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简介：Inthispaper,theoptimalcontrolofaclassofgeneralaffinenonlineardiscrete-time(DT)systemsisundertakenbysolvingtheHamiltonJacobi-Bellman(HJB)equationonlineandforwardintime.Theproposedapproach,referrednormallyasadaptiveorapproximatedynamicprogramming(ADP),usesonlineapproximators(OLAs)tosolvetheinfinitehorizonoptimalregulationandtrackingcontrolproblemsforaffinenonlinearDTsystemsinthepresenceofunknowninternaldynamics.Boththeregulationandtrackingcontro...

简介：Foranentirefunctionf(z),letM(f,r)=maxisapolynomialofdegreen,then,ingeneral,itisdifficulttoobtainalowerboundfarM(p’,1).Butifthezerosofthepolynomialareclosetotheorigin,thenvariouslowerboundsforM(p’,1)havebeenobtainedinthepast.Inthispaper,wehaveconsideredpolynomialshavingalltheirzerosin,withapossiblezerooforderm(m>0)attheoriginandhaveobtainedalowerboundforM(p’,1),whichisbetterthanmostoftheknownlowerbounds.Ourboundissharpform=0.

简介：Inthispaper,weaimtosolvethefinitehorizonoptimalcontrolproblemforaclassofdiscrete-timenonlinearsystemswithunfixedinitialstateusingadaptivedynamicprogramming(ADP)approach.Anew-optimalcontrolalgorithmbasedontheiterativeADPapproachisproposedwhichmakestheperformanceindexfunctionconvergeiterativelytothegreatestlowerboundofallperformanceindiceswithinanerroraccordingtowithinfinitetime.Theoptimalnumberofcontrolstepscanalsobeobtainedbythepropo...

简介：ForsatateformlineargramasFangandsaodeinedandapproachwhichwouldfindanoptimalsolutionbysolvingananconstrainedconvexdualprogramming.ThedualwasconstruciedbyapplyinganemropicpeturbationandasimpleInequalityInz0n,Inthispaper,wesuggestthanapaperbationfunctiontaketheplaceofInxsuchthatthenewapprodthasgoodnumericalstabilityandhasallpropertiesoftheoriginalmethod

简介：InthispaperweextendEnestrom-Kakeyatheoremtoalargeclassofpolynomialswithcomplexcoefficientsbyputtinglessrestrictionsonthecoefficients.Ourresultsgeneraliseandextendmanyknownresultsinthisdirection.

简介：Thef(x)∈C[-1,1]isgiven,amodificationisgiventotheinterpolationpolynomialQn(f;x)(thepower,lessthanλn,1

简介：LetP(z)beapolynomialofdegreen,havingallitszerosin|z|≤1Inthispaper,weestimatekthpolarderivativeofP(z)on|z|=1andtherebyobtaincompactgeneralizationsofsomeknownresultswhichamongotherthingsyieldsarefinementofaresultduetoPaulTura'n.

简介：Denotebyn（f）thedegreeofcopositiveapproximationtof（x）bypolynomialsofdegree≤n.Forfunctionf（x）∈Ck[-1,1]whichalternatesinsignfinitelymanytimesin[-1,1],theauthorobtainsthefollowingJacksontypeestimatesn（f）≤Cn-kw(fk,1/n)foaanypositiveintegerk.

