中国科学院数学与系统科学研究院期刊网

15 July 2013, Volume 56 Issue 4
    

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  • Xiang Chun XIAO, Ming Ling DING, Yu Can ZHU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 433-440. https://doi.org/10.12386/A2013sxxb0044
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    We give kinds of methods to construct K-fusion frames in Hilbert spaces, including that we use the synthesis operator of a K-fusion frame to construct another K-fusion frame, and we use two fusion-Bessel sequences and a bounded linear operator K to construct K-fusion frame. In the end we use a bounded linear operator SVW with respect to two fusion-Bessel sequences to construct new K-fusion frames.
  • Zhong Yan SHEN, Tian Xin CAI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 441-450. https://doi.org/10.12386/A2013sxxb0045
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    In this note, using harmonic shuffle relation, we obtain the following identities,
    .
  • Ling Yun GAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 451-458. https://doi.org/10.12386/A2013sxxb0046
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    In this paper, by Nevanlinna theory of the value distribution of meromorphic functions, we will investigate the problem of the existence and the growth of solutions of two types of complex higher-order difference equations, Malmquist type theorem of one type of difference equations is established, and the growth order of solutions of the other type of complex difference equation is estimated. Some examples show that our results are precise.
  • Xiao Fei QI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 459-468. https://doi.org/10.12386/A2013sxxb0047
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    Let R be a ring with unit I and a nontrivial idempotent P. Assume that Φ : R → R is an additive map, A,BR. It is shown that, under some mild conditions, the following three statements hold: (1) Φ satisfies Φ(A)B=AΦ(B)=Φ(P) whenever AB=P if and only if Φ is a centralizer; (2) Φ satisfies Φ(A)B(B)A=Φ(P) (AΦ(B)+BΦ(A)=Φ(P)) whenever AB+BA=P if and only if Φ is a left (right) centralizer; (3) Φ satisfies Φ(A)B+Φ(B)A=0 (AΦ(B)+BΦ(A)=0) whenever AB+BA=0 if and only if Φ is a left (right) centralizer. Based on the above results, the characterizations of centralizers on triangular algebras, von Neumann algebras and nest algebras are obtained.
  • Lei DAI, Xiao Hong CAO, Na Na XIAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 469-478. https://doi.org/10.12386/A2013sxxb0048
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    An operator T ∈ B(H) is said to admit a generalized Kato decomposition, if there exists a pair of T-invariant closed subspaces (M,N) such that H=M⊕N, the restriction T|M is upper semi-Fredholm with ind(T|M) ≤ 0 and T|N is nilpotent. In this paper, using the property of generalized Kato decomposition of T ∈ B(H), we investigate the stability of the Weyl type theorem under compact perturbations. Also, we characterize 2×2 upper triangular operator matrices for which the Weyl type theorem is stable under compact perturbations.
  • Hao LIANG, Jun Ming XU
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 479-486. https://doi.org/10.12386/A2013sxxb0049
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    In 1978, Caccetta and Häggkvist made an open conjecture: Any digraph on n vertices with minimum outdegree at least r contains a directed cycle of length at most [n/r]. We prove that if α ≥ 0.28724, then any digraph on n vertices with minimum outdegree at least αn contains a directed cycle of length at most 4.
  • Zhong Xiang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 487-504. https://doi.org/10.12386/A2013sxxb0050
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    In this paper, the hyper-complex forms of equations for the plane and the sphere in R3 are given. Then, the concept of symmetric points with respect to the plane and the sphere in R3 is introduced, equivalent equations for symmetric points respect to the plane and the sphere are given. Some special Möbius transformations in hyper-complex space Cl3 are considered. Some properties of the mentioned Möbius transformation are given. For example, the Möbius transformation maps the plane and the sphere in R3 one-to-one onto the plane or the sphere, the Möbius transformation preserves the symmetric points with respect to the plane and the sphere in Cl3, the cross ratio of four distinct points is also invariant under the Möbius transformation. A relation between the monogenic function and Möbius transformation is shown. Secondly, a generalized Cauchy theorem and generalized Cauchy integral formula over the sphere for monogenic functions are proved. By combining the Cauchy integral formula for monogenic functions with the integral representation at the symmetric point with respect to the sphere, the Poisson integral representation for monogenic function is obtained. Finally, based on the properties of Möbius transformations, integral formulas for change of variables under Möbius transformations are constructed.
  • Hua WANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 505-518. https://doi.org/10.12386/A2013sxxb0051
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    Let w be a Muckenhoupt weight and WHwp(Rn) be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of WHwp(Rn), we will show that the maximal Bochner-Riesz operators T*δ are bounded from WHwp(Rn) to WLwp(Rn) when 0 < p ≤ 1 and δ > n/p-(n+1)/2. Moreover, we will also prove that the Bochner-Riesz operators TRδ are bounded on WHwp(Rn) for 0 < p ≤ 1 and δ > n/p-(n+1)/2. Our results are new even in the unweighted case.
