有需要的同學(xué)可以-美賽mcm寫作模版各部分

第一段：寫解決什么問1：“Handmove”irrigation,acheapbutlabor-intensivesystemusedonsmallfarms,consistsofamovablepipewithsprinklerontopthatcanbeattachedtoastationarymain.2:……isareal-lifecommonphenomenonwithmany3：Aneffectiveplan)iscrucial1：Wefindtheoptimalnumberoftollboothsinahighwaytoll-plazaforagivennumberofhighwaylanes:thenumberoftollboothsthatminimizesaveragedelayexperiencedbycars.例2：Abrand-newuniversityneedstobalancethecostofinformationtechnologysecuritymeasureswiththepotentialcostofattacksonitssystems.例3：Wedeterminethenumberofsprinklerstousebyyzingtheenergyandmotionofwaterinthepipeandexaminingtheengineeringparametersofsprinklersavailableinthemarket.例4:Aftermathematically yzingthe……problem,ourmodelinggroupwouldliketopresentourconclusions,strategies,(and mendations)tothe…….5：Ourgoalis...thatminimizesthetimeWithoutimplementingdefensivemeasure,theuniversityisexposedtoanexpectedlossof$8.9millionperyear.Passes(QP),reservationslipsthatideallyallowanindividualtospendlesstimewaitinginline.1Weformulatetheproblemasanetworkflowinwhichverticesarethelocationsofescortswheelchair2:Ana?vestrategywouldbetoemploytheminimumnumberofescortstoguaranteethatallpassengersreachtheirgatesontime.3：Wedividethejumpintothreephases:flyingthroughtheair,punchingthroughthestack,andlandingontheground.第二、三段：具體分在什么模型中/1：Weformulateadifferentialmodeltoaccountfortheratesofchangeoftheseusesandhowthischangewouldaffecttheoverallconsumptionofwaterwithinthestudiedregion.例2:Weexaminedthemathematicaleffectsof.Wedevelopedadetailed……(simulationmethodology)totestourideasandtofythedifferencesbetween(among)different……(strategies).3：Basedon(writeyourbasis.suchasthetheoryofsupplyanddemand),weestablishamodel(suchasdifferentialequationsystemthatincludesdemand,supply).4：To(writetheaimsweestablishacriterion(writethe5：Webuildamodeltodeterminehowtolayoutthepipeeachtimetheequipmentis6：Wedetermine7：Webuildamodelto例8：Weformulateamodelfor………Byyzing…and1：UsinghistoricaldatafromtheUnitedStateswedetermineinitialconditionsforour2:Softwarepackingreaches………bycalculatingand1：togroundthismodelinrealityweincorporateextensivedemographicdataand例2：Wefitthemodifiedmodeltodata(suchas1970-2003.).Weconcludethat(writethelast1：Wephysicallycharacterizethesystem2：Weprovideastrategy(writethelogical3：The…modelisefficient,intuitive,andflexible)andcouldbeapplied例4：Tomeettheneedsofpeopletodaywithout,weestablishacriterionofrational(合理的標準)oil Weshowthatthisstrategyisnotoptimalbutcanbeimprovedbyassigningdifferent1：IfDeltaAirlinesweretoutilizethena?vestrategyatAtlantaInternationalAirport,thecostwouldbe……2Wethemodelto(otherfield).3：OurresultsaresummarizedintheformulafortheoptimalnumberBoftollbooths例：Forvarioussituationsweproposeanoptimal1：weelicitthata例2：Weconcludewithaseriesof mendationsforhowbestto…例：Inadditiontothemodel,wealsodiscusspoliciesfor例:Todemonstratehowourmodelworks,weapplyitto最后一段：寫總的結(jié)例：Oursuggestedsolution,whichiseasytoimplement,includesadetailedtimetableandthearrangementofpipes.