2015年数模美赛ABCD题目
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。
美国大学生数学建模竞赛赛题翻译
2015年美国大学生数学建模竞赛赛题翻译2015年美国大学生数学竞赛正在进行，比赛时间为北京时间：20１5年2月６日(星期五)上午9点—２月10日上午9点.竞赛以三人(本科生）为一组，在四天时间内,就指定的问题，完成该实际问题的数学建模的全过程,并就问题的重述、简化和假设及其合理性的论述、数学模型的建立和求解(及软件)、检验和改进、模型的优缺点及其可能的应用范围的自我评述等内容写出论文。
2０15 ＭＣM/ICM Ｐｒｏblems总计4题，参赛者可从MＣM Pｒoｂlｅm A, MＣM Problem B，ICM Pｒoblem C oｒICM Ｐｒｏbｌem D等四道赛题中自由选择。
201５Contest ProｂｌemsMCM ＰROBLEMSPROBLEM A: Erａdiｃating EbｏlaThe wｏrｌｄmedical assoｃiatiｏn has ａnnounced that ｔheｉｒneｗmｅdiｃatioｎcouｌd stop Ｅbola anｄcｕｒｅｐａtｉents ｗhose dｉsease ｉs not aｄｖanced. Ｂuild a realistｉc, sensｉblｅ, ａnｄusefｕｌmodel thaｔｃｏnsiders not onlｙｔhｅsｐｒead of the dｉsease，ｔｈｅqｕaｎtｉｔy of ｔhｅmedｉcine needed，ｐｏｓsｉble ｆeasible delivｅｒy sysｔemｓ（seｎdiｎg ｔhe meｄiｃine to where iｔis neｅdｅｄ), （gｅｏgrａphiｃal）loｃatioｎs of ｄelｉvery，ｓｐeed of mａｎufacturing of tｈe ｖa ｃcine ｏｒｄruｇ, but also ａｎy oｔheｒcriticａl factors your ｔeam cｏnｓidｅrs ｎecessaｒｙas ｐarｔｏf thｅｍodel to ｏpｔimize thｅerａdicaｔioｎoｆEｂola，oｒａt lｅａｓt ｉts current sｔrain. Iｎadd ｉtion ｔo your ｍodｅling apprｏach fｏr thｅcontest, prepare ａ１—2 page ｎon-teｃｈnical ｌettｅr for ｔhe wｏrld ｍｅｄicaｌａｓsocｉation ｔｏuse ｉｎtheir announｃｅmｅｎt．中文翻译：问题一：根除埃博拉病毒世界医学协会已经宣布他们的新药物能阻止埃博拉病毒并且可以治愈一些处于非晚期疾病患者。
2015年MCM美赛题目及翻译
PROBLEM A: Eradicating（根除）EbolaThe world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced（晚期的）. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible （可行的）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（压力）. 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.PROBLEM B: Searching for a lost planeRecall the lost Malaysian flight MH370. Build a generic（一般的）mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to（恐怕） have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed （坠落的） plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.。
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。
●以下所有时间都是美国东部时间EST（北京时间比美国东部时间早13个小时）●递交参赛论文后，意味参赛者同意以下条款：⏹论文提交后，出版权归COMAP, Inc所有；⏹COMAP可以使用，编辑，引用和出版论文，用于宣传或任何其他目的，包括在线展示，出版电子版，在UMAP杂志刊登或其他方式，并且没有任何形式的补偿；⏹COMAP可以在没有进一步的通知，许可，或补偿的情形下，使用这次比赛相关材料，团队成员、指导老师的名字，以及和他们的背景资料。
●递交参赛论文后，意味参赛者作出以下承诺：⏹论文中出现的所有的图像，数据，照片，图表，图画，如果未注明，都是由参赛者创建；如果引用其它资源，都在参考文献中列出，并在引用的具体位置标注来源。
⏹不论是直接，还是转述方式的文字引用，都在参考文献中列出，并在引用的具体位置标注来源；直接的文字引用使用引号标注。
比赛之前注册报名1.报名截至时间：2015年2月5日下午2：00 EST。
截止日期后，注册系统将自动关闭，不再接受任何新的注册，没有例外。
2.每支参赛队伍都必须有一位来自参赛机构（institute）的教师担任导师（faculty advisor），不允许学生担任导师。
由指导老师负责为其指导队伍注册报名，每位指导老师可注册的队伍数目没有限制。
2015全国大学生数学建模竞赛A题解析
V
是' 无变位时的显示储油量。
i
以下为附加内容
不需要的朋友下载后 可以编辑删除，谢谢
让更多的农民成为新型职业农民 中央农业广播电视学校 刘天金
2013˙05˙07 陕西
农业部部长韩长赋： 这是一项基础性工程、创新性工作，
要大抓特抓、坚持不懈。
——让更多的农民成为新型职业农民（目标） ——生产更多更好更安全的农产品供给社会（方向）
由于本问较复杂，需要分情况建立模型，可以先考 虑只发生纵向变位的情况。
三、解题思路（续）
球冠Ⅰ的体积表达式为：
其中
三、解题思路（续）
球冠III的体积表达式为：
其中
三、解题思路（续）
圆柱体II的体积表达式为：
其中
三、解题思路（续）
在不考虑罐体横向变位的情况下（即 ） ，0 储油罐 的体积与辅助变量 的H 关1 系表达式为：
2r,
r(1cos)h纵2r
由于罐体只产生纵向变位时油位高度 与h 纵储油量 V (, h纵) 的对应关系已得到，再根据上面推导出的 h 与纵 同 时发生纵向和横向变位时油位高h，就可以求出一般情 况下，即罐体同时产生纵向和横向变位的油位高h与储
油量V之间的关系模型 VF(。,,h)
三、解题思路（续）
二、问题分析（续）
（3）对于（2）得到的实验罐在纵向倾斜变位情形 下油位高度与储油量的模型，将变位参数 4.1 代入 计算，得出修正后的油位高度间隔为1cm的罐容表标定 值。并与原标定值比较，分析罐体变位的影响。
第二部分：根据实际检测数据，识别实际储油罐罐 体是如何变位的，估计出变位参数，给出实际罐罐容表 的修正标定方法和结果。并分析检验模型的正确性和方 法的可靠性。
2015年全国大学生数学建模竞赛A题
太阳影子定位技术问题的数学模型摘要本文涉及的是太阳影子定位技术问题。
在已知视频中物体的太阳影子变化的情况下，要确定视频的拍摄地点和拍摄日期。
首先，分析了文中四个问题的关系，发现前三个问题的已知条件逐步减少，问题难度依次递进。
第四问则给出一个实际问题，该问题需要转化成数学模型利用前三问的方法求解；随后，建立了L-G模型、MinZ-模型等，并应用非线性最小二乘法、遗传算法等算法对模型求解。
得到基于模型的合理结果。
最后，将第四问的实际问题转化数学模型并求解，进而解决问题。
对于问题一，要解决的问题是杆长与影子长度的关系，根据天文、几何知识，我们建立了模型来刻画问题给出的参数之间联系，如赤纬角模型、时角模型、太阳高度角模型、影子长度模型（L-G模型）等；分析了各参数对影子长度的影响；最后运用MATLAB绘制出具体给定参数下的3米高直杆的影子变化曲线；从曲线可以看出在9:00到15:00这段时间里，影子长度先变短后变长，最短为3.627米，最长为7.182米。
问题二提供了一个关于时间、影子坐标的附件1，杆长未知，为了确定直杆所处的地点，本问建立了MinZ-模型，首先将经度、纬度、杆长离散化，搜索出大概的可行解，然后运用非线性最小二乘算法，选取matlab中的lsqcurvefit命令，以可行解为初值，再运用非线性最小二乘算法，选取MATLAB中的lsqcurvefit命令，在控制残差在10−8之内范围的情况下得到了三个可能地点皆在海南省昌江县内，最小误差的地点为海南省江黎族自治县，北纬19.3025°，东经108.6988°，此时对应直杆高度为2.0219m。
同时，将结果代入问题一的模型进行检验，验证了模型的稳定性和算法的合理性。
问题三沿用问题一的模型和问题二的算法，由于一个已知量变成一个变量，根据算法特点，在增加一个变量的情况下，算法搜索影长差时只需要增加一重循环。
关于附件2数据，残差最小对应的位置为北纬39.8926°，东经79.7438°，具体地点在新疆维吾尔自治区喀什地区巴楚县。
2015年美赛数学建模题目
2015 Contest ProblemsMCM PROBLEMSPROBLEM 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.PROBLEM B: Searching for a lost planeRecall the lost Malaysian flight MH370. Build a generic mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.ICM PROBLEMSPROBLEM C: Managing Human Capital in OrganizationsClick the title below to download a PDF of the 2015 ICM Problem C.Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.Managing Human Capital in OrganizationsPROBLEM D: Is it sustainable?Click the title below to download a PDF of the 2015 ICM Problem D.Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.Is it sustainable?。
美国数学大联盟杯赛五年级试卷
2015-2016年度美国“数学大联盟杯赛”(中国赛区)初赛(五年级)(初赛时间：2015年11月14日，考试时间90分钟，总分200分)学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论， 我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。
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1. A 6 by 6 square has the same area as a 4 by ? rectangle.A) 3 B) 6 C) 8 D) 9 2. Every prime has exactly ? positive divisors.A) 1B) 2C) 3D) 4 or more3. If I answered 34 out of 40 questions on my math test correctly, I answered ? % of the questions correctly.A) 75B) 80 C) 85 D) 904. 120 ÷ 3 ÷ 4 × 12 =A) 1 B) 10 C) 12 D) 120 5. 10 × 20 × 30 × 40 = 24 × ?A) 1000B) 10 000C) 100 000D) 1000 0006. One of my boxes contains 1 pencil and the others each contain 5 pencils. If there are 101 pencils in my boxes, how many boxes do I have?A) 19B) 20C) 21D) 227. An electrical company imports 2016 light bulbs. Unfortunately, 25% of those are damaged. How many light bulbs are not damaged?A) 25 B) 504 C) 1512 D) 2016 8. 