-不确定的前景2002年：A题：风和喷水池B题：航空公司超员订票C题：如果我们过分扫荡自己的土地，将会失去各种各样的蜥蜴。
2003年：A题：特技演员B题：Gamma刀治疗方案C题：航空行李的扫描对策2004年：A题：指纹是独一无二的吗？B题：更快的快通系统C题：安全与否？2005年：A题：flood planningB题：tollboothsC题: Nonrenewable Resources2006年：A题：Positioning and Moving SprinklerSystems for IrrigationB题：Wheel Chair Access at AirportsC题：Trade-offs in the fight againstHIV/AIDS2007年：A题：GerrymanderingB题：The Airplane Seating ProblemC题：Organ Transplant: The Kidney Exchange Problem2008年：A题：Take a BathB题：Creating Sudoku PuzzlesC题：Finding the Good in Health Care Systems2009年：A题：Designing a Traffic CircleB题：Energy and the Cell PhoneC题：Creating Food Systems: Re-Balancing Human-Influenced Ecosystems。
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。
美国大学生数学建模竞赛试题AB题中文
A 题热水澡一个人进入浴缸洗澡放松。
浴缸的热水由一个水龙头放出。
然而浴缸不是一个可以水疗泡澡的缸，没有辅助加热系统和循环喷头，仅仅就是一个简单的盛水容器。
过一会，水温就会显著下降。
因此必须从热水龙头里面反复放水以加热水温。
浴缸的设计就是当水达到浴缸的最大容量，多余的水就会通过一个溢流口流出。
做一个有关浴缸水温的模型，从时间和地点两个方面来确定在浴缸中泡澡的人能采用的最佳策略，从而泡澡过程中能保持水温并在不浪费太多水的情况下使水温尽量接近最初的水温。
用你的模型来确定你的策略多大程度上依赖于浴缸的形状和容量，浴缸中的人的体型/体重/体温，以及这个人在浴缸中做出的动作。
如果这个人在最开始放水的时候加入了泡泡浴添加剂，这将会对你的模型结果有什么影响？要求提交一页MCM的总结，此外你的报告必须包括一页给浴缸用户看的非技术性的解释，其中描述了你的策略并解释了在泡澡过程中为什么保持平均的水温会非常困难。
B题太空垃圾地球轨道周围的小碎片的数量受到越来越多的关注。
据估计，目前大约有超过50万片太空碎片被视为是宇宙飞行器的潜在威胁并受到跟踪，这些碎片也叫轨道碎片。
2009年2月10号俄罗斯卫星科斯莫斯-2251与美国卫星iridium-33相撞的时候，这个问题在新闻媒体上就愈发受到广泛讨论。
已经提出了一些方法来清除这些碎片。
这些方法包括小型太空水流喷射器和高能量激光来瞄准具体的碎片，还有大型卫星来清扫碎片等等。
这些碎片数量和大小不一，有油漆脱离的碎片，也有废弃的卫星。
碎片高速转动使得定位清除变得困难。
建一个随时间变化的模型来确定一个最佳选择或组合的选择提供给一家私人公司让它以此为商业机遇来解决太空碎片问题。
你的模型应该包括对成本、风险、收益的定量和/或定性分析以及其他重要因素的分析。
你的模型应该既能够评估单个的选择也能够评估组合的选择，且能够探讨一些重要的”what if ”情景。
用你的模型来确定是否存在这样的机会，在经济上很有吸引力；或是根本不可能有这样的机会。
2019美赛数学建模A题论文
Winter is approaching, may the dragon’s wings grow moreabundantSummaryIn 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 .table of ContentsWinter is approaching, may the dragon’s wings grow more abundant (1)Summary (1)table of Contents (2)1 Introduction (3)1.1 restatement (3)1.2 Problem Analysis (3)2 Assumptions and reasons (4)3 Symbol Definition (4)4. Mathematical modeling (5)4.1 About Dragon Flight and Spitfire Consumption (5)4.2 About the relationship between dragon's body length and weight and age (7)4.3 About Dragon's Food Supply (8)4.4 Regulating the area of dragons by region (9)5 Sensitivity analysis (10)6 Model evaluation and outlook (11)6.1 Model evaluation (11)6.2 Further discussion (12)7 to a letter from George RR Martin (12)8.Appendix: (13)8.1 References (13)8.2 Matlab code (13)1 Introduction1.1 restatementIn the magical TV series "Game of Thrones", Daenerys Targaryen, known as the Mother of Dragons, raised three dragons as an aggressive army. Dragons have always been the most mysterious monsters in Eastern and Western cultures, but if Dragons live in the present era, how should we feed the three dragons in pursuit of maximum growth? In this article, we assume that the growth rules of dragons are in line with basic biology. To study them, we build mathematical models to solve problem.a. Analyze the change of the dragon's weight length with age, and estimate the value of the dragon's weight length corresponding to the age group.b. Investigate the loss of self energy during dragon fire, flight, and breathing, so as to estimate the minimum supply value of dragon for external activitiesc. Dragons need food and survival areas like other animals in the real world. Through certain assumptions and calculations, we can determine the total amount of food that dragons need daily and the size of living areas in three areas.d. Sensitivity