15 September 2012, Volume 55 Issue 5

    

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  On the Unitriangular Group over the Integral Ring(Ⅲ)

  He Guo LIU, Zuo Hui WU

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 769-780. https://doi.org/10.12386/A2012sxxb0074

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  Let Tr₁(n,Z)be the group of all n×n (upper) unitriangular matrices over the integral ring. Let k_ij (1≤i＜j≤n)be given positive integers and
  
  If G is a subgroup of Tr₁(n,Z),and its upper central series coincides with its lower central series,then the associated Lie ring L(G)of G is isomorphic to the Lie ring R,where the Lie product of A,B is defined as [A,B]=AB-BA for arbitrary two elements A and B of R.That is to say,we obtain the matrix representation of L(G).
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  An Isomorphism Theorem Between Equivariant Cohomology and Čech Hypercohomology

  Hai Bo YANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 781-790. https://doi.org/10.12386/A2012sxxb0075

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  We first show that each equivariant smooth manifold has an equivariant good cover,and the equivariant good covers are cofinal in the set of open covers.We further this result to get an isomorphism theorem between equivariant cohomology and Čech hypercohomology.Such result can be applied to the study of Deligne cohomology of the real algebraic varieties.
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  The Normalizer Property for Integral Group Rings of Extensions of Finite Nilpotent Groups by Simple Groups

  Jin Ke HAI, Zheng Xing LI

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 791-796. https://doi.org/10.12386/A2012sxxb0076

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  Let G be an extension of finite nilpotent group by a simple group,i.e.G has a nilpotent normal subgroup N such that G/N is a simple group.It is shown that the normalizer property holds for such groups G.In particular,the normalizer property holds for inner solvable groups.
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  Cauchy Problem for an N-Dimensional Nonlinear Wave Equation

  Guo Wang CHEN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 797-810. https://doi.org/10.12386/A2012sxxb0077

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  We prove that the Cauchy problem for the nonlinear wave equation υtt-αΔυtt-Δυ=g(υ)-αΔg(υ),χ∈R^N,t>0, ⁽¹⁾ υ(χ,0)=υ₀(χ),υt(χ,0)=υ₁(χ),χ∈R^{N (2)} has a unique global generalized solution υ in C²([0,∞);H^s(R^N))(s>N/2) and a unique global classical solution υ in C²([0,∞);H^s(R^N))(s>2+N/2),i.e.,υ∈C²([0,∞);C_B²(R^N)). We also prove that the Cauchy problem(1),(2)admits a unique global generalized solution υ in C ³(0,∞);W ^m,p(R^N)∩L^∞(R^N))(m≥0,1≤p≤∞)and a unique global classical solution υ in C ³(0,∞);W ^m,p(R^N)∩L^∞(R^N))(m>2+N/P,i.e.,υ∈C³([0,∞;C²(R^N)∩L^∞(R^N)).
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  Lie Triple Systems Associated with the Laurent Polynomial Algebra C[x₁^±1,x₂^±1]

  Zhao LI, Bo ZENG, You An CAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 811-816. https://doi.org/10.12386/A2012sxxb0078

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  Let A be the Laurent polynomial algebra in commutative variables x₁,x₂. Denote the derivation algebra Der A of A by M.In this paper,we determine the involution automorphisms of A,M.We use the involution automorphisms of M to construct some infinitely Diffensional simple Lie triple systems.The automorphisms of these simple Lie triple systems are also determined by discussing the relationships between the automorphisms and the involution automorphisms of M.
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  Existence of the Traveling Wave Solutions for a Chemotaxis Equations

  Xue Yong CHEN, Yin YANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 819-828. https://doi.org/10.12386/A2012sxxb0079

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  We study a strong coupling nonlinear partial differential equations,which modeling the chemotaxis phenomenon.In terms of similar phase plane method,some necessary or suffcient conditions for the existence of traveling wave solutions are obtained.
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  Generating Minimal Forbidden Subgraphs for a Non-Orientable Surface

  Deng Ju MA, Han REN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 829-840. https://doi.org/10.12386/A2012sxxb0080

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  A graph G is a minimal forbidden subgraph for a surface S if G has no vertices with degree less than three,and if G is not embeddable in S but G-e is embeddable in S for any edge e of G.In the paper we give four methods generating minimal forbidden subgraphs for a non-orientable surface,i.e.,amalgamating a vertex, edges of a graph replaced by other graphs,amalgamating two vertices and placing a graph in faces of an embedding of another graph in a surface.
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  Fuzzy Stability of a Functional Equation Deriving from Additive, Quadratic,Cubic and Quartic Functions

  Li Guang, WANG Bo LIU

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 841-854. https://doi.org/10.12386/A2012sxxb0081

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  We investigate the Hyers-Ulam stability of the following mixed type functional equations f(x+ky)+f(x-ky)=k²f(x+y)+k²f(x-y)+2(1-k²)f(x) +k²(k²-1)/12( (2y)-4 (y))in fuzzy Banach spaces where k>1 is a fixed integer and (y)=f(y)+f(-y).
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  Value Distribution of Some Divided Difference

  Mei Ru CHEN, Zong Xuan CHEN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 855-860. https://doi.org/10.12386/A2012sxxb0082