50 × (16 + 24) is the square ofA) -40 B) -4 C) 4 D) 80 9. Which of the following numbers has exactly 3 positive divisors?A) 49B) 56C) 69D) 10010. Ten people stand in a line. Counting from the left, Jerry stands at the 5th position. Counting from the right, which position is he at?A) 4B) 5C) 6D) 711. On a teamwork project, Jack contributed 2/7 of the total amount of work, Jill contributed 1/4 of the work, Pat contributed 1/5 of the work, and Matt contributed the rest. Who contributed the most toward this project?A) Jack B) Jill C) Pat D) Matt 12. Which of the following numbers is a factor of 2016? A) 5 B) 11 C) 48 D) 99 13. 2 × 4 × 8 × 16 × 32 × 64 =A) 210B) 215C) 221D) 212014. On a game show, Al won four times as much as Bob, and Bob won four times as much as Cy. If Al won $1536, how much did Al, Bob, and Cy win together?A) $96 B) $384 C) $1920 D) $2016 15. The sum of two composites cannot beA) odd B) even C) 11 D) 1716. If a and b are positive integers such that a /b = 5/7, then a + b isA) 12 B) 24 C) 36 D) not able to be determined 17. What is the greatest odd factor of the number of hours in all the days of the year 2015? A) 3B) 365 C) 1095 D) 3285 18. If the current month is February, what month will it be 1 199 999 months from now?A) JanuaryB) FebruaryC) MarchD) April19. Two angles are complementary. One of these angles is 36° less than the other. What is the measure of the larger angle?A) 36° B) 54° C) 63° D) 72° 20. (The square root of 16) + (the cube root of 64) + (the 4th root of 256) = A) 12 B) 24 C) 32 D) 64 21. In ∆ABC , m ∠A – m ∠B = m ∠B – m ∠C . What is the degree measure of ∠B ?A) 30B) 60C) 90D) 12022. For every 3 math books I bought, I bought 2 biology books. I bought 55 books in all. How many of those are math books?A) 11B) 22C) 33D) 4423. John wrote a number whose digits consists entirely of 1s. This number was a composite number. His number could contain exactly ? 1s.A) 17B) 19C) 29D) 3224. Weird Town uses three types of currencies: Cons, Flegs, and Sels. If 3 Sels = 9 Cons and 2 Cons = 4 Flegs, then 5 Sels = ? Flegs.A) 12 B) 24 C) 30 D) 3625. If the length of a rectangular prism with volume V is doubled while the width and the height are halved, the volume of the new prism will be第1页，共4页A) 4V B) V/2 C) V D) 2V26.Rick and Roy each stands at different ends of a straight road that is 64 m long. They runtoward each other. Rick’s speed is 3 m/s and Roy’s speed is 5 m/s. They will meet in? seconds.A) 1 B) 2 C) 4 D) 827.If the area of a certain circle is 2016, its radius isA) sqrt(2016/π) B) sqrt(4032/π)C) 2016/πD) 1008/π28.In a toy shop, the cost of a Teddy Bear is 200% as much as that of a toy train. The cost ofa toy train is 6/5 the cost of a pack of the wooden blocks. The cost of a pack of woodenblocks is $50. What is the cost, in dollars, of the Teddy Bear?A) 60 B) 100 C) 120 D) 20029.In the sequence 2016, 225, 141, 66, 432, 99, 1458 …, each term after the first term is thesum of the cubes of the digits of the previous term. What is the 100th term of thissequence?A) 153 B) 351 C) 370 D) 37130.What is the sum of all the positive divisors of 210?A) 210 – 1 B) 211 – 1 C) 212 – 1 D) 213 – 131.It takes 4 hours for Mike and Lucy to finish a task. It takes Lucy and Jerry 5 hours tofinish the same task. And it takes 6 hours for Mike and Jerry to finish the same task. Lucy and Jerry first work on the task for 1 hour and 45 minutes. Then Mike takes over the task on his own. How many more hours does it take for Mike to finish the task?A) 3 B) 4 C) 5 D) 632.If you sell a cloth at its current price, you get $40 profit. The total profit you get selling 10clothes at 70% of its current price is equal to the total profit you get selling 20 clothes at $82 per cloth. What is the current price of a cloth?A) 80 B) 100 C) 120 D) 12533.There are 6 identical squares in the figure on the right. The side length of eachsquare is 1. Of all the triangles constructed by connecting three of the 18vertices in the figure, how many of them are triangles whose area is 2 andwhich has at least one vertical or horizontal side?A) 12 B) 16 C) 24 D) 2834.Pick up N numbers from 1 to 2015 inclusively, such that the sum of any three of the Nnumbers is divisible by 24. What is the maximum value of N?A) 83 B) 84 C) 168 D) 25235.汤姆有一件花了64美金买来的衬衫，他打算以比原价高出25%的价格出售，他会卖出多少钱？A) $16 B) $32 C) $48 D) $8036.满足以下条件的最小整数是多少：“除以3余2，除以5余4，除以7余6。
2015IMC国际数学竞赛初二组决赛详解(独家发布)
初二年级初赛试题姓名_____________ 学校_____________ 得分____________ 一、填空题Ⅰ（每小题6分，共60分）1. 三角形的两条中线长分别为6和9，如果第三边长为整数，那么其最大值为答案：9 解答：如图，根据重心定理得到OB =6，OC =4，BC <4+6=10，故第三边长最大值为2. 如图，小正方形的面积为2，弓形过A 、B 、C 三个格点，那么这个弓形的面积为___________；答案：5.7解答：如图，圆心在O 处，OC =∠AOC =90°,2211=510 5.742S ππ-=-=阴.3. 在梯形ABCD 中，AB //CD ，∠A =90°，AB =2，BC =3，E 是AD 的中点，BE 平分∠ABC ，则①CD =1；②CE ⊥BE ；③CE 平分∠BCD ；④12BCE S S ∆=梯形；⑤BE ．成立的结论共有___________个；答案：5解答：5个结论都对．4. 分解因式：22(1)(2)12x x x x ++++-=___________；答案：2(1)(2)(5)x x x x -+++解答：原式=222(1)(1)12x x x x +++++- =22(14)(13)x x x x +++++- =2(1)(2)(5)x x x x -+++5. 一个凸多边形的内角均不相等，按从小到大排列后，最小的内角为120°，每一个都比前一个大5°，则这个多边形的对角线为___________条； 答案：27解答：设这个多边形为凸n 边形，(1)1205(2)1802120(1)5180n n n n n -⎧+⨯=-⨯⎪⎨⎪+-⨯<⎩，解得n =9，对角线有9⨯6÷2=27条．6. 如图，正方形ABCD 和菱形DBEF ，延长FE 过C 点，则∠EBC =___________度； 答案：15解答：如图，连结AC 交BD 于O ，过E 作EG ⊥BD 于G ，可以得到12GE BE =，所以∠EBD =30°，∠EBC =45°-30°=15°．7. 正整数m 、n满足915m n +-=___________；答案：3解答：2150--=3)0=30+>5=所以，41m n =⎧⎨=⎩原式=22+31+42412⨯⨯⨯-+=3．8. 如图，一牧童在A 处放马，牧童家在B 处，A 、B 到河岸CD 的距离分别为500米和700米，且CD 长为500米，天黑前牧童从A 点将马牵到河边饮水，再赶回家，那么牧童最少要走_________米； 答案：1300解答：如图，作点A 关于河边的对称点E ，连结BE ，过E 作EF ⊥BF 于根据勾股定理得到BE =1300，即牧童最少走1300米．9. 已知2a ≤，3b ≤，6c ≤，且214a b c --=，则201320142015a b c⨯=答案：112-解答：222223614a b c a b c a b c --≤++≤++≤+⨯+=，当且仅当b 、c 同号、a 与它们异号时取等号．1）当a =2、b =-3、c =-6时，原式=1232(3)1(6)12⨯-=--； 2）当a =-2、b =3、c =6时，原式=123(2)31612-⨯=-． 综上所述：原式=112-．10. 一个直角三角形的两条边之差为2，另一边长为10，那么这个三角形的周长为___________；答案：24或60解答：设其中一边为x ，222(2)10x x ++=或22210(2)x x +=+ 解得x =6或x =24，求得周长为24或60．二、填空题Ⅱ（每小题8分，共40分）11. 如图，在Rt △ABC 中，∠ACB =90°,M 、N 分别为AB 的三等分点，且CM=，CN=，那么△ABC 的面积为___________cm 2；答案：解答：如图，分别过M 、N 作BC 的垂线，交BC 于D 、E ，设BE =x ，NE =y ， 利用勾股定理列方程组．