中国科学院数学与系统科学研究院期刊网

15 July 2004, Volume 47 Issue 4
    

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  • Jian Yong QIAO,Jun Yang GAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 625-628. https://doi.org/10.12386/A2004sxxb0079
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    Baker established the existence of Fatou component of any given connectivity by using the method of quasiconformal mappings. Furthermore, Shishikua suggested giving explicit examples of rational mappings with a Fatou component of a given con- nectivity number. In this paper, we prove a rather perfect result on the basis of Beardon's research.
  • Ming Ju LIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 629-640. https://doi.org/10.12386/A2004sxxb0080
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    Let F be a regular homogeneous distribution of degree λ,-Q≤λ<0. We study the boundedness of operators g * F on Lebesgue spaces with power weight and Herz-type Hardy spaces, where g is a suitable function. Moreover, the bounded- ness properties of some commutators [b, T] on Herz spaces are proved, where [b, T] is generated by b ∈ BMO(H~n) and T is a linear operator.
  • Chuan Xi ZHU(1),Zong Ben XU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 641-646. https://doi.org/10.12386/A2004sxxb0081
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    In this paper, new concepts of random forced operator and random powerful monotonous operator are introduced. Random solution of a class of random operator equations is investigated in the Hilbert space. In the meantime, the famous Kras- noselkii's theorem is generalized.
  • Jie FANG(1),Li Yun WU(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 647-652. https://doi.org/10.12386/A2004sxxb0082
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    In this paper, we investigate some properties of ideals and filters of a pO- algebra.
  • Gui Mei AN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 653-656. https://doi.org/10.12386/A2004sxxb0083
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    In this paper, we show that the isometry between the unit spheres of certain normed space and its dual space can be extended to a real linear isometry on the whole space. Furthermore, we give a characterization of the isometry from the unit sphere of a smoothly normed reflexive Banach space onto that of its dual space.
  • Ming XU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 657-670. https://doi.org/10.12386/A2004sxxb0084
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    In this paper, we consider the L~p boundedness of generalized Riesz transform associated with nondivergent elliptic operators, and solve by means of wavelets the probelm about the L~p (2≤p<∞) boundedness of Riesz transform under the condition that its BMO norm of coefficients is small enough.
  • Li Huang TU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 671-676. https://doi.org/10.12386/A2004sxxb0085
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    We generalize the Clemens-Schmid exact sequence to the where that the singular fiber of one-parameter family has arbitrary singularities.
  • Lu LIN(1),Ya Sheng YE(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 677-686. https://doi.org/10.12386/A2004sxxb0086
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    In this paper, we give an improved second main theorem and a unique- ness theorem concerning multiple value for meromorphic functions of several complex variables (see [1-16]).
  • Xiao Chun FANG,Rong CHENG, Bo
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 687-694. https://doi.org/10.12386/A2004sxxb0087
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    This paper is about the C~*-algebras of possibly row-infinite directed graphs. For a possibly row-infinite directed graph E, we introduce the set s(μ,ν), by which the strong operator topology on the row-infinite vertices is algebraically represented. Moreover, a *-algebra H_E with rich structure is constructed, by which the existence of the universal C~*-algebra generated by Cuntz-Krieger E-family {s_e, p_ν} is proved. We also proved that the H_E and C~*(E) are the isomorphism invariants of E.
  • Ming Qiang WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 695-702. https://doi.org/10.12386/A2004sxxb0088
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    Let H denote the set of all nature numbers N such that N≡a+b~2 (mod q) has solutions in reduced residues a, b mod q, for any positive integer q. Let E(x) be the number of all N
  • Yu Shen HUANG(1), Liang Yu LIN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 703-710. https://doi.org/10.12386/A2004sxxb0089
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    By using the technique of integral transformation, the authors give a new definition of Hadamard principal value of singular integrals of higher order partial derivatives for the integral of Bochner-Martinelli type on a closed smooth orientable manifold in C~n. The Plemelj formula and compsite formula of higher order singular integral are obtained. The regularization of differential singular integral equations with linear variable coefficients is discussed. The differential singular integral equation can be transformed into an equivalent Fredholm equation, whose characteristic equation has an unique solution in L~* under suitable boundary value conditions.
  • Xie Ping DING
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 711-722. https://doi.org/10.12386/A2004sxxb0090
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    In this paper, some new generalized KKM type theorems for G-KKM, gener- alized G-KKM and generalized S-KKM mappings with finitely closed values and with finitely open values are established in noncompact G-convex spaces. By using these KKM type theorems, some new Ky Fan type minimax inequalities and saddle poiat theorems are obtained in G-convex space. These results generalize a number of known results in the recent literature.
  • Ji Gen PENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 723-730. https://doi.org/10.12386/A2004sxxb0091
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    This paper is concerned with the representation problem of nonlinear semi- group of Lipschitz operators. By developing a series of novel dual notions of Banach space and Lipschitz operator, it is shown that a nonlinear semigroup of Lipschitz op- erators can induce a C_0~*-semigroup in Lipschitz dual space. Hence, it is proved that a nonlinear semigroup of Lipschitz operators can be isometrically embedded into a certain C_0-semigroup. On the basis of these results, a series of novel representation formulas for this type of nonlinear semigroup are therefore established.
