2015年美国数学建模竞赛A题
2015年数学建模国赛A题
二、 问题分析
问题一要建立直杆影子长度变化的数学模型， 首先需知道太阳影子长度计算 公式，故引入太阳高度角[1]这个概念。即若已知某时刻太阳高度角的大小和直 杆高度，根据其满足的三角函数关系便可得到此时太阳影子长度。太阳高度角与 观测地地理纬度、地方时角和太阳的赤纬[2]相关。其中太阳赤纬是太阳直射点 所在纬度，与日期有关；时角由当地经度及其所用时区时间决定，故根据影长、 太阳赤纬、时角计算公式可求得直杆影子长度变化模型，并根据模型分析影子长 度关于各参数的变化规律。将附件一中直杆的有关数据直杆影长变化模型中，可 求出该直杆的具体影长变化公式。根据所建立的模型，运用 MATLAB 软件便可得 到影子长度随时间的变化曲线。 问题二需根据某固定直杆在水平地面上的太阳影子顶点坐标数据， 建立数学 模型确定直杆所处的地点。首先由问题一可推测影子长度与时间的关系，故可将 太阳影子长度与对应时间进行拟合，得到影长与时间关系模型。当某个时刻影长 得到极小值时，该时刻为太阳与直杆距离最近，即地方时正午 12 时，结合当地 所使用的标准时间便可得到当地经度。 最后利用太阳高度角与直杆长度以及影长 满足的三角关系式，便可得到影长关于直杆高度、直杆所在地点的纬度的函数关 系式，即得到了有关太阳影子顶点坐标与直杆地点经纬度的模型。将附件一中影 子顶点坐标数据应用于该直杆位置模型，可得到直杆所在位置。用相对误差分析 法分析误差[3](168-169 页)，若所得的相对误差小于 2.5%，认为得到的模型合 理。 问题三可根据光照成影原理和太阳高度角计算公式建立影长与时间变 化模型，根据相关数据，运用 MATLAB 软件拟合可得到直杆所在位置的经纬 度。令年份均为 2015 年，根据太阳赤纬角计算公式，可求解具体的日期。 将附件 2 和附件 3 时间和对应直杆影长数据分别代入模型中，通过拟合计
2015年美国数学建模竞赛第二次模拟赛题
Problem A Warmer Days or Sour Grapes ?The high quality of wines（葡萄酒）produced in the Finger Lakes Region（五指湖区）of upstate （北部）New York is widely known. Proximity（接近）to lakes tempers the climate and makes it more suitable for growing several varieties of premium（独特）grapes: R iesling（雷司令）, G ewürztraminer（琼瑶浆）,C hardonnay（霞多丽）, M erlot（梅洛）, P inot Noir（黑比诺）, and CabernetF ranc（品丽珠）. (There are many more, but we will restrict（限制）the discussion to these six to simplify（简化）the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility（感受性）to diseases and ability to withstand（抵抗）short periods of unusually cold temperature.As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery（酒厂）has hired your team to help with the long-term planning. You will need to recommenda) the proportion（比例）of the total vineyard（葡萄园）to be used for growing each of the above six varieties;b) and when should these changes be implemented （实施）(based on observed temperatures and/or current market prices for each type of wine).Naturally, the winery is interested in maximizing its annual profit. But since the latter （后者）is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs （权衡）between optimizing the expected/average case versus the worst(-realistic-)scenario（情景）.Things to keep in mind:Climate modeling is complicated（复杂）and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca（伊萨卡）, NY will increase by no more than 4°C by the end of this century.It is not all about the average temperature – a short snap（临时）of sub- zero（零度）temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter.It takes at least 3 years for a newly planted vine to start producing grapes suitable for winemaking.Problem B Outlook of Car-to-Car TechSAN FRANCISCO -- After more than a decade of research into car-to-car communications, U.S. auto safety regulators took a step forward today by unveiling their plan for requiring cars to have wireless gear that will enable them to warn drivers of danger.These vehicle-to-vehicle (V2V) transmitters and software could save thousands of lives and prevent hundreds of thousands of crashes each year by providing cars with information they never will be able to gather simply from cameras and sensors. “Safety is our top priority, and V2V technology represents the next great advance in saving lives,” Transportation Secretary Anthony Foxx said in an announcement. “This technology could move us from helping people survive crashes to helping them avoid crashes altogether.”Requirement 1: Present a mathematical model to discuss the reduction of the number of traffic accidents and road fatalities/injuries in San Francisco by V2V technology. Requirement 2: Determine the maximum number of cars in San Francisco due to the V2V technology.Requirement 3: Discuss the benefits of V2V technology to alleviate road congestion. Requirement 4: Provide your recommendation to the government.Prblem C Forest FiresOne major environmental concern is the occurrence of forest fires (also called wildfires), which affect forest preservation, bring economical and ecological damage and endanger human lives. Such phenomenon is due to multiple causes (e.g. human negligence and lightnings). Despite an increasing of state expenses