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:《数学课程标准》要求学生所掌握的空间与图形内容如下:能够借助不同的方法探索几何对象的有关性质;能够使用不同的方式表达几何对象的大小、位置与特征;能够在头脑里构建几何对象,进行几何图形的分解与组合,能够对某些图形进行简单的变换;能够借助数学证明的方法确认数学命题的正确性。图形与证明是空间与图形的核心内容之一,课标要求学生掌握基本的图形基础知识与基本技能;了解证明的含义,掌握证明的方法,体会证明的过程;能把所学的公理、定理和基本事实正确运用到证明的过程中,在合情推理的基础上发展初步的演绎推理能力;初步通过观察、实验、归纳、类比、推测获得数学猜想,体验数学活动充满着探索性和创造性,感受证明的必要性、证明过程的严谨性及结论的稳定性,它贯穿在整个几何知识的学习及运用之中.
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.
简介:Itisprovedthataprobabilitymeasureisdominatedbyg-expectationεμ[·]ifandonlyifitcanbegeneratedbyGirsanovtransformationviaaprocesswhichisuniformlyboundedbyμ.