MCM写作模版(各部分)

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：“Handmove^^irrigation,acheapbutlabor-intensivesystemusedonsmallfarms,consistsof

amovablepipewithsprinklerontopthatcanbeattachedtoastationarymain.

(列2：......isareal-lifecommonphenomenonwithmanycomplexities.

｛列3；An(effectiveplan)iscrucialto............

b.直接指出问题：

例1：Wefindtheoptimalnumberoftollboothsinahighwaytoll-plazaforagivennumberof

highwaylanes:thenumberoftollboothsthatminimizesaveragedelayexperiencedbycars.

例2：Abrand-newuniversityneedstobalancethecostofinformationtechnologysecurity

measureswiththepotentialcostofattacksonitssystems.

例3：Wedeterminethenumberofsprinklerstousebyanalyzingtheenergyandmotionofwater

inthepipeandexaminingtheengineeringparametersofsprinklersavailableinthemarket.

例4-Aftermathematicallyanalyzingthe........problem,ourmodelinggroupwouldliketo

presentourconclusions,strategies,(andrecommendations)tothe.........

例5：Ourgoalis...that(minimizesthetime).............

2.解决这个问题的伟大意义

反面说明。如果没有……

Withoutimplementingdefensivemeasure,theuniversityisexposedtoanexpectedlossof$8.9

millionperyear.

3.总的解决概述

a.通过什么方法解决什么问题

例：Weaddresstheproblemofoptimizingamusementparkenjoymentthroughdistributing

QuickPasses(QP),reservationslipsthatideallyallowanindividualtospendlesstimewaitingin

line.

b.实际问题转化为数学模型

例1Weformulatetheproblemasanetworkflowinwhichverticesarethelocationsofescorts

andwheelchairpassengers.

例2:区naivestrategywouldbetoemploytheminimumnumberofescortstoguaranteethatall

passengersreachtheirgatesontime.

c.将问题分阶段考虑

例3：Wedividethejumpintothreephases:flyingthroughtheair,punchingthroughthestack,

andlandingontheground.

第二、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：Weformulateadifferentialmodeltoaccountfortheratesofchangeoftheseuses,andhow

thischangewouldaffecttheoverallconsumptionofwaterwithinthestudiedregion.

例2：Weexaminedthemathematicaleffectsof.........Wedevelopedadetailed........

(simulationmethodology)totestourideasandtoquantifythedifferencesbetween(among)

different........(strategies).

例3：Basedon(writeyourbasis.suchasthetheoryofsupplyanddemand),weestablishamodel

(suchasdifferentialequationsystemthatincludesdemand,supply).

例4：To(writetheaims),weestablishacriterion(writethecriterion),

b.模型非主流

｛列5：Webuildamodeltodeterminehowtolayoutthepipeeachtimetheequipmentismoved.

佛J6；Wedetermine................

例7：Webuildamodeltodetermine.............

例8：Weformulateamodelfor............Byanalyzing...andexamining......

2.分析模型(使用什么数据，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-cantestsoftheirrigationsystem

and.....

例2：Softwarepackingreaches............bycalculatingandcomparing...............

c.运用数据模拟

例1：togroundthismodelinreality,weincorporateextensivedemographicdataandrun.....

例2：Wefitthemodifiedmodeltodata(suchas1970-2003.).Weconcludethat(writethelast

conclude),

d.讲详细分析

例1：Wephysicallycharacterizethesystemthat...

彳列2：Weprovideastrategy(writethelogicalstrategy).

例3：The...modelis(efficient,intuitive,andflexible)andcouldbeappliedto...

例4：Tomeettheneedsofpeopletodaywithout,weestablishacriterionofrational合理的

标准)oilallocation(分配).

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：Weshowthatthisstrategyisnotoptimalbutcanbeimprovedbyassigningdifferent

numbers.....

b.说明如果用这个模型，结果如何

例1：IfDeltaAirlinesweretoutilizethenaivestrategyatAtlantaInternationalAirport,thecost

wouldbe......