  • Zheng Xing LI, Jin Ke HAI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 519-526. https://doi.org/10.12386/A2013sxxb0052
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    Let G be an extension of a finite nilpotent group N by a symmetric group Sm of degree m. It is shown that, the normalizer property holds for G. This generalizes a result due to Petit Lobão and Sehgal which states that, if   is the natural wreath product of a finite nilpotent group N by a symmetric group Sm of degree m, then the normalizer property holds for G. Techniques used in this paper are different from that used by Petit Lobão and Sehgal.
  • Ying Qing XIAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 527-536. https://doi.org/10.12386/A2013sxxb0053
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    In this paper, using the mass distribution principle, we show that the homogeneous perfect set of Hausdorff dimension 1, defined by a bounded sequence of positive integers is minimal for 1-dimensional quasisymmetric maps.
  • Jun Li SHEN, Alatancang
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 537-544. https://doi.org/10.12386/A2013sxxb0054
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    We prove the following assertions: (1) If T is a quasi-*-A(n) operator, then T is normaloid. (2) if E is the Riesz idempotent for a non-zero isolated point λ of the spectrum of a quasi-*-A(n) operator T, then E is self-adjoint and R(E)=N(T-λ)=N(T-λ)*. (3) If T or T* is an algebraically quasi-*-A(n) operator, then Weyl's theorem holds for f(T) for every f ∈ H(σ(T)). (4) If T* is an algebraically quasi-*-A(n) operator, then a-Weyl's theorem holds for f(T) for every f ∈ H(σ(T)).
  • Fang Fang XIAO, Hong Ping CAO, Gui Yun CHEN
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 545-552. https://doi.org/10.12386/A2013sxxb0055
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    We show that the automorphism groups of Suzuki-Ree groups 2F4(q),q=2f,2G2(q),q=3f and the Tits simple Group 2F4(2)', which f=3s, s be positive integer are characterized by their order components.
  • Xiao Hui ZHANG, Jian Hua ZHANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 553-560. https://doi.org/10.12386/A2013sxxb0056
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    Let AlgN and AlgM be non-trivial nest algebras on a complex separable Hilbert space H, and φ: AlgN → AlgM be a unital bijection. In the paper, we prove that if φ satisfies φ(AoB)=φ(A)oφ(B) for any A,B ∈ AlgN with AB=0, then φ is either an isomorphism or an anti-isomorphism.
  • Wei Yin FEI, Yong LIANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 561-574. https://doi.org/10.12386/A2013sxxb0057
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    In this paper, a class of stochastic set differential equations (SSDEs) driven by a continuous local martingale under the non-Lipschitzian condition is studied. Such equations can be useful in modelling of stochastic systems, where the phenomena are subjected to a random outcome being multivalued. The solutions of SSDEs are the setvalued stochastic processes. Thus, the existence and uniqueness of solutions to SSDEs under the non-Lipschitzian condition is first proven. Then the stability of solutions to SSDEs is investigated.
  • Zhi Jun WEI, Wei CAO
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 575-582. https://doi.org/10.12386/A2013sxxb0058
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    We investigate a class of special polynomial systems over finite fields, and obtain some sufficient conditions for orthogonality via character sums, which can be used to construct orthogonal systems of this type.
  • Li Guang WANG, Jing LI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 583-596. https://doi.org/10.12386/A2013sxxb0059
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    We introduce a new class of functional equations
    f(x + 2y) + f(x − 2y) = f(x + y) + f(x − y) + 3f(2y) − 6f(y)
    deriving from additive mappings and quadratic mappings and consider its Hyers-Ulam stability on quasi-β-normed linear spaces.
  • Jian Quan LIAO, Jin Xun WANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 597-604. https://doi.org/10.12386/A2013sxxb0060
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    Let be the Dirac operator and let φ(x) be an octonionvalued function defined in a non-empty open set Ω ⊂ R8. In this paper, we prove that D(φ(εx))=0 for all ε ∈ O if and only if φ is a Stein-Weiss analytic function in Ω.
  • Articles
  • Wei Ping LI, Tian Ze WANG
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 605-612. https://doi.org/10.12386/A2013sxxb0061
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    Using Davenport-Heilbronn method, this paper shows that if μ1, . . . , μr are non-zero real numbers, not both negative, at least one of μj (1≤ jr) is irrational, and k,m, r are positive integers satisfying k ≥ 4, r ≥ 2k-1+1, then there exist infinitely many primes p1, . . . , pr, p such that [μ1p1k+···+μrprk]=mp. In particular, [μ1p1k+···+μrprk] represents infinitely many primes.
  • Shao Guang SHI
    Acta Mathematica Sinica, Chinese Series. 2013, 56(4): 613-624. https://doi.org/10.12386/A2013sxxb0062
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    The one-sided version of singular integral operators T+ with Hörmander type kernels are studied. We give a new proof of the weighted Lp (1 < p < ∞) boundedness for T+ by adopting the well known good λ inequality of Coifman and Fefferman's to one-sided case. As we will see in the paper, we avoid some classical techniques comparing with Lorente-Riveros-Toorre's theorem, such as Fefferman-Stein inequality. The corresponding weighted weak type (1, 1) estimates are also obtained by using one-sided C-Z decomposition. Particularly, we show that the weighted boundedness is sharp in some sense.