中国科学院数学与系统科学研究院期刊网

15 May 2013, Volume 56 Issue 3
    

  • Select all
    |
    Articles
  • Ru Yun MA, Rui Peng CHEN, Jie Mei LI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 289-300. https://doi.org/10.12386/A2013sxxb0030
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We are concerned with the existence of positive solutions of the nonlinear Neumann problem (p(t)u')'+q(t)u=f(t, u), t ∈ (0, 1), u'(0)=u'(1)=0, where p, qC[0, 1] with p > 0, 0 < q < b* in [0, 1], b* is the first eigenvalue of the Robin problem (p(t)u')'+bu=0, u'(0)=0, u(1)=0. By applying the topological degree theory and global bifurcation techniques, we establish the existence results of positive solutions for above problem.
  • Kun Li ZHANG, Huai Xin CAO, Zhi Hua GUO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 301-310. https://doi.org/10.12386/A2013sxxb0031
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Representations of abstract effect algebras was introduced in the literature [Sci. Sin. Math., 2011, 41(3): 279-286], some examples of representable effect algebras and unrepresentable effect algebras were given there. However, a general criterion about the representations of effect algebras was not obtained. Based on the idea of the GNS structure of an abstract C*-algebra, we guess that abstract effect algebras admitting much enough states should be representable. Thus, the existence of states and the representations of state spaces seem to be important in the representation theory and the classification problem of abstract effect algebras. This paper is devoted to discussing the existence of states and valuations of effect algebras. General forms of states and state spaces of some typical effect algebras are obtained. Especially, the existence theorem of states of representable effect algebras is proved and nonempty convex subsets of state space and valuation space of an effect algebra are given, respectively.
  • Jin XIA, Xiao Feng WANG, Guang Fu CAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 311-330. https://doi.org/10.12386/A2013sxxb0032
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We characterize the bounded ness and compact ness of the Toeplitz operators on the harmonic Dirichle space; discuss the algebraic properties of the Toeplitz operators; and obtain the short exact sequences with respect to the Toeplitz algebra and the Hankel algebra. We also compute the Fredholm index of Fredholm operator in the Toeplitz algebra and the Hankel algebra, and obtain the K0 and K1 groups of the Toeplitz algebra and the Hankel algebra.
  • Jing Cheng DONG, Hui Xiang CHEN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 331-342. https://doi.org/10.12386/A2013sxxb0033
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let kG be a group algebra, and D(kG) the quantum double of kG. We first prove that the structure of representation ring of D(kG) can be described in terms of the representation ring of centralizer subgroups of representatives of conjugate classes of G. As an application, we then describe the structure of representation ring of D(kGn), where k is a field of characteristic 2, n is odd, and Dn is a dihedral group of order 2n.
  • Pin Ling WANG, Dan LIU, Ming Liang FANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 343-352. https://doi.org/10.12386/A2013sxxb0034
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    It is mainly proved: let k ≥ 2 be a positive integer, M a positive number, let c (≠0) be a finite value, and let F be a family of meromorphic functions in a domain D, all of whose zeros are of multiplicity k at least. If, for each function fF, f(z)=0⇔f(k)(z)=0, f(k)(z)=c⇒|f(k+1)(z)| ≤ M, then F is normal in D. And c ≠ 0 is necessary.
  • Gui Qiao XU, Yang LIU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 353-368. https://doi.org/10.12386/A2013sxxb0035
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, for the approximation in Lp-norm, we determine the weakly asymptotic order for the p-average errors of a kind of quasi-Hermite interpolation sequence on the 1-fold integrated Wiener space. By the result it is known that in the sense of Information-Based Complexity, if permissible information functions are Hermite data, then the p-average errors of this interpolation sequence are weakly equivalent to the corresponding minimal p-average radius of nonadaptive information.
