数学建模美赛论文中可以用到的短语

1MCM论文写作常用句型（长文，建议收藏）Theexpressionof...canbeexpandedas:......的表达式可扩展为...AisexponentiallysmallerthanB,soitcanbeneglected.A对B来说呈指数级减小，所以可以忽略不计。Equation(1)isreducedto:方程（1）化简为：Substitutethevaluesintoequation(3),weget...把这些值代入方程3，我们得到...AccordingtoourfirstassumptiononPage1,根据我们第一页的第一个假设，Thuswearriveattheconclusion：因此我们得到结论：Fromthemodelof...,wefindthattheoretically,itisalmosttruethat...由...模型，我们从理论上证明了...是真实可信的。Thatisthetheoreticalbasisfor...inmanyapplicationareas.这是...在很多领域应用的理论基础。Toquantitativelyanalyzethedifferentrequirementsofthetwoapplications,weintroducetwomeasures:为了定量的分析这两种应用的不同要求，我们介绍来两个量度标准。Wegivethecriterionthat...我们给出了...的判别标准Accordingtothecriterionof...根据...的标准Soitsexpressioncanbederivedfromequation(3)withsmallchange.所以它的表达式可以由方程3做微小改动而推出。Supposethat...refersto...假设...指的是...2Wecangetthedistributionof...我们可以得到...的分布Alongxandyaxes沿着x和y轴Forafurtherdiscussionofthismodel,pleaseseeAppendixA.参见附录A(DetailedinAppendixI)（详见附录一）...isfittedtothenormaldistribution，withthemeanat0andvarianceofσ=1.342....符合均值为0，方差为1.342的正态分布。conformto符合Fig.4shows...图4表明...Thus,if...isgiven,isdetermined.因此，如果给定...，...就也确定了。Foragivenr,wecancalculate...对于给定的r,我们可以算出...Thetwodistributionsareindependent.这两个分布是相互独立的。Bycalculationweobtain...通过计算，我们得到...Soitisexpressedasbelow:所以它可以表示为：...isultimatelydeterminedby......最终由...决定WefixAandexaminethechangeofBwithrespecttoC.我们固定A然后观测B随C的变化。thelogarithmvaluesof......的对数值3ThatexplainswhythevalueofAdecreasesasBincreases.这就解释了为什么A的值随B的增加而减少。Ifrincreases,p(r)increasesaccordingly.如果r增长，p(r)也相应地增长。dueto由于Aisthelengthof...inunitof...A是...的长度，以...为单位。WecanseeavalleybetweentwocurvedfaceswhichdenotedthepointswhereA=B.我们可以看到在两个曲面之间有一个低谷，表示A=B的那些点。AandBalwayschangeinoppositedirection.A和B总是呈相反变化。Sowhenseekingtheminimumof...,weshouldconsiderhowtobalanceAandB.所以当寻求...的最小值时，我们应该考虑如何平衡A和B。Sowesettheoptimalfunctionas:所以我们列出最优方程如下：However,puttingequalweightonAandBisnotalwaysdesirable.然而，给A和B相同的权数并不总是令人满意的。Insomesituations,wemustfavoroneovertheother.在一些情况下，我们必须偏重一方。inputtheinitialization输入初值Theprogramsolvestheoptimalfunctionandoutputa,b,candd.程序求最优解,并输出a,b,c和d的值.Inconsiderationof考虑到...Weapplythisstrategytofourtypicalsituationsandlisttheresultshere.4我们将这种方案应用于四种典型情况，并列出结果如下。theprobabilityofoccurrence发生的概率Theoretically,recognizationcanalwaysbesuccessful.理论上说，识别应该总是成功的。theexpectationvalueof......的期望值Weleta=b我们令a=bnumericalresults数值解Wewriteaprogram(AppendixII)inVC++toobtaintheresult.我们用vc++写了一个程序来求解。AsshowninTab.4,如表4所示,Theaboveresultsshowthat(+句子),whichmeans(或者用thatis),(+句子)以上结果说明...,也就是说...Sowearriveat(或者用cometo)theconclusionthat(+句子)因此,我们得到结论...Moreover,fromtheaspectof...,而且，从...方面来看,Onthecontrary,正相反，sensitivityanalysis灵敏性分析robustness稳健性altermby5%5将m改变5%Theyareveryclose.这两个值非常接近。ThisisconsistentwiththephenomenonshownintheFig.4.这和图4所示是一致的。inverselyrelated负相关intermsof...根据...；在...方面Equation/equality等式Wecanrewritethefirstinequalityasfollows：我们可以改写第一个不等式如下：Wedevelopamodeltodesign....我们建立了一个模型用来设计...Themodelisbasedonconservationofenergy.这个模型的建立基于能量守恒Wefurtherclassify...intothreecomponents:...我们进一步将...分成三部分：...Tovalidateourmodel为了验证我们的模型Duetothelackofaccuratedatafor...由于缺少...方面的准确数据Ourprimaryaimisto...我们的主要目标是......and...areregardedasonesystem....和...被看成是一个系统。notation符号6遗传算法(GeneticAlgorithms,GA)并行遗传算法ParallelingGeneticAlgorithm,PGA数据结构DataStructures自然选择naturalselection种群population个体individual基因库genepool编码coding解码decoding量纲dimensions随机过程randomprocessesflowchart流程图constraintcondition约束条件maximizecustomerenjoyment最大化顾客的愉悦Havingensuredthis,weshouldminimize...在确保这个之后，我们要将...最小化befarfromoptimalinpractice在实践中远不是最优implement贯彻实行Theunderlyingideaisfairlysimple.下面的想法很简单。theappealofthesesystemstoamusementparksistwo-fold:这些系统对游乐园的吸引力有两个方面：addresstheseissues致力于这些问题Hence…hascomeintoquestion.因此,...开始成为问题。Apartfromconsiderationof...,fromthe...'spointofview...除去考虑...，从...的角度考虑，...integrate积分Markovchainmodel马尔科夫链模型Wevalidatedourmodelusingtestsforrigorinbothrobustnessandsensitivity.通过对稳健性和灵敏性的测试，我们验证了我们模型。7Wefindthatinrobustnesstestcasesthatourmodelmakespredictionsthatcorrelatewellwithempiricalevidence.在稳健性测试中我们发现，我们的模型预测值能够很好的与经验值相适应。improveefficiencyby36%onaverage效率平均提高了36%contendwith对付disposal处置n.higherproductivityandgreatercustomersatisfaction更高的生产率和更高的顾客满意度specifytheboardinganddeplaningsequence详细列单说明登机下机次序callfor要求degradecustomers'perceptionofquality降低顾客对质量的认可度significantstochasticvariability显著的随机可变性beproportionalto和什么成比例theorem定理,法则corollary推论proposition命题itisnecessarytonoticethat注意...是十分必要的stochasticapproach随机方法numericalsolution数值解differentialequations微分方程partialdifferentialequations偏微分方程numericallyintegratethem将其数值积分generaterandomnumbersets生成随机数序列formulate用公式表示/display显示/show显示/describe描述/phrase用短语表达plotoutdata将数据以图输出customizethemtoyourparticularproblem使其服务于你的特殊的问题periodically周期性地,定时性地theprimaryobjective主要目标asasecondaryobjective作为第二目标8beratedby由什么定价Thiscanbeinterpretedas这个已被理解为....Notethat注意thediagonallengthoftheface表面的对角线的长度beapproximatelyequalto约等于sth.ofdimensiona*b*c/sth.indimensionsa*b*c...的尺寸是a*b*c4metershigh,4meterswide,4metersl