查看更多>>摘要：For any integer k ≥ 2,a graph G is called k-leaf-connected if|V(G)|≥ k+1 and given any subset S C V(G)with|S|=k,G always has a spanning tree T such that S is precisely the set of leaves of T.In this paper,we prove best possible sufficient conditions for a graph to be k-leaf-connected in terms of the first Zagreb index,second Zagreb index and hyper-Zagreb index of G or its complement.
查看更多>>摘要：Let G be a strongly connected directed weighted graph with vertex set {vi,V2,…,vn},in which each edge e is assigned with an arbitrary nonzero weight w(e).For any two vertices vi,vj of G,the distance dij from vi to vj is defined as dij=min P∈P(vi,vj)∑e∈Pw(e),where P(vi,vj)denotes the set consisting of all the directed paths from vi to vj in G.Given a nonzero indeterminant q,following the definitions from Yan and Yeh(Adv.Appl.Math.,2007),and Bapat et al.(Linear Algebra Appl.,2006),one can define the exponential distance matrix of G as FqG=(qdij)n×n,and define the q-distance matrix of G as DqG=(dqij)n×n with dqij={1-qdij/1-q,if q≠1,dif,if q=1,extending the original definitions only for the undirected unweighted connected graphs.One of the remarkable results about the distance matrices of graphs is due to the Graham-Hoffman-Hosoya theorem(J.Graph Theory,1977).In this paper,we present some Graham-Hoffman-Hosoya type theorems for the exponential distance matrix FqG and q-distance matrix DqG,ex-tending all the known Graham-Hoffman-Hosoya type theorems.
查看更多>>摘要：Recently,Andrews and Paule established the generating functions for the k-elongated plane partition function dk(n)and proved a large number of results on dk(n)with k=2,3.In particular,they posed some conjectures on congruences modulo powers of 3 for d2(n).Their work has attracted the attention of da Silva,Hirschhorn,Sellers and Smoot.Very recently,Smoot proved a congruence family for d2(n)which implies one conjecture due to Andrews and Paule by using the localization method.In this paper,we prove the rest two conjectures given by Andrews and Paule.
查看更多>>摘要：In this paper,we define the cohomology of a Reynolds Leibniz algebra with coefficients in a suitable representation.We also introduce the notion of Reynolds Leibniz 2-algebras,and prove that strict Reynolds Leibniz 2-algebras are equivalent to crossed modules of Reynolds Leibniz algebras.
查看更多>>摘要：In this paper,we consider Lie conformal algebras with derivations.A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair.We introduce a cohomology theory for LieCDer pair with coefficients in a representation.Furthermore,we study abelian extensions of a LieCDer pair as an application of cohomology theory.Finally,we consider homotopy derivations on 2-term conformal Loo-algebras and 2-derivations on conformal Lie 2-algebras.The category of 2-term conformal Loo-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.
查看更多>>摘要：In this paper,a new subclass of close-to-convex harmonic functions defined by d-ifferential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,inclusion relations,coefficient inequalities,growth and convex combination problems are obtained.In addition,the radius of starlike,the radius of convexity and convolution properties of this class are obtained.
查看更多>>摘要：Let(x,d,p)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M(α)b formed by b ∈(RBMO)(μ)and the fractional maximal function M(α)is bounded from Lebesgue spaces Lp(µ)into spaces Lq(μ),where 1/q=1/p-α for α ∈(0,1)and p ∈(1,1/α).Furthermore,the boundedness of the M(α)b on Orlicz spaces LΦ(μ)is established.
查看更多>>摘要：We study a class of nonlinear elliptic equations with nonstandard growth condition.The main feature is that two lower order terms,a non-coercive divergence term divΦ(x,u)and a gradient term H(x,u,▽u)with no growth restriction on u,appear simultaneously in the variable exponents setting.These characteristics prevent us from directly obtaining the existence of solutions by employing the classical theory on existence results.By choosing some appropriate test functions in the perturbed problem,some a priori estimates are obtained under the variable exponent framework.Based on these estimates,we prove the almost everywhere convergence of the gradient sequence{▽u∈}∈,which helps to pass to the limit to find a weak solution.
查看更多>>摘要：Using the harmonic map theory,we study the geometry of conformal minimal two-spheres immersed in Q6,or a real Grassmannian manifold G(2,8;R)equivalently.Then we classify the linearly full reducible conformal minimal immersions with constant Gaussian curva-ture from S2 to Q6 under some conditions.We also construct specific examples of non-congruent two-spheres with the same Gaussian curvature,up to SO(8)-equivalence,for each case.
查看更多>>摘要：The explicit solution to the Poisson equation corresponding to the Q-matrix of a single birth process is obtained,thus the explicit inverse(if exists)is presented directly.As an application,inspired by the inverse power method,combining the explicit inverse with Collatz-Wielandt formula,a powerful approximation theorem for the maximal eigenpair corresponding to the Q-matrix of a single birth process is presented.Different from the classical acceleration method using some fixed shift in the iteration,the shift in each iteration step is varying and the sequence formed by these shifts is strictly monotone and increases to the eigenvalue needed,which effectively reduces the number of iterations.Some examples are studied to illustrate the power of these results.
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