简介：Inthispaper,thenotionoftheboundedcompactapproximationproperty(BCAP)ofapair[Banachspaceanditssubspace]isusedtoprovethatifXisaclosedsubspaceofL∞withtheBCAP,thenL∞/XhastheBCAP.WealsoshowthatX*hastheλ-BCAPwithconjugateoperatorsifandonlyifthepair(X,Y)hastheλ-BCAPforeachfinitecodimensionalsubspaceY∈X.LetMbeaclosedsubspaceofXsuchthatM⊥iscomplementedinX*.IfXhasthe(bounded)approximationpropertyoforderp,thenMhasthe(bounded)approximationpropertyoforderp.

简介：Experimentswereconductedinawatertunnelbytomographictime-resolvedparticleimagevelocimetry(Tomo-TRPIV).TheReynoldsnumberReθis2460onthebaseofmomentumthickness.Accordingtothephysicalmechanismofthestretchandcompressionofmulti-scalevortexstructuresinthewall-boundedturbulence,thetopologicalcharacteristicsofturbulencestatisticsinlogarithmiclayerwereillustratedbylocal-averagedvelocitystructurefunction.Duringcoherentstructuresbursting,resultsrevealthatthetopologicalstructuresofvelocitygradients,velocitystrainratesandvorticitiesbehaveasantisymmetricquadrupolemodes.Athree-layerantisymmetricquadrupolevortexpacketconfrmsthatthereisatightrelationshipbetweentheouterlayerandthenear-walllayer.

简介：Uncertaintyisinherentandunavoidableinalmostallengineeringsystems.Itisofessentialsignificancetodealwithuncertaintiesbymeansofreliabilityapproachandtoachieveareasonablebalancebetweenreliabilityagainstuncertaintiesandsystemperformanceinthecontroldesignofuncertainsystems.Nevertheless,reliabilitymethodswhichcanbeuseddirectlyforanalysisandsynthesisofactivecontrolofstructuresinthepresenceofuncertaintiesremaintobedeveloped,especiallyinnon-probabilisticuncertaintysituations.Inthepresentpaper,theissueofvibrationcontrolofuncertainstructuresusinglinearquadraticregulator(LQR)approachisstudiedfromtheviewpointofreliability.Ane?cientnon-probabilisticrobustreliabilitymethodforLQR-basedstaticoutputfeedbackrobustcontrolofuncertainstructuresispresentedbytreatingboundeduncertainparametersasintervalvariables.Theoptimalvibrationcontrollerdesignforuncertainstructuresiscarriedoutbysolvingarobustreliability-basedoptimizationproblemwiththeobjectivetominimizethequadraticperformanceindex.Thecontrollerobtainedmaypossessoptimumperformanceundertheconditionthatthecontrolledstructureisrobustlyreliablewithrespecttoadmissibleuncertainties.Theproposedmethodprovidesanessentialbasisforachievingabalancebetweenrobustnessandperformanceincontrollerdesignofuncertainstructures.Thepresentedformulationsareintheframeworkoflinearmatrixinequalityandcanbecarriedoutconveniently.Twonumericalexamplesareprovidedtoillustratethee?ectivenessandfeasibilityofthepresentmethod.