简介:在这篇论文,包含的微分方程未知函数重申,与一个复杂参数一,在复杂的域ℂ被调查为分析答案的存在。首先,我们在参数上讨论存在和连续依赖一of上述方程的分析答案,由使用,Banach修理了点定理。然后,以及在许多以前的工作,我们与Schröder转变x(z)=y减少方程(αy−1(z))到下列另外一个没有被调用一个辅助方程的未知函数的重复的功能的微分方程。由构造辅助方程的本地可颠倒的分析答案,表格y的分析答案(为原来的反复的微分方程的αy−1(z))被获得。我们讨论在夸张案例中在Schröder转变给的这些α不仅0<|α|<1并且回声,即,在回声附近的统一,而且那些α的一条根(即,接近统一的一条根)在Brjuno状况下面。最后,我们借助于一个周期性的公式为原来的反复的微分方程介绍明确的分析解决方案,并且给在力量函数形式的一些特别解决方案什么时候=0。
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简介:ThevalueofaEuropeanoptionsatisfiestheBlack-Scholesequationwithappropriatelyspecifiedfinalandboundaryconditions.Wetransformtheproblemtoaninitialboundaryvalueproblemindimensionlessform.Therearetwoparametersinthecoefficientsoftheresultinglinearparabolicpartialdifferentialequation.Forarangeofvaluesoftheseparameters,thesolutionoftheproblemhasaboundaryoraninitiallayer.Theinitialfunctionhasadiscontinuityinthefirst-orderderivative,whichleadstotheappearanceofaninteriorlayer.Weconstructanalyticallytheasymptoticsolutionoftheequationinafinitedomain.Basedontheasymptoticsolutionwecandeterminethesizeoftheartificialboundarysuchthattherequiredsolutioninafinitedomaininxandatthefinaltimeisnotaffectedbytheboundary.Also,westudycomputationallythebehaviourinthemaximumnormoftheerrorsinnumericalsolutionsincasessuchthatoneoftheparametersvariesfromfinite(orprettylarge)tosmallvalues,whiletheotherparameterisfixedandtakeseitherfinite(orprettylarge)orsmallvalues.Crank-Nicolsonexplicitandimplicitschemesusingcenteredorupwindapproximationstothederivativearestudied.Wepresentnumericalcomputations,whichdetermineexperimentallytheparameter-uniformratesofconvergence.Wenotethatthisrateisratherweak,dueprobablytomixedsourcesoferrorsuchasinitialandboundarylayersandthediscontinuityinthederivativeofthesolution.
简介:Fromthemolecularcurrentviewpoint,ananalyticexpressionexactlydescribingmagneticfielddistributionofrectangularpermanentmagnetsmagnetizedsufficientlyinonedirectionwasderivedfromtheBiot-Savart'slaw.Thisexpressionisusefulnotonlyforthecaseofonerectangularpermanentmagnetbulk,butalsoforthatofseveralrectangularpermanentmagnetbulks.Byusingthisexpression,therelationsbetweenmagneticfielddistributionandthesizeofrectangularpermanentmagnetsaswellasthemagnitudeofmagneticfieldandthedistancefromthepointinthespacetothetop(orbottom)surfaceofrectangularpermanentmagnetswerediscussedindetail.Allthecalculatingresultsareconsistentwithexperimentalones.Fortransversemagneticfieldwhichisamainmagneticfieldofrectangularpermanentmagnets,inordertodescribeitsdistribution,twoquantities,oneistheuniformityinmagnitudeandtheotheristheuniformityindistributionofmagneticfield,weredefined.Furthermore,therelationsbetweenthemandthegeometricsizeofthemagnetaswellasthedistancefromthesurfaceofpermanentmagnetswereinvestigatedbytheseformulas.Thenumericalresultsshowthatthegeometricsizeandthedistancehaveavisibleinfluenceontheuniformityinmagnitudeandtheuniformityindistributionofthemagneticfield.