简介：（ｘ）？Ｓ．Ｉｆｇ（ｘ）＝０，Ｓ＊（ｘ）＝Ｓ＊．ＭｏｍｎｉｔＳ／０ａｎｄｎｉｔＳ（ｘ）２ｎｉｔＳ，ｎｉｔＳ（ｘ）／０．Ｈｅｌｌｃｅ（Ｓ（ｘ））＊＝Ｓ＊（ｘ）ｈａｓａｃｏｍｐａｃｔｃｏｎｖｅｘｂａｓｅ，ｄｅｎｏｔｅｄｂｙＡ，ａｎｄｔｈｅｃｏｍｐａｃｔｃｏｎｖｅｘｂａｓｅｏｆＱ＊ｉｓｄｅｎｏｔｅｄｂｙＢ．｛０｝＊＝Ｒｅ．ＬｅｔＣ＝｛ｘＥＲｅ：ＩＩｘｌｌ＝１｝．ＴｈｅｎＣｉｓａｃｏｍｐａｃｔｂａｓｅｏｆ｛０｝＊．Ｌｅｔｓｕｐｐｏｓｅｔｈａｔ（３ｄＯＥＲ＂）（ＶＰＥＶ＊＼｛０｝）（ＰＴｐ）＂（ｘ；ｄｏ）＜０，ｆｒｏｍＬｅｍｍａ２．３ｔｈｅｒｅｅｄｅｓｔｓａｄＥＲ＂ｔｏｇｅｔｈｅｒｗｉｔｈｂ＞０ｓｕｃｈｔｈａｔＩｎｐａｒｔｉｃｕｌａｒ，ｆｉｘｉｎｇＴＥＢａｎｄＡ６Ａ，ｓｅｔｔｉｎｇｐ￣（ＥＴ，ａｃ，￣）ＥＶ＊ｗｉｔｈＥ＞０ａｎｄｕｅＣ，ｗｅＩｎｄｅｅｄ，ｉｆｔｈｅｒｅｅｘｉｓｔｓａａｌＥ（０，６）ｓｕｃｈｔｈａｔｈ（ｘ＋ａ＇ｄ）／０，ｗｅｃａｎｃｈｏｏｓｅＦＩＥＣｓａｔｉｓｆｙｉｎｇＵ，＂ｈ（ｘ＋ａ＇ｄ）＞０．Ｉｎ（４），ｌｅｔｔｉｎｇＥ－０，ｉｔｆｏｌｌｏｗｓｔｈａｔＵ＂ｈ（ｘ＋ｒｓ＇ｄ）＜０，ｗｈ?

简介：Basedupontheresearchtotheeconomicequilibriumproblems,wepresentakindofnewmathematicalprogrammingproblem-interactionprogrammingproblem(abbreviatedbyIPP).TheIPPiscomposedoftwoormultipleparametricprogrammingproblemswhichisinterrelatedwitheachother.TheIPPreflectstheequalityandmutualbenefitrelationshipbetweentwo(oramongmultiple)economicplannersinaneconomicsystem.Inessence,theIPPissimilartothegeneralizedNashequilibria(GNE)gamewhichhasbeengivenseveralnamesintheliterature:socialequilibriagames,pseudo-Nashequilibriagames,andequilibriumprogrammingproblems.Inthispaper,weestablishthemathematicalmodelandsomebasicconceptstotheIPP.WeinvestigatethestructureandthepropertiesoftheIPP.WealsogiveanecessaryandsufficientconditionsfortheexistenceoftheequilibriumpointstoakindoflinearIPP.

简介：Thispaperproposesasufficientcondition,ifthepropertiesofthebilevelprogrammingsatisfiedthecondition,wecansolvethebilevelprogrammingbysolvingsinglelevelprogramming.Itbecomeseasyandsimpletosolvethebilevelprogramming.

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简介：在这份报纸，作者计算同类的Grushin泛音函数的空格的尺寸，并且给他们的一个直角的基础。而且，作者描述这些同质的Grushin泛音基础的节的曲线。作为直角的基础的一个应用程序，作者为Grushin操作符证明一条Liouville类型定理，那是Grushin泛音函数如果如此的一个函数的频率等于某常数，是同类的多项式。

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简介：LetP(z)beapolynomialofdegreenandforanycomplexnumberα,letDαP(z)=nP(z)+(α-z)P′(z)denotethepolarderivativeofP(z)withrespecttoα.Inthispaper,weobtaincertaininequalitiesforthepolarderivativeofapolynomialwithrestrictedzeros.Ourresultsgeneralizeandsharpensomewell-knownpolynomialinequalities.

简介：ByusingthegeneralizedPoincaréindextheoremitisprovedthatifthen^2criticalpointsofann-polynomialsystemformaconfigurationoftype(2n-1)-(2n-3)+(2n-5)-…+(-1)^n-1,andthe2n-1outmostanti-saddlesformtheverticesofaconvex(2n-1)-polygon,thenamongthese2n-1anti-saddlesatleastonemustbeanode.

简介：Inthepresentpaperweconsiderquarticpiecewisepolynomialforapproximationtothefunctionf∈C2[0,1].Aconvextypeconditionhasbeenimposedinthepartitionsothatthematrixinvolvedforthecomputationofppfunctionsisoflowerband.Thisreducesthecomputationforconstructionsoftheppfunctionsfortheapproximation.

简介：ThispaperproposesametalanguageTrapMLfortransformationalprogramming,whichisdesignedbasedontheanalysisofitsdesignprinciples,structuresandfunctions.Ithasthefacilitiestodescribethesyntaxofobjectlanguages,thesetoftransformationrulesandstrategies.Thebehaviouroftransformationsystemscanbeconvenientlyexpressed.BothaccurateandvaguestrategiescanbewritteninTrapML.Metaprogramisofhigherreliability.