中国科学院数学与系统科学研究院期刊网

15 November 2012, Volume 55 Issue 6
    

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  • Jian Yong WANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 961-974. https://doi.org/10.12386/A2012sxxb0092
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    For 0 < β ≤ 1, finite measure space (Ω,Σ, μ) and Hilbert space X, this paper deals with the representation problem of the conjugate cone [Lβ(μ, X)]β* of locally β-convex space Lβ(μ, X). If the normed conjugate space (Xβ*, ‖·‖) has the Randon- Nikodym property with respect to μ, this paper show the subrepresentaion theorem [Lβ(μ, X)]β*~ L(μ, Xβ*). Introducing the concept of quasi-additivity and to transform a general element in [Lp(μ,X)]p* into its adjoint functional are the key techniques of this paper.
  • Yu Lei WANG, He Guo LIU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 975-980. https://doi.org/10.12386/A2012sxxb0093
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    Let G be a group. A set X of elements of G is said to be non-commuting if xyyx for any x, yX with xy. If |X| ≥ |Y| for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a generalized extraspecial p-group is determined.
  • Articles
  • Zhao Jun WU, Shao Hua ZHANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 981-990. https://doi.org/10.12386/A2012sxxb0094
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    Using the theory of covering surface by Ahlfors we prove the existence theorem of T direction of meromorphic function f with rational function as targets under the condition