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  We investigate value distribution problems of some Difference expressions. Let n, m∈N, n>m, c ∈ C\ {0}, f(z)be a transcendental meromorphic function,P(z) be a non-zero polynomial.A number of results are proved concerning the existences of zeros of
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  Weighted BMO Estimates for Commutators of Singular Integrals with Non-Smooth Kernels

  Xiao Li CHEN, Jie Cheng CHEN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 861-868. https://doi.org/10.12386/A2012sxxb0083

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  This paper is concerned with the pointwise estimates for the sharp maximal function of the commutator [b,T] which generalized by a BMO(ω)function b and singular integral operator T with non-smooth kernels,and shows that the commutator [b,T] is bounded from L^p(μ) to L^p(ν),whereω=(μν^-1)^1/p and μ,ν∈A_p,1＜p＜∞.
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  Pseudorandom Binary Sequences with Composite Moduli

  Hua Ning LIU, Jing GAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 869-880. https://doi.org/10.12386/A2012sxxb0084

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  Let m be a modulus of“RSA type”,i.e.,it is the product of two primes not far apart,say, m=pq,p,q are primes,p＜q＜2p.Rivat and Sárközy gave two families of pseudorandom binary sequences with composite moduli.In this paper we present two new families of binary sequences with composite moduli,and show that they are pseudorandom.
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  Weighted Estimates for Iterated Commutators of Multilinear Fractional Integral Operators

  Wen Ming LI, Li Mei XUE

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 881-894. https://doi.org/10.12386/A2012sxxb0085

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  For the iterated commutators of multilinear fractional integral operators, we give two-weight suffcient conditions for the strong boundedness,which is Fefferman- Phong type condition.For these operators we also obtain Fefferman-Stein type weighted inequalities and Coifman type weighted estimates.
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  Generalized Hausdorff Operators on Weighted Morrey-Herz Spaces

  Ji Chang KUANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 895-902. https://doi.org/10.12386/A2012sxxb0086

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  We introduce the new generalized Hausdorff operators.It includes many famous operators as special cases.We obtain the necessary and suffcient conditions for these operators to be bounded on the weighted Morrey-Herz spaces,the corresponding new operator norm inequalities are obtained.They are significant improvements and generalizations of many known results.
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  Classical Agarwal-O'Regan Method on Singular Nonlinear Boundary Value Problems

  Qing Liu YAO

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 903-918. https://doi.org/10.12386/A2012sxxb0087

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  The classical Agarwal-O'Regan method on singular nonlinear boundary value problems is improved.The local existence and multiplicity of positive solutions are established for the singular nonlinear(p,n-p)conjugate boundary value problems by applying this improved method,where the nonlinear term is allowed to be singular with respect to both the time and space variables.Main tools are the Guo Krasnosel'skii fixed point theorem of cone expansion-compression type and the exact apriori estimation technique.Particularly,the nonautonomous singular nonlinear second,third,fourth-order conjugate boundary value problems are considered.
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  The Stability of the Single Valued Extension Property for the Asymptotic Intertwining Operators

  Xiao Hong CAO, Jun Qiang YIN

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 919-928. https://doi.org/10.12386/A2012sxxb0088

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  An operator T∈B(H)is said to have the single-valued extension property, if for every open set U⊆C,the only analytic solution f:U→X of the equation (T-λI)f(λ)=0 for all λ∈U is zero function on U.Clearly the point spectrum of any operator which has empty interior must have the single-valued extension property. In this paper,we investigate the stability of the single-valued extension property under compact perturbations for the Asymptotic Intertwining operator.Also,we characterize 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.
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  Boundary Layers for the Viscous Lake Equations with Navier Boundary Conditions

  Xiao Jing CAI, Quan Sen JIU, Dong Juan NIU

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 929-946. https://doi.org/10.12386/A2012sxxb0089

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  We consider the inviscid limit of the two-dimensional viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundaries of the general regular domains.Our results show that the boundary layer of the viscous lake equations with Navier boundary is always nonlinearly stable in some Sobolev spaces and we justify an asymptotic expansion which involves a weak amplitude boundary layer,with the same thickness as in asymptotic theory and a linear behavior.
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  A Representation of Right Inverse to the Ⅲ-Posed Partial Dirichlet Boundary Value Problem

  Da Yong LI, Ji Li FU, Yu Wen WANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 947-952. https://doi.org/10.12386/A2012sxxb0090

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  We further study on the definition of general solution of ill-posed partial boundary value problem that Weiping Cao and Jipu Ma obtained.We prove that this problem is equivalence to the weak solution of homogeneous Dirichlet and Neumann mix boundary problem to the same PDE and obtained the representation of right inverse to the general solution of the ill-posed problem.
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  ξ-Lie Derivable Maps on Triangular Algebras by Jordan Zero Products

  Mei Yuan HUANG Jian Hua ZHANG

  Acta Mathematica Sinica, Chinese Series. 2012, 55(5): 953-960. https://doi.org/10.12386/A2012sxxb0091

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  In this paper,the structure of ξ-Lie derivable maps on triangular algebras by Jordan zero products is given.As an application,the form of ξ-Lie derivable maps on nest algebras by Jordan zero products is obtained.