2025年数学建模美赛试题

2025 年数学建模美赛试题（MCM） 来源： 谢音的日志 以下是 11 年的美赛试题，没有参加的同学可以看看，挺有意思的。。。后悔没参加拉！2025Contest Problems MCMPROBLEMS PROBLEMA: Snowboard Course Determinethe shape of a snowboard course (currently known as a “half pipe”) tomaximize the production of “vertical air” by a skilled snowboarder. "Verticalair" is the maximum vertical distance above the edge of the half pipe. Tailorthe shape to optimize other possible requirements, such as maximum twist in theair. Whattradeoffs may be required to develop a “practical” course? 问题 A：单板滑雪课程 请设计一个单板滑雪场（现为“半管”或“U 型池”）的形状，以便能使熟练的单板滑雪选手最大限度地产生垂直腾空。 “垂直腾空“是超出“半管”边缘以上的最大的垂直距离。 制定形状时要优化其他可能的要求，如：在空中产生最大的身体扭曲。 在制定一个“有用”的场地时可能需要权衡哪些因素？ PROBLEMB: Repeater Coordination TheVHF radio spectrum involves line-of-sight transmission and reception. Thislimitation can be overcome by “repeaters,” which pick up weak signals, amplifythem, and retransmit them on a different frequency. Thus,using a repeater, low-power users (such as mobile stations) can communicatewith one another in situations where direct user-to-user contact would not bepossible. However, repeaters can interfere withone another unless they are far enough apart or transmit on sufficientlyseparated frequencies. Inaddition to geographical separation, the “continuous tone-coded squelch system”(CTCSS), sometimes nicknamed “private line” (PL), technology can be used tomitigate interference problems. This system associatesto each repeater a separate sub-audible tonethat is transmitted by all users who wish to communicate through that repeater.Therepeater respondsonly to received signals with its specific...