简介：设G是一个图.设g和f是两个定义在V(G)上的整值函数使得对V(G)所有的顶点x有g(x)f(x).图G被称为(g,f,n)-临界图,如果删去G的任意n个顶点后的子图都含有G的(g,f)-因子.本文给出了图是(a,b,n)-临界图几个充分条件.进一步指出这些条件是最佳的.例如,如果对V(G)所有的顶点x和y都有g(x)＜f(x),n+g(x)dG(x)和g(x)/(dG(x)-n)f(y)/dG(y),则G是(g,f,n)-临界图.

简介：在简单图的顶点度和f-因子的关系方面,本文在Tutte定理的基础上给出了图G不存在f-因子时的一个结论.

简介：设G是一个图，具有顶点集V（G）和边集E（G）．设g和f是定义在V（G）上的整数值函数且对每个x∈y（G）有g（x）≤f（x）．本文证明了如下的结果：若G是一个（mg＋kr，mf-kr）一图，且对每个x∈V（G）有g（x）≥r-1，H和G的任意给定的有kr条边的子图，则G中含有一个子图R，使R有（g，f）-因子分解r-正交于H，其中m，k和r是正整数且k〈m.

简介：一个图称为分数（g，f，m）一消去图若删除任意m条边后的剩余子图依然存在分数（g，f）一因子．本文证明若图G的阶为n，1≤n≤g（x）≤f（x）-△≤b-△对任意顶点x∈V（G）成立，δ（G）≥（b-△）（b＋1）/a＋2m,n≥（a＋b）（2（a＋b）＋2m-1）/a＋△且｜NG（x1）∪NG（x2）｜≥（b-△）n/a＋b对任意不相邻顶点x1和x2都成立，则G是分数（g，f，m）-消去图．这个领域并条件在一定程度上是最好的．

简介：本文讨论，f(f^（k）)^n的值分布的定量估计并改进了C.K.Tsc与C.C.Yang的一个结果。

简介：TheauthorconsiderstheFeigenbaum'sfunctionalequationf^P(λx)=λf(x)foreachp≥2.TheexistenceofevenunimodalC^1solutionstothisequationisdiscussedandafeasiblemethodtoconstructsuchsolutionsisgiven.

简介：§1.IntroductionLetEbeanon-zerocomplexBanaohspace,&(JET)theBanaohalgebraofalltheoperatorsfromEintoitself.Operatormeans'boundedlinearoperator'throughout.Anoperatorfunction/fromadomain(openset)Dinthecomplexplaneto@l(T￡}issaidtobeanalytic,ifforanyx^Eandq>￡E*(thedualspaceofE\9>(/(z)aOisanalyticintheclassical’senseinD([1],p.92).Wedenotebyja/B(D)thesetofalltheanalyticoperatorfunctionsfromDinto

简介：一个单圈图G的邻接矩阵是奇异的当且仅当G含完美匹配和4m(m∈N)阶圈,或G和从G中删去唯一圈中的顶点及其关联边后得到的导出子图均不含完美匹配.单圈图的邻接矩阵的最大行列式是4.

简介：ＢＭＯ空间中ｆ与ｆ_Ｎ的范数比较刘为铨（安徽芜湖师专）设ｆ（ｘ）为定义于Ｒ上的局部可积函数，Ｑ为Ｒ中的任一立方体。｜Ｑ｜为Ｑ的Ｌｅｂｅｓｅｕｅ测度，ｆ（Ｘ）在Ｑ上的平均值记作若ｆ（Ｘ）满足条件则称人工）为有界平均振动函数，一切有界平均振动函数所构成的?..

简介：得到如下结果：设f(z)为非常数亚纯函数，f与f^(k)以1为CM公共值，如果N^-(r，f)+N^-(r，1/f^(k))＜λT(r，f)，k=1，0＜λ＜1/6;或3N^-(r，f)+N^-(r，1/f^k)＜λT(r，f)，k≥2，0＜λ＜1/3;或N^-(r，1/f)+3N^-(r，1/f^(k))＜λT(r，f)，k≥3，0＜λ＜1/6，则f^(k)-1/(f-1)≡C，其中C为某一非零常数。

简介：设图G是一个简单图，图G的补图记为^-G，如果G的谱都是整数，就称G是整谱图．鸡尾酒会图CP（n）=K2n-nK2（K2n是2n阶完全图）和完全图Kα都是整谱图．本文确定了图类^-αKα∪βCP（b）中的所有整谱图．

简介：LetGbeagraphwithvertexsetV(G)andedgesetE(G)andletgandfbetwointeger-valuedfunctionsdefinedonV(G)suchthat2k-1≤g(x)≤f(x)forallx∈V(G).LetHbeasubgraphofGwithmkedges.Inthispaperitisprovedthatevery(mg+m-1,mf-m+1)-graphGhas(g,f)-factorizationsrandomlyκ-orthogonaltoHandshownthattheresultisbestpossible.

