數(shù)學建模美國賽論文常用句式分析解析

經(jīng)典句式美賽參賽Theexpressionof...canbeexpandedas:...…的表達式可擴展為...AisexponentiallysmallerthanB,soitcanbeneglected.A對B來說呈指數(shù)級減小，所以可以忽略不計。Equation(1)isreducedto:方程(1)化簡為：Substitutethevaluesintoequation(3),weget...把這些值代入方程3,我們得到...AccordingtoourfirstassumptiononPage1,根據(jù)我們第一頁的第一個假設，Thuswearriveattheconclusion:因此我們得到結論：Fromthemodelof...,wefindthattheoretically,itisalmosttruethat...由...模型，我們從理論上證明了...是真實可信的。Thatisthetheoreticalbasisfor...inmanyapplicationareas.這是...在很多領域應用的理論基礎。Toquantitativelyanalyzethedifferentrequirementsofthetwoapplications,weintroducetwomeasures:為了定量的分析這兩種應用的不同要求，我們介紹來兩個量度標準。Wegivethecriterionthat...我們給出了...的判別標準Accordingtothecriterionof...根據(jù)...的標準Soitsexpressioncanbederivedfromequation(3)withsmallchange.所以它的表達式可以由方程3做微小改動而推出。Supposethat...refersto...假設...指的是...Wecangetthedistributionof...我們可以得到...的分布alongxandyaxes沿著x和y軸Forafurtherdiscussionofthismodel,pleaseseeAppendixA.參見附錄A(detailedinAppendixI)(詳見附錄一)...isfittedtothenormaldistribution,withthemeanat0andvarianceofo-=1.342符合均值為0,方差為1.342的正態(tài)分布。conformto符合Fig.4shows...圖4表明...Thus,if...isgiven,...isdetermined.因此，如果給定...，...就也確定了。Foragivenr,wecancalculate...對于給定的r,我們可以算出...Thetwodistributionsareindependent.這兩個分布是相互獨立的。Bycalculationweobtain...通過計算，我們得到...Soitisexpressedasbelow:所以它可以表示為：...isultimatelydeterminedby最終由…決定WefixAandexaminethechangeofBwithrespecttoC.我們固定A然后觀測B隨C的變化。thelogarithmvaluesof的對數(shù)值ThatexplainswhythevalueofAdecreasesasBincreases.這就解釋了為什么A的值隨B的增加而減少。Ifrincreases,p(r)increasesaccordingly.如果r增長，p(r)也相應地增長。dueto由于Aisthelengthof...inunitof...A是...的長度，以...為單位。Wecanseea"valley"betweentwocurvedfaceswhichdenotedthepointswhereA=B.我們可以看到在兩個曲面之間有一個低谷，表示A=B的那些點。AandBalwayschangeinoppositedirection.A和B總是呈相反變化。Sowhenseekingtheminimumof...,weshouldconsiderhowtobalanceAandB.所以當尋求...的最小值時，我們應該考慮如何平衡A和B。Sowesettheoptimalfunctionas:所以我們列出最優(yōu)方程如下：However,puttingequalweightonAandBisnotalwaysdesirable.然而，給A和B相同的權數(shù)并不總是令人滿意的。Insomesituations,wemustfavoroneovertheother.在一些情況下，我們必須偏重一方。inputtheinitialization輸入初值Theprogramsolvestheoptimalfunctionandoutputa,b,candd.程序求最優(yōu)解，并輸出a,b,c和d的值.Inconsiderationof考慮到...Weapplythisstrategytofourtypicalsituationsandlisttheresultshere.我們將這種方案應用于四種典型情況，并列出結果如下。theprobabilityofoccurrence發(fā)生的概率Theoretically,recognizationcanalwaysbesuccessful.理論上說，識別應該總是成功的。theexpectationvalueof的期望值Weleta=b我們令a=bnumericalresults數(shù)值解Wewriteaprogram（AppendixII）inVC++toobtaintheresult.我們用vc++寫了一個程序來求解。AsshowninTab.4,如表4所示，Theaboveresultsshowthat（+句子）,whichmeans（或者用thatis）,（+句子）以上結果說明...,也就是說...Sowearriveat（或者用cometo）theconclusionthat（+句子）因此,我們得到結論...Moreover,fromtheaspectof...,而且，從...方面來看，Onthecontrary,正相反，sensitivityanalsis靈敏性分析robustness穩(wěn)健性altermby5%將m改變5%Theyareveryclose.這兩個值非常接近。ThisisconsistentwiththephenomenonshownintheFig.4.這和圖4所示是一致的。inverselyrelated負相關intermsof...根據(jù)...；在...方面equality等式Wecanrewritethefirstinequalityasfollows:我們可以改寫第一個不等式如下：Wedevelopamodeltodesign我們建立了一個模型用來設計...Themodelisbasedonconservationofenergy.