2015美赛C题O奖论文33900

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大学生英语竞赛（NECCS）C类非英语专业决赛真题2015年

⼤学⽣英语竞赛（NECCS）C类⾮英语专业决赛真题2015年⼤学⽣英语竞赛(NECCS)C类⾮英语专业决赛真题2015年Part Ⅰ Listening C o m p r e h e n s i o nSection AD i r ec t i o n s: In this section, you will hear 10 short recordings. At the beginning of each recording, a question will be asked about what was said. Both the question and the recording will be read only once. After e a c h recording, there will be a pause. During the pause, you must read the three choices marked A, B and C, a nd decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the ce n t r e.1.A.Asking the customer's opinion.B.Offering a cheap sample.C.Explaining a price rise.B [听⼒原⽂]You are walking round the market when you hear this woman talking to a customer. What is she doing? —Look, I'll tell you what. You just take a couple home tonight. I'll knock off 50 pence. How's that? And try them, you'll love them. I promise you. And then tomorrow you can come and tell me if I'm not right. What do you say to that then? I cannot say fairer than now, can I?2.A.She didn't know they were wanted.B.It wasn't part of her job to do it.C.Sh e didn't know which notes to send.A [听⼒原⽂]You're in the doctor's waiting room when you overhear the nurse on the phone. Why didn't she send off the notes?—No, I haven't received anything. Well, I do, normally, but even if our receptionist had, she'd have told me straight away. Of course, I'll go and look the notes, though, now, and send them off straight away. Now what was the patient's name again?3.A.A bowl.B.A lamp.C.A vase.C [听⼒原⽂]You're in a gallery when you hear a couple talking. What are they looking at?—It's very lovely, isn't it?—Well, I suppose so, but it's not really practical, is it? I mean it's so tall and thin. You'll be afraid of knocking it over. Or would you actually put flowers in it?—Oh, really. You put it somewhere where the light could shine through. Just look at it. You wouldn't want to use it, not at that price.4.A.Repairing a printer.B.Positioning a personal computer.C.Selecting a CD player.B [听⼒原⽂]You are visiting a large company. And you hear two people talking. What're they discussing?—Look, we can put it here on the table.—Yes, that'll leave the desk clear for papers and things. But will the light be OK? You don't want it reflecting on the screen.—No, that's all right. I can turn it at an angle. Shall I go and get the discs and the things?—No, don't bother. I'll bring them up later.5.A.At a swimming pool.B.In a sports hall.C.On a football field.A [听⼒原⽂]You hear someone introducing a program on the radio. Where is he?—I'm here outside now and there's quite a crowd beginning to build up behind the fence. They're hoping to get in to see what the new changing rooms are like. Supposed to be really luxurious compared to the old ones. And also the new dining area which I understand is overlooked by the café should make that the good place to pass the time while you are getting dry. And now here's the Mayor of Tonton arriving to actually perform the opening ceremony.6.A.Both of them.B.The boy.C.The girl.C [听⼒原⽂]These friends are talking about a film. Who will go to see it?—I really think you ought to give it a chance. You are usually so narrow-minded.—I'm not. But Tom said his dad really enjoyed it. We've got nothing in common as far as I know. So I know what it'll be like.—Well, I think you're silly. You'll be sorry when I tell you how funny it was.7.A.The boss is unfair to him.B.He has been ill.C.He has too much to do.A [听⼒原⽂]—I don't know what Jim's got to grumble about. My work load has doubled in the past year and I still manage. He is not doing anything different from when he arrived, as far as I can see.—Yeah, but he's not as energetic as you are. Well, no one is. But the boss doesn't blame me when I get a bit behind. He is very understanding with me. But with Jim, he goes on and on.—I haven't noticed it. But you're probably right. I wonder why he does it.8.A.Cancel her booking.B.Postpone her flight.C.Change her destination.B [听⼒原⽂]Listen to this woman phoning a travel agent. What does she want to do?—On the 4th of June, yes, Amsterdam, Holland. Now my problem is my brother's there and he was supposed to be fixing accommodation for me. But he has a problem with his work right now. And he asked me to reserve it from here. Yeah, well, what it is, I don't really want to spend my vocation going around the city alone. So I wanted to ask you whether it would cost a lot to alter the flight, say, to later in the summer when maybe he will be freer and we might even get to visit a few more places?9.A.A repair man.B.A friend.C.A retailer.A [听⼒原⽂]Listen to this man telephoning someone about his washing machine. Who is he talking to?—I've been in touch with them already and they said it's not up to them because the guarantee doesn't cover it. So I was wondering whether he might be able to come and have a look. I don't suppose you could give me any idea of what the charge might be.—Yes, I see. The thing is I've got some friends coming around this weekend and...—Oh, that'd be great.10.A.A supermarket.B.A concert hall.C.A racetrack.C [听⼒原⽂]You switch on the radio and hear this report. Where is it coming from?—There's a tremendous crowd here today. Everyone is mailing about looking very excited. There's laughter and music and lots of chatter. I've been talking to some of the people around me and there's no doubt that there's a fair amount of money changing hands as well. And now we'll go over to Arnell Bums who has been watching the runners coming up to the start.Section BD i r ec t i o n s: In this section, you will hear 10 short news items. After each item, there will be a pause. Du r i ng the pause, youcorresponding letter on the Answer Sheet with a single line through the ce n t r e.1. What does this news item mainly talk about?A.Adults' health.B.Young people's health.C.Children's health.C [听⼒原⽂]It's no secret that too many adults around the world are overweight. But when 20 million children under the age of 5 are considered too fat, researchers worry about the risk of chronic illness as these kids grow older. Now research of at least 3600 children in North America shows that poor eating habits and lack of exercise are producing risk factors for heart disease, including high cholesterol and diabetes. To make matters worse, tests on some of these kids indicated narrowing and hardening of the arteries. That is a condition normally associated with adults.2. Which country didn't press Burma to speed up its reforms?A.Vietnam.B.The Philippines.C.Thailand.B [听⼒原⽂]For the Association of Southeast Asian Nations, Burma is an increasingly difficult issue, as international pressure mounts against its government. But Burma's military, in power for over 40 years shows no signs of allowing major political reform. And ASEAN states are divided over Burma, which joined the group in 1997. Malaysia, the Philippines, Indonesia and Thailand have pressed Burma to speed up reforms. Others such as Vietnam and Laos, both one-party states, are more reticent to push for change.3. Which year is expected to be the hottest year on record?A.2006.B.2007.C.2008.B [听⼒原⽂]Stronger typhoons more flooding in low line region's deepening drought or possible if not likely, according to a report from British primatologist. They say 2007 has a 60% probability of being the hottest year on record. Citing high levels of Greenhouse gases in the atmosphere and El Nino. Now operating in the Pacificand expected to last until May. Temperature studies for 2006 are not yet complete but the new study noting that the world's 10 warmest years since 1850 have occurred in the past decade says 2006 is set to be the 6th warmest year globally and 2007 is likely to set a new all-time high.4. Why did the Iraqi government arrest the person?A.He was one of the Saddam's close followers.B.He opposed the current Iraqi government.C.He made a video of Saddam's execution.C [听⼒原⽂]An adviser to Iraqi Prime Minister Nouri al-Maliki said Wednesday that an individual has been detained and is underfilm had poor audio and grainy pictures, but clearly showed the former Iraqi strong man at the gallows and then in some Internet versions, falling through the trap door and hanging to death.5. When did they find that 13 people were dead in the accident?A.On Monday.B.On Friday.C.On Saturday.B [听⼒原⽂]The mayor of Chicafa, Albero Mecombo said Sunday that efforts to recover bodies at an open pit mine on the outskirts of the town will be suspended until Monday. Thirteen bodies were recovered during the initial rescue and recovery operation organized in the hours after the accident early Friday. Local residents worked until night fall, trying to save those buried. 3 people working in the 15 meter deep trench survived. No more survivors or bodies were found in rescue efforts on Saturday. But Mecombo said it is difficult to know how many people were working at the mine at the time of the accident. More victims, she said, might still be buried in the pit.6. Why did Oprah Winfrey open a school for poor gifts in South Africa?A.To provide poor girls with a first-class education.B.To raise revenue for South Africa.C.To please President Nelson Mandela.B [听⼒原⽂]It begins as a promise Oprah Winfrey made to former South African President Nelson Mandela 7 years ago: A pledge to build a school that will give poor girls a first-class education. Many of Hollywood stars were on hand for this week's opening ceremony, including singer Mariah Carey, film maker Spike Lee and singer Tina Turner. But the true stars were the 152 poor girls chosen to be the first class students. Winfrey hopes this school will change the way women are perceived in South Africa and that the young girls educated here will go on to be their countries future leaders.7. How many former American presidents attended Gerald Ford's funeral service?A.5.B.3.C.4.B [听⼒原⽂]After lying in state and Capitol building for the past few days, Gerald Ford's casket was taken by motorcade to the streets of Washington to the National Cathedral for a funeral service attended by about 300,000 mourners. That included President Bush and the three living former U.S. presidents, Jimmy Carter, George H. W. Bush, and Bill Clinton.8. Whose major responsibilities are for Iraqi issues?A.John Negroponte.B.Mike McConnell.C.Donald Rumsfeld.B [听⼒原⽂]The long-anticipated ambassadorial changes complete a new administration policy team that is to implement the Iraq strategyappointment a new director of national intelligence, Mike McConnell, while the incumbent in that post, John Negroponte, was named to be Deputy Secretary of State with major responsibilities for Iraq.9. Which two countries led the boom in 2006?A.China and Japan.B.India and Japan.C.China and IndiaC [听⼒原⽂]2006 was the boom year for Asian nations for the Asian development projecting 7.7% per year growth for the region's developing countries. India and China together account for over 50% of the region's gross domestic product and may lead the boom. China's GDP grew more than 10% in 2006. And India expanded for more than 8%. Japan, the world's second largest economy, also give the region a lift for its last period of recovery since falling into a slump more than a decade ago.10. What did Rice discuss with the Russian leaders?A.Human rights issues.B.North Korean issues.C.American and Russian military issues.B [听⼒原⽂]Condoleezza Rice met behind closed doors with President Vladimir Putin and Russia's Foreign and Defense ministers to discuss North Korea. However, no statements were made during or after the meetings, which come on the last stop of Rice's tour that has included stops in Japan, South Korea, and China. The goal of her trip has mostly focused on ensuring the UN sanctions adopted against North Korea last week will be fully enforced. But confusion remains about whether North Korean leader Kim Jong-ll apologized for the recent nuclear test and promised there would not be another one.Section CD i r ec t i o n s: In this section, you will hear a teacher telling new students about their course. For questions 21—30, listen to what she says and complete the notes. You will need to write a word or a short ph r a s e. Remember to write the answers on the Answer Sheet.Classes in Studio e v e r y a f t e r n oo nR oo m 51 on 1On Fridays can use 2 for private studyExtra c o u r s e s:Monday: 3Tuesday: 4We dn e sd a y: 5F o r m s t o r e g i s t e r fo r e x t r a c o u r s e s f r o m: 6Saturday c o u r s e on computer-aided d e s i g n:Open to 7 students onlyM u s t p r ov i d e ow n 8F o r s h o r t ab s e n ce s, ph o n e 9F o r ab s e n ce s of m o r e t han t wo da ys, w r i t e t o 10Thursday(s)[听⼒原⽂]Well, I'm very glad to welcome you all to the practical model of our design course at the beginning of the New Year. As you've no doubt realized, we have people here from years one to three and we find that as most of the work is in small groups or individually based. This works out pretty well, even though we are a b it shor t of space.Now I'm going to go through some administrative staff and then we'll get on to project planning. So first of all, we are in the studio here every afternoon except one. So we do have a sort of base, which is quite n ice, bu t once a week we have to move out. That's into Room 51 which is on Thursdays. It's a bit of a nuisance because it's not as big as in here. But we'll manage somehow and on Fridays you can use the big space over the back of the hall which is called the gallery for private study if you want to spread out a bit. That's only on Fridays, though, I'm afraid.Now as far as extra courses go, you should have already selected these and the days for them are as follows: Monday is the only day when the dock room is free, so that's photography. Tuesdays John Howard comes in here to take sessions on print technology. And Wednesday I'm here for model making. Now if you haven't selected your options for this term, you need to get a move on. When we finish now, I'll be showing you around the rest of the department and you can get a form from the academic secretary on the way. Oh, you also need to get one if you want to do the full day course which is on Saturdays on computer-aided design, but that only applies to your third year students of course. And do you know where the office is? Now that's nearly all except a reminder to you all that we provide all the equipment you need for practical work, including card and photographic papers. But you must bring your own stationery. You should have proper notebooks and we don't expect to have to find bits of paper for you to make notes on when you forget them.And lastly about absence. If you're not well, if it's just a couple of days, you can phone the administration assistant and ask him to pass the message on to this department. If it's more than a couple of days, you mustsend a written explanation to the department head, otherwise you could be penalized in your course grade for absence without permission. Ok, well, you've been warned. Now, for you new guys, let's go and look around the rest of the place. The rest of you, no doubt, have things to be getting on with.2.the Gallery3.Photography4.Print Technology5.Model-making6.academic secretary7.third-year8.stationery/notebooks9.the administration assistant10.the Department HeadPart ⅡVo c abu l a r y, Grammar andThere are 15 incomplete sentences in this section. For each blank there are four choices marked A, B, C a nd D. Choose the one that best completes the sentence. Then mark the corresponding letter on the Answer Sheet with a single line through the ce n t r e.Section A Vo c abu l a r y and G r a mm a r1. The manager wants to know whether his proposals at the meeting have been agreed .A.withB.onC.toD.aboutC[解析] 本题含义是“经理想知道他的提议是否在会议上被同意”。

