Table of Content

30 March 2016, Volume 31 Issue 1

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Complete Convergence for Weighted Sums of WOD Random Variables

ZHANG Ying , ZHANG Yu , SHEN Ai-ting

2016, 31(1):  1-8.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.001

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In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables. 

Ground State Solutions for SchrÄodinger-Poisson Systems

XU Na

2016, 31(1):  9-18.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.002

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This paper deals with a class of SchrÄodinger-Poisson systems. Under some conditions, we prove that there exists a ground state solution of the system. The proof is based on the compactness lemma for the system. Our results here improve some existing results in the literature. 

Some Results of Biharmonic Maps

FENG Shu-xiang, PAN Hong

2016, 31(1):  19-26.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.003

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In this paper, we investigate biharmonic maps from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain some non-existence results for these maps. 

A Remark on Global Existence, Uniqueness and Exponential Stability of Solutions for the 1D Navier-Stokes-Korteweg Equations

ZHANG Jian-lin, CAO Jie, SU Xing

2016, 31(1):  27-38.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.004

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In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod（1984） and J E Dunn and J Serrin（1985）. We establish the existence, uniqueness and exponential stability of global solutions in H²×H¹× H¹ for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C0-semigroups S（t） on H²× H¹× H¹. 

Bohr Inequality for Multiple Operators

LIAN Tie-yan, TANG Wei

2016, 31(1):  39-43.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.005

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An absolute value equation is established for linear combinations of two operators.When the parameters take special values, the parallelogram law of operator type is given. In addition, the operator equation in literature [3] and its equivalent deformation are obtained.Based on the equivalent deformation of the operator equation and using the properties of conjugate number as well as the operator, an absolute value identity of multiple operators is given by means of mathematical induction. As Corollaries, Bohr inequalities are extended to multiple operators and some related inequalities are reduced to, such as inequalities in [2]and [3]. 

Vertex Algebra Sheaf Structure on Torus

SUN Yuan-yuan

2016, 31(1):  44-50.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.006

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In this paper, we first give a 1-1 corresponds between torus C/Λ and cubic curve C in PC2. As complex manifold, they are isomorphic, therefore we can treat C/Λ as a variety and construction a vertex algebra sheaf on it. 

The Asymptotic Limit for the 3D Boussinesq System

LI Lin-rui, WANG Ke, HONG Ming-li

2016, 31(1):  51-59.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.007

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In this paper, we show the asymptotic limit for the 3D Boussinesq system with zero viscosity limit or zero diffusivity limit. By the classical energy method, we prove that as viscosity(or diffusivity) coefficient goes to zero the solutions of the fully viscous equations converges to those of zero viscosity(or zero diffusivity) equations, which extend the previous results on the asymptotic limit under the conditions of the zero parameter(zero viscosity ν = 0 or zero diffusivity η = 0) in 2D case separately. 

An Efficient Construction of Secure Network Coding

ZHANG Jing-li, TANG Ping, MA Song-ya

2016, 31(1):  60-68.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.008

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Under the assumption that the wiretapper can get at most r（r < n） independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^-1. They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the（n- r） ×（n- r）and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction. 

Analysis of an Implicit Finite Di®erence Scheme for Time Fractional Di®usion Equation

MA Yan

2016, 31(1):  69-81.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.009

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Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈（0, 1）. In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper. 

Two Notes on Topological Groups

ZHANG Ke-xiu, LIU Xin, TANG Zhong-bao

2016, 31(1):  82-86. 

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In this short paper, we firstly give a short proof of Birkhoff-Kakutani Theorem by Moore metrizable Theorem. Then we prove that G is a topological group if it is a paratopological group which is a dense G_δ-set in a locally feebly compact regular space X. 

Mixed Finite Element Formats of any Order Based on Bubble Functions for Stationary Stokes Problem

CAO Ji-wei, LIU Ming-fang, CHEN Shao-chun

2016, 31(1):  87-95.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.011

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Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved. 

On n-K Width of Certain Function Classes Defined by Linear Operators in L₂ Space

YU Rui-fang, WU Ga-ridi

2016, 31(1):  96-101.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.012

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Let M（u） be an N-function, L_r（f, x） and K_r（f, x） are Bak operator and Kantorovich operator, W_M（L_r（f）） and W_M（K_r（f）） are the Sobolev-Orlicz classes defined by L_r（f, x）, K_r（f, x） and M（u）. In this paper we give the asymptotic estimates of the n-K widths d_n（W_M（L_r（f））, L₂[0, 1]） and d_n（W_M（K_r（f））, L₂[0, 1]）. 

A Remark on Persistence of Regularity for the Nonlinear Boussinesq System in Dimension Two

SU Xing, CAO Jie, ZHANG Jian-lin

2016, 31(1):  102-110.  doi:10.13371/j.cnki.chin.q.j.m.2016.01.013

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This paper investigates the Cauchy problem for the nonlinear Boussinesq system in dimension two, and prove that for any initial data（u₀, θ₀） in H^1+s×H^1+s, where s ∈（0, 1）,the persistence of regularity holds.