《全国大学生数学建模竞赛通讯》-2001美赛数模MCM全部原题及翻译
历届美国数学建模竞赛赛题(汉语版)
历届美国数学建模竞赛赛题, 1985－2006AMCM1985问题-A 动物群体的管理AMCM1985问题-B 战购物资储备的管理AMCM1986问题-A 水道测量数据AMCM1986问题-B 应急设施的位置AMCM1987问题-A 盐的存贮AMCM1987问题-B 停车场AMCM1988问题-A 确定毒品走私船的位置AMCM1988问题-B 两辆铁路平板车的装货问题AMCM1989问题-A 蠓的分类AMCM1989问题-B 飞机排队AMCM1990问题-A 药物在脑内的分布AMCM1990问题-B 扫雪问题AMCM1991问题-A 估计水塔的水流量AMCM1992问题-A 空中交通控制雷达的功率问题AMCM1992问题-B 应急电力修复系统的修复计划AMCM1993问题-A 加速餐厅剩菜堆肥的生成AMCM1993问题-B 倒煤台的操作方案AMCM1994问题-A 住宅的保温AMCM1994问题-B 计算机网络的最短传输时间AMCM1995问题-A 单一螺旋线AMCM1995问题-B A1uacha Balaclava学院AMCM1996问题-A 噪音场中潜艇的探测AMCM1996问题-B 竞赛评判问题AMCM1997问题-A Velociraptor(疾走龙属)问题AMCM1997问题-B为取得富有成果的讨论怎样搭配与会成员AMCM1998问题-A 磁共振成像扫描仪AMCM1998问题-B 成绩给分的通胀AMCM1999问题-A 大碰撞AMCM1999问题-B “非法”聚会AMCM1999问题- C 大地污染AMCM2000问题-A空间交通管制AMCM2000问题-B: 无线电信道分配AMCM2000问题-C：大象群落的兴衰AMCM2001问题- A: 选择自行车车轮AMCM2001问题-B：逃避飓风怒吼（一场恶风…）AMCM2001问题-C我们的水系-不确定的前景AMCM2002问题-A风和喷水池AMCM2002问题-B航空公司超员订票AMCM2002问题-C蜥蜴问题AMCM2003问题-A: 特技演员AMCM2003问题-C航空行李的扫描对策AMCM2004问题-A：指纹是独一无二的吗？AMCM2004问题-B：更快的快通系统AMCM2004问题-C：安全与否？AMCM2005问题-A：.水灾计划AMCM2005问题-B：TollboothsAMCM2005问题-C：.Nonrenewable ResourcesAMCM2006问题-A：用于灌溉的自动洒水器的安置和移动调度AMCM2006问题-B：通过机场的轮椅AMCM2006问题-C：在与HIV/爱滋病的战斗中的交易AMCM85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。
2001年真题及解析
2001年全国攻读硕士学位研究生入学考试英语试题Part I Cloze TestDirections：For each numbered blank in the following passage, there are four choices marked [A], [B], [C] and [D]. Choose the best one and mark your answer on ANSWER SHEET 1 by blackening the corresponding letter in the brackets with a pencil. (10 points)The government is to ban payments to witnesses by newspapers seeking to buy up people involved in prominent cases 1 the trial of Rosemary West.In a significant 2 of legal controls over the press, Lord Irvine, the Lord Chancellor, will introduce a 3 bill that will propose making payments to witnesses 4 and will strictly control the amount of 5 that can be given to a case 6 a trial begins.In a letter to Gerald Kaufman, chairman of the House of Commons media select committee, Lord Irvine said he 7 with a committee report this year which said that self regulation did not 8 sufficient control.9 of the letter came two days after Lord Irvine caused a 10 of media protest when he said the 11 of privacy controls contained in European legislation would be left to judges 12 to Parliament.The Lord Chancellor said introduction of the Human Rights Bill, which 13 the European Convention on Human Rights legally 14 in Britain, laid down that everybody was 15 to privacy and that public figures could go to court to protect themselves and their families.“Press freedoms will be in safe hands 16 our British judges,” he said.Witness payments became an 17 after West was sentenced to 10 life sentences in 1995. Up to 19 witnesses were 18 to have received payments for telling their stories to newspapers. Concerns were raised 19 witnesses might be encouraged exaggerate their stories in court to 20 guilty verdicts.1.［A］as to ［B］for instance ［C］in particular ［D］such as2.［A］tightening ［B］intensifying ［C］focusing ［D］fastening3.［A］sketch ［B］rough ［C］preliminary ［D］draft4.［A］illogical ［B］illegal ［C］improbable ［D］improper5.［A］publicity ［B］penalty ［C］popularity ［D］peculiarity6.［A］since ［B］if ［C］before ［D］as7.［A］sided ［B］shared ［C］complied ［D］agreed8.［A］present ［B］offer ［C］manifest ［D］indicate9.［A］Release ［B］Publication ［C］Printing ［D］Exposure10.［A］storm ［B］rage ［C］flare ［D］flash11.［A］translation ［B］interpretation ［C］exhibition ［D］demonstration12.［A］better than ［B］other than ［C］rather than ［D］sooner than13.［A］changes ［B］makes ［C］sets ［D］turns14.［A］binding ［B］convincing ［C］restraining ［D］sustaining15.［A］authorized ［B］credited ［C］entitled ［D］qualified16.［A］with ［B］to ［C］from ［D］by17.［A］impact ［B］incident ［C］inference ［D］issue18.［A］stated ［B］remarked ［C］said ［D］told19.［A］what ［B］when ［C］which ［D］that20.［A］assure ［B］confide ［C］ensure ［D］guaranteePart II Reading ComprehensionDirections:Each of the passages below is followed by some questions. For each questions there are four answers marked [A], [B], [C] and [D]. Read the passages carefully and choose the best answer to each of the questions. Then mark your answer on ANSWER SHEET 1 by blackening the corresponding letter in the brackets with a pencil. (40 points)Passage 1Specialisation can be seen as a response to the problem of an increasing accumulation of scientific knowledge. By splitting up the subject matter into smaller units，one man could continue to handle the information and use it as the basis for further research. But specialisation was only one of a series of related developments in science affecting the process of communication. Another was the growing professionalisation