简介：AdegreeelevationformulaformultivariatesimplexsplineswasgivenbyMicchelli[6]andextendedtoholdformultivariateDirichletsplinesin[8].Wereportsimilarformulaeformultivariateconesplinesandboxsplines.Tothisend,weutilizearelationduetoDahmenandMicchelli[4]thatconnectsboxsplinesandconesplinesandadegreereductionformulagivenbyCohen,Lyche,andRiesenfeldin[2].

简介：WestructureakindofrationalsplinesfarintroducingsomeofthePadeapproximenttechniquesintorationalsplines.Inthispaper,theresultsontheexistence,uniquenessandalgorithmoftherationalsplinearegivenandanumericalexampleisprovided.

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简介：ThemultivariatesplineswhichwerefirstpresentedbydeBooorasacompletetheoreticalsystemhaveintriguedmanymathematicianswhohavedevotedmanyworksinthisfieldwhichisstillintheprocessofdevelopment.Theauthorofthispaperisinterestedintheareaofinter-polationwithspecialemphasisontheinterpolationmethodsandtheirapproximationorders.ButsuchB-splines(bothunivariateandmultivariate)donotinterpolateddirectly,soIap-proachedthisprobleminanotherwaywhichistoextendmyinterpolatingsplineofdegree2n-1inunivariatecase(See[7])tomultivariatecase.Iselectedtriangulatedregionwhichisinspiredbyothermathematicians’works(e.g.[2]and[3])andextendtheinterpolatingpolynomialsfromunivariatetom-variatecase(See[10])Inthispapersomeresultsinthecasem=2arediscussedandprovedinmoreconcretedetails.Basedonthesepolynomials,theinterpolatingsplines(itisdefinedbymeaspiecewisepolynomialsinwhichtheunknownpar-tialderivativesaredeterminedundercertaincontinuousconditions)arealsodiscussed.Theapproximationordersofinterpolatingpolynomialsandofcubicinterpolatingsplinesareinverstigated.Welunitedourdiscussionontherectangulardomainwhichispartitionedintoequalrighttriangles.Astothecaseinwhichtherectangulardomainispartitionedintounequalrighttrianglesaswellasthecaseofmorecomplicateddomains,wewilldiscussinthenextpa-per.

简介：Locccalsplmesarepresentedfartheapproximationoffunctionsofoneandmanyvariables,whichareana-lyticinthedomamswhereUi(zi)isaunitdiskinthecomplexplaneCi,i=1,2,...l,l=1,2,...Resultsarcgivenforfunctionswhoser-orderderivativesbelongtotheHardy’sclassHp,1≤p≤∞,ItisshownthattheapproximationconvergetothefunctionattherateAexp(-Cn(r-1/p)forfunctionsofonevariableandAn-(r-1/p)/(I-1)forfunctionsoflvariables,wherenisthenumberofpointsoflocalsplinesandAandCarepositrveconstants.

简介：InthispaperweconsiderpolynomialsplinesS(x)withequidistantnodeswhichmaygrowa5O(|x|~5).Wepresentanintegralrepresentationofsuchsplineswithadistributionkernel.Thisrepre-sentationisrelatedtotheFourierintegralofslowlygrowingfunctions.ThepartoftheFourierex-ponentialsherewithplaythesocalledexponentialsplinesbySchoenberg.Theintegralrepresentationprovidesaflexibletoolfordealingwiththegrowingequidistantsplines.First.itallowsustocon-structarichlibraryofsplinespossessingthepropertythattranslationsofanysuchsplineformaba-sisofcorrespondingsplinespace.Itisshownthatanysuchsplineisassociatedwithadualsplinewhosetranslationsformabiorthogonalbasis.Asexampleswepresentsolutionsoftheproblemsofprojectionofagrowingfunctionontosplinespacesandofsplineinterpolationofgrowingfunc-tion.Wederiveformulasforapproximateevaluationofsplinesprojectingafunctionontothesplinespaceandestablishtherewithexactestimationsoftheapproximationerrors.

