中国科学院数学与系统科学研究院期刊网

15 March 2011, Volume 54 Issue 2
    

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  • Min KU, Jin Yuan DU, Dao Shun WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 177-186. https://doi.org/10.12386/A2011sxxb0019
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    The holomorphic functions of several complex variables are closely related to the so-called isotonic Dirac system in which different Dirac operators in the half dimension act from the left and from the right on the functions considered. In this paper we mainly study the boundary properties of the isotonic Cauchy type integral operator over the smooth surface in Euclidean space of even dimension with values in a complex Clifford algebra. We obtain Privalov theorem inducing Sokhotskii-Plemelj formula as the special case for the isotonic Cauchy type integral operator with Hölder density functions taking values in a complex Clifford algebra, and show that Privalov theorem of the classical Bochner-Martinelli type integral and the classical Sokhotskii- Plemelj formula over the smooth surface of Euclidean space for holomorphic functions of several complex variables may be derived from it.

     

  • Sheng Jun FAN, Long JIANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 187-194. https://doi.org/10.12386/A2011sxxb0020
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    This paper establishes an existence and uniqueness result for the solution to a one-dimensional backward stochastic differential equation (BSDE for short) whose generator satisfies Constantin’s condition in y and is uniformly continuous in z, which generalizes some known results.

     

  • Hong Wei LI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 195-210. https://doi.org/10.12386/A2011sxxb0021
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    We investigate the regular cryptogroup construction of the Rees matrix semigroup over a Clifford semigroup with identity; secondly prove that the two conditions are equivalent on a Rees matrix semigroup S over a Clifford semigroup with identity: (1) the congruence ρ of S is a completely simple semigroup congruence; (2) there is an order-preserving bijection from the congruences of S to the admissible triples of S; finally prove that the lattice of completely simple congruences on a Rees semigroup over a Clifford semigroup with identity is semimodular.

     

  • He Guo LIU, Zuo HuiWU, Fang ZHOU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 211-218. https://doi.org/10.12386/A2011sxxb0022
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    Let Tr1(n,Z) be the group of all n×n (upper) unitriangular matrices over the integral ring. Let kij (1 ≤ #em/em# < jn) be given positive integers and
    Then G is a subgroup of Tr1(n,Z) if and only if kij divides dij(2), where dij(2) denotes the greatest common divisor of all kirkrj (1 ≤ #em/em# < r < jn). Moreover, when G is a subgroup of Tr1(n,Z), both the upper central series and the lower central series of G coincide if and only if kij = dij(r), (1 ≤ rj-i), where dij(r) (2 ≤ rj-i) denotes the greatest common divisor of all kilkll2 · · · klrj (1 ≤ #em/em# < l1 < l2 < · · · < lr < jn) and dij(1) = kij if j - i = 1.-1-111  
  • Jia XU, Yong YAO
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 219-226. https://doi.org/10.12386/A2011sxxb0023
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    In this paper, the principle of finite kernel is used to complete the successive difference substitution. Then a complete algorithm for deciding positive semi-definite polynomial is presented. This algorithm can be applied further to compute the global optimization of rational function. Being different from any other common methods of numerical optimization, the method in this paper gets accurate symbolic solution.

     

  • Yong Shun LIANG, Wei Yi SU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 227-240. https://doi.org/10.12386/A2011sxxb0024
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    An analytic expression of von Koch curve has been given. Based on this complex-valued function, we give estimation of fractal dimension of its fractional calculus. Graphs of Weyl-Marchaud fractional derivative of this function have been given. Such function can also be transferred into certain self-affine fractal function. Finally, we set up the linear connection between fractal dimension of this function and order of fractional calculus. Graphs and numerical results of certain examples have been shown.

     

  • Jian Hua MA, Sheng Fan ZHOU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 241-256. https://doi.org/10.12386/A2011sxxb0025
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    The synchronization of the n-dimensional second order lattices of coupled oscillators with external periodic forces under Dirichlet, Neumann, Periodic boundary conditions are studied by introducing a new norm in the phase space. For the system with Dirichlet boundary condition, if the first order partial derivatives of the nonlinear term are bounded, and the coupled coefficients are both large enough, the system will be bounded dissipative and the solutions of the system will be synchronized to each other. For the system with Neumann or Periodic boundary condition, if the variation of the out force of different subsystems and the variation of the nonlinear terms of different subsystems are both small, the system is bounded dissipative and the coupled coefficients are both large enough, then all the components of any one solution of the system will be asymptotic synchronized to each other. Moreover, for the above two cases, when the coupled coefficients c1 → +∞, c2 → +∞, all the components of any one solution of the systems will be synchronized to each other.

     

  • Yin Ying KONG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 257-264. https://doi.org/10.12386/A2011sxxb0026
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    By using Ahlfors’ covering surface method, we establish the existence theory on a new singular radius of an algebroidal function in the unit disc, namely T-radius, and apply a Type-function of infinite order to extend some results of meromorphic functions.

