简介：Basedonthetheoryofcalculusofvariation,somesuffcientconditionsaregivenforsomeEuler-LagrangcequationstobeequivalentlyrepresentedbyfiniteoreveninfinitemanyHamiltoniancanonicalequations.Meanwhile,somefurtherapplicationsforequationssuchastheKdVequation,MKdVequation,thegenerallinearEulerLagrangeequationandthecylindricshellequationsaregiven.

简介：TheproblemofdistributedcoordinatedtrackingcontrolfornetworkedEuler-Lagrangesystemswithoutvelocitymeasurementsisinvestigated.Undertheconditionthatonlyaportionofthefollowershaveaccesstotheleader,slidingmodeestimatorsaredevelopedtoestimatethestatesofthedynamicleaderinfinitetime.Tocopewiththeabsenceofvelocitymeasurements,thedistributedobserverswhichonlyusepositioninformationaredesigned.Basedontheoutputsoftheestimatorsandobservers,distributedtrackingcontrollawsareproposedsuchthatallthefollowerswithparameteruncertaintiescantrackthedynamicleaderunderadirectedgraphcontainingaspanningtree.Itisshownthatthedistributedobserver-controllerguaranteesasymptoticalstabilityoftheclosed-loopsystem.Numericalsimulationsareworkedouttoillustratetheeffectivenessofthecontrollaws.

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简介：ItisaclassicalresultofBernsteinthatthesequenceofLagrangeinterpolationpolynomialsto|x|atequallyspacednodesin[-1,1]divergeseverywhere,exceptatzeroandtheend-points.InthispaperweshowthatthesequenceofLagrangeinterpolationpolynomialscorrespondingtothefunctionswhichpossessbettersmoothnessonequidistantnodesin[-1,1]stilldivergeseverywhereintheintervalexceptatzeroandtheend-points.

简介：Thispaperconsiderstoreplace△m（x）=（1-x2）2（1/2）/n+1/n2inthefollowingresultforsimultaneousLagrangeinterpolatingapproximationwith（1-x2）2（1/2）/n:Letf∈C-1.10andr=[（q+2）/2],then|fk（x）-P^{k（f,x）|=O（1）△na-k（x）ω(fa,△（x）)（‖Ln-‖+‖Ln‖）,0≤k≤q,wherePn（f,x）istheLagrangeinterpolatingpolynomialofdegreen+2r-1offonthenodesXnUYn（seethedefinitionofthetext）,andthusgiveaproblemraisedin[XiZh]acompleteanswer.}

简介：IntheprocessofsolvingEulervectorsbasedonGNSShorizontalmovementfield,thenumberofestimatedparameterscanaffectEulervectorresults.Thisissueisanalyzedthroughtheoreticaldeductionandpracticalexampleinthispaper.Firstly,thedifferencebetweentheresultsofEulervectorsindifferentsolvingmodelsisdeduced.Meanwhile,basedonGNSShorizontalmovementfieldintheChinesemainlandfrom2004to2007,twocommonmodels(RRMandREHSM)areusedtodiscusstheimpactofsolvingmodelsonEulervectorsandthefollow-upstudy.Theresultshowsthatthemaximumvalueofthedifferenceinablock’sentirerotationcanreach2.6mm/a,andshouldnotbeignored.Therefore,theresultsofhorizontalmovementaredifferentusingdifferentkinematicblockmodels,andthisshouldbepaidmoreattentionintheanalysisofcrustalhorizontalmovement.

简介：PropertiesofLebesguefunctionforLagrangeinterpolationonequidistantnodesareinvestigated.ItisprovedthatLebesguefunctioncanbeformulatedbothintermsofahypergeometricfunction2F1andJacobipolynomials.Moreover,anintegralexpressionofLebesguefunctionisalsoobtainedandtheasymptoticbehaviorofLebesgueconstantisstudied.

简介：文章主要探讨微积分学中辅助函数的构造,给出以Rolle定理为基础,用不同的构造辅助函数的方法来证明Lagrange定理,这里仅从分析法、尝试法、几何法来进行讲解说明。

简介：用广义Lagrange中值定理讨论凸函数,得到条件较弱的定理,并分析了该定理的一些应用.

