数学建模论文英文写作

美国数学建模写作2015.1.30论文结构Title（论文题目）Abstract（摘要）Introduction（背景介绍）ProblemandApproach（待解决问题和使用方法）ModelandResults（模型和结果）Conclusion（分析模型，误差分析，灵敏度分析等，给出结论）Reference（参考文献）Attachment（附录，程序）摘要第一段：写论文解决什么问题问题的重述解决这个问题的伟大意义总的解决概述第二、三段：具体分析在什么模型中/建立了什么模型分析模型（使用什么数据，怎么做，一般三句话）总结该模型的结果/得到什么结论最后一段：写总的结论a.说明结论的可行性b.说明算法的广泛性c.说明模型可用于其他领域第一段1.问题的重述a.介绍重点词开头：例1：“Handmove”irrigation,acheapbutlabor-intensivesystemusedonsmallfarms,consistsofamovablepipewithsprinklerontopthatcanbeattachedtoastationarymain.例2:……isareal-lifecommonphenomenonwithmanycomplexities.例3：An(effectiveplan)iscrucialto………第一段b.直接指出问题：例1：Wefindtheoptimalnumberoftollboothsinahighwaytoll-plazaforagivennumberofhighwaylanes:thenumberoftollboothsthatminimizesaveragedelayexperiencedbycars.例2：Abrand-newuniversityneedstobalancethecostofinformationtechnologysecuritymeasureswiththepotentialcostofattacksonitssystems.例3：Wedeterminethenumberofsprinklerstousebyanalyzingtheenergyandmotionofwaterinthepipeandexaminingtheengineeringparametersofsprinklersavailableinthemarket.例4:Aftermathematicallyanalyzingthe……problem,ourmodelinggroupwouldliketopresentourconclusions,strategies,(andrecommendations)tothe…….例5：Ourgoalis...that(minimizesthetime)……….第一段2.解决这个问题的伟大意义反面说明。如果没有……例：Withoutimplementingdefensivemeasure,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.第一段b．实际问题转化为数学模型例1:Weformulatetheproblemasanetworkflowinwhichverticesarethelocationsofescortsandwheelchairpassengers.例2:Anaïvestrategywouldbetoemploytheminimumnumberofescortstoguaranteethatallpassengersreachtheirgatesontime.c.将问题分阶段考虑例3：Wedividethejumpintothreephases:flyingthroughtheair,punchingthroughthestack,andlandingontheground.第二、三段1.在什么模型中/建立了什么模型a.主流模型

例1：Weformulateadifferentialmodeltoaccountfortheratesofchangeoftheseuses,andhowthischangewouldaffecttheoverallconsumptionofwaterwithinthestudiedregion.例2:Weexaminedthemathematicaleffectsof…….Wedevelopedadetailed……(simulationmethodology)totestourideasandtoquantifythedifferencesbetween(among)different……(strategies).例3：Basedon(writeyourbasis.suchasthetheoryofsupplyanddemand),weestablishamodel(suchasdifferentialequationsystemthatincludesdemand,supply).例4：To(writetheaims),weestablishacriterion(writethecriterion).第二、三段b.模型非主流例5：Webuildamodeltodeterminehowtolayoutthepipeeachtimetheequipmentismoved.例6：Wedetermine…………例7：Webuildamodeltodetermine……….例8：Weformulateamodelfor………例9：Byanalyzing…andexamining…..第二、三段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-cantestsoftheirrigationsystemand……例2:Softwarepackingreaches………bycalculatingandcomparing………..第二、三段c.运用数据模拟例1：Togroundthismodelinreality,weincorporateextensivedemographicdataandrun……例2：Wefitthemodifiedmodeltodata(suchas1970-2003.).Weconcludethat(writethelastconclude).d.讲详细分析例1：Wephysicallycharacterizethesystemthat…例2：Weprovideastrategy(writethelogicalstrategy).例3：The…modelis(efficient,intuitive,andflexible)andcouldbeappliedto…例4：Tomeettheneedsofpeopletodaywithout,weestablishacriterionofrational(合理的标准)oilallocation(分配).第二、三段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：Weshowthatthisstrategyisnotoptimalbutcanbeimprovedbyassigningdifferentnumbers……b.说明如果用这个模型，结果如何例1：IfDeltaAirlinesweretoutilizethenaïvestrategyatAtlantaInternationalAirport,thecostwouldbe……例2：Wemodifythemodeltoreflect(sometrendsuchasexponentiallyincreasing……)andgeneralizethemodelto(otherfield).例3：Ourresultsaresummarizedintheformulafortheoptimalnumber…第二、三段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:Weconcludewithaseriesofrecommendationsforhowbestto…e.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,weapplyitto………..最后一段a.说明结论的可行性例：Oursuggestedsolution,whichiseasytoimplement,includesadetailedtimetableandthearrangementofpipes.b.说明算法的广泛性

