MCM写作举例.docx

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1、MCM写作举例摘要第一段：写论文解决什么问题1.问题的重述a.介绍重点词开头：例1：Handmoveirrigation,acheapbutlabor-intensivesystemusedonsmallfarms,consistsofamovablepipewithsprinklerontopthatcanbeattachedtoastationarymain.例2:isareal-lifecommonphenomenonwithmanycomplexities.例3：n(effectiveplan)iscrucialtob.干脆指出问题：例1：Wefindtheoptimalnumbero

2、ftollboothsinahighwaytoll-plazaforagivennumberofhighwaylanes:thenumberoftollboothsthatminimizesaveragedelayexperiencedbycars.例2：Abrand-newuniversityneedstobalancethecostofinformationtechnologysecuritymeasureswiththepotentialcostofattacksonitssystems.例3：Wedeterminethenumberofsprinklerstousebyanalyzin

3、gtheenergyandmotionofwaterinthepipeandexaminingtheengineeringparametersofsprinklersavailableinthemarket.例4:.Aftermathematicallyanalyzingtheproblem,ourmodelinggroupwou1d1iketopresentourconclusions,strategies,(andrecommendations)tothe.例5：Ourgoalis.that(minimizesthetime).2.解决这个问题的宏大意义反而说明。假如没有Withoutim

4、plementingdefensivemeasure,theuniversityisexposedtoanexpectedlossof$8.9millionperyear.3.总的解决概述a.通过什么方法解决什么问题例：WeaddresstheproblemofoptimizingamusementparkenjoymentthroughdistributingQuickPasses(QP),reservationslipsthatideallyallowanindividualtospendlesstimewaitinginline.b.实际问题转化为数学模型例1Weformulatethe

5、problemasanetworkflowinwhichverticesarethelocationsofescortsandwheelchairpassengers.例2:navestrategywouldbetoemploytheminimumnumberofescortstoguaranteethatallpassengersreachtheirgatesontime.c.将问题分阶段考虑例3：Wedividethejumpintothreephases:flyingthroughtheair,punchingthroughthestack,andlandingontheground.其

6、次、三段：具体分析1.在什么模型中/建立了什么模型a.主流模型例1：Wcformulateadifferentialmode1toaccountfortheratesofchangeoftheseuses,andhowthischangewouldaffecttheoverallconsumptionofwaterwithinthestudiedregion.例2:Weexaminedthemathematicaleffectsof.Wedevelopedadetailed(simulationmethodology)totestourideasandtoquantifythedifferen

7、cesbetween(among)different(strategies).例3：Basedon(writeyourbasis.suchasthetheoryofsupplyanddemand),weestablishamodel(suchasdifferentialequationsystemthatincludesdemand,supply).例4：To(writetheaims),weestablishacriterion(writethecriterion),b.模型非主流例5：Wcbuildamodeltodeterminehowtolayoutthepipeeachtimethe

8、equipmentismoved.例6：Wcdetermine例7：Webuildamodeltodetermine.例8：WeformulateamodelforByanalyzingandexamining.2.分析模型(运用什么数据，怎么做，一般三句话)a.写历史数据例1：UsinghistoricaldatafromtheUnitedStates,wedetermineinitialconditionsforourmodel.b.写计算机模拟例1：thismodelleadstoacomputersimulationofcatch-cantestsoftheirrigationsyst

9、emand例2:Softwarepackingreachesbycalculatingandcomparing.c.运用数据模拟例1：togroundthismodelinreality,weincorporateextensivedemographicdataandrun例2：Wcfitthemodifiedmode1todata(suchas1970-2003.).Weconcludethat(writethelastconclude).d.讲具体分析例1：WephysicalIycharacterizethesystemthat例2：Wcprovideastrategy(writethe

10、logicalstrategy).例3：Themode1is(efficient,intuitive,andflexible)andcouldbeappliedto例4：Tomeettheneedsofpeopletodaywithout,weestablishacriterionofrational(合理的标准)oilallocation(安排).3.总结该模型的结果/得到什么结论a.说明不是最优但能产生作用例：Weshowthatthisstrategyisnotoptimalbutcanbeimprovedbyassigningdifferentnumbersb.说明假如用这个模型，结果

