数学季刊

宋常修

2007, 22(4): 475-481.

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In this paper, the author studies the boundary value problems for a p-Laplacian functional diference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.

四元数体上Hermitian矩阵空间保秩1的加法映射

韩敬稳, 郑宝东

2007, 22(4): 482-491.

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Let Q be the quaternion division algebra over real field F. Denote by H_n(Q)the set of all n×n hermitian matrices over Q. We characterize the additive maps from H_n(Q) into H_m(Q)that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn(QR) into Hm(QR)that preserve rank-1 matrices are also given.

双线形元的各向异性后验误差估计

尹丽, 职桂珍

2007, 22(4): 492-499.

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The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilinear finite element for the second order problem under anisotropic meshes.By using some novel approaches and techniques,the optimal error estimates and some superconvergence results are obtained without the regularity assumption and quasi-uniform assumption requirements on the meshes.Then,based on these results, we give an anisotropic posteriori error estimate for the second problem.

挠理论中的相对内射模

宋贤梅, 陈建龙

2007, 22(4): 500-503.

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For a hereditary torsion theory T,this paper mainly discuss properties of A_-τ- injective modules,where A is a fixed left R-module.It is proved that if M is an A_-τ-injective, B is a submodule of A,then 1)M is A/B-τ-injective;2)M is B_-τ-injective when B isτ- dense in A.Furthermore,we show that if A₁,A_2,…,A_n are relatively injective modules, then A₁⊕A₂⊕…⊕A_n is self-τ-injective if and only if A_{i i}s self_-τ-injective for each i.

格蕴涵代数的LI-理想空间

陈树伟, 姜保庆, 杨晓伟

2007, 22(4): 504-511.

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In this paper,a topological space based on LI-ideals of a lattice implication algebra is constructed,and its topological properties,such as separability,compactness and connectedness are discussed.

右半平面上的零级Dirichlet 级数的增长性

田宏根, 孙道椿

2007, 22(4): 512-517.

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The Dirichlet series of zero order in the half plane is studied and two theorems on their growth are obtained in this paper.

二元域上线性含错方程

夏建国

2007, 22(4): 518-522.

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In this paper,we will give a method to solve linear error equationon on F₂,by using linear algebra on fields F₂ and partition theory.

离散模型解的收敛性与周期性

宾红华

2007, 22(4): 523-529.

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The discrete-time network model of two neurons with function f(u)=... is considered. We obtain sufficient conditions that solution of system is convergent or periodic.

网络最短的最优解集结构

张振坤, 王斌

2007, 22(4): 530-537.

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The shortest path problem in a network G is to find shortest paths between some specified source vertices and terminal vertices when the lengths of edges are given. The structure of the optimal solutions set on the shortest paths is studied in this paper. First,the conditions of having unique shortest path between two distinguished vertices s and t in a network G are discussed;Second,the structural properties of 2-transformation graph G on the shortest-paths for G are presented heavily.

非Lipschitz条件下两边界反射型倒向随机微分方程的解

胡兰英, 朱跃峰, 夏宁茂等

2007, 22(4): 538-549.

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In this paper,we derive the existence and uniqueness theorem for the adapted solution to backward stochastic differential equations with two barriers under non-Lipschitz condition via penalization method.

卡拉比-丘成桐定理的一个新证明

傅小勇

2007, 22(4): 550-551.

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We give a new proof of Calabi-Yau’s theorem on the volume growth of Rie- mannian manifolds with non-negative Ricci curvature.

关于亚纯函数导数的特征函数的一点注记

窦盼英, 肖泽昌

2007, 22(4): 552-557.

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In this paper,the characteristic function of the derivative of meromorphic function is studied.A expression of characteristic function T(r,f') is given.

一类非线性互补问题的信赖域算法

欧宜贵

2007, 22(4): 558-566.

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In this paper,an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed.A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration,thus avoiding the need for solving a quadratic subproblem with a trust region bound.Under some conditions,it is proven that this algorithm is globally and locally superlinear convergent.The limited numerical examples show its efficiency.

L²（R^s）上尺度函数的研究

黄永东, 李华, 吴国昌

2007, 22(4): 567-573.

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In this paper,using the orthonormal multiresolution analysis(MRA)of L2(R?), we get two important properties of the scaling function with dilation matrix A=MI of L2(R?).These properties are characterized by some inequalities and equalities.

