简介:Inthispaper,wefirstdeterminetherelationsamongthebestboundsAandBoftheg-frame,theg-frameoperatorSandthepre-frameoperatorQandgiveanecessaryandsufficientconditionforag-framewithboundsAandBinacomplexHilbertspace.Wealsointroducethedefinitionofag-framesequenceandobtainanecessaryandsufficientconditionforag-framesequencewithboundsAandBinacomplexHilbertspace.Lastly,weconsiderthestabilityofag-framesequenceforacomplexHilbertspaceunderperturbation.
简介:A(k;g)-graphisak-regulargraphwithgirthg.A(k;g)-cageisa(k;g)-graphwiththeleastpossiblenumberofvertices.Letf(k;g)denotethenumberofverticesina(k;g)-cage.Thegirthpairofagraphgivesthelengthofashortestoddandashortestevencycle.Afc-regulargraphwithgirthpair(g,h)iscalleda(k;g,h)-graph.A(k;g,h)-cageisa(k;g,h)-graphwiththeleastpossiblenumberofvertices.Letf(k;g,h)denotethenumberofverticesina(k;g,h)-cage.Inthispaper,weprovethefollowingstrictinequalityf(k;h-1,h)
简介:In[1],ShenGuangyuconstructedseveralclassesofnewsimpleLiealgebrasofcharacteristic2,whicharecalledthevariationsofG2.Inthispaper,theauthorsinvestigatetheirderivationalgebras.ItisshownthatG2anditsvariationsallpossessuniquenondegenerateassociativeforms.TheauthorsalsofindsomenonsingularderivationsofViGfori=3,4,5,6,andtherebyconstructsomeleft-symmetricstructuresonViGfori=3,4,5,6.Someerrorsaboutthevariationsofsi(3,F)in[1]arecorrected.
简介:Thispaperprovesthat,underthehypothesisg(t,0,0)≡0andsomenaturalassumptions,thegeneratorgofabackwardstochasticdifferentialequationcanbeuniquelydeterminedbythecorrespondingg-expectationswithallterminalconditions.ThemainresultofthispaperalsoconfirmsandextendsPengShige'sconjecture.
简介:IntroductionGuillain-Barresyndrome(GBS)isconsideredtobeanautoimmunedisorderofperipheralnervoussystem’.Thebalanceofsympatheticnervesandparasympatheticnervesisdisturbed,whichleadstocompleteparalysisi’2’3.Moslpatientsshowthetypicalsymptomsafterbeinginfe...
简介:Alooplessgraphonnverticesinwhichverticesareconnectedatleastbyaandatmostbybedgesiscalleda(a,b,n)-graph.A(b,b,n)-graphiscalled(b,n)-graphandisdenotedbyKbn(itisacompletegraph),itscomplementbyKbn.Anonincreasingsequencep=(d1,…,dn)ofnonnegativeintegersissaidtobe(a,b,n)graphicifitisrealizablebyan(a,b,n)-graph.Wesayasimplegraphicsequencep=(d1,…,dn)ispotentiallyK4—K2[K2-graphicifithasaarealizationcontaininganK4—K2[K2asasubgraphwhereK4isacompletegraphonfourverticesandK2[K2isasetofindependentedges.Inthispaper,wefindthesmallestdegreesumsuchthateveryn-termgraphicalsequencecontainsK4—K2[K2assubgraph.