Chinese Quarterly Journal of Mathematics

Quasi-con form ally Flat Manifolds with Constant Scalar Curvature

Song Hongzao, Wu Baoqiang, He Huixia

1998, 13(4): 1-6.

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Goldberg and Wu studied a conformally flat manifold M with constant scalar curvature. When the Ricci curvature of M is of bounded below or positive,the conditions of M becoming a constant curvature manifold are obtained. In this paper,we consider conharmonically flat manifolds and quasi conformally flat manifolds with constant saclar curvature. The corresponding results are generalized.

The Non-standard Characteristics of Functional SpacesK（X） and C₀（X）

Chen Dongli

1998, 13(4): 7-9.

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In this paper,the non standard characteristics of functional spaces K(X) and C₀(X) are presented and proved.

A New Third S.N.Bernstein Interpolation Polynomial

He Jiaxing, Li Xiaoniu

1998, 13(4): 10-16.

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In this paper，a new third type S．N．Bernstein interpolation polynomial H _n（ f ；x ，r ） with zeros of the Chebyshev ploynomial of the second kind is constructed．H n（ f ；x ，r） converge uniformly on ［－1，1］ for any continuous function f （ x ）．T he convergence order is the best order if f （ x ） ∈C^j［－1，1］，0≤j ≤r，where r is an odd natural number．

Lattice Im plication Homom orphism inIm plication Filter Spaces

Song Zhenming, Wang Jianping

1998, 13(4): 17-23.

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In this paper，we investigate some special properties of lattice implication homomorphism in implication filter spaces．We show that lattice implication homomorphism is a continuous function with respect to implication filter topology．Moreover，we give a structural characterstic of left-translation topology and right-translation topology，which finally leads to the structural characteristics of product topology．

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅱ)——Also on the unity of the Continuous Induction,the Mathem atical Induction and the Transfinite Induction

Xiao Zhijing, Xiong Ping

1998, 13(4): 24-28.

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In this paper，a common characteristic of real number system and well ordered set is revealed and proved to be an quivalent form of the Dedekind Axiom or the Continuous Induction in R．Basing on it，we get the unified form of the mathematical induction，the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic．

The Inner Radius of Univalency of the Rhom busDom ain

Zheng Xueliang

1998, 13(4): 29-32.

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The inner radius of univalency of a domain is greater than zero if and only if the domain is a quasidisc．However，little is known about the value of the inner radius of univalency for various quasidiscs．In this paper，we will use the comparison principal and obtain the value of the inner radius of univalency of the rhombus domain．

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Feng Libo

1998, 13(4): 33-34.

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This paper deals with a class of second order nonlinear neutral functional differential equation，the author gives a oscillatory criteria．

About Moore-Sm ith Convergence on l-Module

Yuan Jian, Xu Yang

1998, 13(4): 35-40.

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In this paper，we first defined an important concept of convergence on l*-module，which is a double lattice-ordered algebraic sturcture，then discussed the properties about the convergence，finally built up a topology named l*-topology．

The Property about Space of Q^＃_pFunctions

Gou Jidong

1998, 13(4): 41-43.

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In this paper，we extended prof Yao Bi Yunʾs conclusion to Q^＃_p spaces which wider than BM OM ，Prof Yao Bi Yun article can be found in volume15（1986），advances in M athmatics．

On the Structure of the B-cocleft Module Coalgebra

Jiao Zhengming, Wang Shuanhong, Zhao Wenzheng

1998, 13(4): 44-47.

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In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H-weakly comodule coalgebras and Hmodule coalgebras．T he main result is to prove a structure theorem about B-cocleft H-module coalgebras．

Reducible Dehn Surgery and Annular Dehn Surgery (Ⅰ)

Qiu Ruifeng, Li Zihao

1998, 13(4): 48-52.