analysis: As temperature and climate change, dragons will also migrate to different regions. Therefore, we need to analyze the differences in the impact of dragons on the survival of arid regions, temperate regions, and cold regions.1.2 Problem AnalysisBecause dragons do not exist in real life, we need to use some things in the real world to compare dragons in order to achieve the purpose of studying dragons. In analyzing the biological morphological characteristics of dragons, we use the knowledge of ecology and basic elements of biology Let's conceive the basic biological characteristics of the dragon such as weight and body length. For the energy loss model of the dragon, we have studied three aspects to describe its loss. Here we compare the modern flamethrower and establish related chemical equations to achieve the research of the dragon. Spitfire loss. In addition, in TV series such as "Game of Thrones" we will find that dragons can fly in common sense, so we have derived the dragon's flight loss. Of course, all aerobic organisms can breathe. Dragons are no exception, so there is a loss of breathing to maintain body temperature. At the same time, in order to make up for the loss of dragons in daily activities, we have established a material reserve model, in which materials are cattle and sheep in real life, etc. Finally, during the cyclical changes in climate and food, the dragons we feed will also migrate to some extent, so we analyzed the impact of different regions on the growth of dragons.Into account various factors that we can more scientific training of dragons, have achieved our purpose.2 Assumptions and reasonsAfter a comprehensive analysis of the problem, in order to increase the enforceability, we make the following assumptions to ensure the rationality of our model establishment.2.1 Assumptions: The basic biological characteristics of dragons are in line with the law of biological growth. In modern life, the growth and development of dragons should also be similar to other animals and conform to basic biology.2.2 Assumption: The dragon will spit fire and fly, and its flight conforms to the physical environment of fluid mechanicsReason: In Game of Thrones, the image of the dragon was once able to fly and spit fire.2.3 Assumption: In the single field we are studying, the environment of a certain area will not change abruptly and maintain a dynamic stability.2.4 Hypothesis: Dragons are top predators in the food chain, but dragons do not cause devastating harm to the biosphere.2.5 Assumption: The weight distribution of the dragon is uniform, and the body length reaches 30 to 40 cm at the time of birth.Reason 2.6: We refer to ancient biology and some dinosaur fossils.2.7 Hypothesis: Except for the skull, heart, liver, lungs, kidneys, bones, etc., the sum of other body masses is proportional to the cube of height.Reason: The hypothesis is obtained by counting the relationship between body length and weight of modern organisms.2.8 Hypothesis: The dragon is a constant temperature animal whose body temperature is not affected by external factors.Reason: A few pterosaur fossils have traces of "hair" on the surface, while the dragons in Game of Thrones are similar to pterosaurs.2.9 Hypothesis: The dragon is fully aerobic during the flight to provide energy2.10 Hypothesis: A certain fixed ratio of the amount of energy that is not assimilated by the growth and metabolism of the dragon's breathing and other