2015年美赛O奖论文A题Problem_A_32150

For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
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

2015年美赛C题翻译

6. 你的上司把这种对于人力的管理叫做“团队科学”。她给你提供以下资料作为参考：
E. Salas, N.J. Cooke, and M.A. Rosen. (2008). On Teams, Teamwork, and Team Performance: Discoveries and Developments. Human Factors: The Journal of the Human Factors and Ergonomics Society June 2008 vol. 50 no. 3 540-547.D.
3.人力资源问题就是尽可能地把员工安排到最正确合适的岗位上，利用他所掌握的知识和技能来发挥他的最大优势。目前每个员工都会获得一个基于他们自身表现的年度评估，而这些评估一般是主管决定的。但这些评级目前不适用于人力资源办公室。
4. ICM 集团意识到，中层干部（初级经理、有经验的主管、无经验的主管）经常会感到很少有升职的机会因而觉得职位到了瓶颈，这样如果他们找到了一个相近或更好的工作就很可能会跳槽。这些中层职位往往都有很高的人事变动率（大概是其他职位的两倍），并且随时都需要补充。
5. 招聘高素质的员工是有难度的，而且费时费钱。在任何时候 ICM 集团的 370 个岗位中经常只有 85%是满的，由于管理的延迟、办公室的容量以及内部晋升等种种原因。人力资源部正在积极地招聘总岗位的 8%-10%员工（也就是大概空缺职位的三分之二）。 6. 为了晋升到更高的职位，员工需要先在特定的职位上积累几年的工作经验。这也构成了人力资源部的主要障碍。 7. 员工流失率一直在稳步增长，特别对于中层经理。ICM 集团的人力资源部把这一点视为公司面临的最大挑战。首席执行官（CEO）当听到现在的流失率达到了每年 18%时表示很惊恐。 8. 因为 ICM 集团很担心人手不足，所以一些勉强合格和不合格的员工都被招入进行试用期，以此来降低员工流失率，这样很少有员工被解雇。但这也就导致了一些低水平的员工经常会一直在公司里。员工水平问题（部分员工水平低下）已经引起了管理层的重视，但是现在还没有一个人给出确切的解决方案。 9. 你的机构一直以良好的 CEO-员工工资比引以为傲。（CEO 的工资到是所有员工工资中位数的 10 倍，而其他很多公司这一比率会达到几百倍以上）

2015美赛D题获一等奖论文

Team # 35630
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Contents
I. Introduction....................................................................................................................................3 1.1 Problem Background.............................................................................................................3 II. Symbols, Definitions and Assumptions...................................................................................... 3 2.1 Symbols and Definitions....................................................................................................... 3 2.2 General Assumptions............................................................................................................ 4 III. Articulate our metrics................................................................................................................ 4 3.1 Collect data............................................................................................................................4 3.2 Preprocess data......................................................................................................................6 IV. Task 1:Judging a sustainable country....................................................................................... 7 4.1 Model I: Grey Relation Grade Analysis................................................................................7 4.1.1 Obtain the index weight............................................................................................. 7 4.1.2 Results & analysis...................................................................................................... 8 4.2 Model II: K-means Clustering Analysis............................................................................... 9 4.2.1 Modeling step.............................................................................................................9 4.2.2 Results & analysis...................................................................................................... 9 4.3 Model III: RBF&BP neural network.................................................................................. 10 4.3.1 Enlarge the amount of data...................................................................................... 11 4.3.2 Forecast the score..................................................................................................... 11 V. Task 2:A sustainable development plan....................................................................................12 5.1 First stage............................................................................................................................ 13 5.2 Second stage........................................................................................................................14 5.3 Third stage...........................................................................................................................15 VI. Task 3:The additional environmental factors’ influence...................................................... 15 VII .Task4:The Strengths and Weakness......................................................................................18 7.1 Strengths：..........................................................................................................................18 7.2 Weaknesses:.........................................................................................................................18 VIII.References................................................................................................................................19

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。

●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年数学建模竞赛网络挑战赛C题荒漠区动植物关系的研究

数学建模网络挑战赛承诺书我们仔细阅读了第八届“认证杯”数学中国数学建模网络挑战赛的竞赛规则。

我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究讨论与赛题有关问题。

我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。

我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。

如有违反竞赛规则的行为，我们接受相应处理结果。

我们允许数学中国网站()公布论文，以供网友之间学习交流，数学中国网站以非商业目的的论文交流不需要提前取得我们的同意。

我们的参赛队号为：4272参赛队员 (签名) ：队员1：队员2：队员3：参赛队教练员 (签名)：参赛队伍组别（例如本科组）：本科组数学建模网络挑战赛编号专用页参赛队伍的参赛队号：（请各个参赛队提前填写好）：竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：荒漠区动植物关系的研究【摘要】群落的格局和动态是群落生态学和生态系统生态学研究的基础问题，也是揭示群落结构和功能的核心问题。

本文主要研究荒漠区在两种不同人为干扰下植物生物量和动物生物量的变化趋势，以及在不同干扰下的他们之间的相互关系；进一步对啮齿动物群落稳定性进行研究，进而揭示干扰对于啮齿动物群落的影响。

对数据进行整理分析，建立拟合模型，线性回归的显著性检验模型，典型相关分析模型，以及使用M.Godron稳定性测定方法模型。

使用EXCEL,SPSS等软件进行操作，得到问题的相应结果。

针对问题一，本文对原始数据进行加工处理，求出草本生物量，灌木生物量以及啮齿动物捕获率的平均值，使用控制变量法，利用SPSS软件绘出不同干扰下对植物生物量，动物生物量的影响趋势图，从而分析得出不同干扰下植物生物量，动物生物量的变化趋势。

进一步运用多元回归方程的显著性检验，探讨植物生物量和动物生物量之间的显著性关系；之后建立了典型相关分析模型，运用SPSS软件求出植物群落与动物群落的典型相关系数，最后得出动物群落变量与植物群落变量中的草本关系最为突出，且啮齿动物生物量与草本的盖度和地上生物量呈负相关关系。

