中国科学院数学与系统科学研究院期刊网

15 February 2004, Volume 47 Issue 2
    

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  • Yao Chen ZHU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 209-218. https://doi.org/10.12386/A2004sxxb0028
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    In the present note the algebraic independence of values of certain functions denned by infinite products at algebraic and transcendental points is given.
  • Lu Chuan ZENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 219-228. https://doi.org/10.12386/A2004sxxb0029
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    The purpose of this paper is to investigate the problem of approximating to the fixed points of uniformly Lipschitzian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors. Under the condition of removing the restriction limn→∞βn = 0 we prove that Professor Zhang Shisheng's results (Acta Math. Appl. Sinica, 2001, 24 (2): 236-241) remain true. On the other hand, we also extend his results to the case of the modified Ishikawa iterative sequences with errors.
  • Dong Hai LIU,Bai Qi MIAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 229-240. https://doi.org/10.12386/A2004sxxb0030
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    In our paper, under the condition that u1(t) is increasing, and the vector function tu1(‖t‖) is Lipschitz continuous and other mild conditions, we show the recursive algorithms proposed are strongly consistent.
  • Ting Fang ZHANG(1),Ding Xing Z
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 241-250. https://doi.org/10.12386/A2004sxxb0031
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    In this paper, we prove the reduction of codinemsion for the surfaces in Sn with vanishing Moebius form and flat Moebius normal bundle, and classify this sort of surfaces. Moreover, we also give a classification of the surfaces with vanishing Moebius form in Sn.
  • Jing Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 251-258. https://doi.org/10.12386/A2004sxxb0032
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    In this paper, the σ-semi-convexity is introduced and a general Ekeland's variational principle in locally convex spaces is given.
  • Xiao Hong CAO,Mao Zheng GUO,Bi
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 259-264. https://doi.org/10.12386/A2004sxxb0033
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    If T is a regular operator on a Banach space X, with finite dimensional intersection K(T) ∩ N(T) and K(T) closed, and if 5 is invertible, commutes with T and has sufficiently small norm, then T - S is an upper semi-Fredholm operator. If in addition K(T) + N(T) or R(T) + N(T) has a complementary subspace with finite dimension, then T ?S is a Fredholm operator.
  • Li Hong CUI(1),Qi Xiang YANG(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 265-272. https://doi.org/10.12386/A2004sxxb0034
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    Q spaces (or Qp, or Qα spaces), are studied heavily by many authors. In particular, Wu and Xie generalized Q spaces to the Qpα,q spaces in recently. In this paper, we show first the equivalence of some real variable characterization and wavelet characterization for general Q spaces. Our main idea is to use In dimensional wavelet to analyze the elements in Qpα,q on Rn. Furthermore, we construct the pre-dual spaces Ppα,q of Qpα'q, where Ppα,q are generated by atoms which are denned by wavelets.
  • Jun LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 273-278. https://doi.org/10.12386/A2004sxxb0035
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    In this paper, we will prove some new inequalities on sequences. As applications of our theorems, we introduce a new kind of iterative procedure, and give a proof of the convergence for it. Furthermore, we show that it is equivalent to the Ishikawa iterative sequence which is well known.
  • Hui Li YAO(1),Chuan Yi ZHANG(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 279-284. https://doi.org/10.12386/A2004sxxb0036
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    In this paper, we give the conditions of existence of positive almost periodic type solutions for some nonlinear delay integral equations.
  • Qing De ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 285-290. https://doi.org/10.12386/A2004sxxb0037
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    Let f(z) be a nonlinear meromorphic function in the complex plane satisfying Ni(r,1/f) = S(r, f), and c be any nonzero complex number. Then we have T(r, f) < 11{N(r, f) +N(r, 1/f'-c} + S(r, f), where N1(r, 1/f) denotes the counting function of the simple zeros of the function f(z).
  • Yan SONG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 291-298. https://doi.org/10.12386/A2004sxxb0038
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    This paper discusses the Poincare bifurcation for a class of cubic Hamiltonian systems with a global center. We prove that its Poincare bifurcation can produce two limit cycles at most and may produce two limit cycles.
  • Shi Ping LU(1),Wei Gao GE(2),Z
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 299-304. https://doi.org/10.12386/A2004sxxb0039
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    By employing the continuation theorem of coincidence degree theory developed by Mawhin, we study a kind of Rayleigh equation with a deviating argument as follows x11(t) + f(x'(t)) + g(x(t -?τ(t))) = p(t), and some new results on the existence of periodic solutions are obtained. Our work generalizes the knowen result (see [8]).
  • Guang Sheng WEI,Zong Beng XU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 305-316. https://doi.org/10.12386/A2004sxxb0040
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    In this paper, a necessary and sufficient condition for an operator to be a bound-limited self-adjoint extension of a singluar Sturm-Liouville operator is obtained. As a consequence, all possible forms of the bound-limited self-adjoint extensions are characterized via complete classification of the self-adjoint boundary conditions. Also, this result can answer directly the equal cases of the inequalites among the minimal eigenvalues for singular Sturm-Liouville problems.