2222448427x y x y ⎧+=⎪⎨+=⎪⎩，解得正数解2x y =⎧⎪⎨⎪⎩ABC 的面积为(2⨯3)⨯(32=12.已知2013M ++，48124028=13355720132015N -+-+⨯⨯⨯⨯，那么2(21)2M N +=___________；答案：1008解答：2015M ++ 111111111201611335572013201520152015N ⎛⎫⎛⎫⎛⎫⎛⎫=+-+++-++=+= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭ABC MNAB CMND E原式=20162015201510082⨯=．13. 已知22()()2015c a b b a c +=+=，且b c ≠，则abc =___________；答案：-2015解答：由b c ≠，22()()()()0c a b b a c c b ab ac bc +-+=-++=，得到0ab ac bc ++=，所以2()()2015abc ac bc c c a b =--=-+=-．14. 如图，矩形ABCD 的对角线相交于点O ，AE 平分∠BAD 交BC 于E ，∠CAE =15°，则∠AOE =___________°； 答案：135解答：可证△AOB 为等边三角形，△BOE 为等腰三角形，0006075135AOE ∠=+=．15. 像三棱锥、长方体、五棱台等都是简单的几何体，又叫做多面体，著名的数学家欧拉发现这些多面体的顶点数（V ）、面数（F ）、棱数（E ）之间的规律为V +F -E =2．根据这个规律，若一个多面体恰好由一些正五边形和正六边形构成，则这个多面体是___________面体；答案：32解答：设正五边形有x 个，正六边形有y 个，1156(56)231(56)22V x y x y E x y F x y V F E ⎧==⨯=+⎪⎪⎪=+⎨⎪=+⎪⎪+-=⎩，解得1220x y =⎧⎨=⎩，所以这个多面体共12+20=32个面．。
2015美赛D题H奖论文
For office use onlyT1________________ T2________________ T3________________ T4________________Team Control NumberProblem ChosenDFor office use onlyF1________________F2________________F3________________F4________________2015Mathematical Contest in Modeling(MCM)Summary Sheet(Attach a copy of this page to your solution paper.)Type a summary of your results on this page.Do not includethe name of your school,advisor,or team members on this page.Sustainable development refers to the development that not only meets the needs of the present,but also brings no harm to the ability of future generation in meeting their own needs.How to determine the degree of a country’s sustainability,how to forecast the developing tendency and how to create the most effective sustainable development plan that based on the current situation of a certain country is one of the most far-reaching research issues in the world.This paper discusses the above problems and analyzes deeply to obtain the result with great value.First of all,in order to determine the degree of sustainability of a country,we propose two models to measure the sustainable level.In the first model,we use PCA and AHP to divide sustainability into three levels.On this basis,we introduce the concept of coordination degree to help the analysis of the degree of the coordination among each indicator.In addition,in order to further define the degree of sustainability of a country,we establish coupling model.It introduces the variable of time,making the judgment of a country’s sustainability far more accurate in degree and in time.Then,we choose a LCD country.In order to raise its level of sustainable development, through the establishment of grey model,we form a sustainable development plan for the country which based on the forecast of its development situation in the future20years.After that,we use the first model to evaluate the effect of the20-year sustainability plan.Proceed from the LDC country’s actual conditions,we also consider other factors that may affect the sustainable degree, and accordingly improve the first model.By using the new model,we evaluate the effect of the20-year plan again and find out the increase of the sustainable degree of this country becomes lower, which is in accord with the fact.So it verifies the reasonability of the new model.Finally,in order to achieve our final goal to create a more sustainable world,we find out the most effective program or policy of sustainable development for this LDC country.We solve the problem in two ways.One is to consider the influence of policies on the sustainability measure. Another is taking cost into account.We introduce the concept of the actual benefit,and establish the cost-benefit model.In this model,we calculate each strategy’s ratio of benefit and cost,so as to determine the optimal strategy.Key words:analytic hierarchy process,coupling model,cost-benefit model,sustainability measureMake a Sustainable WorldContent1Introduction (2)2Measure of Sustainability (2)2.1Assumptions (2)2.2Model One (3)2.2.1Introduction (3)2.2.2Nomenclatures (3)2.2.3Pretreatment:The Selection and Classify of Metrics for Assessment (3)2.2.4Model Building and Solving (4)2.2.5Strengths and Weaknesses (6)2.3Model Two:A modified model——Coupling model (7)2.3.1Introduction (7)2.3.2Useful Notation (7)2.3.3Model Building and Solving (7)2.3.4Strength and weakness (11)3Prediction and Plan (11)3.1Model Three:Grey Prediction (11)3.1.1Introduction (11)3.1.2Assumptions (12)3.1.3Model Building and Testing (12)3.1.4Model Analysis (13)3.1.5Strengths and Weaknesses (14)3.2Making Plan (14)3.2.1Program and Policy (14)3.2.2Assistance (15)4Plan Evaluation (16)5Model Four:Improvement Based on Model One (16)6Determine the Most Effective Programs or Policies (17)6.1Ignoring Cost (17)6.1.1Comparing the Difference (17)6.1.2Considering the Weight (17)6.2Model Five:Comparison ofη (18)6.2.1Introduction (18)6.2.2Some notation (18)6.2.3Model Building (18)7References (19)1IntroductionWhat is sustainability?The1987Report of the Brundtland Commission,Our Common Future, defined sustainable development as,“meeting the needs of the present generation without compromising the ability of future generations to meet their own needs.”Although there is several sustainability models such as3-legged stool model,3-overlapping-circles model that might help explain what a sustainable society looks like,these models will not be able to fully show when and how a country is sustainable or unsustainable.To help the International Conglomerate of Money (ICM)make a more sustainable world,we are expected to develop a reasonable,comprehensive and effective technique to provide a measure for distinguishing more sustainable countries and policies from less sustainable ones.2Measure of Sustainability2.1Assumptions●Assume that the world’s climate don’t have dramatic changes●Assume that there aren’t development aids,foreign investment,natural disasters,orgovernment instability.