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Table of Content
30 December 2007, Volume 22 Issue 4
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Positive Solutions of p-Laplacian Functional Difference Equations
SONG Chang-ziu
2007, 22(4): 475-481.
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p-Laplacian operator; functional difference equations; positive solution; cone
Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra
HAN Jing-wen, ZHENG Bao-dong
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.
An Anisotropic Posteriori Error Estimator of Bilinear Element
YIN Lil, ZHI Gui-zhen
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.
Relatively Injective Modules with Respect to Torsion Theory
SONG Xian-mei, CHEN Jian-long
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 A
1
,A
2,
…,A
n
are relatively injective modules, then A
1
⊕A
2
⊕…⊕A
n
is self-τ-injective if and only if A
i i
s self
-τ
-injective for each i.
LI-ideal Spaces of Lattice Implication Algebra
CHEN Shu-wei, JIANG Bao-qing, YANG Xiao-wei
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.
The Growth of the Zero Dirichlet Series in Right Half Plane
TIAN Hong-gen, SUN Dao-chun
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.
Linear Error Equation on Field F
2
XIA Jian-guo
2007, 22(4): 518-522.
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In this paper,we will give a method to solve linear error equationon on F
2
,by using linear algebra on fields F
2
and partition theory.
Convergence and Periodicity of Solutions for a Discrete Model
BIN Hong-hua
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.
The Structure of the Optimal Solution Set on the Shortest Paths for Networks
ZHANG Zhen-kun, WANG Bina
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.
On Solutions of BSDE with Two Barriers Under Non-Lipschitz Condition
HU Lan-ying, ZHU Yue-feng, XIA Ning-mao, REN Yong
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.
A New Proof of Calabi-Yau's Theorem
FU Xiao-yong
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.
A Note on the Characteristic Function of Mermophic Function Derivative
DOU Pan-ying, XIAO Ze-chang
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.
Trust Region Algorithm for a Class of Nonlinear Complementarity Problem
OU Yi-gui
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.
The Study on Scaling Function of L
2
（R
s
）
HUANG Yong-dong, LI Hua, WU Guo-chang
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.
Boundedness of the θ-type Calderón-Zygmund Operators on Weighted Herz-type Hardy Spaces
CHEN Shu-quan, SHU Li-sheng
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.
On θ-completions for Maximal Subgroups
ZAN Li-bo
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.
Nonsmooth Control-Lyapunov Function and Stabilization of Nonlinear Switching Systems
CHEN Jin-huan, GAO Yong-liang
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.
On the Continuity of Julia Sets and Hausdorff Dimension of NCP and Parabolic Maps
ZHUANG Wei
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
n
is 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)).
The Single Machine Parallel Batch Scheduling Problem with Job Compatibility Constraints
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.
The Equivalence of the Complete Einstein-Kahler Metric and the Bergman Metric on Y
Ⅲ
WANG Gui-xia
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.
A Remark on Global Existence in H
4
for a Nonlinear Thermoviscoelasticity Equations with Non-monotone Pressure
QIN Yu-ming, A Zhi-yong, HUANG Lan
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.
Global Asymptotic Stability of Zero Solution for Delay Difference Equations
QI Zheng-shen, WANG Hong-yan
2007, 22(4): 612-620.
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The difference equation△x
n
+p
n
x
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,l
1
,…,l
m
∈{0,1,2,,…}.Some sufficient conditions for the global asymp- totic stability of zero solution of the equation are obtained.
Incompressible Surfaces in Almost Alternating Link Exteriors
HAN You-fa, NIU Fang-ping, ZHANG Fang
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.
A New Proof of Superclose of a Crouzeix-Raviart Type Finite Element for Second Order Elliptic Equation
PENG Yu-cheng, SHI Dong-yang
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.
