简介：Wededuceacompletewavepropagationequationthatincludesinhomogeneityofthedielectricconstantandpresentthispropagationequationincompactvectorform.Althoughsimilarequationsareknowninnarrowfieldssuchasradiowavepropagationintheionosphereandelectromagneticandacousticwavepropagationinstratifiedmedia,wedevelophereanovelapproachofusingsuchequationsinthemodelingoflaserbeampropagationinnonlinearmedia.Ourapproachsatisfiesthecorrespondenceprinciplesinceinthelimitofzero-lengthwavelengthitreducesfromphysicaltogeometricaloptics.

简介：Inthispaper,wederivealawoflargenumbersunderthenonlinearexpectationgeneratedbybackwardstochasticdifferentialequationsdrivenbyG-Brownianmotion.

简介：Sequentialmeasurementprocessingisofbenefittobothestimationaccuracyandcomputationalefficiency.Whenthenoisesarecorrelatedacrossthemeasurementcomponents,decorrelationbasedoncovariancematrixfactorizationisrequiredinthepreviousmethodsinordertoperformsequentialupdatesproperly.Anewsequentialprocessingmethod,whichcarriesoutthesequentialupdatesdirectlyusingthecorrelatedmeasurementcomponents,isproposed.Andatypicalsequentialprocessingexampleisinvestigated,wheretheconvertedpositionmeasurementsareusedtoestimatetargetstatesbystandardKalmanfilteringequationsandtheconvertedDopplermeasurementsarethenincorporatedintoaminimummeansquarederror(MMSE)estimatorwiththeupdatedcross-covarianceinvolvedtoaccountforthecorrelatederrors.Numericalsimulationsdemonstratethesuperiorityoftheproposednewsequentialprocessingintermsofbetteraccuracyandconsistencythantheconventionalsequentialfilterbasedonmeasurementdecorrelation.

简介：Atheoreticalmodelofanonlinearhyperbolicmetamaterialispresentedintheformofastackofsubwavelengthlayersoflinearplasmonicandnonlineardielectricmaterials.Abroadpictureofthepropertiesofevanescentwaves(high-kmodes)inthisstackisinvestigatedbyplottingglobaltransmissiondiagrams.Thepresenceofnonlinearitystronglymodifiesthesediagrams.Theemergenceandmodificationofnonlinearevanescentwavesisobserved.Somesignaturesofnonlinearphenomenonsuchasformationoforbitsandtrajectoriesaroundfixedpointsarealsoseeninourwork.

简介：ThispaperisconcernedwiththeexistenceandthenonlinearasymptoticstabilityoftravelingwavesolutionstotheCauchyproblemforasystemofdissipativeevolutionequations{ξt=-θx+βξxx,θt=vξx+(ξθ)x+αθxx,withinitialdataandendstates(ξ,θ)(x,0)=(ξ0,θ0)(x)→(ξ±,θ±)asx→±∞.Weobtaintheexistenceoftravelingwavesolutionsbyphaseplaneanalysisandshowtheasymptoticnonlinearstabilityoftravelingwavesolutionswithoutrestrictionsonthecoefficientsαandvbythemethodofenergyestimates.

简介：Inthispaper,weestablishanexistencecriterionoftriplepositivesolutionsofaclassofnonlinearfourth-orderthree-pointboundaryvalueproblembytheLeggettWilliamsfixedpointtheorem.Theinterestingpointisthatthenonlineartermisinvolvedwithalllow-levelderivatives.

简介：Inthispaper,weconsidertheuniformstabilityanduniformlyasymptoticalstabilityofnonlinearimpulsiveinfinitedelaydifferentialequations.InsteadofputtingallcomponentsofthestatevariablexinoneLyapunovfunction,severalLyapunov-Razumikhinfunctionsofpartialcomponentsofthestatevariablexareusedsothattheconditionsensuringthatstabilityaresimplerandlessrestrictive;moreover,examplesarediscussedtoillustratetheadvantageoftheresultsobtained.

简介：Nonlinearacousticpropagationgeneratedbyapistoninafinitehornisnumericallystudied.Aquasi-one-dimensionalnonlinearmodelwithvaryingcross-sectionuseshigh-orderlow-dispersionnumericalschemestosolvethegoverningequation.Becauseofthenonlinearwavedistortionandreflectedsoundwavesatthemouth,broadbandtime-domainimpedanceboundaryconditionsareemployed.Theimpedanceapproximationcanbeoptimizedtoidentifythecomplex-conjugatepole-residuepairsoftheimpedancefunctions,whichcanbecalculatedbyfastandefficientrecursiveconvolution.Thenumericalresultsagreeverywellwithexperimentaldatainthesituationsofweaknonlinearwavepropagationinanexponentialhorn,itisshownthatthemodelcandescribethebroadbandcharacteristicscausedbynonlineardistortion.Moreover,finite-amplitudeacousticpropagationintypesofhornsissimulated,includinghyperbolic,conical,exponentialandsinusoidalhorns.Itisfoundthatsoundpressurelevelsatthehornmoutharestronglyaffectedbythehornprofiles,thedrivingvelocityandfrequencyofthepiston.Thepaperalsodiscussestheinfluenceofthehorngeometryonnonlinearwaveformdistortion.

