中国科学院数学与系统科学研究院期刊网
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15 October 2011, Volume 27 Issue 10
    

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  • On the Boundedness of Rough Oscillatory Singular Integrals on Triebel-Lizorkin Spaces
    Hussain AL-QASSEM, Leslie CHENG, Yi Biao PAN
    Acta Mathematica Sinica. 2011, 27(10): 1881-1898. https://doi.org/10.1007/s10114-011-0410-3
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    We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory integrals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.  
  • The Roman k-domatic Number of a Graph
    Seyed Mahmoud SHEIKHOLESLAMI, Lutz VOLKMANN
    Acta Mathematica Sinica. 2011, 27(10): 1899-1906. https://doi.org/10.1007/s10114-011-0385-0
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    Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set {f1, f2, . . . , fd} of distinct Roman k-dominating functions on G with the property that ∑i=1d fi(v) ≤ 2 for each v ∈ V (G), is called a Roman k-dominating family (of functions) on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by dkR(G). Note that the Roman 1-domatic number d1R(G) is the usual Roman domatic number dR(G). In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for dkR(G). In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and Volkmann in 2010 for the Roman domatic number.  
  • Approximate (m,n)-Cauchy-Jensen Additive Mappings in C*-algebras
    John Michael RASSIAS, Kil Woung JUN, Hark-Mahn KIM
    Acta Mathematica Sinica. 2011, 27(10): 1907-1922. https://doi.org/10.1007/s10114-011-0179-4
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    Concerning the stability problem of functional equations, we introduce a general (m, n)- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general (m, n)-Cauchy-Jensen additive mappings in C*-algebras, which generalize the results obtained for Cauchy-Jensen type additive mappings.  
  • On the Strong Limit Theorems for Double Arrays of Blockwise M-dependent Random Variables
    Ulrich STADTMÜLLER, Le Van THANH
    Acta Mathematica Sinica. 2011, 27(10): 1923-1934. https://doi.org/10.1007/s10114-011-0110-z
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    For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1, n ≥ 1}, strong laws of large numbers are established for double sums ∑i=1m∑j=1n Xij , m ≥ 1, n ≥ 1. The main results are obtained for (i) random variables {Xmn,m ≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and (ii) random variables {Xmn,m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case (i) generalizes the main result of Móricz et al. [J. Theoret. Probab., 21, 660-671 (2008)] from dyadic to arbitrary blocks, whereas the result in Case (ii) extends a result of Gut [Ann. Probab., 6, 469-482 (1978)] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.  
  • The Harnack Estimate for a Nonlinear Parabolic Equation under the Ricci Flow
    Song Bo HOU
    Acta Mathematica Sinica. 2011, 27(10): 1935-1940. https://doi.org/10.1007/s10114-011-0074-z
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    Let (M,g(t)), 0 ≤ t ≤ T, be an n-dimensional closed manifold with nonnegative Ricci curvature, |Rc| ≤ (C/t) for some constant C > 0 and g(t) evolving by the Ricci flow  In this paper, we derive a differential Harnack estimate for positive solutions to parabolic equations of the type ut = Δu - aulogu - bu on M × (0, T], where a > 0 and b ∈ R.  
  • A General Law of Moment Convergence Rates for Uniform Empirical Process
    Qing Pei ZANG, Wei HUANG
    Acta Mathematica Sinica. 2011, 27(10): 1941-1948. https://doi.org/10.1007/s10114-011-9752-0
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    Let {Xn; n ≥ 1} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process Fn(t) = n-12∑i=1n(I{Xi≤t} - t), 0 ≤ t ≤ 1, ‖Fn‖ = sup0≤t≤1 |Fn(t)|. In this paper, the exact convergence rates of a general law of weighted infinite series of E{‖Fn‖ - εgs(n)}+ are obtained.  
  • The Martingale Hardy Type Inequality for Marcinkiewicz-Fejér Means of Two-dimensional Conjugate Walsh-Fourier Series
    Ushangi GOGINAVA
    Acta Mathematica Sinica. 2011, 27(10): 1949-1958. https://doi.org/10.1007/s10114-011-9551-7
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    The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ Hp such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space Lp.  
  • How to Recognize Nonexpansive Mappings and Isometric Mappings
    Guang Gui DING, Yu Mei MA
    Acta Mathematica Sinica. 2011, 27(10): 1959-1966. https://doi.org/10.1007/s10114-011-9470-7
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    In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.  