简介：作者为概括Euler数字E2n(x),建立一个明确的公式并且获得包含高顺序的Euler数字，Stirling数字，中央因素的数字和Riemann希腊语的第六个字母功能的价值的一些身份和一致。

简介：对Lagrange中值定理的证明,在高等数学的传统证法中,通常都是采用引入一个"辅助函数",将适合定理的函数转换成适合Rolle中值定理的函数的办法.为了进一步开阔思路,更好地理解和掌握Lagrange中值定理,本文给出了行列式证法、旋转变换证法和区间套定理证法等几种证明方法.

简介：Inthispaper,weproposeamortarelementmethodwithLagrangemultiplierforincompressibleStokesproblem,i.e.,thematchingconstraintsofvelocityonmortaredgesareexpressedintermsofLagrangemultipliers.WealsopresentP_1noncon-formingelementattachedtothesubdomains.Byprovinginf-supcondition,wederiveoptimalerrorestimatesforvelocityandpressure.Moreover,weobtainsatisfactoryapproximationfornormalderivativesofthevelocityacrosstheinterfaces.

简介：Kizmaz[13]学习了差别顺序空格?∞(Δ)，c(Δ)，和c0(Δ)。几篇文章处理了哪个被围住的m-th顺序差别的序列的集合，对零会聚，或会聚。Altay和Ba?ar[5]并且Altay，Ba?ar，和Mursaleen[7]介绍了Euler顺序空格e(r)0，e(r)c，和e(r)∞分别地。这篇文章的主要目的是介绍空格e(r)0(Δ(m))，e(r)c(Δ(m))，并且e(r)∞(Δ(m))由其m(th)命令差别在Euler空格的所有序列组成e(r)0，e(r)c，和e(r)∞分别地。而且，作者给一些拓扑的性质和包括关系，并且决定空格e(r)的α-，β-，和γ-duals0(Δ(m))，e(r)c(Δ(m))，并且e(r)∞(Δ(m))，并且空格e(r)的Schauder基础0(Δ(m))，e(r)c(Δ(m))。文章的最后节在顺序空间e(r)c(Δ(m)上被奉献给一些矩阵地图砰的描述)。给词调音：顺序m的差别顺序空格；Schauder基础；α-，β-，和γ-duals；矩阵地图砰

简介：近年来，若干文章对“Lagrange微分中值定理的逆问题”进行了讨论，但其表述均不完整，且证明也较繁琐。本文使用严格凸（严格凹）函数的性质，给出该问题一个条件较弱且表述较完整的结果，其证明也较简洁。

简介：用变分方法研究非自治Lagrange系统周期解的问题转化为研究Lagrange作用泛函的临界点问题.对Lagrange系统,人们用变分方法已经获得了一系列可解性条件,但是除在超二次条件下,Lagrange作用泛函都是下方有界的.这里的目的是给出Lagrange作用泛函无界的Lagrange系统周期解的其它可解性条件.这时的主要困难是对应的Lagrange作用泛函不再是下方有界的.这里用临界点理论中的鞍点定理得到了Lagrange系统周期解的存在性.

简介：S.M.LozinskiiprovedtheexactconvergencerateatthezeroofLagrangeinterpolationpolynomialsto|x|basedonequidistantnodesin[-1,1].In2000,M.RevergeneralizedS.M.Lozinskii'sresultto|x|α(0≤α≤1).Inthispaperwewillpresenttheexactrateofconvergenceatthepointzerofortheinterpolantsof|x|α(1＜α＜2)..

简介：TheregularsolutionsoftheisentropicEulerequationswithdegeneratelineardampingforaperfectgasarestudiedinthispaper.Andacriticaldegeneratelineardampingcoefficientisfound,suchthatifthedegeneratelineardampingcoefficientislargerthanitandthegasliesinacompactdomaininitially,thentheregularsolutionwillblowupinfinitetime;ifthedegeneratelineardampingcoefficientislessthanit,thenundersomehypothesesontheinitialdata,theregularsolutionexistsglobally.

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