15 September 2013, Volume 56 Issue 5

    

• Select all
  |

Articles
• Select
  Efficiency of Smoothed Distribution Function Estimator with Left Truncated and Right Censored Data

  Yu Tao LIU, Xing Jie SHI, Yong ZHOU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 625-636. https://doi.org/10.12386/A2013sxxb0063

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  A smoothed distribution estimator is proposed when the data are subject to random left truncation and right censorship. The asymptotic properties of the smoothed distribution estimator are established. A relative deficiency is suggested for the smoothed estimator of distribution to the empirical estimator. Under some assumptions, the smoothed distribution estimator is better than the empirical one. In addition, simulation study is conducted and it shows that the smoothed estimator outperforms the empirical one.
• Select
  Existence of Strong Solutions for the 3D Axisymmetric Boussinesq Equations with Swirl

  Wan Rong YANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 637-650. https://doi.org/10.12386/A2013sxxb0064

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper aims at the global existence and uniqueness of strong solutions concerning the 3D axisymmetric Boussinesq equations with swirl in the region away from the symmetry axis. Based on the L4 estimation of velocity u and density ▽ρ, we obtain the prior estimates of u,u_t and ρ,ρ_t. Finally, by Galerkin method, we obtain the global existence and uniqueness of strong solutions. In particular, this criterion extends the corresponding results of 3D axisymmetric Navier-Stoke equations to the case of 3D axisymmetric Boussinesq equations.
• Select
  A Lower Bound on Judicious Balanced Bipartition Problem of Graphs

  Hai Yan LI, Bao Gang XU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 651-660. https://doi.org/10.12386/A2013sxxb0065

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  A balanced bipartition of a graph G is a bipartition V₁ and V₂ of V (G) such that -1≤|V₁|-|V₂|≤1. Let G be a graph with n vertices and m edges, and let r be a real number greater than 4. In this paper, it is proved that: (1) G admits a minimum balanced bipartition V₁, V₂ such that e(V₂}≥m/r, e(V₂}≥(k-1)m/4k if it is k-regular with k ≥ 3; and (2) G admits a minimum balanced bipartition such that e(V₂}≥m/r provided that Δ(G)≤[(3r-4)/(r+4)]δ(G)-[2r/(r+4)] if n is even, and Δ(G)≤[(3r-4)/(r+4)]δ(G)-[8r/(r+4)] if n is odd, where e(V_i) denotes the number of edges of G with both ends in V_i.
• Select
  The Geometric Analysis of SU(3) Gauge Fields in Artin Space

  He SHI

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 661-668. https://doi.org/10.12386/A2013sxxb0066

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper aims to study the linearizations of SU(3) Yang-Mills gauge fields in Artin space which is 4-dimensional. First, the Yang-Mills equation is discussed, and the concept of exact Yang-Mills equation is given, and it has explicit geometric meanings. Then a kind of differential transformation, which is called characteristic transformation of SU(3) Yang-Mills gauge fields in Artin space, is constructed. The characteristic transformation is obtained by the method of mathematics mechanization. The linearizations of exact Yang-Mills equations are obtained via characteristic transformations. Thus, the existence of SU(3) Yang-Mills gauge fields is proved.
• Select
  Linear Dependence of Mean Curvature Vector Fields of Submanifold

  Jin LIU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 669-686. https://doi.org/10.12386/A2013sxxb0067

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  A class of functionals is found in space forms such that its critical points include r-minimal submanifolds and minimal submanifolds as special cases. The critical points are defined as -parallel submanifolds. We obtain algebraic, differential and variational characterizations of the -parallel submanifolds. Moreover, we prove a Simons' type nonexistence theorem which says that in the unit sphere there exists no stable -parallel submanifold with its corresponding -function positive.
• Select
  On Improvements of Minkowski Inequality for Convex Bodies

  Chang Jian ZHAO

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 687-692. https://doi.org/10.12386/A2013sxxb0068

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In the paper, some sharp Minkowski-type inequalities for volume differences are established. Our results provide new estimates on inequalities of these types.
• Select
  Dimension of Graphs of Fractional Derivatives of Self-Affine Curves

  Kui YAO, Yong Shun LIANG, Wei Yi SU, Ze Qing YAO

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 693-698. https://doi.org/10.12386/A2013sxxb0069

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper investigates the fractional derivatives of self-affine fractal curves. The upper box-counting dimension of the graphs of self-affine curves is obtained. It shows that differentiation of fractional order increases the dimension of self-affine curves.
• Select
  Estimates for Some Parabolic Operators with Certain Potentials on Weighted L^p Spaces and Morrey Spaces

  Wen Hua GAO, Yin Sheng JIANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 699-710. https://doi.org/10.12386/A2013sxxb0070

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The uniformly parabolic operator L=∂_t-∑ⁿ_i,j=1∂_i(a_i,j(x)∂_j)+V(x) is considered in this paper, where the potential V(x) is a non-negative function on Rⁿ(n≥3), and belongs to reverse Hölder class. The estimate for the gradient of the fundamental solution of the operator L is studied and several estimates for VL^-1,V^1/2▽L^-1 and V^1/2L^-1/2 on weighted L^p(Rⁿ⁺¹) spaces and Morrey spaces are obtained under certain assumptions on a_i,j, V and p.
• Select
  Asymptotic Properties of a Class of Nonlinear Stochastic Functional Differential Equations with Markovian Switching

  Lin WANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 711-726. https://doi.org/10.12386/A2013sxxb0071

