2011mcm 求各位点题，讨论

sibingqian

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.

sibingqian

MCM的问题



问题A：单板滑雪课程

确定一个滑雪场（现为“半管”）的形状，最大限度地利用熟练的滑雪板“垂直空气”的生产。

“垂直的空气”是最大的半管以上的边缘的垂直距离。

定制优化其他可能的要求，如空气中的最大扭曲，形状。

什么权衡可能需要制定一个“实用”的课程？




B题：直放站协调

涉及的甚高频无线电频谱线的视线传输和接收。这种限制是可以克服的“中继器”，它拿起微弱信号，放大后发他们在不同的频率。因此，使用一个中继器，低功耗的用户（如移动站）与一个可以沟通的情况下直接用户到用户的联系将是不可能的另一个。然而，中继器可以互相干扰，除非他们足够远或传送在充分分离频率。

除了地理上的分隔，“连续音频编码静噪系统”（亚音频），有时也称为“专用线路”（特等），技术可用于减轻干扰的问题。该系统为每个员工一个单独的中继subaudible音，其所有用户谁希望通过该通信中继传输。中继器只响应其具体的PL接收到的信号音。有了这个系统，附近两个中继器可以共享相同的频率对（用于接收和发送）;让更多中继器（因此更多的用户）可以在一个特定区域安置。

对于一个圆半径40海里为半径的平坦区域，确定必要的留级容纳1000个并发用户的最小数目。假设频谱提供145至148兆赫，在一个中继器发射频率为600 kHz的任一高于或低于600千赫频率接收器，并有54个不同的发光色调可用。

您的解决方案如何改变，如果有10,000个用户？

讨论的情况下可能会有缺陷线的视线山区繁殖引起的。

fanmj

这个翻译有点。。。。

eulerzhu

哈哈 不说了 秘密

sibingqian

回复 3# fanmj


google翻译的

lst_hit

求点题+1。。。。。。