中国科学院数学与系统科学研究院期刊网

15 December 2002, Volume 18 Issue 4
    

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  • Chun Lei CAO, Yue Fei WANG
    Acta Mathematica Sinica. 2002, 18(4): 625-630. https://doi.org/10.1007/s10114-002-0217-3
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    We shall show that for certain holomorphic maps, all Fatou components are simply connected. We also discuss the relation between wandering domains and singularities for certain meromorphic maps.
  • Tian Liang TU
    Acta Mathematica Sinica. 2002, 18(4): 631-646. https://doi.org/10.1007/s10114-002-0202-x
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    Let D be a smooth domain in the complex plane. In D consider the simultaneous approximation to a function and its ith (0 ≤iq) derivatives by Hermite interpolation. The orders of uniform approximation and approximation in the mean, are obtained under some domain boundary conditions. Some known results are included as particular cases of the theorems of this paper.
  • Yong Gao CHEN, Chun Gang JI
    Acta Mathematica Sinica. 2002, 18(4): 647-660. https://doi.org/10.1007/s10114-002-0212-8
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    Let Fp,t(n) denote the number of the coefficients of (x1+x2+…+xt)j, 0 ≤jn-1, which are not divisible by the prime p. Define Gp,t(n) = Fp,t/nθ and β(p,t) = lim infFp,t)(n)/nθ, where θ = (log (t/p + t -1))/(logp). In this paper, we mainly prove that Gp,t can be extended to a continuous function on R+, and the function Gp,t is nowhere monotonic. Both the set of differential points of the function Gp,t and the set of non-differential points of the function Gp,t are dense in R+.
  • Yin Sheng JIANG
    Acta Mathematica Sinica. 2002, 18(4): 661-670. https://doi.org/10.1007/s10114-002-0215-5
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    The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderón-Zygmund operators on these Hardy spaces are studied.
  • An Ping LIAO, Zhong Zhi BAI
    Acta Mathematica Sinica. 2002, 18(4): 671-678. https://doi.org/10.1007/s10114-002-0204-8
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    We study the symmetric positive semidefinite solution of the matrix equation AX1AT + BX2BT = C, where A is a given real m×n matrix, B is a given real m×p matrix, and C is a given real m×m matric, with m, n, p positive integers; and the bisymmetric positive semidefinite solution of the matrix equation DT XD = C, where D is a given real n×m matrix, C is a given real m×m matrix, with m, n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.
  • Wan MA, Gen Sun FANG
    Acta Mathematica Sinica. 2002, 18(4): 679-686. https://doi.org/10.1007/s10114-002-0198-2
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    The exact order of ε-complexity is determined in Lp (2 ≤p < ∞) spaces for the second kind of Fredholm integral equations with kernels belonging to an isotropic Sobolev class.
  • Yong Zheng ZHANG
    Acta Mathematica Sinica. 2002, 18(4): 687-700. https://doi.org/10.1007/s10114-002-0205-7
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    Let F be a field of characteristic p > 3, and L = ⊕i≥minus;1 Li the finite-dimensional transitive Z-graded simple Lie superalgebral over F. In this paper L is determined if the Z-graded Lie superalgebra L-1L0 is isomorphic to the L-1pl (L-1) or L-1spl (L-1).
  • Bao She WEI
    Acta Mathematica Sinica. 2002, 18(4): 701-718. https://doi.org/10.1007/s10114-002-0180-z
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    In this paper, we consider certain mappings, M, sufficiently close to an integrable one, which is weakly reversible with respct to the mappings G sufficiently close to an involution of tye (m, n), where m, nZ+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for providing the existence of a Cantor family of m-tori invariant under the reversible mappings M and the reversing mapping G.
  • Si Long PENG
    Acta Mathematica Sinica. 2002, 18(4): 719-726. https://doi.org/10.1007/s10114-002-0206-6
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    In this paper, a large class of two-dimensional orthogonal wavelet filters, (lowpass and highpass), are presented in explicit expression. We also characterize the filters with linear phase in this case. Some examples are also given, including non-separable filters with linear phase.