例2：Wemodifythemodeltoreflect(sometrendsuchasexponentiallyincreasing.......)and

generalizethemodelto(otherfield).

例3：OurresultsaresummarizedintheformulafortheoptimalnumberBoftollboothsfor

c.通过其上情况的列举得到的结论

例：Forvarioussituations,weproposeanoptimalsolution.

d.得出了结论

例1：weelicitthataconclusion.

例2：Weconcludewithaseriesofrecommendationsforhowbestto...

已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

例:Todemonstratehowourmodelworks,wcapplyitto.......

最后一段：写总的结论

a.说明结论的可行性

例：Oursuggestedsolution,whichiseasytoimplement,includesadetailedtimetableandthe

arrangementofpipes.

b.说明算法的广泛性

份J1：Ouralgorithmisbroadenoughtoaccommodatevariousairportconcourses,flight

schedules,andflightdelays.

例2：Ouranalysisbeganbydeterminingwhatfactorimpact....,Ourconclusionsare

presented....

c.说明模型可用于其他领域

例：Sinceourmodelisbasedon....itcanbeappliedto（otherdomain）.

其他（承上启下的连接词/常用词组）

例:Inadditiontothemodel,wealsodiscuss...

引言部分

（1）1口1顾研究背景，常用词汇有review,summarize,present,outline,describe等

（2）说明写作目的，常用词汇有pupose,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研尢范围，常用词汇有study,present,include,focus,emphasize,

emphasis,attention等

方法部分

（1）介绍研究或试验过程，常用词汇有teststudy,investigate,examine,experiment,discuss,

consider,analyze,analysis等

（2）说明研究或试验方法，常用词汇有measure,estimate,calculate等

（3）介绍应用、用途，常用词汇有等

结果部分

（1）展示研究结果，常用词汇有show,result,present等

（2）介绍结论，常用词汇有summary,introduce,conclude等

讨论部分

（1）陈述论文的论点和作者的观点，常用词汇有suggest,repot,present,expect,describe等

（2）说明论证，常用词汇有等support,provide,indicate,identify,find,demonstrate,

confirm,clarify

（3）推荐和建议，常用词汇有suggest,suggestion,recommend,recommendation,propose,

necessity,necessary,expect等。

摘要中常用的词语卷

critical至关重要的

algorithm运算法则

amethodofevaluating评价方法

appropriate近似的

consider考虑

configurations布局

optimal统一的

maximize使…最大化

strategy策略

parameter参数，主要的决定因素

accuracy精确性

strengthsandweaknesses优点和缺点

contact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：

Wemakethefollowingassumptionsabout........processinthispaper.

a.不考虑因素

例1：Wedonottakeintoaccountinteractionsbetweenfactors.

例2：Theinfluenceof...canbeneglected

例3：…is"ideal”in...canbeneglected.

b.为了简化模型，之后反驳不正确，但是合理。

例1：Infact(inreality)factorseffecteachothers,butinordertosimplifythemodel,weignorethe

interactionsbetweenfactors.

例2：Infactinrealityfactorseffecteachothers,butinordertosimplifythemodel,weignorethe

interactionsbetweenfactors.

c.近似

例1：.......canbeapproximatedasalinerfunctionof....

例2：...areassumedtobethesame.Inpractice,thereisaslightdifference.

例3：.......canbeapproximatedasalinerfunctionof....

d.细致考虑(可附原因)

仞ij1：Anairportconsistsof1to10concourses,eachofwithconsistsof2to50gates.Gatesinthesame

concoursearegenerallylocatedclosetooneanother,whilethetraveltimebetweenconcoursescanbequite

lengthy.Hence,weassumeihaiinier-concourseiravelismuchlengthierthaninira-concoursetravel.

例2：Aaveragefastwalkingspeedis250ft/min(3mph),butaveragespeedwhenarmsareimmobilized

(aswhenpushingawheelchair)isonly180ft/min(2mph)[GrossandShi2001].Wcassumethatanescort

walksatthesespeeds.