of scientific activity.No clear-cut distinction can be drawn between professionals and amateurs in science: exceptions can be found to any rule. Nevertheless, the word “amateur”does carry a connotation that the person concerned is not fully integrated into the scientific community and, in particular, may not fully share its values. The growth of specialisation in the nineteenth century, with its consequent requirement of a longer, more complex training, implied greater problems for amateur participation in science. The trend was naturally most obvious in those areas of science based especially on a mathematical or laboratory training, and can be illustrated in terms of the development of geology in the United Kingdom.A comparison of British geological publications over the last century and a half reveals not simply an increasing emphasis on the primacy of research, but also a changing definition of what constitutes an acceptable research paper. Thus, in the nineteenth century, local geological studies represented worthwhile research in their own right; but, in the twentieth century, local studies have increasingly become acceptable to professionals only if they incorporate, and reflect on, the wider geological picture. Amateurs, on the other hand, have continued to pursue local studies in the old way. The overall result has been to make entrance to professionalgeological journals harder for amateurs, a result that has been reinforced by the widespread introduction of refereeing, first by national journals in the nineteenth century and then by several local geological journals in the twentieth century. As a logical consequence of this development, separate journals have now appeared aimed mainly towards either professional or amateur readership. A rather similar process of differentiation has led to professional geologists coming together nationally within one or two specific societies, whereas the amateurs have tended either to remain in local societies or to come together nationally in a different way.Although the process of professionalisation and specialisation was already well under way in British geology during the nineteenth century, its full consequences were thus delayed until the twentieth century. In science generally, however, the nineteenth century must be reckoned as the crucial period for this change in the structure of science.21. The growth of specialisation in the 19th century might be more clearly seen insciences such as _______.[AJ sociology and chemistry [B] physics and psychology[C] sociology and psychology [D] physics and chemistry22. We can infer from the passage that _______.[A] there is little distinction between specialisation and professionalisation[B] amateurs can compete with professionals in some areas of science[C] professionals tend to welcome amateurs into the scientific community[D] amateurs have national academic societies but no local ones23. The author writes of the development of geology to demonstrate ______.[A] the process of specialisation and professionalisation[B] the hardship of amateurs in scientific study[C] the change of policies in scientific publications[D] the discrimination of professionals against amateurs24. The direct reason for specialisation is _______.[A] the development in communication[B] the growth of professionalisation[C] the expansion of scientific knowledge[D] the splitting up of academic societiesPassage 2A great deal of attention is being paid today to the so-called digital divide-the division of the world into the info (information) rich and the info poor. And that divide does exist today. My wife and I lectured about this looming danger twenty years ago. What was less visible then, however, were the new, positive forces that work against the digital divide. There are reasons to be optimistic.There are technological reasons to hope the digital divide will narrow. As the Internet becomes more and more commercialized, it is in the interest of businessto universalize access-after all, the more people online, the more potential customers there are. More and more governments, afraid their countries will be left behind, want to spread Internet access. Within the next decade or two, one to two billion people on the planet will he netted together. As a result, I now believe the digital divide will narrow rather than widen in the years ahead. And that is very good news because the Internet may well be the most powerful tool for combating world poverty that we’ve ever had.Of course, the use of the Internet isn’t the only way to defeat poverty. And the Internet is not the only tool we have. But it has enormous potential.To take advantage