简介：Inthisnotesomerecurrencerelationsforthedimensionsofthesplinespacesonsocalled0-starsarepresented.

简介：SurfacereconstructionfromunorganizeddatapointsisachallengingprobleminComputerAidedDesignandGeometricModeling.Inthispaper,weextendthemathematicalmodelproposedbyJüttlerandFelis(Adv.Comput.Math.,17(2002),pp.135-152)basedontensorproductalgebraicsplinesurfacesfromfixedmeshestoadaptivemeshes.WestartwithatensorproductalgebraicB-splinesurfacedefinedonaninitialmeshtofitthegivendatabasedonanoptimizationapproach.Bymeasuringthefittingerrorsovereachcellofthemesh,werecursivelyinsertnewknotsincellsoverwhichtheerrorsarelargerthansomegiventhreshold,andconstructanewalgebraicsplinesurfacetobetterfitthegivendatalocally.Thealgorithmterminateswhentheerrorovereachcellislessthanthethreshold.WeprovidesomeexamplestodemonstrateouralgorithmandcompareitwithJüttler'smethod.Examplessuggestthatourmethodiseffectiveandisabletoproducereconstructionsurfacesofhighquality.

简介：Inthispaperweconsidertwoproblems.Thefirstisconnectedwiththeoptimalrecoveryoffunctionssatisfyiogboundaryconditions.Thesecondisthecharacterizationoftheuniquefunc-tionwhoser-thderivativehasminimumL_∞-norm,takinggivenvaluesofalternatingsignsandsatisfyingboundaryconditions.

简介：ThispapergivesanadditionaldefinitiontomultivariatetruncatedpowerT(x|x1,…,xn)whentheknotsx1,…,xndonotspanthewholespacetowhichx1,…,xnbelong.Bywhich,togetherwiththerecurrencerelation,thepracticalevaluationofT(x|x1,…,xn)willbeveryconvenientandefficient.Thesamediscussionisalsodonetoboxsplines.

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简介：Thegasdynamicandelectromagneticfactorsaffectingthepositionofarcrootsinatubulararcheaterareanalyzed.Magnitudesofthevariousfactorsareestimatedthroughnumericalmodelling,andtheoverallactiononthearcassessed.Itisfoundthattheactionsonthearcintherearelectrodecanbebalancedinastablemannerandthearcrootcanbestabilizedatacertainaxialposition.Inthefrontelectrode,thevariousfactorscannotbebalanced,andthearerootcanonlystaywithintheelectrodethroughthemechanismofrecurrentshunting.Theseconclusionsagreewithexperimentalobservations.

简介：煤气的金属弧焊(GMAW)的数字模型正在试着联合液体(VoF)的弧和体积的magnetohydrodynamics(MHD)模型的电流金属转移当模特儿。他们忽视蒸发并且为弧区域假定氩气氛，因为它是为煤气的钨弧焊的模型的普通实践。这些模型在20000K和类似于钨的温度分布上面预言温度惰性的气体(TIG)弧。然而，在GMAW弧的当前的分光镜的温度大小表明低得多的弧温度。与TIG弧相对照，他们发现了光线的温度分发的中央本地最小。纸论述考虑金属蒸汽的一个GMAW弧模型并且它在与试验性地观察的温度的一个很好的协议。而且，模型能第一次在光线的温度和光线的电流密度分布预言本地中央最小。向轴的方向焊接火炬，工作片，电线和弧(液体领域)的对称的模型象在氩的狂暴的混合和金属蒸汽的热demixing一样实现MHD。从模拟获得的铁蒸汽的集体部分在2000～5000K在弧的穗上在弧核心和另一累积显示出累积。demixing效果导致在这二个区域之间的铁的很低的集中。敏感分析证明运输的影响和金属蒸汽的放射性质喂。最后模型预言与Zieliska等的测量结果相比。

简介：LetGbeaPolyafrequencydensityandGitsperiodization.Wegettheexactvalueofupperapproxi-mationofS1（G）,whichisaconvolutionclasswithkernelG.bycardinalsplinescprrespndingtoG.SimilarresulthasbeenobtainedforperiodicconvolutionclasswithkernelGaswell.