organisms2.11 Hypothesis: Dragon's Flight Similar to Modern Fighter3 Symbol Definition4. Mathematical modeling4.1 About Dragon Flight and Spitfire Consumption4.1.1 Proposed modelConsidering that dragons fly and spit fire during activities, we have established an energy loss model. Comparing the principle of dragon's spitfire with modern flamethrowers, modern flamethrowers consume hydrocarbons or alcohols. It does not cause any impact, so the dragon's fire-breathing principle is in line with the alcohol flame-thrower principle. Considering that the formaldehyde produced by the metabolism of methanol in the animal body is harmful to the body, we stipulate that ethanol is the fuel used by the dragon's flame. In the process, the relationship between the dragon's flight speed and glucose energy consumption is obtained according to fluid mechanics. In this process, we assume that the aerobic respiration is completely performed, and the energy consumed by the dragon due to flight is obtained according to the glucose consumption. In summary, the dragon energy loss model is obtained. .4.1.2 Establishment and Solution of Dragon's Spitfire ModelThe thermochemical equation for ethanol combustion is: C2H5OH (l) + 3O2 (g) = 2CO2 (g) + 2H2O (l) △H = -12KJ / gSpecify the energy released per unit mass of ethanol combustion x1When the dragon spit fire in unit time t, the unit mass of ethanol consumption is a fixed valueThe energy consumed by the fire time t1 is w1The mass consumed by the fire time T1 is m4Let the energy emitted by the combustion of unit mass of ethanol be w1 'Then W1 = x1 * tm4=W1/W1’Solve m4 = x1 * t / W1 '4.1.3 Establishment and Solution of Dragon Flight ModelDuring the flight of the dragon, it will be affected by the air resistance. In the ideal situation, the dragon's flight can be considered as a uniform acceleration and then a uniform speed, and it will decelerate when it is about to reach its destination.When Long uniform acceleration is specified, the acceleration is aSince the flight of the dragon is similar to that of a fighter, a = 30m / s ^ 2The speed of the dragon during uniform motion is v0The total flight length of the dragon during flight is sBecause air resistance is proportional to the speed of movement, that is, F1 = k * v (where k is a constant)Since the dragon's flight is similar to an airplane, we can get k = 3.2325Available according to the relevant kinematic formulaThe flying distance of the dragon during uniform acceleration is s1 = (v0) ^ 2 / 2aThe flying distance of the dragon during uniform deceleration is s3 = (v0) ^ 2 / 2aThe flying distance of the dragon during uniform motion is s2 = s-s1-s3Average air resistance during uniform acceleration F1 '= k * (0 + v0) / 2The average air resistance during uniform motion is F1 '' = k * v0Average air resistance during uniform deceleration f1 '' '= k * (v0 + 0) / 2According to the law of conservation of energyThe energy w2 consumed by the dragon during flight is all used for air resistance workW2=F1’*s1+F1’’*s2+F1’’’*s3Solve W2 = 3.2325 * v0 * s-3.2325 * (v0) ^ 3 / (2 * 30)During the flight of the dragon, the principle of energy provided by aerobic respiration isC6H12O6+6O2=6CO2+6H2OAmong them, the energy produced when 1g of glucose is completely consumed is 16KJThen the weight consumed in this process is m6 = W2 / 16[v,s]=meshgrid(0:0.1:100;0:0.1:100);m=3.2325*v*s-3.2325*v^3/60mesh(v,s,m)4.2 About the relationship between dragon's body length and weight