例1：Ouralgorithmisbroadenoughto modatevariousairportconcourses,flightschedules,andflightdelays.例2：Our ysisbeganbydeterminingwhatfactorimpact……,Ourconclusionsare例：Sinceourmodelisbasedon……itcanbeappliedto(other其他（承上啟下的連接詞/常用詞組例:Inadditiontothemodelwealsoreviewsummarizepresentoutlinedescribepurposeattemptaim等，另外還可以用動詞不定式充當目的狀介紹的重點內(nèi)容或研究范圍，常用詞匯有study,present,include,focus,emphasize,emphasis,attention等consider,yze,ysis等,show,resultpresentsummaryintroduceconclude等陳述的論點和作者的觀點，常用詞匯有suggest,repot,present,expect,describe說明論證，常用詞匯有等support,provide,indicate,identify,find,demonstrate,confirm,clarify推薦和建議，常用詞匯有suggest,suggestion, mendation,propose,necessity,necessary,expect等。中常用的詞語匯criticalalgorithm methodofevaluatingappropriateconsiderconfigurationsoptimalizestrategyparameteraccuracystrengthsandweaknessescontact相關(guān)的contract建立，構(gòu)造calculate計算establish建立formula公式modify改進rational合理的countermeasure對策criterionWemakethefollowingassumptionsabout……processinthis例1：Wedonottakeintoaccountinteractionsbetween例2：Theinfluenceofcanbe例3：…isidealincanbe1：Infact（inreality）factorseffecteachothers,butinordertosimplifythemodel,weignoretheinteractionsbetweenfactors.例2：Infactinrealityfactorseffecteachothers,butinordertosimplifythemodelweignoretheinteractionsbetweenfactors.近例1：……canbeapproximatedasalinerfunctionof2…areassumedtobethesame.Inpracticethereisaslight例3：……canbeapproximatedasalinerfunctionof細致考慮（可附原因1：Anairportconsistsof1to10concourseseachofwithconsistsof2to50gatesGatesinthesameconcoursearegenerallylocatedclosetooneanother,whilethetraveltimebetweenconcoursescanbequitelengthy.Hence,weassumethatinter-concoursetravelismuchlengthierthanintra-concoursetravel.2：Aaveragefastwalkingspeedis250ft/min(3mph),butaveragespeedwhenarmsareimmobilized(aswhenpushingawheelchair)isonly180ft/min(2mph)[GrossandShi2001].Weassumethatanescortwalksatthesespeeds.例3：Anescortcanoperateonlyonewheelchairatatime.U.S.Dept.oftransportationguidelinesdiscouragesleavingWPsunattended.HencetheescorttakesaWPtotheconnectingflightandremainsuntiltheflight直接定義(假設(shè)例1：Tomeasurethe……,we例2：Yearlyindustrystatisticscanbeused例3：Sthmayberepresented例4：….areindependentandrandomlyAdditionalassumptionsaremadetosimplifyysisforindividualsections.Theseassumptionswillbediscussedattheappropriatelocations.由假設(shè)得到公WeassumelaminarflowanduseBernoulli’sequation:（由假設(shè)得到的公式Accordingtotheassumptions,ateveryjunctionwehave（由于假設(shè)由原因得到公Becauseourfieldisflatwehave公式sotheheightofoursourcerelativetooursprinklersdoesnotaffecttheexitspeedv2（由原因得到的公式；Sincethefluid pressible(由于液體是不可壓縮的we用原來的公式推出公Pluggingv1intotheequationforv2weobtain（12中得到Puttingthesetogether(把公式放在一起becauseofthelawofconservationofenergyThereforefrom2),(3),(5wehavetheithjunction（由前幾個公式得Putting(1)-(5)together,wecanobtainpupateveryjunction.infact,atthelastjunction,wePuttingtheseinto1weget（1中WhichmeansthattheCommonly,hisFromtheseequations,（從這個公式中我們知道）weknowthat引出約束條UsingpressureanddischargedatafromRainBird結(jié)果Wefindtheattenuationfactor（得到衰減因子，常數(shù)，系數(shù)）to計算結(jié)Tofindthenewpressureweusethe00),whichstatesthatthevolumeofwaterflowinginequalsthevolumeofwaterflowingout:（為了找到新值，我們用什么方程）()is;;SolvingforVNweobtain公式的解WherenistheWehavethefollowingdifferentialequationsforspeedsinthex-andy-Whosesolutionsare（解Weusethefollowinginitialconditions(使用初值todeterminethedrag根據(jù)原有公Weapplythelawofconservationofenergy（根據(jù)能量守恒定律）TheworkdonebytheforcesThedecreaseinpotentialenergyis（勢能的減少Theincreaseinkineticenergyis動能的增加Drugactsdirectlyagainstvelocity,sotheaccelerationvectorfromdragcanbefoundNewton’slawF=maas:(第二定律)WhereaistheaccelerationvectorandmisUsingtheNewton’sSecondLaw,wehavethatF/m=aSoSettingthetwoexpressionsfort1/t2equalandcross-multiplyingWeapproximatethebinomialdistributionofcontenderswithanormalWherexisthecumulativedistributionfunctionofthestandardnormaldistribution.ClearingdenominatorsandsolvingtheresultingquadraticinBgivesAsanyticapproximationto.fork=1,wegetB=c26．Integrating,（使結(jié)合）wegetPVT=constantwhereThemaincompositionoftheairisnitrogenandoxygen,soi=5andr=1.4,AccordingtoFirstLawofThermodynamics,weWhere ).wealsothenWherePisthepressureofthegasandVisthevolume.WeputthemintotheIdealGasInternal對公式變DefineA=nlwtobethe )（定義）rearranging1)produces（將公式變形得到 izeEforeachlayersubjecttotheconstraint2Thecalculationsareeasierifweminimize1/E.（為了得到最大值，求他倒數(shù)的最小值）Neglectingconstantfactors（忽略常數(shù)）,weminimize使服從約束條Subjecttotheconstraint（使服從約束條件WhereBisconstantdefinedin2Howeveraslongasweareobeyingthisconstraintwecanwrite（根據(jù)約Andthusfdependsonlyonhthefunctionfisminimizedat（求最小值A(chǔ)tthisvalueofh,theconstraintreduces結(jié)果說Thisimplies（暗示）thattheharmonicmeanoflandwshouldSo,intheoptimalsituation.Thisvalueshowsverylittlelossduetofriction.（結(jié)果說明）TheescapespeedwithfrictionWeuseasimilarprocesstofindthepositionofthedroplet,resultingWitht=0.0001s,errorfromtheapproximationisvirtuallyWecalculateditstrajectory(軌道Forthatcase,usingthesameexpansionforeasSolvingfortandequatingittotheearlierexpressionfort,weRecallingthatinthisequalityonlynisafunctionoff,wesubstitutefornandsolveforf.theresultAsv=…,this essingular單數(shù)的由語句得到公TherevenuegeneratedbytheflightThenweWedifferentiatetheideal-gasstateWeeliminatedTfromthelasttwoequationstoget（排除因素得到Wefistexaminethepaththatthemotorcyclefollows.Takingtheairintoaccount,wegettwodifferentialequationsWherePistherelativepressureWemustfirstfindthespeedv1ofwateratoursource:（找初值圖Firstwestudythe文獻)，showingundertheThecompressionprocessisdividedintothree(數(shù)字phasesasshownintheThefirstphase:……deformation,accordingto……;thesecondphase:……pressiongrowsmoreslowlyandreachestheum.Thethirdphase:……deformation:Aftercompressionreachestheum,therateofdeformationstartstofall.Theunrecoverabledeformationgoesonincreasing.(2003—65)Amodelofflowrateforinstanttotalfailureisrighttriangular【U.SArmyCorpsofEngineers1997】.(seeFigure1)(2005—53\54)WevalidateourmodelbyexamininghistoricalHIVratesfromprenatalclinicsinSouthAfricabetween1995and2005(Figure1).(2006—244)Figure1showsthenumberofbagsstillleftfortheEDStoprocessatairportAaftereachminuteinairportB,theresultsaresimilar.(2003—260)Todemonstratebetterthechangeinflowratewithtimewhenthebreachbeginstform,weplotoverashorterrangeoftimeinFigure5.(2005—55)

