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Table of Content
30 September 1997, Volume 12 Issue 3
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An Oscillation Criterion for Second Order Superlinear Differential Equations#br#
Chen Wendeng, Yu Yuanhong
1997, 12(3): 1-6.
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A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t)+ p(t)x′(t) + q(t)｜x(t)｜αsgnx(t) = 0, t ≥ t
0
,where α>1,p and q are continuous functions on [t
0
,∞). This criterion extends and unifies some of the results obtained in [1]- [5].
The Homomorphism and Isomorphism on Hypergroup
Zhong Yubin
1997, 12(3): 7-14.
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Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.
On the Oscillation of Solutions of Second OrderNonlinear Difference Equations
Lin Shizhong, Yu Yuanhong
1997, 12(3): 15-19.
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On the Favard Class of Cosine Operator Function
Hao Yong
1997, 12(3): 20-23.
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In this paper we give some basic properties of the Favard class of cosine operator function, and concern with the question when for a given cosine fuction we have Fav(A) = D(A).
Fixed Point Theorems of Mixed Monotone Operators with Applications#br#
Xie Shengli, Zhang Qingzheng
1997, 12(3): 24-30.
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In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
On Stable Minimal Cylinders in 3-manifolds#br#
Zhao Di, Li Hongyi, Li Shuyi
1997, 12(3): 31-34.
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The purpose of this paper is to improve an important Theorem of Fisher-Colbrie- Schoen'sin[1].
Convergence on Finite Difference Solution for Semilinear Wave Equation in One Space Variable
Lu Bainian, Fang Shaomei
1997, 12(3): 35-40.
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In this paper,the convergence and stability of the 'Leap-frog' finite difference scheme for the semilinear wave equation are proved by using of the bounded extensive method under more generalized condition for the nonlinear term. The more complex standard a priori estimates are avoided so that the theoretical results are complemented for the scheme which was presented by Perring and Skyrne (1962).
The Representation of Continuous Linear Operator by Integral
Zeng Renying
1997, 12(3): 41-44.
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In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
On Periodic Solution of Nonconservative Systems
Li Weiguo, Chen Kunting
1997, 12(3): 45-49.
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In this paper,we consider the following systems x″+ Bx′+ gradG（x,t） = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if ‖B‖2<1.
A Kind of Generalized Hankel Operator
Luo Luo, Shi Jihuai
1997, 12(3): 50-58.
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In this paper,we introduce some opeators on Bergman space (B) that generalize a kind of generalized Hankel operator defined by M. M. Peloso. For such operators we prove boundedness, compactness and Schatten class property criteria.On the eut-off c(N) we know that the phenomenon founded by Peloso is an exceptional case.
The Higher Derivatives of Bianalytic Functions
Xie Chunping, Liu Tao
1997, 12(3): 59-62.
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By using the Cauchy integral formula of bianalytic functions, the formula of higher derivatives of bianalytic functions and Weierstrass Theorem are obtained.
Admissibility for Nonhomogeneous Linear Estimates on Multivariate Random Regression Coefficients and Parameters
Ai Mingyao, Liu Jingmin
1997, 12(3): 63-70.
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I-ring which Satisfies A. D. C. C on Principal Left Ideals#br#
Hu Changliu, Tian Jinjun
1997, 12(3): 71-74.
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In this paper,the I-ring which satisfies almost descending chain conditions (shorten writting A. D. C. C) on principal left ideals is studied. Two main results are gaven: (1) I-ring which satisfies A. D.C. C on principal left ideals is Boolen. (2) Ring with identity whose principal left ideals satisfy A. D. C. C and of which each element except identity is a left zero-divisor, is Boolean.These results generalize the results of [1],[2] and [3].
One Hundred and Eighty-nine Homeomorphism Classes of the G. M.
Yuan Fuyong
1997, 12(3): 75-86.
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In this paper the homeomorphism number of G. M.has been finded with the method of that push the negative edges in inner tier and outer tier into the middle tier as far as possible.
Existence and Life Span of Periodic Solutions for the First Order Quasilinear Hyperbolic Equations
Wang Youan, Wang Yanling
1997, 12(3): 87-94.
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In this paper the authors consider Cauchy problem of first order quasilinear hyperbolic and prove that existence of its periodic solutions and estimates of life span of solutions. This results reveals the relationship of dissipation and smoothness of periodic solutions.
Generalized Convexity and Generalized Quasi-variational Inequality
Zhang Xiaolan
1997, 12(3): 95-100.
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The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.
An Application of Machine Computation for Studying Graphlike Manifolds (Ⅱ)
Zhang Qun, Song Zhongshan
1997, 12(3): 101-110.
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In this note, we designed algorithm and program for homeomorphic classification of graphlike manifolds.counted the numbers of homeomorphic classes of graphlike manifolds with respect to scores contractions of 6-vertexes and noticed a mistake in [7].