to control this disaster, each year millions of forest hectares (ha) are destroyed all around the world.Fast detection is an important element for successful firefighting. Traditional human surveillance is expensive and affected by subjective factors, there has been an emphasis to develop automatic solutions, such as satellite-based, infrared/smoke scanners and local sensors (e.g. meteorological). Propagation models try to describe the future evolution of the forest fire given an initial scenario and certain input parameters. Modeling the dynamical behavior of fire propagation in a forest is helpful for creating scheme to control and fight fire.Requirement 1 Describe several different metrics that could be used to evaluate the effectiveness of fire detection. Could you combine your metrics to make them even more useful for measuring quality?Requirement 2 Model the dynamical behavior of fire spread in a forest. Requirement 3 Discuss the factors to affect fire occurrence. Which factors are the most critical in causing fires. Build mathematical models to predict the burned area of fires using Meteorological Data.Requirement 4 Give y our suggestion for preventing from forest fire and fighting against it.Problem D Wearable Activity RecognitionThe percentage of EU citizens aged 65 years or over is projected to increase from 17.1% in 2008 to 30.0% in 2060. In particular, the number of 65 years old is projected to rise from 84.6 million to 151.5 million, while the number of people aged 80 or over is projected to almost triple from 21.8 million to 61.4 million (EUROSTAT: New European Population projections 2008–2060). It has been calculated that the purely demographic effect of an ageing population will push up health-care spending by between 1% and 2% of the gross domestic product (GDP) of most member states. At first sight this may not appear to be very much when extended over several decades, but on average it would in fact amount to approximately a 25% increase in spending on health care, as a share of GDP, in the next 50 years (European Economy Commission, 2006). The effective incorporation of technology into health-care systems could therefore be decisive in helping to decrease overall public spending on health. One of these emerging health-care systems is daily living physical activity recognition.Daily living physical activity recognition is currently being applied in chronic disease management (Amft & Troter, 2008; Zwartjes, Heida, van Vugt, Geelen, & Veltink, 2010), rehabilitation systems (Sazonov, Fulk, Sazonova, & Schuckers, 2009) and disease prevention (Sazonov, Fulk, Hill, Schutz, & Browning, 2011; Warren et al., 2010), as well as being a personal indicator to health status (Arcelus et al., 2009). One of the principal subjects of the health related applications being mooted is the monitoring of the elderly. For example, falls represent one of the major risks and obstacles to old people’s independence (Najafi, Aminian, Loew, Blanc, & Robert, 2002; Yu, 2008). This risk is increased when some kind of degenerative disease affects them. Most Alzheimer’s patients, for exa mple, spend a long time every day either sitting or lying down since they would otherwise need continuous vigilance and attention to avoid a fall.The registration of daily events, an important task in anticipating and/or detecting anomalous behavior patterns and a primary step towards carrying out proactive management and personalized treatment, is normally poorly accomplished by patients’ families, healthcare units or auxiliary assistants because of limitations in time and resources. Automatic activity-recognition systems could allow us to conduct a completely detailed monitoring and assessment of the individual, thus significantly reducing current human supervision requirements.Most wearable activity recognition systems assume a predefined sensor deployment that remains unchanged during runtime. However, this assumption does not reflect real-life conditions. During the normal use of such systems, users may place the sensors in a position different from the predefined sensor placement. Also, sensors may move from their original location to a different one, due to a loose attachment. Activity recognition systems trained on activity patterns characteristic of a given sensor deployment may likely fail due to sensor displacements.Your task is as follows.