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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：Fromthegroupmovementofthebedloadwithinthebottomlayer,detailsofthenonlineardynamiccharacteristicsofbedloadmovementarediscussedinthispaper.Whetherthesedimentisinitiatedintomotioncorrespondstowhethertheconstanttermintheequationisequaltozero.Ifconstanttermiszeroandnodispersiveforceisconsidered,theequationrepresentsthetraditionalShieldsinitiationcurve,andifconstanttermiszerowithoutthedispersiveforcebeingconsidered,thenanewShieldscurvewhichismuchlowerthanthetraditionaloneisgot.Thefixedpointoftheequationcorrespondstotheequilibriumsedimenttransportofbedload.Inthemutationanalysis,wehavefoundthattheinflectionpointisthedemarcationpointofbreaking.Intheory,thebreakingpointcorrespondstothedividingboundaryline,acrosswhichthebedformchangesfromflatbedtosandrippleorsanddune.ComparedwiththeexperimentaldataofChatouHydraulicLabinFrance,theconclusionsareverified.

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.

简介：Startingfromnonlinearequationsonthef-planecontainingfrictionaldissipationundertheBoussinesqapproximation,anewkindofgeneralizedenergyisproposedastheLyapunovfunction,andaveragesaretakenasanyfunctionsof(x,z)insteadofthecommonly-usedmeansofbilinearfunctionsof(x,z),therebyresultinginanewcriterionofgeneralizednonlinearsymmetricstability.Itshowsthatnotonlymustthedissipativecoefficientbegreaterthanacertaincriticalvaluebuttheinitialdisturbanceamplitudemustbesynchronouslysmallerthananothermarginalvalueaswell.Itfollowsthatthelatterimposesacrucialconstraintontheformer,thusleadingtothefactthatwhentheamplitudeisbiggercomparedtoanothercriticalvalue,generalizednonlinearsubcriticalsymmetricalinstabilitymayoccur.Thenewcriterioncontributesgreatlytotheimprovementofthepreviousresultsofitskind.

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简介：Inanormalousdispersionofmonomodeopticalfiber,opticalsolitonsareevolvedfromopticalpulseswhenthedispersionisbalancedbythenonlinearity.Undistortedtransmissioncanberealizedbyusingopticalsolitons,whichcanoffermuchgreaterthetransmissioncapacityandextendtherepeaterspacingofthefibercommunicationsystem.Themechanismofthegenerationofopticalsolitonsisexpounded.Afewformsofnonlineartransmissionequationareobtainedbyusingaconcisemethod.Thegeneralcompleteexpressionofelementarysolitonsolutionofthenonlineartransmissionequationwithoutlossisgiven,andthedesignofthesolitontransmissionsystemisdiscussed.

简介：Someofthemathematicalpropertiesoftheinterfacebetweentwoincompressibleinviscidandimmisciblefluidswithdifferentdensitiesundertheinfluenceofaconstantgravityfieldgareinvestigated.ThepurposeofthispaperistoprovethatlinearlyunstablemodesforRayleigh-Taylorinstabilitiesgivebirthtononlinearinstabilitiesforthefullnonlinearsystem.Themainingredientisageneralinstabilitytheoreminananalyticframeworkwhichenablesustogofromlineartononlinearinstabilities.

简介：§1.IntroductionAssociatedwiththeeigenvalueproblem

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简介：完美的改编描述一个生物系统的能力在被环境骚乱影响以后精确恢复它的生物函数到不安前水平。算术地，有完美的改编的一个生物系统能作为输入产量被建模产量的非线性的系统，通常决定生物函数，在担心的所有输入骚乱下面是asymptotically稳定的。在这份报纸，相当一般的输入产量数学模型被雇用并且生物功能(FBF)功能-产量Lyapunov功能-被探索调查它的完美的改编能力。足够的状况与FBF为系统被建立完成完美的改编。然后，一个足够、必要的条件被获得让线性系统拥有一个输出Lyapunov函数。而且，这被显示出受体功能活动在E的完美的改编模型存在。coli趋化性。与存在不同完美的改编，其大多数基于控制理论的立场，上的数学调查我们首先用非线性的系统分析的方法调查这个问题。

简介：我们在某些合理假设下面考虑有弹性的薄盘子的颤动。我们由哈密尔顿原则为这个模型导出非线性的方程。在为起始的数据的hyperbolicity上的条件下面，我们建立本地时间well-posedness为起始并且由Picard重复的边界值问题为解决方案策划，并且获得估计。

简介：交换非线性的系统的一个类的稳定在纸被调查。担心的系统具有(概括)交换了Byrnes-Isidori正规形式，它都交换了模型在(概括)Byrnes-Isidori正规形式。首先，交换系统的稳定性结果被获得。然后，解决交换非线性的控制系统的稳定问题被用来。另外，必要；足够的条件为是等价于的反馈的一个交换仿射的非线性的系统被获得(概括)交换Byrnes-Isidori正规系统被介绍。最后，作为一个应用程序，交换lorenz系统的稳定性被调查。