查看更多>>摘要：In this paper,we study non-abelian extensions of 3-Leibniz algebras through Maurer-Cartan elements.We construct a differential graded Lie algebra and prove that there is a one-to-one correspondence between the isomorphism classes of non-abelian extensions in 3-Leibniz algebras and the equivalence classes of Maurer-Cartan elements in this differential graded Lie algebra.And also the Leibniz algebra structure on the space of fundamental elements of 3-Leibniz algebras is analyzed.It is proved that the non-abelian extension of 3-Leibniz algebras induce the non-abelian extensions of Leibniz algebras.
查看更多>>摘要：In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrödinger equations with different large forcing terms and(2p+1)-nonlinearities iut-△u+ψi((ω)1t)u+ψ2((ω)2t)|u|2pu=0,t ∈(R),x ∈ T2 under periodic boundary conditions.As a result,the existence of a Whitney smooth family of small-amplitude reducible quasi-periodic solutions is obtained.
查看更多>>摘要：Given a list assignment of L to graph G,assign a list L(v)of colors to each v∈V(G).An(L,d)*-coloring is a mapping π that assigns a colorπ(v)∈ L(v)to each vertex v ∈ V(G)such that at most d neighbors of v receive the color v.If there exists an(L,d)*-coloring for every list assignment L with|L(v)|≥k for all v ∈ V(G),then G is called to be(k,d)*-choosable.In this paper,we prove every planar graph G without adjacent k-cycles is(3,1)*-choos-able,where k ∈ {3,4,5}.
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