中国科学院数学与系统科学研究院期刊网

15 May 2002, Volume 45 Issue 5
    

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  • Lan Zhe LIU(1),Shan Zhen LU(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 833-840. https://doi.org/10.12386/A2002sxxb0108
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    In this paper, the boundedness properties of some sublinear operators on Herz type Hardy spaces are obtained, and the boundedness of Bochner-Riesz operator on Herz type Hardy spaces is proved.
  • Yi Sheng HUANG,Yu Ying ZHOU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 841-846. https://doi.org/10.12386/A2002sxxb0109
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    By using the variational method, we discuss the existence of solution of the boundary value problem-△pu=μQ(x)|u|p-2u+f(x,u), u∈D01,p(Ω), where Ω is an open set of RN, 10 and both functions Q and f may change sign.
  • Jian Lin LI(1),Guang Sheng WEI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 847-850. https://doi.org/10.12386/A2002sxxb0110
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    Let f(w) be an analytic and univalent function in a convex domain D. Sharp bounds on the estimates of |f(n)(w)/f'(w)| are found for all w in D and 2≤n≤8. These estimates generalize several known results.
  • Cai Shi WANG(1),Zhi Yuan HUANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 851-862. https://doi.org/10.12386/A2002sxxb0111
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    A nonlinear quantum stochastic Cable equation in terms of generalized operators and their Wick products is investigated. The existence and uniqueness of the solution are established, and the continuous dependence on the initial process and other properties are proved for the solution.
  • Zhao Fang BAI(1),Jin Chuan HOU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 863-870. https://doi.org/10.12386/A2002sxxb0112
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    Let H be a complex Hilbert space, B(H) denote the algebra of all linear bounded operators on H. In this note, the additive maps on B(H) preserving orthogonality and the additive maps on von Neumann algebra commuting with | ?|k are characterized.
  • Qing Cai ZHANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 871-876. https://doi.org/10.12386/A2002sxxb0113
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    The purpose of this paper is to study a question of G. Prank concerning that meromorphic functions share two finite values with their derivatives, and the following result is proved: Let f be a nonconstant meromorphic function, b be a nonzero finite complex constant. If f and f' share 0 CM, and share b IM, then f=f' or f=2b/1-ce-2x, where c is a nonzero finite complex constant.
  • Yi HONG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 877-884. https://doi.org/10.12386/A2002sxxb0114
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    In this paper, we study the eigenvalues and eigenfunctions of the symmetric space Sp(n)/U(n) by means of the group representation theory.
  • Jing Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 885-890. https://doi.org/10.12386/A2002sxxb0115
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    A locally convex space (E, T0) is called a WCM space if for any locally convex topology T weaker than T0, (E,T) and (E,T0) have the same weakly compact absolutely convex sets. We investigate the existence of such spaces and the relationship between the class of WCM spaces and the other classes of locally convex spaces. Moreover, we give a mapping characterization of WCM spaces.
  • Xiao Lin WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 891-898. https://doi.org/10.12386/A2002sxxb0116
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    Let (?) be a closed smooth contour in the complex plane, which boundsa finite region D+ and is continuous on D+∪(?). Using the generalized inverse of singular integral operators, we solve the following normal type of singular integral equations with kernel having singularities of order one: Applying the results obtained, we also give the solution of singular integral equations in the case when k(z) is a class of rational functions. The classical results for singular integral equation with Cauchy kernel and Hilbert kernel are thus extended.
  • Qiang ZHANG(1),Ke LIU(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 899-904. https://doi.org/10.12386/A2002sxxb0117
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    This paper discusses Lebesgue decomposition theorem of more general set functions, which generalizes the corresponding results in classical measure theory. And we also provide a new proof method for Lebesgue decomposition theorem of classical additive measure.
  • Zhi Dong TENG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 905-918. https://doi.org/10.12386/A2002sxxb0118
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    In this paper we study the permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with infinite delays. Some new sufficient conditions are established.
  • Guo Jun WANG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 919-924. https://doi.org/10.12386/A2002sxxb0119
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    Let Ω be the set of all Lukasiewicz valuations from the set F(S) of all propositions into the unit interval. This paper introduces in a natural way a fuzzy topology δ on Ω, and proves that δ is second countable and zero-dimensional and N-compact. Moreover, it is proved that the cut topology of δ on Ω is second countable, compact, and Hausdorff.
  • Xiao Jun HUANG,Yong Xing GU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 925-928. https://doi.org/10.12386/A2002sxxb0120
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    Let F be a family of meromorphic functions on a domain D and a, b, c be finite complex values, a≠6, c≠0. It is proved that F is a normal family, provided that for each f ?F, all zeros of f are of multiplicity at least k, andwhere we write . At the same time we show that the condition on multiple zeros of f is necessary.
  • Wei Hong HE(1),Zuo Ling ZHOU(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 929-934. https://doi.org/10.12386/A2002sxxb0121
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    In this paper, we construct a topologically mixing system whose measure center is a singleton, thus showing that a mixing system is complicated from the viewpoint of topology, but it can be very simple in the sense of ergodicity.
