中国科学院数学与系统科学研究院期刊网

15 July 2015, Volume 58 Issue 4
    

  • Select all
    |
    Articles
  • Some Results of Levine-O'Sullivan Sequence
    Shi Chun YANG, Zi Guo JIANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 529-534. https://doi.org/10.12386/A2015sxxb0054
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let q1 = 1 and qn be the largest value of (k + 1)(n - qk) (1 ≤ k ≤ n - 1) for n ≥ 2. The sequence Q = {q1, q2, …} is called Levine-O'Sullivan sequence, is very useful for studying the characteristical of sum-free sequences, and plays an important role. In this paper, we consider the estimates of the terms of Levine- O'Sullivan sequence, and study two conjectures of the sequence posed by Chen. We give some results about the term qn, and obtain that the reciprocal sum of Q satisfying 3.028464 < ρ(Q) < 3.029891.
  • Weighted Simultaneous Approximation by Bernstein Operators for Functions with Singularities
    Dan Sheng YU
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 535-550. https://doi.org/10.12386/A2015sxxb0055
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We construct a new type of Bernstein operators by using Lagrange interpolation to replace the values of f(x) at endpoints, which enable us to approximate the functions with singularities. The direct result of the weighted pointwise simultaneous approximation of the new operators is given.
  • Generalized Derivations of Hom-Lie Algebras
    Jia ZHOU, Yan Jun NIU, Liang Yun CHEN
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 551-558. https://doi.org/10.12386/A2015sxxb0056
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We give some basic properties of the generalized derivation algebra, quasiderivation algebra and center derivation algebra of a Hom-Lie Algebra L. Moreover, we prove that GDer(L) = QDer(L) + QC(L). We also prove that QDer(L) can be embedded as derivations in a larger Hom-Lie algebra.
  • Derivations and Automorphisms of a Class of W-Algebras
    Wei WANG, Yong Ping WU, Chun Guang XIA
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 559-570. https://doi.org/10.12386/A2015sxxb0057
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    A class of W-algebras is studied, which contains the generalized centerless Virasoro subalgebra. In this paper, the derivations and automorphisms of this Lie algebra are precisely determined.
  • Regularity Exponent of Modulation Space and Its Application
    Qiang HUANG, Rui BU
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 571-576. https://doi.org/10.12386/A2015sxxb0058
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We use a composite concept of Modulation space to describe the conditions of well and ill posedness of Navier-Stokes equations in Modulation space. Finally we get sharp conditions about this problem.
  • Hardy Type Inequality and Unique Continuation on Carnot Groups
    Jia Lin WANG, Dong Ni LIAO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 577-584. https://doi.org/10.12386/A2015sxxb0059
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We show Lp weighted Hardy type inequalities for 1 < p < +∞ on general Carnot groups. Using the previous inequalities, we also obtain a Hardy-Sobolev type inequality. As an application, doubling property and unique continuation of the weak solution to p-sub-Laplacian with singular weights are established.
  • Strong Disjointness of Frames and Constructions of Tight Frames
    Xun Xiang GUO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 585-592. https://doi.org/10.12386/A2015sxxb0060
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson. There are lots of useful properties on disjoint frames. In this paper, firstly we use strongly disjoint tight frames to construct new tight frames. In particular, we give some sufficient or some sufficient and necessary conditions such that the linear combinations of normalized tight frames with operator coefficients to be certain tight frames. We also give a necessary and sufficient condition such that a frame has tight dual frame with certain frame bound. Then we study the corresponding problems in real Hilbert spaces.
  • α-Carleson Measure Associated with Families of Multilinear Operators
    Ting MEI, Yong DING, Bo Lin MA
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 593-600. https://doi.org/10.12386/A2015sxxb0061
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We define a class of α-Carleson measures (0 < α ≤ 1) by a family of the multilinear integral operators {Θt}t >0. As an application, we prove that the multilinear paraproduct defined by (f)(x) = ∫0∞ ηt* ((φt * f)Θt(b1,..., bm))(x) dt/t, is a bounded operator from L2(H∞d) to L2(Rn), where H∞d denotes the d-dimensional Hausdorff capacity (d = αn) on Rn.
  • Strong and Weak Convergence for Common Elements of Fixed Point Sets and Zero Point Sets
    Li Juan ZHANG, Hui TONG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 601-612. https://doi.org/10.12386/A2015sxxb0062
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We introduce two iterative schemes for finding common elements of the fixed point set of asymptotically strictly pseudocontractive mappings and the zreo point set of the operator which is the sum of inverse strongly monotone mappings and maximal monotone operators in a Hilbert space. We obtain strong and weak theorem for common element of the two sets under some conditions.