  • Jian Hua YIN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 369-380. https://doi.org/10.12386/A2013sxxb0036
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    An r-graph is a loopless undirected graph in which no two vertices are joined by more than r edges. An r-complete graph on m+1 vertices, denoted by Km+1(r), is an r-graph on m+1 vertices in which each pair of vertices is joined by exactly r edges. A non-increasing sequence π=(d1, d2,..., dn) of nonnegative integers is said to be r-graphic if it is the degree sequence of some r-graph on n vertices. An r-graphic sequence π is said to be potentially (resp. forcibly) Km+1(r)-graphic if π has a realization containing Km+1(r) as a subgraph (resp. every realization of π contains Km+1(r) as a subgraph). Let σ(Km+1(r), n) (resp. τ (Km+1(r), n)) denote the smallest even integer t such that each r-graphic sequence π=(d1,d2,..., dn) with ∑i=1ndit is potentially (resp. forcibly) Km+1(r)-graphic. Clearly, σ(Km+1(r), n) is an extension from 1-graph to r-graph of a conjecture due to Erdös et al and τ (Km+1(r), n) is an extension from 1-graph to r-graph of the classical Turán's theorem. In this paper, we give two simple sufficient conditions for an r-graphic sequence to be potentially Km+1(r)-graphic, which imply two main results due to Yin and Li (Discrete Math., 2005, 301: 218-227) and the value of σ(Km+1(r), n) for n ≥ max{m2+3m+1-[m2+m/r], 2m+1+[m/r]}. Moreover, we also determine the value of τ(Km+1(r), n) for nm+1.
  • Yong Min LIU, Yan Yan YU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 381-390. https://doi.org/10.12386/A2013sxxb0037
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the authors characterize the boundedness and compactness of the integral-type operator Pg from mixed norm spaces H(p, q, φ) to Zygmund-type spaces on the unit ball and some necessary and sufficient conditions of the integral-type operator Pg to be bounded and compact are obtained.
  • Zai Yun PENG, Xin Min YANG, Yong ZHAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 391-400. https://doi.org/10.12386/A2013sxxb0038
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, using a scalarization technique, we provide sufficient conditions for the upper/lower semicontinuity of the solution mappings to parametric setvalued weak vector equilibrium problems without monotonicity and C-concavity in linear metric spaces. These results improve the recent ones in the literature. Some examples are given for illustration of our results.
  • Shu Yu CUI, Gui Xian TIAN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 401-408. https://doi.org/10.12386/A2013sxxb0039
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The skew energy ES(D) of a digraph D is defined as the energy of its skewadjacency matrix. In this paper, employing many operations of digraphs, we construct several classes of digraphs, each one of which satisfies its skew energy is the same as the energy of its underlying graph. This work partly answers a problem proposed by Adiga et al. [The skew energy of a digraph, Linear Algebra Appl., 2010, 432: 1825-1835].
  • Ling JIA
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 409-412. https://doi.org/10.12386/A2013sxxb0040
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the elementary symmetric functions μ0, μ1,..., μn and the intrinsic volumes V0,V1,..., Vn are investigated. We show that the elementary symmetric function basis {μ0, μ1,..., μn} and the intrinsic volume basis {V0,V1,..., Vn} defined on Ln (also the quermassintegral basis {W0,W1,..., Wn}) are equivalent.
  • Jiang Hua LI, Yan Ni LIU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 413-418. https://doi.org/10.12386/A2013sxxb0041
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The main purpose of this paper is using the properties of Gauss sums and the analytic method to study the the hybrid mean value problem involving between the Gauss sums and the general Kloosterman sums, and to give several interesting identities of it.
  • Fang Wei CHEN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 419-426. https://doi.org/10.12386/A2013sxxb0042
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, the elementary symmetric functions μ0, μ1,..., μn and the intrinsic volumes V0,V1,..., Vn are investigated. We show that the elementary symmetric function basis {μ0, μ1,..., μn} and the intrinsic volume basis {V0,V1,..., Vn} defined on Ln (also the quermassintegral basis {W0,W1,..., Wn}) are equivalent.
  • Ling Ling DONG, De Yu ZHANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(3): 427-432. https://doi.org/10.12386/A2013sxxb0043
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let n > 1 be an integer, and n=∏i=1tpiai, τk(e)(n)=∏piaindk(ai). In this paper we study the sum D=∑nxd and get the asymptotic formula for it, where d=∑n=ab12bk2 1. We get the mean value for the exponential divisor function, which improves the previous result.