例3：Anescortcanoperateonlyonewheelchairatatime.U.S.Dept.oftransportationguidelines

discouragesleavingWPsunattended.Hence,theescorttakesaWPtotheconnectingflightandremainsuntil

theHightleaves.

e.直接定义(假设)：

例1：Tomeasurethe........,wedefine........

例2：Yearlyindustrystatisticscanbeusedvalid.

例3；Sthmayberepresentedby

例4：....arcindependentandrandomlydistributed

总结：

Additionalassumptionsaremadetosimplifyanalysisforindividualsections.Theseassumptions

willbediscussedattheappropriatelocations.

公式

由假设得到公式

1.WeassumelaminarflowanduseBernoulli'sequation:(由假设得到的公式)

公式

Where

符号解释

Accordingtotheassumptions,ateveryjunctionwehave(由于假设)

公式

由原因得到公式

2.Becauseourfieldisflat,wehave公工sotheheightofoursourcerelativetooursprinklersdoesnotaffect

theexitspeedv2(由原因得到的公式)；

公式

Sincethefluidisincompressible(由于液体是不可压缩的),wchave

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),wehavetheithjunction(由前几个公式得)

公式

Putting(1)-(5)together,wecanobtainpupateveryjunction.infact,atthelastjunction,wehave

公式

Pullingtheseinlo(1),weget(把这些公式代入1中)

公式

Whichmeansthatthe

Commonly,hisabout

Fromtheseequations,（从这个公式中我们知道）weknowthat...........

引出约束条件

4.UsingpressureanddischargedatafromRainBird结果，

Wefindtheattenuationfactor（得到衰减因子，常数，系数）tobe

公式

计算结果

6.Tbfindthenewpressure,weusethe（00）,whichstatesthatthevolumeofwaterflowinginequalsthe

volumeofwaterflowingout:（为了找到新值，我们用什么方程）

公式

Where

0is；；

7.SolvingforVNweobtain（公式的解）

公式

Wherenisthe.....

8.Wehavethefollowingdifferentialequationsforspeedsinthex-andy-directions:

公式

Whosesolutionsare（解）

公式

9.Weusethefollowinginitialconditions（使用初值）todeterminethedragconstant:

公式

根据原有公式

10.Weapplythelawofconservationofenergy（根据能量守恒定律）.Theworkdonebytheforcesis

公式

Thedecreaseinpotentialenergyis（势能的减少）

公式

Theincreaseinkineticenergyis（动能的增加）

公式

Drugactsdirectlyagainstvelocity,sotheaccelerationvectorfrondragcanbefoundNewton\lawF=maas:

（牛顿第二定律）

Whereaistheaccelerationvectorandmismass

UsingtheNewton'sSecondLaw,wehavethatF/m=aand

公式

Sothat

公式

Settingthetwoexpressionsfortl/t2equalandcross-multiplyinggives

公式

22.Weapproximatethebinomialdistributionofcontenderswithanormaldistribution:

公式

Wherexisihecumulativedistribudonfunctionof（hestandardnormaldisiribmion.Clearingdenominatorsand

solvingtheresultingquadraticinBgives

公式

Asananalyticapproximationto.fork=1,wegetB=c

26.Integrating,（使结合）wegelPVT=constant,where

公式

Themaincompositionoftheairisnitrogenandoxygen,soi=5andr=1.4,so

23.AccordingtoFirstLawofThermodynamics,weget

公式

Where（）.wcalsothenhave

公式

WherePisthepressureofthegasandVisthevolume.WeputthemintotheIdealGasInternalFormula:

公式

Where

对公式变形

13.DefineA=nlwtobethe（）（定义）;rearranging（1）produces（将公式变形得到）

公式

WemaximizeEforeachlayer,subjecttotheconstraint（2）.Thecalculationsareeasierifweminimize1/E.（为

了得到最大值，求他倒数的最小直）Neglectingconstantfactors（忽略常数），wemininrze

公式

使服从约束条件

14.Subjecttotheconstraint（使服从约束条件）

公式

WhereBisconstantdefinedin（2）.However,aslongasweareobeyingthisconstraint,wecanwrite（根据约

束条件我们得到）

公式

Andthusfdependsonlyonh,thefunctionfisminimizedat（求最小值）

公式

Atthisvalueofh,theconstraintreducesto

公式

结果说明

15.Thisimplies（暗示）thattheharmonicmeanof1andwshouldbe

公式

So,intheoptimalsituation..............