(1) Build models to recognize daily living activities.(2) Explore the effects of sensor displacement induced by both the intentionalmisplacement of sensors and self-placement by the user.(3) Verify your recognition models’ toleranc e to sensor displacement.Data Set Information:The REALDISP (REAListic sensor DISPlacement) dataset has been originally collected to investigate the effects of sensor displacement in the activity recognition process in real-world settings. It builds on the concept of ideal-placement, self-placement and induced- displacement. The ideal and mutual-displacement conditions represent extreme displacement variants and thus could represent boundary conditions for recognition algorithms. In contrast, self-placement reflects a users perception of how sensors could be attached, e.g., in a sports or lifestyle application. The dataset includes a wide range of physical activities (warm up, cool down and fitness exercises), sensor modalities (acceleration, rate of turn, magnetic field and quaternions) and participants (17 subjects). Apart from investigating sensor displacement, the dataset lend itself for benchmarking activity recognition techniques in ideal conditions.Dataset summary:#Activities: 33#Sensors: 9#Subjects: 17#Scenarios: 3ACTIVITY SET:A1: WalkingA2: JoggingA3: RunningA4: Jump upA5: Jump front & backA6: Jump sidewaysA7: Jump leg/arms open/closedA8: Jump ropeA9: Trunk twist (arms outstretched)A10: Trunk twist (elbows bent)A11: Waist bends forwardA12: Waist rotationA13: Waist bends (reach foot with opposite hand)A14: Reach heels backwardsA15: Lateral bend (10_ to the left + 10_ to the right)A16: Lateral bend with arm up (10_ to the left + 10_ to the right)A17: Repetitive forward stretchingA18: Upper trunk and lower body opposite twistA19: Lateral elevation of armsA20: Frontal elevation of armsA21: Frontal hand clapsA22: Frontal crossing of armsA23: Shoulders high-amplitude rotationA24: Shoulders low-amplitude rotationA25: Arms inner rotationA26: Knees (alternating) to the breastA27: Heels (alternating) to the backsideA28: Knees bending (crouching)A29: Knees (alternating) bending forwardA30: Rotation on the kneesA31: RowingA32: Elliptical bikeA33: CyclingSENSOR SETUP:Each sensor provides 3D acceleration (accX,accY,accZ), 3D gyro (gyrX,gyrY,gyrZ), 3D magnetic field orientation (magX,magY,magZ) and 4D quaternions (Q1,Q2,Q3,Q4). The sensors are identified according to the body part on which is placed respectively:。
(最新整理)数学建模美赛试题
2015数学建模美赛试题编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（2015数学建模美赛试题）的内容能够给您的工作和学习带来便利。
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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。
2015数学建模A题论文介绍
2015数学建模A题论⽂介绍A题太阳影⼦定位摘要本⽂⾸先确定了不同地点不同⽇期的直杆影长的模型，利⽤该模型解决了不同地点不同⽇期直杆影⼦变化和时间的的关系，为分析视频的拍摄地点和⽇期提供了模型上的基础。
对于问题⼀，为了确⽴直杆的影长与时间的关系，建⽴了地球坐标系和天球坐标系，引⼊太阳⾼度⾓、⾚纬、太阳时⾓、时差等参数变量。
利⽤太阳⾼度⾓和时间的关系建⽴了影长和时间的关系模型。
利⽤MATLAB软件求得影长关于时间的变化曲线，从9点到15点影⼦长度先减⼩后增⼤，在北京时间12点14分直杆影长最短，最短为3.5⽶，在北京时间9点直杆影长最长，长度为7.3⽶。
对于问题⼆，结合问题⼀中各参数变量之间的关系，使⽤Bourges算法和太阳⽅位⾓与时间的关系，得到确定直杆所在地点的数学模型，将附件1所给数据带⼊模型，利⽤excel和MATLAB软件进⾏求参数和拟合函数图像，求得直杆所处的可能地点为北纬19.21，东经108.43。
该地点在海南。
或者为南纬3.9412度，东经137.3度。
该地点在为印度尼西亚纳⽐雷附近。
对于问题三，由所给影⼦顶点坐标数据计算出各时间点的太阳⽅位⾓，利⽤excel 软件拟合出太阳⽅位⾓与时间的关系，进⽽确定直杆点的经度，结合问题⼆的数学模型得到直杆地点和⽇期求法的数学模型。
再次通过MATLAB进⾏求参数和拟合函数图像，求出了附件2地点可能为北纬39.88，东经79.7925或南纬39.88，东经79.7925，可能⽇期为：5⽉25号和7⽉20号或1⽉17号和1⽉26号。
对于问题四，提取出视频所有的帧数，等差得选取其中的20张进⾏模拟，利⽤3DMAX 软件仿真出视频的场景，通过测量所建模型中影⼦长度，确定出20组影⼦顶点坐标数据，再⽤问题⼆中所⽤到的模型进⾏求解，得到经纬度为北纬15.2，东经113.9.拍摄地点在海南省的三沙市。
⽤问题三中的模型求解得到拍摄地点纬度为0，东经123.8度在印度尼西亚，⽇期为3⽉21号或10⽉23号。
2015年美赛O奖论文A题Problem_A_32150
Team Control Number
For office use only F1 ________________ F2 ________________
32150
Problem Chosen
A
F3 ________________ F4 ________________
