简介：Theresistanceseenintotheportinann-cubeformedbytwoverticesofdistancen-1isexactlyformulatedforanyposiiveintegern.Theresistancesseenintotheportinann-cubeformedbyanytwoverticesisalsofoundbyexperimentsfor1≤n≤7.

简介：Laser-inducedbreakdownspectroscopy(LIBS)hasbeenextensivelyappliedduetothecapabilitiesofreal-time,multi-phaseandmulti-elementanalysis.Withtheadvantages,portableLIBSisinrapiddevelopmentwithgreatpotentialoffieldmeasurements.Inthiswork,aportableLIBSwasdevelopedbya50μJlevellaserforexcitationandanobjectivelensforfocusingorimaging.Elementdetectionwassuccessfullyachievedbythissetup,andalsothemicroscopicobservationcouldbeobtainedwiththemagnificationof350×.ApreliminaryinvestigationwascarriedoutformineralrecognitionbythedevelopedportableLIBS.Theobtainedresultsindicatethattheelementdetectioncombinedwithmicroobservationwasaneffectivewayforrecognizingminerals,especiallyforsimilarmineralidentificationordiscrimination.Itissuggestedthatthemicro-joulelasercouldbealternativeforthecommercialportableLIBS,andtheon-sitemineralorrockrecognitionisapromisingfieldfortheapplication.