W1forvaluesofBfrom6to13,instepsof0.25,togetherwiththebest-fitquartic,inFigureFitting式子tothedatain表wegetthecurveinFigure1,forthefunction公式2005—211)WeusethegraphinFigure1tosimulatethearrivalofpassengers.(2003—201)ThesimulationmodelalsogeneratessystemcharacteristicsfortheETDmachinesatairportA.TheseresultsareshowninFigure3.(2003—232)Wetake2001asthestartingpoint,whentotalremainingoilwas1.1178bbl.Wecalculatethetimetooilexhaustionunderdifferentcases:GDPgrowingat10%,5%,3%,and1%.(Figure3)For10%,......;for5%,……;for3%,……;for1%,…….(2005—213\233) Tosolvethedifferentialequationsinourmodel,weuse(theODE45numericalintegrator)in (式子)tofindtheresultsinFigure3.(2005—232)Generallyspeaking,theshapeofthetargetisnottooirregular,sowechoosefivetypicalshapesofthetargetsindifferentsizes.InFigure3a,weillustratethe umsectionofatypicalbean-shapedtarget,whoseumdimensionis35mm.Usingtheskeletongenerationalgorithm,wegetcorrespondingskeletonshowninFigure3b.ThenweapplytheGA-basedshotplacementalgorithm,resultinginthreeshotsforthetarget:one14mmhelmetandtwo8mmhelmets.Thelocationsandsizesofthehelmetsin2DareindicatedinFigure3c,while3DshotplacementsareshowninFigure4.(2003—130)TheirrigationorderandpositionofsprinklersarepresentedinFigure4.(2006—ThisalgorithmcanbeviewedintheflowchartinFigure3.Wedefinesomeoftheobjectsfoundinthechart.表1 InTable1,wesummarizetheminimumnumberofescortsneededtoreacheachserviceForeachairport,thedifferencebetweentheGoodandAdequateservicelevelsisroughlyafactoroftwo,withslightlyincreasingreturnstoscale;withlargerscales,thestaffarespreadmoreuniformly,soitislesslikelythatajobwillcropupwithnobodycloseenoughtotakeit.（前面的說出數(shù)據(jù)的來源，然后篩選出比較代表性的數(shù)據(jù)進行說明）Wedeterminedabsoluteandrelativecriticalityvaluesforeachcountryforwhichallthedatausedincomputingparameterswasavailable(108countries).Wethenusedrelativecriticalityinselectingourmostcriticalcountries,bycontinent.Hadweusedabsolutecriticalityitwouldhavegivenprecedencetolargenations,despiterelativelymildHIV/AIDSsituations.例Thetablebelowisthegeneratedirrigationschedulefortherepositioningofthesprinklers,given12-hourworkdayforarancher.Eachpipeissetinplacefor5hours.例Andsomedataprocessingwecangettherelevantstatisticaldatainformationofpatientanddonorcharacteristicsforthesimulation.例ThegraftsurvivalratesshowinthefollowingUNOSdataforkidneytransplantsintheU.S(basedonOPTNdataasof2006):Table9showslinearfitparametersforallthreemodels.Notethatallthreemodelsarewelldescribedbyalinearequation.例Usingthecellularautomatamodel,wecomputewaitingtimeasafunctionofboththenumberoflanesandthenumberoftollbooths.ForafixedL,wecompareallvaluesofCtotalandchoosethelowestone.TheresultsofthismethodarepresentedinTable6.例Accordingtotheabovedata,wecanseethatmanyoftheEuropeancountrieshavethehighratesofthedonor,particularlyinSpain.ThisphenomenonshowsthattheorgantransplantisalsohotinEurope.AlthoughtherelevantpoliciesandstatutesinthesecountriesarelesscomprehensivethanthatinU.S,therestillalotwhatU.Scouldlearnfrom.Here,wemainly yzetheorgantransplantpoliciesinSpain,U.KandKoreathisthreecountries.