模板.docx
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模板.docx
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模板
Abstract:
Webuildamathematicalmodelto
Keywords:
Contents
1.Abstract............................................................................................................................................................1
2.Introduction...................................................................................................................................................3
1.1Whydoestollwaycollectstoll?
………………………………………….…………………....3
1.2Tollmodes……………………………………………………………………………………………...3
1.3Tollcollectionmethods……………………………………………………………………….…...3
3.TheDescriptionofProblem….............................................................................................................5
2.1Howdoweapproximatethewholecourseofpayingtoll?
...........................................5
2.2Howdowedefinetheoptimalconfiguration?
........................…………….……….5
2.2.1Fromtheperspectiveofmotorist…………………………………….………………...5
2.2.2Fromtheperspectiveofthetollplaza………………………………………………..6
4.Models……………..........................................................................................................................................7
3.1BasicModel...........................................................................................................................................7
3.1.1SymbolsandDefinitions………………………………..…...…………………………….7
3.1.2Assumptions……………………………………………………………….……..……………8
3.1.3TheFoundationofModel………………………………………………………………....9
3.1.4SolutionandResult……………………………………………………………….……….11
3.1.5AnalysisoftheResult……………………………………………….………………………..………..11
3.1.6StrengthandWeakness………………………………………………….…………….…13
3.2ImprovedModel………………………………………………….…………….…………………..14
3.2.1ExtraSymbols……………………………………..………………………...………………….................14
3.2.2AdditionalAssumptions………………………………………………...…..……………………….14
5.Conclusions.................................................................................................................................................19
4.1Conclusionsoftheproblem……………………………………………….…………………………..…….19
4.2Methodsusedinourmodels…………………………………...……………………..………...19
4.3Applicationofourmodels…………………………………………………..………………..…19
6.FutureWork.............................................................................................................................................19
5.1Anothermodel……………………………………………………………………………………....19
5.2Anotherlayoutoftollplaza………………………………………………………..…………...23
5.3Thenewly-adoptedchargingmethods………………………………………..…………....23
7.References.....................................................................................................................................................23
8.Appendix......................................................................................................................................................23
Programsandcodes………………………………………………………………..…………………...24
.Introduction
Inordertoindicatetheoriginofthetollwayproblems,thefollowingbackgroundisworthmentioning.
1.1
1.2
1.3
1.4
1.5
Thismodelraisesmanyquestions.Whichfrequenciesgetexcitedand
why?
.RestatementandanalysisoftheProblem
Theproblemneedsustobuildamathematicalmodeltodescribeand….
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Weanalyzetheproblemaboveandthencomeupwiththefollowingapproachtowardsresult.
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.TerminologyandConventions
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●SymbolsandDefinition
Table5:
symbolsandDefinition
.Models
4.1ASimpleExample
4.1.1TheBasicAssumption
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1.Thisassumptionisnotfullyrealistic,butitshouldnotaffectourendresultstoomuchanditmakesthemodeleasiertoimplement.WecanstillhavetheunexpectedarrivalofWPs.
2.Thisassumptionisunrealistic,butourmodelcouldeasilybechangedtohandlefinaldestinationsaswell,
3.AlthoughthisassumptionmightbefalsearoundthetimeoftheSpecialOlympicsorotherspecificevents,foratypicaldayitisreasonable.
4.2PreviousModels
Assumethetemperatureintheovenisdistributedevenlyattheupperandlowersurfaceofthebakingcakeinthepan,andthematerialinthepanisuniform.Therefore,thedifferenceoftheamountofheatenteringthesurfaceonlyoccursattheedgeofthecakebecauseofthegeometricdifferencealongtheedge.Basedontheassumption,onlytheheatcrossingtheedgesisconsideredinthispaperandtheproblemistakenasatwodimensionalproblem.
Let
betheregionofthepanand
bethe temperatureat
attimet.Sincethereisnoheatsourceinthepan,usatisfiestheheatconductionequation
(1)
Theinitialvalueis
(2)
Andtheboundaryconditionis
(3)
WhereT0isthenormalatmospherictemperatureandT1isthestabletemperatureintheoven.Inashortperiodt0,thetemperatureintheovenraiserapidlyfromT0toT1.
Tofindtherelationoftheshapeofedgetotheamountofheatcrossingtheedge.Theproblem
(1)-(3)hastobesolvedfirst.
4.3MathematicsofOurModel
4.3.1SimulationandAnalysis
4.3.2Results
4.3.3StrengthandWeakness
Strength:
●Algorithmoptimalwithperfectknowledge
●Provedaninterestingtheorem
●Efficientalgorithmruntime.
.ImprovedModel
5.1AdditionalAssumptions
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5.2TheFoundationofModel
5.3results
5.4StrengthandWeakness
●Hardtoexplainalgorithmtononmathematicians.
●Algorithmusesonlyfactualknowledgeoftoday,nostatisticalprojections.OuralgorithmplansbasedoncurrentknowledgeofscheduledarrivalsbutmakesnoattempttoguesswhereaWImayappear.
.SensitivitytoParameters
.Conclusion
.Reference
[1]Halmos,P.,andH.Vaughan.1950.Themarriageproblem.AmericanJournalofMathematics72:
214-215.
[2]ChicagoDepartmentofAviation.2001.TheChicagoAirportSystempreparespassengersforThanksgivingholidaytravel.(16November2001).http:
//ww.flychicago.com/doa/avi-news/doa-avi-news-pr-73.shtm
[3]
[4]
.Appendix
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