●Assume that there aren’t interactions between metrics.●Assume that the data we searched is reliable.2.2Model One2.2.1IntroductionIn order to evaluate the ability of sustainable development of a country,we define the sustainable development comprehensive index (F)as standard to distinguish the different levels of sustainability between different countries.The index relates to the contributions of the subsystems,so we adopt the analytic hierarchy process to figure out the weight of each subsystem.In addition,in order to fully understand the situation of sustainable development of a country,we introduce the concept of coordination degree [1].The closer are the value of five subsystems,the more coordinate is the development process of the country.2.2.2Nomenclatures Nomenclatures Explanationijy normalized value of the th j index of the th i country ij m original data of the th j index of the th i countryj σstandard deviation of the th j indexj m average value of the th j indexk F evaluation value of sustainability of the th k subsystemF value of sustainable development comprehensive indexn numbers of index in each subsystemk w weight of the th k subsystemi αcoordination degree of the th i countryi M average evaluation value of subsystems of the th i countryi S standard deviation value of subsystems of the th i country..C I The coincident indicatormaxλThe maximum eigenvalue of Ajp weight of the th j index in each subsystem 2.2.3Pretreatment:The Selection and Classify of Metrics for AssessmentThe Selection of Metrics for AssessmentEvaluating the sustainability of a country is a result of a country’s population,population growth rate,territory area,percentage shares in GDP,agricultural labor force,life expectancy at birth,transport and many other factors.To simplify the model,we choose population growth,life expectancy at birth,GDP per unit of energy use,arable land (hectares per person),food production index,improved water source and several other Metrics.The Classify of Metrics for AssessmentThe essence of sustainable development is to realize harmonious development of nature system and social system in a certain time.Its core is to realize sustainable,stable,balanced,orderly development of different elements,like population,resource,economy,environment,etc.In the field of sustainable development,the mutual action and mutual restriction between population,resource,economy,environment and technology formed a dynamic and open complex giant system,which called PREEST system [2].In PREEST system,the target locations of the five subsystems (P,R,E,E,and ST)are different.The population subsystem is the target and goal;the resource subsystem is the basis and guarantee;the economy subsystem is the core and emphases;the environment subsystem is the conditions and constraints and the technology subsystem is the sustention and platform of the harmonious development of the PREEST system [3].Based on the PREEST system model,we divide the above-mentioned indexes into five groups,as it shows in the table below.Tab 1Sustainable development index system Based on PREEST systemPopulation subsystem Population growthLife expectancy at birthResource subsystem Arable landRenewable internal freshwater resources percapitaEconomy subsystem Food production indexLabor force participation rateGDP per capitaEnvironment subsystem GDP per unit of energy useimproved water source2CO emissionsScience &Technology subsystem Scientific and technical journal articles2.2.4Model Building and SolvingCalculation of the comprehensive evaluation value based on AHPStep 1standardized treatment for the original data ：ij ij jjm y m -=Step 2evaluation value of sustainability calculation of single subsystem:Based on the hierarchical analysis,we can figure out j p ,the weight of each index in eachsubsystem.1nk ij j j F y p ==∑Step 3According to domain experts’advice,we get the significance judgment matrix of PREEST system [4].The result of this method is presented in the table below.Tab 2Significance judgment matrix of PREEST systemPopulation subsystem Resource subsystem Economy subsystem Environment subsystem STsubsystemPopulation subsystem 1.0000.8000.7000.5000.600Resource subsystem1.250 1.0000.8750.6250.750Economy subsystem 1.429 1.143 1.0000.7140.857Environment subsystem2.000 1.600 1.400 1.000 1.200ST subsystem 1.667 1.333 1.1670.833 1.000It was clear from table above that the relative importance degree of P,R,E,E,STsubsystems in PREEST system is respectively:0.1361,0.1701,0.1945,0.2723,0.2269,andsatisfying:max ..()/(1)C I n n =--0.0040.1=<That is,the judgment of the relative importance degree of each subsystem in table ise the relative importance degree as the contribution rate k w of sustainabledevelopment of each subsystem.Step 4according to the formula below51100k k k F F w ==⨯∑After substituting the data of several countries of a period of years (2009-2013)[5],we canget the figure below.Figure 1Sustainable Development Ranking of Several CountriesSubstitute the data of 131countries in 2003,then we can get another figure shown in the below.Figure 2Distribution of Countries’SustainabilityWe can see the different level of each country from the table.From the above,we can seethe evaluation value of the sustainable development ability in many countries.Reference to relative researches of sustainable development,and according to textual research on actual situation of countries’sustainable development,we divided sustainable development into three levels by the difference of parameters between the better and the worse in different country.As shown in the table below,the larger the value F,the higher the sustainable development level.Tab 3Sustainable development evaluation standardsGrade Comprehensive evaluation value(F)Sustainability10<F<35Less sustainable235≤F ≤55Medium sustainable355<F<100More sustainableThe calculation of coordination degree The closer are the evaluation value of sustainable development of the five subsystems,the more coordinate is the development process of the country.So the coordination degree of the th i country is defined as:1ii iS M =-2.2.5Strengths and WeaknessesStrengths●A corresponding strength of our model is that it would be relatively easy to distinguish moresustainable countries and policies from less sustainable ones.