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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。

简介：在现在的纸，我们学习几个复杂变量的分析函数的多项式近似。几个复杂变量的分析功能的概括类型的描述以近似和插值错误被获得了。

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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：ItisshownthatthereexistsaJ-convexsubsetCofacomplexHilbertspaceX,suchthattheJ-couvexhullofthesetofallJensenboundarypointsofCisdifferentfromC.

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：现在的纸的主要目标是调查象包括关系那样的很多个有用性质，失真界限，系数估计，隶属结果，Fekete-Szeg吗？为分析功能的一个新子类的问题和某其它，它借助于线性操作员这里被定义。这里介绍，那些在更早的工作获得了的结果的相关连接也被指出。

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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