简介：Byusingtherefinementofthestandardintegralaveragingtechnique,weobtainsomeoscillationcriteriaforsecondordermixednonlinearellipticequations.Theresultsestablishedinthispaperextendandimprovesomeexistingoscillationcriteriaforhalf-linearPDEintheliterature.

简介：Theprimaryresonancesofaquadraticnonlinearsystemunderweakandstrongexternalexcitationsareinvestigatedwiththeemphasisonthecomparisonofdifferentanalyticalapproximateapproaches.Theforcedvibrationofsnap-throughmechanismistreatedasaquadraticnonlinearoscillator.TheLindstedt-Poincar′emethod,themultiple-scalemethod,theaveragingmethod,andtheharmonicbalancemethodareusedtodeterminetheamplitude-frequencyresponserelationshipsofthesteady-stateresponses.Itisdemonstratedthatthezeroth-orderharmoniccomponentsshouldbeaccountedintheapplicationoftheharmonicbalancemethod.Theanalyticalapproximationsarecomparedwiththenumericalintegrationsintermsofthefrequencyresponsecurvesandthephaseportraits.Supportedbythenumericalresults,theharmonicbalancemethodpredictsthatthequadraticnonlinearitybendsthefrequencyresponsecurvestotheleft.Iftheexcitationamplitudeisasecond-ordersmallquantityofthebookkeepingparameter,thesteady-stateresponsespredictedbythesecond-orderapproximationoftheLindstedtPoincar′emethodandthemultiple-scalemethodagreequalitativelywiththenumericalresults.Itisdemonstratedthatthequadraticnonlinearsystemimpliessofteningtypenonlinearityforanyquadraticnonlinearcoefficients.

简介：自相关函数并且有非线性的推迟时间的反馈的一个自治随机的系统跨关联被使用随机的模拟方法调查。在一个自治随机的系统的关联上二次的推迟时间的反馈和立方的推迟时间的反馈的角色之间有突出的差别。在二次的推迟时间的反馈下面，非线性的时间延期没能改进自治随机的系统的吵闹的状态，自相关单调地减少到零，并且跨关联的增加单调地到零与腐烂时间。在立方的推迟时间的反馈下面，非线性的时间延期能改进自治随机的系统的吵闹的状态；自相关和跨关联的表演期刊摆动和变细，最后与腐烂时间趋于到零。比较系统在之间的关联与非线性的推迟时间的反馈和线性推迟时间的反馈，我们发现非线性的推迟时间的反馈降低自治随机的系统的关联力量。

简介：这份报纸建议为非线性的平等的一个缩小的过滤器行搜索算法抑制了优化。一个缩小的过滤器，是传统的过滤器的修正，在算法被采用。当步尺寸接近零，缩小的过滤器的信封变得越来越薄。这个新算法为试用步的接受有更多的灵活性并且与传统的过滤器算法相比要求不太计算的费用。建议算法的全球、本地的集中在一些合理条件下面被给。数字实验被报导显示出缩小的过滤器算法的有效性。

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简介：ThisworkisaimedtorigorouslymanagevoltagesaturationandmaximumcurrentconstraintsinShuntActiveFilters.Inthisrespect,assuming'unconstrained'controlalgorithmshavealreadybeendefinedtoachievestandardobjectivesforsuchdevices(i.e.currenttrackingforharmoniccompensationandDC-busvoltageboundness),aplug-inunit,orientedtoextendthesystemoperatingregionandatthesametimepreservinggoodperformanceunderlargetransientsandoverloadconditions,ispresented.Thissolutionallowstoimproveavailability,robustnessandcomposabilityofShuntActiveFilters,whichareexpectedtobekeyfeaturesinpresentandnextgenerationcomplexandpossibly'smart'powergrids.Theproposedunitiscomposedbytwoparts.First,asuitableanti-windupstrategyisdefinedinordertodealwithcontrolinputsaturation.Itsmainpurposeistopreservetheoriginal'unconstrainederrordynamics',infaceofinputsaturation,whileguaranteeinglowcomputationalburdenandreducedperformanceimpairment(thelattergoal,inharmoniccompensationcontext,leadstorathernon-standardproblemformulation).Tothisaim,theanti-windupactsonthecurrentreferencesthroughasuitably-designedadditionaldynamics.Then,inordertocopewithcurrentlimitations,anadditionalstrategyhasbeendesigned;againthecurrentreferencesissuitablyshapedtocomplywiththefeaturesandboundsofthesystem,augmentedwiththeabove-mentionedanti-windupsolution.TheproposedschemecanbesimplyjoinedtoanykindofunconstrainedcontrolleradoptedtosteerShuntActiveFilters.Inthiswork,anInternal-Model-basedcurrentcontrollerisadoptedasabenchmarkcase.Theproposedapproachisvalidatethroughextensivesimulationtests.