這個模型的建立基于能量守恒Wothreecomponents:...我們進一步將...分成三部分：...Tovalidateourmodel為了驗證我們的模型Duetothelackofaccuratedatafor...由于缺少...方面的準確數(shù)據(jù)Ourprimaryaimisto...我們的主要目標是and...areregardedasonesystem和...被看成是一個系統(tǒng)。notation符號遺傳算法(GeneticAlgorithms,GA)并行遺傳算法ParallelingGeneticAlgorithm,PGA數(shù)據(jù)結構DataStructures自然選擇naturalselection種群population個體individual基因庫genepool編碼coding解碼decoding量綱dimensions隨機過程randomprocessesflowchart流程圖constraintcondition約束條件maximizecustomerenjoyment最大化顧客的愉悅Havingensuredthis,weshouldminimize...在確保這個之后，我們要將...最小化befarfromoptimalinpractice在實踐中遠不是最優(yōu)implement貫徹實行Theunderlyingideaisfairlysimple.下面的想法很簡單。theappealofthesesystemstoamusementparksistwo-fold:這些系統(tǒng)對游樂園的吸弓I力有兩個方面：addresstheseissues致力于這些問題Hence,...hascomeintoquestion.因止匕，…開始成為問題。Apartfromconsiderationof...,fromthe...'spointofview,除去考慮...，從...的角度考慮，...integrate積分Markovchainmodel馬爾科夫鏈模型Wevalidatedourmodelusingtestsforrigorinbothrobustnessandsensitivity.通過對穩(wěn)健性和靈敏性的測試，我們驗證了我們模型。Wefindthatinrobustnesstestcasesthatourmodelmakespredictionsthatcorrelatewellwithempiricalevidence.在穩(wěn)健性測試中我們發(fā)現(xiàn)，我們的模型預測值能夠很好的與經(jīng)驗值相適應。improveefficiencyby36%onaverage效率平均提高了36%contendwith對付disposal處置n.higherproductivityandgreatercustomersatisfaction更高的生產(chǎn)率和更高的顧客滿意度specifytheboardinganddeplaningsequence詳名田歹U單說明登機下機次序callfor要求degradecustomers'perceptionofquality降彳氐顧客對質(zhì)量的認可度ignificantstochasticvariability顯著的隨機可變性eproportionalto和什么成比例theorem定理，法貝Ucorollary推論proposition命題itisnecessarytonoticethat注意...是十分必要的stochasticapproach隨機方法numericalsolution數(shù)值解differentialequations微分方程partialdifferentialequations偏微分方程numericallyintegratethem將其數(shù)值積分generaterandomnumbersets生成隨機數(shù)序歹Uformulate用公式表示/display顯示/show顯示/describe描述/phrase用短語表達plotoutdata將數(shù)據(jù)以圖輸出customizethemtoyourparticularproblem使其服務于你的特殊的問題periodically周期性地，定時性地theprimaryobjective主要目標asasecondaryobjective作為第二目標beratedby由什么定價Thiscanbeinterpretedas這個已被理解為Notethat注意thediagonallengthoftheface表面的對角線的長度beapproximatelyequalto約等于sth.ofdimensiona*b*c/sth.indimensionsa*b*c...的尺寸是a*b*c4metershigh,4meterswide,4meterslonginthez-direction在z軸方向Eq.1方程1187Joules187焦耳correspondto相應priceperbox每個箱子的價格whereais...其中（往往用在公式后用于說明符號的含義后是...thus因此（常用于公式后的進一步推導）safelywithstand在安全的情況下經(jīng)受住risgivenby+公式r由…公式給出letrbe...令r等于asafunctionoftime作為時間的函數(shù)Thereforewearriveat:...因止匕我們得至Udboundedby234d限制在234Given...給定...requireatleast需要至少cometorest變?yōu)殪o止Conversely,ifweinsteadhaveanideaof...相反如果我們認為Wecaneasilycomputethat我們很容易計算得到thecalculationfor的計算dissipatetheenergy消耗能量,i.e.@#$%A&也就是@#$%人&thekineticenergy動能thechangeinenergy能量變化量regardlessof不考慮Wecalculatesth.bysolvingthefolllowingdifferentialequation我4」計算sth.通過下歹U微分方程firstorderequations一階微分方程Itwouldbeunwisetoignoreaieresistance忽略空氣阻力是不明智的o...將什么合并入什么Ideallyrshouldbezero,butsmallvariationsmayoccur.理想情況...，但會/」、的偏差發(fā)生uncertaininitialcondition不確定的初始條件Weassumethefollowinguncertainties我們假設如下不確定性TheseareshowninFig.5.