简介：这篇论文讨论加速为解决非线性的抛物线的方程的含蓄的计划的反复的方法。二个新非线性的反复的方法由theimplicit明确的伪说出--牛顿(IEQN)方法和衍生物免费的含蓄明确的伪--牛顿(DFIEQN)方法被介绍，在哪个结果从linearization的线性方程能保存原来的部分微分方程的抛物线的特征。重复方法的反复的顺序能集成二次的联盟者到含蓄的计划的答案，这被证明。而且与Jacobian免费Newton-Krylov(JFNK)方法相比，theDFIEQN方法有一些优点，例如，它的实现是容易的，并且它与一个明确的系数矩阵给一个线性代数学的系统，以便线性(内部)重复没被限制为Krylov方法。由IEQN，DFIEQN，JFNK和Picard重复方法的计算结果在理论的证实和这些方法的表演的比较被介绍。

简介：Abstract.OgrobjectinthisartlcleistodescribetbeGalerklnschemeandnonlin-eaxGalerkinschemefortheapproximationofnonlinearevolutionequations,andtostudythestabilityoftheseschemes.SpatialdiscretizatloncanbepedormedbyeitherGalerklnspectralmethodornonlinearGalerldnspectralmethod;timediscretizatlortisdonehyEulersin.heinewklchisexplicitorimplicitinthenonlinearterms.Accordingtothestabilityanalysisoftheaboveschemes,thestabilityofnonllneexGalerklnmethodisbetterthanthatofGalexklnmethod.

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简介：ALaplacedecompositionalgorithmisadoptedtoinvestigatenumericalsolutionsofaclassofnonlinearpartialdiferentialequationswithnonlineartermofanyorder,utt+auxx+bu+cup+du2p1=0,whichcontainssomeimportantequationsofmathematicalphysics.Threedistinctinitialconditionsareconstructedandgeneralizednumericalsolutionsaretherebyobtained,includingnumericalhyperbolicfunctionsolutionsanddoublyperiodicones.Illustrativefiguresandcomparisonsbetweenthenumericalandexactsolutionswithdiferentvaluesofpareusedtotesttheefciencyoftheproposedmethod,whichshowsgoodresultsareachieved.

简介：Weexperimentallyinvestigatedthenonlinearopticalresponseinfew-layeroxidizedblackphosphorus(OBP)bythefemtosecondZ-scanmeasurementtechnique,andfoundthatOBPnotonlypossessesstrongultrafastsaturableabsorptionbutalsoanonlinearself-defocusingeffectthatisabsentinblackphosphorus(BP).Thesaturableabsorptionpropertyoriginatesmainlyfromthedirectbandstructure,whichisstillmaintainedinOBP.Theemergenceofself-defocusingmightoriginatefromthecombinedconsequencesoftheoxygen-induceddefectsinBP.Ourexperimentalfindingsmightconstitutethefirstexperimentalevidenceonhowtodynamicallytuneitsnonlinearproperty,offeringaninroadintailoringitsopticalpropertiesthroughchemicalmodification(oxidation,introducingdefects,etc.).Theversatileultrafastnonlinearopticalproperties(saturableabsorptionandself-defocusing)implyasignificantpotentialofthelayeredOBPinthedevelopmentofunprecedentedoptoelectronicdevices,suchasmodelockers,opticalswitches,laserbeamshapers,andwavelengthconverters.

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简介：各种各样的途径为解决许多连续全球优化问题被开发了。但是直到现在，更少的工作被奉献给由于固有的困难解决非线性的整数编程问题。这篇论文设法把一般非线性的整数编程问题转变成一个equivalent'专辑连续全球最小化问题。因此，任何有效全球优化算法能被用来解决非线性的整数编程问题。这结果将也在全球优化上支持研究。我们在场一个间隔Branch-and-Bound算法。数字实验证明这条途径是有效的。(作者摘要)11个裁判员。

简介：LetXdenoteacomplexanalyticmanifold,andletAut(X)denotethespaceofinvertiblemapsofagerm(X,a)toagerm(X,b);thisspaceisobviouslyagroupoid;roughlyspeaking,a'Liegroupoid'isasubgroupoidofAut(X)definedbyasystemofpartialdifferentialequations.ToafoliationwithsingularitiesonXoneattachessuchagroupoid,e.g.thesmallestonewhoseLiealgebracontainsthevectorfieldstangenttothefoliation.Itiscalled'theGaloisgroupoidofthefoliation'.Someexamplesareconsidered,forinstancefoliationsofcodimensionone,andfoliationsdefinedbylineardifferentialequations;inthislastcaseonerecuperatestheusualdifferentialGaloisgroup.