  • Wen Sheng WANG
    Acta Mathematica Sinica. 2002, 18(4): 727-736. https://doi.org/10.1007/s10114-002-0185-7
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    Let {W(t); t≥ 0} be a standard Wiener process and S be the Strassen set of functions. We investigate the exact rates of convergence to zero (as T→∞) of the variables 0 ≤ tT-aT inf fS sup 0≤x≤1|Yt, T(x)-f(x)| and 0 ≤ tT-aT sup 0≤x≤1|Yt, T(x)-f(x)| for any given fS, where Yt, T(x)=(W(t+xaT)-W(t))(2aT(logTaT-1+loglogT))-1/2. We establish a relation between how small the increments are and the functional limit results of Csörgö-Révész increments for a Wiener process. Similar results for partial sums of i.i.d. random variables are also given.
  • Lin Ping PENG
    Acta Mathematica Sinica. 2002, 18(4): 737-754. https://doi.org/10.1007/s10114-002-0196-4
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    In this paper, we make a complete study of the unfolding of a quadratic integrable system with a homoclinic loop. Making a Poincaré transformation and using some new techniques to estimate the number of zeros of Abelian integrals, we obtain the complete bifurcation diagram and all phase portraits of systems corresponding to different regions in the parameter space. In particular, we prove that two is the maximal number of limit cycles bifurcation from the system under quadratic non-conservative perturbations.
  • Bao SHI
    Acta Mathematica Sinica. 2002, 18(4): 755-764. https://doi.org/10.1007/s10114-002-0188-4
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    In this paper, we first consider a delay difference equation of neutral type of the form:
    (1*)
    and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241-248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n → ∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form:
    ×Ω (2*)
    study various cases of p in the neutral term and obtain that if p ≥ -1 then every non-oscillatory solution of (2*) tends uniformly in m ∈ Ω to zero as n → ∞; if p = -1 then every solution of (2*) oscillates and if p < -1 then every non-oscillatory solution of (2*) goes uniformly in m ∈ Ω to infinity or minus infinity as n → ∞ under some hypotheses.
  • Jian Hua CHEN
    Acta Mathematica Sinica. 2002, 18(4): 765-778. https://doi.org/10.1007/s10114-002-0189-3
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    In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from to space forms Mn(c) by introducing 2-parameter loop algebra.
  • Shu Qing MA, Qian Shun CHANG
    Acta Mathematica Sinica. 2002, 18(4): 779-800. https://doi.org/10.1007/s10114-002-0207-5
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    In this paper we consider a semi-dicretized nonlinear Schrödinger (NLS) equation with local integral nonlinearity. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds for the Hausdorff and fractal dimensions of the discrete attractors are obtained, and the various bounds are independent of the mesh sizes. Furthermore, numerical experiments are given and many interesting phenomena are observed such as limit cycles, chaotic attractors and a so-called crisis of the chaotic attractors.
  • Yi Hu YANG
    Acta Mathematica Sinica. 2002, 18(4): 801-802. https://doi.org/10.1007/s101140100152
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    In this note, we will show that no nonuniform lattice of SO (3, 1) can be the fundamental group of a quasi-compact Kähler manifold. Thus, combining with the result in[1], one gets that a nonuniform latice in SO(n, 1)(n≥ 3) cannot be π1 of any quasi-compact Kählerian manifold.
  • Xiang ZHANG
    Acta Mathematica Sinica. 2002, 18(4): 803-816. https://doi.org/10.1007/s101140100167
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    In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanquian Ye.
  • Qiang Xiang HUANG, Ji Xiang MENG, Fu Ji ZHANG
    Acta Mathematica Sinica. 2002, 18(4): 817-822. https://doi.org/10.1007/s10114-002-0220-8
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    In this paper, we completely determine the connectivity of every infinite circulant digraphs and prove that almost all infinite circulant digraphs are infinitely strongly connected and therefore have both one-and two-way infinite Hamiltonian paths.
  • Xiao Dong ZHANG, Jiong Sheng LI
    Acta Mathematica Sinica. 2002, 18(4): 823-832. https://doi.org/10.1007/s10114-002-0222-6
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    In this paper, we prove that the set of all factorization indices of a completely positive graph has no gaps. In other words, we give an affirmative answer to a question raised by N. Kogan and A. Berman[8] in the case of completely positive graphs.