2015 Mathematical Contest iow to Eradicate Ebola? The breakout of Ebola in 2014 triggered global panic. How to control and eradicate Ebola has become a universal concern ever since. Firstly, we build up an epidemic model SEIHCR (CT) which takes the special features of Ebola into consideration. These are treatment from hospital, infectious corpses and intensified contact tracing. This model is developed from the traditional SEIR model. The model’s results (Fig.4,5,6), whose parameters are decided using computer simulation, match perfectly with the data reported by WHO, suggesting the validity of our improved model. Secondly, pharmaceutical intervention is studied thoroughly. The total quantity of the medicine needed is based on the cumulative number of individuals CUM (Fig.7). Results calculated from the WHO statistics and from the SEIHCR (CT) model show only minor discrepancy, further indicating the feasibility of our model. In designing the delivery system, we apply the weighted Fuzzy c- Means Clustering Algorithm and select 6 locations (Fig.10, Table.2) that should serve as the delivery centers for other cities. We optimize the delivery locations by each city’s location and needed medicine. The percentage each location shares is also figured out to facilitate future allocation (Table.3,4). The average speed of manufacturing should be no less than 106.2 unit dose per day and an increase in the manufacturing speed and the efficacy of medicine will reinforce the intervention effect. Thirdly, other critical factors besides those discussed early in the model, safer treatment of corpses, and earlier identification/isolation also prove to be relevant. By varying the value of parameters, we can project the future CUM . Results (Fig.12,13) show that these interventions will help reduce CUM to a lower plateau at a faster speed. We then analyze the factors for controlling and the time of eradication of Ebola. For example, when the rate of the infectious being isolated is 33% - 40%, the disease can be successfully controlled (Table.5). When the introduction time for treatment decreases from 210 to 145 days, the eradication of Ebola arrives over 200 days earlier. Finally, we select three parameters: the transmission rate, the incubation period and the fatality rate for sensitivity analysis. Key words: Ebola, epidemic model, cumulative cases, Clustering Algorithm
美国数学学会中学生数学竞赛真题和答案解析2015AMC8 Solutions
This Solutions Pamphlet gives at least one solution for each problem on this year’s exam and shows that all the problems can be solved using material normally associated with the mathematics curriculum for students in eighth grade or below. These solutions are by no means the only ones possible, nor are they necessarily superior to others the reader may devise.We hope that teachers will share these solutions with their students. However, the publication, reproduction, or communication of the problems or solutions of the AMC 8 during the period when students are eligible to participate seriously jeopardizes the integrity of the results. Dissemination at any time via copier, telephone, email, internet or media of any type is a violation of the competition rules.Correspondence about the problems and solutions should be addressed to:Prof. Norbert Kuenzi, AMC 8 Chair934 Nicolet AveOshkosh, WI 54901-1634Orders for prior year exam questions and solutions pamphlets should be addressed to:MAA American Mathematics CompetitionsAttn: PublicationsPO Box 471Annapolis Junction, MD 20701© 2015 Mathematical Association of AmericaWe thank the following donors for their generous support of the MAA American Mathematics Competitions, MOSP and the IMOPatron’s CircleAkamai FoundationSimons FoundationWinner’s CircleAmerican Mathematical SocietyThe D.E. Shaw GroupDropboxMathWorksTwo SigmaTudor Investment CorporationAchiever’s CircleArt of Problem SolvingJane Street CapitalMath for AmericaSustainer’s circleAcademy of Applied ScienceArmy Educational Outreach ProgramCollaborator’s CircleAmerican Statistical AssociationCasualty Actuarial SocietyConference Board of the Mathematical SciencesExpii, Inc.IDEA MATHMu Alpha ThetaNational Council of Teachers of MathematicsSociety for Industrial and Applied MathematicsStar League。
