Chinese Quarterly Journal of Mathematics

周介良

1988, 3(3): 1-12.

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A subfamily of dpda,Total-RT(K)dpda,was defined in this paper.
The general dpda can be approached by this subfamily.It was proved that the equivalence problem and the containtment problem for Total- RT(K)dpda are decidable.

拟凸条件下变分问题解的正则性

于锦海

1988, 3(3): 13-25.

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映射对的公共不动点定理

张宪

1988, 3(3): 26-32.

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Let (X,d) be complete metric space and f,g be self-mappings on X.We introduced Some contractive type conditions labeled(A),(B),(C),(D) and(E). We showed that if (f,g),(g,f)∈{(A),(B),(C),(D),(E)}, then there exists unique common fixed point of f,g.

关于序集碰撞数问题深度贪心算法的最优性

闻振卫

1988, 3(3): 33-42.

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Let L=x₁…x,be a linear extension of a poset P.Call(x,x+1)a bump of L if x₁<x+1(P).The number of bumps in L is denoted by B(L). A linear extension L*of P is optimal if B(L*)=min{B(L):L is a linear extension of P},Fishburn and Gehrlein conjectured that,for any poset P, there exists an optimallinear extension gnerated by an algorithm which is greedy with respect to the depth.In this paper,we prove that this
conjecture is true and that if a poset P is N-free,then all its linear extensions generated by this algorithm are optimal.

常微分方程解的渐近性质(Ⅰ)

赵怀忠

1988, 3(3): 43-51.

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In this paper,the asymptotic behavior of ordinary differential equations is studied.Set stability,set uniform stability,set unstability,set asymptotic stability,set globally asymptotic stability,set qusicontractive stability,set globally qusicontractive stability,set contractive stability and set globally contractive stability,are consldered some theorems for all kinds of stability mentioned-above are proved by means of the Lyapuovlike functions.

支撑树参数值的分布

徐济超

1988, 3(3): 52-54.

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In this paper,we show that the distributions of some main parame- ters(except diameter)are intervals of integral set Z by using a foundama- ntal theorem.A counter example given in this paper shows that the diam- eter of spanning tree has no the property mentioned above.

联合最佳逼近的特征和唯一性

郭元明

1988, 3(3): 55-60.

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In this paper,we define the concept of a“strict sun”in a normed linear space,which is a generalization of a convex set.The charactriza- tion and unicity of the best simultaneous approximation are given when the approximating set is a strict sun.we also obtain the characterization of the best simultaneous approximation when the approximating set is a arbitray subset.

图中最长的导出路

Fred Buckley, Frank Harary

1988, 3(3): 61-65.

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本文讨论了导出迂回数的极值问题，特别地在给出顶点数和边数的所有图及所有二分图中找到了导出迂回数的最大值.

证明论及其发展

徐云从

1988, 3(3): 66-72.

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This paper expounds the growth and development on proof Theory.
It covers several main achievements from Hilbert to Friedman's work in recent years.

算子的一种更弱的相似性与互逆性

席俊

1988, 3(3): 73-84.

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In this note we introduce the sub-quasisimilarity of two operators,it is a much weaker relation than quasisimilarity,so weak that two normal operators may be sub-quasisimilar but not unitarily equivalent.
The purpose of this note is to investigate what properties of opera- tors are preserved by sub-quasisimilarity and what are not.In §4,we generalize some results of [3]and [9],and these generalizations give a partial answer to a question on reductive operators.

斜群环及其上的模

张兆基

1988, 3(3): 85-92.

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We investigate the primality,maximum condition,semisimplicity, and self-injectivity of skew group rings.Our results are satisfactory.Me- anwhile,we present the definition and some properties of skew group modules.

关于一些代数问题的复杂性下界

李磊, 游兆永

1988, 3(3): 93-96.

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This paper discussed the lower bound of complexity of some al- gebraic problems.The results make known that further improvement of these fast algorithms will perfect1y be dependent on research nf Discrete Fourier Transformation.

补充定义法

黄乘规

1988, 3(3): 97-104.

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作者1979年首先在“两相微积分”〔3〕中引入了补充定义法，今将此法与实和复分析中其他方法结合去求微分方程的数值解。对边值问题：u”=1+u²+u'",u(0)=u(2)=0, 我们在复平面做补充，取两条积分路径得到两个复近似解，其初条件为： u'(0) =-0.15892256D+01+0.13558504 D+01i(u(2)=0.48810022D-06-0.50833822 D -06i) 和 u'(0)=-0.15892243D+01-0.13558505D+01i(u(2)=0.15517996 D-06-0.20780524D-06i), 此问题没有实解.对特征问题：- d²y/dx²+x²y/4=Fy ,-∞<x<+∞, 我们在同空间中做补充，去解-d²y/dx²+x²y/4=Fy,-8≤x ≤8. 得到六个近似特征值：F=0.500000,1.500000,2.500000,3.499999,4.499999,5.499999,他们很接近于理论值。此法对非线性和线性方程同样有效，可达指定精度，迭代次数少，并可广泛地用于常微和偏微的应用问题。

一类适合于多变量散乱结点的插值方法及其收敛性分析

吴宗敏

1988, 3(3): 105-110.

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A global interpolations method for multivariate scattered data is established and the convergence rate of the interpolation 'is analysed.

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