中国科学院数学与系统科学研究院期刊网

15 January 2005, Volume 48 Issue 1
    

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  • Guo Jun WANG(1), Yong Cheng BA
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 1-10. https://doi.org/10.12386/A2005sxxb0001
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    It is proved that linear structures can be constructed by means of metrics on translation spaces under certain conditions. The concept of sub-normed Z-linear spaces is introduced and it is clarified that a translation space is a sub-normed Z-linear space if and only if its translation group is Abelian. Analogues the bounded linear operator theorem, the Hahn-Banach theorem and the resonance theorem are established in sub-normed Z-linear space.
  • Lun Hai LONG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 11-16. https://doi.org/10.12386/A2005sxxb0002
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    In this paper give an effective method to calculate the Hausdorff measure of Marion sets on straight line and show how to calculate the Hausdorff measures of fractals on straight line with some examples.
  • Bo ZHOU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 17-24. https://doi.org/10.12386/A2005sxxb0003
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    Let A be an n x n Boolean matrix with period p, 1≤i≤n. The generalized index of convergence k(A, i) of A is the least nonnegative integers k such that i rows of Ak and Ak+p are mutually equal. We characterize the extremal matrices of generalized indices of convergence of the n×n Boolean matrices with exactly d (1≤d≤n) non-zero diagonal entries.
  • Zhong Li WEI(1), Zhi Tao ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 25-34. https://doi.org/10.12386/A2005sxxb0004
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    This paper investigates the existence of positive solutions of singular su-perlinear boundary value problems of fourth order ordinary differential equations. A necessary and sufficient condition for the existence of C2[0,1] positive solutions as well as C3[0,1] positive solutions is given by means of the fixed point theorems on cones.
  • Bin LIU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 35-50. https://doi.org/10.12386/A2005sxxb0005
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    In this paper, we discuss the existence of positive solutions for a singular boundary value systems with p-Laplacian (φp(x'))' + α1 (t)f(x(t),y(t)) = 0, (φp(y'))' +α2(t)g(x(t),y(t)) = 0, x(0) - β1x'(0) = 0, x(1) +δx'(1) = 0, y(0) - β2y'(0) = 0, y(1) + δ2y'(1) = 0, where φp(x) = |x|p-2x, p > 1. By using the fixed-point index theorem, the sufficient conditions of the existence of one or multiple positive solutions for the boundary value systems under some conditions are established. These results can be applied to the study of the existence of the radial solutions for the elliptic boundary value systems.
  • Fei Long CAO
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 51-62. https://doi.org/10.12386/A2005sxxb0006
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    This paper investigates the relationship between the multivariate Stancu polynomials and the modulus of continuity. First, it is shown that the property of modulus of continuity is preserved by the multivariate Stancu polynomials and hence a corresponding one to univariate Bernstein polynomials is generalized. Then, by means of the Ditzian-Totik's modulus of continuity, the estimates of upper and lower bounds of rate for the polynomials approximating the continuous function are given. A necessary and sufficient condition on the smoothness of function is also obtained from the estimates so that the rate of approximation is O(n-a) (0 < a < 1).
  • Wu Hua CHEN(1), Zhi Hong GUAN(
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 63-74. https://doi.org/10.12386/A2005sxxb0007
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    In this paper, a one-dimensional perturbed neutral delay difference equation of the form: △(x(n) - cx(n - k)) = f(n,xn) + g(n,xn), n ∈ Z+ is considered. It is shown that under some conditions, the zero solution of the above equation is uniformly asymptotically stable provided that the zero solution of the corresponding equationwithout perturbation: △(x(n) - cx(n - k)) = f(n,xn), n∈Z+ is uniformly asymptotically stable. Some known results associated with this equation are extended and improved.
  • Wen Long WANG(1), Gen Qi XU(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 75-80. https://doi.org/10.12386/A2005sxxb0008
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    In this paper, a new characterization of eventually norm continuous semigroups on Hilbert space is given. By using the resolvent of the generator, we give the sufficient and necessary conditions for the semigroups to be being eventually norm continuous.
  • Qin Hai ZHANG, Li Fang WANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 81-88. https://doi.org/10.12386/A2005sxxb0009
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    A subgroup H of a group G is said to be semipermutable if it is permutable with every subgroup K of G with (|H|, |K|) = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. In this paper, we extend and improve some of Asaad and Pingchao Wang's results by examining the influence of s-semipermutability on the structure of groups.
  • Jing Hui QIU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 89-98. https://doi.org/10.12386/A2005sxxb0010
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    The relationship between the tangent cone, the tangent manifold and the tangent space of a convex a-body and the subdifferential of the Minkowski functional of the convex α-body is investigated. For each algebraic boundary point of a convex α-body, there exists a quasi-direct sum decomposition such that in the algebraic sense the boundary point is both a subspace smooth point and a quasi-complementary subspace strictly extreme point. The general results obtained are efficiently applied to the theory of polyhedral normed spaces.