简介：我们考虑决定作为生气的节有一条开的弧的薄绝缘的无限的柱体的形状的反的散布问题。假设电场在TM模式被极化，这为在R2在一条开的弧的外表定义的Helmholtz方程导致一个混合边界价值问题。我们假定弧混合了Dirichlet阻抗边界状况，并且试着由使用因式分解方法通过远地模式恢复弧的形状。然而，我们不能使用樱桃酒介绍对待远地操作员F的基本定理，并且一些辅助操作员不得不被考虑。到我们的问题的因式分解方法的理论确认在这份报纸被给，并且一些数字结果被介绍显示出我们的方法的生存能力。[从作者抽象]

简介：Thearcsprayingprocessisdividedintotwostages:thefirststageisatomization-sprayingstream(ASS)andthesecondoneissprayingdeposition(SD).Thenstudystatusisdescribedofbothstages'physicalmodelandcorrespondingcontrolling-equation.Basedontheanalysisofstudystatus,theconclusionasfollowsisgot.TheheatandmasstransfermodelswithtwoorthreedimensionsinASSstageshouldbeestablishedtofardeeplyanalysesthedynamicalandthermalbehavioroftheoverheatdroplet.Thestatisticslawofoverheateddropletsshouldbefurtherstudiedbyconnectingsimulationwithexperiments.MorepropervalidationexperimentsshouldbedesignedforflatteningsimulationtomodifythemodelsinSDstage.

简介：AprototypeofPulsedPlasmaArcCladdingsystemwasdeveloped,inwhichsinglepowersourcesuppliesbothtransferredplasmaarc(TPA)andnon-transferredplasmaarc(N-TPA).BothplasmasworkinturninahighfrequencycontrolledbyanIGBTconnectingnozzleandworkpiece.TheworkingfrequencyofIGBTrangesfrom50～7000Hz,inwhichtheplasmascanworkinturnsmoothly.Higherthan500HzofworkingfrequencyissuggestedforpromotionofcladdingqualityandprotectionofIGBT.DragphenomenonofTPAintensifiesasthefrequencygoesup,whichtendstoincreasethecurrentproportionofTPAandsuppressN-TPA.TheoccupationratioofIGBTcanberegulatedfrom5%～95%,whichbalancesthepowersuppliesofbothplasmas.Anoccupationratiohigherthan50%givesadequateproportionofarccurrentforN-TPAtopreheatpowder.

简介：Forgivendata(ti,yi),I=0,1,…,n,0=t0＜t1＜…＜tn=1westudyconstrainedinterpolationproblemofFavardtypeinf{‖f'‖∞|f∈W2∞[0,1],f(ti)=yi,i=0,…,n,l(f;[0,1])≤l0},wherel(f';[0,1])=∫10/1+f'2(x)dxisthearclengthoffin[0,1].Weprovetheexistenceofasolutionf*oftheaboveproblem,thatisaquadraticsplinewithasecondderivativef'*,whichcoincideswithoneoftheconstants-‖f'*‖∞,0,‖f'*‖∞betweeneverytwoconsecutiveknots.Thus,weextendaresultofKarlinconcerningFavardproblem,tothecaseofrestrictedlengthinterpolation.

简介：TherecurrencealgorithmisgivenforthecalculationofNUAHB-splinesinthespaceSn+1=span{sinht,cosht,tn-3,...,t2.t,1}(n≥3).ThecaseofNUAHB-splinebasesofloworderwithmultipleknotsequencesisstudied.ThelimitingcasesofUAHB-splinesarerecoveredwhenshapeparametersa's→0+and+∞.ThenthecorrespondingNUAHB-splinecurveisdefinedanditsmainpropertiessuchasshape-preservingpropertiesareinvestigated.

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