●The analytic hierarchy process (AHP)has been perfectly used in our models,and the results areconsistent with the reality.Weaknesses●Some special data can’t be found,and it makes that we have to do some proper assumptionbefore the solution of our models.A more abundant data resource can guarantee a better result in our models.●Evaluation contains many factors.We didn’t consider all of the indexes,but just part of them.●We didn’t consider the interaction between causal factors and each subsystem.2.3Model Two:A modified model——Coupling model2.3.1IntroductionIn the above model,we can easily distinguish which countries are stronger in terms of sustainable development,and which countries weaker.In order to make a better assessment of when a country should be considered as sustainable or unsustainable,and its degree of sustainability,we established a coupling model based on entropy method.2.3.2Useful Notation Notation Explanationje Entropy of the th j indicator ijp the th j indicator of the th i sample jg redundancy ij w Weight of the th j indicator2.3.3Model Building and SolvingCoupling analysisA country’s sustainable development roots in the limitation of resources and environment.Its core problem lies in that the social economic development cannot exceed the carrying capacity of resources and environment.So it is very important to realize the coordinated development of the two.Based on a definite relationship between resource environment and economy of a country,we can use the ideas of systematic evolution theory to establish a model of coordinated development evaluation.So we can analyze coupling relationship and dynamic evolution process between the two.Step1Establish general functions between resource environment(R)system and social economy system(S)Both of resource environment and social economic systems are nonlinear systems.According to the first approximate theorem of Lyapunov,we approximate the evolution equation (1)and get approximate linear system equation (2).Based on approximate linear system(近似线性系统),we establish general functions between R and S.r:the element of resource environment systems:the element of social economic systemp and q is the weight of each element.12()(,,...);1,2,...,n dx t f x x x i n dt ==(1)1(),1,2,...,ni i i dx t a x i n dt ===∑(2)11()()n i ii n i iif R p r f S q s ====∑∑1,2,...,i n =(3)Step2Establish the relationship between R and SDue to the interaction,the coupling of resource environment system and social economicsystem,to meet the system,the evolution equation of the composite system can be expressed as:1212()()(),(4)()()(),(5)M N df R dM M M f R M f S V dt dtdf S dN N N f R N f S V dt dt==+===+=M,N respectively represent evolutionary states of resource environment system that under the internal and the external influence,sustainable development subsystem of social economic system.M V ,N V are the evolution rate.The whole system contains only two elements()f R and ()f S .We define that the whole system is coordinated developed when ()f R and ()f S has progressed in coordination.Step3Establish a model of evolution rate:(,)M N V f V V =.By controlling M V and N V ,we analyze thevariation of V to consider a country’s sustainable development.We set M V and N V as variables to plane coordinate system ，the changing trajectory of V is aellipse(the changes of resource environment is slower than economy,with smaller amplitude).Therefore,we determined the evolutionary state of a national system by tan α.tan M NV V α=（6）MV (0,b)NV (-a,0)(a,0)(0,-b)αABWeighted entropy methodStep1Select and clarify the indicatorsWe take two aspects into consideration which are the main indicators,involving the health of human,safety about food,access to clean drinking water and energy,quality of the local environment,means of livelihood,vulnerability of our society,and so on.These indicators can be clarified into two sides as below.Tab 4R&S IndicatorsSort IndicatorResource and environment Arable landCombustible renewables and wasteCO2emissionsEnergy useDepth of the food deficitAlternative and nuclear energyEnergy productionCPIA business regulatory environment ratingImproved water sourceEnergy useCereal yield……Social and economy TradeLife expectancy at birthForeign direct investment,net inflowsLabor force participation rateElectric power consumptionGDP growthHigh-technology exportsMortality ratePopulation growthHealth expenditureGDP per capitaPrevalence of undernourishmentStep2Definition of entropy indicatorsSupposing there are m evaluation objects and n pieces of indicators in the indicator system,which form the original data matrix X=()ij m n x ⨯,after normalization,we can get 'ij x .According to the definition of entropy,entropy of the indicator is determined by:11ln ''1ln mj ij iji ij ij m ij j e k p p x p x k m===-==∑∑Step3Calculation of the indicator’s entropy weightEntropy weight of the th j indicator is determined by11j jjij mji g e g w g ==-=∑Stage divisionThe stage of development of a country can be divided into four stages.Tab 5The relationship of evolution between R and S Stage αRelationship between ()f R and ()f S Relationship betweenM V and NV More sustainable stage(I)0oα=In the period of early social economic development,resource environment is unaffected by economy.Development isunlimited by