數(shù)學建模論文英文寫作

美國數(shù)學建模寫作2015.1.30論文結構Title（論文題目）Abstract（摘要）Introduction（背景介紹）ProblemandApproach（待解決問題和使用方法）ModelandResults（模型和結果）Conclusion（分析模型，誤差分析，靈敏度分析等，給出結論）Reference（參考文獻）Attachment（附錄，程序）摘要第一段：寫論文解決什么問題問題的重述解決這個問題的偉大意義總的解決概述第二、三段：具體分析在什么模型中/建立了什么模型分析模型（使用什么數(shù)據，怎么做，一般三句話）總結該模型的結果/得到什么結論最后一段：寫總的結論a.說明結論的可行性b.說明算法的廣泛性c.說明模型可用于其他領域第一段1.問題的重述a.介紹重點詞開頭：例1：“Handmove”irrigation,acheapbutlabor-intensivesystemusedonsmallfarms,consistsofamovablepipewithsprinklerontopthatcanbeattachedtoastationarymain.例2:……isareal-lifecommonphenomenonwithmanycomplexities.例3：An(effectiveplan)iscrucialto………第一段b.直接指出問題：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.解決這個問題的偉大意義反面說明。如果沒有……例：Withoutimplementingdefensivemeasure,theuniversityisexposedtoanexpectedlossof$8.9millionperyear.3.總的解決概述a．通過什么方法解決什么問題例：WeaddresstheproblemofoptimizingamusementparkenjoymentthroughdistributingQuickPasses(QP),reservationslipsthatideallyallowanindividualtospendlesstimewaitinginline.第一段b．實際問題轉化為數(shù)學模型例1:Weformulatetheproblemasanetworkflowinwhichverticesarethelocationsofescortsandwheelchairpassengers.例2:Ana?vestrategywouldbetoemploytheminimumnumberofescortstoguaranteethatallpassengersreachtheirgatesontime.c.將問題分階段考慮例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（使用什么數(shù)據，怎么做，一般三句話）a.寫歷史數(shù)據例1：UsinghistoricaldatafromtheUnitedStates,wedetermineinitialconditionsforourmodel.b.寫計算機模擬例1：Thismodelleadstoacomputersimulationofcatch-cantestsoftheirrigationsystemand……例2:Softwarepackingreaches………bycalculatingandcomparing………..第二、三段c.運用數(shù)據模擬例1：Togroundthismodelinreality,weincorporateextensivedemographicdataandrun……例2：Wefitthemodifiedmodeltodata(suchas1970-2003.).Weconcludethat(writethelastconclude).d.講詳細分析例1：Wephysicallycharacterizethesystemthat…例2：Weprovideastrategy(writethelogicalstrategy).例3：The…modelis(efficient,intuitive,andflexible)andcouldbeappliedto…例4：Tomeettheneedsofpeopletodaywithout,weestablishacriterionofrational(合理的標準)oilallocation(分配).第二、三段3．總結該模型的結果/得到什么結論a.說明不是最優(yōu)但能產生作用例：Weshowthatthisstrategyisnotoptimalbutcanbeimprovedbyassigningdifferentnumbers……b.說明如果用這個模型，結果如何例1：IfDeltaAirlinesweretoutilizethena?vestrategyatAtlantaInternationalAirport,thecostwouldbe……例2：Wemodifythemodeltoreflect(sometrendsuchasexponentiallyincreasing……)andgeneralizethemodelto(otherfield).例3：Ourresultsaresummarizedintheformulafortheoptimalnumber…第二、三段c.通過其上情況的列舉得到的結論例：Forvarioussituations,weproposeanoptimalsolution.d.得出了結論例:Weconcludewithaseriesofrecommendationsforhowbestto…e.進一步說明其他因素對模型的影響例：Inadditiontothemodel,wealsodiscusspoliciesfor…..f.用真實數(shù)據檢驗模型例:Todemonstratehowourmodelworks,weapplyitto………..最后一段a.說明結論的可行性例：Oursuggestedsolution,whichiseasytoimplement,includesadetailedtimetableandthearrangementofpipes.b.說明算法的廣泛性