and age4.2.1 Proposed ModelFirst, in order to study the relationship between the weight, length, and age of the dragon, that is, morphological characteristics, we established a model of elasticity during growth. The above-mentioned change curve is continuous, so we use the weight of the dragon at birth, and consider the weight and length of the dragon. The relationship between age changes can be used to derive the normal weight and body length of dragons in all ages. When analyzing the weight changes of dragons, biological knowledge shows that the amount of assimilation of the dragon is equal to the intake amount minus the amount of unassimilated amount Considering that the growth rate of the dragon in adulthood is a watershed, we use the saturation value of the dragon's head, heart, and liver as a cutoff value to estimate the relationship between the dragon's weight and age, respectively. When studying the body length of the dragon, according to the existing morphological knowledge, the head to hip of the dragon is used as the length standard. Because the weight of the dragon is proportional to the cube of the dragon's length, we get the weight and length Functional relationship. Of course, the daily weight gain of the dragon must be less than the daily energy consumption. In summary, we have a dragon intake model.4.2.2 Model establishmentSpecify the weight of the dragon as mDragon was born with a weight of m0 (known m0 = 10kg)Assume that the mass of cattle and sheep fed by a train every day is m2The assimilation amount of the dragon is fixed at a%A certain fixed ratio of the amount of unabsorbed energy due to growth and metabolism of organisms such as dragon's respiration, recorded as b%The weight gain of the dragon is m 'The sum of the weight of the dragon's head, heart, liver, lungs, kidneys, bones, etc. m1 increases with age y until adulthoodDragon is y1 when he is an adultThe growth rate of m1 is v1The mass of m1 at birth is m0Before the dragon reaches y1m1=m0+v1*yAfter the dragon reaches y1m1’=m0+v1*y14.2.3 Model Solvingm’=m2*(1-a%)*(1-b%)-m4-m6So the weight of the dragon m = m '+ m0Except for the dragon, except for the head, heart, liver, lungs, kidneys, bones, etc., the sum of other body masses is proportional to the cube of height, and the body length is recorded as l When the age of the dragon does not reach y1, l = (m-m1) ^ (1/3)When the age of the dragon reaches y1, l '= (m-m1') ^ (1/3)M2 =y=0:0.1:20function[y]= (m2*(1-a%)*(1-b%)-m4-m6-v1*y)y=20:0.1:100function[y]= (m2*(1-a%)*(1-b%)-m4-m6-v1*20)power(y,1/3)4.3 About Dragon's Food Supply4.3.1 Proposed modelBased on the above analysis, we studied the living area of the three dragons in the region andtheir impact on the ecological community in the region. For the sake of research, we assume that the other creatures in the region are cattle and sheep, and the competitiveness of the three dragons is comparable, Being a top predator in the food chain.4.3.2 Model establishmentThe local food chain can be approximated as: grass → cow or sheep → dragonAssume that the weight of the grass in the arid region, the warm temperate region, and the Arctic region is the same as m8.Remember that the mass of each cow and sheep is the same as m7We provide the same initial number of cattle and sheep in all three regionsAssume that the daily growth rate of cattle and sheep is c%The initial number of cattle and sheep is n1And n1 is the number of populations reaching k in the