2016美国大学生数学建模大赛C题特等奖(原版论文)C42939Tsinghua University, China

For ofﬁce use only T1T2T3T4T eam Control Number42939Problem ChosenCFor ofﬁce use onlyF1F2F3F42016Mathematical Contest in Modeling(MCM)Summary Sheet (Attach a copy of this page to each copy of your solution paper.)SummaryIn order to determine the optimal donation strategy,this paper proposes a data-motivated model based on an original deﬁnition of return on investment(ROI) appropriate for charitable organizations.First,after addressing missing data,we develop a composite index,called the performance index,to quantify students’educational performance.The perfor-mance index is a linear composition of several commonly used performance indi-cators,like graduation rate and graduates’earnings.And their weights are deter-mined by principal component analysis.Next,to deal with problems caused by high-dimensional data,we employ a lin-ear model and a selection method called post-LASSO to select variables that statis-tically signiﬁcantly affect the performance index and determine their effects(coef-ﬁcients).We call them performance contributing variables.In this case,5variables are selected.Among them,tuition&fees in2010and Carnegie High-Research-Activity classiﬁcation are insusceptible to donation amount.Thus we only con-sider percentage of students who receive a Pell Grant,share of students who are part-time and student-to-faculty ratio.Then,a generalized adaptive model is adopted to estimate the relation between these3variables and donation amount.Weﬁt the relation across all institutions and get aﬁtted function from donation amount to values of performance contributing variables.Then we divide the impact of donation amount into2parts:homogenous and heterogenous one.The homogenous inﬂuence is modeled as the change inﬁt-ted values of performance contributing variables over increase in donation amount, which can be predicted from theﬁtted curve.The heterogenous one is modeled as a tuning parameter which adjusts the homogenous inﬂuence based on deviation from theﬁtted curve.And their product is increase in true values of performance over increase in donation amount.Finally,we calculate ROI,deﬁned as increase in performance index over in-crease in donation amount.This ROI is institution-speciﬁc and dependent on in-crease in donation amount.By adopting a two-step ROI maximization algorithm, we determine the optimal investment strategy.Also,we propose an extended model to handle problems caused by time dura-tion and geographical distribution of donations.A Letter to the CFO of the Goodgrant FoundationDear Chiang,Our team has proposed a performance index quantifying the students’educational per-formance of each institution and deﬁned the return of investment(ROI)appropriately for a charitable organization like Goodgrant Foundation.A mathematical model is built to help predict the return of investment after identifying the mechanism through which the donation generates its impact on the performance.The optimal investment strategy is determined by maximizing the estimated return of investment.More speciﬁcally,the composite performance index is developed after taking all the pos-sible performance indicators into consideration,like graduation rate and graduates’earnings. The performance index is constructed to represents the performance of the school as well as the positive effect that a college brings to students and the community.From this point of view, our deﬁnition manages to capture social beneﬁts of donation.And then we adopt a variable selection method toﬁnd out performance contributing vari-ables,which are variables that strongly affect the performance index.Among all the perfor-mance contributing variables we select,three variables which can be directly affected by your generous donation are kept to predict ROI:percentage of students who receive a Pell Grant, share of students who are part-time and student-to-faculty ratio.Weﬁtted a relation between these three variables and the donation amount to predict change in value of each performance contributing variable over your donation amount.And we calculate ROI,deﬁned as increase in the performance index over your donation amount, by multiplying change in value of each performance contributing variable over your donation amount and each performance contributing variable’s effect on performance index,and then summing up the products of all performance contributing variables.The optimal investment strategy is decided after maximizing the return of investment according to an algorithm for selection.In conclusion,our model successfully produced an investment strategy including a list of target institutions and investment amount for each institution.(The list of year1is attached at the end of the letter).The time duration for the investment could also be determined based on our model.Since the model as well as the evaluation approach is fully data-motivated with no arbitrary criterion included,it is rather adaptable for solving future philanthropic educational investment problems.We have a strong belief that our model can effectively enhance the efﬁciency of philan-thropic educational investment and provides an appropriate as well as feasible way to best improve the educational performance of students.UNITID names ROI donation 197027United States Merchant Marine Academy21.85%2500000 102711AVTEC-Alaska’s Institute of Technology21.26%7500000 187745Institute of American Indian and Alaska Native Culture20.99%2000000 262129New College of Florida20.69%6500000 216296Thaddeus Stevens College of Technology20.66%3000000 229832Western Texas College20.26%10000000 196158SUNY at Fredonia20.24%5500000 234155Virginia State University20.04%10000000 196200SUNY College at Potsdam19.75%5000000 178615Truman State University19.60%3000000 199120University of North Carolina at Chapel Hill19.51%3000000 101648Marion Military Institute19.48%2500000187912New Mexico Military Institute19.31%500000 227386Panola College19.28%10000000 434584Ilisagvik College19.19%4500000 199184University of North Carolina School of the Arts19.15%500000 413802East San Gabriel Valley Regional Occupational Program19.09%6000000 174251University of Minnesota-Morris19.09%8000000 159391Louisiana State University and Agricultural&Mechanical Col-19.07%8500000lege403487Wabash Valley College19.05%1500000 Yours Sincerely,Team#42939An Optimal Strategy of Donation for Educational PurposeControl Number:#42939February,2016Contents1Introduction51.1Statement of the Problem (5)1.2Baseline Model (5)1.3Detailed Deﬁnitions&Assumptions (8)1.3.1Detailed Deﬁnitions: (8)1.3.2Assumptions: (9)1.4The Advantages of Our Model (9)2Addressing the Missing Values93Determining the Performance Index103.1Performance Indicators (10)3.2Performance Index via Principal-Component Factors (10)4Identifying Performance Contributing Variables via post-LASSO115Determining Investment Strategy based on ROI135.1Fitted Curve between Performance Contributing Variables and Donation Amount145.2ROI(Return on Investment) (15)5.2.1Model of Fitted ROIs of Performance Contributing Variables fROI i (15)5.2.2Model of the tuning parameter P i (16)5.2.3Calculation of ROI (17)5.3School Selection&Investment Strategy (18)6Extended Model186.1Time Duration (18)6.2Geographical Distribution (22)7Conclusions and Discussion22 8Reference23 9Appendix241Introduction1.1Statement of the ProblemThere exists no doubt in the signiﬁcance of postsecondary education to the development of society,especially with the ascending need for skilled employees capable of complex work. Nevertheless,U.S.ranks only11th in the higher education attachment worldwide,which makes theﬁnancial support from large charitable organizations necessary.As it’s essential for charitable organizations to maximize the effectiveness of donations,an objective and systematic assessment model is in demand to develop appropriate investment strategies.To achieve this goal,several large foundations like Gates Foundation and Lumina Foundation have developed different evaluation approaches,where they mainly focus on spe-ciﬁc indexes like attendance and graduation rate.In other empirical literature,a Forbes ap-proach(Shifrin and Chen,2015)proposes a new indicator called the Grateful Graduates Index, using the median amount of private donations per student over a10-year period to measure the return on investment.Also,performance funding indicators(Burke,2002,Cave,1997,Ser-ban and Burke,1998,Banta et al,1996),which include but are not limited to external indicators like graduates’employment rate and internal indicators like teaching quality,are one of the most prevailing methods to evaluate effectiveness of educational donations.However,those methods also arise with widely acknowledged concerns(Burke,1998).Most of them require subjective choice of indexes and are rather arbitrary than data-based.And they perform badly in a data environment where there is miscellaneous cross-section data but scarce time-series data.Besides,they lack quantiﬁed analysis in precisely predicting or measuring the social beneﬁts and the positive effect that the investment can generate,which serves as one of the targets for the Goodgrant Foundation.In accordance with Goodgrant Foundation’s request,this paper provides a prudent def-inition of return on investment(ROI)for charitable organizations,and develops an original data-motivated model,which is feasible even faced with tangled cross-section data and absent time-series data,to determine the optimal strategy for funding.The strategy contains selection of institutions and distribution of investment across institutions,time and regions.1.2Baseline ModelOur deﬁnition of ROI is similar to its usual meaning,which is the increase in students’educational performance over the amount Goodgrant Foundation donates(assuming other donationsﬁxed,it’s also the increase in total donation amount).First we cope with data missingness.Then,to quantify students’educational performance, we develop an index called performance index,which is a linear composition of commonly used performance indicators.Our major task is to build a model to predict the change of this index given a distribution of Goodgrant Foundation$100m donation.However,donation does not directly affect the performance index and we would encounter endogeneity problem or neglect effects of other variables if we solely focus on the relation between performance index and donation amount. Instead,we select several variables that are pivotal in predicting the performance index from many potential candidates,and determine their coefﬁcients/effects on the performance index. We call these variables performance contributing variables.Due to absence of time-series data,it becomes difﬁcult toﬁgure out how performance con-tributing variables are affected by donation amount for each institution respectively.Instead, weﬁt the relation between performance contributing variables and donation amount across all institutions and get aﬁtted function from donation amount to values of performance contribut-ing variables.Then we divide the impact of donation amount into2parts:homogenous and heteroge-nous one.The homogenous inﬂuence is modeled as the change inﬁtted values of performance contributing variables over increase in donation amount(We call these quotientsﬁtted ROI of performance contributing variable).The heterogenous one is modeled as a tuning parameter, which adjusts the homogenous inﬂuence based on deviation from theﬁtted function.And their product is the institution-speciﬁc increase in true values of performance contributing variables over increase in donation amount(We call these values ROI of performance contributing vari-able).The next step is to calculate the ROI of the performance index by adding the products of ROIs of performance contributing variables and their coefﬁcients on the performance index. This ROI is institution-speciﬁc and dependent on increase in donation amount.By adopting a two-step ROI maximization algorithm,we determine the optimal investment strategy.Also,we propose an extended model to handle problems caused by time duration and geographical distribution of donations.Note:we only use data from the provided excel table and that mentioned in the pdfﬁle.Table1:Data SourceVariable DatasetPerformance index Excel tablePerformance contributing variables Excel table and pdfﬁleDonation amount PdfﬁleTheﬂow chart of the whole model is presented below in Fig1:Figure1:Flow Chart Demonstration of the Model1.3Detailed Deﬁnitions&Assumptions 1.3.1Detailed Deﬁnitions:1.3.2Assumptions:A1.Stability.We assume data of any institution should be stable without the impact from outside.To be speciﬁc,the key factors like the donation amount and the performance index should remain unchanged if the college does not receive new donations.A2.Goodgrant Foundation’s donation(Increase in donation amount)is discrete rather than continuous.This is reasonable because each donation is usually an integer multiple of a minimum amount,like$1m.After referring to the data of other foundations like Lumina Foundation,we recommend donation amount should be one value in the set below:{500000,1000000,1500000, (10000000)A3.The performance index is a linear composition of all given performance indicators.A4.Performance contributing variables linearly affect the performance index.A5.Increase in donation amount affects the performance index through performance con-tributing variables.A6.The impact of increase in donation amount on performance contributing variables con-tains2parts:homogenous one and heterogenous one.The homogenous inﬂuence is repre-sented by a smooth function from donation amount to performance contributing variables.And the heterogenous one is represented by deviation from the function.1.4The Advantages of Our ModelOur model exhibits many advantages in application:•The evaluation model is fully data based with few subjective or arbitrary decision rules.•Our model successfully identiﬁes the underlying mechanism instead of merely focusing on the relation between donation amount and the performance index.•Our model takes both homogeneity and heterogeneity into consideration.•Our model makes full use of the cross-section data and does not need time-series data to produce reasonable outcomes.2Addressing the Missing ValuesThe provided datasets suffer from severe data missing,which could undermine the reliabil-ity and interpretability of any results.To cope with this problem,we adopt several different methods for data with varied missing rate.For data with missing rate over50%,any current prevailing method would fall victim to under-or over-randomization.As a result,we omit this kind of data for simplicity’s sake.For variables with missing rate between10%-50%,we use imputation techniques(Little and Rubin,2014)where a missing value was imputed from a randomly selected similar record,and model-based analysis where missing values are substituted with distribution diagrams.For variables with missing rate under10%,we address missingness by simply replace miss-ing value with mean of existing values.3Determining the Performance IndexIn this section,we derive a composite index,called the performance index,to evaluate the educational performance of students at every institution.3.1Performance IndicatorsFirst,we need to determine which variables from various institutional performance data are direct indicators of Goodgrant Foundation’s major concern–to enhance students’educational performance.In practice,other charitable foundations such as Gates Foundation place their focus on core indexes like attendance and graduation rate.Logically,we select performance indicators on the basis of its correlation with these core indexes.With this method,miscellaneous performance data from the excel table boils down to4crucial variables.C150_4_P OOLED_SUP P and C200_L4_P OOLED_SUP P,as completion rates for different types of institutions,are directly correlated with graduation rate.We combine them into one variable.Md_earn_wne_p10and gt_25k_p6,as different measures of graduates’earnings,are proved in empirical studies(Ehren-berg,2004)to be highly dependent on educational performance.And RP Y_3Y R_RT_SUP P, as repayment rate,is also considered valid in the same sense.Let them be Y1,Y2,Y3and Y4.For easy calculation and interpretation of the performance index,we apply uniformization to all4variables,as to make sure they’re on the same scale(from0to100).3.2Performance Index via Principal-Component FactorsAs the model assumes the performance index is a linear composition of all performance indicators,all we need to do is determine the weights of these variables.Here we apply the method of Customer Satisfaction Index model(Rogg et al,2001),where principal-component factors(pcf)are employed to determine weights of all aspects.The pcf procedure uses an orthogonal transformation to convert a set of observations of pos-sibly correlated variables into a set of values of linearly uncorrelated variables called principal-component factors,each of which carries part of the total variance.If the cumulative proportion of the variance exceeds80%,it’s viable to use corresponding pcfs(usually theﬁrst two pcfs)to determine weights of original variables.In this case,we’ll get4pcfs(named P CF1,P CF2,P CF3and P CF4).First,the procedure provides the linear coefﬁcients of Y m in the expression of P CF1and P CF2.We getP CF1=a11Y1+a12Y2+a13Y3+a14Y4P CF2=a21Y1+a22Y2+a23Y3+a24Y4(a km calculated as corresponding factor loadings over square root of factor k’s eigenvalue) Then,we calculate the rough weights c m for Y m.Let the variance proportions P CF1and P CF2 represent be N1and N2.We get c m=(a1m N1+a2m N2)/(N1+N2)(This formulation is justiﬁedbecause the variance proportions can be viewed as the signiﬁcance of pcfs).If we let perfor-mance index=(P CF 1N 1+P CF 2N 2)/(N 1+N 2),c m is indeed the rough weight of Y m in terms of variance)Next,we get the weights by adjusting the sum of rough weights to 1:c m =c m /(c 1+c 2+c 3+c 4)Finally,we get the performance index,which is the weighted sum of the 4performance indicator.Performance index= m (c m Y m )Table 2presents the 10institutions with largest values of the performance index.This rank-ing is highly consistent with widely acknowledged rankings,like QS ranking,which indicates the validity of the performance index.Table 2:The Top 10Institutions in Terms of Performance IndexInstitutionPerformance index Los Angeles County College of Nursing and Allied Health79.60372162Massachusetts Institute of Technology79.06066895University of Pennsylvania79.05044556Babson College78.99269867Georgetown University78.90468597Stanford University78.70586395Duke University78.27719116University of Notre Dame78.15843964Weill Cornell Medical College 78.143341064Identifying Performance Contributing Variables via post-LASSO The next step of our model requires identifying the factors that may exert an inﬂuence on the students’educational performance from a variety of variables mentioned in the excel table and the pdf ﬁle (108in total,some of which are dummy variables converted from categorical variables).To achieve this purpose,we used a model called LASSO.A linear model is adopted to describe the relationship between the endogenous variable –performance index –and all variables that are potentially inﬂuential to it.We assign appropriate coefﬁcient to each variable to minimize the square error between our model prediction and the actual value when ﬁtting the data.min β1J J j =1(y j −x T j β)2where J =2881,x j =(1,x 1j ,x 2j ,...,x pj )THowever,as the amount of the variables included in the model is increasing,the cost func-tion will naturally decrease.So the problem of over ﬁtting the data will arise,which make the model we come up with hard to predict the future performance of the students.Also,since there are hundreds of potential variables as candidates.We need a method to identify the variables that truly matter and have a strong effect on the performance index.Here we take the advantage of a method named post-LASSO (Tibshirani,1996).LASSO,also known as the least absolute shrinkage and selection operator,is a method used for variableselection and shrinkage in medium-or high-dimensional environment.And post-LASSO is to apply ordinary least squares(OLS)to the model selected byﬁrst-step LASSO procedure.In LASSO procedure,instead of using the cost function that merely focusing on the square error between the prediction and the actual value,a penalty term is also included into the objective function.We wish to minimize:min β1JJj=1(y j−x T jβ)2+λ||β||1whereλ||β||1is the penalty term.The penalty term takes the number of variables into con-sideration by penalizing on the absolute value of the coefﬁcients and forcing the coefﬁcients of many variables shrink to zero if this variable is of less importance.The penalty coefﬁcient lambda determines the degree of penalty for including variables into the model.After min-imizing the cost function plus the penalty term,we couldﬁgure out the variables of larger essence to include in the model.We utilize the LARS algorithm to implement the LASSO procedure and cross-validation MSE minimization(Usai et al,2009)to determine the optimal penalty coefﬁcient(represented by shrinkage factor in LARS algorithm).And then OLS is employed to complete the post-LASSO method.Figure2:LASSO path-coefﬁcients as a function of shrinkage factor sFigure3:Cross-validated MSEFig2.displays the results of LASSO procedure and Fig3displays the cross-validated MSE for different shrinkage factors.As speciﬁed above,the cross-validated MSE reaches minimum with shrinkage factor between0.4-0.8.We choose0.6andﬁnd in Fig2that6variables have nonzero coefﬁcients via the LASSO procedure,thus being selected as the performance con-tributing variables.Table3is a demonstration of these6variables and corresponding post-LASSO results.Table3:Post-LASSO resultsDependent variable:performance_indexPCTPELL−26.453∗∗∗(0.872)PPTUG_EF−14.819∗∗∗(0.781)StudentToFaculty_ratio−0.231∗∗∗(0.025)Tuition&Fees20100.0003∗∗∗(0.00002)Carnegie_HighResearchActivity 5.667∗∗∗(0.775)Constant61.326∗∗∗(0.783)Observations2,880R20.610Adjusted R20.609Note:PCTPELL is percentage of students who receive aPell Grant;PPTUG_EF is share of students who are part-time;Carnegie_HighResearchActivity is Carnegie classiﬁca-tion basic:High Research ActivityThe results presented in Table3are consistent with common sense.For instance,the pos-itive coefﬁcient of High Research Activity Carnegie classiﬁcation implies that active research activity helps student’s educational performance;and the negative coefﬁcient of Student-to-Faculty ratio suggests that decrease in faculty quantity undermines students’educational per-formance.Along with the large R square value and small p-value for each coefﬁcient,the post-LASSO procedure proves to select a valid set of performance contributing variables and describe well their contribution to the performance index.5Determining Investment Strategy based on ROIWe’ve identiﬁed5performance contributing variables via post-LASSO.Among them,tu-ition&fees in2010and Carnegie High-Research-Activity classiﬁcation are quite insusceptible to donation amount.So we only consider the effects of increase in donation amount on per-centage of students who receive a Pell Grant,share of students who are part-time and student-to-faculty ratio.We denote them with F1,F2and F3,their post-LASSO coefﬁcients withβ1,β2andβ3.In this section,weﬁrst introduce the procedure used toﬁt the relation between performance contributing variables and donation amount.Then we provide the model employed to calcu-lateﬁtted ROIs of performance contributing variables(the homogenous inﬂuence of increase in donation amount)and the tuning parameter(the heterogenous inﬂuence of increase in dona-tion amount).Next,we introduce how to determine stly,we show how the maximiza-tion determines the investment strategy,including selection of institutions and distribution of investments.5.1Fitted Curve between Performance Contributing Variables and Donation AmountSince we have already approximated the linear relation between the performance index with the3performance contributing variables,we want to know how increase in donation changes them.In this paper,we use Generalized Adaptive Model(GAM)to smoothlyﬁt the relations. Generalized Adaptive Model is a generalized linear model in which the dependent variable depends linearly on unknown smooth functions of independent variables.Theﬁtted curve of percentage of students who receive a Pell Grant is depicted below in Fig4(see the other two ﬁtted curves in Appendix):Figure4:GAM ApproximationA Pell Grant is money the U.S.federal government provides directly for students who needit to pay for college.Intuitively,if the amount of donation an institution receives from other sources such as private donation increases,the institution is likely to use these donations to alleviate students’ﬁnancial stress,resulting in percentage of students who receive a Pell Grant. Thus it is reasonable to see aﬁtted curve downward sloping at most part.Also,in commonsense,an increase in donation amount would lead to increase in the performance index.This downward sloping curve is consistent with the negative post-LASSO coefﬁcient of percentage of students who receive a Pell Grant(as two negatives make a positive).5.2ROI(Return on Investment)5.2.1Model of Fitted ROIs of Performance Contributing Variables fROI iFigure5:Demonstration of fROI1Again,we useﬁtted curve of percentage of students who receive a Pell Grant as an example. We modeled the blueﬁtted curve to represent the homogeneous relation between percentage of students who receive a Pell Grant and donation amount.Recallﬁtted ROI of percentage of students who receive a Pell Grant(fROI1)is change in ﬁtted values(∆f)over increase in donation amount(∆X).SofROI1=∆f/∆XAccording to assumption A2,the amount of each Goodgrant Foundation’s donation falls into a pre-speciﬁed set,namely,{500000,1000000,1500000,...,10000000}.So we get a set of possible ﬁtted ROI of percentage of students who receive a Pell Grant(fROI1).Clearly,fROI1is de-pendent on both donation amount(X)and increase in donation amount(∆X).Calculation of ﬁtted ROIs of other performance contributing variables is similar.5.2.2Model of the tuning parameter P iAlthough we’ve identiﬁed the homogenous inﬂuence of increase in donation amount,we shall not neglect the fact that institutions utilize donations differently.A proportion of do-nations might be appropriated by the university’s administration and different institutions allocate the donation differently.For example,university with a more convenient and well-maintained system of identifying students who needﬁnancial aid might be willing to use a larger portion of donations to directly aid students,resulting in a lower percentage of under-graduate students receiving Pell grant.Also,university facing lower cost of identifying and hiring suitable faculty members might be inclined to use a larger portion of donations in this direction,resulting in a lower student-to-faculty ratio.These above mentioned reasons make institutions deviate from the homogenousﬁtted func-tion and presents heterogeneous inﬂuence of increase in donation amount.Thus,while the homogenous inﬂuence only depends on donation amount and increase in donation amount, the heterogeneous inﬂuence is institution-speciﬁc.To account for this heterogeneous inﬂuence,we utilize a tuning parameter P i to adjust the homogenous inﬂuence.By multiplying the tuning parameter,ﬁtted ROIs of performance con-tributing variables(ﬁtted value changes)convert into ROI of performance contributing variable (true value changes).ROI i=fROI i·P iWe then argue that P i can be summarized by a function of deviation from theﬁtted curve (∆h),and the function has the shape shown in Fig6.The value of P i ranges from0to2,because P i can be viewed as an ampliﬁcation or shrinkage of the homogenous inﬂuence.For example,P i=2means that the homogeneous inﬂuence is ampliﬁed greatly.P i=0means that this homogeneous inﬂuence would be entirely wiped out. The shape of the function is as shown in Fig6because of the following reasons.Intuitively,if one institution locates above theﬁtted line,when deviation is small,the larger it is,the larger P i is.This is because the institution might be more inclined to utilize donations to change that factor.However,when deviation becomes even larger,the institution grows less willing to invest on this factor.This is because marginal utility decreases.The discussion is similar if one institution initially lies under theﬁtted line.Thus,we assume the function mapping deviation to P i is similar to Fig6.deviation is on the x-axis while P i is on the y-axis.Figure6:Function from Deviation to P iIn order to simplify calculation and without loss of generality,we approximate the function。

