国际竞赛题英文版.docx

1、国际竞赛题英文版Contents1996 American MCM Problems 1Problem A 1Problem B 11997 American MCM Problems 1Problem A The Velociraptor Problem 1Part1 1Part2 2Problem B Mix Well For Fruitful Discussions 21998 American MCM Problems 2Problem A MRI Scanners 2Problem 3Data Sets 3Summary 3Problem B Grade Inflation 3Bac

2、kground 3Problem 3Data Sets 4Mathematical Contest in Modeling 1999 Problems 4Problem B - Unlawful Assembly 42000 Mathematical Contest in Modeling 4Problem A Air traffic Control 4Problem B Radio Channel Assignments 52001 Mathematical Contest in Modeling (MCM) 5Problem A: Choosing a Bicycle Wheel 5Pro

3、blem B: Escaping a Hurricanes Wrath (An Ill Wind.) 62002 Contest Problems 7Problem A Wind and Waterspray 7Problem B Airline Overbooking 72003 Contest Problems 7Problem A The Stunt Person 7Problem B Gamma Knife Treatment Planning 82004 MCM 8PROBLEM A: Are Fingerprints Unique? 8PROBLEM B: A Faster Qui

4、ckPass System 8Problem CTo Be Secure or Not to Be? 92005 MCM Problem 112006 年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题 12PROBLEM A: Positioning and Moving Sprinkler Systems for Irrigation 12PROBLEM B: Wheel Chair Access at Airports 13PROBLEM C: Trade-offs in the fight against HIV/AIDS 132007 年美国大学生数学建模竞赛(MCM

5、)和交叉学科建模竞赛(ICM)赛题 PROBLEM A: Gerrymandering 19PROBLEM B: The Airplane Seating Problem 19Problem C Organ Transplant: The Kidney Exchange 192008 年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题 23PROBLEM A: Take a Bath 23PROBLEM B : Creating Sudoku puzzles 232008 ICM Problem C Finding the Good in Health Care Systems

6、 232009 年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题 242009 MCM A: Designing a Traffic Circle 242009 MCM B: Energy and the Cell Phone 252009ICM:Creating Food Systems: Re-Balancing Human-Influenced Ecosystems 262010年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题 262010 MCM A: The Sweet Spot 262010 MCM B: Criminology 262010 I

7、CM: The Great Pacific Ocean Garbage Patch 272011年美国大学生数学建模竞赛(MCM)和交叉学科建模竞赛(ICM)赛题 28PROBLEM A: Snowboard Course 28PROBLEM B: Repeater Coordination 28PROBLEM C: How environmentally and economically sound are electric vehicles?Is their widespread use feasible and practical? 291996 American MCM Problem

8、s Problem AThe worlds oceans contain an ambient noise field. Seismic disturbances, surface shipping, and marine mammals are sources that, in different frequency ranges,contribute to this field. We wish to consider how this ambient noise might be used to detect large moving objects, e.g., submarines

9、located below the ocean surface. Assuming that a submarine makes no intrinsic noise, developa method for detecting the presence of a moving submarine, its size, and its direction of travel, using only information obtained by measuring changes to the ambient noise field. Begin with noise at one fixed

10、 frequency and amplitude.Problem BWhen determining the winner of a competition like the Mathematical Contest inModeling, there are generally a large number of papers to judge. Lets saythere are P=100 papers. A group of J judges is collected to accomplish thejudging. Funding for the contest constains

11、 both the number of judges that canbe obtained and amount of time that they can judge. For eample if P=100, thenJ=8 is typical.Ideally, each judge would read paper and rank-order them, but there are toomany papers for this. Instead, there will be a number of screening rounds inwhich each judge will

12、read some number of papers and give them scores. Thensome selection scheme is used to reduce the number of papers under consideration: If the papers are rank-ordered, then the bottom 30% that eachjudge rank-orders could be rejected. Alternatively, if the judges do not rank-order, but instead give th

13、em numerical score (say, from 1 to 100),then all papers below some cut-off level could be rejected.The new pool of papers is then passed back to the judges, and the process is repeated. A concern is then the total number of papers that judge reads must besubstantially less than P. The process is sto