regionDragons live in this area. When the number of cattle and sheep reaches k / 2, in order to ensure the balance of the ecological environment, the dragons need to be moved to other regions.4.3.3 Model SolvingThe initial amount of cattle and sheep on day 1 is: n1The initial amount of cattle and sheep on the second day is: N2 = (N1-3 * m2 / m7) * (1 + c%) The initial amount of cattle and sheep on the third day is: N3 = ((N1-3 * m2 / m7) * (1 + c%)-3 * m2 / m7) * (1 + c%)……From this we can get the initial amount of Ni of cattle and sheep on day iI can be solved by the equation Ni = K / 2That is, the dragon needs to change a living area after living in the area for i days.4.4 Regulating the area of dragons by region4.4.1 Proposed modelIn order to ensure the normal growth of the dragon, we provide fixed-quality cattle and sheep as the supply of resources for the survival of the dragon region, and assume that the number of cattle and sheep is proportional to the size of the regional living area. Considering the growth rate of cattle and sheep, we have established a differential The equation draws the relationship between the growth rate of cattle and sheep and the age of the dragon. However, cattle and sheep will reach a growth saturation value at a certain moment, we will consider it in segments to ensure that the data is more scientific. In order to comply with ecology, cattle The supply of sheep should also have a lower limit. In summary, we have established a dragon-cow-sheep-living area function model.4.4.2 Model establishmentRemember that the assimilation rate of cattle and sheep grazing in this area is d%Because the solar energy received by the surface area of the three areas is different, the total area required for the grass under the same quality conditions is different. The utilization rate of the solar energy is required to be e% (0.5 <e <1 under the natural conditions of the search data)The solar energy per unit area in the arid area is q1Unit area solar energy in warm zone is q2Solar energy per unit area in the Arctic is q34.4.3 Model SolvingAccording to the utilization of solar energy, we can find:Area required to support the arid areas where the three dragons live: S1 = m8 / (q1 * e%)Warm zone: S2 = m8 / (q2 * e%)Arctic region: S3 = m8 / (q3 * e%)5 Sensitivity analysisImpact of climatic conditions on dragon lifeThe effect of climatic conditions on dragon growth can be obtained from the logistic growth model dm/dt=r*m*(1-m/k)That is m = 15 / (4 * t + 20);(Where m is the mass that the dragon can eventually grow into)Where m0 = 10 (k is the maximum carrying capacity of the ecosystem and r is a parameter of the environmental carrying capacity)k is 0.75r is 0.8dm/dt=0.8*m*(1-m/0.75)t=0:0.1:100;m=15./(4*t+20);plot(t,m)6 Model evaluation and outlook6.1 Model evaluationFor the idealized model of Yanglong, we have performed various aspects of modeling and solving, and the scope is relatively broad. Of course, the content has been streamlined to facilitate understanding and application. We have used physical and biological models based on The mathematical formulas are also encountered in the middle school stage. In these more basic models, we have solved efficiently, and at the same time, for the interdisciplinary problems of question a, we have considered the field that the ideal biology of dragons may involve and solve The process is relatively complete. In addition, the four models are closely related and