rolip美国大学生数学建模竞赛试题
1996 American MCM Problems Problem A
howareyoudoingThe world's oceans contain an ambient noi 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 noi might be ud to detect large moving objects, e.g., submarines located below the ocean surface. Assuming that a submarine makes no intrinsic noi, developa method for detecting the prence of a moving submarine, its size, and its direction of travel, using only information obtained by measuring changes to the ambient noi field. Begin with noi at one fixed frequency and amplitude.
Problem B
When determining the winner of a competition like the Mathematical Contest inModeling, there are generally a large number of papers to judge. Let's saythere are P=100 papers. A
group of J judges is collected to accomplish thejudging. Funding for the contest constains 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 read some number of papers and give them scores. Thensome lection scheme is ud 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 them numerical score (say, from 1 to 100),then all papers below some cut-off level could be rejected.
ourThe new pool of papers is then pasd 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 stopped when there are only W papersleft. There are the winners. Typically for P=100, W=3.
Your task is to determine a lection 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",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 example, 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)?
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corner1997 American MCM Problems
冷菜Problem A The Velociraptor Problem
The velociraptor,Velociraptor 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 obrve its hunting behavior in the 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 similar 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 conds. After the initial burst of speed ,the animal needed to stop and recover from a buildup of lactic acid in its muscles.
Suppo 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. for long period of time.
Part1
Assuming 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 detect 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. This radius is estimated to be three times the animal's hip height. On the other hand, the Thescelosaurus is extremely agile and has a turning radius of 0.5 meters.
英语六级成绩查询入口which从句
Part2
Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptor stalking and chasing a single Thescelosaurus as well as the evasive strategy of the prey. U the other assumptions a
剪纸英语nd limitations given in Part 1.
Problem B Mix Well For Fruitful Discussions
Small group meeting for the discussions of important issues, particular long-range planning ,are gaining 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 舌尖上的英国 board meetings the board will meet in small groups to discuss issues before meeting as a whole, the smaller groups still tun the risk of control by a dominant personality. In an attempt to reduce this danger it is common to schedule veral ssions with a different mix of people in each group.
