2012年美国大学生数学建模竞赛（MCM/ICM）成绩已公布。来自全球各高校的5026个队参加此次竞赛，评出特等奖（Outstanding Winner）17个，特等奖提名奖（Finalist Winner）21个，一等奖（Meritorious Winner）530个，二等奖（Honorable Mentions）1689个。获得特等奖的学校有：

• 香港浸会大学
• 新加坡国立大学（Ben Fusaro Award）
• 上海外国语学校（INFORMS Prize Recipient）
• 浙江大学（SIAM Prize Recipient）
• Bethel University
• 北京大学
• University of Colorado（MAA Prize Recipient）
• University of Colorado（INFORMS Prize Recipient）
• University of Louisville（SIAM Prize Recipient）
• Western Washington University（Fank Giordano Award）
• Cornell University (INFORMS Prize Recipient)
• 华中科技大学
• Mathematical Modeling Innovative Practice Base
• 南京信息工程大学
• 西北工业大学
• 上海交通大学
• 电子科技大学

祝贺所有获奖同学。

详情请到以下网址查询：http://www.comap.com/undergraduate/contests/mcm/contests/2012/results/

近日，汤志高同学分享了他参加各类数模竞赛的多篇论文全文，参见：自己多年的论文原文，共享给大家。。请到他的Blog上查阅。

汤志高同学所在的团队曾获2006年全国赛一等奖，2007年全国赛“高教社杯”，2008年美国赛一等奖，2008年研究生数模竞赛一等奖。

感谢汤志高同学共享论文，欢迎更多的同学分享自己的论文。

"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:

• Why do leaves have the various shapes that they have?

• Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?

• Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?

• How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?

In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.

PROBLEM B: Camping along the Big Long River

Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish.. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor. Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible. In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one page summary sheet, prepare a one page memo to the managers of the river describing your key findings.

ICM PROBLEM

PROBLEM C: Modeling for Crime Busting

Click the title below to download a ZIP file containing the 2012 ICM Problem.

Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.

Modeling for Crime Busting

http://www.comap-math.com/mcm/

http://www.mathismore.net/mcm/index.html

IMPORTANT CHANGE TO CONTEST RULES FOR MCM/ICM 2011:

Teams (Student or Advisor) are now required to submit an electronic copy of their solution paper by email to solutions@comap.com. Your email MUST be received at COMAP by the submission deadline of 8:00 PM EST, February 14, 2011.

COMAP Mirror Site: For more in:
http://www.comap.com/undergraduate/contests/mcm/

MCM: The Mathematical Contest in Modeling
ICM: The Interdisciplinary Contest in Modeling

2011 Contest Problems

MCM PROBLEMS

PROBLEM A: Snowboard Course

Determine the shape of a snowboard course (currently known as a “halfpipe”) to maximize the production of “vertical air” by a skilled snowboarder.

"Vertical air" is the maximum vertical distance above the edge of the halfpipe.

Tailor the shape to optimize other possible requirements, such as maximum twist in the air.

What tradeoffs may be required to develop a “practical” course?

PROBLEM B: Repeater Coordination

The VHF radio spectrum involves line-of-sight transmission and reception. This limitation can be overcome by “repeaters,” which pick up weak signals, amplify them, and retransmit them on a different frequency. Thus, using a repeater, low-power users (such as mobile stations) can communicate with one another in situations where direct user-to-user contact would not be possible. However, repeaters can interfere with one another unless they are far enough apart or transmit on sufficiently separated frequencies.

In addition to geographical separation, the “continuous tone-coded squelch system” (CTCSS), sometimes nicknamed “private line” (PL), technology can be used to mitigate interference problems. This system associates to each repeater a separate subaudible tone that is transmitted by all users who wish to communicate through that repeater. The repeater responds only to received signals with its specific PL tone. With this system, two nearby repeaters can share the same frequency pair (for receive and transmit); so more repeaters (and hence more users) can be accommodated in a particular area.