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简介：Inthispaper,aBoussinesqhierarchyinthebilinearformisproposed.ABacklundtransformationforthishierarchyispresentedandthenonlinearsuperpositionformulaisprovedrigorously.

简介：Ageneralnonlinearconstitutivemodelisproposedformagnetostrictivematerials,basedontheimportantphysicalfactthatanonlinearpartoftheelasticstrainproducedbyapre-stressisrelatedtothemagneticdomainrotationormovementandisresponsibleforthechangeofthemaximummagnetostrictivestrainwiththepre-stress.Toavoidthecomplicityofdeterminingthetensorfunctiondescribingthenonlinearelasticstrainpart,thispaperproposesasimplifiedmodelbymeansoflinearizingthenonlinearfunction.Fortheconvenienceofengineeringapplications,theexpressionsofthe3-D(bulk),2-D(film)and1-D(rod)modelsare,respectively,givenforanisotropicmaterialandtheirapplicablerangesarealsodiscussed.BycomparisonwiththeexperimentaldataofaTerfenol-Drod,itisfoundthattheproposedmodelcanaccuratelypredictthemagnetostrictivestraincurvesinlow,moderateandhighmagneticfieldregionsforvariouscompressivepre-stresslevels.Thenumericalsimulationfurtherillustratesthat,foreithermagnetostrictiverodsorthinfilms,theproposedmodelcaneffectivelydescribetheeffectsofthepre-stressorresidualstressonthemagnetizationandmagnetostrictivestraincurves,whilenoneoftheknownmodelscancaptureallofthem.Therefore,theproposedmodelenjoyshigherprecisionandwiderapplicabilitythanthepreviousmodels,especiallyintheregionofthehighfield.

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简介：为非强迫的优化在方法上介绍研究。学习的假设；主要结果；在简化Armijo类型下面的方法的集中性质衬里搜索。

简介：Thedynamicresponseofthenon-linearelasticsimplysupportedbeamsubjectedtoaxialforcesandtransverseperiodicloadisstudied.Melnikovmethodisusedtoconsiderthedynamicbehav-iorofthesystemwhosepost-bucklingpathissteady.Theeffectofthehigherordertermsinthecon-trollingequationistakenintoaccount.Itisfoundthatthefifth-ordertermshaveagreatinfluenceonthedynamicbehaviorofthesystem.Theresultshowsthatthereexisteitherhomoclinicorbitsorhete-roclinicorbitsinthesystem.Inthispaper,thecriticalvaluesofthesystementeringchaoticstatesaregiven.Thediagramofanexampleisshown.

简介：在这篇论文，一条新非线性的闭图定理被建立，其结果实质地改进一条最近知道重要结论。

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

简介：Theconjugategradientmethodforunconstrainedoptimizationproblemsvarieswithascalar.Inthisnote,ageneralconditionconcerningthescalarisgiven,whichensurestheglobalconvergenceofthemethodinthecaseofstrongWolfelinesearches.ItisalsodiscussedhowtousetheresulttoobtaintheconvergenceofthefamousFletcher-Reeves,andPolak-Ribiere-Polyakconjugategradientmethods.Thattheconditioncannotberelaxedinsomesenseismentioned.

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简介：Someofthemathematicalpropertiesoftheinterfacebetweentwoincompressibleinviscidandimmisciblefluidswithdifferentdensitiesundertheinfluenceofaconstantgravityfieldgareinvestigated.ThepurposeofthispaperistoprovethatlinearlyunstablemodesforRayleigh-Taylorinstabilitiesgivebirthtononlinearinstabilitiesforthefullnonlinearsystem.Themainingredientisageneralinstabilitytheoreminananalyticframeworkwhichenablesustogofromlineartononlinearinstabilities.

简介：§1.IntroductionAssociatedwiththeeigenvalueproblem