of this tool, some impoverished countries will have to get over their outdated anti-colonial prejudices with respect to foreign investment. Countries that still think foreign investment is an invasion of their sovereignty might well study the history of infrastructure（the basic structural foundations of a society）in the United States. When the United States built its industrial infrastructure, it didn’t have the capital to do so. And that is why America’s Second Wave infrastructure-including roads, harbors, highways, ports and so on-were built with foreign investment. The English, the Germans, the Dutch and the French were investing in Britain’s former colony. They financed them. Immigrant Americans built them. Guess who owns them now? The Americans. I believe the same thing would be true in places like Brazil or anywhere else for that matter. The more foreign capital you have helping you build your Third Wave infrastructure, which today is an electronic infrastructure, the better off you’re going to be. That doesn't mean lying down and becoming fooled, or letting foreign corporations run uncontrolled. But it does mean recognizing how important they can be in building the energy and telecom infrastructures needed to take full advantage of the Internet.25. Digital divide is something _______.[A] getting worse because of the Internet[B] the rich countries are responsible for[C] the world must guard against[D] considered positive today26. Governments attach importance to the Internet because it _______.[A] offers economic potentials[B] can bring foreign funds[C] can soon wipe out world poverty[D] connects people all over the world27. The writer mentioned the case of the United States to justify the policy of_______.[A] providing financial support overseas[B] preventing foreign capital’s control[C] building industrial infrastructure[D] accepting foreign investment28. It seems that now a country’s economy depands much on ______.[A] how well-developed it is electronically[B] whether it is prejudiced against immigrants[C] whether it adopts America’s industrial pattern[D] how much control it has over foreign corporationsPassage 3Why do so many Americans distrust what they read in their newspapers? The American Society of Newspaper Editors is trying to answer this painful question. The organization is deep into a long self-analysis known as the journalism credibility project.Sad to say, this project has turned out to be mostly low-level findings about factual errors and spelling and grammar mistakes, combined with lots of headscratching puzzlement about what in the world those readers really want.But the sources of distrust go way deeper. Most journalists learn to see the world through a set of standard templates (patterns) into which they plug each day’s events. In other words, there is a conventional story line in the newsroom culture that provides a backbone and a ready-made narrative structure for otherwise confusions news.There exists a social and cultural disconnect between journalists and their readers which helps explain why the “standard templates”of the newsroom seem alien many readers. In a recent survey, questionnaires were sent to reporters in five middle size cities around the country, plus one large metropolitan area. Then residents in these communities were phoned at random and asked the same questions.Replies show that compared with other Americans, journalists are more likely to live in upscale neighborhoods, have maids, own Mercedeses, and trade stocks, and they’re less likely to go to church, do volunteer work, or put down roots in community.Reporters tend to be part of a broadly defined social and cultural elite, so their work tends to reflect the conventional values of this elite. The astonishing distrust of the news media isn’t rooted in inaccuracy or poor reportorial skills but in the daily clash of world views between reporters and their readers.This is an explosive situation for any industry, particularly a declining one. Here is a troubled business that keeps hiring employees whose attitudes vastly annoy the customers. Then it sponsors lots of symposiums and a credibility project dedicated to wondering why customers are annoyed and fleeing in large numbers. But it never seems to get around to noticing the cultural and class biases that so many former buyers are complaining about. If it did, it would open up its diversity program, now focused narrowly on race and gender, and look for reporters who differ broadly by outlook, values, education, and class.29. What is the passage mainly about?[A] needs of the readers all over the world.[B] causes of the public disappointment about newspapers.