简介:本文首先给出integralfromato+∞f(x)dx收敛≠lim+∞f(x)=0的一更强的例子,然后给出一个与级数收敛的必要条件类似的,integralfromato+∞f(x)dx收敛的必要条件。在许多工科高等数学教材中,广义积分敛散性的判别,一般都在级数中讨论,因而一部分同学和个别教师往往把级数的一些重要性质,直接推广到广义积分integralfromato+∞f(x)dx上。最典型的错误是把级数收敛的必要条件推广到广义积分上,即integralfromato+∞f(x)dx收敛?lim?+∞f(x)=0.这类错误较为普遍。
简介:Temperatureanddensityasymmetrydiagnosisiscriticaltoadvanceinertialconfinementfusion(ICF)science.Amultimonochromaticx-rayimager,MMI,recordsthespectralsignaturefromanICFimplosioncorewithtimeresolution,2Dspatialresolutionandspectralresolution.Whilenarrow-bandimagesand2Dspace-resolvedspectrafromtheMMIdataconstrainthetemperatureandthedensityspatialstructureofthecore,theaccuracyoftheimagesandthespectrahighlydependsonthequalityoftheMMIdataandtheprocessingtools.Here,wesyntheticallyinvestigatethecriterionforreliableMMIdiagnosticsanditseffectsontheaccuracyofthereconstructedimages.Thepinholearraytiltdeterminestheobjectspatialsamplingefficiencyandtheminimumreconstructionwidth,w.Whenthespectralwidthassociatedwithwissignificantlynarrowerthanthespectrallinewidth,thelineimagesreconstructedfromtheMMIdatabecomereliable.TheMMIsetuphastobeoptimizedforeveryapplicationtomeetthiscriterionforreliableICFdiagnostics.
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简介:Magnetoplasmonicsensorsareattractivecandidatesforultrasensitivechemicalandbiomedicalsensorapplications.Avarietyofferromagneticmetalthinfilmshavebeenusedformagnetoplasmonicdeviceapplications,yetthedependenceofsensorperformanceontheopticalandmagneto-opticalpropertiesofferromagneticmetalmaterialshasbeenrarelystudied.Inthiswork,wereportthestudyofenhancedmagneto-opticalKerreffect(MOKE)andsensingperformanceinAu∕FexCo1-xbilayermagneto-opticalsurfaceplasmonresonance(MOSPR)transducers.TheopticalconstantsofFexCo1-x(x=0,0.29,0.47,0.65,and1)inasputter-depositedAu∕FexCo1-xdevicearecharacterizedbytheattenuatedtotalinternalreflection(ATR)method.FexCo1-xthinfilmsshowdifferentMOKEsasafunctionofthechemicalconcentration,withthehighesttransverseMOKEsignalobservedinFe0.7Co0.3.Indexsensingperformanceiscloselyrelatedtothematerial’sopticalandmagneto-opticalconstants.BystudyingthesensingperformanceintheparameterspaceoftheAu∕FexCo1-xbilayerthicknesses,thehighestsensitivityisfoundtobe0.385(theoretical)and0.306RIU-1(experimental)intheAu∕Fe0.7Co0.3MOSPRdevices.OurresearchhighlightstheinfluenceoftheopticalpropertiesofferromagneticmaterialtodevicesensitivityinMOSPRtransducers.ThehighsensitivityinAu∕FexCo1-xMOSPRdevicesmakethesestructuresattractivecandidatesforchemicalandbiomedicalsensingapplications.
简介:AnovelcrystalcharacterizationinstrumenthasbeenbuiltupinwhichacombinationofX-raymultiplediffractionandX-raytopographyisappliedtoenablingthecross-correlationbetweenmicro-crystallographicsymmetryanditsspatialdependenceinrelationtolatticedefects.Thisfacilityisusedtoexamine,inaselfconsistentmanner,growthsector-dependantchangestoboththecrystallographicstructureandthelatticedefectsassociatedwiththeactionofhabit-modifyingadditivesinanumberofrepresentativecrystalgrowthsystems.Inaddition,thenewinstrumentcanbeusedtoprobemicro-crystallographicaspects(suchasdistortiontocrystalsymmetry)andrelatetheseinaspatiallyresolvedmannertothecrystaldefectstructureincrystalsdopedwithknownhabitmodifiers.
简介:Non-smallcelllungcancer(NSCLC)accountsfor85%oflungcancer,whichistheleadingcauseofdeathinlungcancerpatient.RoutinetreatmentofNSCLCcannoteffectivelychangethesurvivalrateofpatients,oneimportantreasonistheincreasedradioresistanceoftumorcellsafterconventionalradiotherapy.