数学季刊

谢峰

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 .

李安纳特方程的稳定性和有界性

周先锋, 蒋威

2003, 18(1): 7-12.

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This paper aims to investigate the retarded Liénard-type equation
x＋ f₁（ 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 ,f₁,f₂,f₃,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

具有公共值集和亏值的亚纯函数唯一性

吕巍然, 王珺

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 .

三维抛物型方程的一族两层高精度显示格式

王同科, 马明书, 任宗修

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 ( Δt² +Δx⁴ ） and the stability condition is r = Δt/Δx² = Δt/Δy²=Δt/Δz²≤ 1／6.

一类传染病中立型积分方程模型的多个正解的存在性

赵华祥, 孙兴旺

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 .

映入 E(p,q)的复合算子

刘永民

2003, 18(1): 29-34.

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Composition operators are used to study the E（ p ,q）spaces．The boundedness of these opera- tors is also considered．The criteria for these operators to be bounded are given in terms of the Carleson measure .

交换分配半环上的最小分配格同余

李师正, 李善海, 于晓明

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 .

奇摄动非线性边值问题

葛红霞

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 .

关于无界连续函数逼近

郑成德, 王仁宏

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 .

一类二阶非线性微分方程系统解的有界性

刘炳文, 钟益林, 彭乐群

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 . .

一个广义Sierpinski地毯的Hausdorff测度

崔振文, 杨永琴, 王彩芬

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．

关于二元四次型正定问题的若干注记

陈宝兴

2003, 18(1): 68-73.

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In this paper ,we discuss the positive definite problem of a binary quartic form and obtain a necessary and sufficient condition．In addition we give two examples to show that there are some errors in the paper［1］.

Nilpotent Lie群上Herz空间及它的某些应用

朱月萍, 李登峰

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.

线性模型中基于SVD的一个新的有偏估计类

归庆明, 段清堂, 郭建锋, 周巧云

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.

R²中广义次仿射弹性曲线的一个注记

黄荣培

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）.

证券监督政策不一致性的博弈分析

王性玉, 贾兴琴

2003, 18(1): 93-98.

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Hamilton连通图的一个充分条件

殷志祥, 白玫

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 .

不动点定理在奇摄动非线性初值问题的套层解中的应用

程燕

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 .

关于L-fuzzifying TOP范畴

张友, 王书臣

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.

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