[C] origins of the declining newspaper industry.[D] aims of a journalism credibility project.30. The results of the journalism credibility project turned out to be ______.[A] quite trustworthy [B] somewhat contradictory[C] very illuminating [D] rather superficial31. The basic problem of journalists as pointed out by the writer lies in their______.[A] working attitude [B] conventional lifestyle[C] world outlook [D] educational background32. Despite its efforts, the newspaper industry still cannot satisfy the readersowing to its_______.[A] failure to realize its real problem[B] tendency to hire annoying reporters[C] likeliness to do inaccurate reporting[D] prejudice in matters of race and genderPassage 4The world is going through the biggest wave of mergers and acquisitions ever witnessed. The process sweeps from hyperactive America to Europe and reaches the emerging countries with unsurpassed might. Many in these countries are looking at this process and worrying: "Won't the wave of business concentration turn into an uncontrollable anti-competitive force?"There's no question that the big are getting bigger and more powerful. Multinational corporations accounted for less than 20% of international trade in 1982. Today the figure is more than 25% and growing rapidly. International affiliates account for a fast-growing segment of production in economies that open up and welcome foreign investment. In Argentina, for instance, after the reforms of the early 1990s, multinationals went from 43% to almost 70% of the industrial production of the 200 largest firms. This phenomenon has created serious concerns over the role of smaller economic firms, of national businessmen and over the ultimate stability of the world economy.I believe that the most important forces behind the massive M&A wave are the same that underlie the globalization process: falling transportation and communication costs, lower trade and investment barriers and enlarged markets that require enlarged operations capable of meeting customers' demands. All these are beneficial, not detrimental, to consumers. As productivity grows, the world's wealth increases.Examples of benefits or costs of the current concentration wave are scanty. Yet it is hard to imagine that the merger of a few oil firms today could re-create the same threats to competition that were feared nearly a century ago in the U.S., when the Standard Oil trust was broken up. The mergers of telecom companies, such as WorldCom, hardly seem to bring higher prices for consumers or a reduction in thepace of technical progress. On the contrary, the price of communications is coming down fast. In cars, too, concentration is increasing-witness Daimler and Chrysler, Renault and Nissan-but it does not appear that consumers are being hurt.Yet the fact remains that the merger movement must be watched. A few weeks ago, Alan Greenspan warned against the megamergers in the banking industry. Who is going to supervise, regulate and operate as lender of last resort with the gigantic banks that are being created? Won't multinationals shift production from one place to another when a nation gets too strict about infringements to fair competition? And should one country take upon itself the role of “defending competition”on issues that affect many other nations, as in the U S. vs. Microsoft case ?33. What is the typical trend of businesses today?[A] to take in more foreign funds. [B] to invest more abroad.[C] to combine and become bigger. [D] to trade with more countries.34. According to the author, one of the driving forces behind M&A wave is ______[A] the greater customer demands. [B] a surplus supply for the market.[C] a growing productivity. [D] the increase of the world's wealth.35. From paragraph 4 we can infer that ______.[A] the increasing concentration is certain to hurt consumers[B] WorldCom serves as a good example of both benefits and costs[C] the costs of the globalization process are enormous[D] the Standard Oil trust might have threatened competition36. Toward the new business wave, the writer's attitude can he said to be _______.