  • Projective Prime Submodules of a Free Module
    Fang Gui WANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 613-620. https://doi.org/10.12386/A2015sxxb0063
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let R be a domain with a prime element u and let M be a projective submodule of a finitely generated free module F. In this paper it is proved that if R/(u) is both a GE ring and PF ring, and either F/M is a projective R/(u)-module or M is a (u)-primary submodule of F and F/M is cyclic, then M is free.
  • A Note for Ramanujan's Circular Summation Formula
    Qiu Ming LUO
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 621-634. https://doi.org/10.12386/A2015sxxb0064
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We generalized Ramanujan's circular summation formula and give an elementary proof of them. We also show some applications and obtain some new identities of theta functions.
  • Estimates for Eigenvalues of Fourth-order Elliptic Operators in Divergence Form on Complete Riemanian Manifolds
    Feng DU, Chuan Xi WU, Guang Han LI, Chang Yu XIA
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 635-648. https://doi.org/10.12386/A2015sxxb0065
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the eigenvalue problem of the fourth-order elliptic operators in divergence form on complete Riemannian manifolds and obtain a general inequality. By using this general inequaity, we prove universal inequalities for eigenvalues of the fourth-order elliptic operators in divergence form on complete Riemannian manifolds admitting special functions and give some examples for these Riemannian manifolds admitting special functions. Moreover, we solve Chen-Zheng-Yang's conjecture in these complete Riemannian manifolds admitting special functions.
  • A Regularized Sparse Representation Method
    Feng ZHOU, Xue Ying ZENG, Li Hua YANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 649-660. https://doi.org/10.12386/A2015sxxb0066
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We propose a regularized method to sparsely represent signals using a given dictionary. Our method differs from the widely used models in the literatures in two respects. Firstly, we directly use the l0 norm rather than the alternative l1 norm to measure the sparsity in the model. Secondly, we add a regularization term to the model to select an optimal representation from all of the possible representation ways that can approximately attain the sparsity. The frame potential is used in the regularization term to measure the quality of the selected atoms. We use the twice continuously differentiable and concave functions to approximate the l0 norm in the proposed model and develop a minimization algorithm. Our numerical experiments demonstrate that the proposed method can represent the signals using the atoms with less mutual coherence than the widely used models.
  • A Brand New Multiple Hilbert-Type Integral Inequality
    Bing HE, Jun Fei CAO, Bi Cheng YANG
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 661-672. https://doi.org/10.12386/A2015sxxb0067
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, by introducing a distinctive kernel and using the way of weight functions, a brand new multiple Hilbert-type integral inequality with a best constant factor is given. The operator expressions, equivalent forms, reverse inequalities and particular cases are considered.
  • Criterion on Affine Bessel Sequences
    Wei WANG, Xian Liang SHI
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 673-678. https://doi.org/10.12386/A2015sxxb0068
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    By introducing Bessel control functions, and studying its necessary conditions and sufficient conditions, a new criterion for affine Bessel sequences with control functions is established. Furthermore, some open questions are posed.
  • The Application of BHV Theorem to Diophantine Equation xy+yx=zz
    Hua Ming WU
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 679-684. https://doi.org/10.12386/A2015sxxb0069
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Using the BHV theorem on the existence of primitive divisors of Lucas numbers, we prove that the equation xy+yx=zz has no positive integer solutions (x, y, z) such that min{x, y, z} > 1 and z is odd.
  • Uniqueness of Some Meromorphic Functions that Sharing a Rational Function
    Hui Ling QIU
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 685-690. https://doi.org/10.12386/A2015sxxb0070
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We use the theory of value distribution and study the uniqueness of meromorphic functions. We will prove the following result: Let q(z) be a rational function of degree k, f(z) and g(z) be two transcendental meromorphic functions, and let q have no same poles as fg, n be a positive integer and n ≥ max{11, k + 1}. If fn(z)f'(z) and gn(z)g'(z) share q(z) CM, then either f(z) = c1ec∫q(z)dz, g(z) = c2e-c∫q(z)dz, where c1, c2 and c are three constants satisfying (c1c2)n+1c2 = -1, or f(z) ≡ tg(z) for a constant t such that tn+1 = 1.
  • The Classification of All Quantifier-Eliminable Directed or Undirected Trees with a Root
    Ying Ying FU, Fu Xing SHEN
    Acta Mathematica Sinica, Chinese Series. 2015, 58(4): 691-704. https://doi.org/10.12386/A2015sxxb0071
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We put forward three special formulas to describe the structural characteristics of directed or undirected trees with a root. On this basis, quantifier elimination property for directed or undirected trees with root r in the language L0 = {E, r} and its expansion is discussed and four classification results are proposed.
Journal Online
News More