查看更多>>摘要：The equitable total coloring of a graph G is a total coloring such that the numbers of elements in any two colors differ by at most one.The smallest number of colors needed for an equitable total coloring is called the equitable total chromatic number.This paper contributes to the equitable total coloring of Fibonacci graphs F△,n.We determine the equitable total chromatic numbers of F△,n for △=3,4,5 and propose a conjecture on that for △＞=6.
查看更多>>摘要：An equitable(O1k,O2k,...,Omk)-partition of a graph G,which is also called a k cluster m-partition,is the partition of V(G)into m non-empty subsets Vi,V2,...,Vmsuch that for every integer i in {1,2,...,m},G[Vi]is a graph with components of order at most k,and for each distinct pair i,j in {1,...,m},there is-1＜|Vi|-|Vj|＜1.In this paper,we proved that every planar graph G with minimum degree δ(G)≥ 2 and girth g(G)≥ 12 admits an equitable(O17,O27,...,Om7)-partition,for any integer m ≥ 2.
查看更多>>摘要：Let G be a cyclic group of order pq,where q|p-1,q,p are prime numbers and let F be a field of characteristic p.Let V be a finite-dimensional G-module over F.We refer to the maximal degree of indecomposable polynomials in the invariant algebra F[V]G as the Noether number of the invariant algebra F[V]G,denoted β(F[V]G).In this paper,we determine the Noether number of the invariant algebra F[V]G.Furthermore,we prove that for such a cyclic group of order pq,Wehlau's conjecture holds.
查看更多>>摘要：A partition reduction method is used to obtain new upper bounds for the inverses of H-matrices and S-strictly diagonally dominant(S-SDD)matrices.The estimates are expressed via the determinants of third order matrices.Numerical experiments with various random ma-trices show that they are stable and better than the estimates presented in literatures.We use these upper bounds to improve known error estimates for linear complementarity problems with H-matrices and S-SDD matrices.
查看更多>>摘要：In this paper,we introduce the notion of embedding tensors on 3-Hom-Lie algebras and show that embedding tensors induce naturally 3-Hom-Leibniz algebras.Moreover,the co-homology theory of embedding tensors on 3-Hom-Lie algebras is defined.As an application,we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent,then their infinitesimals belong to the same cohomology class in the first cohomology group.
查看更多>>摘要：A subgroup H of a group G is said to be self-conjugate-permutable if HHx=HxH implies Hx=H for any x of G.A finite group G is called an SC-group(PSC-group,respectively)if all cyclic subgroups of G of order 2 or order 4(prime order or order 4,respectively)are self-conjugate-permutable in G.In this paper,we first investigate the structure of finite non-solvable groups all of whose second maximal subgroups are SC-groups;then we mainly investigate the structure of finite groups in which all of maximal subgroups of even order are PSC-groups.In fact,we describe the structure of finite groups which are not PSC-groups but all of whose maximal subgroups of even order are PSC-groups.
查看更多>>摘要：In this paper,we define a new class of Pm-factorizable topological groups.A topo-logical group G is called Pm-factorizable if,for every continuous function f:G → M to a metrizable space M,one can find a perfect homomorphism π:G → K onto a second-countable topological group K and a continuous function g:K → M such that f=goπ.We show that a topological group G is Pm-factorizable if and only if it is PR-factorizable.And we get that if G is a Pm-factorizable topological group and K is any compact topological group,then the group G × K is Pm-factorizable.
查看更多>>摘要：In this paper,we will prove that the system of differential-difference equations｛(f(z)f'(z))n+p21(z)gm(z+η)=Q1(z),(g(z)g'(z))n+p22(z)fm(z+η)=Q2(z),has no transcendental entire solution(f(z),g(z))with ρ(f,g)＜∞ such that λ(f)＜ρ(f)andλ(g)＜ρ(g),where P1(z),Q1(z),P2(z)and Q2(z)are non-vanishing polynomials.
查看更多>>摘要：This article explores the existence results and finite time stability of nonlinear Riemann-Liouville fractional oscillatory differential equations of order 1＜(e)＜2 with pure delay.The approaches we adopted to explore the existence results are fixed point theorems.What's more,based on some important inequalities,we explore the finite time stability of the system.In the end,the rationality of our conclusion is verified by a case.
查看更多>>摘要：In this paper,cohyponormal weighted composition operators on the Fock space over CN are characterized completely.We also consider a class of weighted composition operators on the Fock space over CN which are both posinormal and coposinormal.As an application,we obtain the characterization of hyponormal,cohyponormal,posinormal and coposinormal com-position operators on the Fock space over CN.
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