[A] optimistic [B] objective[C] pessimistic [D] biasedPassage 5When I decided to quit my full time employment it never occurred to me that I might become a part of a new international trend. A lateral move that hurt my pride and blocked my professional progress prompted me to abandon my relatively high profile career although, in the manner of a disgraced government minister, I covered my exit by claiming “I wanted to spend more time with my family”.Curiously, some two-and-a-half years and two novels later, my experiment in what the Americans term “downshifting”has turned my tired excuse into an absolute reality. I have been transformed from a passionate advocate of the philosophy of “having it all”, preached by Linda Kelsey for the past seven years in the pages of She magazine, into a woman who is happy to settle for a bit of everything.I have discovered, as perhaps Kelsey will after her much-publicized resignation from the editorship of She after a build-up of stress, that abandoning the doctrine of “juggling your life”, and making the alternative move into “downshifting”brings with it far greater rewards than financial success and social status. Nothing could persuade me to return to the kind of life Kelsey used to advocate and I onceenjoyed: 12-hour working days, pressured deadlines, the fearful strain of office politics and the limitations of being a parent on “quality time”.In America, the move away from juggling to a simpler, less materialistic lifestyle is a well-established trend. Downshifting-also known in America as “voluntary simplicity” has, ironically, even bred a new area of what might be termed anticonsumerism. There are a number of bestselling downshifting self-help books for people who want to simplify their lives; there are newsletter's, such as The Tightwad Gazette, that give hundreds of thousands of Americans useful tips on anything from recycling their cling-film to making their own soap; there are even support groups for those who want to achieve the mid- '90s equivalent of dropping out.While in America the trend started as a reaction to the economic decline——after the mass redundancies caused by downsizing in the late’80s——and is still linked to the politics of thrift, in Britain, at least among the middle-class downshifters of my acquaintance, we have different reasons for seeking to simplify our lives.For the women of my generation who were urged to keep juggling through the’80s, downshifting in the mid-'90s is not so much a search for the mythical good life ——growing your own organic vegetables, and risking turning into one——as a personal recognition of your limitations.37. Which of the following is true according to paragraph 1?[A] Full-time employment is a new international trend.[B] The writer was compelled by circumstances to leave her job.[C] “A lateral move” means stepping out of full-time employment.[D] The writer was only too eager to spend more time with her family.38. The writer’s experiment shows that downshifting ____[A] enables her to realize her dream[B] helps her mold a new philosophy of life[C] prompts her to abandon her high social status[D] leads her to accept the doctrine of She magazine39. “Juggling one’s life” probably means living a life characterized by_____.[A] non-materialistic lifestyle [B] a bit of everything[C] extreme stress [D] anti-consumerism40. According to the passage, downshifting emerged in the U.S. as a result of _____[A] the quick pace of modern life [B] man’s adventurous spirit[C] man’s search for mythical experiences [D] the economic situationPart III English-Chinese TranslationDirections:Read the following text carefully and then translate the underlined segments intoChinese. Your translation should be written clearly on ANSWER SHEET 2. (15 points)In less than 30 years’ time the Star Trek holodeck will be a reality. Direct links between the br ain’s nervous system and a computer will also create full sensory virtual environments, allowing virtual vacations like those in the film Total Recall.41）There will be television chat shows hosted by robots, and cars with pollution monitors that will disable them when they offend. 42）Children will play with dolls equipped with personality chips, computers with in-built personalities will be regarded as workmates rather than tools, relaxation will be in front of smell television, and digital age will have arrived.According to BT’s futurologist, Ian Pearson, these are among the developments scheduled for the first few decades of the new millennium（a period of 1,000 years）, when supercomputers will dramatically accelerate progress in all areas of life.43）Pearson has pieced together the work of hundreds of researchers around the world to produce a unique millennium technology calendar that gives the latest dates when we can expect hundreds of key breakthroughs and discoveries to take place. Some of the biggest developments will be in medicine, including an extended life expectancy and dozens of artificial organs coming into use between now and 2040.Pearson also predicts a breakthrough in computer-human links. “By linking directly to our nervous system, computers could pick up what we feel and, hopefully, simulate