11、如何例1：IfDeltaAirlinesweretoutilizethenavestrategyatAtlantaInternationalAirport,thecostWoUldbe例2：Wemodifythemodeltoreflect(sometrendsuchasexponentialIyincreasing)andgeneralizethemodelto(otherfield).例3：OurresultsaresummarizedintheformulafortheoptimalnumberBoftolIboothsforc.通过其上状况的列举得到的结论例：Forvarioussit

12、uations,weproposeanoptimalsolution,d.得出了结论例1：weelicitthataconclusion.例2：Weconcludewithaseriesofrecommendationsforhowbesttoe.进一步说明其他因素对模型的影响例：Inadditiontothemodel,wealsodiscusspoliciesfor.f.用真实数据检验模型:Todemonstratehowourmodelworks,weapplyitto.最终一段：写总的结论a.说明结论的可行性例：Oursuggestedsolution,whichiseasytoimp

13、lement,includesadetailedtimetableandthearrangementofpipes,b.说明算法的广泛性例1：Ouralgorithmisbroadenoughtoaccommodatevariousairportconcourses,flightschedules,andflightdelays.例2：Ouranalysisbeganbydeterminingwhatfactorimpact,Ourconclusionsarepresentedc.说明模型可用于其他领域例：Sinceourmodelisbasedonitcanbeappliedto(other

14、domain).其他(承上启下的连接词/常用词组)例：InadditiOntothemodel,wealsodiscuss弓I言部分（1）回顾探讨背景，常用词汇有review,SUmmarize,present,outline,describe等（2）说明写作目的，常用词汇有purpose,attempt,aim等，另外还可以用动词不定式充当目的状语来表达（3）介绍论文的重点内容或探讨范围，常用词汇有study,present,include,focus,emphasize,emphasis,attention等方法部分（1）介绍探讨或试验过程，常用词汇有testStu用,investigat

15、e,examine,experiment,discuss,consider,analyze,analysis等（2）说明探讨或试验方法，常用词汇有mCaSUre,estimate,calculate等（3）介绍应用、用途，常用词汇有等结果部分（1）展示探讨结果，常用词汇有show,resu11,present等（2）介绍结论，常用词汇有summary,introduce,conclude等探讨部分（1）陈述论文的论点和作者的观点，常用词汇有suggest,report,present,expect,describe等（2）说明论证，常用词汇有等support,provide,indicate,

16、idcntify,find,demonstrate,confirm,clarify（3）举荐和建议，常用词汇有suggest,suggestion,recommend,recommendation,propose,necessity,necessary,expect等。摘要中常用的词语汇：critical至关重要的algorithm运算法则amethodofevauating评价方法appropriate近似的consider考虑configurations布局OPtimaI统一的maximize使最大化strategy策略parameter参数，主要的确定因素accuracy精确性stren

17、gthsandweaknesses优点和缺点COnlaCt相关的contract建立，构造calculate计算establish建立formula公式modify改进rational合理的countermeasure对策criterion标准，准则ASSUmPtionS引出：Wemakethefollowingassumptionsaboutprocessinthispaper.a.不考虑因素例1：Wcdonottakeintoaccountinteractionsbetweenfactors.例2：Theinfluenceofcanbeneglected例3：isidealin,canbe

18、neglected.b.为了简化模型，之后反对不正确，但是合理。例1：Infact(inreality)factorseffecteachothers,butinordertosimplifythemodel,weignoretheinteractionsbetweenfactors.例2：Infactinrealityfactorseffecteachothers,butinordertosimplifythemodel,weignoretheinteractionsbetweenfactors,c.近似例1：canbeapproximatedasalinerfunctionof.例2：ar

19、eassumedtobethesame.Inpractice,thereisaslightdifference.例3：canbeapproximatedasalinerfunctionof.d.细致考虑(可附缘由)例1：nairportconsistsof1to10concourses,eachofwithconsistsof2to50gates.Gatesinthesameconcoursearegenerallylocatedclosetooneanother,whiIethetraveltimebetweenconcoursescanbequitelengthy.Hence,weassu

20、methatinter-concoursetravelismuchlengthierthanintra-concoursetravel.例2：Aaveragefastwalkingspeedis250ftmin(3mph),butaveragespeedwhenarmsareimmobilized(aswhenpushingawheelchair)isonly180ft/min(2mph)GrossandShi2001.Wcassumethatanescortwalksatthesespeeds.例3：nescortcanoperateonlyonewheelchairatatime.U.S.