5.Thisvalueshowsverylittlelossduetofriction.（结果说明）Theescapespeedwithfrictionis

公式

16.Weuseasimilarprocesstofindthepositionofthedroplet,resultingin

公式

Witht=0.0001s,errorfromtheapproximationisvirtuallyzero.

17.Wecalculateditstrajectory（轨道）using

公式

18.Forthatcase,usingthesameexpansionforeasabove,

公式

19.Solvingfortandequatingittotheearlierexpressionfort,weget

公式

20.Recallingthatinthisequalityonlynisafunctionoff,wesubstitutefornandsolveforf.theresultis

公式

Asv=...,thisequationbecomessingular(单数的).

由语句得到公式

21.Therevenuegeneratedbytheflightis

公式

24.Thenwehave

公式

Wedifferentiatetheideal-gasstateequation

公式

Getting

公式

25.WeeliminatedTfromtheIasitwoequalionstoget(排除因素得至『)

公式

22.Wefistexaminethepaththatthemotorcyclefollows.Takingtheairresistanceintoaccount,wegettwo

differentialequations

公式

WherePistherelativepressure.Wemustfirstfindthespeedvlofwateratoursource:(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：

Firstwestudythe.......(文献)，showing.........underthesituation.

分阶段图的引出：

Thecompressionprocessisdividedintothree(数字)phases,asshowninthefigure:

Thefirstphase:.......deformation,accordingto........;thesecondphase:.......deformation.The

compressiongrowsmoreslowlyandreachesthemaximum.Thethirdphase:.......deformation:After

compressionreachesthemaximum,therateofdeformationstartstofall.Theunrecoverabledeformationgoes

onincreasing.(2003―65)

2、引用已有的模型图：

Amodelofflowraleforinstanttotalfailureisrighttriangular[U.S.ArmyCorpsofEngineers1997].

(seeFigure1)(2005—53\54)

3、通过历史数据作图：

WevalidateourmodelbyexamininghistoricalHIVratesfromprenatalclinicsinSouthAfricabetween

1995and2005(Figure1).(2006—244)

4、拟合的图形：

Figure1showsthenumberofbagsstillleftfortheEDStoprocessatairportAaftereachminutein

airportB.theresultsarcsimilar.(2003—260)

自己根据计算所画的图：

1、为了…….(目的)，我们作了…….图。

Todemonstratebetterthechangeinflowratewithtimewhenthebreachbeginstform,weplotovera

shorterrangeoftimeinFigure5.(2005—55)

WeplotforvaluesofBfrom6to13,instepsof0.25,togetherwiththebest-fitquanic,inFigure2

(2005—92)

2、根据数据拟合的图：

Fitting(式了)tothedatain(表)，wcgetthecurveinFigure1,forthefunction(公式).(2005—211)

WeusethegraphinFigure1tosimulatethearrivalofpassengers.(2003—201)

ThesimulationmodelalsogeneratessystemcharacteristicsfortheETDmachinesatairportA.These

resultsareshowninFigure3.(2003—232)

3、根据取值不同画图：

Wetake2001asthestartingpoint,whentotalremainingoilwas1.1178bbLWccalculatethetimetooil

exhaustionunderdifferentcases:GDPgrowingat10%,5%,3%,andl%.(Figure3)

For10%,……;for5%,.......;for3%,........;forI%,.........(2005—2I3\233)

4、用软件(如MATLAR)画图：

Tosolvethedifferentialequationsinourmodel,weuse(theODE45numericalintegrator)inMATLAB

on(式子)tofindtheresultsinFigure3.(2005—232)