這些在圖5中顯示AillustrationofthiseffectisshowninFig.6.fartoocomplextomedelaccurately太復雜以致不能精確模擬makethefollowingassumptionstoapproximateandsimplifytheproblem做以下假設，來近似簡化問題twodimensionalspace二維空間Werestrictourattentionto我們集中精力在Thereisnoreasonfor...什么是沒有理由的Makingthissimplificationdoesaffectthepossibilityof做這個簡化，確實影響到什么的概However,wewilllatershowthattheseeffectsarenegligibleinmostcases.然而，稍后我們將證明這個影響在大多數(shù)情況下是可以忽略的ignorefurtherinteractionwith...忽略和誰的進一步交互作用Thevelocitymagnitudeisreducedbutthedirectionisunchanged.速度的大小減小了但方向未改變auniformlevel相同的水平...isrepresentedby...什么有什么來代表代替Wemodify...accordingto...我們根據(jù)什么調(diào)整什么sth.describedinthefollowingsection(seeEq.2)...在下部分被描述的(參見方程2)Weusethisprocesstoaccountfortheeffectsoffriction.我們用這個過程來計算解釋摩擦的作用horizontal水平vertical豎直Theverticalcompomentofthevelocityissettozero.速度的豎直分量被置為0rectangle長方形、矩形triangle三角形slowhisdescent降低他的降落速度Thisisagoodapproximationintheaverageofalargenumberofcollisions.這是一個很好的近似，在大量撞擊的平均水平Wearetakingthemaximumheretoavoid...這里我們?nèi)∽畲笾?，以避?..Toshowthatsth.arenegligible,wevary...為了證明什么是可忽略的，我們改變...stepsize步長nodistinguishablechange沒有顯著改變Thisverifiesthatsth.ishighlyinsensitiveto...這證實了sth.X...高度不敏感conservationofenergy能量守恒conservationofmomentum動量守恒thechangeinhisvelocity速度的變化量Weusethisequationtocalculate...stabilityandsensitivityanalsisasafunctionoftimethediscretewayHypothesis假設Theresultsindicatethattype(1)isoptimal.figureout計算出beshownindetailinFig.2finalrecommendationrumor瘤humor幽默rumor流言謠言resultin導致resultfrom產(chǎn)生causeaminimaleffecton弓I起最小限度的影響10secondsuptoacouplehoursundervariousconditionsbefairlyindependentof...與什么無關twocomplementarymeasures兩個補充方法Wetabulatetherelationshipbetweenand我們將列成表格beproportionaltothesquareofvelocity和速度的平方成比例theaboveconsiderationsleadustoformulate...Thisispreciselytheeffectthatwewishtocapture.modifiedpoissonprocess改良的泊松過程testanddemonstrateouralgorithm測試和證明我們的算法Thedefinationof"simple"isuptoyou.beimplementedin在某處實施ItalsoshowsthatDukeisnotaloneinthistrend.這也顯示了不僅杜克大學符合這種趨勢Itisapparentlythat...彳艮顯然generality一般性Throughtrialanderrorwedeterminedapossiblecoefficientof0.2.figureout/calculate/compute計算formulate用公式表明intermsof根據(jù)，按照，用...的話，在...方面Forthisreason,classsizeisnotdirectlyinvolvedinthemodel.bereflectedin...反映在某方面tendtoward趨向themostextremecaseaslongas只要index指數(shù)指標,therebyreducingtheamountoftimetakentoselectatreatmentplan因止匕threedimensionalimage三維圖像fittingdata擬合數(shù)據(jù)thebottomtwocurves下部的兩條曲線Weagreeverywellwith1cubicmillimeter一立方毫米Thisalgorithmmakesuseof...to...禾1J用besimilarto相似Theendresultisthat...withregardto/withrespectto關于intherangeof7.1to7.5自己總結：centreofgravity重心centreofmass質(zhì)心checkdigit校驗位deliverycost,petrol油料運輸費用minimumcostsolution最底費用解optimumsolution最優(yōu)解non-conformingsamples不合格抽樣potentialenergy勢能weightingfactors加權因子differentialequations微分方程mathematicalinduction數(shù)學歸納法exponentialmodel嘉函數(shù)模型equilibriumpoint平衡點Wecanverifythatp=5,000isanequilibriumpointnumericallybycomputing*******D(p)=c*5000-500p,wherepdenotespriceandcisconstant其中p是指價格pl=20ppm.Theabbreviationppmstandsforpartspermillion.