logical. First, we consider the consumption of dragons in daily life, and use the results of consumption to calculate the weight and length of the dragon at various ages. In order to meet the requirements of all ages, we have established the ecological supply model of dragons, and discussed the problem of periodic alternating fields. Second, the fields are also scoped. Therefore, we calculated the scope of three areas with different climates. Interval problems. However, the models we build are idealized, the data is also streamlined, and the assumptions set are also fallible. In reality,The data is diverse and complex, and our considerations are obviously lacking, and further optimization is needed in the later stage. In summary, the model we built is very consistent with the solution of the problem. Although there are some flaws, it does not affect the specific Specific analysis of the problem.6.2 Further discussionCombining the models and evaluations described above, we will improve in the later stages. If this model is used in a specific environment, by statistic large amounts of real data, we can optimize the model. At the same time research also It will be more scientific and rigorous, and it will be more efficient for raising a fictional creature.7 to a letter from George RR MartinDear George RR MartinHope you are wellAfter reading the Song of Ice and Fire, we watched the "Game of Thrones". We became very curious about the mysterious giant that appeared in it-the dragon. Dragons are not uncommon in Eastern and Western cultures. In previous impressions However, there are few studies on dragons. So if we imagine that dragons live in modern times, what would it look like?According to the description of the dragon in the novel, we discussed the following questions. What are the ecological impacts and requirements of the dragon? What is the energy consumption of the dragon, what are their calorie intake requirements? How much area is needed to support the three dragons? Energy loss during fire? In response to these problems, we constructed a multivariate non-linear objective programming model of dragon's growth index and function, size, diet, growth changes, and other animal-related features. Considering the physical characteristics of dragons, we will Its fire-spitting ability is analogized to modern flame-throwers to ensure scientific and rational research.Based on these, we have established a mathematical model. The weight and length of the dragon also grows with the age of the dragon. When the dragon grows slowly at the initial 10 kilograms, the mass of sheep it needs each year also varies The growth of the supply chain of resources and the size of the ecological community should also change. The fire and flight of the dragon will also have a certain impact on the ecological environment. As the dragon and other creatures will migrate with changes in temperature, we choose The three regions of the cold zone, temperate zone and arid zone were taken as key research objects to find out the impact of climate change on Long.Therefore, we make the following suggestions, hoping that the survival of the dragon in the realm of science is more reasonable and scientific.When the herd resource is saturated, the dragon needs to expand the area living area.Dragons like warm, hydrated areas, and migrate to warm areas in the cold winter.A dragon has a certain weight and length when it is just born, and it will grow over time, but