例1：Ouralgorithmisbroadenoughtoaccommodatevariousairportconcourses,flightschedules,andflightdelays.例2：Ouranalysisbeganbydeterminingwhatfactorimpact…c.說明模型可用于其他領域例：Sinceourmodelisbasedon……itcanbeappliedto(otherdomain).摘要摘要中常用的詞匯：critical至關重要的algorithm運算法則

amethodofevaluating評價方法appropriate近似的

consider考慮contact相關的configurations布局optimal最優(yōu)的maximize使…最大化

strategy策略parameter參數(shù)，主要的決定因素accuracy精確性strengthsandweaknesses優(yōu)點和缺點contract建立，構造calculate計算

establish建立formula公式

modify改進rational合理的

countermeasure對策criterion標準，準則詞組其他（承上啟下的連接詞/常用詞組）例:Inadditiontothemodel,wealsodiscuss……引言部分（1）回顧研究背景，常用詞匯有review,summarize,present,outline,describe等（2）說明寫作目的，常用詞匯有purpose,attempt,aim等，另外還可以用動詞不定式充當目的狀語來表達（3）介紹論文的重點內容或研究范圍，常用詞匯有study,present,include,focus,emphasize,emphasis,attention等方法部分（1）介紹研究或試驗過程，常用詞匯有teststudy,investigate,examine,experiment,discuss,consider,analyze,analysis等（2）說明研究或試驗方法，常用詞匯有measure,estimate,calculate等摘要結果部分（1）展示研究結果，常用詞匯有show,result,present等（2）介紹結論，常用詞匯有summary,introduce,conclude等討論部分（1）陳述論文的論點和作者的觀點，常用詞匯有suggest,report,present,expect,describe等（2）說明論證，常用詞匯有support,provide,indicate,identify,find,demonstrate,confirm,clarify等（3）推薦和建議，常用詞匯有suggest,suggestion,recommend,recommendation,propose,necessity,necessary,expect等Assumptions引出：Wemakethefollowingassumptionsabout……processinthispaper.a.不考慮因素例1：Wedonottakeintoaccountinteractionsbetweenfactors.例2：Theinfluenceof…canbeneglected例3：…is“ideal”in…,…canbeneglected.b.為了簡化模型，之后反駁不正確，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.細致考慮（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.直接定義(假設)：例1：Tomeasurethe……,wedefine……例2：Yearlyindustrystatisticscanbeusedvalid.總結：Additionalassumptionsaremadetosimplifyanalysisforindividualsections.Theseassumptionswillbediscussedattheappropriatelocations.公式由假設得到公式1.WeassumelaminarflowanduseBernoulli’sequation:（由假設得到的公式）公式，Where符號解釋2.Accordingtotheassumptions,ateveryjunctionwehave（由假設）公式由原因得到公式1.Sincethefluidisincompressible(由于液體是不可壓縮的),wehave公式，Where公式用原來的公式推出公式1.Pluggingv1intotheequationforv2,weobtain（將公式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（把這些公式代入1中）公式,whichmeansthat…5.Fromtheseequations,（從這個公式中我們知道）weknowthat…公式引出約束條件1.UsingpressureanddischargedatafromRainBird結果,Wefindtheattenuationfactor（得到衰減因子，系數(shù)）tobe公式計算結果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:公式對公式變形1.DefineA=nlwtobethe()（定義）;rearranging(1)produces（將公式變形得到）公式公式根據原有公式1.Weapplythelawofconservationofenergy（根據能量守恒定律）.Theworkdonebytheforcesis公式2.Thedecreaseinpotentialenergyis（勢能的減少）公式3.Theincreaseinkineticenergyis(動能的增加)公式4.UsingtheNewton’sSecondLaw,wehavethatF/m=aand公式.Sothat公式使服從約束條件1.Subjecttotheconstraint（使服從約束條件）公式WhereBisconstantdefinedin(2).However,aslongasweareobeyingthisconstraint,wecanwrite（根據約束條件我們得到）公式公式結果說明1.Thisimplies（暗示）thattheharmonicmeanoflandwshouldbe公式So,intheoptimalsituation…2.Thisvalueshowsverylittlelossduetofriction.（結果說明）

Theescapespeedwithfrictionis公式由語句得到公式1.Wefirstexaminethepaththatthemotorcyclefollows.Takingtheairresistanceintoaccount,wegettwodifferentialequations公式WherePistherelativepressure.Wemustfirstfindthespeedv1ofwateratoursource:（找初值）公式圖引用的文獻數(shù)據所畫的圖：1、分階段圖的引入：Firstwestudythe……(文獻)，showing……underthesituation.

