简介:Wewilldefineandcharacterizeε-pseudoChebyshevandε-quasiChebyshevsubspacesofBanachspaces.WewillprovethataclosedsubspaceWisε-pseudoChebyshevifandonlyifWisε-quasiChebyshev.
简介:Itwillbedeterminedunderwhatconditionstypesofproximinalityaretransmittedtoandfromquotientspaces.Inthefinalsection,bymanyexamplesweshowthattypesofproximinalityofsubspacesinBanachspacescannotbepreservedbyequivalentnorms.
简介:StabilizedorChebyshevexplicitmethodshavebeenwidelyusedinthepasttosolvestiffordinarydifferentialequations.MakinguseofspecialpropertiesofChebyshev-likepolynomials,thesemethodshavefavorablestabilitypropertiescomparedtostandardexplicitmethodswhileremainingexplicit.Anewclassofsuchmethods,calledROCK,introducedin[Numer.Math.,90,1-18,2001]hasrecentlybeenextendedtostiffstochasticdifferentialequationsunderthenameS-ROCK[C.R.Acad.Sci.Paris,345(10),2007andCommun.Math.Sci,6(4),2008].InthispaperwediscusstheextensionoftheS-ROCKmethodstosystemswithdiscretenoiseandproposeanewclassofmethodsforsuchproblems,theT-ROCKmethods.Onemotivationforsuchmethodsisthesimulationofmulti-scaleorstiffchemicalkineticsystemsandsuchsystemsarethefocusofthispaper,butournewmethodscouldpotentiallybeinterestingforotherstiffsystemswithdiscretenoise.TwoversionsoftheT-ROCKmethodsarediscussedandtheirstabilitybehaviorisanalyzedonatestproblem.ComparedtotheT-leapingmethod,asignificantspeed-upcanbeachievedforsomestiffkineticsystems.Thebehavioroftheproposedmethodsaretestedonseveralnumericalexperiments.
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简介:Weraiseandpartlyanswerthequestion:whetherthereexistsaMarkovsystemwithrespecttowhichthezerosoftheChebyshevpolynomialsaredense,butthemaximumlengthofazerofreeintervalofthenthChebyshevpolynomialdoesnottendstozero.Wealsodrawtheconclu-tionthataMarkovsystem,underanadditionalassumption,isdenseifandonlyifthemaxi-mumlengthofazerofreeintervalofthenthassociatedChebyshevpolynomialtendstozero.
简介:Inthispaper,weintroduceandstudyanewclassofquasivariationalinequalities.Using’essentiallytheprojectiontechniqueanditsvariantforms,weestablishtheequivalencebetweengeneralizednonlinearquasivariationalinequalitiesandthefixedpointproblems.Thisequivalenceisthenusedtosuggestandanalyzeanumberofnewiterativealgorithms.Thesenewresultsincludethecorrespondingknownresultsforgeneralizedquasivariationalinequalitiesasspecialcases.
简介:Thespectraldensityofthequasi-homogeneous(QH)lighthasbeenknownwhenitscattersonQHmediaorpropagatesinfreespace.ThecasethatQHsourcesaresurroundedbyQHmediaisproposedinthispaper.Undertheparaxialapproximation,thespectraldensityoftheQHlightpropagatingthroughQHmediaisderived.AmodifiedscalinglawforthepropagationoftheQHlightthroughQHmediaisalsoobtained.Thislawalsoholdstrueinthefarfieldbeyondtheparaxialapproximation.
简介:Inthispaper,weestablishanewtypeofalternationtheoryformoregeneralrestrictedrangesChebyshevapproximationwithequalities.Theuniquenessandstronguniquenesstheoremsaregiven.Applyingtheresults,weobtainthealternationtheoremanduniquenesstheoremforbestcoposiliveapproximation.
简介:ONEXCHANGEALGORITHMFORNONLINEARBESTCHEBYSHEVAPPROXIMATIONWITH LGHCONDITIONXiongGuijing(熊规景);WeiDan(韦旦)(Inst.ofMath.Sci.,Chin....
简介:性质awc1被许多作者使用由弱Chebyshevsubspaces的元素有关近似获得结果。在这份报纸,作者在细节学习这个性质,由收集有关它并且由发现新的散布结果。