    Results are obtained to extend some related results proved by H. Guo, J. H. Zheng, and T. W. Ng and to give an affirmative answer of Zheng’s question.
  • Run Ling AN, Jin Chuan HOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 991-1000. https://doi.org/10.12386/A2012sxxb0095
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    Let H be an infinite dimensional complex Hilbert space and S(H) be the Jordan algebra of all symmetric operators in B(H). We show that if bijective maps Φ : S(H) → S(H) with Φ(I) = I, then the following conditions are equivalent: (1) Φ(ABA) = Φ(A)Φ(B)Φ(A), ∀ A,BS(H); (2) Φ((1/2)(AB + BA)) = (1/2)Φ(A)Φ(B)+ (1/2)Φ(B)Φ(A), ∀ A,BS(H); (3) Φ(ABC +CBA) = Φ(A)Φ(B)Φ(C)+ Φ(C)Φ(B)Φ(A), ∀ A,B,CS(H); (4) Φ((1/2)(ABC + CBA)) = 1 2Φ(A)Φ(B)Φ(C) + (1/2)Φ(C)Φ(B)Φ(A), ∀ A,B,CS(H); (5) Φ is a Jordan ring isomorphism on S(H); (6) there exists a bounded invertible linear or conjugate linear operator A : HH with At = A-1 such that Φ(X) = AXAt for every XS(H). New characterizations of Jordan ring isomorphism on S(H) were got.
  • Jing Shi XU, Fang Jun ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1001-1012. https://doi.org/10.12386/A2012sxxb0096
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    Let μ be a Radon measure on Rd satisfying a certain growth condition. Then Toeplitz operators generated by Calderón-Zygmund operators and RBMO(μ) functions are bounded on Lebesgue spaces and Morrey spaces with measure μ.
  • Chun Tai LIU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1013-1018. https://doi.org/10.12386/A2012sxxb0097
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    Let La,b be the level set of Redemacher series, being induced by a real sequence {an}, for which the upper limit of the part summation is b and the lower limit is a. By the tools named the density of natural numbers and local Holder continuity in the symbol space, the author proved that the Hausdorff dimension of La,b is one if the sequence {an}n=1 doesn’t belong to l1 with the general term tending to zero.
  • Ji Qing TIAN, Hai Bo YU, Hao ZHAO
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1019-1026. https://doi.org/10.12386/A2012sxxb0098
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    Let p > 3 be a prime. Using homotopy decomposition, under certain dimensional restrictions, we obtained upper bounds for the p-primary H-homotopy exponents of complex Stiefel manifolds as well as complex Grassman manifolds.
  • Yun Hua ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1027-1032. https://doi.org/10.12386/A2012sxxb0099
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    Let σ : AA be a topologically mixing finite type shift. For two almost additive potentials, we give some equivalent conditions for which the two potentials generate the same Gibbs measure. As an application, we give some sufficient conditions for which an almost additive potential generate the maximal entropy measure.
  • Ying WANG, Xin Min HOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1033-1038. https://doi.org/10.12386/A2012sxxb0100
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    Let γc(G) denote the connected domination number of a graph G. A graph G is called k-connected-domination-critical, or briefly k-c-critical, if γc(G) = k, but γc(G+e) ≤ k - 1 for any edge eE(G). A graph G is factor-bicritical, if G-u-v has a perfect matching for every pair of distinct vertices u, vV (G). In this paper, following the work of Ananchuen, Ananchuen and Plummer [Matching properties in connected domination critical graphs, Discrete Math., 2008], we show that: (1) If a graph G is 3-connected 3-c-critical of order 2n (n ≥ 4) satisfying d(x) + d(y) ≥ 2n - 2 for any two nonadjacent vertices x, y in G, then G is factor-bicritical, this generalizes a result of Ananchuen, Ananchuen and Plummer (Theorem 2.1 in their paper). (2) Let G be a 3-connected 3-c-critical graph of order 2n (n ≥ 4). If for any two distinct vertices u and v in G with distance two, we have max{d(u), d(v)} ≥ n, then G is factor-bicritical. (3) If G is a 3-connected 3-c-critical K1,4-free graph of even order, then G is factorbicritical, this improves a result of Ananchuen, Ananchuen and Plummer (Theorem 2.2 in their paper).
  • Xin Xing WU, Pei Yong ZHU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1039-1054. https://doi.org/10.12386/A2012sxxb0101
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    For a couple of Furstenberg families F1 and F2, we introduce the notions of dense (F1,F2)-chaos, dense (F1,F2)-δ-chaos, general (F1,F2)-chaos, general strong (F1,F2)-chaos and (F1,F2)-sensitivity. Next, some equivalent conditions of F-sensitivity and general (F1,F2)-chaos are obtained. Finally, some properties of chaos via a couple of Furstenberg families in inverse limit systems and product systems are discussed.
  • Rong Xia HAO, Jin Xin ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1055-1066. https://doi.org/10.12386/A2012sxxb0102
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    The alternating group network ANn (n ≥ 3) is defined as the Cayley graph on the alternating group An of degree n with respect to {(1 2 3), (1 3 2), (1 2)(3 i) | 4 ≤ i ≤ n}. Zhou and Xiao [Information Processing Letters, 110 (2010), 403-409] deduced the fault tolerance of alternating group network with the number of fault vertices |F| ≤ 3n - 10. In this paper, we discuss the fault tolerance of alternating group network with |F| ≤ 6n - 24, and completely characterize all small components, of ANn\F with |F| ≤ 6n - 18 for n ≥ 5.
  • Yun Ge XU, Chao ZHANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1067-1084. https://doi.org/10.12386/A2012sxxb0103
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    It is well known that the Hochschild (co)homology of a finite dimensional algebra is closely related to its global dimension and the support variety. In this paper we consider the Hochschild cohomology of some classes of Koszul algebras. As a consequence, we provide more counterexamples to Happel’s question and Snashall-Solberg’s conjecture which generalize many counterexamples to these conjectures studied in the literature. In particular, we show that a family of Zn × Zn-Galois covering algebras of quantized exterior algebra Aq in two variables answer negatively to Happel’s question, and meanwhile, the one-point coextensions of Zn and Zn×Zm-Galois covering algebras of Aq negate the Snashall-Solberg’s conjecture.
  • Bin YI, Min SU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1085-1094. https://doi.org/10.12386/A2012sxxb0104
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    We proved that there exists a set S1 with 2 elements and a set S2 with 3 elements, such that for any two nonconstant entire functions f and g satisfying E(Sj,f) = E(Sj,g) (j = 1, 2), we have fg; and there exists a set S1 with 2 elements and a set S2 with 9 elements, such that for any two nonconstant meromorphic functions f and g satisfying E(Sj,f) = E(Sj,g) (j = 1, 2), are have fg; and there exists a set S1, S2, S3 with 1 element, 2 elements, 7 elements respectively, such that for any two nonconstant meromorphic functions f and g satisfying E(Sj,f) = E(Sj,g) (j = 1, 2, 3), we have fg.
  • Bai Yun SU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1095-1100. https://doi.org/10.12386/A2012sxxb0105
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    In this paper, using a completely different proof of Y. H. Zhang and G. T. Deng, we obtian growth properties for a class of harmonic functions at infinity in the upper half space, which extend results obtained by them.
  • Gui Lian GAO, Xiao YU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1101-1110. https://doi.org/10.12386/A2012sxxb0106
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    We obtain the boundedness of a class of generalized Hardy operators on some function spaces, such as the Herz spaces and the Morrey-Herz spaces. Furthermore, the λ-central BMO estimate for the generalized Hardy operator on λ-central Morrey spaces is also obtained.
  • Wei Dong WANG, Tong Yi MA
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1111-1118. https://doi.org/10.12386/A2012sxxb0107
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    Associated with the Lp-harmonic radial combination of star bodies, Wang and Leng in 2005 introduced the notion of Lp-dual mixed quermassintegrals. In this paper, we prove a property of the Lp-dual mixed quermassintegrals under linear transformation. Further, two inequalities for this notion are obtained. Finally, as the application of this notion, we give a characterization of the Lp-mixed centroid body.
  • Hong Bo WU, Hui Jun SHI
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1119-1130. https://doi.org/10.12386/A2012sxxb0108
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    Topological system has been proposed by Steven Vikers in his work “Topology via Logic” through synthesizing the methods of topology and the theory of logics, which also is applied to study of computers theory. In the present paper, the new algebras system-Heyting system is put forward with the help of the idea of topological system and the properties enjoyed by Frame structure and Heyting algebras, which takes the Heyting algebras as its principal body; the H-continuous mapping connecting Heyting systems is established; the H-Localification of Heyting system is given, and the related properties are investigated.
  • Xiang Chun XIAO, Xiao Ming ZENG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1131-1144. https://doi.org/10.12386/A2012sxxb0109
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    We characterize the continuous g-frames and the continuous g-Riesz basis by the synthesis operator and a bounded operator L associated with two continuous g-Bessel sequences; we also construct new continuous g-frames from a given continuous g-frame. Finally we show that, under some proper conditions, the remainder of some given continuous g-frame by deleting some elements can also be a continuous g-frame.
  • Yuan Hong REN, Gai Juan CHEN, Qian LIU, Ning WANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(6): 1145-1152. https://doi.org/10.12386/A2012sxxb0110
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    In this paper, by discussing the von Neumann algebras L″ generated by the invariant subspace lattices L in M3(C), the authors have classified all Kadison- Singer lattices in the 3-order matrix algebra with respect to similarity.