2015年数模美赛ABCD题目
A题The world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.世界医学协会日前宣布，其新的药物可以阻止埃博拉病毒和治愈患者的疾病，谁的病没有进入晚期。
因此，建立一个现实的、合理的，并且有用的模型是认为制造的疫苗或药物的不仅是这种疾病的传播、所述药物的所需要的数量、可能的可行交付系统、交付地点、制造的疫苗或药物的速度，但也可以是任何你的团队认为有必要为模型做贡献的其他关键因素，以便优化消灭埃博拉病毒或者至少抑制其目前的压力。
2015美赛A题优秀论文
2.4 2.5 2.6
Model Modeling Objectives . . . . . . . . . . . . . . . . . . . . Problem Space . . . . . . . . . . . . . . . . . . . . . . . The Multi-Layer State Based Stochastic Epidemic Model 2.3.1 Individual Layer - Stochastic State Based Model . 2.3.2 Inter-Region Layer modeling . . . . . . . . . . . . 2.3.3 Human Mobility Model . . . . . . . . . . . . . . . 2.3.4 Supply Distribution Model . . . . . . . . . . . . . 2.3.5 A note on GLEAM . . . . . . . . . . . . . . . . . Implementation . . . . . . . . . . . . . . . . . . . . . . . Additional Considerations . . . . . . . . . . . . . . . . . 2.5.1 Modeling of Hospitals . . . . . . . . . . . . . . . Consequences of Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2015年美国(国际)大学生数学建模竞赛
比赛时间：美国东部时间：2015年2月5日（星期四）下午8点-2月9日下午8点（共4天）北京时间：2015年2月6日（星期五）上午9点-2月10日上午9点农历：十二月十八～十二月廿二重要说明：●COMAP是所有的规则和政策的最后仲裁者，对不遵循竞赛规则和程序的任何队伍，拥有唯一的自由裁量权，取消参赛资格或拒绝登记。
●评委、竞赛组织者、以及UMAP杂志的编辑拥有最终裁定权。
●如果参赛队伍违反竞赛规则，其指导老师一年内将不能指导其他团队，其所在参赛单位将被处以一年的察看处理。
●如果同一机构第二次被抓到违反规则的队伍，该学校将至少不被允许参加下一年度的赛事。
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2015数模美赛A题翻译
PROBLEM A: Eradicating EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose diseases not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.A消除埃博拉病毒世界医学协会已经宣布他们的新疗法可以阻止埃博拉疫情和治愈非晚期患者。
构建一个现实的、合理的和有用的模型,不仅要考虑疾病的传播,所需药物的数量,可能且可行的给药系统,给药地点,生产疫苗或药物的速度,而且还要考虑其他关键因素（你的团队认为有必要要考虑的）作为模型的一部分以优化消除埃博拉病毒，或至少是现行毒株。
2015年美国大学生数学建模竞赛A题
PROBLEM A: Eradicating EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement.问题一：根除病毒世界医疗联盟声称，他们的新药物可以制止埃博拉病毒，并且治愈病情没有恶化的患者。
建立一个现实的，明智的，并且有用的模型，需要考虑的不仅是疾病的扩散、所需要的药物、可能并且可行的发放系统、发放的地点、生产疫苗或药物的速度，还有你们队伍认为在优化消灭埃博拉（或至少它的现在的同类血亲）模型之中重要的因素。
2015年数模A题
2.2问题二的分析
第二个问题根据对竞赛评委有不同的基本素质要求，给出合理的度量评委基本素质的指标体系。我们根据题目附件给出的数据，去发掘测评评委基本素质要求的一些指标体系。测评基本素质指标体系主要三个方面构成：指标一是评委打分的准确度，指标二是评委打分的稳定度，指标三是评委打分的偏差度。为了使指标准确可靠，需要把不同的论文的结果分为两大类，一个是得奖论文，另一个是未得奖论文。为简化问题的复杂度，我们从得奖论文入手，分别找到这三个指标的评价标准：
序号
阅卷号
评委
打分
标准分
1
A1
评委A04
35
46.25937
2
A2
评委A11
53
55.66406
3
A3
评委A06
46
60.54732
……
……
……
……
……
353
A9020
评委A03
62
61.27679
354
A9021
评委A12
28
46.8965
355
A9022
评委A11
30
36.32556
2015年北美数学建模赛(MCM)A题二等奖论文honorable mention
36837
Problem Chosen
A
F4 ________________
2015
Mathematical Contest in Modeling (MCM/ICM) Summary Sheet
Summary
Ebola viral disease(EVD) has become a problem threatening not only western Africa, but the world. The world medical association has announced their new medication. This paper aims at tackling the following problems: Describing and predicting the spread of EVD based on current statistics; determing the quantity of medicine needed; deciding the speed of manufacturing the vaccine or drug under the principle of meeting demands and lowering costs; locating the delivery center and establish an efficient delivery system. When analyzing demand and supply, an additional factor, inventory level is taken into account. First an improved SIR epidemic model is built. The population of epidemic area is divided into 5 parts instead of 3, to be more comprehensive. By solving a set of differential equations and computing several parameters, we obtained the fitting function of cumulative cases of EVD. Compared with current statistics, the imitative effect is satisfying. Second, by predicting through the fitting function obtained from Model one, we get the approximate demand curve of medicine. Considering efficiency and inventory costs, an approximate speed function of manufacturing is obtained. In the updated model, the proper inventory level is discussed based on EOQ model of short-supply not allowed and time-needed supplying. Third, a three-level delivery system is built based on Model two where supply is guaranteed to be sufficient. Centroid method and analytic hierarchy process (AHP) are combined to select optimal location of distribution center, and the severeness of the epidemic in different places, the distances and transportation costs are considered. In addition, an emergency dispatch scheme is built to response to sudden outbreak. By randomly simulation, we test the sensitivity of Model three, and conclude that it is steady and effective.Team Nhomakorabea#36837
