通 讯
CUMCM Newsletter
全国大学生数学建模
竞赛组织委员会主办
创新意识 团队精神 重在参与 公平竞争
目 录
2011 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………………………………(1)
COMAP 宣布一个新的竞赛：MCM-ICM 媒体竞赛……………………………(5)
我国学生参加 2011 年美国大学生数学建模竞赛(MCM)
和交叉学科建模竞赛(ICM)情况简介…………………………(6)
“走进企业 研讨数学建模应用”
——全国大学生数学建模竞赛组委会赴天津市滨海新区考察交流……(15)
数学建模竞赛 20 周年宣传周与广播稿…………………………………(16)
2011 年全国大学生数学建模夏令营题目…………………………………(17)
数学建模竞赛 20 周年题词…………………………………………………(21)
图片新闻…………………………………………………………………(封底)
《全国大学生数学建模竞赛通讯》2011 年第 2 期 (2011 年 6 月, 总第 36 期）
主办：全国大学生数学建模竞赛组织委员会
地址：北京清华大学数学科学系（邮编：100084） 网址：http://mcm.edu.cn
电话：010-62781785 传真：010-62773400 责任编辑：孟大志
1
2011 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
（叶其孝译, 吴庆宝校，原题来源于 http://www.comap.com)
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?
A 题: 单板滑雪运动场地的设计
试确定一个单板滑雪运动场地(现称为“半管”, 即 U 形场地)的形状, 使得熟练的单板滑雪运
动员能最大限度地产生“垂直腾空”.
“垂直腾空“是指超出“半管”边缘以上的最大的垂直距离.
调整场地形状以优化诸如能在空中产生最大的身体翻转等其他可能的要求.
在设计一个“实际可行”的场地时需要权衡哪些因素？
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.
B 题: 中继站的协调
甚高频无线电频谱涉及电磁波的视距传输和和接收. 这种局限性可以通过设置“中继站”来克
服, 中继站接收到微弱的信号, 把信号放大, 再用不同的频率重新发送. 这样, (诸如移动台那样
2
的)低功耗的用户, 在不能进行用户对用户地直接联系的地方可以通过中继站来保持相互间的通讯
联系. 但是,中继站之间会互相干扰, 除非彼此之间有足够远的距离或通过充分分离的频率来传输.
除了地域上的分离外, “连续音频编码静噪系统 (CTCSS)”, 有时被人们起绰号为“私人专线
(PL)”的这项技术可以减轻干扰问题. 该系统对每个中继站都伴随有一个不同的亚音频音调, 所有
希望通过该中继站来进行通讯的用户都向该中继站发送该亚音频音调. 中继站只回应接收到的带有
其特殊 PL 音调的信号. 通过这种系统,两个相距不远的中继站可以共享(接收和发送)相同的频率
对; 所以在一个特定的区域可以容纳更多的中继站(从而更多的用户).
对一个半径为 40 英里的平坦的圆形区域，确定要容纳 1000 同时在线用户所必需的中继站的最
小数目. 假设频谱范围是 145 到 148 兆赫, 中继站的发射机的频率要么高于接收机频率 600 千赫,
要么低于接收机频率 600 千赫, 而且有 54 个不同的 PL 音调可用.
如果这里有 10,000 个用户, 你的解决方案将会发生怎样的变化?
讨论由于山区引起的视距传播中可能有的缺陷的情形.
PROBLEM C: How environmentally and economically sound are electric vehicles? Is
their widespread use feasible and practical?
Here are some issues to consider, but, of course, there are many more, and you will not be
able to consider all the issues in your model(s):
• Would the widespread use of electric vehicles actually save fossil fuels or would we
merely be trading one use of fossil fuel for another given that electricity is currently mostly
produced by burning fossil fuels? What conditions would need to be put in place to maximize
the savings through use of electric vehicles?