简介:ThispaperstudiesRabinovitch'scompressionexperimentsongraniteandchalkandproposesanoscillatingdipolemodeltoanalyseandsimulatetheelectromagneticradiationphenomenoncausedbyfractureofrocks.Ourmodelassumesthattheelectromagneticradiationpulsesareinitiatedbyvibrationsofthechargedrockgrainsonthetipsofthecrack.Thevibrationsoftherockgrainsarestimulatedbythepulsesofthecracks.OursimulationsshowcomparableresultswithRabinovitch'scompressionexperiments.Fromthesimulationresults,itverifiesanassumptionthatthecrackwidthisinverselyproportionaltothecircularfrequencyelectromagneticradiation,whichispresentedbyRabinovitchetal.Thesimulationresultsalsoimplythat,byusingouroscillatingdipolemodeltogetherwithRabinovitch'stwoequationsaboutthecracklengthandcrackwidth,wecanquantitativelyanalyseandsimulatetheelectromagneticradiationphenomenon,whichisinducedfromthefractureoftherocks.
简介:Recently,tosavethecurrentdrivepowerandtoobtainmorefavorableconfinementmeritforatokamakreactor,largefractionofbootstrapcurrentsustainedequilibriumhasattractedgreatinterestsboththeoreticallyandexperimentally.WeuseanpowerfulexpandingtechniqueandthetokamakorderingtoexpandtheGSh-Etoobtainaseriesofordinarydifferentialequationswhichallowfordifferentsetsofinputprofiles.Thefullybootstrapcurrentsustainedtokamakequilibriaarethensolvedanalytically.
简介:Byusingtwodifferenttransformations,severaltypesofexactanalyticsolutionsforaclassofnonlinearcoupledscalarfieldequationareobtained,whichcontainsolitonsolutions,singularsolitarywavesolutionsandtrianglefunctionsolutions.Theseresultscanbeappliedtoothernonlinearequations.Inaddition,partsofconclusionsinsomereferencesarecorrected.
简介:Inthisarticle,Hasemanboundaryvalueproblemforaclassofmeta-analyticfunctionsisstudied.TheexpressionofsolutionandtheconditionofsolvabilityforHasemanboundaryvalueproblemareobtainedbychangingtheproblemdiscussedintotheequivalentHasemanboundaryvalueproblemofbi-analyticfunction.Andtheexpressionofsolutionandtheconditionofsolvabilitydependonthecanonicalmatrix.
简介:Onthebasisofthedressed-atommodel,thegeneralanalyticexpressionsfortheeigenenergies,eigenstatesandtheiropticalpotentialsoftheA-configurationthree-levelatomsystemarederivedandanalysed.Fromthecalculationofdipolematrixelementofdifferentdressedstates,weobtainthespontaneous-emissionratesinthedressed-atompicture.Wefindthatourgeneralexpressionsofopticalpotentialsforthethree-leveldressedatomcanbereducedtothesameasonesinpreviousreferencesundertheapproximationofasmallsaturationparameter.Wealsoanalysethedependencesoftheopticalpotentialsofathree-level^85Rbatomonthelaserdetuningandthedependencesofspontaneous-emissionratesontheradialpositioninthedarkhollowbeam,anddiscusstheprobability(population)evolutionsofdressed-atomiceigenstatesinthreelevelsinthehollowbeam.
简介:Inthisarticle,westudyontheexistenceofsolutionforasingularitiesofasystemofnonlinearfractionaldifferentialequations(FDE).WeconstructaformalpowerseriessolutionforourconsideringFDEandproveconvergenceofformalsolutionsunderconditions.WeusetheCaputofractionaldifferentialoperatorandthenonlinearitydependsonthefractionalderivativeofanunknownfunction.
简介:LetR0,nbetherealCliffordalgebrageneratedbye1,e2,···,ensatisfyingeiej+ejei=-2δij,i,j=1,2,···,n.e0istheunitelement.Letbeanopenset.AfunctionfiscalledleftgeneralizedanalyticiniffsatisfiestheequationLf=0,(0.1)whereL=q0e0θx0+q1e1θx1+···+qnenθxn,qi>0,i=0,1,···,n.Inthisarticle,wefirstgivethekernelfunctionforthegeneralizedanalyticfunction.Further,theHilbertboundaryvalueproblemforgeneralizedanalyticfunctionsinRn+1+willbeinvestigated.
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