  • Xue Kun LIU(1),Dao Chun(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 731-734. https://doi.org/10.12386/A2004sxxb0092
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    In this paper, a new normal criterion of algebroidal function is proposed by applying the main theorems on covering surface, which overcomes some difficulties caused by the multivaluedness and bifurcation points. We continue to prove the fol- lowing result: For those algebroidal function families where the bifurcation points are shared, the function family is normal, if every function in these families is not equal to three different values.
  • Qian LU(1),Run Sheng HAN(2),Yo
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 735-740. https://doi.org/10.12386/A2004sxxb0093
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    Let f(z) be a function meromorphic on the plane |z|<+∞ with finite order. We point out that F_δ-sets of Valiron deficient functions of f(z) must be μ-sets, eliminating the restriction for the pole of f(z) in the Chen's result. Finally we find that the corresponding conclusion also holds for meromorphic functions with infinite order.
  • Xian WU,Fu Kun ZHAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 741-746. https://doi.org/10.12386/A2004sxxb0094
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    In the present paper, a new fixed point theorem for upper semi-continuous multivalued mappings in H-spaces is established, and as its applications, two new existence theorems for the solutions of quasi-variational inequalities are obtained.
  • Luan Chuan ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 747-750. https://doi.org/10.12386/A2004sxxb0095
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    Let E be a Hilbert C~*-module. We prove that each closed submodule of E is a complemented submodule if and only if each non-zero hereditary C~*-subalgebra B of K(E) has the form B = pK(E)p, where p is a projection in L(E).
  • Di GENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 751-762. https://doi.org/10.12386/A2004sxxb0096
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    In this paper, a class of Dirichlet boundary problem of p-Laplacian operators is studied. The problem involves non-odd symmetric critical nonlinearity. Existence of infinitely many solutions of this problem is obtained with improved Compactness- Concentration principle.
  • Ming Shu PENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 763-768. https://doi.org/10.12386/A2004sxxb0097
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    In this paper, we offer some new criteria for the study of the oscillatory properties of solutions to a class of second-order quasilinear differential equations, which correct, improve and extend some results obtained in some recent papers.
  • Jun LI,Suo Ping LI,Ya Feng XIA
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 769-780. https://doi.org/10.12386/A2004sxxb0098
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    By the use of the infinite product of evenly distributed probability spaces, this paper introduces the theory of truth degrees in Lukasiewicz n-valued propositional logic. It is proved that the set of truth degrees of propositions with 3≤n≤17 is dense in [0, 1], and the expressions of truth degrees are obtained. Morever, a pseudo- metric on the set of propositions is defined by means of the concept of truth degrees of propositions and a possible framework for approximate reasoning is proposed.
  • Jin Bao JIAN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 781-792. https://doi.org/10.12386/A2004sxxb0099
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    In this paper, the nonlinear inequality constrained optimization problems without the strict complementarity condition are discussed, and a new algorithm of se- quential systems of linear equations (i.e. SSLE) for the problems is proposed. At each iteration, the algorithm solves only one system of linear equations or computes a gen- eralized gradient projection, where the approximate Hessian of the Lagrange function is not necessary positive definite. Under weaker coditions, we prove that the algo- rithm possesses global, strong, and supperlinear convergence, and a rate of quadratic convergence. Some efficieat numerical experiments are given.
  • Liu Juan CHEN(1),Jian Hua SUN(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 793-798. https://doi.org/10.12386/A2004sxxb0100
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    In this paper, we consider a class of predator-prey models with functional response kx~θ and prove that the system has a unique limit cycle if and only if the singular point in the first quadrant is unstable.
  • Si Ze LI,Chuan Qi LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 799-804. https://doi.org/10.12386/A2004sxxb0101
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    Let A be an Artin algebra, Γ_A be Auslander-Reiten quiver of A. We obtain that a preprojective component Γ of Γ_A is a τ-preprojective component of Γ_A if Γ contains no oriented cycles, and that Γ is a preprojective componeat of Γ_A if and only if Γ is a τ-preprojective component of Γ_A for a quasitilted algebra A.
  • La Mei HE
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 805-810. https://doi.org/10.12386/A2004sxxb0102
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    In this paper, a new kind of Pickands-type estimator is proposed when the index of an extreme-value distribution is negative. The consistency, rate of strong convergency and asymptotic distribution of the estimator are established.
  • Zhao Hong SUN(1),Chang HE(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 811-818. https://doi.org/10.12386/A2004sxxb0103
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    In the paper, we obtain some iterative approximation theorems of fixed points for asymptotically nonexpansive mappings with error member in uniformly convex Banach space. Our results improve and extend some recent results. Also, the methods of proof given in this paper are quite different.
  • Zhao Hui XIONG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 819-824. https://doi.org/10.12386/A2004sxxb0104
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    In this paper, we shall prove the following theorem: Let X be the inverse limit of an inverse system {X_α,π_β~α, } and || = λ. Suppose that each projeetion π_α: X→X_α is an open and onto map and X is λ-paracompact and λ-Screenable. If each X_α is σ-fully normal (resp., screenab1e, σ-collectionwise normal), then X is σ-full normal (resp., screenable, σ-collectionwise normal). As a corollary of the result the normal σ-fully normality satisfies the inverse limit theorem in the usual type as in [1]. Moreover, we shall obtain the anologous result for hereditarily σ-fully normality.
  • Guo Dong LIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(4): 825-828. https://doi.org/10.12386/A2004sxxb0105
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    For any prime p≡5 (mod 8), we prove E_((p-1)/2) 0 (mod p), where E_(2n) are Euler numbers.