美国2011年大学生数学建模大赛题目.doc

PROBLEMA:SnowboardCourseDeterminetheshapeofasnowboardcourse(currentlyknownasa“halfpipe”)tomaximizetheproductionof“verticalair”byaskilledsnowboarder."Verticalair"isthemaximumverticaldistanceabovetheedgeofthehalfpipe.Tailortheshapetooptimizeotherpossiblerequirements,suchasmaximumtwistintheair.Whattradeoffsmayberequiredtodevelopa“practical”course?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。定制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“实用”的场地时哪些权衡因素可能需要？PROBLEMB:RepeaterCoordinationTheVHFradiospectruminvolvesline-of-sighttransmissionandreception.Thislimitationcanbeovercomeby“repeaters,”whichpickupweaksignals,amplifythem,andretransmitthemonadifferentfrequency.Thus,usingarepeater,low-powerusers(suchasmobilestations)cancommunicatewithoneanotherinsituationswheredirectuser-to-usercontactwouldnotbepossible.However,repeaterscaninterferewithoneanotherunlesstheyarefarenoughapartortransmitonsufficientlyseparatedfrequencies.Inadditiontogeographicalseparation,the“continuoustone-codedsquelchsystem”(CTCSS),sometimesnicknamed“privateline”(PL),technologycanbeusedtomitigateinterferenceproblems.Thissystemassociatestoeachrepeateraseparatesubaudibletonethatistransmittedbyalluserswhowishtocommunicatethroughthatrepeater.TherepeaterrespondsonlytoreceivedsignalswithitsspecificPLtone.Withthissystem,twonearbyrepeaterscansharethesamefrequencypair(forreceiveandtransmit);somorerepeaters(andhencemoreusers)canbeaccommodatedinaparticulararea.Foracircularflatareaofradius40milesradius,determinetheminimumnumberofrepeatersnecessarytoaccommodate1,000simultaneoususers.Assumethatthespectrumavailableis145to148MHz,thetransmitterfrequencyinarepeateriseither600kHzaboveor600kHzbelowthereceiverfrequency,andthereare54differentPLtonesavailable.Howdoesyoursolutionchangeifthereare10,000users?Discussthecasewheretheremightbedefectsinline-of-sightpropagationcausedbymountainousareas.甚高频无线电频谱包含信号的发送和接受。这种限制可以被中继站所克服。中继站可以捕捉到微弱的信号，然后把它放大，再用不同的频率重新发送。这样，低功耗的用户，例如移动电话用户，在不能直接与其他用户联系的地方可以通过中继站来保持联系。然而