历年MCM考题

sapientia

我也很想看看历年icm得优秀论文 我今年参赛 可是只熟悉mcm 那位大虾能帮帮我啊
不胜感激
我的QQ:85868970

peaceworker

有没有2003年的题目啊？？

peaceworker

求1990 A，1989 B，1988 A，1991 A的MCM考题。谢谢！
还有请问斑竹，这些论文在哪里找到的啊？？

panzervi

1990 A - The Brain-Drug Problem
Researches on brain disorders test the effects of the new medical drugs -- for example, dopamine against Parkinson's disease -- with intracerebral injections. To this end, they must estimate the size and the sape of the spatial distribution of the drug after the injection, in order to estimate accurately the region of the brain that the drug has affected.
The research data consist of the measurements of the amounts of drug in each of 50 cylindrical tissue samples (see Figure 1 and Table 1). Each cylinder has length 0.76 mm and diameter 0.66 mm. The centers of the parallel cylinders lie on a grid with mesh 1mm X 0.76mm X 1mm, so that the sylinders touch one another on their circular bases but not along their sides, as shown in the accompanying figure. The injection was made near the center of the cylinder with the highest scintillation count. Naturally, one expects that there is a drug also between the cylinders and outside the region covered by the samples.

Estimate the distribution in the region affected by the drug.

One unit represents a scintillation count, or 4.753e-13 mole of dopamine. For example, the table shows that the middle rear sylinder contails 28353 units.


Table 1. Amounts of drug in each of 50 cylindrical tissue samples.
Rear vertical section 164  442  1320  414  188  
480  7022  14411  5158  352  
2091  23027  28353  13138  681  
789  21260  20921  11731  727  
213  1303  3765  1715  453  
Front vertical section 163  324  432  243  166  
712  4055  6098  1048  232  
2137  15531  19742  4785  335  
444  11431  14960  3182  301  
294  2061  1036  258  188  

panzervi

1989 B - Aircraft Queueing
A common procedure at airports is to assign aircraft (A/C) to runways on a first-come-first-served basis. That is, as soon as an A/C is ready to leave the gate ("push-back"), the pilot calls ground control and is added to the queue. Suppose that a control tower has access to a fast online database with the following information for each A/C:

the time it is scheduled for pushback;
the time it actually pushes back; the number of passengers who are scheduled to make a connection at the next stop, as well as the time to make that connection; and
the schedule time of arrival at its next stop Assume that there are seven types of A/C with passenger capacities varying from 100 to 400 in steps of 50. Develop and analyze a mathematical model that takes into account both the travelers' and airlines' satisfaction.

panzervi

1988 A - The Drug Runner Problem
Two listening posts 5.43 miles apart pick up a brief radio signal. The sensing devices were oriented at 110 degrees and 119 degrees, respectively, when the signal was detected; and they are accurate to within 2 degrees. The signal came from a region of active drug exchange, and it is inferred that there is a powerboat waiting for someone to pick up drugs. it is dusk, the weather is calm, and there are no currents. A small helicopter leaves from Post 1 and is able to fly accurately along the 110 degree angle direction. The helicopter's speed is three times the speed of the boat. The helicopter will be heard when it gets within 500 ft of the boat. This helicopter has only one detection device, a searchlight. At 200 ft, it can just illuminate a circular region with a radius of 25 ft.

Develop an optimal search method for the helicopter.
Use a 95% confidence level in your calculations.

panzervi

1991 A - Water Tank Flow
Some state water-right agencies require from communities data on the rate of water use, in gallons per hour, and the total amount of water used each day. Many communities do not have equipment to measure the flow of water in or out of the municipal tank. Instead, they can measure only the level of water in the tank, within 0.5% accuracy, every hour. More importantly, whenever the level in the tank drops below some minimum level L, a pump fills the tank up to the maximum level, H; however, there is no measurement of the pump flow either. Thus, one cannot readily relate the level in the tank to the amount of water used while the pump is working, which occurs once or twice per day, for a couple of hours each time. Estimate the flow out of the tank f(t) at all times, even when the pump is working, and estimate the total amount of water used during the day. Table 1 gives real data, from an actual small town, for one day[ table omitted]. The table gives the time, in, since the first measurement, and the level of water in the tank, in hundredths of a foot. For example, after 3316 seconds, the depth of water in the tank reached 31.10 feet. The tank is a vertical circular cylinder, with a height of 40 feet and a diameter of 57 feet. Usually, the pump starts filling the tank when the level drops to about 27.00 feet, and the pump stops when the level rises back to about 35.50 feet.