21、Dept.oftransportationguidelinesdiscouragesleavingWPsunattended.Hence,theescorttakesaWPtotheconnectingflightandremainsuntiltheflighleaves.e.干脆定义(假设)：例1：Tomeasurethe,wedefine例2：Yearlyindustrystatisticscanbeusedvalid.例3：Sthmayberepresentedby例4：.areindependentandrandomlydistributed总结:Additionalassumptio

22、nsaremadetosimplifyanalysisforindividualsections.Theseassumptionswi11bediscussedattheappropriatelocations.公式由假设得到公式1.WeassumelaminarflowanduseBernoullisequation:（由假设得到的公式）公式Where符号说明ACCOrdingtotheassumptions,ateveryjunctionwehave（由于假设）公式由缘由得到公式2.Becauseourfieldisflat,wehave公式，sotheheightofoursourcer

23、elativetooursprinklersdoesnotaffecttheexitspeedv2（由缘由得到的公式）：公式Sincethefluidisincompressible（由于液体是不行压缩的），wehave公式Where公式用原来的公式推出公式3.Pluggingvlintotheequationforv2,weobtain（将公式1代入公式2中得到）公式11.Puttingthesetogether（把公式放在一起），becauseofthelawofconservationofenergy,yields：公式12.Therefore,from（2）,（3）,（5）,wehav

24、etheithjunction（由前几个公式得）公式Putting（1）-（5）together,wecanobtainpupateveryjunction.infact,atthelastjunction,wehave公式Puttingtheseinto（1）,weget（把这些公式代入1中）公式WhichmeansthattheCommon1y,hisaboutFromtheseequations,（从这个公式中我们知道）weknowthat引出约束条件4.UsingpressureanddischargedatafromRainBird结果，Wefindtheattenuationfac

25、tor（得到衰减因子，常数，系数）tobe公式计算结果6.Tofindthenewpressure,wcusethe（OO）,whichstatesthatthevolumeofwaterflowinginequalsthevolumeofwaterflowingout:（为了找到新值,我们用什么方程）公式WhereOis：7.SolvingforVNweobtain（公式的解）公式Wherenisthe.8.Wehavethefollowingdifferentialequationsforspeedsinthe-andy-directions:公式Whosesolutionsare（解）公

26、式9.Wcusethefollowinginitialconditions（运用初值）todeterminethedragconstant:公式依据原有公式10.Weapplythelawofconservationofenergy（依据能量守恒定律）.Theworkdonebytheforcesis公式Thedecreaseinpotentialenergyis（势能的削减）公式Theincreaseinkineticenergyis（动能的增加）公式Drugactsdirectlyagainstvelocity,sotheaccelerationvectorfromdragcanbefou

27、ndNewtonslawF=maas:（牛顿其次定律）WhereaistheaccelerationvectorandmismassUsingtheNewtonsSecond1.aw,wehavethatFm=aand公式Sothat公式Settingthetwoexpressionsfortlt2equalandcross-multiplyinggives公式22.Weapproximatethebinomialdistributionofcontenderswithanormaldistribution:公式Wherexisthecumulativedistributionfunction

28、ofthestandardnorma1distribution.ClearingdenominatorsandsolvingtheresultingquadraticinBgives公式sananalyticapproximationto.fork=l,WegetB=C26.Integrating,（使结合）wegetPVT=Constant,where公式Themaincompositionoftheairisnitrogenandoxygen,soi=5andr=l.4,so23.AccordingtoFirst1.awofThermodynamics,weget公式Where（）.wea

29、lsothenhave公式WherePisthepressureofthegasandVisthevolume.WeputthemintotheIdealGasInternalFormula:公式Where对公式变形13.DefineA=nwtobethe（）（定义）；rearranging（1）produces（将公式变形得到）公式WemaximizeEforeachlayer,subjecttotheconstraint（2）.Thecalculationsareeasierifweminimize1E.（为了得到最大值，求他倒数的最小值）Neglectingconstantfactors

