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中文
Table of Content
30 March 2003, Volume 18 Issue 1
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Singular Perturbation of a Class of Dirichlet Exterior Problems for Elliptic Equations
XIE Feng
2003, 18(1): 1-6.
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In this paper ,we consider a class of singularly perturbed Dirichlet exterior problems for ellip- tic equations． Under the appropriate conditions we construct the formally asymptotic solution of the problem described． Using differential inequaltiy theory we prove the existence of the solution of original problem and the uniforly validity of the formal solution .
Stability and Boundedness of Retarded Liénard-type Equation
ZHOU Xian-feng, JIANG Wei
2003, 18(1): 7-12.
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This paper aims to investigate the retarded Liénard-type equation
x＋ f
1
（ x）x˙ + f
2（
x）x˙（ t - τ) + f
3（
x）x˙2 + φ（ x）＋ g（ x（ t - τ)) = 0,
where τis a nonnegative constant ,f
1
,f
2
,f
3
,φ and g are continuous functions on R．Using Liapunov functional method ,we establish a sufficient condition on the stability and boundedness of the solutions of above equation．This will generalize the main results of reference［2］.
Key words：retarded Liénard-type equation；stability ；boundedness
CLC number：O175．21
The Uniqueness of Meromorphic Functions with Common Range Sets and Deficient Values
LV Wei-ran, WANG Jun
2003, 18(1): 13-16.
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In this paper ,the uniqueness of meromorphic functions with common range sets and deficient values are studied．This result is related to a question of Gross .
A Class of Two-level High-order Accuracy Explicit Difference Scheme for Solving 3-D Parabolic Partial Differential Equation
WANG Tong-ke, MA Ming-shu, REN Zong-xiu
2003, 18(1): 17-20.
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A class of two-level high-order accuracy explicit difference scheme for solving 3-D parabolic P．D．E is constructed． Its truncation error is ( Δt
2
+Δx
4
） and the stability condition is r = Δt/Δx
2
= Δt/Δy
2
=Δt/Δz
2
≤ 1／6.
Multiple Positive Solutions for Some Neutral Integral Equatious Modeling Infectious Disease
ZHAO Hua-xiang, SUN Xing-wang
2003, 18(1): 21-28.
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By using fixed point index theory of cone mapping and extension method ,this paper discusses the existence of multiple positive solution of nonlinear neutral integral equatious modeling infectious dis- ease .
Composition Operators Mapping into the E(p,q) Spaces
LIU Yong-min
2003, 18(1): 29-34.
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The Least Distributive Lattice Congruence on Commutative Distributive Semiring
LI Shi-zheng, LI Shan-hai, YU Xiao-ming
2003, 18(1): 35-37.
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In this paper ,we describe the least distributive lattice congruence on a commutative distribu- tive semiring .
Singularly Perturbed Nonlinear Boundary Value Problems
GE Hong-xia
2003, 18(1): 38-43.
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In this paper ,a class of singularly perturbed Volterra type of integral differential equations nonlinear boundary value problems are discussed．Under the proper assumptions ,using the method of composite expand and the theory of differential inequalities ,the existence and any order approximation of the solution are obtained .
On Approximation of Nonbounded Continuous Functions
ZHENG Cheng-de, WANG Ren-hong
2003, 18(1): 44-48.
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This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators ,and as an example ,Bernstein poly - nomial operators are analysed and studied．This paper gives a certain theorem as a general rule to ap- proximate any nonbounded continuous functions .
Boundedness of the Solutions of a Second Order Nonlinear Differential System
LIU Bing-wen, ZHONG Yi-lin, PENG Le-qun
2003, 18(1): 49-56.
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In this paper ,author obtain sufficient condition for the boundedness of solutions of the second order nonlinear differential system ...
The result can be applied to the Liénard-type system ,which substantially extends and imporves some important results associated with the same problems in the literatures［1－10］et al . .
The Hausdorff Measure of a Generalized Sierpinski Carpet
CUI Zhen-wen, YANG Yong-qin, WANG Cai-fen
2003, 18(1): 57-67.
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In this paper,first ,we prove that the Sierpinski carpet E is equivalent to the set R ．Then we define a mass distribution on R ．Using a certain of mass distribution,we obtain the lower bound about the Hausdorff measure of R ．Therefore the exact value of Hausdorff measure of E is given．
Some Notes on the Positive Definite Problem of a Binary Quartic Form
CHEN Bao-xing
2003, 18(1): 68-73.
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Herz Spaces on Nilpotent Lie Groups and Its Applications
ZHU Yue-ping, LI Deng-feng
2003, 18(1): 74-81.
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In this paper,we define Herz type spaces on nilpotent Lie groups and give the boundedess of heat kernel and Riesz transform on Herz spaces.
A Class of Biased Estimators Based on SVD in Linear Model
GUI Qing_ming, DUAN Qing_tang, GUO Jian_feng, ZHOU Qiao_yun
2003, 18(1): 82-87.
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In this paper,a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill-conditioning in the design matrix．Some important properties of these new estimators are obtained．By appropriate choices of the biased parameters,we construct many useful and important estimators．An application of these new estimators in three-dimensional position adjustment by distance in a spatial coordiate surveys is given．The results show that the proposed biased estimators can effectively overcome ill-conditioning and their numerical stabilities are preferable to ordinary least square estimation.
A Note on the Generalized Subaffine Elastica in R
2
HUANG Rong-pei
2003, 18(1): 88-92.
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In this paper ,we discuss the generalized subaffine elastica in R 2 ,the critical point of the to- tal polynomial subafficne curvature functional．We completely solve the generalized subaffine elastica by using the Killing field and the classfication of the conjugacy class of sl（2,R）.
An Analysis on the Inconsistency of the Security Supervision Policy in the Method of Game Theory
WANG Xing-yu , JIA Xing-qin
2003, 18(1): 93-98.
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A Sufficient Condition of Hamilton Connected Graph
YIN Zhi-xiang , BAI Mei
2003, 18(1): 99-102.
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Let G be a 3-connected graph with n vertices．The paper proves that if for each pair of verti- ces u and v of G ,d（ u ,v ）＝ 2,has | N（ u）∩ N（ v ）|≤ α( αis the minimum independent set num -
ber）,and then max｛d（ u）, ,then G is a Hamilton connected graph .
The Application of the Fixed-point Theory in Jacketed Solution of Singularly Perturbed Nonlinear Problem
CHENG Yan
2003, 18(1): 103-107.
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In this paper,the fixed-point theorem is used to estimated an asymptotic solution of initial val- ue problems for a class of third nonlinear differential equations which has double initial-layer properties . We obtain the uniformly valid asymptotic expansion of any orders including boundary layers .
On the Category of L-fuzzifying TOP#br#
ZHANG You , WANG Shu-chen
2003, 18(1): 108-110.
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In this paper,the category of L-FTOP and the relations with the categories of TOP , L α-FTOP are discussed.