2015数学建模A题
嫦娥三号软着陆轨道设计与控制策略摘要在整个“嫦娥三号”软着陆过程中发动机的燃耗问题是整个着陆过程的关键问题之一，其利用率直接影响到整个着陆过程的成果与否，本文主要利用数学建模的方法对整个软着陆过程进行分析，使得整个软着陆过程发动机能耗最优。
针对问题一，首先需建立一个三维立体坐标系，根据牛顿第二定律，结合科氏定律整理得到嫦娥三号在月固定坐标系中的运动方程，再以卫星运行轨道切面为基面建立二维平面坐标系，将嫦娥三号软着陆问题简化为平面几何问题，求解出主减速阶段嫦娥三号水平位移的距离。
通过坐标变换求得位置。
最后根据天体运动规律得到近日点与远日点速度分别为s6226.1。
km.1、skm7006针对问题二，通过寻找一个制导律u,来调整推力的大小和方向,使嫦娥三号在月面实现燃耗最优着陆轨道，应用极大值原理设计这个最优制导律。
在障碍规避过程中，将动力学模型进行进一步简化，忽略了月球的自转角速度等相关因素。
再利用双线性插值的方法求取规则的采样点处的高程值，这样有利于方便的建立障碍检测算法并对着陆区表面的障碍进行提取，最后利用基于平面拟合的障碍检测算法取得着陆区域内某局部区域内的地形平面，我们将利用这个地表平面来对障碍物进行识别，达到安全着陆的目的。
针对问题三，影响制导精度的误差源主要有偏离标准飞行轨迹的初始条件误差和导航与控制传感器误差。
初始条件误差由主制动段以前的任务决定，传感器误差则由导航系统和传感器本身决定，通过建立误差模型，可以很好地对初始状态偏差、传感器测量偏差等不同因素造成的误差进行分析。
关键词：月球着陆轨道能耗最优打靶法最优制导律控制策略一问题重述嫦娥三号于2013年12月2日1时30分成功发射，12月6日抵达月球轨道。
嫦娥三号在着陆准备轨道上的运行质量为2.4t，其安装在下部的主减速发动机能够产生1500N到7500N的可调节推力，其比冲（即单位质量的推进剂产生的推力）为2940m/s，可以满足调整速度的控制要求。
2015数学建模获奖论文A题
③6 月 22 日—12 月 22 日，在太阳直射点向南移动过程中，北回归线及其 以北各地的正午太阳高度逐渐减小，那么其日影逐渐增长；
④12 月 22 日，太阳直射南回归线，北回归线及其以北各地的正午太阳高度 达到全年最小，其日影也达到全年最长。
一年中，各地的日影长度会随季节变化而变化，这种变化主要体现在正午的 日影长短上。它与当地的正午太阳高度有直接关系：正午太阳高度越大，日影越 短；正午太阳高度越小，日影越长。例如：
①12 月 22 日—6 月 22 日，在太阳直射点向北移动过程中，北回归线及其以 北各地的正午太阳高度逐渐增大，那么其日影逐渐缩短；
图 4 天安门广场 15 年 10 月 22 日影子长度随时间(9 点到 15 点)变化图
在该问题中，影子长度的变化曲线根据计算出是一个关于真太阳时 12 点对 称的二次函数拟合曲线，所以我们利用题中所给的时间数据运用 MATLAB（附 录二）求解该附件的拟合曲线的表达式为
l(t) = 0.3179 t2 - 7.7982t + 51.4250
对于地球上的某个地点，太阳高度角是指太阳光的入射方向和地平面之间的 夹角，专业上讲太阳高度角是指某地太阳光线与通过该地与地心相连的地表切线 的夹角。太阳高度角简称高度角。当太阳高度角为 90°时，此时太阳辐射强度 最大；当太阳斜射地面时，太阳辐射强度就小。
图 1 太阳高度角示意图
太阳方位角即太阳所在的方位，指太阳光线在地平面上的投影与当地经线的 夹角，可近似地看作是竖立在地面上的直线在阳光下的阴影与正南方的夹角。方 位角以目标物正北方向为零，顺时针方向逐渐变大，其取值范围是 0—360°。 因此太阳方位角一般是以目标物的北方向为起始方向，以太阳光的入射方向 为 终止方向，按顺时针方向所测量的角度。
2014-2015年度美国”数学大联盟杯赛“(中国赛区)初赛-(十、十一、十二年级).doc
2014-2015年度美国”数学大联盟杯赛“（中国赛区）初赛（十、十一、十二年级）一、选择题（每小题10分，答对加10分，答错不扣分，共100分，请将正确答案A 、B 、C 或者D 写在每题后面的圆括号内。
）正确答案填写示例如下：=-⨯⨯20522 ？ （A ）A)5 B)15 C)25 D)301. Meg loves her megaphone! The large circular end has a circumference that is the reciprocal of its diameter. What is the area of the circle? ( )A)π14 B) π12 C) 14 D) 122. How many solutions does the equation x x +=233 have? ( )A)0 B)1 C)2 D)43. If y x =-1, which of the following is always true for any value of x ? ( )A) ()()x y -=-2211B) ()()x x y y -=-222211 C) ()()x x y y --=-222211 D) ()()()()x x y y -+=-+22221111 4. Lee the crow ate a grams of feed that was 1% seed, b grams of feed that was 2% seed, and c grams of feed that was 3% seed. If combined, all the feed he ate was 1.5% seed. What is a in terms of b and c ?( )A)b c +3B)b c +3 C)b c +23 D)b c +32 5. If <x 0 and <.x 2001, then x -1 must be ( )A)less than -10B)between-0.1 and 0 C)between 0and 0.1 D) greater than 106. At 9:00 A.M., the ratio of red to black cars in a parking lot was 1 to 5. An hour later the number of red cars had increased by 2, the number of black cars had decreased by 5, and the ratio of red to black cars was 1 to 4. How many black cars were in the lot at 10:00 A.M.? ( )A)13 B)15 C)60 D)657. If x ≠1and x ≠-1, then ()()()x x x x x --++-32241111=( ) A)x -21 B) x +21 C) x -241 D) x -341 8. The Camps are driving at a constant rate. At noon they had driven 300 km.At 3:30 P.M. they had driven 50% further than they had driven by 1:30 P.M.What is their constant rate in km/hr? ( )A)150 B)120 C)100 D)909. The letters in DIGITS can be arranged in how many orders without adjacent I ’s? ( )A)240 B)355 C)600 D)71510. Al, Bea, and Cal each paint at constant rates, and together they are painting a house. Al and Bea togethercould do the job in 12 hours; Al and Cal could to it in 15, and Bea and Cal could do it in 20. How many hours will it take all three working together to paint the house?