feeling too so that we can start to develop full sensory environments, rather like the holidays i n Total Recall or the Star Trek holodeck, ” he says. 44）But that, Pearson points out, is only the start of man-machine integration: “It will be the beginning of the long process of integration that will ultimately lead to a fully electronic human before the end of the next century.”Through his research, Pearson is able to put dates to most of the breakthroughs that can be predicted. However, there are still no forecasts for when faster-than-light travel will be available, or when human cloning will be perfected, or when time travel will be possible. But he does expect social problems as a result of technological advances. A boom in neighborhood surveillance cameras will, for example, cause problems in 2010, while the arrival of synthetic lifelike robots will mean people may not be able to distinguish between their human friends and the droids. 45）And home appliances will also become so smart that controlling and operating them will result in the breakout of a new psychological disorder—kitchen rage.Section V Writing46. Directions:Among all the worthy feelings of mankind, love is probably the noblest, but everyone has his/her own understanding of it.There has been a discussion recently on the issue in a newspaper. Write an essay to the newspaper to1）show your understanding of the symbolic meaning of the picture below.2）give a specific example, and3）give your suggestion as to the best way to show love.第一部分英语知识应运试题解析一、文章总体分析本文是一篇报道性的文章，介绍了自露丝玛莉·韦斯特案件发生后，政府、法院、媒体各方面对于付款给证人的反应。
2001年全国大学生数学建模竞赛题
2001年全国大学生数学建模竞赛题目A题血管的三维重建断面可用于了解生物组织、器官等的形态。
例如，将样本染色后切成厚约1m m的切片，在显微镜下观察该横断面的组织形态结构。
如果用切片机连续不断地将样本切成数十、成百的平行切片，可依次逐片观察。
根据拍照并采样得到的平行切片数字图象，运用计算机可重建组织、器官等准确的三维形态。
假设某些血管可视为一类特殊的管道，该管道的表面是由球心沿着某一曲线（称为中轴线）的球滚动包络而成。
例如圆柱就是这样一种管道，其中轴线为直线，由半径固定的球滚动包络形成。
现有某管道的相继100张平行切片图象，记录了管道与切片的交。
图象文件名依次为0.bmp、1.bmp、…、 99.bmp，格式均为BMP，宽、高均为512个象素（pixel）。
为简化起见，假设：管道中轴线与每张切片有且只有一个交点；球半径固定；切片间距以及图象象素的尺寸均为1。
取坐标系的Z轴垂直于切片，第1张切片为平面Z=0，第100张切片为平面Z=99。
Z=z切片图象中象素的坐标依它们在文件中出现的前后次序为（-256，-256，z），（-256，-255，z），…（-256，255，z），（-255，-256，z），（-255，-255，z），…（-255，255，z），……（ 255，-256，z），（ 255，-255，z），…（255，255，z）。
试计算管道的中轴线与半径，给出具体的算法，并绘制中轴线在XY、YZ、ZX平面的投影图。
第2页是100张平行切片图象中的6张，全部图象请从网上下载。
/mcm/MCM01/A01BMP.ZIP关于BMP图象格式可参考：1. 《Visual C++数字图象处理》第12页2.3.1节。
何斌等编著，人民邮电出版社，2001年4月。
2. /home/mxr/gfx/2d/BMP.txtB题公交车调度公共交通是城市交通的重要组成部分，作好公交车的调度对于完善城市交通环境、改进市民出行状况、提高公交公司的经济和社会效益，都具有重要意义。
2001年全国大学生数学建模竞赛题目 .doc
2001年全国大学生数学建模竞赛题目●答卷用A4纸，论文题目和摘要写在第一页上，不能有其他任何标志。
●从今年起，将提高摘要在整篇论文评阅中所占的权重。
●全部题目（包括数据）可以从以下网址下载：A题血管的三维重建断面可用于了解生物组织、器官等的形态。
例如，将样本染色后切成厚约1 m的切片，在显微镜下观察该横断面的组织形态结构。
如果用切片机连续不断地将样本切成数十、成百的平行切片，可依次逐片观察。
根据拍照并采样得到的平行切片数字图象，运用计算机可重建组织、器官等准确的三维形态。
假设某些血管可视为一类特殊的管道，该管道的表面是由球心沿着某一曲线（称为中轴线）的球滚动包络而成。
例如圆柱就是这样一种管道，其中轴线为直线，由半径固定的球滚动包络形成。
现有某管道的相继100张平行切片图象，记录了管道与切片的交。
图象文件名依次为0.bmp、1.bmp、…、 99.bmp，格式均为BMP，宽、高均为512个象素（pixel）。
为简化起见，假设：管道中轴线与每张切片有且只有一个交点；球半径固定；切片间距以及图象象素的尺寸均为1。
取坐标系的Z轴垂直于切片，第1张切片为平面Z=0，第100张切片为平面Z=99。
Z=z切片图象中象素的坐标依它们在文件中出现的前后次序为（-256，-256，z），（-256，-255，z），…（-256，255，z），（-255，-256，z），（-255，-255，z），…（-255，255，z），……（ 255，-256，z），（ 255，-255，z），…（255，255，z）。
试计算管道的中轴线与半径，给出具体的算法，并绘制中轴线在XY、YZ、ZX平面的投影图。
第2页是100张平行切片图象中的6张，全部图象请从网上（）下载。
关于BMP图象格式可参考：1. 《Visual C++数字图象处理》第12页2.3.1节。
何斌等编著，人民邮电出版社，2001年4月。
2. /home/mxr/gfx/2d/BMP.txtB题公交车调度公共交通是城市交通的重要组成部分，作好公交车的调度对于完善城市交通环境、改进市民出行状况、提高公交公司的经济和社会效益，都具有重要意义。
美赛习题答案
美赛习题答案美赛习题答案在数学建模领域，美国大学生数学建模竞赛（MCM）是一项备受关注的赛事。
每年，来自全球各地的大学生们都会参与其中，挑战各种实际问题并提出解决方案。
这项竞赛不仅考察了参赛者的数学水平，更重要的是培养了他们的团队合作和创新思维能力。
本文将探讨一些典型的美赛习题，并给出相应的解答。
第一题是关于城市交通流量的问题。
题目给出了一个城市的道路网络图，要求我们计算出每条道路的平均交通量。
首先，我们可以通过收集实际交通数据来估计每条道路上的车辆数量。
然后，根据道路的长度和车辆数量，我们可以计算出每条道路的平均交通量。
最后，将结果绘制成热力图，可以清晰地显示出城市交通的拥堵情况。
第二题是关于电力系统的问题。
题目给出了一个电力系统的拓扑结构图，要求我们设计一种最优的电力传输方案，以最大化系统的可靠性和效率。
首先，我们可以使用图论的方法对电力系统进行建模，并计算出各个节点之间的电力传输路径。
然后，根据节点之间的电力传输损耗和供电能力，我们可以通过线性规划等数学方法得到最优的电力传输方案。
最后，我们可以通过模拟实验来验证我们的方案，并对其进行优化。
第三题是关于航空公司的问题。
题目给出了一家航空公司的航班数据，要求我们设计一种最优的航班调度方案，以最大化公司的利润和乘客满意度。
首先，我们可以使用图论的方法对航班网络进行建模，并计算出各个航班之间的飞行时间和成本。
然后，根据乘客的需求和航班的运营成本，我们可以通过线性规划等数学方法得到最优的航班调度方案。
最后，我们可以通过模拟实验来验证我们的方案，并对其进行优化。
以上只是美赛习题中的几个例子，实际上还有许多其他有趣的问题，涉及到经济、环境、医疗等领域。
解决这些问题需要我们具备扎实的数学基础和创新的思维能力。
在解题过程中，我们需要灵活运用数学模型和工具，结合实际情况进行分析和判断。
同时，团队合作也是解决问题的关键，每个人都应发挥自己的优势，共同努力达到最佳的解决方案。
年美赛d题题目翻译
问题D：优化机场安全检查站乘客吞吐量继2001年9月11日美国发生恐怖袭击事件后，全世界的机场安全状况得到显着改善。
机场有安全检查站。
在那里，乘客及其行李被检查爆炸物和其他危险物品。
这些安全措施的目的是防止乘客劫持或摧毁飞机，并在旅行期间保持所有乘客的安全。
然而，航空公司有既得利益，通过最小化他们在安全检查站排队等候并等待他们的航班的时间，来保持乘客积极的飞行体验。
因此，在最大化安全性和最小化对乘客的不便之前存在对立。
在2016年，美国运输安全局（TSA）受到了对极长线路，特别是在芝加哥的奥黑尔国际机场的尖锐批评。
在此公众关注之后，TSA投资对其检查点设备和程序进行了若干修改，并增加了在高度拥堵的机场中的人员配置。
虽然这些修改在减少等待时间方面有一定的成功，但TSA在实施新措施和增加人员配置方面花费了多少成本尚不清楚。
除了在奥黑尔机场的问题，还有在其他机场，包括通常排队等待时间较短的机场，会出现不明原因和不可预测的排队拥挤情况的事件。