  • Ke Mei ZHANG(1), Jing Xian SUN
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 99-108. https://doi.org/10.12386/A2005sxxb0011
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    In this paper, existence of the multiple solutions for a kind of superlinear operator equations is discussed via two coupled parallel sub-super solutions. The results obtained in this paper essentially improve the famous Amann three-solution theorem. As applications, a second order system of differential equations is considered.
  • San Yang LIU, Yu Qiang FENG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 109-114. https://doi.org/10.12386/A2005sxxb0012
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    In this paper, the techniques of partial order theory are used to study the solvability of a class of operator equations Lx = NX, where neither L nor N need to be continuous. Existence and multiplicity results are obtained in complete metric space and Banach space respectively, and then applied to a periodical boundary value problem of an intergro-differential equation.
  • Ren Xing NI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 115-124. https://doi.org/10.12386/A2005sxxb0013
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    In this paper, characteristic condition is given for a generalized steepest descent method to converge to the zeros of quasi-accretive locally bounded operators defined on proper subsets of a uniformly smooth real Banach space. These results extend and unify the corresponding ones by Xu Zhongben and Jiang Yaolin, and others.
  • Bing Ru ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 125-132. https://doi.org/10.12386/A2005sxxb0014
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    In this paper, by studying the factorization of adjoint polynomials of Γ-class graphs, we prove that structure characteristics of the chromatically equivalent graphs and chromatically non-uniqueness of their complement graphs.
  • Cai Feng YI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 133-140. https://doi.org/10.12386/A2005sxxb0015
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    Let A0,A1,…,An-1be entire functions with finite order, which are not all polynomials. In this paper we study the angular distribution as well as the removable sets of zeors of solutions of differential equations f(n) + An-1f(n-1) +…+ A0f = 0.
  • Yu Feng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 141-152. https://doi.org/10.12386/A2005sxxb0016
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    In this paper, a subalgpbra A2 of the Lie algebra A2 is constructed, which gives a corresponding loop algebra A2 by properly choosing the gradation of the basis elements. It follows that an isospectral problem is established. Furthermore, a new Liouville integrable Hamiltonian hierarchy of equations is obtaind by the use of Tu scheme, from which the hierarchy reduces to a nonlinear evolution equation of rational fractal form. By making use of a matrix transformation, a subalgebra A2 of the Lie algebra A1 is presented, which possesses the same communicative operations of basis elements as those in A2. Again we expand the Lie algebra A1 into a high-dimensional loop algebra G, and a type of expanding integrable system of the hierarchy obtained above is worked out.
  • Mao Hua LE
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 153-156. https://doi.org/10.12386/A2005sxxb0017
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    Let a be a positive integer. Let D = 3a2 + 1 and p = 4a2 + 1, where p is a prime. In this paper we prove that if a is not a multiple of 4, then the equation x2 + Dm = pn has exactly two solutions (x, m, n) = (a, 1,1) and (8a3 + 3a, 1,3), except for (D,p) = (4,5), in which case the equation has exactly three solutions (x,m, n) = (1,1,1), (3,2,2) and (11,1,3).
  • Liu Gen XUE
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 157-170. https://doi.org/10.12386/A2005sxxb0018
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    The estimator σ_n~2 of error variance in semiparametric regression model is given by using the least squares method and local linear smoothers. It is provend that the Berry-Esseen bound of σ_n~2 can attain the accuracy of O(n-1/2) under suitable conditions.
  • Zhi Min HE(1), Wei Gao GE(2)
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 171-176. https://doi.org/10.12386/A2005sxxb0019
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    This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
  • Tong Suo WU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 177-180. https://doi.org/10.12386/A2005sxxb0020
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    In this paper, the exchange rings R whose primitive factor rings are Artinian is studied. The K0-groups of R is characterized and it is proved that the uniqueness of n-th roots always holds in the category of finitely generated projective R-modules.
  • Xiao Dong ZHANG, Jiong Sheng L
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 181-184. https://doi.org/10.12386/A2005sxxb0021
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    We present an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.
  • Zhong YI
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 185-192. https://doi.org/10.12386/A2005sxxb0022
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    Some equivalent characterizations for a skew group ring to be a Dubrovin valuation ring are given, among them all the prime ideals of a Dubrovin valuation skew group ring are characterised.
  • Yong DING(1), Shan Zhen LU(1),
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 191-200. https://doi.org/10.12386/A2005sxxb0023
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    In this paper, the authors study the continuity properties of higher order commutators generated by the homogeneous fractional integral and BMO functions on certain Hardy spaces, weak Hardy spaces and Herz-type Hardy spaces.
  • Zhi Hua CHEN, De Kang XU
    Acta Mathematica Sinica, Chinese Series. 2005, 48(1): 201-204. https://doi.org/10.12386/A2005sxxb0024
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    It is proved that every proper holomorphic self-mapping of some kinds of Generalized Hartogs Triangles is an automorphism, and its explicit expression is given.