2015年数学建模全国一等奖论文

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5.2
问题二：
5．2．1 模型的准备
模型建立之前，我们分析数据得到所给影子顶点坐标并非以标准的东西南北方向坐标系下的坐标，所以我们必须进行矫正，把坐标系修正成正南正北的坐标系。而后确定时差来确定经度，进而得到纬度。
（8）
（9）
获得新的坐标（x1,y1）。注：矫正坐标系以东西方向为 x 轴，南北方向为 y 轴。
图6
8
（2）时差的求解通过所给坐标在 matlab 中进行拟合，得到一条影长 L 关于时间 ts 的抛物线方程： L=ats2-bts+c 其中 L 为影长，t 为时间。解出最低点坐标 t0，利用北京时间 12：00 时影子最短，利用比例关系 (10)
5.1.3 模型的求解
模型中及为影长 L 和时间 t，纬度φ，以及日期 n 的函数关系。当其中两个自变量确定后，就可建立影长 L 和另外一个自变量的模型。（1）影长 L 和时间 t 的模型给定日期 n 和纬度φ，模型就变成了影长 L 和时间 t 的一元函数，应用 Matlab 即可得到影长的变化曲线。在此，我们验证了赤道上 1 月 1 日的影长变化（如图 2）由图可以看出，当 1 月 1 日时，9:00 到 15:00 的曲线为开口向上的抛物线，在早上 9:00 时，由于太阳直射南半球，所以影子长，到了当地正午 12:00 时影子最短，下午又开始增长，符合实际，模型基本成立。