  • Ming Shu PENG(1),Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 935-940. https://doi.org/10.12386/A2002sxxb0122
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    In this paper, we obtain a global existence and uniqueness theorem for a second-order impulsive delay differential equation. Some sufficient conditions are also offered for the preservation of nonoscillatory behavior of solutions of second-order linear delay differential equations under impulsive perturbations, which extend and improve on some results obtained in the literature.
  • Xian Hua TANG(1),Jian She YU(2
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 941-952. https://doi.org/10.12386/A2002sxxb0123
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    In this paper, it is considered that the global existence and global attractivity of Logistic type functional differential equations with impulseswhich satisfies the initial conditions x(t)=(?)(t),t∈[g(0),0], (?)> PC(t). The theorems obtained contain and improve the existing results.
  • Jian XIAO,Li Ren SHENG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 953-958. https://doi.org/10.12386/A2002sxxb0124
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    In this paper, we study the structure problems of Dulac function for quadratic systems of type (II). As its application, we discuss the question of the non-existence of limit cycles and obtain some new results.
  • De Ming ZHU,Yu Zhen BAI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 959-968. https://doi.org/10.12386/A2002sxxb0125
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    A generalized KAM theorem for lower dimensional tori in Hamiltonian systems is obtained, which applies to the case where there are normal frequencies and hyperbolic normal components simultaneously. The proof is based on the combination of a smoothness of J. G. You's theorem and the theory of normally hyperbolic invariant manifolds. Two other generalizations are also given.
  • Li Xin LIU(1),Rong WU(2)
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 969-978. https://doi.org/10.12386/A2002sxxb0126
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    In this paper, we give some probability inequalites and moment inequalites of maximal partial sum for sequence of NA random variables, and some laws of the iterated logarithm of Teicher type and Egorov type for sequences of NA random variables are obtained.
  • Ting Fan XIE
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 979-986. https://doi.org/10.12386/A2002sxxb0127
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    In this paper, we give some new results of the mean convergence of Hermite-Fejer interpolation operators based on the nodes {xk}k=0n1, where X0=-1, xn+1=-1, xk (k=1,2,...,n) are the zeros of the n-th Jacobi polynomial.
  • Ji Cheng HOU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 987-990. https://doi.org/10.12386/A2002sxxb0128
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    Recently, Wu and Yuan in [1] extended Brouwer-Schauder-Tychonoff fixed point theorem to H- Spaces. The purpose of this paper is to establish a new fixed point theorem which improves on and generalizes Wu and Yuan's result in [1], by using a new approximation selection theorem for upper semicontinuous multivalued mappings.
  • Guang Shi Lv(1),Wen Guang ZHAI
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 991-100. https://doi.org/10.12386/A2002sxxb0129
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    Let △(x) be the error term in the asymptotic formula for D*(a, b;x)= 1 (1 0, △(x)
  • Xiang Yun XIE(1),Yong Lin CAO(
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 1005-101. https://doi.org/10.12386/A2002sxxb0130
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    In this paper, some characterizations for an ordered semigroup S to be a semilattice of archimedean semigroups, in particular, a chain of archimedeam subsemi-groups are given by some binary relations on S and the properties of radical subset of the ideals of S. The result that every semiprime ideal of S is the intersection of prime ideals containing it is proved by the concept of m-system of S. Furthermore, using the prime radical theorem, we prove that an ordered semigroup S is a chain of archimedean semigroups if and only if S is a semillatice of archimedean semigroups and all prime ieals of S is a chain. As an application the corresponding results [1] on semigroups without orders can be obtained by moderate modificaitons.
  • Yue Ping JIANG(1),Yu Ming CHU(
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 1011-101. https://doi.org/10.12386/A2002sxxb0131
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    In this paper, two invariants under conjugation of higher dimensional Mobius transformations are given and then two geometric J(?)rgensen's inequalities of discrete non-elementary Mobius groups in higher dimensions are obtained by using the given invariants and cross ratios of the fixed points. In particular, these inequalities are invariant under conjugation.
  • Zheng Hong YANG(1),Gong Ning C
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 1017-102. https://doi.org/10.12386/A2002sxxb0132
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    This paper introduces the so-called confluent generalized Cauchy matrix and deals with its displacement structure, inversion formula, invertibility criterion and its connection with the matrix rational tangential interpolation problem, and gives the fast algorithm for solving linear systems with such coefficient matrices. This paper generalizes the results of [1] and [2].
  • Bing XU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 1025-103. https://doi.org/10.12386/A2002sxxb0133
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    The main purpose of this paper is to present a new way to establish convergence of the weighted sums for strongly mixing sequences. Aa an application to the regression model, we give a strong consistent estimation of the regression function.
  • Xue Liang ZHENG
    Acta Mathematica Sinica, Chinese Series. 2002, 45(5): 1035-104. https://doi.org/10.12386/A2002sxxb0134
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    In this paper, we study the extensions on the upper half plane of the homeo-morphisms on the real axis.Using the quasisymmetric function, we get a relatively fine estimate of the dilatation function. In the meantime, we give a further characterization on D and p near the boundary by an induced boundary function. As applications, sufficient conditions of the existence of ID homeomorphism and IID homeomorphism are respectively presented.