it also has an upper limit. It cannot grow endlessly.The daily energy intake of the dragon is limited, and the dragon spitfire flight consumes energy, which requires that the dragon's flight distance and spitfire time are limited, and it is related to the age of the dragon body.Because the living conditions of the three areas are different, the unit area will also receive solar energy differently, resulting in different resource distributions in each area, which means thatthe speed of dragon growth should also be different in different areas.The environmental carrying capacity of each area is limited, and the dragon does not stay in one place for long.The above content is the result of our research on the Queen of Dragons. We sincerely hope that you can adopt it, and we have been looking forward to your new book.Your fans: 27 groupsJanuary 7, 20208.Appendix:8.1 References1) Chen Yun.Research on Environmental Carrying Capacity of Yuhuan County [j] .Energy and Energy Conservation, 2014 (4): 31-33.2) Zhu Ziqiang.Aerodynamic design of modern aircraft [m] .Beijing: National Defense Industry Press, 2011-10-13) Jin Lan.Environmental Ecology [m] .Higher Education Press, 19928.2 Matlab codeModeling the flight of a dragon[v,s]=meshgrid(0:0.1:100;0:0.1:100);m=3.2325*v*s-3.2325*v^3/60mesh(v,s,m)Sensitivity Analysis of the Impact of Climate Conditions on Lifet=0:0.1:100;m=15./(4*t+20);plot(t,m)。
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5.1个基本的感知
在一个长方形的锅烘烤时，为什么热会集中在4个角落？
图3。
一个布朗尼在矩形盘示意图（a）和圆形盘示意图（b）
假设图3中所示的长方体（a）是在矩形盘烤制的一个布朗尼，长方体的彩色部分是在右下角的一个狭窄的空间。
不同于其他长方体，这是温暖的热量只能从一个方向并且有足够的空间来传递热量给内部区域，这部分热从三个方向并且由于缺乏空间的开放热积累在角是很难扩散的。
因此，热量分布不均匀，四个角落的温度高于其他的部位，巧克力在角落会比较容易烤糊。
在一个圆形的锅烘烤时，为什么热均匀地分布在整个外边缘？
类似上面的例子，如图3所示的磁盘（b）也可以被想象成一个布朗尼在一个圆形烤锅烤制。
曲面上的边和表面平坦的底部都是只能从一个方向（即加热的表面的法线矢量）传热，他们都有足够的开放空间传递热量进入内部，使温度保持在一定范围内的边缘水平。
因此，热量均匀地分布在整个的外边缘而且温度不会太高而使巧克力蛋糕烤糊。
一个布朗尼在矩形或圆形锅烤炙有以上两点留在感性认知上。
虽然我们已经获得总热量的基本知识分布，而且更明确的、直观的方法必须说明他们的确切热分布。
为了测试我们的基本的看法，我们继续我们的探索机理分析的理论验证。
当
最好计划是：
很容易得出结论：当炉子的宽度和长度的比值（λ）是一个常数，随P锅数增加而增加，但是平均热减小（例如（1）和（2））。
当重量P是一个常数，锅的数量随着λ的增大而减小，平均热也减小。
因此，实际的计划应以您的特定需求为基础。
结论
总之，我们的团队是非常肯定的是，我们想出的方法是有效的热分布分析。
根据我们的模型，锅的边越多，热分布越均匀。
与离散转换的方法，我们知道当比炉子的宽度和长度（γ）是一个常数，锅的数量随着P含量增加，但平均热量减小。
当重量P是一个常数，锅的数量
随γ锅的数目增加而减少，而且平均值也减小。
因此，实际的计划
应该是在您的特定需求的基础。
优势和弱点
优势
•难以避免
在模型1中，我们转向另一种工作，模拟的热分布而不是直接热传导。
首先，我们模拟了辐射热不热传导使其远离复杂的偏微分方程。
然后，我们创建将每个变量从整个空间段转换的一种独特的方法。
换句话说，我们解决了一切在热辐射转换成热是矛盾的问题。
•贴近现实。
我们的模型同时考虑了热辐射和反射面，这比较接近实际情况。
•提供的灵活性。
我们的算法的灵活性的一项伟大的工作。
在截面的热分布图从整个空间的热分布图截取的。
各种形状的部分可用于算法。
产生在整个空间的热分布基于电加热管的热衰减曲线的位置，它可以在任何时间修改。
•创新性
根据我们的模型，一个烤箱的空间从不同角度可以分为六个不同部分的分布。
为了充分利用内部空间，我们发明了一种新的锅，它允许用户同时做六种不同种类的食物，。
在文章的结尾发表了这个广告。
弱点
•锅的热导率被忽略。
热既来自电加热管，而且也来自热传导他们的锅。
但锅的热传导在模型中被忽略，这可能引起小的误差。
•热导电加热管被忽视
它是假定有两个烤箱电加热管而且被放置在一个具体位置。
管的初始温度所需的恒定的温度。
换句话说，时间电加热管加热自己被忽视了，这种简化会导致一定的误差。
•线性简化。
在模型2中，烤箱的长度是离散的，使得锅数线性变化。
通过简单的整数线性的计算方法。
这将导致我们的模型的结果不够准确。
•应用
我们已经讨论了模型1烤箱的温度分布。
热分布在图1和图2所示。
如图，烤箱的边缘分布的最热，两边的地区分布的热最小，而中部地区比边缘吸收的更少。
因此我们可以将炉区分成六部分，如下所述：
基于我们的结论，我们发明一种新的组合锅，IPAN，可同时烘烤三种食物。
例如，一个想要一点点面包，香肠片，午餐吃鸡翼和一个比萨饼。
如果他只是一个烤箱，他将不得不等待至少30分钟吃午饭。
中国有句俗话，“熊掌和鱼不在一起”。
利用IPAN可以为他解决问题，他可以把面包放在锅1，比萨放在2锅，鸡翼香肠放在锅5和锅6，一起加热。
因此，至少10分钟他就可以有他美味的午餐。
所以，熊掌和鱼均可得到。
我们在本文的最后做一个印象美食杂志的广告。
广告片
工具书类
[ 1 ]热辐射，
/view/f5ed1619cc7931b765ce1599.html, 第4页。
[ 2 ]G. S.兰添纳斯，黑体辐射，
/article/10.1007%2Fs12045-008-0028-7?LI=true#, 2013年2月
[ 3 ]开庆路，热传递的化学基础，高等函授教育（自然科学版），第3卷：第33页，1996
[ 4 ]标记M.米尔斯切特，数学建模（第三版），中国：中国机械工业出版社，可能。
2009
[ 5 ]张建，蒙特卡罗方法，数学的实践与认识，第1卷草28，1974年
[ 6 ]浅层水方程，http：／／ /维基/浅_水_方程。