2015immc优秀论文3

2015 IM2C Problem Movie SchedulingTeam 2015004Team # 20150042 / 44SummaryArranging a movie’s shooting schedule can mean a lot of hard work. Different actors and actresses have their own schedules, various resources need to be booked, and special restrictions of some scenes must be considered. In order to offer a satisfactory solution, we have developed a model capable of finding possible schedules and selecting several better schedules based on our clients’ preferences. We have also provided solutions that help our clients adjust their plan if an accident happens, as well as helping them identify the most important constraints that would most greatly affect their schedule if varied.In the first part of our model, we search the possible shooting schedules according to the information that our clients provided, which may include the available time periods of each actor, specific sites and special resources. We sort out the various available dates by scenes, and using a 0-1 matrix to represent the availability of each scene on each of possible shooting dates. We then use the backtracking method, which is commonly used in solving constraint satisfaction problems and combinatorial search, to find arrangements that satisfy each scene’s availability dates. Moreover, in order to further shorten the running time of our program, we pre-arranged the order of scenes, so that the scenes with the strictest restrictions would be considered first, enabling the program using the backtracking method to find more results more quickly.In the second part of our model, we consider other special restrictions requested (for example, the required order of some scenes) and the general preference of our clients. We filter the solutions drawn from the previous part (which could be up to 10000 solutions), by first deleting the deficient solutions based on special restrictions, and then arraying the remaining solutions from the best to the worst. Our model can calculate the total shooting schedule length, the frequency of location changes, and required number of studios in a solution. And along with the average cost to rent a studio, the intended frequency of flexible day, the total budget, and traffic budget of our clients, we can assess the general appropriateness1and some characteristics of a schedule, based on which we array the solutions and provide 11 top schedules to our clients. The solutions include 5 overall best solutions, 2 solutions with least number of location changes, 2 solutions with least number of studios2, and 2 solutions with least number of shooting days.Extending our model, we provide ways to adjust an original schedule to various accidents. When our clients provide us with information of the original schedule they selected, accidents occurred and new restrictions, we can return a new schedule with feasible adjustments. These adjustments are achieved by running the program with the new data while leaving intact the scenes that have already happened or that are not expected to change. In this way, the computational complexity would be greatly reduced and the new schedule would involve as few changes as possible. Lastly, we can also evaluate the most important constraints for our clients by calculating the differences in average characteristic value of top solutions before and after a constraint is changed. Having access to such information, our clients would be able to pay more attention to those important constraints and prevent major delays of their original shooting schedule.1We use the characteristic value to evaluate the appropriateness of a solution. For further explanation, please see 2.2, where we explain in detail how we calculate the characteristic value of a solution.2 Different settings cannot be constructed or shooting simultaneously at the same studio, so more than one studio may be required.Content1. Problem interpretation (4)1.1 Problem restatement (4)1.2 Assumptions and Justifications (4)1.3 The goal of modeling (5)2 Model (5)2.1 Overview of the model (5)2.2 Definition of variables (5)2.3 Relations between variables (8)2.4 Algorithm of finding all possible schedules (9)2.5 Algorithm of finding the best schedule (10)2.6 Adjustment for accidents (11)3 Programming Approach (11)3.1 Overview of the program (11)3.2 Introduction of the program (12)3.2.1 Inputs (12)3.2.2 Algorithm of finding (12)3.2.3 Algorithm of filtering (12)3.2.4 Outputs (13)4. Case Analysis (13)4.1 Overview of the case (13)4.1.1 Roles and the available times of their actors (13)4.1.2 Scenes (14)4.1.3 Available time of sites (15)4.1.4 Preparation time of settings (15)4.1.5 Restriction of specific orders (15)4.1.6 Other constraints (16)4.1.7 Other settings (16)4.2 Case solving (16)4.2.1 The optimal schedule (16)4.2.2 Schedule analysis (17)4.3 Adjustment for accidents (17)4.3.1 Assumed accidents (17)4.3.2 Adjustment realization (17)4.3.3 Results (18)5 The way of finding the most important constraints (19)5.1 Overview of the algorithm (19)5.2 Description of the algorithm (19)6 Reviews and Prospect (20)7 Reference Material (21)8 Appendix (22)1. Problem interpretation1.1 Problem restatementAs one of the major types of popular entertainment, motion picture has become a fast-growing industry. The constant demand for new excellent films makes effective filmmaking an important job. Therefore, it is necessary for every producer to develop a good filming schedule within certain constraints, such as the availability dates of stars and specific resources. We hope to use mathematical models to come up with this optimal schedule.1.2 Assumptions and Justifications1) The filming schedule has a limited time span whose starting point and ending point are both reachable.2) The filming schedule must conform to the following restrictions, which are inflexible and cannot be violated:i.The availability dates of some stars.ii.The availability dates of specific sites.iii.The availability dates for specific resources.iv.The time required to construct and film on a list of sets.v.Some scenes cannot be shot until after certain computer generated content is defined and other physical items are constructed.vi.Some scenes cannot be shot until other scenes are finished. For example, if a set is finally destroyed, all other scenes related to this set are supposed to be shot beforeit happens.vii.Extra time is needed for redoing some shots if they turn out to be inadequate after editing and review.viii.Extra time is needed for making up some delay or changes.ix.During the filming process, the director might decide to add some new scenes, which will influence the schedule.3) The schedule breaks down time into days for further allocation.‐Filming schedules always choose “Day” as their unit, which is pretty reasonable.First, it is small enough, because most scenes require one or several days to be shot.Second, it is still flexible, because in every single day small delays can becompensated by working overtime, and night shoots can be compensated by morerests in the daytime.4) Several scenes cannot be shot at the same time.‐Every time a scene is shot, the director must be present.5) The construction of sets does not interfere with the filming process.‐Workers can build the sets themselves without being monitored by the director.6) If multiple schedules are available, the studio will consider the continuity of locations.‐ Since the crews do not wish to move frequently, a small number of changes infilming locations is preferred.7) Since we can rent several filming studios, it is possible to build different settings at the same time. However, renting more filming studios will increase the cost, so we hope that these constructions do not conflict with each other.8) Although the crew may not work every day, we should pay for them as long as the shoot is not finished. Therefore, the whole time span is not likely to be too long.9) To deal with problems of delays and reshoots, the filming crews usually have a “flexible day” for every two weeks. On this “flexible day”, they can shoot the scenes that were not completely finished before. Each day without a shooting plan can be seen as a flexible day.1.3 The goal of modelingAccording to the assumptions given above, the optimal schedule derived from our model is an arrangement that:‐ satisfies all the inflexible restrictions in 2nd assumption;‐ promises relatively less changes in locations;‐ has relatively less conflicts in construction of different settings;‐ has an appropriate time span;‐ has enough flexible day for problems of delays and reshoots.In this model, we attempt to find a schedule that can excel in all these criteria.2 Model2.1 Overview of the modelThe whole model consists of two parts: “finding” solutions and “filtering” solutions. For each specific situation, our model first figures out all possible schedules, and then picks up the best ones among them. The model can also adjust previous schedules to deal with new accidents, such as delays in some aspects or changes in the availability of some assets.2.2 Definition of variablesIn order to build a reasonable model, we first introduced some variables:max T : The maximum time length of filming schedule, which is the difference between the latestdate and the earliest date appearing in the input sheets. A movie cannot be finished if the span of shooting schedule is longer than max T .min T : The minimum time length of filming schedule, which is the actual shooting time. k A : The personal schedule of actor k , which is a 0-1 array within the spread of max T . A ‘0’ as the n th element means that the actor cannot work on the n th day. Similarly, ‘1’ means the actor can join shooting on that day.l B : The availability dates of site l . We can simply regard a site as an actor, because toaccomplish a shooting task, we need both the actors and the sites available at the same time. If one element is unavailable, the shooting cannot be accomplished. Thus we describel B in the same way as that of k A ; that is, a 0-1 array with the length of max T . Additionally, we define B as the number of sites.m C : The availability dates of setting m . Similar to sites, a setting can be treated just like an actor. We define C as the number of the settings.n D : The availability dates of special resource n , such as a helicopter or a tank, which is only available at certain time intervals. Since resources also can be treated as actors, we use k A to record n D to simplify the model. We define A as the total number of actors and specialresources. (The reason why we do not combinel B and m C with k A is that information about sites and settings are required for other calculations in the “filtering” process.)o N : A set that records the time required (a.k.a. time length) to film scene o and the elements (e.g. actors, special resources, and a site or a setting) involved. o N cannot be an empty set; it has to contain at least one actor and one site or setting. Generally, its time length cannot be changed, which already contains a little flexible time for preparation and transportation. Moreover, we consider a scene the smallest part of shooting, which means that a scene cannot be divided. When all scenes are finished, the shooting task is done. We defineo N as the time length of this scene,which is an element of the set. i Q : A sequence showing a specific arrangement of all o N s. i Q is a time plan for all scenes. o N t : The number of possible ways to arrange scene o , regardless of arrangements of all otherscenes.i x : The actual shooting time length of i Q .*k A : An “Invisible actor” that has the same character as a real actor. We can use this idea to fulfill the special requirements, such as a specific scene that can be shot in several particular time intervals. This variable depends on requirements of the clients.p E : A special restriction p that i Q must conform to. For example, the restriction that 1Nmust be shot before2N are accomplished. This variable depends on requirements of the clients. P : A value between 0 and 1 that measures the ability of a schedule to deal with delays and reshoots. We define that in every 1P days, one flexible day is used to compensate delays and reshoots. Small delays or quick reshoots, which need only a few hours, can be adjusted on the very day it occurs, so that the whole schedule will not be affected. If delays or reshoots cost a longer time, we can resort remaining scenes into a new schedule. So that only when delays and reshoots need one day or several days, the flexible day in the 1P days is needed. P is an average value, which satisfies 01P £<. This variable depends on requirements of the clients.i K : The number of changes in sites or settings (a.k.a. location changes) that occur in an arrangement i Q .0K : The least possible number of location changes.i L : The number of required filming studios.i y : The extra number of i Q ’s location changes. Since we want to avoid unnecessary location changes, the smaller i y is, the better i Q is.i z : The extra number of filming studios that are required. We say that the more filming studios are used, the more money is spent, and the less efficient the schedule is.budget M : Total budget of the movie, which is given by our client.totaltraffic M : Total traffic budget of the movie, which is also decided by our client.itrafficpertime M : The average cost of a location change, which is the money spent on travelling andtransportation.studio M : The average cost of one studio, including the construction cost and art design cost. It is decided by client. h : The budget per day. This variable builds a connection between time and money, so that we can find the equivalent of a certain amount of money in some measure of time. However, it is just an estimation variable, time is always invaluable.i q : Penalty coefficient of i y (illustrated below).a : Penalty coefficient of i z (illustrated below).2.3 Relations between variables According to the definitions of these variables, we can come up with some basic relationships:min =o T N å (2.3-1)min max i T x T ££ (2.3-2)0=1K B C +- (2.3-3)0i i y K K =- (2.3-4)when 0i L ¹,1i i z L =-; when 0i L =, 0i z = (2.3-5)=i totaltraffic trafficpertime i M M K (2.3-6) min budgetM T h = (2.3-7)We believe that a large number of changes in locations are “bad” for a shooting schedule; too many filming studios are “bad”, too. In order to describe the how bad they are, we can transform their financial cost into time of equal value. So we have=itrafficperday i M q h(2.3-8) =studio M a h (2.3-9)Moreover, when the constraints are too loose, most of possible solutions will be far from optimal. To prevent this condition, we add another limit:max min 21T T P êú£êúêú+ëû(2.3-10) This means that max T cannot be too long. max T should be longer than min T by a period of time no more than min 2PT , or there will be too much idle time. Since too much idle time causes the increase of possible solutions, if the case holds false to the formula, we know that there are too many i Q s.2.4 Algorithm of finding all possible schedulesFinding possible schedules is a process of trial and error, which is meant to include both successes and failures. However, in order to reduce the mass of calculation, we hope to obtain all solutions with the least number of failures. To achieve this, we can determine the relatively inflexible times first, and leave the flexible ones for permutations later.Since o N t , the number of possible ways to arrange scene o (regardless of all other scenes), is anindication of o N ’s flexibility in time, we can arrange all o N s by ascending order of o N t{}*****1231,,,......,,q q N N N N N -This arrangement enables us to settle these scenes in an efficient order.Then we use backtracking algorithm to find all of i Q .In fact, the finding process is like finding all**1q N N path -s in a directed graph:First, we choose one *o N . Then we pick oneof the available choices of *1o N +. If wecannot find a *1o N +, which means that thechosen *o N is unfeasible, we will go backto the last order and find another *o N . Wewill continual to repeat this procedure untilwe get a complete **1q N N path -. Everytime we obtain a path, we record it and go back to the last order.Even though the crotches of tree are numerous and unknown, we have promised the least number of crotches by arranging o N by o N t . After reducing a large amount of computations, the newlyderived *o N is suitable for finding i Q .2.5 Algorithm of finding the best scheduleAfter all possible schedules are found, we need to evaluate each of them to find the top solutions. First, we have to follow the restrictions in E . If i Q does not accord with p E , it should be eliminated from our consideration.Second, we need to assess how good i Q is. In an optimal situation, we can assume a numerical relationship among several variables:min min i i i i x T y z T P q a ---» (2.5-1)i x is the whole time span of i Q , while min T is the real shooting time, and i q and a are the time spent on transportations and constructions. Therefore, the left side of the equation stands for the actual flexible time ready to deal with delays and reshoots, which is expected to be min PT Based on formula (11), we introduce a new index ()i S Q :min min min ()()=ln i i i i i T P x T y z S Q T Pq a ----() (2.5-2) The function ()i S Q , a characteristic value, indicates the superiority of each i Q . The less ()i S Q is, the more orderly i Q is, and the better the schedule is.In the best solution whose free time is just appropriate, min min ()=0i i i i T P x T y z q a ----, and ()-i S Q ®¥.If free time is too little, and flexible days are just enough to cover the penalty time (time spent on transportations and constructions) but not enough to compensate for delays and reshoots, we will have min ()0i i i i x T y z q a ---=, and ()0i S Q =.If free time is too much, and the time for delays and reshoots are twice as much as needed, we will have min min ()2T i i i i x T y z P q a ---=, the characteristic value ()i S Q also equals to 0. Eventhough the two cases above are different, they are both considered as mediocre choices, and their()i S Q values are the same.2.6 Adjustment for accidentsIf the clients encounter an accident that cannot be solved by existing flexible days (for example, significant delays in one aspect or the availability of some asset changes) during the filming process, we can provide a model for them to rearrange the future plan. The rearrangement can be achieved through a similar program, so they could quickly obtain the new schedule after changing some basic information and running the program.This adjustment is based on information in several aspects:1) The change in constraints (if any). For example, if the delay is caused by change in availability of an actor, a site or a resource, the new available time must be known.2) The present achievements. Since some tasks are already finished, the schedule before the present day cannot change anymore.3) The future dates that are hard to change. Some appointments with actors and specific resources (such as a helicopter) cannot be cancelled or changed, so the related scenes have to stay at the same date.After these information are entered, the program will add new constraints {}****123,,,......,r A A A A and the unchangeable scenes {}''''123,,,......,r N N N N (unchangeable scenes will be considered as “Invisible actors”, and the detailed procedure is discussed in 2.2) and give solution based on the new circumstances. Therefore, if these information are known, the program can provide an optimal future schedule for the clients when an accident happens.3 Programming Approach3.1 Overview of the programBased on our model, we developed a computer program that is capable of generating possible schedules as well as determining the priority of each schedules according to their characteristic values and sorting them by the priority in descending order.3.2 Introduction of the program3.2.1 InputsOur program contains a function that can read an Excel file so that it is very convenient for clients to input data. The Excel has 6 sheets which contain the information of actors, places, sets, scenes and two kinds of restrictions.The input function named ‘Read’ works by transferring information in Excel into four variables (Data form: double) named Ifm_Actors, Ifm_Places, Ifm_Sets, Ifm_Scenes and Cmd_Time.3.2.2 Algorithm of finding3.2.2.1 Preliminary filteringFirst of all, the program will check whether a possible solution exists. If there’s obviously no possible solution3, it will display an error and terminates the program.3.2.2.2 Estimation and tipsUse the formula (10) to determine whether the restrictions are too loose so that the quantity of possible schedules might be too large. If the case holds false to the formula, the program would display a warning.3.2.2.3 Searching for possible schedulesThe program generates 0-1 matrixes Ifm_Actors, Ifm_Places, Ifm_Sets and Ifm_Scenes with 1 representing available days and 0 representing occupied days. In this way we can figure out the intersection of available time by multiplying the correspondent row.Then, by rearranging the 0-1 matrix in order of the method that was mentioned in 2.4, the computational complicity is significantly reduced.Finally, we use the backtracking method to search for all possible schedules within the 0-1 matrix. Solutions are saved in variable All_Solutions (data form: cell).During the searching, if the number of solutions is too large, the program simply stops searching when 1000 solutions are recorded.3.2.3 Algorithm of filteringAfter generating all solutions, our program will follow time restrictions to delete those solutions that don’t fit in. Then, the program determines the changing times of places and sets, and calculates the characteristic values with function (12) to judge whether a solution is practical enough. The solutions are rearranged according to their characteristic values.3 For example, if the schedules of two actors who cooperate in a specific scene do not have intersection, the scene obviously cannot be shot.3.2.4 OutputsFinally, the output function of the program creates an Excel file and writes 11 possible scheduleswith the top priority in four different criteria. They include 5 overall best schedules, 2 scheduleswith least number of location changes, 2 schedules with least number of studios, and 2 scheduleswith least number of shooting days. In each schedule, scenes are arranged chronologically.4. Case Analysis4.1 Overview of the caseFor most movies, the detailed information about the preparing process are not open to public,which makes it hard to find a realistic case to test our model. However, we gathered some basicfacts about film shooting from internet and libraries, and used them to create a mostly reliable caseto test our model.This movie tells the stories of a group of physicists. It contains 18 roles, 9 sites, 11 settings, and 29 scenes. The studio wants the whole filming to be finished within 60 days. They also give some constraints, which are all displayed as below.4.1.1 Roles and the available times of their actorsThe following chart displays all the roles included in the film and the available dates of theiractors:Role Available dates of actorRydberg 13-14 Thomson 26-2824-25,29-30 Rutherford 1-5,29-30 Chadwick 4-5,Planck 11-12, 16-17, 23, 29-30Bohr 1-3,7,9,26-28, 34-35, 51-54Landau 21 Fermi 41-50 Oppenheimer 22, 41-47, 51-52Feynman 44-4734-35 Schrödinger 18-20,34-35 Compton 24-25,De Broglie 34-35, 40-60Einstein 6, 8, 16, 17, 21, 34-40Heisenberg 7-9, 23, 31-36, 53-60Dirac 31-35,51-52 Pauli 10,34-35 Born 10,19-20,34-35 4.1.2 ScenesThe following chart displays all the scenes in the film, the locations of and roles in them, and thetime needed to shoot them. There are two types of locations, sites and settings, which will bespecifically discussed in following paragraphs.Scene Location Roles Time(day)Solvay Conference Brussels Einstein, Bohr, Planck, Dirac,Born, Pauli, Schrödinger,Compton, De Broglie, Heisenberg2Experiment 1 Lab 1 Rydberg, Bohr 2 Experiment 2 The University of Manchester Rutherford, Bohr 3 Experiment 3 The University of Cambridge Thomson, Chadwick 3 Story 1 The University of Manchester Rutherford, Chadwick 2 Story 2 The University of Cambridge Rutherford, Einstein 2 Story 3 Humboldt University of Berlin Planck, Einstein 2 Story 4 Auditorium 1 Landau 1 Story 5 The University of Chicago Fermi, Oppenheimer, Feynman 4 Story 6 The University of Cambridge Dirac, Heisenberg 2 Story 7 Humboldt University of Berlin Schrödinger 1 Story 8 House 1 Einstein, Heisenberg 1 Story 9 House 2 Planck, Heisenberg 1 Story 10 Auditorium 2 Einstein 1 Story 11 Meeting room 1 Einstein 1 Experiment 4 University of Copenhagen Dirac, Bohr, Oppenheimer 2 Experiment 5 Lab 2 Compton, Rutherford 2 Story 12 Auditorium 2 Heisenberg, Bohr 1 Story 13 University of Copenhagen Heisenberg, Bohr 2 Story 14 University of Göttingen Pauli, Born 1 Experiment 6 Lab 3 Planck 2 Story 15 Meeting room 2 Heisenberg, Bohr 1 Story 16 Princeton University Einstein 2 Story 17 House 1 Einstein 2 Story 18 Humboldt University of Berlin Schrödinger, Born 2 Story 19 House 3 Oppenheimer 1 Story 20 Lab 4 Oppenheimer, Fermi 2 Story 21 National Library Fermi 3 Story 22 University of Copenhagen Heisenberg 24.1.3 Available time of sitesFor some specific reasons, a few sites cannot be shot all the time. The following chart displays theavailable dates of each site:date Place Available University of Copenhagen 50-60Humboldt University of Berlin 15-20Brussels 1-60 The University of Manchester 1-7The University of Cambridge 25-33The University of Chicago 44-60University of Göttingen 1-57Princeton University 1-42National Library 48-604.1.4 Preparation time of settingsThe time of preparation for settings is a determinant of the number of filming studios. Thefollowing chart displays this preparation time:time(day) Set PreparationHouse 1 4House 2 3House 3 6Meeting room 1 0Meeting room 2 0Lab 1 0Lab 2 0Lab 3 0Lab 4 0Auditorium 1 0Auditorium 2 0We assume in this way because compared to filming in meeting rooms, labs and auditoriums, it isharder to film in a realistic house (For example, a high filming position cannot be reached).Therefore, we must build some “houses” in the filming studio, which requires several days toprepare.4.1.5 Restriction of specific ordersThe studio also requires some specific orders of scenes to be shot:“Story 20” must go after “Experiment 1”.“Story 13” must go after “Experiment 5”, and “Experiment 5” must go after “Experiment 2”.。