30、（忽视常数），weminimize公式使听从约束条件14.Subjecttotheconstraint（使听从约束条件）公式WhereBisconstantdefinedin（2）.However,aslongasweareobeyingthisconstraint,wecanwrite（依据约束条件我们得到）公式Andthusfdependsonlyonh,thefunctionfisminimizedat（求最小值）公式Althisvalueofh,theconstraintreducesto公式结果说明15.ThiSimPlies（示意）thattheharmonicmeanof1and

31、wshouldbe公式So,intheoptimalsituation.5.Thisvalueshowsverylittlelossduetofriction.（结果说明）Theescapespeedwithfrictionis公式16.WeuseasimiIarprocesstofindthepositionofthedroplet,resultingin公式Witht=0.OOOls,errorfromtheapproximationisvirtuallyzero.17.Wecalculateditstrajectory（liM）using公式18.Forthatcase,usingthe

32、sameexpansionforeasabove,公式19.Solvingfortandequatingittotheearlierexpressionfort,weget公式20.Recalli11gthatinthisequalityonlynisafunctionoff,wesubstitutefornandsolveforf.theresultis公式Asv=,thisequationbecomesSingUIar（单数的）.由语句得到公式21.Therevenuegeneratedbythefightis公式24.Thenwehave公式Wedifferentiatetheideal

33、-gasstateequation公式Getting公式25.WeeliminatedTfromthelasttwoequationstoget（解除因素得到）公式22.Wefistexaminethepaththatthemotorcyclefollows.Takingtheairresistanceintoaccount,wegettwodifferentialequations公式WherePistherelativepressure.Wcmustfirstfindthespeedvlofwateratoursource:（找初值）公式图引用的文献数据所画的图：1、分阶段图的引入：Fir

34、stwestudythe（文献），showingunderthesituation.分阶段图的引出：Thecompressionprocessisdividedintothree（数字）phases,asshowninthefigure:Thefirstphase:deformation,accordingto：thesecondphase:deformation.Thecompressiongrowsmoreslowlyandreachesthemaximum.Thethirdphase:deformation:Aftercompressionreachesthemaximum,therat

35、eofdeformationstartstofall.Theunrecoverabledeformationgoesonincreasing.(200365)2、引用已有的模型图：Amodelofflowrateforinstanttotalfailureisrighttriangular【U.S.ArmyCorpsofEngineers1997.(seeFigurel)(20055354)3、通过历史数据作图：WevalidateourmodelbyexamininghistoricalHIVratesfromprenatalclinicsinSouthAfricabetween1995an

36、d2005(Figure1).(2006244)4、拟合的图形：Figure1showsthenumberofbagsstillleftfortheEDStoprocessatairportaftereachminuteinairportB,theresultsaresimilar.(2003260)自己依据计算所画的图：1、为了.(目的)，我们作了.图。Todemonstratebetterthechangeinflowratewithtimewhenthebreachbeginstform,weplotoverashorterrangeoftimeinFigure5.(200555)Wep

37、lotIWforvaluesofBfrom6to13,instepsof0.25,togetherwiththebest-fitquartic,inFigure2(200592)2、依据数据拟合的图:Fitting(式子)tothedatain(表)，wegetthecurveinFigure1,forthefunction(公式).(2005211)WeusethegraphinFigure1tosimulatethearrivalofpassengers.(2003201)ThesimulationmodelalsogeneratessystemcharacteristicsfortheE

38、TDmachinesatairport.TheseresultsareshowninFigure3.(2003232)3、依据取值不同画图：Wetake200lasthestartingpoint,whentotalremainingoi1was1.1178bbl.Wecalculatethetimetooi1exhaustionunderdifferentcases:GDPgrowingat10%,5%,3%,and1%.(Figure3)For10%;for5%,;for3%,;for1%,.(2005213233)4、用软件(如MT1.B)画图：Tosolvethedifferentia

39、lequationsinourmode】，weuse(theODE45numericalintegrator)inMT1.Bon(式子)tofindtheresultsinFigure3.(2005232)5,图形的改进:Generallyspeaking,theshapeofthetargetisnottooirregular,sowechoosefivetypicalshapesofthetargetsindifferentsizes.InFigure3a,weillustratethemaximumsectionofatypicalbean-shapedtarget,whosemaxim