宿寫的ppm代表..theamount****dependsmoredirectlyon*****thanon******Thederivativeofthecurvey=x+2isdy/dx如何弓I出導數(shù)thedominantcontrollablefactoraffecting是影響。。。主要因素wherepisthedensityof。。。。。。密度是數(shù)學專業(yè)英語詞匯英漢對照Tag:數(shù)學專業(yè)英語詞匯英漢1概率論與數(shù)理統(tǒng)計詞匯英漢對照表Aabsolutevalue絕對值accept接受acceptableregion接受域additivity可加性adjusted調(diào)整的alternativehypothesis對立彳段設analysis分析analysisofcovariance協(xié)方差分析analysisofvariance方差分析arithmeticmean算術平均值association相關性assumption假設assumptionchecking假設檢驗availability有效度average均值Bbalanced平衡的band帶寬barchart條形圖beta-distribution貝塔分布betweengroups組間的bias偏倚binomialdistribution二項分布binomialtest二項檢驗Ccalculate計算case個案category類別centerofgravity重心centraltendency中心趨勢chi-squaredistribution卡方分布chi-squaretest卡方檢驗classify分類clusteranalysis聚類分析coefficient系數(shù)coefficientofcorrelation相關系數(shù)collinearity共線性column歹Ucompare比較comparison對照components構成，分量compound復合的confidenceinterval置信區(qū)間consistency一致性constant常數(shù)continuousvariable連續(xù)變量controlcharts控制圖correlation相關covariance協(xié)方差covariancematrix協(xié)方差矩陣criticalpoint臨界點criticalvalue臨界值crosstab歹U聯(lián)表cubic三次的，立方的cubicterm三次項cumulativedistributionfunction累力口分布函數(shù)curveestimation曲線估計Ddata數(shù)據(jù)default默認的definition定義deletedresidual剔除殘差densityfunction密度函數(shù)dependentvariable因變量description描述designofexperiment試驗設計deviations差異df.(degreeoffreedom)自由度diagnostic診斷dimension維discretevariable離散變量discriminantfunction判別函數(shù)discriminatoryanalysis判別分析distance距離distribution分布D-optimaldesignD-優(yōu)化設計Eeaqual相等effectsofinteraction交互效應efficiency有效性eigenvalue特征值equalsize等含量equation方程error誤差estimate估計estimationofparameters參數(shù)估計estimations估計量evaluate衡量exactvalue精確值expectation期望expectedvalue期望值exponential指數(shù)的exponentialdistributon指數(shù)分布extremevalue極值Ffactor因素，因子factoranalysis因子分析factorscore因子得分factorialdesigns析因設計factorialexperiment析因試驗fit擬合fittedline擬合線fittedvalue擬合值fixedmodel固定模型fixedvariable固定變量fractionalfactorialdesign部分析因設計frequency頻數(shù)F-testF檢驗fullfactorialdesign完全析因設計function函數(shù)Ggammadistribution伽瑪分布geometricmean幾何均值group組Hharmomicmean調(diào)和均值heterogeneity不齊性histogram直方圖homogeneity齊性homogeneityofvariance方差齊性hypothesis假設hypothesistest假設檢驗Iindependence獨立independentvariable自變量independent-samples獨立樣本index指數(shù)indexofcorrelation相關指數(shù)interaction交互作用interclasscorrelation組內(nèi)相關intervalestimate區(qū)間估計intraclasscorrelation組間相關inverse倒數(shù)的iterate迭代Kkernal核Kolmogorov-Smirnovtest柯爾莫哥洛夫-斯米諾夫檢驗kurtosis峰度Llargesampleproblem大樣本問題layer層least-significantdifference最小顯著差數(shù)least-squareestimation最小二乘估計least-squaremethod最小二乘法level水平levelofsignificance顯著性水平leveragevalue中心化杠桿值life壽命lifetest壽命試驗likelihoodfunction似然函數(shù)likelihoodratiotest似然比檢驗linear線性的linearestimator線性估計linearmodel線性模型linearregression線性回歸linearrelation線性關系linearterm線性項logarithmic對數(shù)的logarithms對數(shù)logistic邏輯的lostfunction損失函數(shù)Mmaineffect主效應matrix矩陣maximum最大值maximumlikelihoodestimation極大似然估計meansquareddeviation(MSD)均方差meansumofsquare均方和measure衡量media中位數(shù)M-estimatorM估計minimum最小值missingvalues缺失值mixedmodel混合模型mode眾數(shù)model模型MonteCarlemethod蒙特卡羅法movingaverage移動平均值multicolli