数学季刊

A Combinatorial Approach for Topological Classification of Graphlike Manifolds

林诒勋, 王勤

1998, 13(3): 1-11.

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The concept of graphlike manifolds was presented in ［1］ and the problem of counting the homeomorphic classes of graphlike manifolds has been studied in a series of articles，e．g．，［1～8］．In this paper we suggest an approach based on the graph colouring，Abelian group and the combinatorial enumeration method．

On Torsion Theories of Regulars and V-Rings

张力宏

1998, 13(3): 12-17.

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In the paper，we proved that R is τυring if and only if R is τ-regular ring and studied their properties further．

Some Properties of Fuzzy Filter and Its Category

郭天榜, 程伟

1998, 13(3): 18-22.

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This paper is devoted to the study of some properties of fuzzy filters in lattice implication algebras. The structure theorem of fuzzy filters and the category of the sets of fuzzy filters were established with some basic properties of it were discussed.

Variational Inclusions for Fuzzy Mappings

柏传志

1998, 13(3): 23-28.

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In this paper,a perturbed iterative algorithm for finding approximate solutions of variational inclusions for fuzzy mapping,is presented and a convergence result which includes,as a special case,some known results in this field,is given.

Computation of K₀^...

郝志峰

1998, 13(3): 29-31.

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Let T ＝... and θ＝0．We use a complete different technique to obtain the generalize results for K0 （ T ），i．e．，... .

A Duality Theorem Associated with the Smash Product of Graded Ring and G-set

孙建华, 王卿文

1998, 13(3): 32-35.

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Let G be a group, H<=G and R a G graded ring. We study the duality Theorem for G actions and smash products R#G/H of the G graded ring R and the G set G/H.

Theta Subgroups and the Solvability of Finite Groups

李秀玲, 赵耀庆

1998, 13(3): 36-42.

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For a maximal subgroup M of a finite group G ,a θ subgroup for M is any subgroup C of G such that ... and Core G(M∩C) is maximal among normal subgroups of G properly contained in C . This concept is motivated by the concept of θ pairs which was introduced by N .P.Mukherjee and P.Bhattacharya. The present paper represents an attempt to carry the studies on θ pairs further.We study intrinsic properties of a given family of maximal subgroups and its associate θ subgroups which imply a group to be solvable, π solvable and supersolvable. All of these results are effective improvements of known relative results on θ pairs.

On the Auslander-Reiten Quiver with Oriented Cyclesof Representation-finite Algebras

姚海楼

1998, 13(3): 43-47.

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Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A) we give counterexamples to the assertion.

Generalized ExcellentExtension and Hom ologicalDim ension

赵志新, 刘仲奎

1998, 13(3): 48-51.

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We introduce generalized excellent extension of ring R in [4]. If S is a generalized excellent extension of R, we prove that (1) wgldim S≤ wgldim R and glodim S≤ gldim R; (2) the relations between rings R and rings S.

Sem ilinear Equationswith CriticalExponentsonthe Heisenberg Group

钮鹏程, 张吉慧, 文成林

1998, 13(3): 52-58.

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We consider the semilinear subelliptic Laplace equation -Δ Hn u=u p+f(x,u) in Ω,u>0 in Ω,u=0 on Ω . Under suitable assumptions on f and p ,some existence and nonexistence results are obtained.

Extension of Proper μ-holomorphic Mappings

苏简兵

1998, 13(3): 59-63.

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In this paper,we prove that a proper μ-holomorphic mapping f:D₁→D₂ between bounded domains with some convexity,such that f satisfies some growth condition,extends smoothly to bD₁-{z:U(z)=0}.

Minimum Ellipsiod and Optim alDesign

郑兆顺

1998, 13(3): 64-67.

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This paper deals with the constructing of optimal designs in regression with geometrical methods. It is proved that the covariance matrix of optimal design is fixed by its geometrical constructure. The necessary and sufficient conditions are given to construct optimal design.

On the Existence of Positive Solution for n OrderSingular Boundary Value Problems

史国良

1998, 13(3): 68-73.

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In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 00,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u). n is positive integer and n. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and the TransfiniteInduction

萧治经, 熊萍

1998, 13(3): 74-80.

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In this paper,a converse and negated form of the continuous induction is indicated. We use it to prove six basic theorems of completeness of real numbers system,the existence theorem of limes superiores and limes inferiores of seqence and the properties of continuous function in closed interval by mode of unification.

Generalized Quasi-Variational Inequalities on Paracompact Sets

张昌斌, 李岱

1998, 13(3): 81-85.

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Taking advantage of result in [1], this paper studied generalized quasi variational inequalities on paracompact sets, unified and extended corresponding results in [4-6].

The Semigroup Characterizations of Positive Implicative BCK-algebras

徐少贤, 黄文平

1998, 13(3): 86-90.

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Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.

Metrization of Topological Spaces with a cs-regular Base

李克典, 石玉强

1998, 13(3): 91-94.

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In this paper,we introduce the notions of a cs * regular base,a cs * development and the discretely cs * θ expandability for topological spaces and use these notions to give some metrization theorems. That is a generaliztion of several theorems in [1].

The Matrix Equation A_mnX_nsB_st=Cover an Arbitrary Skew Field

林春艳, 晏曾申

1998, 13(3): 95-101.

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The matrix equation A_mnX_nsB_st=Cover an arbitrary skew field is considered. A necessary and sufficient condition for the consistency and the expression for general solutions of the above mentioned matrix equation are presented.Moreover,a practical method of solving one is also given.

Travelling Wave Solutions for Generalized Fisher Equation

王书彬, 吕延华, 鲁丽萍

1998, 13(3): 102-110.

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In this paper,we obtain some exact travelling wave solutions for the GF equation,the KdV Burgers equation and the RLW Burges equation with the aid of the balanced principle of the homogeneous terms.

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