5_ Judges' Commentary_ The Ultimate Brownie Pan Papers

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1、Judges'Commentary141Judges'Commentary:TheUltimateBrowniePanPapersKellyBlackDept.ofMathemaficsClarksonUniversityP.O.Box5815Potsdam,NY13699-5815kjblackOgmail.comIntroductionThefocusofthisyear'sproblemwashowtobalancethecompromisebetweenqualityversusquantity.Theteamswereaskedtodeterm.inethebestwaytos

2、trikethebalancebetweenthetwocompetinginterestsforagivencompromise.Thecontextforthisdecisionwastodesignthepansusedtobakebrownies.Onthesideofquality,thepansthemselvesshouldbedesignedsothatthetemperaturedistributionofthebrowniemixshouldbeasuniformaspossible.Thegoalwastoreducethelargetemperaturegradi

3、entsthatcanoccurnearthecornersofrectangularpans.Forthisaspectoftheproblem,acircularpanisthebestchoicetoachievethemostevenheatingandthebestbrownies.Onthesideofquantity,thepansshouldbedesignedtoreducetheamountofemptyspaceononeoftheracksintheoven.Thegoalhereistoputasmanypansaspossibleintoanoventhath

4、asarectangularshape.Forthisaspectoftheproblem,thebestchoice,asawaytoachievetheleastamountofemptyspace,isapanwithanaspectratiothatmatchestheaspectratioofahorizontalcrosssectionoftheoven.Inthiscommentary,wefirstdescribethejudgingprocess,thendiscussthethreequestionsthattheteamswereaskedtoaddress.The

5、nexttopicistheissueofsensitivityandassumptions,followedbyadiscussiononidentifyingthestrengthsandweaknessesofagivenapproach.Finally,wegiveabriefdiscussiononthedifferencebetweenreferencesandcitations.TheUMAPJournal34(2-3)(2013)141-149.©Copyright2013byCOMAP,Inc.Allrightsreserved.Permissiontomakedigi

6、talorhardcopiesofpartorallofthisworkforpersonalorclassroomuseisgrantedwithoutfeeprovidedthatcopiesarenotmadeordistributedforprofitorcommercialadvantageandthatcopiesbearthisnotice.Abstractingwithcreditispermitted,butcopyrightsforcomponentsofthisworkownedbyothersthanCOMAPmustbehonored.Tocopyotherwi

7、se,torepublish,topostonservers,ortoredistributetolistsrequirespriorpermissionfromCOMAP.142TheUMAPJournal34.2-3(2013)TheProcessIgiveanoverviewofthejudgingprocess,whichhastwoprimaryactivi-ties:thetriageroundsandthefinalr