2015年美国数学建模竞赛第二次模拟赛题c题

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 1Describe 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 2Model 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.。

85-09历年美赛（MCM）中文试题

85-09历年美赛（MCM）中文试题校苑资源网整理历年美国大学生数学建模赛题目录MCM85问题-A 动物群体的管理.............................................................................................- 3 - MCM85问题-B 战购物资储备的管理.....................................................................................- 3 - MCM86问题-A 水道测量数据.................................................................................................- 4 - MCM86问题-B 应急设施的位置.............................................................................................- 4 - MCM87问题-A 盐的存贮.........................................................................................................- 5 - MCM87问题-B 停车场.............................................................................................................- 5 - MCM88问题-A 确定毒品走私船的位置.................................................................................- 5 - MCM88问题-B 两辆铁路平板车的装货问题.........................................................................- 6 - MCM89问题-A 蠓的分类.........................................................................................................- 6 - MCM89问题-B 飞机排队.........................................................................................................- 6 - MCM90问题 A 药物在脑内的分布.........................................................................................- 6 - MCM90问题-B 扫雪问题.........................................................................................................- 7 - MCM91问题-B 通讯网络的极小生成树.................................................................................- 7 - MCM 91问题-A估计水塔的水流量........................................................................................- 7 - MCM92问题-A 空中交通控制雷达的功率问题.....................................................................- 7 - MCM 92问题-B 应急电力修复系统的修复计划....................................................................- 7 - MCM93问题-A 加速餐厅剩菜堆肥的生成.............................................................................- 8 - MCM93问题-B 倒煤台的操作方案.........................................................................................- 8 - MCM94问题-A 住宅的保温.....................................................................................................- 9 - MCM 94问题-B 计算机网络的最短传输时间........................................................................- 9 - MCM-95问题-A 单一螺旋线..................................................................................................- 10 - MCM95问题-B A1uacha Balaclava 学院................................................................................- 10 - MCM96问题-A 噪音场中潜艇的探测...................................................................................- 11 - MCM96问题-B 竞赛评判问题...............................................................................................- 11 - MCM97问题-A Velociraptor(疾走龙属)问题..........................................................................- 11 - MCM97问题-B 为取得富有成果的讨论怎样搭配与会成员................................................- 12 - MCM98问题-A 磁共振成像扫描仪.......................................................................................- 12 - MCM98问题-B 成绩给分的通胀...........................................................................................- 13 - MCM99问题-A 大碰撞...........................................................................................................- 13 - MCM99问题-B “非法”聚会...............................................................................................- 14 - MCM2000问题-A 空间交通管制............................................................................................- 14 - MCM2000问题-B: 无线电信道分配......................................................................................- 14 -MCM2001问题- A: 选择自行车车轮.....................................................................................- 15 - MCM2001问题-B 逃避飓风怒吼（一场恶风…）...............................................................- 15 - MCM2001问题-C我们的水系-不确定的前景.......................................................................- 16 - MCM2002问题-A风和喷水池................................................................................................- 16 - MCM2002问题-B航空公司超员订票....................................................................................- 16 - MCM2002问题-C 蜥蜴问题...................................................................................................- 16 - MCM2003问题-A: 特技演员..................................................................................................- 18 - MCM2003问题-B: Gamma刀治疗方案.................................................................................- 18 - MCM2003问题-C航空行李的扫描对策................................................................................- 19 - MCM2004问题-A：指纹是独一无二的吗？.........................................................................- 19 - MCM2004问题-B：更快的快通系统.....................................................................................- 19 - MCM2004问题-C安全与否？................................................................................................- 19 - MCM2005问题 A.水灾计划....................................................................................................- 19 - MCM2005问题 B 收费站问题...............................................................................................- 19 - MCM2005问题C：不可再生的资源.....................................................................................- 20 - MCM2006问题A: 用于灌溉的自动洒水器的安置和移动调度..........................................- 20 - MCM2006问题B: 通过机场的轮椅......................................................................................- 20 - MCM2006问题C : 抗击艾滋病的协调.................................................................................-21 - MCM2007 问题A：不公正的选区划分................................................................................- 23 - MCM2007 问题B：飞机就座问题........................................................................................- 24 - ICM2007 问题C：器官移植：肾交换问题...........................................................................- 24 - MCM2008问题A:给大陆洗个澡............................................................................................- 27 - MCM2008问题B：建立数独拼图游戏.................................................................................- 27 - ICM 2008问题C：寻找好的卫生保健系统...........................................................................- 27 - MCM2009 问题 A 设计一个交通环岛..................................................................................- 28 - MCM2009问题B 能源和手机...............................................................................................- 28 - ICM2009问题C 构建食物系统: 重新平衡被人类影响的生态系统...................................- 29 -校苑数学建模论坛整理MCM85问题-A 动物群体的管理在一个资源有限，即有限的食物、空间、水等等的环境里发现天然存在的动物群体。

数学建模美赛O奖论文

Team Control Number For ofﬁce use only T1 T2 T3 T4
34103
Problem Chosen
For ofﬁce use only F1 F2 F3 F4
A
2015 Mathematical Contest in Modeling (MCM) Summary Sheet
4.3
Model 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . escription . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . Model Establishment . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Concerning the natural transmission of Ebola, an infection disease model is built by the method of ODE (Ordinary Differential Equation).This model estimates the tremendous effects of Ebola in the absence of effective prevention and control measures. With consideration of effective vaccine and medicine, this paper simulates the prevention and control measures against Ebola in the case of sufﬁcient medicine, by modifying the SIQR (Susceptible Infective Quarantine Removed) model. For the problem of transporting the vaccine and medicine, we use the method of MST (Minimum Spanning Tree) to reduce the overall cost of transportation, set the time limit and security points and form a point set of the target areas where the security points, as transit stations, can reach within a limited period of time. And then we use BFS (Breadth-First Search) to search every program which can cover all the points with minimal transfer stations and assign points to their nearest transfer stations to distribute the medicine. This program has taken cost, time and security during the transportation into consideration, in order to make analysis of the optimal solution. Then with the help of the modiﬁed SIQR model, the development of epidemic situation in the whole area can be predicted under the circumstance that vaccine quantity supplied in a supply cycle is determined. Thus a treatment evaluation system is established through calculating the actual mortality rate. On the other hand, vaccine quantity demanded in a supply cycle could be calculated when a certain mortality rate is expected. In the end of this paper, the other factors which may have impacts are considered too, in order to reﬁne the model. And the future works are proposed. In conclusion, four models are established for controlling Ebola. Epidemic situation development are predicted under different circumstances ﬁrstly. Then we built a medicine delivery system for transferring medicine efﬁciently. Based on these, death rate and vaccine quantity demanded could be calculated.

