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Table of Content
30 March 1997, Volume 12 Issue 1
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Involutive Solutions and Commutator Representations of the Dirac Hierarchy
Qiao Zhijun
1997, 12(1): 1-3.
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The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the nonlinearization of Lax pair the involutive solutions of Dirac hierarchy are obtained.
On the Gracefulness of Two Family of t
he
Hexagonal Graphs
Yang Yanchang, Wang Guangxuan
1997, 12(1): 4-12.
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In the paper,we construct two families of the hexagonal graphs G₁(n)and G₂(n),and prove their gracefulness.
A Criterion of Decomposable Elements in V
(2)
Zhu Zhongnan
1997, 12(1): 13-17.
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In this paper, a criterion of decomposable element in V
(2)
is obtained , i. e.,... is decomposable if and only if its adjacent coordinate matrices are all "row 1≤i≤j≤n commute" equivalent.
Asympototic Behavior of Semilinear Periodic-Parbolic Boundary Value Problem
Feng Xiufang, Yang Wanli
1997, 12(1): 18-24.
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We study a class of semilinear periodic-parabolic boundary value problem with small diffusion coefficients,give its asymptotic behavior when the diffusion cofficients go to limit zero.
On the Characterization of a Class of π-inverse Semigroups
Qiao Zhanke, He Wansheng
1997, 12(1): 25-29.
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As a generalization of strongly π-inverse semigroups given in [1],the notion of strongly right π-inverse semigroup is introduced and some of its characterizations are given. A necessary and suffiient condition is obtained for the class of strongly right π-inverse semigroups.
On Filters of Double MS-algebras
Fang Jie
1997, 12(1): 30-34.
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Here some properties on filters of double MS-algebras are descripted. We show that,for a normal filter F of a double MS-algebra (L;0, + )(x,y) ∈θ(F) (a,b ∈ F) (x ∧α)∨b+= (y ∧ a)∨ b+.
A Class of Nonlinear Singularly Perturbed Problems of Fourth Order
Mo Jiaqi, Liu Shude
1997, 12(1): 35-37.
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A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.
Oscillation of Neutral Equations with Variable Coefficients
Zhou Yong
1997, 12(1): 38-42.
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Consider the neutral equation with variable coefficients dt[x(t) - P(t)x(t - γ)] + Q(t)x(t -σ) =0 where P,Q∈C[[t
0
,,∞),R+] and σ,∈R+. We obtain some new sufficient conditions for the oscillation of soutions of the.abave equation without the restriction:0<= P(t)<=1 or P(t)>= 1.
On Periodic Solutions of a Class of Differential Equation with Periodic Coefficients
Feng Zhaosheng, Fei Shumin
1997, 12(1): 43-46.
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In the present paper we are concerned with the following differential equation with pcriodic coefficients y' = f(t,y) = A(t)y" + B(t)y + C(t) (m>=2,m ∈N) (1)and obtain the theorems for the existence and the number of equation (1). Our results extend and improve the corresponding ones in [1,4].
The Semimodularity of Cardinal Power of Posets
Hu Changliu
1997, 12(1): 47-51.
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Let X,Y be any posets,the semimodularity of cardinal power YX with base Y and exponent X is studied. Some necessary or sufficient conditions for YX to be semimodular are gaven.
Finite Difference Method of First Boundary Problem of a Generalized Diffusion Model in Population
Guo Xiulan, Li Guoqiang
1997, 12(1): 52-60.
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The solution of nonlinear parabolic equation arising from population dynamics with boundary and initial value are established by the finite difference method,as well as it denotes the unique generalized global solution.
Meta-projective Modules, Tensor Products and Limits
Feng Lianggui
1997, 12(1): 61-64.
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In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field R
1,
R
2
be K-algebras, we also obtain a sufficient condition for lgldim (R
1
R
2
,)≥lgldim R
1
+lgldimR
2
, and wgldim (R
1
) ≥wgldimR
1
+wgldimR
2
.
Some Characterizations of Nil Ideals in BCI-algebras
Huang Wenping, Xu Shaoxian
1997, 12(1): 65-69.
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Some properties of nil ideals in BCI-algebras are discussed. The notion of k-associative BCI-algebras which is a generalization of associative and quasi-associative BCI-algebras is introduced. Moreover,several characterizations of k-associative BCI-algebras are given.
Totally Real Minimal Submanifolds in a Quaternion Projective Space
Shu Shichang, Jia Xingqin
1997, 12(1): 70-75.
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Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
On the Uniqueness of the Positive Solution for a Semilinear Elliptic Problem with Critical Exponent
Yuan Jian
1997, 12(1): 76-80.
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This paper discussed the uniqueness of the positive solution for a semilinear elliptic problem with critical exponent.
Existence of Solutions for Nonlinear Implicit Complementarity Problems in Reflexive Banach Spaces
Zeng Luchuan
1997, 12(1): 81-86.
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In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.
The Least Square Solutions to the Quaternion Matrix Equation AX=B
Xue Youcai
1997, 12(1): 87-90.
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A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
On the Smallest Base of the Stone Space
Bai Ruipu
1997, 12(1): 91-94.
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In this paper,first we define the concept of strong open set for topological space. Then we prove: 1 ) a distributive lattice L possesses the smallest set of generating elements if and only if the Stone space (L) of L possesses a smallest base constructed by strong open sets; 2) a Bollean lattice B possesses the smallest set of generating elements if and only if B is a finite Boolean lattice.
A Fixed Point Theorem for Multi-valued Composite Increasing Operators in Partially Ordered Spaces
Yang Xinhua
1997, 12(1): 95-97.
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In this paper,we give a fixed point theorem for multi-valued composite increasing operators,in partially ordered spaces,which generalizes the results of [1]-[3] and [5]- [8].
On Torsion-free Connections in Finsler Geometry
Guo Ruizhi
1997, 12(1): 98-103.
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We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
Minimum Cycle of Row Vector of a Generalized Circulant Fuzzy Matrix
1997, 12(1): 104-110.
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