     

  • Yan XU, Jian Ming CHANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 265-270. https://doi.org/10.12386/A2011sxxb0027
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    Let F be a family of meromorphic functions defined in a domain D, let ψ ( 0) be a holomorphic function in D, and k be a positive integer. If, for every f ∈ F, f ≠ 0, f(k) ≠ 0 and all zeros of f(k)(z) - ψ(z) have multiplicities at least (k + 2)/k, then F is normal in D.  
  • Fang Gui WANG, Jia Li LIAO
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 271-284. https://doi.org/10.12386/A2011sxxb0028
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    Let R be a ring and let S be a family of left modules. A left module E is called S-injective if ExtR1(N,E) = 0 for any N ∈ S. In this paper it is shown that if S is a Baer family of modules, then the Baer Criterion for S-injective modules holds and that if S is a complete family of modules, then every module has an S-injective envelope. A module E is called max-injective if ExtR1(N,E) = 0 for any simple module N. A module E over a commutative ring R is called reg-injective if ExtR1(N,E) = 0 for any torsion module N. It is shown that every module has a max-injective envelope and that a commutative ring R is an SM ring if and and if the reg-injective envelope e(T/R) of T/R is Σ-reg-injective, where T = T(R) is the total quotient ring of R; if and only if every GV -torsion-free reg-injective module is Σ-reg-injective.

     

  • Zheng Jie CHENG, Shang Zhi LI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 285-292. https://doi.org/10.12386/A2011sxxb0029
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    It is shown that every finit p-group is isomorphic to certain subgroups of U(n,Zp) for some positive integrer n, and the maximal subgroups and sub-maximal subgroups of U(n,Zp) are obtained.

     

  • Jing Cheng DONG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 293-300. https://doi.org/10.12386/A2011sxxb0030
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    Let k be an algebraically closed field of characteristic zero, H a semisimple Hopf algebra of dimension pq2 of Frobenius type, where p, q are distinct prime numbers. This paper proves that if p > q and H* is also of Frobenius type then H is a biproduct of a group algebra A of dimension q2 and a Yetter-Drinfeld Hopf algebra R over A of dimension p. That is HR#A. As an example, this paper then proves that every semisimple Hopf algebra of dimension 63 or 68 is of Frobenius type.

     

  • Yong Zhen PEI, Hui Na WANG, Chang Guo LI, Shu Jing GAO
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 301-312. https://doi.org/10.12386/A2011sxxb0031
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    A basic model of immune with Logistic growth and Holling type-II functional response has been studied. By choosing the time delay as the parameter, the stability of the positive equilibrium and the existence of the Hopf bifurcation are investigated. By using the normal form theory and the center argument, the explicit formulae which determine the stability and the direction are derived. Finally, numerical simulations supporting our theoretical results are also included.

     

  • Yun Nan ZHANG, Li Qiong LIN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 313-320. https://doi.org/10.12386/A2011sxxb0032
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    This paper discusses the K0-group of the operator algebra B(X) on Banach space X and gives two sufficient conditions for K0(B(X)) = Z2.

     

  • Wei Ping LI, Tian Ze WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 321-328. https://doi.org/10.12386/A2011sxxb0033
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    The present paper proved that if λ, μ are non-zero real numbers, not both negative, λ is irrational, and k is a positive integer, then there exist infinitely many primes p and pairs of primes p1, p2 such that [λp1p22] = kp. In particular [λp1p22] represents infinitely many primes.

     

  • Zhao Xiang LI, Han REN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 329-332. https://doi.org/10.12386/A2011sxxb0034
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    In this paper, the estimation of the number of maximum genus nonorientable embeddings of graphs is studied, and an exponential lower bound for such number is found. Applying the theory of current graph, K12s has at least 23s-2 distinct minimum genus embedding in non-orientable surfaces; K12s+3 has at least 22s distinct minimum genus embedding in non-orientable surfaces; K12s+7 has at least 22s+1 distinct minimum genus embedding in non-orientable surfaces.

     

  • Ai Ju DONG, Cheng Jun HOU, Jun TAN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 333-342. https://doi.org/10.12386/A2011sxxb0035
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    We study Kadison-Singer lattices in the matrix algebra Mn(C), and prove that each Kadison-Singer lattice generating M3(C) as an algebra is similar to L0 or I-L0, where L0 is the KS lattice generated by a maximal nest of diagonal projections and a rank one projection matrix with nonzero entries in M3(C), hence each Kadison-Singer algebra with trivial diagonal in M3(C) has dimension 4. In addition, we give some examples of nonisomorphic Kadison-Singer lattices which generate M4(C).

     

  • Xiao Feng YE
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 343-352. https://doi.org/10.12386/A2011sxxb0036
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    In the setting of homogeneous space (X, ρ, μ), it is shown that the commutators of Calderón-Zygumund operator and Potential operator with BMO function are bounded in Grand Morrey space, which contains the grand Lebesgue space and Morrey space. Moreover, all results are new even for Euclidean spaces.