resource environment,itonly influenced by its own factors.M V =0,N V →plus limit 00032α<<Social economic and resource environment start to influencing each other and achieving common development.0<M N V V <0.618(golden ratio),M V ,N V >0032α=Social economic develops in harmony with resource environment M N V V =0.618,M V ,N V >0003290α<<The pace of economic development is conditioned by the current amount of resources.In order to meet the needs ofsocial economic development,thegrowth of resource environment at afaster rate than economic development.M N V V >0.618,M V ,N V >090oα=Economic growth reached a limit in the influence of resource environment.At the request of the limit value ofeconomic growth,resource growthpresents infinite growth trend.M V →plus limit ，N V =0sustainable stage(II)90180o oα<<Resource environment growth began toslow,the economic growth went intoreverse,and the country is in a processof entropy increase.MV>0,NV<0 180oα=The speed of economic developmentreaches the trough,and the developmentof resource environment also stops.MV=0,NV→minus limitBottom sustainable stage(III)00180212α<<At the same time with resourceenvironment recession,the economicrecessions has eased a bit,but stillcontinue to be in negative growth.0<MNVV<0.618,MV,NV<0 0212α=The negative effect between resourceenvironment and social economy bringsthe biggest side-effect to the nationaldevelopment.MNVV=0.618,MV,NV<0 00212270α<<While the recession of resource andenvironment continues to deepen,economic recession starts to slow down.MNVV>0.618,MV,NV<0 270oα=The economic recession stops,resourceenvironment presents the down trend.MV→minus limit,NV=0Unsustainable stage(IV)270360o oα<<Through the self-organization ofresource environment and society,economy starts to recover,the recessionof resource environment slows down,and the country enters a new evolutioncycle.MV<0,NV>0From the indexαin the corresponding stage in the table above,we can consider a nation’s sustainable development.We can also change the value of some index,observe the changes ofα, to consider the sustainability of the policy.We determine180oα=as critical conditions,the corresponding time t is the basis for judgment of a nation’s sustainable development.2.3.4Strength and weaknessStrength●Our main model's strength is its enormous applicability.It can be applied to most countries.●Our coupling model agrees with reality on different aspects,implying it behaves as we want.●The models used in our paper is promotional,in view of different consideration,Weakness●Weaknesses of the model include assumptions made for simplicity that likely do not hold.●We didn’t consider all of the indexes,but just part of them.3Prediction and Plan3.1Model Three:Grey Prediction3.1.1IntroductionIn order to devise an effective20year sustainable development strategy for our selected LDC country—Nepal,we firstly need to predict the future trend in terms of each subsystem.In view of current situation,we adopt a Grey Forecasting Model to get data with higher reliability,thus successfully making the plans.3.1.2Assumptions●In fact in reality factors affect each other,but in order to simplify the model,we ignore theinteractions between factors.●The influence of some factors such as natural disasters,the world’s climate and governmentinstability can be neglected●Additional assumptions are made to simplify analysis for individual sections.Theseassumptions will be discussed at the appropriate locations.3.1.3Model Building and TestingFirstly,we need to do the necessary inspection with the known data column in order to guarantee the feasibility of modeling method.Suppose the original sequence is(0)(0)(0)(0)((1),(2),...,())x x x x n =Its ratio is(0)(0)(1)(),2,3,...,()x k k k n x k λ-==If 2212()n n e k e λ-++<<is correct for all k,the sequence can be used as the data of GM (1,1)Model.Otherwise,we need to deal with the original sequence to meet the requirements.Building the GM (1,1)Model,we can get the predicted value:(1)(0)(0)(1)(1)(1)(1),1,2,...,1(1)(1)(),1,2,...,1ak b b x k x e k n a a x k x k x k k n -⎛⎫+=-+=- ⎪⎝⎭+=+-=-Suppose residual is(0)(0)(0)()()(),1,2,...,()x k x k k k n x k ε-==According to the data of Nepal [6],the testing result is shown in the table below.Tab 6ResidualPopulation subsystem Resource subsystem Economy subsystem Environment subsystem ST subsystem Wholesystem-0.0001-0.00130.0021-0.00050.00670.0156-0.00130.0019-0.00190.00040.0041-0.10400.00270.0002-0.00250.00060.0117-0.0258-0.0014-0.00080.0023-0.00060.00910.0207We can see in the table that ()k ε<0.1is correct for all data,which meet the generalrequirements.Suppose residual of ratio is10.5()1()10.5a k k a ρλ-⎛⎫=-⎪+⎝⎭The testing result is shown in the table below according the data of Nepal[7].Tab7Residual of ratioPopulation subsystem ResourcesubsystemEconomysubsystemEnvironmentsubsystemSTsubsystemWholesystem-0.0031-0.0007-0.01280.00340.0138-0.0049-0.00610.0032-0.00320.0015-0.0355-0.00660.0051-0.0017-0.00050.0003-0.0249-0.0039-0.0052-0.00090.0039-0.00190.06400.0116 We can see in the table that()k<0.1is correct for all data,which also meet the general requirements.Above all,the prediction is relatively reliable.Therefore,the GM(1,1)Model is efficient and accurate.3.1.4Model AnalysisThe result of prediction is show in the figure below.Fig3Prediction of the futureIt is clear from the tendency chart of the various indicators to measure sustainable development,the sustainable state index of each indicators(population,economy,science and technology)represent an increase,which indicates that the sustainable degree of each aspects in Nepal(population,economy,science and technology)will be gradually increased in the whole international environment in the next20years.Bur we cannot ignore the hidden problems.For example,the sustainable state index of Nepalese