( )A)8.5 B)9 C)10 D)10.5二、填空题（每小题10分，答对加10分，答错不扣分，共200分）11. What is the sum of the degree-measures of the angles at the outer points ,,,A B C D and E of a five-pointed star, as shown? Answer: . 12. What is the ordered pair of positive integers (,k b ), with the least value of k , which satisfiesk b ⋅⋅=34234?Answer: .13. A face-down stack of 8 playing cards consisted of 4 Aces (A ’s) and 4 Kings (K ’s).After I revealed and then removed the top card, I moved the new top card to thebottom of the stack without revealing the card. I repeated this procedure until thestack without revealing the card. I repeated this procedure until the stack was leftwith only 1 card, which I then revealed. The cards revealed were AKAKAKAK ,in that order. If my original stack of 8 cards had simply been revealed one card at atime, from top to bottom (without ever moving cards to the bottom of the stack),in what order would they have been revealed?Answer: .14. For what value of a is one root of ()x a x a -+++=222120 twice the other root?Answer: .15. Each time I withdrew $32 from my magical bank account, the account ’sremaining balance doubled. No other account activity was permitted. My fifth$32 withdrawal caused my account ’s balance to become $0. With how manydollars did I open that account?Answer: .16. In how many ways can I select six of the first 20 positive integers, disregarding the order in which these sixintegers are selected, so that no two of the selected integers are consecutive integers?Answer: .17. If, for all real ,()()xx f x f x =-21, what is the numerical value of f (3)?Answer: .18. How many pairs of positive integers (without regard to order) have a least common multiple of 540?Answer: .19. If the square of the smaller of consecutive positive integers is x , what is the square of the larger of thesetwo integers, in terms of x ?Answer: .20. A pair of salt and pepper shakers comes in two types: identical and fraternal.Identical pairs are always the same color. Fraternal pairs are the same colorhalf the time. The probability that a pair of shakers is fraternal is p andthat a pair is identical is .q p =-1 If a pair of shakers is of the same color, AE DCBword 格式-可编辑-感谢下载支持 determine, in terms of the variable q alone, the probability that the pair is identical. Answer: .21. As shown, one angle of a triangle is divided into four smaller congruentangles. If the lengths of the sides of this triangle are 84, 98, and 112, as shown,how long is the segment marked x ?Answer: .22. How long is the longer diagonal of a rhombus whose perimeter is 60, if threeof its vertices lie on a circle whose diameter is 25, as shown?Answer: .23. The 14 cabins of the Titanic Mail Boat are numbered consecutively from1 through 14, as are the 14 room keys. In how many different ways canthe 14 room keys be placed in the 14 rooms, 1 per room, so that, for everyroom, the sum of that room ’s number and the number of the key placed inthat room is a multiple of 3?Answer: .24. For some constant b , if the minimum value of ()x x b f x x x b -+=++2222is 12, what is the maximum value of ()f x ? Answer: .25. If the lengths of two sides of a triangle are 60cos A and 25sin A , what is the greatest possible integer-length of the third side?Answer: .26. {}n a is a geometric sequence in which each term is a positive number. If a a =5627, what is the value oflog log log ?a a a +++3132310Answer: . 27. What is the greatest possible value of ()=sin cos ?f x x x ++3412Answer: .28. Let C be a cube. Triangle T is formed by connecting the midpoints of three edges of cube C . What is the greatest possible measure of an angle of triangle T ?Answer: .29. Let a and b be two real numbers. ()sin f x a x b x =++34 and (lg log )f =3105. What is the value of (lg lg )f 3?Answer: .30. Mike likes to gamble. He always bets all his chips whenever the number of chips he has is <=5. He always bets n （10-）chips whenever the number of chips he has is greater than 5 and less than 10. He continues betting until either he has no chips or he has more than 9 chips. For every round, if he bets n chips. The probability that he wins or loses in each round is 50%. If Mike begins with 4 chips, what is the probability that he loses all his chips?Answer: .1129884xword格式-可编辑-感谢下载支持。