2015年美国数学建模C题获奖成绩

2015 Interdisciplinary Contest in Modeling®Press Release—April 4, 2015COMAP is pleased to announce the results of the 17th annual Interdisciplinary Contest in Modeling (ICM). This year 2137 teams representing institutions from seven countries participated in the contest. Nine teams were designated as OUTSTANDING WINNERS representing the following schools:∙Humboldt State University, (Rachel Carson Award)∙NC School of Science and Mathematics, (INFORMS winner) ∙Xi'an Jiaotong University, China, (Leonhard Euler Award)∙Zhejiang University, China∙Xidian University, China∙Shanghai Jiao Tong University, China∙Xi'an Jiaotong University, China∙Tsinghua University, China∙National University of Defense Technology, ChinaAlso winning as a FINALIST is:∙University of Colorado Denver, (Finalist), (INFORMS winner) This year’s conte st ran from Thursday, February 5 to Monday, February 9, 2015. During that time, teams of three students researched, modeled, and communicated a solution to an open-ended interdisciplinary modeling problem. The 2015 ICM was primarily an online contest, where teams registered and obtained contest materials through COMAP’s ICM W ebsite.Teams chose one of the following two problems: The C Problem involved modeling churn in an organization with the intent of aiding managers and decision makers to build successful systems for recruiting, hiring, training, and evaluating employees. This year the new Problem D focused on the theme of environmental science. Consistent with other ICM problems, the environmental problem challenged teams to utilize science, mathematics, and analysis in their modeling and problem solving. The environmental problem involved developing a model for sustainability and a 20-year sustainable development plan for one country on the United Nations Least Developed Countries list. The teams used their model to evaluate the effect of their 20-year plan on the country’s sustainability. Teams searched for pertinent data and grappled with how economic development must consider ecosystem health and social equitability. Teams came up with creative and geographically relevant solutions.Both problems also had the ever-present ICM requirements to use thorough data analysis, creative modeling, and scientific methodology, along with effective writing and visualization to communicate their teams' results in a 20-page report. A selection from the Outstanding solution papers will be featured in The UMAP Journal, along with commentaries from the problem author and judges. This year’s judges remarked that due to the multi-disciplinary nature of the problems, teams were able to solve these problems using a variety of tools. This allowed teams to showcase their strengths in areas including economics, ecology, environmental sciences, health sciences, public policy, dynamical systems, geo-spatial techniques and network science.2015 ICM Statistics∙2137 Teams participated∙641 Problem C submissions∙1496 Problem D submissions∙45 US Teams (2%)∙2092 Foreign Teams (98%) from China, France, Germany, Indonesia, Singapore and United Kingdom ∙9 Outstanding Winners (1%)∙21 Finalist Winners (1%)∙324 Meritorious Winners (15%)∙919 Honorable Mentions (43%)∙864 Successful Participants (40%)ICM is associated with COMAP’s Mathe matical Contest in Modeling (MCM), which was held during the same weekend. ICM is designed to develop and advance interdisciplinary problem-solving skills in science, technology, engineering, mathematics (STEM) and the humanities, as well as competence in data science and written communication. Over the years the ICM problems have included topics in environmental science, biology, chemistry, resource management, operations research, information science, public health, and network science. Each team is expected to include advisors and team members who represent a range of disciplinary and interdisciplinary interests in applied problem solving and modeling. COMAP is pleased to announce that next year the ICM will add another problem to the options for contestants in the MCM/ICM. In addition to the two ICM problems involving network science and environmental sciences, the ICM will add a third problem in policy modeling. To obtain additional information about the ICM and to obtain a complete listing of all the team designations, please visit the ICM Website at: . Major start-up funding for the ICM was provided by a grant from the National Science Foundation (through Project INTERMATH) and COMAP. Additional support is provided by The Institute for Operations Research and the Management Sciences (INFORMS). COMAP's Mathematical Contest in Modeling and Interdisciplinary Contest in Modeling are unique among modeling competitions in that they are the only international contests in which students work in teams to find a solution. Centering its educational philosophy on mathematical modeling, COMAP uses mathematical tools to explore real-world problems. It serves the educational community as well as the world of work by preparing students to become better informed—and prepared—citizens, consumers, workers, and community leaders.Administered byThe Consortium for Mathematicsand Its ApplicationsContest DirectorsChris Arney, United States Military Academy, NY Tina Hartley, United States Military Academy, NY Executive DirectorSolomon A. Garfunkel, COMAP, Inc., MA。

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 美赛题目及翻译

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.问题A：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可治愈那些得非晚期疾病的患者。

建立一个可行的，明智的，有用的模型，模型不仅要考虑疾病的蔓延、药物的需求量、可能可行的输送系统、输送的位置、疫苗或药物的生产速度，也要考虑你的团队认为有必要作为模型的一部分来优化根除埃博拉病毒，或者至少解决目前压力的其他重要因素。