5、图形的改进：

Generallyspeaking,theshapeofthetargetisnottooirregular,sowechoosefivetypicalshapesofthe

targetsindifferentsizes.InFigure3a,weillustratethemaximumsectionofatypicalbean-shapedtarget,

whosemaximumdimensionis35mm.Usingtheskeletongenerationalgorithm,wegetcorrespondingskeleton

showninFigure3b.ThenweapplytheGA-basedshotplacementalgorithm,resultinginthreeshotsforthe

target:one14mmhelmetandtwo8mmhelmets.Thelocationsandsizesofthehelmetsin2Dareindicatedin

Figure3c,while3DshotplacementsarcshowninFigure4.(2003—130)

6、画示意图：

TheirrigationorderandpositionofsprinklersarepresentedinFigure4.(2(X)6—127)

ThisalgorithmcanbeviewedintheflowchartinFigure3.Wedefinesomeoftheobjectsfoundinthe

chan(2006—164\165)

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,wesummarizetheminimumnumberofescortsneededtoreacheachservice

level

表的解释部分

Foreachairport,thedifferencebetweentheGoodandAdequateservicelevelsisroughlyafactor

oftv/o,withslightlyincreasingreturnstoscale;withlargerscales,thestaffarespreadmore

uniformly,soitislesslikelythatajobwillcropupwithnobodycloseenoughtotakeit.

Table1.

Numbersofescortsneededtoacliieveseivicelevels.

AirportTrafficPassengersservedNumberofescorts

AdequateServiceGoodSendee

Linelight4209

heavy841018

Loganlight78917

hea\y1551531

O'Harelight2752756

heavy55047106

例2

表的解释部分

(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)。

Wedeterminedabsoluteandrelativecriticalityvaluesforeachcountryforwhichallthedata

usedincomputingparameterswasavailable(108countries).Wethenusedrelativecriticalityin

selectingourmostcriticalcountries,bycontinent.Hadweusedabsolutecriticalityitwouldhave

givenprecedencetolargenations,despiterelativelymildHIV/AIDSsituations.

Table2:MostCriticalCoimtriesbyContinent

CountryContinentCriticality(Relative)

BotswanaAfiica4.097469

ThailandAsia0.283505

TongaAustralia0.06667

UkraineEurope0.135426

BahamasNorthAmerica0.614664

GuyanaSouthAmerica0.4312

例3

Thetablebelowisthegeneratedirrigationschedulefortherepositioningofthesprinklers,given12-hour

workdayforarancher.Eachpipeissetinplacefor5hours.

Irrigationschedule

DayTimeSprinklerposition(xposition,yposition)inmetersfromthelowerleftcornerofthefield

Day18am1.23.75

Day11pm23.75,23.75(movethesprinklerandpipeset.tonewlocation)

Day16pmTurnoffsprinklertoavoidoverirrigation.

Day28am46.75,23.75

Day21pmG9.5.23.75

Day26PmTurnoffsprinklertoavoidoverirrigation.

Day38am10.6.25

Day31pm32.75,6.25

Day3GpmTurnoffsprinklertoavoidoverirrigation.

Day48am55.5,6.25

Day41pm78.25,6.25

Day46pmTurnoffsprinklertoavoideverirrigation.

Day5Repeatschedule.

例4

Andsomedataprocessingwecangettherelevantstatisticaldatainformationofpatientand

donorcharacteristicsforthesimulation.

Table5:Agedistributionsfornewpatientsusedinthesimulations

DeceasedDonorPercentLivingDonorPercentAllDonorTypesPercent

Pediatnc17,62918.02%480.06%17,6779.93%

Adult80,13981.92%80.04999.91%160,18890.02%

Unknown520.05%240.03%760.04%

AllAses97,820180.1211177,9411

例5

ThegraftsurvivalratesshowinthefollowingUNOSdataforkidneytransplantsintheU.S

(basedonOPTNdataasof2006):

Table12:KidneyGraftSurvivalRates

TimeafterdonationFromdeceaseddonorsFromlivinJgdonors

Oneyear88.40%94.40%

Thieeyeai-s77.50%87.60%

Fiveyears65.50%78.70%

2、在表后对表的内容进行说明

例1

Table9:ComparisonofLinearFitParametersforourModels

ModelSlopeInterceptR2

BasicCaiTiackmg1.6991.7380.997

Macroscopic1.5981.2150.998

CelliilaiAutomata1.6720.2280.998

Table9showslinearfitparametersforallthreemodels.Notethatallthreemodelsarcwelldescribedbya

linearequation.