  • The Calder′on-Zygmund Decomposition and Interpolation on Weighted Hardy Spaces
    Zhuo Ping RUAN
    Acta Mathematica Sinica. 2011, 27(10): 1967-1978. https://doi.org/10.1007/s10114-011-9338-x
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    We apply discrete Littlewood-Paley-Stein theory, developed by Han and Lu, to establish Calderón-Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hwp for w ∈ A∞ in both the one-parameter and two-parameter cases.  
  • A Class of New Large-Update Primal-Dual Interior-Point Algorithms for P*(κ) Nonlinear Complementarity Problems
    Hua Ping CHEN, Ming Wang ZHANG
    Acta Mathematica Sinica. 2011, 27(10): 1979-1994. https://doi.org/10.1007/s10114-011-9302-9
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    In this paper we propose a class of new large-update primal-dual interior-point algorithms for P*(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.'s for P*(κ) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior- Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.'s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.  
  • The Fejér-Riesz Inequality for the Besov Spaces
    Hasi WULAN, Fang Qin YE
    Acta Mathematica Sinica. 2011, 27(10): 1995-2004. https://doi.org/10.1007/s10114-011-9286-5
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    A Fejér-Riesz inequality for the weighted Besov spaces Bp,q is given. Some characterizations of functions in Bp,q in terms of their Taylor coefficients are obtained.  
  • Small-divisor Equation of Higher Order with Large Variable Coefficient and Application to the Coupled KdV Equation
    Mei Na GAO, Jing ZHANG
    Acta Mathematica Sinica. 2011, 27(10): 2005-2032. https://doi.org/10.1007/s10114-011-0064-1
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    In this paper, we establish an estimate for the solutions of small-divisor equation of higher order with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the coupled KdV equation subject to small Hamiltonian perturbations.  
  • A Lower Bound for Linear Forms in Values of a Continued Fraction
    Xiu Yuan YU, Zhong Hua SHEN
    Acta Mathematica Sinica. 2011, 27(10): 2033-2038. https://doi.org/10.1007/s10114-011-8679-9
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    Let y = y(x) be a function defined by a continued fraction. A lower bound for |Λ| = |β1y1 + β2y2 + α| is given, where y1 = y(x1), y2 = y(x2), x1 and x2 are positive integers, α, β1 and β2 are algebraic irrational numbers.  
  • The Arc Distortion in QH Inner ψ-uniform (or Convex) Domains in Real Banach Spaces
    Man Zi HUANG, Xian Tao WANG
    Acta Mathematica Sinica. 2011, 27(10): 2039-2050. https://doi.org/10.1007/s10114-011-8672-3
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    Let D and D′ be domains in real Banach spaces of dimension at least 2. The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces. In particular, when D′ is a QH inner ψ-uniform domain with ψ being a slow (or a convex domain), we investigate the following: For positive constants c, h,C,M, suppose a homeomorphism f : D → D′ takes each of the 10-neargeodesics in D to (c, h)-solid in D′. Then f is C-coarsely M-Lipschitz in the quasihyperbolic metric. These are generalizations of the corresponding result obtained recently by Väisälä.  
  • Oblique Derivative Problems for Second Order Nonlinear Equations of Mixed Type with Degenerate Hyperbolic Curve
    Guo Chun WEN
    Acta Mathematica Sinica. 2011, 27(10): 2051-2064. https://doi.org/10.1007/s10114-011-8602-4
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    The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point principle. In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients, and then the advantage of complex analytic method can be applied.  
  • Some Homological Characterizations of Semigroups and Semirings
    Javed AHSAN, Zhong Kui LIU, Muhammad SHABIR
    Acta Mathematica Sinica. 2011, 27(10): 2065-2072. https://doi.org/10.1007/s10114-011-8180-5
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    In this paper we characterize semirings all of whose p-injective semimodules are injective. We also classify monoids all of whose p-injective acts are injective.  
  • Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions
    Zeng Qin ZHAO, Fu Shan LI
    Acta Mathematica Sinica. 2011, 27(10): 2073-2084. https://doi.org/10.1007/s10114-011-8023-4
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    By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f(t, u) is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0,1] positive solutions as well as the C1[0, 1] positive solutions.  
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