14、pped when there are only W papersleft. There are the winners. Typically for P=100, W=3.Your task is to determine a selection scheme, using a combination of rank-ordering, numerical scoring, and other methods, by which the final Wpapers will include only papers from among the best 2W papers. (By best

15、,we assume that there is an absolute rank-ordering to which all judges wouldagree.) For example, the top three papers. Among all such methods, the one thatrequired each judge to read the least number of papers is desired.Note the possibility of systematic bias in a numerical scoring scheme. For exam

16、ple, for a specific collection of papers, one judge could average 70points, while another could average 80 points. How would you scale your schemeto accommodate for changes in the contest parameters (P, J, and W)?1997 American MCM Problems Problem A The Velociraptor ProblemThe velociraptor,Velocirap

17、tor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter, and may have hunted in pairs or larger packs .Unfortunately, there is no way to observe its hunting behavior in the

18、wild as can be done with modern mammalian predators. A group of paleontologists has approached your team and asked for help in modeling the hunting behavior of the velociraptor. They hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and simi

19、lar predatory animals.The average adult velociraptor was 3 meters long with a hip height of 0.5 meters and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast at speed of 60 km/hr for about 15 seconds. After the initial burst of speed ,the animal needed to stop and

20、 recover from a buildup of lactic acid in its muscles.Suppose that velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the Velociraptor. A biomachanical analysis of a fossilized Thescelosaurus indicates that it could run at a speed of about 50 km/hr. f

21、or long period of time.Part1Assuming the velociraptor is a solitary hunter, design a mathematical model that describe a hunting strategy for a single velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Assume that the Thescelosaurus can always detec

22、t the velociraptor when it comes within 15 meters .but may detect the predator at even greater ranges (up to 50 meters depending upon the habitat and weather conditions. Additionally ,due to its physical structure and strength, the velociraptorhas a limited turning radius when running at full speed.

23、 This radius is estimated to be three times the animals hip height. On the other hand, the Thescelosaurus is extremely agile and has a turning radius of 0.5 meters.Part2Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two vel

24、ociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. Use the other assumptions and limitations given in Part 1.Problem B Mix Well For Fruitful DiscussionsSmall group meeting for the discussions of important issues, particular long-range planning ,are ga

25、ining popularity. It is believed that large groups discourage productive discussion and that a dominant personality will usually control and direct the discussion. Thus ,in corporate board meetings the board will meet in small groups to discuss issues before meeting as a whole, these smaller groups

26、still tun the risk of control by a dominant personality. In an attempt to reduce this danger it is common to schedule several sessions with a different mix of people in each group.A meeting of An Tostal Corporation will be attended by 29 Board Members of which nine are in-house members(i.e., corpora

27、te employees).The meeting is to be an all-day affair with three sessions scheduled for the morning and four for the afternoon. Each session will take 45 minutes, beginning on the hour from 9:00 A.M. to 4:00 P.M., with lunch scheduled at noon. Each morning session will consist of six discussion group

28、s with each discussion group led by one of the corporations six senior officers. None of these officers are board members. Thus each senior officers will not be involved in the afternoon sessions and each of these sessions will consist of only four different discussion groups.The president of the co

29、rporation wants a list of board-member assignment to discussion groups for each of the seven sessions. The assignments should achieve as muchof a mix of the members as much as possible. The ideal assignment would have each board member in a discussion group the same number of times while minimizing

30、common membership of groups for the different sessions.The assignment should also satisfy the following criteria:1.For the morning sessions ,no board member should be in the same senior officers discussion group twice.2.No discussion group should contain a disproportionate number of in-house members

31、.Give a list of assignments for members 1-9 and 10-29 and officers 1-6.Indicate how well the criteria in the previous paragraphs are met. Since it is possible that some board members will cancel at the last minute or that some not scheduled will show up, an algorithm that the secretary could use to

32、adjust the assignments with an hours notice would be appreciated. It would be ideal if the algorithm could also be used to make assignments for future meetings involving different levels of participation for each type of attendee.1998 American MCM Problems Problem A MRI ScannersIndustrial medical diagnostic machines known as Magnetic Resonance Imager (MRI) scan a three-dimensional object such as a brain, and deliver their results in the form of a three-dimensional array of pixel. Each pixel consist