  • Guo Jun WANG(1),Qing Yan SONG(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 317-326. https://doi.org/10.12386/A2004sxxb0041
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    Let B be a Boolean algebra and Ω be the set of all homomorphisms from B into {0,1}, and μ be a probabitity measure on Ω. We introduce the concepts of sizes of elements of B and similarity degrees of pairs of elements of B by means of μ, and then define therefrom a metric on B. As an application, the recently proposed approximate reasoning theory for propositional logic can be improved.
  • Yan Min YIN(1),Ding Guo WANG(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 327-336. https://doi.org/10.12386/A2004sxxb0042
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    In this paper, we discuss mainly the integral theory for weak quasi-Hopf algebras. First we generalize the fundamental structure theorem on Hopf-modules to weak quasi-Hopf algebras. Introducing the definitions of integral and cointegral we also consider the symmetry and semisimplicity of the finite-dimensional weak quasi-Hopf algebra.
  • Jing Xin BAI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 337-342. https://doi.org/10.12386/A2004sxxb0043
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    In this paper, it is proved that for any positive integer K, ther a exists a planar n-polynomial system which has a series of big limit cycles, and the number of the big limit cycles is at least K. Furthermore, there are many small limit cycles between any of them.
  • Tai Xiang SUN(1),Rong Bao GU(2
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 343-348. https://doi.org/10.12386/A2004sxxb0044
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    Let X be a hereditarily decomposable chainable continuum with finite order, f : X → X be a continuous self-map of X, On(x, f) = {fi(x) : 0 ≤ i ≤ n} be a return trajectory of f, and inf{On(x, f)} < p - f(p) < sup{On(x, f)}. In this paper, we prove that if there exist k centripetal points of f in {fi(x) : Q ≤ i ≤ n - 1} relative to p, then f has periodic points with some odd period 1 < R ≤ (n - 2)/k + 2.
  • Fu Kui GUO(1),Yu Feng ZHANG(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 349-364. https://doi.org/10.12386/A2004sxxb0045
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    First a new isospectral problem with 11 potentials is established in the present paper. That a new Lax pair is presented whence, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses 4-Hamiltonian structures. It is proved that the conjugate operator of the recursive operator is of hereditary symmetry, after making some reductions, the well-known AKNS hierarchy and the other hierarchies of evolution equations are obtained. In addition, in order to illustrate that the soliton hierarchy obtained in the paper possesses 4-Hamiltonian structures exactly, we prove that the linear combination of 4-Hamiltonian operators admitted are also a Hamiltonian operator constantly.
  • Mao Fa WANG,Pei De LIU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 365-370. https://doi.org/10.12386/A2004sxxb0046
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    In this paper, we study the connection between norms of composition operators on the Bergman space and the reproducing kernels. It is shown that when C is compact then the action of its adjoint C* on the set of normalized reproducing kernels of Bergman space determines the norm of C if and only if (0) = 0 or has the affine form z → sz +t for some constants s and t satisfying |s |+ |t| < 1.
  • Hui Sheng PEI,Hong Cun ZHAI,Yo
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 371-378. https://doi.org/10.12386/A2004sxxb0047
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    The relationship between the a-congruences on T(X, Y, θ) and the Tθ -equivalences on the set Y is investigated. It is proved that for each Tθ- equivalence E on Y, the greatest element in the complete sublattice γ-1(E) of C(T(X, Y, θ)) is an α-congruence. And it is verified that the Symons' congruences Z, d are two a-congruences for any sandwich semigroup. The smallest (greatest) α-congruences on S(X, Y, θ) are determined for some topological spaces X, Y.
  • Gen Qiang WANG(1),Ju Rang YAN(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 379-384. https://doi.org/10.12386/A2004sxxb0048
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    In this paper, we discuss the following nonlinear neutral delay equation: [x(t) + cx(t - τ)]" + g(t,x(t - σ)) - p(t), by using the coincidence degree theory. A sufficient condition for the existence of periodic solution of the equation is given.
  • Xian Gao LIU(1),Sheng Hong LI(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 385-388. https://doi.org/10.12386/A2004sxxb0049
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    In this paper, we prove the existence of global weak solutions of the p-harmonic flow with potential between Riemannian manifolds M and N for arbitrary initial data having finite p-energy in the case when the target N is a homogeneous space with a left invariant metric.
  • Huan Yin CHEN(1),Hou Rong QING
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 389-392. https://doi.org/10.12386/A2004sxxb0050
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    We obtain a new substitution for modules over exchange rings satisfying the related comparability. Also we investigate the structure of modules over exchange rings satisfying the power comparability, and provide a new class of exchange rings satisfying the related comparability.
  • Jin Kun LIN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 393-402. https://doi.org/10.12386/A2004sxxb0051
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    This paper constructs a new family in the stable homotopy of spheres πt-6S represented by hng0γ3 ∈ E26,t in the Adams spectral sequence which revisits the bn-1g0γ3-elements ∈ πt-7S constructed in [1], where t - 2pn(p- l) + 6(p2+p+1)(p- 1) and p ≥ 7 is a prime, n ≥ 4.
  • Hong Jun LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(2): 403-412. https://doi.org/10.12386/A2004sxxb0052
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    In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial data, we give an explicit expression of all the curvatures for some Riemannian metric. The method is applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.