40、umdimensionis35mm.Usingtheskeletongenerationalgorithm,wegetcorrespondingskeletonshowninFigure3b.ThenweapplytheG-basedshotplacementalgorithm,resultinginthreeshotsforthetarget:one14mmhelmetandtwo8mmhelmets.Thelocationsandsizesofthehelmetsin2DareindicatedinFigure3c,while3DshotplacementsareshowninFigure

41、4.(2003130)6、画示意图：TheirrigationorderandpositionofsprinklersarepresentedinFigure4.(2006127)ThisalgorithmcanbeviewedintheflowchartinFigure3.Wcdefinesomeoftheobjectsfoundinthechart.(2006164165)表表的格式：表头在上注：红字标记代表可通用的句子1、在表前对表的来源和数据进行说明例1InTable1,wesummarizetheminimumnumberofescortsneededtoreacheachservi

42、celevel表的说明部分Foreachairport,thedifferencebetweentheGoodandAdequateservicelevelsisroughlyafactoroftwo,withslightlyincreasingreturnstoscale;withlargerscales,thestaffarespreadmoreuniformly,soitislesslikelythatajobwillcropupwithnobodyc1oseenoughtotakeit.例2表的说明部分(前面的说出数据的来源，然后筛选出比较代表性的数据进行说明)。Wedetermine

43、dabsoluteandrelativecriticalityvaluesforeachcountryforwhichallthedatausedincomputingparameterswasavailable(108countries).Wethenusedrelativecriticalityinselectingourmostcriticalcountries,bycontinent.Hadweusedabsolutecriticalityitwouldhavegivenprecedencetolargenations,despitcrelativelymildHIV/AIDSsitu

44、ations.例3Thetablebelowisthegeneratedirrigationschedulefortherepositioningofthesprinklers,given12-hourworkdayforarancher.Eachpipeissetinplacefor5hours.例4AndsomedataprocessingWecangettherelevantstatisticaldatainformationofpatientanddonorcharacteristicsforthesimulation.例5Thegraftsurvivalratesshowinthef

45、ollowingUNOSdataforkidneytransplantsintheU.S(basedonOPTNdataasof2006):2、在表后对表的内容进行说明例1Table9shows1inearfitparametersforal1threemodels.Notethatal1threemodelsarewel1describedbyalinearequation.例2Usingthecellularautomatamodel,wecomputewaitingtimeasafunctionofboththenumberoflanesandthenumberoftollbooths.

46、Forafixed1.,wecompareal1VaIUeSofCtotalandchoosethelowestone.TheresultsofthismethodarepresentedinTable6.例3Accordingtotheabovedata,wccanseethatmanyoftheEuropeancountrieshavethehighratesofthedonor,particularlyinSpain.ThisphenomenonshowsthattheorgantransplantisalsohotinEurope.Althoughtherelevantpolicies

47、andstatutesinthesecountriesarelesscomprehensivethanthatinU.S,therestillalotwhatU.Scould1earnfrom.Here,wemainlyanalyzetheorgantransplantpoliciesinSpain,U.KandKoreathisthreecountries.Thepopulationcontainedineachregionissummarizedintable1.(在表后对数据的内容进行总结)例4图表的说明部分AsindicatedinTable6,thereisfairlygoodagr

48、eementbetweentherecommendednumberofboothsforatypicaldayandforpeakhours.However,wenotethattheoptimalboothnumberforatypicaldayneverexceedsthatforrushhour.Rushhourseemstorequireslightlymoreboothsthanatypicaldayinorderfortheplazatooperatemostefficiently.EachvalueinTable6isrepresentativeofapproximately20

49、trials.Throughthesetrials,Wenotedaremarkablestabilityinourmodel.Despitethestochasticnatureofouralgorithm,eachnumberoflaneswasalmostalwaysoptimizedtothesamenumberoftol!booths.Therewereahandfulofexceptions;theyoccurredexclusivelyforsma1numbersofhighwaylanes(3lanes).IntegervaluesarepresentedinTable6onlybecausefractionaltol!boothshavenophysicalmeaning.3、