2015 AMC10A美国数学竞赛试题
What is the value ofProblem2A box contains a collection of triangular and square tiles.There are tiles in the box, containing edges total.How many square tiles are there in the box?Problem3Ann made a3-step staircase using18toothpicks.How many toothpicks does she need to add to complete a5-step staircase?Problem4Pablo,Sofia,and Mia got some candy eggs at a party.Pablo had three times as many eggs as Sofia,and Sofia had twice as many eggs as Mia.Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs.What fraction of his eggs should Pablo give to Sofia?Problem5Mr.Patrick teaches math to students.He was grading tests and found that when hegraded everyone's test except Payton's,the average grade for the class was.After he graded Payton's test,the test average became.What was Payton's score on thetest?The sum of two positive numbers is times their difference.What is the ratio of thelarger number to the smaller number?Problem7How many terms are there in the arithmetic sequence,,,...,,?Problem8Two years ago Pete was three times as old as his cousin Claire.Two years before that, Pete was four times as old as Claire.In how many years will the ratio of their ages be :?Problem9Two right circular cylinders have the same volume.The radius of the second cylinderis more than the radius of the first.What is the relationship between the heights of the two cylinders?Problem10How many rearrangements of are there in which no two adjacent letters are alsoadjacent letters in the alphabet?For example,no such rearrangements could include either or.The ratio of the length to the width of a rectangle is:.If the rectangle hasdiagonal of length,then the area may be expressed as for some constant.What is?Problem12Points and are distinct points on the graph of.What is?Problem13Claudia has12coins,each of which is a5-cent coin or a10-cent coin.There are exactly17different values that can be obtained as combinations of one or more of her coins.How many10-cent coins does Claudia have?Problem14Problem15Consider the set of all fractions where and are relatively prime positive integers. How many of these fractions have the property that if both numerator anddenominator are increased by,the value of the fraction is increased by?Problem16If,and,what is the value of?Problem17A line that passes through the origin intersects both the line and the line.The three lines create an equilateral triangle.What is the perimeter of the triangle?Problem18Hexadecimal(base-16)numbers are written using numeric digits through as well as the letters through to represent through.Among the firstpositive integers,there are whose hexadecimal representation contains onlynumeric digits.What is the sum of the digits of?Problem19The isosceles right triangle has right angle at and area.The raystrisecting intersect at and.What is the area of?Problem20A rectangle has area and perimeter,where and are positive integers.Which of the following numbers cannot equal?Problem21Tetrahedron has,,,,,and.What is the volume of the tetrahedron?Problem22Eight people are sitting around a circular table,each holding a fair coin.All eight people flip their coins and those who flip heads stand while those who flip tails remain seated.What is the probability that no two adjacent people will stand?Problem23The zeros of the function are integers.What is the sum of the possible values of?Problem24For some positive integers,there is a quadrilateral with positive integerside lengths,perimeter,right angles at and,,and.Howmany different values of are possible?Problem25Let be a square of side length.Two points are chosen independently at random onthe sides of.The probability that the straight-line distance between the points is atleast is,where,,and are positive integers with.Whatis?。