θ型Calderón-Zygmund奇异积分算子在加权Herz型Hardy空间上的有界性

陈书权, 束立生

2007, 22(4): 574-580.

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In this paper,we will discuss the boundedness of θ-type Calderón-Zygmund operator on weighted Herz-type Hardy spaces.

极大子群的θ-完备

昝立博

2007, 22(4): 581-585.

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For a maximal subgroup M of a group G,a θ-completion for M is a subgroup C such that C is not contained in M while Ma,the core of M in G,is contained in C and C/MG has no proper normal subgroup of G/MG.This concept was introduced by ZHAO Yao-qing in 1998.In this paper we characterize the solvability of finite groups by means of θ-completions and obtain some new results.

非光滑控制Lyapunov函数及非线性切换系统的镇定问题

陈金环, 高永良

2007, 22(4): 586-591.

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In this paper we consider general nonlinear switching systems.Under an addi- tional assumption,we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.

NCP映射与抛物映射的Julia集及其Hausdorff维数的连续性

庄伟

2007, 22(4): 592-596.

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Denote by HD(J(f))the Hansdorff dimension of the Julia set J(f)of a rational function f.Our first result asserts that if f is an NCP map,and f_n→f horocyclically, preserving sub-critical relations,then f_nis an NCP map for all n》0 and J(f_n)→J(f)in the Hausdorff topology.We also prove that if f is a parabolic map and fn is an NCP map for all n》0 such that f_n→f horocyclically,then J(f_n)→J(f) in the Hansdorff topology, and HD(J(f_n))→HD(J(f)).

带工作相容约束的单机分批排序问题

张群发, 林诒勋

2007, 22(4): 597-601.

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The single machine parallel batch problem with job compatibility is considered to minimize makespan,where the job compatibility constraints are represented by a graph G.This problem is proved to be NP-hard.And when the graph G is limited to be a general bipartite,a complete bipartite and a complete m-partite graph,these problems are solved in polynomial time respectively.

Y_Ⅲ的完备Einstein-Kahler度量与Bergman度量的等价性

王贵霞

2007, 22(4): 602-606.

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In this paper we give the proof about the equivalence of the complete Einstein- Kahler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics.

对具有非单调压力的非线性热粘弹方程在H⁴中解的整体存在性的注记

秦玉明, 马志勇, 黄兰

2007, 22(4): 607-611.

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We consider a one-dimensional continuous model of nutron star,described by a compressible thermoviscoelastic system with a non-monotone equation of state,due to the effective Skyrme nuclear interaction between particles.We will prove that,despite a possible, destabilizing influence of the pressure,which is non-monotone and not always positive,the presence of viscosity and a sufficient thermal dissipation dcscribc the global existence of solutions in H4 with a mixed free boundary problem for our model.

时滞差分方程零解的全局渐近稳定性

亓正申, 王鸿燕

2007, 22(4): 612-620.

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The difference equation△x_n+p_nx_n-k=f(n,x_n-11,…,x_n-1m,n= 0,1,2,…is considered,where{Pn}is a sequence of nonnegative real numbers,m∈{1,2,,…),k,l₁,…,l_m∈{0,1,2,,…}.Some sufficient conditions for the global asymp- totic stability of zero solution of the equation are obtained.

几乎交错环链补中的不可压缩曲面

韩友发, 牛方平, 张放

2007, 22(4): 621-626.

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In this paper,we discuss mainly the properties of incompressible pairwies incom- prcssiblc surfaccs in almost altcrnating link complcmcnts. Lct L bca almost link and lct F be an incompressible palrwise incompressible surface in S3-L.First,we give the properties that the surface F intersects with 2-spheres in S3-L.The intersection consisting of a collection of circles and saddle-shaped discs is called a topological graph.One can compute the Euler Characteristic number of the surface by calculating the characteristic number of the graph.Next,we prove that if the graph is special simple,then the genus of the surface is zero.

一个Crouzeix-Raviart型有限元方法关于二阶椭圆问题超逼近的一个新证明

彭玉成, 石东洋

2007, 22(4): 627-632.

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In this paper,a new proof of superclose of a Crouzeix-Raviart type finite element is given for second order elliptic boundary value problem by Bramble-Hilbert lemma on anisotropic meshes.

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