翻译论文.docx
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翻译论文
Resultsofthe2010MCM
95
ResultsModelingForum
ofthe2010
MathematicalContestinModeling
FrankR.Giordano,MCMDirector
NavalPostgraduateSchool
1UniversityCircle
Monterey,CA93943–5000
frgiorda@nps.edu
Introduction
Atotalof2,254teamsofundergraduatesfromhundredsofinstitutionsand
departmentsin14countries,spentaweekendinFebruaryworkingonapplied
mathematicsproblemsinthe26thMathematicalContestinModeling(MCM)R.
The2010MCMbeganat8:
00P.M.ESTonThursday,February18,andended
at8:
00P.M.ESTonMonday,February22.Duringthattime,teamsofupto
threeundergraduatesresearched,modeled,andsubmittedasolutiontoone
oftwoopen-endedmodelingproblems.Studentsregistered,obtainedcontest
materials,downloadedtheproblemanddata,andenteredcompletiondata
throughCOMAP’sMCMWebsite.Afteraweekendofhardwork,solution
papersweresenttoCOMAPonMonday.Twoofthetoppapersappearinthis
issueofTheUMAPJournal,togetherwithcommentaries.
InadditiontothisspecialissueofTheUMAPJournal,COMAPhasmade
availableaspecialsupplementary2010MCM-ICMCD-ROMcontainingthe
pressreleasesforthetwocontests,theresults,theproblems,andoriginalver-
sionsoftheOutstandingpapers.InformationaboutorderingtheCD-ROM
isatorfrom(800)
772–6627.
Resultsandwinningpapersfromthefirst25contestswerepublishedin
specialissuesofMathematicalModeling(1985–1987)andTheUMAPJournal
(1985–2009).The1994volumeofToolsforTeaching,commemoratingthetenth
anniversaryofthecontest,containsthe20problemsusedinthefirst10years
ofthecontestandawinningpaperforeachyear.Thatvolumeandthespecial
TheUMAPJournal31
(2)(2010)95–104.cCopyright2010byCOMAP,Inc.Allrightsreserved.
Permissiontomakedigitalorhardcopiesofpartorallofthisworkforpersonalorclassroomuse
isgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercial
advantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrights
forcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwise,
torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.
96
TheUMAPJournal
31.2(2010)
MCMissuesoftheJournalforthelastfewyearsareavailablefromCOMAP.The
1994volumeisalsoavailableonCOMAP’sspecialModelingResourceCD-ROM.
AlsoavailableisTheMCMat21CD-ROM,whichcontainsthe20problems
fromthesecond10yearsofthecontest,awinningpaperfromeachyear,and
advicefromadvisorsofOutstandingteams.TheseCD-ROMscanbeordered
fromCOMAPat.
Thisyear,thetwoMCMproblemsrepresentedsignificantchallenges:
baseballbatwheremaximumpoweristransferredtotheballisnotatthe
endofthebatandtodeterminewhether“corking”abat(hollowingitout
andreplacingthehardwoodwithcork)enhancesthe“sweetspot”effect.
·ProblemB,“Criminology,”askedteamstodevelopgeographicalprofiling
toaidpoliceinfindingserialcriminals.
InadditiontotheMCM,COMAPalsosponsorstheInterdisciplinaryCon-
testinModeling(ICM)RandtheHighSchoolMathematicalContestinMod-
eling(HiMCM)R:
offeramodelingprobleminvolvinganenvironmentaltopic.Resultsof
thisyear’sICMareontheCOMAPWebsiteat
undergraduate/contests.Thecontestreport,anOutstandingpaper,and
commentariesappearinthisissue.
theMCM.FurtherdetailsabouttheHiMCMareatap.
com/highschool/contests.
2010MCMStatistics
·2,254teamsparticipated
·15highschoolteams(<1%)
·358U.S.teams(21%)
many,Indonesia,Ireland,Jamaica,Malaysia,Pakistan,Singapore,South
Africa,UnitedKingdom
·9OutstandingWinners(<0.5%)
·12Finalists(0.5%)
·431MeritoriousWinners(19%)
·542HonorableMentions(24%)
·1,245SuccessfulParticipants(55%)
·ProblemA,“TheSweetSpot,”askedteamstoexplainwhythespotona
·TheICMrunsconcurrentlywithMCMandforthenextseveralyearswill
·TheHiMCMoffershighschoolstudentsamodelingopportunitysimilarto
·1,890foreignteams(79%),fromAustralia,Canada,China,Finland,Ger-
Resultsofthe2010MCM
97
ProblemA:
TheSweetSpot
Explainthe“sweetspot”onabaseballbat.Everyhitterknowsthatthereis
aspotonthefatpartofabaseballbatwheremaximumpoweristransferredto
theballwhenhit.Whyisn’tthisspotattheendofthebat?
Asimpleexplanation
basedontorquemightseemtoidentifytheendofthebatasthesweetspot,but
thisisknowntobeempiricallyincorrect.Developamodelthathelpsexplain
thisempiricalfinding.
Someplayersbelievethat“c
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