例2

Usingthecellularautomatamodel,wecomputewaitingtimeasafunctionofboththenumberoflanes

andthenumberoftollbooths.ForafixedL,wecompareallvaluesofCtotaiandchoosethelowestone.

TheresultsofthismethodarcpresentedinTablc6.

例3

Analyzingtheorgantransplantpoliciesinothercountries

ThereisafigureofLegislation,practiceanddonorratesinseveralcountries,e.g..Spain.US,

Fiance.Geniiany.UKandsoon.因

Table4:Legislation,practiceanddonorrates

Donors(pmp)

CoimtiyLegislationActualpractice

aimualrate

SpainPresumedconsentInformedconsent33.8

BelgiumPresumedconsentPresumedconsentandfamilyinformed24.4

AustiiaPresumedconsentPresumedconsent23.3

USInformedconsentwithInformedconsentwith22.1

Accordingtotheabovedata,wecanseethatmanyoftheEuropeancountrieshavethehighrates

ofthedonor,particularlyinSpain.Thisphenomenonshowsthattheorgantransplantisalsohot

inEurope.Althoughtherelevantpoliciesandstatutesinthesecountriesarelesscomprehensive

thanthatinU.S,therestillalotwhatU.Scouldlearnfrom.Here,wemainlyanalyzetheorgan

transplantpoliciesinSpain,U.KandKoreathisthreecountries.

Rrgion#Populntinn%Rpgion#Population%Rpginn#Population%

13.0323.0236.15

43.5153.4363.45

73.4383.2293.50

103.19112.78123.33

133.21143.00153.43

163.38174.43184.76

193.24203.12212.97

223.17233.17243.21

252.44262.12273.66

283.79293.71

Tabic1:PopulationFractionineachLegislativeDistrict

.......Thepopulationcontainedineachregionissummarizedintable1.(在表后对数据的内容进

行总结)

例4

Table6:OptimizationforCellularAutomataModel

Optimal#Booths

HighwayLanesTypicalDavRushHour

一9一7

244

356

477

589

61011

1213

81415

162729

图表的解释部分

AsindicatedinTable6,thereisfairlygoodagreementbetweentherecommendednumberofboothsfora

typicaldayandforpeakhours.However,wenoteIhattheoptimalboothnumberforatypicaldaynever

exceedsthatforrushhour.Rushhourseemstorequireslightlymoreboothsthanatypicaldayinorderfor

theplazatooperatemostefficiendy.

EachvalueinTable6isrepresentativeofapproximately20trials.Throughthesetrials,wenoteda

remarkablestabilityinourmodel.Despitethestochasticnatureofouralgorithm,eachnumberoflanes

wasalmostalwaysoptimizedtothesamenumberoftollbooths.Therewereahandfulofexceptions;they

occurredexclusivelyforsmallnumbersofhighwaylanes(<3lanes).Integervaluesarepresentedin

Table6onlybecausefractionaltollboothshavenophysicalmeaning.

3、表前表后有引入引出，且中间对两表之间进行比较

例1

表的解释部分

WecanobtainthedatawhichisinvolvedwiththestatusoftheAmericanOrgan

Transplantfromthedatabanks.WehavecollectedthedemandofthevariousorgansinUnited

Statestodate,theannualdonors,transplantsandthedemand(Heretakingthekidneyfor

example,byyears1995-2006)

Table1:ThedemandofthevanousorgansinUnitedStatestodate

BasedonOPTNdataAllKidney/Heart/

KidneyLiverPancreasHeartLungIntestine

asofFebruary2,2007OrgansPancreasLuug

Total94.54569,98316.9891,7452,3892,8582.860135239

Peiveut174.021%17.969%1.84(5%