population still at a low level even if it is already improves a bit.Through the reference literature,Nepal has a much larger population density than 100people per square kilometer;it is one of the denseness population areas in the world.And it is also entered the aging society,the problem of population sustainable development is very serious.In addition,the sustainable state index of Nepalese resource and environment are showing adownward trend in the next20years,the sustainable development is not optimistic.Through the reference literature,agriculture is the basic industry and strategic industry of the national economy. There is80%of the population occupied with agriculture.Backward methods of agriculture and illogical use of land resources are the main reasons why the land in Nepal is increasingly scarce, sustainable development of land resources has been badly damaged.We can see from the last tendency chart of Nepalese’s overall state of sustainable development,the sustainable development degree will be gradually increased in the next20years,but it will still stay at a low level.Therefore,it is very necessary for us to design a20-year plan of sustainable development for Nepal.And hoping ICM can stress aid at resource and environment to help Nepal to improve its sustainable development degree faster and more efficiently.3.1.5Strengths and Weaknesses●StrengthsThe advantage of using Grey Forecasting Model is that we can get more reliable results with lacking accessible data,which perfectly fitted with our current situation.●WeaknessesThe data we searched from the Internet may be inaccurate.In addition,the precision of the prediction method is not very high.3.2Making Plan3.2.1Program and PolicyAccording to the above analytical results,we put forward a development plan for20years to promote the sustainable development of Nepal.It includes the plan and policy below:Population●Control population growth,hold population growth rate to0.5%,adopt different policies forurban and rural area management(deal with urban mercifully while rural area strictly).●Governments should strengthen the quality and education of their citizens to reach the worldaverage level.●The problem of population aging is already emerged in Nepal.●To strengthen healthy and active aging,governments should make great efforts that rely oncommunity service and family funding,basis on laws and regulations.[8]Resource●Aiming at the problem of sustainable use of land resource,governments should change thetraditional agriculture production way,develop the ecological agriculture,control the farmland-use,enhance arable land conservation,recede furrow to forests and grazing for steep slope lands with slope grade over25degree.●Set a limitation to resource account,such as tree felling and fishing.Set a limitation to thenumber of the enterprise on a certain business to avoid crowdedness.[9]●Focus on strategic resources deposition;reinforce the protective work over air,land,mineralresource and so on.●According to the correlation relationship and degree between enterprise management(orproduct production)and utilization of sustained resources,encourage development andproductions that beneficial to projects of sustainable development by making specific deration policies.Economic●Take reasonable using,protecting and improving the natural resources and ecologicalenvironment as the core,food production as the main,increase food production capacity to solve the problem of food security for all.Based on large agriculture,integrate and coordinate development of forestry,animal husbandry and fishery industry,increase farmers'income, eliminate rural poverty and achieve unity of economic,social and ecological benefits and sustainable development.●Adjust the industrial structure,improve the overall quality of industry,change roughingextensive product development model mainly in resources and raw materials,innovative high-tech industry,and accelerate the transformation of science and technology to the existing productive forces.[10]Environment●In determining the market price,consider the additional costs of environmental protectionexpenditures and use of cleaner production methods,etc.,such as a higher price of organic agricultural produce as0.5-1.5times more than the same ordinary.●Polluters must take measures to reduce the costs of environmental pollution,such as fertilizerand pesticides production and use are to be taxed.●Achieve minimization,recycling and harmless waste,efforts to improve urban sewage andgarbage disposal rate,control urban sewage,air,noise,solid waste pollution,such as$0.1tax for per bag of garbage collection.Science&Technology●Enact fiscal policy to promote SME Technology Innovation and encourage technology transfer.For example,SMEs,due to technological development and purchase of patents,in addition of subsidizing15%of the study investment costs,government should subsidize another30percent of the cost to support its patent purchase.●Introduce advanced technology,absorb it and innovate.Cultivate technological talents andteams,set up a"scholarship program",earmarked to strengthen personnel training.Technological institutions and universities nurture talent together.3.2.2AssistanceFrom the above,we can see that the index of sustainable development state of resource and environment in Nepal showed a decreasing tendency,suggesting that it urgently needs the assistance from ICM in these two aspects.According to Nepal’s special national population,natural environment,economic,social and political conditions,ICM can give assistance as below:Resource●Enhance the technology popularizing,such as renewable energy technologies.●According to its rich hydro energy resources,ICM can offer the technological scheme of thesustainable development of hydro energy to expand the scale of rural electrification.●To counter the problems of low agricultural productivity,ICM can provide modern agriculture。
