电气工程及其自动化专业毕业设计（论文）外文翻译

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1、英文翻译2010届电气工程及其自动化专业班级姓名学号指导教师职称二О一二年二月十日342.3.NetworksmodelsTheobservationsdescribedintheexamplesofSection2.2haveclearlymotivatedtheintroductionofnewconceptsandmodels.Inthissection,wefocusonthemathematicalmodellingofnetw-orks,discussingsomesimpleandgeneric

2、modelsfromthepointofviewoftheirmotivation,const-ructionprocedureandsignificantproperties.FurtherdetailsonmodelscanbefoundinRefs.[2–4,7].2.3.1.RandomgraphsThesystematicstudyofrandomgraphswasinitiatedbyErdösandRényiin1959withtheorig-inalpurposeofstudying,bymea

3、nsofprobabilisticmethods,thepropertiesofgraphsasafunctionoftheincreasingnumberofrandomconnections.Thetermrandomgraphreferstothedisorderednatureofthearrangementoflinksbetweendifferentnodes.Intheirfirstarticle,ErdösandRényiproposedamodeltogeneraterandomgraphsw

4、ithNnodesandKlinks,thatwewillhenceforthcallErdösandRényi(ER)randomgraphsanddenoteasGERN,K.StartingwithNdisconnectednodes,ERrandomgraphsaregeneratedbyconnectingcouplesofrandomlyselectednodes,prohibitingmultipleconne-ctions,untilthenumberofedgesequalsK[115].W

5、eemphasizethatagivengraphisonlyoneoutcomeofthemanypossiblerealizations,anelementofthestatisticalensembleofallpossiblecombin-ationsofconnections.ForthecompletedescriptionofK,Nonewouldneedtodescribetheensemble34ofpossiblerealizations,thatis,inthematricialrepr

6、esentation,theensembleofadjacencymatrices[116].AnalternativemodelforERrandomgraphsconsistsinconnectingeachcoupleofnodeswithaprobability0

7、rintheensemblewithaprobabilitypK34(1−p)N(N−1)/2−K[14,115,117].Thetwomodelshaveastronganalogy,respectively,withthecanonicalandgrandcanonicalensemblesinstatisticalmechanics[118],andcoincideinthelimitoflargeN[16].NoticethatthelimitN→∞istakenatfixedk,whichcorres

8、pondstofixing2K/Ninthefirstmodelandp(N−1)inthesecondone.Althoughthefirstmodelseemstobemorepertinenttoapplications,analyticalcalculationsareeasierandusuallyareperformedinthesecondmodel.ERrandomgraphsarethe