简介：Inthispaper,weconsiderexistenceanduniquenessofpositivesolutionstothreecouplednonlinearSchrdingerequationswhichappearinnonlinearoptics.Weusethebehaviorsofminimizingsequencesforaboundtoobtaintheexistenceofpositivesolutionsforthreecoupledsystem.Toprovetheuniquenessofpositivesolutions,weusetheradialsymmetryofpositivesolutionstotransformthesystemintoanordinarydifferentialsystem,andthenintegratethesystem.Inparticular,forN=1,weprovetheuniquenessofpositivesolutionswhen0≤β=μ1=μ2=μ3orβ>max{μ1,μ2,μ3}.

简介：Inthispaper,theHyers-Ulamstabilityofathird-ordernonlineardifferentialequationisinvestigated.BytheintegratingmethodandaGronwalltypeinequality,thestabilityresultsareobtainedindifferentsituationsonaboundeddomain.Then,thestudyisextendedtonth-ordernonlineardifferentialequations.

简介：Usingastrongnonlinearsaturationabsorptioneffectisonetechniqueforbreakingthroughthediffractionlimit.Inthistechnique,formationofadynamicandreversibleopticalpinholechannelandtransientsuperresolutioniscritical.Inthiswork,apump–probetransientdetectionandobservation–experimentalsetupisconstructedtoexploretheformationprocessdirectly.AGe2Sb2Te5thinfilmwithstrongnonlinearsaturationabsorptionisinvestigated.Thedynamicevolutionoftheopticalpinholechannelisdetectedandimaged,andthetransientsuperresolutionspotisdirectlycapturedexperimentally.Resultsverifythatthesuperresolutioneffectoriginatesfromthegenerationofanopticalpinholechannelandthattheformationoftheopticalpinholechannelisdynamicandreversible.Agoodmethodisprovidedfordirectdetectionandobservationofthetransientprocessofthesuperresolutioneffectofnonlinearthinfilms.

简介：Inordertostudybucklingpropagationmechanismindeepseapipelines,thecontactbetweenpipeline’sinnerwallsinbucklingprocesswasstudied.Atwo-dimensionalringmodelwasusedtorepresentthepipelineandanonlinearspringmodelwasadoptedtosimulatethecontactbetweeninnerwalls.Basedontheelastoplasticconstitutiverelationshipandtheprincipleofvirtualworktheory,thecouplingeffectofpipeline’snonlinearlargedeformationandwallcontactwasincludedinthetheoreticalanalysiswiththeaidofMATLAB,andtheapplicationscopeofthetheoreticalmodelwasalsodiscussed.Thecalculatedresultsshowthatduringtheloadingprocess,thechangeinexternalpressureiscloselyrelatedtothedistributionofsectionstress,andoncethewallsarecontactingeachother,theexternalpressureincreasesandthenremainsstableafteritreachesaspecificvalue.Withoutfracture,thepipelinesectionwillstopshowingdeformation.Theresultsoftheoreticalcalculationsagreewellwiththoseofnumericalsimulations.Finally,inordertoensurereliabilityandaccuracyofthetheoreticalresults,thecollapsepressureandpropagationpressurewerebothverifiedbynumericalsimulationsandexperiments.Therefore,thetheoreticalmodelcanbeusedtoanalyzepipeline’sbucklingdeformationandcontactbetweenpipeline’sinnerwalls,whichformsthebasisforfurtherresearchonthree-dimensionalbucklingpropagation.

简介：在现在的纸，在粘弹性的基础上在一根僵硬横梁上管理的一个震动的微分方程被调查了。在这个颤动的系统上管理的非线性的微分方程被一条简单、创新的途径解决，它被称为Akbari-Ganjis方法(AGM)。AGM是一个很合适的计算过程并且为解决各种各样的非线性的微分方程是可用的。而且，用哪个的AGM解决一套代数学的方程，没有任何数学操作，复杂非线性的方程能容易被解决。另外，为三个周期每周期失去的抑制比率和精力被调查了。而且，比较被数字方法(Runk45)和AGM在获得的结果之间做了。结果显示出AGM的高精确性。结果也证明由增加颤动(A)的起始的振幅的数量，抑制比率的价值将被增加，并且精力由增加周期的数字每周期减少输了。AGM是为解决微分方程的一条可靠、精确的途径，这被结束。在另一方面，说AGM能处于大多数状况直接解决线性、非线性的微分方程更好。这意味着没有任何无尺寸的过程，最后的答案能被获得。因此，AGM能在非线性的科学被看作重要进步。