简介:Inthispaper,thetheoremsconcerningthesummationofFourierserieswithparameteraregivenbyusingtheLaplacetransforms.BymeansoftheknownresultofLaplacetransforms,manynew,importantproblemsofsummationofFourierserieswithparameterinmechanicscanbesolved.
简介:AnewmethodforapproximatingtheinerseLaplacetransformispresented.WefirstchangeourLaplacetransformequationintoaconvolutiontypeintegralequation,whereTikhonovregularizationtechniquesandtheFouriertransformationareeasilyapplied.WefinallyobtainaregularizedapproximationtotheinverseLaplacetransformasfinitesum
简介:Inthepresentpaper,wehaveconsideredtheapproximationofanalyticfunctionsrepresentedbyLaplace-Stieltjestransformationsusingsequenceofdefiniteintegrals.WehavecharacterizedtheirorderandtypeintermsoftherateofdecreaseofEn(F,b)whereEn(F,b)istheerrorinapproximatingofthefunctionF(s)bydefiniteintegralpolynomialsinthehalfplaneRes≤b〈a.
简介:§0.IntroductionLetXbearealseparableBanachspaceandX*beitsdualspace,LetB(X)betheBorelfield,i.e.,thetopologicalσ-field.Afunctionalu:X→R’iscalledaboundedsmoothfunctional,ifn∈N,f1,…,fn∈X*andφ∈Cb∞(Rn),suchthat
简介:Letfibeaboundedsmoothdomain.Inthispaper,theauthorsdefinetheBesovspacesBpa,pon,establishtheatomicdecompositionofthesespaces,andobtaintheregularityestimateoftheDirichletproblemandtheNeumannproblemfortheLaplaceoperatoronthesespaces.
简介:Inthispaper,weconsidertheCauchyproblemfortheLaplaceequation,whichisseverelyill-posedinthesensethatthesolutiondoesnotdependcontinuouslyonthedata.AmodifiedTikhonovregularizationmethodisproposedtosolvethisproblem.Anerrorestimatefortheaprioriparameterchoicebetweentheexactsolutionanditsregularizedapproximationisobtained.Moreover,anaposterioriparameterchoiceruleisproposedandastableerrorestimateisalsoobtained.Numericalexamplesillustratethevalidityandeffectivenessofthismethod.
简介:Thispaperdevelopsanumericalmethodtoinvertmulti-dimensionalLaplacetransforms.Byavariabletransform,Laplacetransformsareconvertedtomulti-dimensionalHansdorffmomentproblemssothatthenumericalsolutioncanbeachieved.Stabilityestimationisalsoobtained.Numericalsimulationsshowtheefficiencyandpracticalityofthemethod.
简介:Fora〈r〈b,theapproachofLiandZhou(2014)isadoptedtofindjointLaplacetransformsofoccupationtimesoverintervals(a,r)and(r,b)foratimehomogeneousdiffusionprocessbeforeitfirstexitsfromeitheraorb.Theresultsareexpressedintermsofsolutionstothedifferentialequationsassociatedwiththediffusionsgenerator.Applyingtheseresults,weobtainmoreexplicitex-pressionsonthejointLaplacetransformsofoccupationtimesforBrownianmotionwithdrift,BrownianmotionwithalternatingdriftandskewBrownianmotion,respectively.
简介:设M为S^n+1中紧致极小超曲面,Mp,n-p为Sn+1的Clifford极小超曲面,若Spec(M)=Spec(Mp,n-p)在一定条件下,我们可以得出M与Mp,n-p等距同构。
简介:这篇文章考虑,为下列热方程
简介:ALaplacedecompositionalgorithmisadoptedtoinvestigatenumericalsolutionsofaclassofnonlinearpartialdiferentialequationswithnonlineartermofanyorder,utt+auxx+bu+cup+du2p1=0,whichcontainssomeimportantequationsofmathematicalphysics.Threedistinctinitialconditionsareconstructedandgeneralizednumericalsolutionsaretherebyobtained,includingnumericalhyperbolicfunctionsolutionsanddoublyperiodicones.Illustrativefiguresandcomparisonsbetweenthenumericalandexactsolutionswithdiferentvaluesofpareusedtotesttheefciencyoftheproposedmethod,whichshowsgoodresultsareachieved.