简介:AgraphGiscalledchromatic-choosableifitschoicenumberisequaltoitschromaticnumber,namelych(G)=χ(G).Ohba’sconjecturestatesthateverygraphGwith2χ(G)+1orfewerverticesischromaticchoosable.ItisclearthatOhba’sconjectureistrueifandonlyifitistrueforcompletemultipartitegraphs.Recently,Kostochka,StiebitzandWoodallshowedthatOhba’sconjectureholdsforcompletemultipartitegraphswithpartitesizeatmostfive.Butthecompletemultipartitegraphswithnorestrictionontheirpartitesize,forwhichOhba’sconjecturehasbeenverifiedarenothingmorethanthegraphsKt+3,2*(k-t-1),1*tbyEnotomoetal.,andKt+2,3,2*(k-t-2),1*tfort≤4byShenetal..Inthispaper,usingtheconceptoff-choosable(orL0-size-choosable)ofgraphs,weshowthatOhba’sconjectureisalsotrueforthegraphsKt+2,3,2*(k-t-2),1*twhent≥5.Thus,Ohba’sconjectureistrueforgraphsKt+2,3,2*(k-t-2),1*tforallintegerst≥1.
简介:Inordertodeepentheunderstandingoftherelationshipbetweenfundamentalproperties(including:microstructureandcomposition)andphotocatalyticperformance,fourbismuthatecompounds,including:LiBiO3,NaBiO3,KBiO3,andAgBiO3,areregardedasresearchexamplesinthepresentwork,becausetheyhaveparticularcrystalstructuresandsimilarcompositions.Usingdensityfunctionaltheorycalculations,theirstructural,electronic,andopticalpropertiesareinvestigatedandcomparedsystematically.Firstofall,thecalculatedresultsofcrystalstructuresandopticalpropertiesareinagreementwithavailablepublishedexperimentaldata.Basedonthecalculatedresults,itisfoundthatthetunneledorlayeredmicro-structuralpropertiesleadtothestrongerinteractionbetweenbismuthandoxygen,andtheweakerinteractionbetweenalkaline-earthmetaland[BiO6]octahedron,resultinginthefeatureofmulti-bandgapsinthecasesofLiBiO3,NaBiO3,andKBiO3.ThisconclusionissupportedbythecaseofAgBiO3,inwhichthefeatureofmulti-bandgapsdisappears,duetothestrongerinteractionbetweenthenoblemetaland[BiO6]octahedron.Thesepropertieshavesignificantadvantagesinthephotocatalyticperformance:absorbinglowenergyphotons,rapidlytransferringenergycarriers.Furthermore,thefeaturesofelectronicstructuresofbismuthatecompoundsarewellreflectedbytheabsorptionspectra,whichcouldbeconfirmedbyexperimentalmeasurementsinpractice.Combinedwiththecalculatedresults,itcouldbeconsideredthatthecrystalstructuresandcompositionsofthephotocatalystdeterminetheelectronicstructuresandopticalproperties,andsubsequentlydeterminethecorrespondingphotocatalyticperformance.Thus,anovelBi-basedphotocatalystdrivenbyvisible-lightcouldbedesignedbyutilizingspecificcompositionstoformfavorableelectronicstructuresorspecificmicro-structurestoformabeneficialchannelforenergycarriers.
简介:设G是一个简单图,GiG,G1在G中的度定义为d(Gt)=∑v∈v(c)d(v),其中d(v)为v在G中的度数。本文的主要结果是:设G是n≥2阶几乎无桥的简单连通K3-free图,且G≌k1,n-1、Q1和Q2,若对G中任何同构于四个顶点路的导出子图I有d(I)≥n+2,则G有一个D-闭迹,从而G的线图L(G)是哈密顿图。
简介:BecauseERstressisoneofthesignalingpathwaysinvolvedintheregulationofautophagy,wehypothesizedthatERstressmightalsoplayanimportantroleinradiation-inducedautophagy.SHG44andHeLacellswereirradiatedwithX-raysandcarbonionsof30and75keV/mat2Gy.TheexpressionlevelsofBip,amajorindicatorofUPR,at4and24hpost-irradiationareshowninFig.1(a)and(b)forSHG44andHeLacells,respectively.
简介:ThecomplexK3H4GeW9V3O40·8H2OcrystallizedinamonocliiniesystemwithspacegroupP2,Mr=2784.67,a=11.099(3),b=16.452(4),c=13.534(4),β=108.14°,Z=2,V=2348.493,F(000):2456,μ=239.7cm-1,De=3.932g/cm3.ThefinalR=0.083for4528non-zeroreflexions.ThestructureofanionsGeW9V3O40andGeW9O34belongstoA--type.
简介:K1,k┐FACTORIZATIONOFBIPARTITEGRAPHSDUBEILIANGAbstract.Inthispaper,anecessaryconditionforabipartitegraphλKm,ntobeK1,k-factoriz...
简介:SupposethatCisthecomplexplaneandkisanon-negativeinteger.DefinefunctionsNk-(x)=|x|kifkisevenandNk(x)=x|x|k-1ifkisodd.SomeapproximationpropertiesofNk-(x)’sisdiscussedandanewexampleofaTchebycheffsystemisgivenout.
简介:<正>Byusingφ-mappingmethod,wediscussthetopologicalstructureoftheself-dualitysolutioninJackiw-Pimodelintermsofgaugepotentialdecomposition.WesetuprelationshipbetweenChern-Simonsvortexsolutionandtopologicalnumber,whichisdeterminedbyHopfindexandBrouwerdegree.Wealsogivethequantizationoffluxinthisease.Then,westudytheangularmomentumofthevortex,whichcanbeexpressedintermsof,theflux.