【正文】 gle Thescelosaurus as well as the evasive strategy of the prey. Assume that the Thescelosaurus can always detect the velociraptor when it es 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 animal39。美國大學(xué)生數(shù)學(xué)建模競賽試題 1996 American MCM Problems Problem A The world39。s 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, ., submarines 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 frequency and amplitude. Problem B When determining the winner of a petition like the Mathematical Contest inModeling, there are generally a large number of papers to judge. Let39。s hip height. On the other hand, the Thescelosaurus is extremely agile and has a turning radius of meters. 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. Use the other assumptions and limitations given in Part 1. Problem B Mix Well For Fruitful Discussions Small group meeting for the discussions of important issues, particular longrange 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 board meetings the board will meet in small groups to discuss issues before meeting as a whole, these smaller groups still tun the risk of control by a dominant personality. In an attempt to reduce this danger it is mon 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 inhouse members(., corporate employees).The meeting is to be an allday 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 . to 4:00 ., with lunch scheduled at noon. Each morning session will consist of six discussion groups with each discussion group led by one of the corporation39。s discussion group twice. discussion group should contain a disproportionate number of inhouse members. Give a list of assignments for members 19 and 1029 and officers 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 adjust the assignments with an hour39。are implemented only on heavily used dedicated workstations 。 and tend to blur and feather out sharp boundaries between the original pixels. A more faithful, flexible algorithm implemented on a personal puter would be useful. (1)for planning minimally invasive treatments, (2)for calibrating the MRI machines, (3)for investigating structures oriented obliquely in space, such as postmortem tissue sections in a animal research, (4)for enabling crosssections at any angle through a brain atlas consisting (4)for enabling crosssections at any angle through a brain atlas consisting of blackandwhite line drawing To design such an algorithm, one can access the value and locations of the pixels, but not the initial data gathered by the scanners. Problem Design and test an algorithm that produces sections of threedimensional arrays by planes in any orientation in space, preserving the original grayscale value as closely as possible. Data Sets The typical data set consists of a threedimensional array A of numbers A(i,j,k) which indicates the density A(i,j,k) of the object at the location (x,y,z)i,j,k. Typically A(i,j,k) can range from 0 to most applications the data set is quite large. Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely Teams should design data sets to test and demonstrate their algorithms. The data sets should reflect conditions likely to be of diagnostic interest. Teams should also characterize data sets the limit the effectiveness of their algorithms. Summary The algorithm must produce a picture of the slice of the threedimensional array by a plane in space. The plane can have any orientation and any location in space.(The plane can miss some or all data points.)The result of the algorithm should be a model of the density of the scanned object over the selected plane. Problem B Grade Inflation Background Some college administrators are concerned about the grading at A Better Class(ABC) college. On average, the faculty at ABC have been giving out high grades(the average grade now given out is an A),and it is impossible to distinguish between the good and mediocre students .The terms of a very generous scholarship only allow the top 10% of the students to be funded, so a class ranking is required. The dean had the thought of paring each student to the other students in each class ,and using this information to build up a ranking. For example, if a student obtains