例1：Ouralgorithmisbroadenoughtoaccommodatevariousairportconcourses,flightschedules,andflightdelays.例2：Ouranalysisbeganbydeterminingwhatfactorimpact…c.说明模型可用于其他领域例：Sinceourmodelisbasedon……itcanbeappliedto(otherdomain).摘要摘要中常用的词汇：critical至关重要的algorithm运算法则

amethodofevaluating评价方法appropriate近似的

consider考虑contact相关的configurations布局optimal最优的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，准则词组其他（承上启下的连接词/常用词组）例:Inadditiontothemodel,wealsodiscuss……引言部分（1）回顾研究背景，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研究范围，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等摘要结果部分（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,report,present,expect,describe等（2）说明论证，常用词汇有support,provide,indicate,identify,find,demonstrate,confirm,clarify等（3）推荐和建议，常用词汇有suggest,suggestion,recommend,recommendation,propose,necessity,necessary,expect等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,weignoretheinteractionsbetweenfactors.例2：Infactinrealityfactorseffecteachothers,butinordertosimplifythemodel,weignoretheinteractionsbetweenfactors.c.近似例1：……canbeapproximatedasalinearfunctionof….例2：…areassumedtobethesame.Inpractice,thereisaslightdifference.例3：……canbeapproximatedasalinearfunctionof….Assumptionsd.细致考虑（可附原因）例1：Anairportconsistsof1to10concourses,eachofwhichconsistsof2to50gates.Gatesinthesameconcoursearegenerallylocatedclosetooneanother,whilethetraveltimebetweenconcoursescanbequitelengthy.Hence,weassumethatinter-concoursetravelismuchlengthierthanintra-concoursetravel.例2：Aaveragefastwalkingspeedis250ft/min(3mph),butaveragespeedwhenarmsareimmobilized(aswhenpushingawheelchair)isonly180ft/min(2mph)[GrossandShi2001].Weassumethatanescortwalksatthesespeeds.e.直接定义(假设)：例1：Tomeasurethe……,wedefine……例2：Yearlyindustrystatisticscanbeusedvalid.总结：Additionalassumptionsaremadetosimplifyanalysisforindividualsections.Theseassumptionswillbediscussedattheappropriatelocations.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2.Accordingtotheassumptions,ateveryjunctionwehave（由假设）公式由原因得到公式1.Sincethefluidisincompressible(由于液体是不可压缩的),wehave公式，Where公式用原来的公式推出公式1.Pluggingv1intotheequationforv2,weobtain（将公式1代入公式2中得到）

公式2.Puttingthesetogether(把公式放在一起),becauseofthelawofconservationofenergy,yields：

公式3.Putting(1)-(5)together,wecanobtainpupateveryjunction.Infact,atthelastjunction,wehave公式4.Puttingtheseinto(1),weget（把这些公式代入1中）公式,whichmeansthat…5.Fromtheseequations,（从这个公式中我们知道）weknowthat…公式引出约束条件1.UsingpressureanddischargedatafromRainBird结果,Wefindtheattenuationfactor（得到衰减因子，系数）tobe公式计算结果1.SolvingforVNweobtain(公式的解)公式Wherenisthe…..2.Wehavethefollowingdifferentialequationsforspeedsinthex-andy-directions:公式Whosesolutionsare（解）公式3.Weusethefollowinginitialconditions(使用初值)todeterminethedragconstant:公式对公式变形1.DefineA=nlwtobethe()（定义）;rearranging(1)produces（将公式变形得到）公式公式根据原有公式1.Weapplythelawofconservationofenergy（根据能量守恒定律）.Theworkdonebytheforcesis公式2.Thedecreaseinpotentialenergyis（势能的减少）公式3.Theincreaseinkineticenergyis(动能的增加)公式4.UsingtheNewton’sSecondLaw,wehavethatF/m=aand公式.Sothat公式使服从约束条件1.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）公式公式结果说明1.Thisimplies（暗示）thattheharmonicmeanoflandwshouldbe公式So,intheoptimalsituation…2.Thisvalueshowsverylittlelossduetofriction.（结果说明）