……Thepopulationcontainedineachregionissummarizedintable1.（在表后對數(shù)據(jù)的內(nèi)容例AsindicatedinTable6,thereisfairlygoodagreementbetweenthe mendednumberofboothsforatypicaldayandforpeakhours.However,wenotethattheoptimalboothnumberforatypicaldayneverexceedsthatforrushhour.Rushhourseemstorequireslightlymoreboothsthanatypicaldayinorderfortheplazatooperatemostefficiently.EachvalueinTable6isrepresentativeofapproximay20trials.Throughthesetrials,wenotedremarkablestabilityinourmodel.Despitethestochasticnatureofouralgorithm,eachnumberoflaneswasalmostalwaysoptimizedtothesamenumberoftollbooths.Therewereahandfulofexceptions;theyoccurredexclusivelyforsmallnumbersofhighwaylanes(<3lanes).IntegervaluesarepresentedinTable6onlybecausefractionaltollboothshavenophysicalmeaning.3例WecanobtainthedatawhichisinvolvedwiththestatusoftheAmericanTransplantfromthedatabanks.WehavecollectedthedemandofthevariousorgansinUnitedStatestodate,theannualdonors，transplantsandthedemand(Heretakingthekidneyforexample,byyears1995-2006)Fromtheabovetable1,wecanseethatthekidneyaccountsfor73%intotaloftheorgantransplants.Itaccountsforaverylargeproportionasamostimportantorganwhichcanbetransplanted.Therefore,weonlyneedtodiscussthestatusofthekidneytransplanthere,beingabletoachievethe ysisandresearchontheorgantransplant.Accordingtotheabovedata,wecangetthefiguresas例Soaftermanytimessimulationundertheconditionsdiscussedabove,weobtainstatisticresultsasfollow: yzingtheaboveresult,wecanfind:Whentherearemoredonorsresources),thenumberoftransplantwillincreaseobviously,andthematchingratechangesonlyalittle;Whenthenetworkisdividedinto11regions(smallnetworks),thecostsofthetransportandpreservationoftheorganwillbereducedgreatly.例Table7reportsthegeneralpatientstatisticsundereachregimeinthecolumns.Thefirstcolumninthesetablesreportsthetotallivedonortransplantsaspercentageofthepopulationsize,whichisthesumofnexttwocolumns,transplantsfromowncompatibledonorandtransplantsfromtrades.Theforthcolumnisthepercentageofpatientsupgradedtothetopofthewaitlistasheadsofw-chains.Thefifthandsixthcolumnsreportthequalityofmatchesinthelivedonortransplants:theriskofgraftfailurerelativetotheriskunderno-exchangemechanismwithpopulationsizen=400isreportedinthefifthcolumnandthenumberofHLAmismatchesforanaveragetransplantisreportedinthesixthcolumn.Inthetable8,wechangetheninto200.Bycomparison,wecanfoundthatthematchingproportion elittleandthematchingqualitywillgetworseasthetotalnumberofthepatientsdecrease.Theresultisconsistentwiththereality.The30%probabilityofthewaitinglistorlowqualityexchangeisanadjustable例Also,wewishtoexplorethesituationinwhichthereisonelaneper例Theparameterswechoosetomodifyarep(probabilityofadvancement),‘delay’(numberoftimestepsrequiredtoserveavehicleinatollbooth),andq(theprobabilitythataflaggedvehicleoptstoattemptaturn).TheresultsofthisysisarepresentedinTable7.Sincewehaveusedsixlanesasourstandardtestcase,wecontinuewiththischoicehere.AsindicatedinTable7,ourcellularautomatamodelisrelativelyinsensitivetobothpandq.Changes±11%and±5.2%inpandq,respectively,hadnoeffectontheoptimalnumberoftollboothsforasixlanehighway.Ontheotherhand,increasingthedelaytimeby25%shiftedtheoptimalnumberofboothsfrom10to11(10%).Decreasingthedelayby25%hadnoeffectonthesolution.Perhapsadditionalworkcouldleadtoanelucidationoftherelationbetweendelayandoptimalboothnumberthatcouldhelpstabilizethecellularautomatamodel.EvaluationsofsolutionsOurmainmodel'sstrengthisitsenormousedibility.For Includingalltheseintoasingle,robustframework,ourmodelWedevelopedatheoreticallineformationmodelwhichagreeswithoutroughdata.Ourcomputermodelagreeswithbothdespiteworkingondifferentprinciples,implyingitbehavesaswewant.ThisallowsustomakesubstantiveconclusionsFinally,ourmodelisstrongbecauseTheMonteCarlosimulationhasbeenperfectlyusedinourmodels,andthesimulationresultsareconsistentwiththereality.Weintroduced……inordertoimprovetheexchangequality.Thechainrulescanalsomodifiedinadegree.Themodelsusedinourpaperispromotional,inviewofdifferentwecanmodifyourmodelsthemodelisindependentofthesite )modelisthealgorithmisefficientacorrespondingstrengthofourmodelisthatitwouldberelativelyeasytoincludeaparameterforprobabilityof……Ourmodelisparticularlyappropriateforsimulationof……,aproblemthatnaturallylendsitselftosuchdiscretemodeling.ThefundamentalstrengthsofourmodelThemodelisindependentProcessor-basedmodelhasfewinputparameters,leadingtogoodrobustnessandUsesavarietyofmodelingtechniquesinanintegrated,holisticOurmodeleffectivelyachievedallofthegoalswesetinitially.Itwasfastandcouldhandlelargetiesofdata,butalsohadtheflexibilitywedesired.Thoughwedidnottestallpossibilities,weshowedthatourmodeloptimizesstatedistrictsforanyofanumberofvariables.Ifwehadchosentoinput e,poverty,crimeoreducationdataintoourinterestfunction,wecouldhaveproducedhigh-qualityresultswithvirtuallynoaddeddifficulty.Aswell,ourmethodwasrobust.Ourmainmodel'sstrengthisitsenormousflexibility.ForThisallowsustomakesubstantiveconclusionsaboutpolicyissues,evenwithoutextensivedatasets.Byvaryingparameters,allocationrules,andourprogram'sobjectivefunction——allquitefeasiblewithinthestructure——wecanexaminethegutsofpolicymaking:theethicalprinciplesunderlyingapolicy,theimplementationrulesdesignedtofulfillthem,andthesometimesnebulousnumbersthat erntheresults.Finally,ourmodelisstrongbecauseofitsdiscreteThefundamentalstrengthsofourmodelareitsrobustnessandflexibility.Allofthedataisfullyparameterized,sothemodelcanbeappliedto……Somespecialdatacan’tbefound,anditmakesthatwehavetodosomeproperassumptionbeforethesolutionofourmodels.Amoreabundantdataresourcecanguaranteeabetterresultinourmodels.Currentlinelengthisnottakenintoaccountbythelineformationmodel.Inreallife……Weaknessesofthemodelincludedassumptionsmadeforsimplicitythatlikelydonothold.Forinstance,inmostrunsofourmodelon(sides……),cases(impact/conclusion)to……Thisfeatureislikelyaresultofourassumptionthat/Theprimaryweakness ofthismodelisthe( Itshouldbepossibletoeliminatethis, anotherweaknessthat cor