数学季刊

超幂模型与超闭映射

武康平

1989, 4(4): 1-10.

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The relations between ultracompactness of topological spaces and ultra- closedness of mappings,are further studied in this paper.The properties of ultraclosed mappings]are displayed.An expression of D-limits of nets in a space is given by using closure operation.The notions of ultracon- tinuity and ultraperfectness of mappings are presented on the basis of
[6]and [9],and relations between these mappings are,discussed.The main work of this paper is the study of cartesian products and diagonals of map- ping.And a theory on ultraclosed mappings is set up.

p-级数域上的取样定理

肖昌柏

1989, 4(4): 11-14.

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实数群R上的取样定理已有许多数学家研究过,P.L.Butzer在[1]中阐述了该课题的历史及主要结果。程民德、沈燮昌、周民强在[4]中建立了Walsh变换的相应结果。李世雄在[5]中建立了一类局部紧Abel群上的取样定理,推广了上面提到的两种情形,但他要求所讨论的拓扑群的对偶群具有紧生成者,故局部域(见[2])便不在他讨论的范围内,本文建立了一类特殊的局部域(p-级数域)上的取样定理。

B₂型单 G 模 H‘(X)

柏元淮

1989, 4(4): 15-23.

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具有周期系数的三阶线性微分方程解的稳定性

卢德渊, 廖宗璜

1989, 4(4): 24-31.

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In this paper,We give the sufficient conditions of the unstability of zero solution for the third order linear differential equation with periodic coefficients ...

关于β级α-凸函数的一点注记

李建林

1989, 4(4): 32-37.

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In this note,some properties about the a-convex functions of order β is obtained simply,such as subordinate relation,coefficients estimation,etc.In the class of convex functions of order β,we show that the Brickman's conjecture was true.

非负矩阵谱半径的两个性质及其应用

游兆永, 李磊

1989, 4(4): 38-40.

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本文改进了Perron-Frobenius非负矩阵理论中有关非负矩阵谱半径的两条定理,利用该结果给出了文[3]中Jacobi迭代收敛定理的一种简单证明。以下记:n阶方阵A(αij)n×n,非负矩阵|A|(|aij|)n×n,ρ（A）表示A的谱半径,I表示单位矩阵。

关于Gackstatter猜想

詹小平

1989, 4(4): 41-45.

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In this paper,We proved equation ... does not have any admissible solution except that ... ，a be small function. Also we proved some results which improved that of C.C.Yang.

二阶周期系数线性微分方程组零解稳定性的充要条件

郜奉欣, 侯占元, 张振国

1989, 4(4): 46-55.

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Consider the secnod order linear differential system with periodic coefficients

π=A(t)x (*)

and the stability problem of its trivial solution.In this paper,there are several conditions which are given including a necessary and sufficient condition for asymptotic stability,a necessary and sufficient condition for some kind of unstability, and a sufficient condition for stability.These conditions are expressed directly by coefficients A(t) instead of characteristic values of the system (*). Therefore,a feasible method of judging stability of the system(*) is offered.

调和函数的插值问题

文鸣

1989, 4(4): 56-63.

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超解析函数在Jordan开曲线上的Riemann问题

曾岳生

1989, 4(4): 64-72.

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对于2r个实未知函数的广义Beltrami方程组,利用超复数可交换代数（er=0,r∈N;ae=ea,a∈G）,可以写成简单的形式[1]: DW（z）=0,z=x+iy,

复射影空间的正曲率极小子流形

宋鸿藻, 吴报强

1989, 4(4): 73-77.

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We give pinching theorems with respect to thc scalar curvatures of 4- dimensional projectively flat(concircularly flat 、conharmonicly flat 、quasi-conformally flat)totally real minimal submanifolds in a 4-dimensional complex Projective Space.

关于C-分层空间

夏省祥

1989, 4(4): 78-82.

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In this paper we obtain the following results:
(1)Perfect mappings preserve C-stratifiable(C-semi-stratifiable,KC- semi-stratifiable)spaces.
(2)The image of a C-stratifiable space under a closed mapping need not be C-semi-stratifiable space.
(3)The image of a C-stratifiable space under a pseudo-open K-mapping is a C-semi-stratifiable space.

BE-代数上的模与半本原BE-代数

方朝臣, 高振林, 陈辉

1989, 4(4): 83-90.

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文[1]中引进了BE—代数以后,文[2]给出了这种代数的同态、同构定理,本文在[1]、[2]的基础上,把[5]中带算BCK—代数的概念加以抽象化,引进BE—代数上的模概念以及半本原BE—代数和BE—代数的Jacobson根,讨论这种模的一些基本性质,给出Jacobson根的表达式,证明了半本原BE—代数的结构定理。本文中BE—代数均指M(E):(E,·,1)为么半群。所用符号和术语同[1]、[2]、[3]、[4]。

关于正定矩阵的一点注记

陈顺卿, 王子玉, 张文俊, 冯慈璜

1989, 4(4): 91-97.

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In this note,we obtained an Young type inequality about the traces for semi-positivedefinite matrices,which easily gave the Hölder type and Minkowski type inequalities on the same objects.We also got a Polya- Szego type inequality as an answer to the converse problem of Bel1man conjecture.

无限时滞系统的稳定性

特古斯, 唐忠宪

1989, 4(4): 98-99.

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三状态齐次Markov链的嵌入问题

肖果能, 陈安岳

1989, 4(4): 100-102.

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雅各比级数所定义整函数的极大项

王安斌

1989, 4(4): 103-106.

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单位根为结点的Hermite插值

涂天亮, 莫啟吾

1989, 4(4): 107-109.

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关于循环有向图的弧强连通度

徐俊明

1989, 4(4): 110-110.

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