• Consider how much the amount of electricity generated by alternatives such as wind and
solar would need to climb during the twenty-first century to make the widespread use of
electric vehicles feasible and environmentally beneficial. Assess whether or not the needed
growth of these alternate sources of electricity is likely and possible.
• Would charging batteries at off-peak times be beneficial and increase the feasibility of
widespread use of electric vehicles? How quickly would batteries need to charge to
maximize the efficiency and practicality of electric vehicles? How would progress in
these areas change the equation regarding the environmental savings and practicality of
widespread use of electric vehicles?
• What method of basic transportation is most efficient? Is the efficiency of different
methods dependent of the nation or region in which it is used?
• Pollution caused directly by electric vehicles is low, but are there hidden sources of
pollutants associated with electric vehicles? Gasoline and diesel fuel burned in internal
combustion engines for transportation account for nitrites of oxygen, vehicle-born
monoxide and carbon dioxide pollution but are these bi-products something we really should
worry about? What are the short and long term effects of these substances on the climate and
our health?
• How would the pollution caused by the increasing need to dispose of increasing Numbers
of large batteries effect the comparison between the environmental effects of electric vehicles
versus the effects of fossil fuel-burning vehicles?
• You also should consider economic and human issues such as the convenience of Electric
3
vehicles. Can batteries be recharged or replaced fast enough to meet most Transportation
needs or would their ranges be limited? Would electric vehicles have only a limited role in
transportation, good only for short hauls (commuters or light vehicles on short trips) or could
they practically be used for heavier and longer-range transportation and shipping?
Should governments give subsidies to developers of electric vehicle technologies and If so,
why, how much, and in what form?
Requirements:
• Model the environmental, social, economic, and health impacts of the widespread use 哦f
electric vehicles and detail the key factors that governments and vehicle 没anufacturers
should consider when determining if and how to support the development and use of electric
vehicles. What data do you have to validate your model(s)?
• Use your model(s) to estimate how much oil (fossil fuels) the world would save by
widely using electric vehicles.
• Provide a model of the amount and type of electricity generation that would be needed to
support your recommendations regarding the amount and type of electric vehicle use that will
produce the largest number of benefits to the environment, society, business, and individuals.
• Write a 20-page report (not including the summary sheet) to present your model and your
analysis of the key issues associated with the electric vehicle and electricity generation.
Be sure to include the roles that governments should play to insure safe, efficient, effective
transportation. Discuss if the introduction of widespread use of electric vehicles is a
worthwhile endeavor and an important part of an overall strategy to address global energy
needs in the face of dwindling fossil fuel supplies.
References:
Getting reliable global data on controversial issues like this one can be difficult. As a start on
global energy information we provide this link:
http://www.bp.com/liveassets/bp_internet/globalbp/globalbp_uk_english/reports_and_p
ublications/statistical_energy_review_2008/STAGING/local_assets/2010_downloads/stati
stical_review_of_world_energy_full_report_2010.pdf
A concise summary of energy generation and usage in the US is found here:
http://www.eia.doe.gov/aer/pecss_diagram.html
More global data in spreadsheet form are found here:
http://www.eia.doe.gov/iea/
Good luck and have fun modeling!
C 题: 从环保和经济的角度看电动汽车究竟有多少优势？广泛使用电动汽车是切实可
行的吗？
以下是需要你们考虑的一些问题，当然还有更多的问题需要考虑，但是在你们的模型中不可能
考虑所有这些问题：
电动汽车的广泛使用真会节约化石燃料吗, 或者仅仅是用另一种使用化石燃料的方式 — 即目
前主要是由燃烧化石燃料产生的电力来替换一种使用化石燃料的方式？要想通过使用电动汽车来最
多地节约能源, 需要具备什么样的条件？
仔细考虑要想在二十一世纪广泛使用可行且有利于环保的电动汽车, 需要多少由诸如风力和太
阳能那样的替代能源所生成的电力. 评估所需要的这些电力替代能源的增长是否是可能和可行的.