分階段圖的引出：Thecompressionprocessisdividedintothree(數(shù)字)phases,asshowninthefigure:Thefirstphase:……deformation,accordingto……;thesecondphase:……deformation.Thecompressiongrowsmoreslowlyandreachesthemaximum.Thethirdphase:……deformation:Aftercompressionreachesthemaximum,therateofdeformationstartstofall.Theunrecoverabledeformationgoesonincreasing.(2003—65)圖2、引用已有的模型圖：Amodelofflowrateforinstanttotalfailureisrighttriangular【U.S.ArmyCorpsofEngineers1997】.(seeFigure1)(2005—53\54)3、通過歷史數(shù)據作圖：WevalidateourmodelbyexamininghistoricalHIVratesfromprenatalclinicsinSouthAfricabetween1995and2005(Figure1).(2006—244)4、擬合的圖形：Figure1showsthenumberofbagsstillleftfortheEDStoprocessatairportAaftereachminuteinairportB,theresultsaresimilar.(2003—260)圖自己根據計算所畫的圖：1、為了…….(目的)，我們作了…….圖。Todemonstratebetterthechangeinflowratewithtimewhenthebreachbeginstform,weplotoverashorterrangeoftimeinFigure5.(2005—55)2、根據數(shù)據擬合的圖：WeusethegraphinFigure1tosimulatethearrivalofpassengers.(2003—201)3、根據取值不同畫圖：Wetake2001asthestartingpoint,whentotalremainingoilwas1.1178bbl.Wecalculatethetimetooilexhaustionunderdifferentcases:GDPgrowingat10%,5%,3%,and1%.(Figure3)4、用軟件（如MATLAB）畫圖：Tosolvethedifferentialequationsinourmodel,weuse(theODE45numericalintegrator)inMATLABon(式子)tofindtheresultsinFigure3.(2005—232)表表的格式：表頭再上1、在表前對表的來源和數(shù)據進行說明

表的解釋部分

（前面的說出數(shù)據的來源，然后篩選出比較代表性的數(shù)據進行說明）。

Wedeterminedabsoluteandrelativecriticalityvaluesforeachcountryforwhichallthedatausedincomputingparameterswasavailable(108countries).Wethenusedrelativecriticalityinselectingourmostcriticalcountries,bycontinent.Hadweusedabsolutecriticalityitwouldhavegivenprecedencetolargenations,despiterelativelymildHIV/AIDSsituations.表2、在表后對表的內容進行說明Table9showslinearfitparametersforallthreemodels.Notethatallthreemodelsarewelldescribedbyalinearequation.表3、表前表后有引入引出，且中間對兩表之間進行比較表的解釋部分WecanobtainthedatawhichisinvolvedwiththestatusoftheAmericanOrganTransplantfromthedatabanks.WehavecollectedthedemandofthevariousorgansinUnitedStatestodate,theannualdonors，transplantsandthedemand(Heretakingthekidneyforexample,byyears1995-2006)Fromtheabovetable1,wecanseethatthekidneyaccountsfor73%inthetotaloftheorgantransplants.Itaccountsforaverylargeproportionasamostimportantorganwhichcanbetransplanted.Therefore,weonlyneedtodiscussthestatusofthekidneytransplanthere,beingabletoachievetheanalysisandresearchontheorgantransplant.表Accordingtotheabovedata,wecangetthefiguresasfollow優(yōu)缺點Strengths優(yōu)缺點Weaknesses總結Conclusions1、Asourteamsetouttocomeupwithastrategyonwhatwouldbethemostefficientwayto

我們提出了一種最有效的方法去解決……2、Thefirstaspectthatwetookintomajorconsiderationwas…….Otherimportantfindingsthroughresearchmadeitapparentthatthestandard

首先我們考慮到……，其他重要的是我們通過研究使4、Wehaveusedmathematicalmodelingina……toanalyzesomeofthefactorsassociatedwithsuchanactivity。

為了分析這類問題的一些因素，我們運用數(shù)學模型……5、This“cannonproblem”hasbeenusedinmanyformsinmanydifferentialequationscoursesin