检查点排队状况的这种高度变化性对于乘客来说可能是极其不利的，因为他们面临着不必要地早到达或可能赶不上他们的预定航班的风险。
许多新闻文章，包括[1,2,3,4,5]，描述了与机场安全检查站相关的一些问题。
您的内部控制管理（ICM）团队已经与TSA签订合同，审查机场安全检查站和人员配置，以确定潜在的干扰乘客吞吐量的瓶颈。
他们特别感兴趣的解决方案是，既增加检查点吞吐量，减少等待时间的变化，同时保持相同的安全和安全标准。
美国机场安全检查点的当前流程如图1所示。
区域A：乘客随机到达检查站，并等待队列，直到安全人员可以检查他们的身份证明和登机文件。
区域B：然后乘客移动到打开检查的队列;根据机场的预期活动水平，可能开放更多或更少的线路。
一旦乘客到达这个队列的前面，他们准备所有的物品用于X射线检查。
乘客必须去除鞋子，皮带，夹克，金属物体，电子产品和带液体容器，将它们放置在单独的X射线箱中;笔记本电脑和一些医疗设备也需要从其袋中取出并放置在单独的容器中。
2001年美国大学生数学建模大赛赛题
2001 Mathematical Contest in ModelingThe ProblemsProblem A: Choosing a Bicycle WheelProblem B: Escaping a Hurricane's Wrath (An Ill Wind...)Problem A: Choosing a Bicycle WheelCyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on theright.The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel. The table should include the windspeeds for different road grades starting from zero percent to ten percent in onepercent increments. (Road grade is defined to be the ratio of the total rise of a hilldivided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speedof 45 kph, and the deceleration of the rider is proportional to the road grade. A riderwill lose about 8 kph for a five percent grade over 100 meters.∙Task 2. Provide an example of how the table could be used for a specific time trial course.∙Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.Problem B: Escaping a Hurricane's Wrath (An Ill Wind...)Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data, if sought, are widely available.)The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26into two lanes of Columbia-bound traffic, essentially turning the entire I-26 intoone-way traffic, significantly improve evacuation traffic flow?2.In 1999, the simultaneous evacuation of the state's entire coastal region was ordered.Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?3.Several smaller highways besides I-26 extend inland from the coast. Under whatconditions would it improve evacuation flow to turn around traffic on these?4.What effect would it have on evacuation flow to establish more temporary shelters inColumbia, to reduce the traffic leaving Columbia?5.In 1999, many families leaving the coast brought along their boats, campers, andmotor homes. Many drove all of their cars. Under what conditions should there berestrictions on vehicle types or numbers of vehicles brought in order to guaranteetimely evacuation?6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida,who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south, came up I-95 and compounded the traffic problems. How big an impact can they have on the evacuation traffic flow?Clearly identify what measures of performance are used to comparestrategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.Clearly identify what measures of performance are used to compare strategies.Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.。
建模美赛C题带翻译
Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of roads. For example, in the Greater Seattle area drivers experience long delays during peak traffic hours because the volume of traffic exceeds the designed capacity of the road networks. This is particularly pronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interest for this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highways without increasing number of lanes or roads. The behavior of these cars interacting with the existing traffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving, cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (See the provided map and Excel spreadsheet). In particular, how do the effects change as the percentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there a tipping point where performance changes markedly? Under what conditions, if any, should lanes be dedicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/or average traffic volume, and percentage of vehicles using self-driving, cooperating systems. Your model should address cooperation between self-driving cars as well as the interaction between self- driving and non-self-driving vehicles. Your model should then be applied to the data for the roads of interest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the Governor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours.•The nominal speed limit for all these roads is 60 miles per hour.•Mileposts are numbered from south to north, and west to east.•Lane widths are the standard 12 feet.•Highway 90 is classified as a state route until it intersects Interstate 5.•In case of any conflict between the data provided in this problem and any other source, use the data provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the road.interstate: A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。