2015年美赛B题论文

Where is the MH 370?AbstractWhere is the crashed MH 370?This is an issue of global concern. In this article, the search work for the crashed aircraft is divided into three stages:determining the fall area, select the search location, arrange rescue equipment.To solve problems, we have set up three mathematical models.According to physics equations,we have established a differential equations model that can describe the crashed procedure of the aircraft.By combined maritime related cases,we have calculated the theoretical appeared area of the aircraft.Because of the large area of theory, it will be split into many small regions of equal area. With the limited search capability,we need to find a small piece where the aircraft is most likely to exist in.Then we use the conditional probability to establish a maritime search model and have got the actual search area and search paths. Each time a search is completed.We use a Bayesian probability formula to update the appearing probability of the aircraft in each small area if the crashed aircraft is not found.Besides,we resolve the model to acquire the actual search area and search paths.From an economic point of view, we have created a scheduling model of the search appliances with the existed search equipment. Then we made reasonable arrangements for personnel and equipment based on the results of the model.Keywords:Differential Equations Conditional ProbabilityBayesian Methods Nonlinear ProgrammingCONTENTS1. Introduction (2)2. Assumptions (2)3. Explanation of notations (3)4. Model One:the Aircraft Crashed Model4.1 Analysis of Model (4)4.2 Model Building (4)4.3 Solutions to the Model (5)4.3 Testing the Model (6)5. Model Two:the Maritime Search Model5.1 Analysis of Model (6)5.2 Bayesian Methods (7)5.3 Model Building (8)6. Model Three:the Search DevicesScheduling Model6.1 Analysis of Model (8)6.2 Building the Model………………………………………………………….. .86.3 Model Solving........................................................................ (9)7. Conclusions………………………………………………………….………. ..98. Strength and Weakness8.1 Model One (10)8.1 Model Two (10)8.1 Model Three (11)9. References (11)10.Paper Concerning Future Search Plans (12)11. Appendix............................................................................. (14)1.IntroductionAlthough science and technology are advanced rapidly in recent years,the crash incidents still occur now and then .Take Malaysia Airlines MH370 forexample, its crash have already attracted hundreds of millions of people's attention.In the case that it cannot send out any signal, the rescuers have to determine the best search strategy as soon as possible. In addition, due to the diversification of the search appliance, we have given the best scheduling schemes of the search appliance.The problems we have settled are listed as follow:●How to determine fall point of the aircraft in the open sea?●If we can search onlyparticulararea of seaevery time, how to determine thepossible search region?●When some important parameters of search equipment are known,how toget the best scheduling solution of the search devices?In order to deal with those problems above,we found some practical andefficient methods.●At the beginning,we established a physical model to describe theprocedureof the aircraft falling from the sky to the sea and gotthe possible crashedregion of theplane.●Moreover,we built a search model of Bayesian probability updating andobtained more realistic search strategies.●Last but not least,we found optimal scheduling scheme by establishingscheduling model of search equipment based on minimal costs.2. Assumptions●There is no land in the search sea.●The ocean currents in the search sea are very complex.●When the aircraft falls down, the airplane did not explode.●When the aircraft falls down, the plane fuselage remains level.●When the aircraft falls down, its acceleration of gravity remainsunchanged.●There are only two search devices:planes and ships.They can be scheduledtogether.3. Explanation of notationsTable 1 NotationSymbol MeaningG the gravity of the aircraftF rising force of the aircraft from the airf resistanceof the aircraft from the airM quality of the aircrafta horizontal acceleration of the aircraft when falling downxa vertical acceleration of the aircraft when falling downythe density of atmosphereC coefficient of resistancewC coefficient of rising forceuS extension area of aircraftwing1S bottom surface areaof aircraft2v speedin the horizontal directionxv speedin the vertical directionyv advancing speed of searching equipmentT maximum stay time in task searching areaw the width of sweeping the seaS the area of maritime searchregiona the number of the aircraftb the number of the shipv the speed of the aircraft1v the speed of the ship2c the cost of an aircraft per hour1c the cost of a ship per hour2w the scanning width of an aircraft1w the scanning width of a ship2T the maximum time to complete one search taskt the actual time of useto complete one search taskz moving distance of searching equipment in everysmall squarei4. Model One:4.1 Analysis ofModelThe aircraft will fall down after the engine lost power.At this time, the forces of the aircraft are shown in Figure 1. There are the gravity G , rising force F of the aircraft from the air and resistance f of the aircraft from the air.FfGFigure 1the Forces of the AircraftThe acceleration of the aircraft is resolved into horizontal acceleration and vertical acceleration.Thenweestablished dynamic equations in the plane coordinate system.The dynamic equations are:xyf Ma G F Ma =-=Moreover,accelerations are defined as:2222,x y d x d y a a dt dt==By referring to material,we knew about the formulas below.21221212w x u yf C S v F C S v ρρ==4.2 Model BuildingConsequently,the model can be summarized as the differential equations below.222222112122dx d x C S M w dt dt dy d yC S Mg M u dt dt ρρ⎧⎛⎫=⎪ ⎪⎪⎝⎭⎨⎛⎫⎪=- ⎪⎪⎝⎭⎩ The initial conditionsare described as follow:()()00240,000,010000t t dx dy dt dt x y ==⎧==⎪⎨⎪==⎩4.3 Solutions to the ModelBy looking for information,we acquired relevant information of Malaysia Airlines MH370 as shown in Table 2.Table 2 Related Parameters of MH370Use MATLAB to solve the equations.It takes 81.9071 seconds for MH370to crash into the sea.When it crashed into the sea,itsspeedin the horizontal direction is167.3729 minutes per second and speed in the vertical direction is 138.6997 minutes per second.Besides,its Abscissa X is 16328 meters while ordinate Y is 0.0062 meters. Additionally,we obtained curve of solutions for the equations by MATLAB .The crashed track of MH370 is shown in Figure 2.Figure 2the Crashed Track of MH3700.20.40.60.81 1.2 1.4 1.61.82x 104010002000300040005000600070008000900010000Horizontal distance/meterV e r t i c a l d i s t a n c e /m e t e rM 200000kg30.849/kg mw C 0.08 u C1.21S2130m 2S2200m4.4 Testing the ModelIn the Aircraft Crashed Model, we cannot calculate the exact crashed time of the plane due to a computer error. But the error is within a certain range(0.62%), and therefore results of the model are with higher confidence.5. Model Two:the Maritime Search Model5.1 Analysis of ModelIn Model One, we determined the theoretical placement of the aircraft.However, it may still be some distance aheadafter the plane lost contact with the flight.So it is possible to translate the theoretical impact point forward along the original direction of flight of the aircraft.Regard the round having a circle of theoretical placement and a radius of twenty kilometers as the search area.Then round collections whose circles are in a straight line are set as the possible search area, shown in Figure 3.Figure 3 Searching AreaIn order to facilitate the solution to the problem, we make this area approximately a rectangular region, as shown in Figure 4.Figure 4 Rectangle Area of SearchingThis area is divided into small squares with the number of N . What ’s more, we suppose the event ()1,2,,i B i N = stands for the incident that the aircraft is in the small square i and the event A represents the incident that the plane crashed. Therefore, the probability of the plane crashed just into a small square i .()()()i i P A B P B P A B ⋂=Material that we have found shows that:()1i z wi P A B e-=-Here, we assumed that the probability of search at first time.()1,1,2,,i P B i N N==5.2 B ayesian MethodsBayesian analysis, a method of statistical inference (named forEnglish mathematician Thomas Bayes) that allowsone to combine prior information about a population parameter with evidence from information contained in a sample to guide the statistical inference process. A prior probability distribution for a parameter of interest is specified first. The evidence is then obtained and combined through an application of Bayesian theorem to provide a posteriorprobability distribution for the parameter. The posteriordistribution provides the basis for statistical inferences concerning the parameter.The Bayes Formula is represented as follow:1()(|)()(|)(1,2,,)()(|)()i i i i n i i i P A B P B A P A P A B i n P B P B A P A =⋂===∑5.3 Model Building ● Optimization ModelAs a result, we have come to the optimization model search.()()()()(1)(1)()(1)(1)()max 1.,,{1,2,,}n n in x x z wi i i x i x x i i x n f P A B P B e z vT st x x N -===⎛⎫=⋂=- ⎪⎝⎭⎧≤⎪⎨⎪∈⎩∑∑∑● Information UpdatingThe first t + 1 time search, we have to update the probability of the incident according to existing information.The corresponding formulas are represented as follow.As for the small square area having been searched in the first t time search:()()(1)(1)()1{,}()()()ijn n z wt i t i z x wt j t j j x j x x eP B P B eP B P B -+-=∉=+∑∑As for the small square area having not been searched in the first t time search:()()(1)(1)()1{,}()()()j n n t i t i z x wt j t j j x j x x P B P B eP B P B +-=∉=+∑∑6. Model Three: the Search DevicesScheduling Model6.1 Analysis of ModelWe regarded minimum costsas the goal of the model. From this, we can create scheduling model of the search appliances.6.2 Building the ModelBased on the goal of minimum costs, we established scheduling model of the search equipment.121122024300min C =xc t yc t v w t x v w t y S t Txy x a y b ++≥⎧⎪≤⎪⎪≥⎨⎪≤≤⎪⎪≤≤⎩6.3 Model SolvingThrough relevant information, we set some parameters as follow.There are ten aircrafts with the cost of one hundred dollars per hour, a search speed of seven hundred kilometers per hour and the sweep width of one kilometer. There are thirty vessels with the cost of thirty dollars per hour, a search speed of one hundred kilometers per hour and the sweep width of one kilometer.The total search area is 8100 square kilometers and search tasks must be completed within fifteen days.With the LINGO software,we calculated the optimal scheduling scheme: nine aircrafts, three ships. Thus it took 1.23 hours to accomplish search tasks and the smallest search cost is 1,215 dollars7. Conclusions● the Aircraft Crashed ModelBy referring to material, the horizontal velocity and vertical velocity of the airplane cannot disintegrate the plane when it crashed. The assumption that the airplane did not explode has been proved reasonable.But in reality, when the aircraft's engine failed, the pilot would lower theaircraft nose.The aircraft glide a distance as well.Thus falling direction of the aircraft was not level.As a result, there exists a certain bias between the calculation results of the model and the actual situation.● the Maritime Search ModelAfter determining maritime search area, due to the complex situation at sea, when we first searched for the location information of the aircraft, we made no more accurate inference.Therefore, we thought that the probability that the aircraft appeared in any point of search area is the same. So before the first search, all the waters aretheoretically equal area most likely to find the location of the aircraft.If the aircraft is not found after the first end of the search, then we used Bayesian approach to update the probability of finding the aircraft in each region. We re-solved the maritime search model.As expected,we found the aircraft position and the sea search path of the maximum probability.●the Search DevicesScheduling ModelAccording to the actual situation, the best scheduling solution is using nine aircrafts and three ships.This scheme can ensure the completion of the search task with minimal costs. But how much actual work time spent searching is a more important factor, it was not taken into consideration in the program given above.8. Strength and Weakness8.1Model OneStrength●The model is reasonable by model testing.●Solutions to the differential dynamic equations we established are easy toimplement.●We have found the theoretical crashed placement of Malaysia AirlinesMH370.Weakness●Only the method of calculating crashed site is given.●There are no discussions about the possible region that the aircraft may fellinto.8.2Model TwoStrength●Basedon Bayesian methods, we have proposed the practical detectionprobability model.●Discuss the crash probability at various points in the searching area.Weakness●We possibly found additional information about the new discovery ofaircraft debris and the location of black box signal. Additionalinformationhad an effect on Bayesian Information updating. Furthermore, it was nottaken into consideration.8.3Model ThreeStrength●Regard minimalcosts as the goal.●Discuss the dispatch of search and rescue equipmentWeakness●The model may lead to a waste of time owing to the blind pursuit oflowcosts.9. References[1]The Aircraft Lost Contact Search Program Based on Differential Equations and NonlinearProgramming[EB/OL]./link?url=pZh0bMYn_L52FQbTUhqdnqb6pz6pztQ8AqogpF_ E6XVQoOyrotdHIUR1soKPU2FlI5kXdzjana6oIA7Wpn7TG2KVFESRN5J9NrRz9 YG8CPS. 2015-11-2[2]Zhou Changyin, Zhao Yutang, Sun Yaxing.Updating Crashed Plane Detection Probability Model Based on Bayesian Information [J] mathematical modeling and its applications, 2015,4 (2): 71-78[3]Wu ing Mathematical Methods to Find theWreckage[J]. Science Humanities.[4]The Problem of Finding the Black Box Model Based on Maritime Search and GlobalOptimization[EB/OL]./link?url=KrdxNu5Dwuv7iltDrKzx1OQxK1u89X5TqfgUT_F zeORa4jACo_FQAdVu7oIqsIfXO903eHOIYp3RkMXRjx4nR9Pm6X1R4VhXrDt6g TttIWe. 2015-9-610. Paper Concerning Future SearchPlansOn March 8th of 2014,Malaysia Airlines MH370 burst out crashing at twenty-two past oneof Malaysia Local Time. It lost contact with Air Traffic Control during a transition of airspace between Malaysia and Vietnam whilst en-route to Beijing.There were 227 passengers,2 flight crews and 10 cabin crews on board.Today, standing here, we must first extend our deepest apologies to families of the victims, we will try to find the truth about the crash with the fastest speed at all costs to give an account of the victims.For the future of search, we developed a rigorous program, which is divided into three stages: find the general area of the aircraft crashed in the sea, search the most likely location of aircraft in this area, and find equipment and personnel participating in the search arrangements search for work in a timely manner. Next I will describe the three stages in detail:First of all, through studying historical data and information returned before the crash, we identified the aircraft may fall on a rectangular sea. Due to the large area of this sea, we try to find a small sea where the plane is available with the most possibility, in order to ensure the timeliness of search efforts, we mainly use aircraft to search with the aid of ship and work immediately after the best scheduling solution decided, we will continue to repeat the process until we find the crashed plane eventually.We once again express our sympathy to all those who have been affected by the terrible accident. It has been a hard time for all who have tried their best in the search for MH370.We have never wavered in our commitment to continue our efforts to find MH370 and bring closure for everyone, most of all for the families of the passengers and crew of MH370.11. AppendixSolving the plane crashed Model:function [k,vx,vy,xx,yy]=zhuiluo(t0)for t=t0:0.0001:90if(20000-(-7000/849*283^(1/2)*t+5000000/2547*log(1/2*exp(2547/500+21/2500*28 3^(1/2)*t)+1/2*exp(2547/500)))<=0)k=t;break;endendt=0:0.0001:k;x=500000000/11037*log(33111/6250000.*t+1);y=20000-(-7000/849*283^(1/2).*t+5000000/2547*log(1/2*exp(2547/500+21/2500*2 83^(1/2).*t)+1/2*exp(2547/500)));plot(x,y);xx=500000000/11037*log(33111/6250000*k+1);yy=20000-(-7000/849*283^(1/2)*k+5000000/2547*log(1/2*exp(2547/500+21/2500* 283^(1/2)*k)+1/2*exp(2547/500)));vx=240/(33111/6250000*k+1);vy=7000/849*283^(1/2)-7000/849*283^(1/2)*exp(2547/500+21/2500*283^(1/2)*k)/( 1/2*exp(2547/500+21/2500*283^(1/2)*k)+1/2*exp(2547/500));axis([0,20000,0,10000]);grid on;xlabel('Horizontal distance/meter');ylabel('Vertical distance/meter');legend('Plane crashed track');Find the best possible position of aircraft:model:sets:num/1..81/:x;endsetsmax=@sum(num(i):1/810-1/810*e^(-0.01*x(i)));@for(num(i):@sum(num(j):x(j))=300);@for(num:@GIN(x));endThe optimal scheduling program of search device:model:sets:num/1/:x,y,t;endsetsmin=@sum(num:100*x*t+30*y*t);@for(num:700*t*x+100*y*t>=8100);@for(num:t<=24*15);@for(num:y>=x/3);@for(num:@GIN(x);@GIN(y););@for(num:@BND(0,x,10);@BND(0,y,30));end。

2015年全国大学生英语竞赛C类样题参考答案及听力原文

2015年全国大学生英语竞赛C类样题参考答案及听力原文2015National English Competitionfor College Students(Level C-Sample)参考答案及评分标准Part I Listening Comprehension(30marks)Section A(5marks)1—5BBACASection B(5marks)6—10CADCD11—15BCADBSection C(10marks)16—20BADCASection D(10marks)21.marine22.into air23.defense mechanism24.dates back to25.evolved26.hide and escape 27.upward out28.is comparable to29.in popularity30.raised tensionsPart II Vocabulary and Structure(15marks)Section A(10marks)31—35CBDBA36—40BBCADSection B(5marks)41—45ABCDAPart III Cloze(10marks)46.artificially47.being48.modification49.example50.support ers51.shortage52.Nevertheless53.unusual54.lead55.containingPart IV Reading Comprehension(35marks)Section A(5marks)56.F57.T58.T59.F60.TSection B(10marks)61—65GFDBESection C(10marks)66.It is located at the corner of77th Street in New York.67.In1804.68.Because it was founded at a time when the nation wasbarely three decades old and only eccentric were collecting American artifacts and ephemera.69.By the1890s,dozens of volumes had been published about New York,studying its origin and rise, celebrating its progress and its new fame.70.The unsung glories like civic documents,scrapbooks and diaries,architectural drawings,street1--photographs and old books.Section D (10marks)71.proven 72.innocence 73.reach 74.biases 75.fundamentalPart V Translation (15marks)Section A (5marks)76.圣诞节是自我放纵的节日，人们消费大量的甜品和巧克力，这也是一个尽情豪饮的好时机。

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