简介：数学学习离不开思维，数学探索需要通过思维来实现，在初中数学教学中逐步渗透数学思想方法，有助于培养学生的思维能力，形成良好的数学思维习惯，既符合新课程标准的要求，也是进行数学素质教育的一个切入点．

简介：LetB(E,F)bethesetofallboundedlinearoperatorsfromaBanachspaceEintoanotherBanachspaceF,B+(E,F)thesetofalldoublesplittingoperatorsinB(E,F)andGI(A)thesetofgeneralizedinversesofA2B+(E,F).InthispaperweintroduceanunboundeddomainW(A,A^+)inB(E,F)forA2B+(E,F)andA^+2GI(A),andprovideanecessaryandsufficientconditionforT2W(A,A^+).Thenseveralconditionsequivalenttothefollowingpropertyareproved:B=A^+(IF+(T??A)A^+)??1isthegeneralizedinverseofTwithR(B)=R(A^+)andN(B)=N(A^+),forT2W(A,A^+),whereIFistheidentityonF.Alsoweobtainthesmooth(C￥)diffeomorphismMA(A^+,T)fromW(A,A^+)ontoitselfwiththefixedpointA.LetS=fT2W(A,A^+):R(T)\N(A^+)=f0gg,M(X)=fT2B(E,F):TN(X)R(X)gforX2B(E,F)g,andF=fM(X):8X2B(E,F)g.UsingthediffeomorphismMA(A^+,T)weprovethefollowingtheorem:SisasmoothsubmanifoldinB(E,F)andtangenttoM(X)atanyX2S.ThetheoremexpandsthesmoothintegrabilityofFatAfromalocalneighborhooldatAtotheglobalunboundeddomainW(A,A^+).Itseemstobeusefulfordevelopingglobalanalysisandgeomatricalmethodindifferentialequations.

简介：AsubgroupHofagroupGiscalledF-z-supplementedinGifthereexistsasubgroupKofG,suchthatG=HKandH∩K≤Z∞F(G),whereZ∞F(G)istheF-hypercenterofG.WeobtainsomeresultsabouttheF-z-supplementedsubgroupsandusethemtodeterminethestructureofsomegroups.

简介：Analgorithmofcontinuousstage-spaceMCMCmethodforsolvingalgebraequationf(x)=0isgiven.Itisavailableforthecasethatthesignoff(x)changesfrequentlyorthederivativef'(x)doesnotexistintheneighborhoodoftheroot,whiletheNewtonmethodishardtowork.Letnbethenumberofrandomvariablescreatedbycomputerinouralgorithm.Thenafterrn=O(n)transactionsfromtheinitialvalueXo,X^*canbegotsuchthat[f(x^*)|＜e-^cm|f(xo)|bychoosingsuitablepositiveconstantc.Anillustrationisalsogivenwiththediscussionofconvergencebyadjustingtheparametersinthealgorithm.

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简介：ForRiemannianmanifoldswithameasure,westudythegradientestimatesforpositivesmoothf-harmonicfunctionswhenthe∞-Bakry-EmeryRiccitensorandRiccitensorareboundedfrombelow,generalizingtheclassicalonesofYau(i.e.,whenfisconstant).

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简介：TheauthorsmainlyconcernthesetUfofc∈Csuchthatthepowerdeformationzf(z)/zcisunivalentintheunitdisk|z|<1foragivenanalyticunivalentfunctionf(z)=z+a2z2+···intheunitdisk.ItisshownthatUfisacompact,polynomiallyconvexsubsetofthecomplexplaneCunlessfistheidentityfunction.Inparticular,theinteriorofUfissimplyconnected.Thisfactenablesustoapplyvariousversionsoftheλ-lemmafortheholomorphicfamilyzf(z)/zcofinjectionsparametrizedovertheinteriorofUf.ThenecessaryorsufficientconditionsforUftocontain0or1asaninteriorpointarealsogiven.