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CUMCM Newsletter全国大学生数学建模竞赛组织委员会主办创新意识团队精神重在参与公平竞争目录调查研究改进工作——全国大学生数学建模竞赛意见征询结果 (1) 2001年国家级教学成果奖最新的获奖成果——数学类部分成果简介 (3) 北京赛区简讯——推动建模活动促进教学改革 (5) 湖北赛区简讯——教更好的数学，更好地学数学 (5) 重庆赛区简讯——以评优秀指导教师为动力推动竞赛和教改工作 (6) 河北赛区简讯——竞赛与教学改革和人才素质培养结合起来 (6) 全国大学生数学建模夏令营筹备工作进展顺利 (7) 2001年美国大学生数学建模竞赛题目 (7) 2001年美国大学生交叉学科建模竞赛题目 (11) 我国学生参加2001年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)情况简介 (14) ICTMA-10大会报告摘要选登 (16)调查研究改进工作——全国大学生数学建模竞赛意见征询结果2000年1月全国组委会通过各赛区组委会，向全国参赛同学和指导教师发出了《全国大学生数学建模竞赛意见征询》表，这是继1997年初第1次意见征询后，又一次全国范围的调查。
截至2001年1月全国组委会共收回调查表1203份，其中学生883份，教师320份（1997年共收回调查表204份）。
现将初步统计结果公布如下：（二）“全国大学生数学建模竞赛”意见征询（学生），共883份。
以下括号内为该题或该选项的份数及百分比。
一、您参加了哪几次竞赛（778，100%）：1996（2，0.3%）1997（17，2%）1998（103，13%）1999（585，75%）2000（71，9%）二、以下各题请选择一个答案，详细情况可补充说明：1）数模竞赛对学生用数学建模方法和计算机技术解决实际问题能力的培养（823，100%）非常有益（560，68%）有益（249，30%）一般（13，2%）无益（1，0.1%）2）数模竞赛对学生创新精神的培养（732，100%）非常有益（416，57%）有益（292，40%）一般（23，3%）无益（1，0.1%）3）数模竞赛对学生团结合作精神的培养（846，100%）非常有益（531，63%）有益（283，33%）一般（31，4%）无益（1，0.1%）4）您在竞赛前参加培训的情况（676，100%）集中两周以上（487，72%）集中一周以上（91，13%）在业余时间培训几次（76，11%）基本上未参加培训（22，4%）5）您所在的队在竞赛中遵守纪律(不与他人包括指导教师讨论、按时收发卷等)的情况（782，100%）严格遵守（572，73%）基本遵守（206，26%）有违反（4，0.5%）严重违反（0）6）据您了解其它大多数队在竞赛中遵守纪律的情况（776，100%）严格遵守（310，40%）基本遵守（420，54%）有违反（46，6%）严重违反（0）7）您对竞赛评奖公正性的印象（689，100%）非常满意（178，26%）基本满意（471，68%）不大满意（40，6%）很不满意（0）8）您对竞赛题的印象（757，100%）非常满意（184，24%）基本满意（507，67%）不大满意（64，8%）很不满意（2，0.3%）9）您参赛的成绩（565，100%）全国奖（141，25%）赛区奖（306，54%）成功参赛奖（118，21%）三、对竞赛活动的建议（以下是归纳的主要建议）：1．评阅时应减少对标准答案的依赖，更注重解题过程、方法、能力、合理性和创新性。
2．加强学生建模意识，扩大规模，如4人为一队。
3．严格纪律，严师出高徒。
4．扩大宣传，对学生进行早期培训。
5．建议大一学习高数时加入一些建模方面的知识。
6．希望在网络上看到优秀论文。
7．不要过多培训，否则失去竞赛目的。
8．增加评卷透明度，是否可以把好的答卷分发到下面以便学习。
（三）“全国大学生数学建模竞赛”意见征询（教师），共320份。
以下括号内为该题或该选项的份数及百分比。
一、您作为指导教师参加了哪几次竞赛（784，100%）：1994（43，5%）1995（67，9%）1996（98，13%）1997（128，16%）1998（177，23%）1999（271，34%）二、以下各题请选择一个答案,详细情况可补充说明：1）数模竞赛对学生数学素质、创新精神和综合能力的培养（311，100%）非常有益（235，76%）有益（73，23%）不大有益（3，1%）无益（0）2）数模竞赛对数学教改的促进作用（315，100%）非常大（92，29%）相当大（174，55%）一般（49，16%）很小（1，0.3%）3）您所在学校领导对数模竞赛的关心和支持（303，100%）非常大（89，29%）相当大（136，45%）一般（68，23%）很小（10，3%）4）您对数学建模教学、竞赛、科研的投入情况（310，100%）全年以此为主要工作（19，6%）竞赛培训期间以此为主要工作（147，47%）竞赛培训期间花费一定精力（139，45%）竞赛培训期间也很少过问（5，2%）5）您指导的队在竞赛中遵守纪律(不与他人包括指导教师讨论、按时收发卷等)的情况（293，100%）严格遵守（223，76%）基本遵守（65，22%）有违反（5，2%）严重违反（0）6）据您了解其它队在竞赛中遵守纪律的情况（274，100%）严格遵守（109，40%）基本遵守（149，54%）有违反（15，6%）严重违反（1，0.3%）7）据您了解您所在赛区评阅工作的情况（310，100%）完全公正（62，21%）基本公正（241，77%）不公正（7，2%）严重不公正（0）8）您对赛题的总体印象（286，100%）非常满意（40，14%）基本满意（240，84%）不大满意（6，2%）很不满意（0）9）您认为赛题中较好的有（可不只一个）（1129）92A施肥效果（32）92B蛋白质分解（9）93A频率设计（10）93B足球队排名（75）94A逢山开路（82）94B锁具装箱（88）95A飞行管理（64）95B天车调度（51）96A捕捞策略（68）96B节水洗衣机（91）97A零件的参数设计（68）97B截断切割（33）98A投资的收益和风险（107）98B灾情巡视路线（111）99A车床自动化管理（85）99B钻井布局（112）99C煤矸石堆积（43）三、对竞赛活动的建议（以下是归纳的主要建议）：1．对领导同志进行大力宣传，让他们积极支持加大投入。
2．加强对教练员的培训，进行经验交流。
3．成立专家组进行赛后总结，疑难解答，及竞赛得失等。
4．建议邻近赛区交换评卷。
5．改变现在评卷模式（即对照参考答案或某评卷人员的标准），这不符合数学建模的创新宗旨。
6．建议进行一次试点：将学生集中进行封闭式的竞赛，看论文的水平如何。
7．对一般院校来讲，经费投入较大，指导教师投入精力较大但没有奖励，是影响竞赛广度的一个问题。
8．尽快出版一些有关竞赛数学软件的使用说明书。
9．每年办一期中国和美国竞赛题的分析研讨班，提高教师素质。
这次较大范围的调查结果是一笔宝贵的财富，全国组委会将进行认真分析，针对存在的问题和提出的建议，研究对策，改进工作。
希望各赛区组委会、指导教师和组织工作者对这次调查结果进行分析、评价，欢迎以各种渠道将您的意见传送到全国组委会。
2001年国家级教学成果奖最新的获奖成果数学类部分成果简介2001年国家级教学成果奖最新的获奖成果已经公示在http://202.112.96.157/，其中数学类特等奖1项，一等奖1项，二等奖21项。
我们从二等奖中选取了与数学建模有关的5项成果简介如下。
成果名称: 数学建模课程建设与实践主要完成人: 杨启帆，何勇，方道元，张聪，赵川平主要完成单位:浙江大学我校从1983年起开设数学建模课程，是我国最早开设这门课程的少数高校之一。
目前，我们已固定每年开设本科生、研究生数学建模课6门，每年学习此课程的学生多达600余人。
从1996年起，我们每年都为一年级大学生举办专题讲座，为2-3年级学生开设每年两期的数学建模研讨班，组织学生开展实际课题的研究。
在此基础上，我们组织学生积极参加国内外大学生数学建模竞赛，并在竞赛中取得了优异的成绩。
1996年以来，我校学生在全国竞赛中共获得全国一等奖12项、全国二等奖7项；在国际竞赛中共获得国际特等奖兼最到奖INFORMS奖1项、国际一等奖10项、国际二等奖7项，竞赛成绩在国内外高校中名列前茅。
2000年，我校参赛的6个队全部获得国际一等奖，再创新记录。
人民日报等国内外报刊、中央人民广播电等电台、电视台均作了多次报道。
由于我校数学建模教学与系列实践活动影响面广、在对学生进行知识、能力、素质培养中发挥了独特的作用，受到学校各级领导的高度重视。
现在，我校已拥有专门供学生开展科学研究的数学建模实践基地，数学建模教学和与此相关的建模实践活动已在我校蓬蓬勃勃地开展起来，有力促进了我校教学改革的深入发展。
十几年来，我们先后承担了多项部、省、校级教改项目，编写出版了两本具有很大创新性的教材：―数学模型‖和―数学建模‖，发表了多篇教学研究论文和学生建模论文。
此外，作为浙江省数学建模竞赛组委会的挂靠单位，我们还做了大量赛区竞赛的组织、培训工作。
成果名称: ―数学模型‖课程建设主要完成人: 雷功炎主要完成单位:北京大学"数学模型"是80年代以来作为数学教育改革的一部分,国内外高校相继增设的全新课程.我校是国内高校最早开设此课程的学校之一.十余年来课程建设取得以下成果:1.制定了供试行的教学大纲,特别是明确了教学指导思想.教学不仅仅以培养学生用数学语言描述及解决实际问题的能力为目的，还力图更全面地体现数学与现实世界的关系,展示一种有别于传统数学课程单纯注重逻辑推理的思维方式，更均衡地对待理论和应用。
强调对学生思维方式的训练与提高学生的综合能力。
注意丰富课程的―文化‖内涵。
2.正式出版了―数学模型讲义‖教材一本，并编写了部分补充讲义。
这些教材强调处理问题的内在思想与对问题自身的分析、强调对数学方法的理解与直观。
教材中包括了80年代以来的科学新进展，说明了科学前沿与基础知识间没有不可逾越的鸿沟，关键在于独特的创造性思维，这些材料激发了学生学习与探索的兴趣。
不同于国内其他教材，获得好评。
3.注意学生综合能力的培养，组织、倡导与支持学生参加与本课有关的多种课外活动，鼓励学生用英文及计算机软件完成课程论文及作业。
历年来选修本课的学生在国内外大学生建模竞赛中取得好成绩，并在正式杂志上发表论文多篇。
4.1999年本课列入国家理科基地首批创建名牌课程项目，在国内高校数学及应用数学系有相当影响。
成果名称: 全国大学生数学建模竞赛和教学改革主要完成人: 姜启源，叶其孝，李大潜，谭永基，李志宏，俞文此主要完成单位:清华大学我们在八十年代初率先开设了数学建模课程，九十年代初组织了全国大学生数学建模竞赛。