查看更多>>摘要：Assume that G is a finite non-abelian p-group.If G has an abelian maximal subgroup whose number of Generators is at least n,then G is called an Mn-group.For p=2,M2-groups have been classified.For odd prime p,this paper provides the isomorphism classification of M2-groups,thereby achieving a complete classification of M2-groups.
查看更多>>摘要：Assume that S is an nth-order complex sign pattern.If for every nth degree complex coefficient polynomial f(λ)with a leading coefficient of 1,there exists a complex matrix C∈Q(S)such that the characteristic polynomial of C is f(λ),then S is called a spectrally arbitrary complex sign pattern.That is,if the spectrum of nth-order complex sign pattern S is a set comprised of all spectra of nth-order complex matrices,then S is called a spectrally arbitrary complex sign pattern.This paper presents a class of spectrally arbitrary complex sign pattern with only 3n nonzero elements by adopting the method of Schur complement and row reduction.
查看更多>>摘要：Let F be a graph and H be a hypergraph.We say that H contains a Berge-F If there exists a bijection φ:E(F)→E(H)such that for (V)e ∈ E(F),e ⊂ φ(e),and the Turán number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by exr(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated vertices.Let Ln,k be the family of all linear forests of n vertices with k edges.In this paper,Turán number of Berge-Ln,k in an r-uniform hypergraph is studied.When r≥k+1 and 3 ≤ r ≤[k-1/2]-1,we determine the exact value of exr(n,Berge-Ln,k)respectively.When[k-1/2]≤ r ≤ k,we determine the upper bound of exr(n,Berge-Ln,k).
查看更多>>摘要：This paper studies the properties of Nambu-Poisson geometry from the(n-1,k)-Dirac structure on a smooth manifold M.Firstly,we examine the automorphism group and infinitesimal on higher order Courant algebroid,to prove the integrability of infinitesimal Courant automorphism.Under the transversal smooth morphism φ:N → M and anchor mapping of M on(n-1,k)-Dirac structure,it's holds that the pullback(n-1,k)-Dirac structure on M turns out an(n-1,k)-Dirac structure on N.Then,given that the graph of Nambu-Poisson structure takes the form of(n-1,n-2)-Dirac structure,it follows that the single parameter variety of Nambu-Poisson structure is related to one variety closed n-symplectic form under gauge transformation.When φ:N →M is taken as the immersion mapping of(n-1)-cosymplectic submanifold,the pullback Nambu-Poisson structure on M turns out the Nambu-Poisson structure on N.Finally,we discuss the(n-1,0)-Dirac structure on M can be integrated into a problem of(n-1)-presymplectic groupoid.Under the mapping Π:M → M/H,the corresponding(n-1,0)-Dirac structure is F and E respectively.If E can be integrated into(n-1)-presymplectic groupoid(g,Ω),then there exists the only(w),such that the corresponding integral of F is(n-1)-presymplectic groupoid((g),(w)).
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