2015年五一数学建模联赛题目ABC
段之间行驶时间的相关性，并将这种相关性应用到第一问和第二问的最优路径搜索问题中，并设计算法解决考虑相关性的最优路径搜索问题，给出算例验证算法的有效性。
如果可能的话，从理论上分析算法的收敛性、复杂性等性质。
提示：这里的相关性，可以从空间和时间的两个方面考虑。
空间相关性：同一个时间段(例如7:00-8:00之间)，路段a和路段b的相关性。
时间相关性：对于路段a，不同时间段的相关性，例如7:00-8:00和8:00-9:00之间的相关性。
当然，也可以两种相关性同时考虑。
第四问：从不确定性条件下交通网络的实际情况出发，在合理假设下，进一步完善前三问的数学模型和相关算法。
或者，提出一种或多种与前三问不同的最优路径的定义方法，建立相关的数学模型并设计算法，应用数值算例验证算法的有效性。
如果可能的话，从理论上分析算法的收敛性、复杂性等性质。
说明：本题中的所涉及的算例最好能采用真实的交通网络数据，也可以使用自己假设的数据，交通网络的规模越大越好。
B题空气污染问题研究近十年来，我国GDP持续快速增长，但经济增长模式相对传统落后，对生态平衡和自然环境造成一定的破坏，空气污染的弊病日益突出，特别是日益加重的雾霾天气已经干扰到社会的出行秩序和生活质量。
国家能源委员会《新能源产业振兴和发展规划》等“国家新能源发展战略”政策的出台，说明国家已经把能源环境问题上升到国家安全级别，经济发展转型、节能减排、能源利用新途径和发展新能源等方面的问题亟待解决。
一般认为影响空气质量的主要因素有PM2.5、PM10、二氧化氮、二氧化硫、一氧化碳、臭氧、硫化氢、碳氢化合物和烟尘等，以京津冀地区为研究对象解决以下问题：（1）参考现有国标和美标，建立衡量空气质量优劣程度等级的数学模型。
（2）查找数据并列出京津冀地区主要污染源及其污染参数，分析影响空气质量的主要污染源的性质和种类。
（3）建立单污染源空气污染扩散模型，描述其对周围空气污染的动态影响规律。
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。
数学建模竞赛试题 2015
A题飞越北极2000年6月，扬子晚报发布消息：“中美航线下月可飞越北极，北京至底特律可节省4小时”，摘要如下：7月1日起，加拿大和俄罗斯将允许民航班机飞越北极，此改变可大幅度缩短北美与亚洲间的飞行时间，旅客可直接从休斯敦，丹佛及明尼阿波利斯直飞北京等地。
据加拿大空中交通管制局估计，如飞越北极，底特律至北京的飞行时间可节省4个小时。
由于不需中途降落加油，实际节省的时间不止此数。
假设：飞机飞行高度约为10公里，飞行速度约为每小时980公里；从北京至底特律原来的航线飞经以下10处：A1 (北纬31度，东经122度)； A2 (北纬36度，东经140度)；A3 (北纬 53度，西经165度)； A4 (北纬62度，西经150度);A5 (北纬 59度，西经140度)； A6 (北纬 55度，西经135度)；A7 (北纬 50度，西经130度)； A8 (北纬 47度，西经125度)；A8 (北纬 47度，西经122度)； A10 (北纬 42度，西经87度)。
请对“北京至底特律的飞行时间可节省4小时“从数学上作出一个合理的解释，分两种情况讨论：（1）设地球是半径为6371千米的球体；（2）设地球是一旋转椭球体，赤道半径为6378千米，子午线短半轴为6357千米。
B题：DNA限制性图谱的绘制绘制DNA限制性图谱是遗传生物学中的重要问题。
由于DNA分子很长，目前的实验技术无法对其进行直接测量，所以生物学家们需要把DNA分子切开，一段一段的来测量。
在切开的过程中，DNA片段在原先DNA分子上的排列顺序丢失了，如何找回这些片段的排列顺序是一个关键问题。
为了构造一张限制性图谱，生物学家用不同的生化技术获得关于图谱的间接的信息，然后采用组合方法用这些数据重构图谱。
一种方法是用限制性酶来消化DNA分子。
这些酶在限制性位点把DNA链切开，每种酶对应的限制性位点不一样。
对于每一种酶，每个DNA分子可能有多个限制性位点，此时可以按照需要来选择切开某几个位点（不一定连续）。
2015年全国大学生数学建模竞赛A题
太阳影子定位（一）摘要根据影子的形成原理和影子随时间的变化规律，可以建立时间、太阳位置和影子轨迹的数学模型，利用影子轨迹图和时间可以推算出地点等信息，从而进行视频数据分析可以确定视频的拍摄地点。
本文根据此模型求解确定时间地点影子的运动轨迹和对于已知运动求解地点或日期。
直立杆的影子的位置在一天中随太阳的位置不断变化，而其自身的所在的经纬度以及时间都会影响到影子的变化。
但是影子的变化是一个连续的轨迹，可以用一个连续的函数来表达。
我们可以利用这根长直杆顶端的影子的变化轨迹来描述直立杆的影子。
众所周知，地球是围绕太阳进行公转的，但是我们可以利用相对运动的原理，将地球围绕太阳的运动看成是太阳围绕地球转动。
我们在解决问题一的时候，利用题目中所给出的日期、经纬度和时间，来解出太阳高度角ｈ，太阳方位角Α，赤纬角δ，时角Ω，直杆高度Ｈ和影子端点位置（x0，y o），从而建立数学模型。
影子的端点坐标是属于时间的函数，所以可以借助时间写出参数方程来描述影子轨迹的变化。
问题二中给出了日期和随时间影子端点的坐标变化，可以根据坐标变化求出运用软件拟合出曲线找到在正午时纵坐标最小，横坐标最大，影子最短的北京时间，根据时差与经度的关系，求出测量地点的经度。
根据太阳方位角Α，赤纬角δ，时角Ω，可以求出太阳高度角ｈ。
再结合问题一中的表达式，建立方程求解测量地点的纬度Ф。
我们在求解第三问的思路也是沿用之间的模型，但第三问上需要解出日期。
对于问题四的求解，先获取自然图像序列或者视频帧，并对每一帧图像检测出影子的轨迹点；然后确定多个灭点，并拟合出地平线；拟合互相垂直的灭点，计算出仿射纠正和投影纠正矩阵；进而还原出经过度量纠正的世界坐标；在拟合出经过度量纠正世界坐标中的影子点的轨迹，利用前面几问中的关系求出经纬度。
关键字：太阳影子轨迹Matlab曲线拟合（二）问题重述确定视频拍摄地点和拍摄日期是视频数据分析的重要方面，太阳影子定位技术就是通过分析视频中物体的太阳影子变化，确定视频拍摄的地点和日期的一种方法。
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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。
除了为大赛的建模方法，你的队伍还需要准备为世界医学协会发表公告的一份1-2页非技术性的信。
Recall the lost Malaysian flight MH370. Build a generic mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.回想一下失去了马来西亚航班MH370。
建立一个通用的数学模型，可以在规划一个失去了平面有用的搜索辅助“搜索者”恐已坠毁在开阔水域，如大西洋，太平洋，印度洋，南，或北冰洋，而从A点飞行到B 点。
假定没有从被击落的飞机信号。
模型应认识到，有许多不同的机种的量，我们可能会在搜索，而且有许多不同类型的搜索飞机，经常使用不同的电子器件或传感器。
另外，准备一个1-2页的非技术论文，为航空公司在其新闻发布会提出自己未来的搜寻计划。
Managing Human Capital in Organizations管理组织中的人力资本Building an organization filled with good, talented, well-trained people is one of the keys to success. But to do this, an organization needs to do more than recruit and hire the best candidates –they also need to retain good people, keep them properly trained and placed in proper positions, and eventually target new hires to replace those leaving the organization. Individuals play unique roles within their organizations, both formally and informally. Thus, the departure of individuals from an organization leaves important informational and functional components missing that need to be replaced. This is true for sports teams, commercial companies, schools and universities, governments, and almost any formal group or organization of people.建设充满了良好的，有才华的，训练有素的人的组织是成功的关键之一。
但要做到这一点，组织需要比招做多，并聘请最佳人选- 他们还需要保留优秀的人才，让他们适当培训，并放置在适当的位置，并最终瞄准新员工来替换那些离开组织。
个人与组织内发挥独特的作用，无论是正式的和非正式。
因此，个体从一个组织出发离开重要信息和功能组件缺少需要更换。
这是真正的体育团队，商业公司，学校和大学，政府，以及几乎任何正式的团体或组织的人。
Human resource (HR) specialists help senior leadership manage personnel by improving retention and motivation, coordinating training, and building good teams. In particular, leaders seek to create an effective organizational structure, where people are assigned to positions appropriate to their talents and experience, and where efficient communication systems are in place to facilitate development of innovative ideas and quality products (commodities or services). These talent management and team building aspects of HR management are remaking many modern organizations.通过提高保留和激励，协调培训，并建立良好的团队的人力资源（HR）专家帮助高层领导管理人员。
特别是领导寻求建立一个有效的组织结构，那里的人都分配到适合自己的人才和经验职位，并在高效的通信系统到位，以促进创新的理念，优质的产品（商品或服务）的开发。
人力资源管理的这些人才管理和团队建设等方面的改造许多现代组织。
Managing the fluid network of human capital within an organization requires understanding personnel loyalties to the company and to subgroups; building trust in the workplace; and managing the formation, dissolution and retention of formal and informal ties between people. When people leaving for other jobs or retiring are replaced, the resulting turbulence is collectively termed organizational “churn”. Your team has been asked by your HR manager to develop a framework and model for understanding churn within the Information Cooperative Manufacturing (ICM)organization of 370 people. ICM is in a highly competitive market place, leading to challenging issues related to effectively managing its human capital.在一个组织内管理人力资本的流体网络需要了解的人员忠诚于公司，并分组;建立信任在工作场所;和管理的人之间的正式和非正式关系的形成，解散和保留。
当人们前往其他工作或退休所取代，所产生的紊流统称为组织的“流失”。
你的团队已经问过你的人力资源经理制定信息协同制造（ICM）组织的370人之内了解客户流失的框架和模型。