简介:研究了Bernoulli微分方程的通解、积分因子,进而讨论了可化为Bernoulli方程的两类方程,并给了积分方程中的Bernoulli方程和它在数学建模中的应用.
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简介:利用Bernoulli多项式和Bernoulli函数,给出了连续可微函数的Bernoulli表示,并用这种表示来解决一类差分方程的通解问题。
简介:Inthispaper,asteady-stateMarkovianmulti-serverretrialqueueingsystemwithBernoullivacationschedulingserviceisstudied.Usingmatrix-geometricapproach,variousinterestingandimportantsystemperformancemeasuresareobtained.Further,theprobabilitydescriptorslikeidealretrialandvainretrialareprovided.Finally,extensivenumericalillustrationsarepresentedtoindicatethequantifyingnatureoftheapproachtoobtainsolutionstothisqueueingsystem.
简介:Inthispaper,theauthorsdesignboundaryfeedbackcontrollersattheinteriornodetostabilizeastar-shapednetworkofEuler-Bernoullibeams.Thebeamsarepinnedeachother,thatis,thedisplacementsofthestructurearecontinuousbuttherotationsofthebeamsarenotcontinuous.Thewell-posed-nessoftheclosedloopsystemisprovedbythesemigrouptheory.Theauthorsshowthatthesystemisasymptoticallystableiftheauthorsimposeabendingmomentcontroloneachedge.Finally,theauthorsderivetheexponentialstabilityofthesystem.
简介:WeconsideranMX/G/1queueingsystemwithtwophasesofheterogeneousserviceandBernoullivacationschedulewhichoperateunderalinearretrialpolicy.Inaddition,eachindividualcustomerissubjecttoacontroladmissionpolicyuponthearrival.ThismodelgeneralizesboththeclassicalM/G/1retrialqueuewitharrivalsinbatchesandatwophasebatcharrivalqueuewithasinglevacationunderBernoullivacationschedule.Wewillcarryoutanextensivestationaryanalysisofthesystem,includingexistenceofthestationaryregime,embeddedMarkovchain,steadystatedistributionoftheserverstateandnumberofcustomerintheretrialgroup,stochasticdecompositionandcalculationofthefirstmoment.
简介:TheproblemofquickanalysisusingexactgeometrydatawasproposedbyHughesetal.andtheisogeometricanalysisframeworkwasintroducedasasolution.Inthisletter,theexactgeometryconceptiscombinedintothequasi-conformingframeworkandanovelmethod,i.e.,theexactgeometrybasedquasi-conforminganalysisisproposed.Inpresentmethodthegeometryisexactlydescribedbynon-uniformrationalB-splinebases,whilethesolutionspacebytraditionalpolynomialbases.Presentmethodcombinesthemeritsofbothisogeometricanalysisandquasi-conformingfiniteelementmethod.InthisletterEuler-Bernoullibeamproblemissolvedasanexampleandtheresultsshowthatthepresentmethodiseffectiveandpromising.
简介:考虑动态输出反馈控制下Euler-Bernoulli梁的振动抑制问题,证明了系统算子生成的C0-半群,不指数稳定但渐近稳定.且当初值充分光滑时,利用Riesz基方法估计出系统能量多项式衰减.
简介:ThenonlinearvibrationsofviscoelasticEuler–BernoullinanobeamsarestudiedusingthefractionalcalculusandtheGurtin–Murdochtheory.EmployingHamilton'sprinciple,thegoverningequationconsideringsurfaceeffectsisderived.Thefractionalintegro-partialdifferentialgoverningequationisfirstconvertedintoafractional–ordinarydifferentialequationinthetimedomainusingtheGalerkinscheme.Thereafter,thesetofnonlinearfractionaltime-dependentequationsexpressedinastate-spaceformissolvedusingthepredictor–correctormethod.Finally,theeffectsofinitialdisplacement,fractionalderivativeorder,viscoelasticitycoefficient,surfaceparametersandthickness-to-lengthratioonthenonlineartimeresponseofsimply-supportedandclamped-freesiliconviscoelasticnanobeamsareinvestigated.
简介:在小学数学中,列方程解应用题与用算术方法解应用题是有密切联系的。它们都是以四则运算和常见的数量关系为基础,通过分析题里的数量关系,根据四则运算的意义列式解答的。但是,两种解答方法的解题思路却不同。由于数量关系的多样性和叙述方式的不同,用算术方法解答应用题,时常要用逆向思考,列式比较困难,解法的变化也比较多。用列方程的方法解答应用题,由于引进了字母表示未知数,可以使未知数直接参与运算,使题目中的数量关系更加清楚,把未知数当成已知数来用,使我们很容易理