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The main aim of this paper is to give a new condition which assures a class of nonlinear stochastic functional differential equations with Markovian switching have a unique solution and at the same time the moment, the moment average in time of this solution are bounded. The new condition is under the assumption of the local Lipschitz condition but neither the linear growth condition. Here we allow the coefficients of these equations are polynomial or are controlled by polynomial growth speed. An example is also given for illustration.
• Select
  Integral-Type Operators on μ-Bloch Spaces

  Zhong Hua HE, Guang Fu CAO

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 727-734. https://doi.org/10.12386/A2013sxxb0072

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let g∈H(D), and φ,Ψ be holomorphic self-maps of D. We investigate the boundedness and compactness of the following integral-type operators 
  on μ-Bloch spaces B_μ on unit disk D, where μ is a weight.
• Select
  Identifying Q-Matrix of Cyclic Markov Chain

  Xu Yan XIANG, Xiang Qun YANG, Ying Chun DENG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 735-750. https://doi.org/10.12386/A2013sxxb0073

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The sojourn time and hitting time distributions (the mixtures of exponential distributions) are provided for a given subset of state space of Markov chain. Then the derivatives of these distributions at t=0 are related to the Q-matrix. Based on the constraint relationships and the priori information from the structure of Markov chain, an inversion approach is developed to identify the transition rates from the parameters characterizing these distributions. For cyclic Markov chain with finite states, as a result, it is derived that its Q-matrix can be uniquely determined by the distributions of their sojourn time and hitting time at arbitrary two adjacent states. The corresponding algorithm is included to show the validity of such approach.
• Select
  The Hypersurfaces in Sⁿ⁺¹ with Three Distinct Constant Para-Blaschke Eigenvalues

  Ding Xing ZHONG, Hong An SUN, Zu Jin ZHANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 751-766. https://doi.org/10.12386/A2013sxxb0074

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let x : Mⁿ→Sⁿ⁺¹ be a hypersurface in the (n + 1)-dimensional unit sphere Sⁿ⁺¹ without umbilics. Four basic invariants of x under the Möbius transformation group in Sⁿ⁺¹ are Möbius metric g, Möbius second fundamental form B; Möbius form Φ; Blaschke tensor A. Let D = A + λB, where λ is a constant, then D is a symmetric (0; 2) tensor and a Möbius invariant. D is called para-Blaschke tensor of x, the eingenvalues of D is called para-Blaschke eingenvalues of x. If Φ= 0; and the para-Blaschke eingenvalues are constant. Then the hypersurface x : Mⁿ→Sⁿ⁺¹ is called para-Blaschke isoparametric hypersurface. In this paper, we classify the para-Blaschke isoparametric hypersurfaces with three distinct para-Blaschke eingenvalues such that one of them is simple.
• Select
  Compressive Sensing with Noise Based on SCAD Penalty

  Hai ZHANG, Yong LIANG, Zong Ben XU, Xiang Yu CHANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 767-776. https://doi.org/10.12386/A2013sxxb0075

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study the compressive sensing with noise. We propose a new strategy for compressive sensing based on SCAD, and we give an efficient thresholding algorithm for solving the new model. The new method is robust to the observation noise. These fundamental properties of the compressive sensing strategy based on SCAD are supported and demonstrated both by simulations and theoretical results.
• Select
  The Comparison Theorem for Multidimensional BSDEs with Jumps

  Xue Hong ZHU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 777-786. https://doi.org/10.12386/A2013sxxb0076

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study the comparison theorem for multidimensional backward stochastic differential equations (BSDEs in short) with jumps and for matrix-valued BSDEs with jumps. Applying the backward stochastic viability property (BSVP in short) with jumps, we transform the comparison theorem to a viability problem in a closed convex set and obtain a necessary and sufficient condition under which the comparison theorem holds true.
• Select
  U(n+1) Extensions of Several Transformations Formulas on Basic Hypergeometric Series

  Zhi Zheng ZHANG, Yun WU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 787-798. https://doi.org/10.12386/A2013sxxb0077

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  By applying the method of Carlitz inversion technique and series rearrangement, the purpose of this paper is to establish the U(n+1) extensions of several transformations formulas on basic hypergeometric series.
• Select
  K-g-Frames and Dual g-Frames for Closed Subspaces

  Yan ZHOU, Yu Can ZHU

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 799-806. https://doi.org/10.12386/A2013sxxb0078

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We introduce the concept of K-g-frames in Hilbert spaces and study the essential distinctions between K-g-frames and g-frames. Then we characterize K-g frames by using dual g-frames of special closed subspaces and give a way to construct dual g-frames for special closed subspaces. Finally, we study some properties of K-g frames.
• Select
  Decomposition of the Departure Process for a Discrete-Time Geo^λ₁,λ₂/G/1(ES,MV) Queue

  Chuan Yi LUO, Ying Hui TANG, Bao Shan CAO, Kai Li XIANG

  Acta Mathematica Sinica, Chinese Series. 2013, 56(5): 807-816. https://doi.org/10.12386/A2013sxxb0079

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study the departure process of a multi-vacation Geo/G/1 queue with variable input rate. Using probability techniques, renewal process theory and utransform, we discuss the expected number of departures during the time interval (0⁺,n⁺] initiated with general state. The decomposed expression of the expected number of departures during the time interval (0⁺,n⁺] and the corresponding steady result are obtained. It displays the especial structure of the departure renewal process, i.e., the departure renewal process consists of two parts, server busy-state process (busy or idle) and the service renewal process in server busy period, which simplifies the discussion on the departure renewal process. Since the departure process also often corresponds to an arrival process in downstream queues, the results obtained here are significant to study queueing network.