《全国大学生数学建模竞赛通讯》-2003赛数模MCM全部原题及翻译.docxVIP

通讯CUMCMNewsletter全国大学生数学建模竞赛组织委员会主办2003年美国大学生数学建模竞赛题目2003 Mathematical Contest in Modeling（MCM）Problems原文下载网址：/undergraduate/contests/（张立平译，王强校）问题A: 特技演员影片在拍摄中, 一个激动人心的动作场景将要摄入镜头, 而你是特技协调员! 一位特技演员驾驶着摩托车跨越一头大象，随后跌落在借以缓冲的一堆纸箱上. 你需要保护特技演员,而且, 也要使用相对而言较少的纸箱（较低的花费, 不能进入镜头, 等等）。你的工作如下： 确定所用纸箱的大小确定所用纸箱的数目确定纸箱的堆放办法还请确定, 通过对纸箱的各种调整, 是否会有所帮助请把你的研究推广到不同组合重量（特技演员 摩托车）和不同跨越高度的情形留心一下, 在影片“明日帝国”中，角色James Bond 驾驶着摩托车飞过一架直升机.PROBLEM A: The Stunt PersonAn exciting action scene in a movie is going to be filmed, and you are the stuntcoordinator! A stunt person on a motorcycle will jump over an elephant and land ina pile of cardboard boxes to cushion their fall. You need to protect the stuntperson, and also use relatively few cardboard boxes (lower cost, not seen bycamera, etc.).Your job is to:determine what size boxes to usedetermine how many boxes to usedetermine how the boxes will be stackeddetermine if any modifications to the boxes would helpgeneralize to different combined weights (stunt person motorcycle) and differentjump heights Note that, in Tomorrow Never Dies, the James Bond character on a motorcyclejumps over a helicopter.问题B: Gamma刀治疗方案立体定位放射外科, 用单一高剂量离子化射束在X光机精确界定下照射颅内的一个小的3D脑瘤, 与此同时, 并没有处方剂量的任何显著份额伤及周边的脑组织. 在这个领域中,一般有三种形式的射束可以采用，分别是Gamma刀单元, 带电重粒子射束, 以及来自直线加速器的外用高能光子束.Gamma刀单元具备的单一高剂量离子化射束, 是201个钴-60单位源通过厚重的盔状物发射出来的。所有的201条射束同时交会于一个等中心(最大放射剂量点)，从而在有效剂量的水平上形成一个近似球形的剂量分布. 照射这个等中心来达到处方剂量称为一个“shot”.PROBLEM B: Gamma Knife Treatment PlanningStereotactic radiosurgery delivers a single high dose of ionizing radiation to aradiographically well-defined, small intracranial 3D brain tumor withoutdelivering any significant fraction of the prescribed dose to the surroundingbrain tissue. Three modalities are commonly used in this area; they are the gammaknife unit, heavy charged particle beams, and external high-energy photon beamsfrom linear accelerators. The gamma knife unit delivers a single high dose of ionizing radiation emanatingfrom 201 cobalt-60 unit sources through a heavy h