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Let M be a campact，orientable，irreducible，∂-irreducible，atoroidal，anannular 3-man-i fold with one component T of ∂M a torus．Suppose that r₁ and r₂ are two slopes on T ．In this paper，we shall prove that if M（ r₁） is reducible while M （ r₂） contain an essential annulus，then △（ r₁，r₂） ≤3．

The Structure and Stabilization Decom position of Linear Interconnected ControlSystem swith Multidelays

Zhang Xinzheng, Deng Zeming

1998, 13(4): 53-58.

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This paper gives a structural concept for linear interconnected control systems with multidelays，which is based on equivalence method of lyapunovʾs frequency area，a sufficient criteria is obtained for the interconnected stabilization of linear constant control system with mult-idelays，at the same time，the estimation of bound both time-delays and parametric perturbation are given．

Note on Reflexive Algebras with Non-distribut iveInvariant Lattices

Zhao Junxi（赵君喜）

1998, 13(4): 59-63.

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In this note，we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity，automorphism and finite rank operators．

The HeatKernel ofthe Sym m etric Space P_n

Lu Keping

1998, 13(4): 64-69.

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In this paper the heat kernel of the symmetric space P_n is obtained．

The Existential and Uniqueness of Solution for Zakharov-kuznestov Equation#br#

Hu Yue, Deng Jiʾen, Tang Gang

1998, 13(4): 70-76.

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In this paper，we consider the existential and uniqueness of solution for Z-K equation Cauchy problem in H^s（ s＞2）．

Quilitative Analysis of a Class of Simulate Seasons Environm ent Chem ostat Systems

Song Guohua, Yang Xiaozhong, Li Xiuqin

1998, 13(4): 77-82.

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In this paper，a class of chemostat systems with simulate seasons Environment in the following form ... is discussed．It is abstained that the system has not periodic solution when b＝0；if b≠0 and b≪1 then system has 2π-periodic solution of system．globally asymptotically stable as m/Q＜μ*^－1 and is unstable as m/Q＞μ*^－1 and there exists at last one minimal 2π-periodic solution （ s（ t），x （ t）） with x （ t）＞0，0＜s（ t）＜s*（ t）．

A Note on Hilbert's Integral Inequalities

Yang Bicheng

1998, 13(4): 83-86.

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In this note，by introducing a couple of parameters T ，t and estimating the weight function effectively，Hilbertʾs integral inequalities are well generalized．As applications，we give some new Hilbertʾs type inequalities．

Existence and Nonexistence of Global Solution for Quasilinear Parabolic Equation

Song Jinping, Hu Yue, Cui Guozhong

1998, 13(4): 87-93.

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This paper deals with the existence and nonexistence of global positive solutions of the following quasilinear parabolic equations：... is a bounded domain with smooth boundary ∂●，m，n，p are positive constants，γ is the outward normal vector．The necessary and sufficient conditions for the global existence of solutions are obtained．

The H-stability of the Solution for Infinite Delay Functional Differential Equation

Li Xiaoʾai, Shang Deqing

1998, 13(4): 94-98.

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H-stability is a new and important concept．In this paper，we discuss the equation ... and we gain a new decision theorem．Using this decision theorem，we obtained a very extensive result of the H-uniformly asymptotical stability of this equation．That is，eliminating the restriction that a（ t） is bounded．

Some Properties of a Class Self-homomorphism of BCI-algebras

Yuan Minying, Li Yijun

1998, 13(4): 99-102.

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Some properties about stable subset S（ θ_n ） and image Im （ θ_n ） of self-homomorphism θ_n：x →0*xⁿare discussed．The characterization that Im（ θ_n） becomes an ideal of BCI-algebra X is given．

Totally Geodesic Invariant Submanifolds of Contact Metric Manifold

Wan Yong, Song Hongzao

1998, 13(4): 103-105.

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The purpose of this paper is to give a sufficient and necessary condition of totally geodesic on invariant submanifold of contact metric manifold and is to generalize the results in ［3］and ［4］．

A Method to Solve Systems of Fuzzy Linear Equations

Zhang Yanʾe, Sun Jianping, Wang Xizhao

1998, 13(4): 106-110.

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Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α-cuts and interval arithmetic．In this paper，we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations．

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