翻译论文Word格式.docx

翻译论文Word格式.docx

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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-

97

ProblemA:

TheSweetSpot

Explainthe“sweetspot”onabaseballbat.Everyhitterknowsthatthereis

aspotonthefatpartofabaseballbatwheremaximumpoweristransferredto

theballwhenhit.Whyisn’tthisspotattheendofthebat?

Asimpleexplanation

basedontorquemightseemtoidentifytheendofthebatasthesweetspot,but

thisisknowntobeempiricallyincorrect.Developamodelthathelpsexplain

thisempiricalfinding.

Someplayersbelievethat“c