Theescapespeedwithfrictionis公式由语句得到公式1.Wefirstexaminethepaththatthemotorcyclefollows.Takingtheairresistanceintoaccount,wegettwodifferentialequations公式WherePistherelativepressure.Wemustfirstfindthespeedv1ofwateratoursource:（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.Thecompressiongrowsmoreslowlyandreachesthemaximum.Thethirdphase:……deformation:Aftercompressionreachesthemaximum,therateofdeformationstartstofall.Theunrecoverabledeformationgoesonincreasing.(2003—65)图2、引用已有的模型图：Amodelofflowrateforinstanttotalfailureisrighttriangular【U.S.ArmyCorpsofEngineers1997】.(seeFigure1)(2005—53\54)3、通过历史数据作图：WevalidateourmodelbyexamininghistoricalHIVratesfromprenatalclinicsinSouthAfricabetween1995and2005(Figure1).(2006—244)4、拟合的图形：Figure1showsthenumberofbagsstillleftfortheEDStoprocessatairportAaftereachminuteinairportB,theresultsaresimilar.(2003—260)图自己根据计算所画的图：1、为了…….(目的)，我们作了…….图。Todemonstratebetterthechangeinflowratewithtimewhenthebreachbeginstform,weplotoverashorterrangeoftimeinFigure5.(2005—55)2、根据数据拟合的图：WeusethegraphinFigure1tosimulatethearrivalofpassengers.(2003—201)3、根据取值不同画图：Wetake2001asthestartingpoint,whentotalremainingoilwas1.1178bbl.Wecalculatethetimetooilexhaustionunderdifferentcases:GDPgrowingat10%,5%,3%,and1%.(Figure3)4、用软件（如MATLAB）画图：Tosolvethedifferentialequationsinourmodel,weuse(theODE45numericalintegrator)inMATLABon(式子)tofindtheresultsinFigure3.(2005—232)表表的格式：表头再上1、在表前对表的来源和数据进行说明

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）。

Wedeterminedabsoluteandrelativecriticalityvaluesforeachcountryforwhichallthedatausedincomputingparameterswasavailable(108countries).Wethenusedrelativecriticalityinselectingourmostcriticalcountries,bycontinent.Hadweusedabsolutecriticalityitwouldhavegivenprecedencetolargenations,despiterelativelymildHIV/AIDSsituations.表2、在表后对表的内容进行说明Table9showslinearfitparametersforallthreemodels.Notethatallthreemodelsarewelldescribedbyalinearequation.表3、表前表后有引入引出，且中间对两表之间进行比较表的解释部分WecanobtainthedatawhichisinvolvedwiththestatusoftheAmericanOrganTransplantfromthedatabanks.WehavecollectedthedemandofthevariousorgansinUnitedStatestodate,theannualdonors，transplantsandthedemand(Heretakingthekidneyforexample,byyears1995-2006)Fromtheabovetable1,wecanseethatthekidneyaccountsfor73%inthetotaloftheorgantransplants.Itaccountsforaverylargeproportionasamostimportantorganwhichcanbetransplanted.Therefore,weonlyneedtodiscussthestatusofthekidneytransplanthere,beingabletoachievetheanalysisandresearchontheorgantransplant.表Accordingtotheabovedata,wecangetthefiguresasfollow优缺点Strengths优缺点Weaknesses总结Conclusions1、Asourteamsetouttocomeupwithastrategyonwhatwouldbethemostefficientwayto

我们提出了一种最有效的方法去解决……2、Thefirstaspectthatwetookintomajorconsiderationwas…….Otherimportantfindingsthroughresearchmadeitapparentthatthestandard

首先我们考虑到……，其他重要的是我们通过研究使4、Wehaveusedmathematicalmodelingina……toanalyzesomeofthefactorsassociatedwithsuchanactivity。

为了分析这类问题的一些因素，我们运用数学模型……5、This“cannonproblem”hasbeenusedinmanyformsinmanydifferentialequationscoursesin