For a circular flat area of radius 40 miles radius, determine the minimum number of repeaters necessary to accommodate 1,000 simultaneous users. Assume that the spectrum available is 145 to 148 MHz, the transmitter frequency in a repeater is either 600 kHz above or 600 kHz below the receiver frequency, and there are 54 different PL tones available.

How does your solution change if there are 10,000 users?

Discuss the case where there might be defects in line-of-sight propagation caused by mountainous areas.

ICM PROBLEM

PROBLEM C: How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?

Click the title below to download a PDF of the 2011 ICM Problem.

Your ICM submission should consist of a 1 page Summary Sheet and a 20 page solution for a total of 21 pages.

How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?

© 2011 COMAP, The Consortium for Mathematics and Its Applications
May be reproduced for academic/research purposes
For More information on COMAP and this project visit http://www.comap.com

下载C题：How environmentally and economically sound are electric vehicles? Is their widespread use feasible and practical?

• 明确强调无论电子版或打印版，都不能出现队员、指导老师和学校的任何信息，只能以控制号（control number）标识。电子版尤其需要注意这一点，指南中两次强调。
• 要确保组委会在2月25日前收到论文。
• 将Finalist（特等奖提名奖）明确为一个奖励等级，介于Meritorious（一等奖）与Outstanding Winner（特等奖）之间。
• 解释了Ben Fusaro Award（Fusaro特别奖）将颁发给一个特别有创意，但由于有明显缺点而无法获得特等奖的参赛队。

华中科技大学、浙江大学、北京交通大学、杭州电子科技大学荣获特等奖。

祝贺所有获奖的同学及指导老师。

Download THE complete MCM PROBLEM A results report (pdf)

Download THE complete MCM PROBLEM B results report (pdf)

DOWNLOAD THE complete ICM results report in portable document format (pdf)

A题

Judges' Commentary: Traffic Circles

Author: Kelly Black

Date: 2009-04-15

点击下载A题评委评论

B题

Judges' Commentary--Problem B

Author: Marie Vanisko

Date: 2009-04-10

点击下载B题评委评论

注：所谓“评委评论”（Judges' Commentary）是每年 MCM/ICM 竞赛试题命题人或评阅负责人关于题目要点及论文评阅情况的综述性文章，具有较高的参考价值。往年，评委评论通常与特等奖论文一同发表在The UMAP Journal杂志上，时间较晚且不免费提供。今年是组委会首次在竞赛成绩揭晓之后不久即公布评委评论，建议所有参赛选手及指导教师尽快下载。

http://www.comap-math.com/mcm/2009Certs/1111.pdf

Download THE complete MCM PROBLEM A results report in portable document format (pdf)

The FOUR Outstanding Winners of the continuous MCM (A) Problem are:

• Harvard University, MA — SIAM Prize Recipient
• Harvey Mudd College, CA— MAA Prize Recipient
• Tsinghua University, China
• University of Colorado - Boulder, CO — INFORMS Prize Recipient

University of Iowa, IA — Ben Fusaro Award (Meritorious Winner)

2009 MCM Problem B Results

DOWNLOAD THE COMPLETE MCM PROBLEM B RESULTS REPORT IN PORTABLE DOCUMENT FORMAT (PDF)

The FIVE Outstanding Winners of the Discrete MCM (B) Problem are:

• Clarkson University, NY — MAA Prize Recipient
• Cornell University, NY — INFORMS Prize Recipient
• Southwestern University, TX — SIAM Prize Recipient
• The College of Idaho, ID
• University of Delaware, DE

Lawrence Technological University, MI — Ben Fusaro Award (Meritorious Winner)

2009 ICM Problem C Results

DOWNLOAD THE complete ICM results report in portable document format (pdf)

The TWO Outstanding Winners of the INTERDISCIPLINARY ICM (C) Problem are:

• China University of Mining and Technology, China — INFORMS Prize Recipient
• United States Military Academy, NY

                  http://www.comap.com/undergraduate/contests/mcm/results.php

清华大学和中国矿业大学（徐州）获得特等奖。