Chinese Quarterly Journal of Mathematics

The Structure of Involutive Rings Which in the Residue Class Rings

Yang Zixu

1994, 9(3): 1-5.

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A associative ring R with an unit element is called an Involutive Ring,if every element of the muttiplicative group U(R),which consists of all the units of R,satisfies equation z²=e,where e is the unit element of R:In this paper,we have proved that the residue class ring Z.modulo n>1 is an involutive ring if and only if n are the fnllowing numbers:
2,3,4,6,8.12,24. Moreover,we call a ring R is an U-cyclic ring if the unit group U(R)is a cyclic group. We have proved also that the involutive ring Z,modulon>1is an U-cyclic if and only if n are the following integer numbers:2.3,1,6.

On the Initial Value Problem and Fundamental Solution for a Class of Homogeneous Left Invariant Differential Operators on the Heisenberg Group

Niu Pengcheng, Zheng Zhujun

1994, 9(3): 6-12.

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In this paper we will study the wellposed of the initial value problem associated to the homogeneous left invariant differential operator on the Heisenberg group by the method of group Forier anasis ... where a,>0,r∈R)on the Heisenberg group,then obtain the explicit expression of the fundamental solutions for the generalized heat operator and the operator L.

The Improvement of Fischer's Inequality and Hadamard's Inequality

Huang Liping

1994, 9(3): 13-18.

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This paper improves Fischer's inequality and Hadamard's inequality as follows: IfA=(a,) is either an × totally nonnegative matrix with or a n×n nonsingular M-matrix or a n×n positive definite Hermitian matrix,then ... where aC(m>={1,2,…,x} and d=(m》-a.

The Property of Bair in r-Space

Song Zhenming

1994, 9(3): 19-20.

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In this paper,we study properties of Bair by symmetric difference.

The Spectral Characterizations of Some Minimal Submanifolds of a Sphere

Zhou Zhenrong

1994, 9(3): 21-25.

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In this paper,we characterize by the spectra a Clifford minimal hypersurface and the totally geodesic submanifold of a unit sphere,and generalize the result of paper [4].

Coupled Quasisolutions of Volterra Intergral Equations with Discontinuons Terms in Banach Spaces

Zhou Zhi, Yu Zhaoxia

1994, 9(3): 26-31.

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This paper investigates coupled minimal and maximal quasisofutions of volterra integral equations with discontinuous terms via monotone iterative method in Banch spaces.Main conclusions in this paper generalize and improve some well-known results.

Application of Generalized Legendre Polynomial in Combinatorial Identities

Zhang Zhizheng, Lei Zhijun, Tian Weisheng

1994, 9(3): 32-36.

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The purpose of this paer is to establish some identities from generalized Legendre polynoials. These results eneralize the results of P.C.Joshi and N.Balakrishnon in [1].

Congruent Pairs On a Set

Zhu Zuotong, Huang Junmin

1994, 9(3): 37-40.

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In this paper,we introduce concepts of stabiliser subsets of a set and congruent pairs,and generalize and discuss Oehmkes'problems.Specially we have got relative results of semigroups for Oehmkesproblems.

Existence and Uniquenss of Best Simultaneous Approximation

Liu Ruizhen

1994, 9(3): 41-43.

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Oscillations of Second Order Nonlinear Neutral Differential Equations

Wang Qiru, Wu Yewei

1994, 9(3): 44-48.

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This paper discusses a class of second order nonlinear neutral differential equations with variable coefficients and variable deviations. Oscillation oriteria for all solutions of the equations are established and sufficient conditions are also given to ensure those derivatives.of all differentiable solutions of the equations to be oscillatory.

Curvature Estimates for Strongly Stable Domains on Surfaces with Constant Mean Curvature in Space Forms

Wang Zhiguo, Wu Zhiqing, Sun Min

1994, 9(3): 49-52.

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In this paper the authors give the curvature estimates for complete strongly stable surfaces with constant mean curvature in space forms and extend the related results.

Global Regularity of Weak Solutions to Degenerate Eliptic Systems in Triangular Form

Ye Ruifen, Chen Jie

1994, 9(3): 53-68.

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In this paper,using direct method,we prove the global Holder continuiy of weak solutions to degenerate eliptic systems in triangular form.

On Existence of the Maximum Solution and Estmates on Moments of Absolutes Maximum of the Solution for Poisson S．D．E in the Plane

Zhang Sujing

1994, 9(3): 69-75.

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Let M be the poisson point process on R.=[0,z_o].wher ∈0=(0,c)×[0,∞], ∴ N be the characteristic measure and poisson compense of M,respec:ively. The existence of the maximum solution,estimates on moments of absolutes supremum of the solutions for poisson S.D.E in the piane. ... are obtained in this paper.

The Robust Design with the Pole Assignment

Zhou Qingquan, Wang Ping, Liu Xianxing, Hou Junxia, Xi Tiezhuang

1994, 9(3): 76-81.

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The paper presents the robust design method for the linear time-invariant systems that are designed the control law by means of the pole assignment.The design makes the systems having the more powerfu!robustness.

The Bergman Kernel Function and Full Group of Holomorphic Automorphism on a Reinhardt Domain

Guan Binxin, Wang An

1994, 9(3): 82-87.

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By using the transformation rule for the Bergman kernel functions under proper holomorphic mappings and the theorem ofLu Qikeng,the Bergman kernel function and full group of holomorphic automorphism for a Reinbardt domain are given in this note.

Integral Solution Operators for the Cauchy－Riemann Equations on an Open Set with Piecewise C¹－Boundary

Ma Zhongtai

1994, 9(3): 88-94.

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The methods of Niles p vrelid which he used in strictly pseudoconvex domains are cosulted,in this paper,and not only for imhomogeneous Cauchy-Riemann equations on some cases that for bounded open sets with C'-Boundary,bounded open sets with piecewise C¹-boundary,and peudoconvex domains with C¹-boundary are discussed,but also their linear integral operators solutions and elementary estimated are corresponding given.

On the Left Classical Quotient Rings of the Superprime Rings

Chen Peici(

1994, 9(3): 95-101.

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In this paper,we define the left rank of a ring Rand discuss the relations between a left ore reng Rand its left classical quotient ring Q on the properties of their ideals and left ranks.Also we gave four equivalent types of the proposition:a ring Rhas a left classical quotient ring Qand Qis a division ring.As an application of this result,we gave a brief proof method which different from [2]on the theorem of the Goldie Prime rings.

A Method for Solving Exact Solution to Two－dimensional Korteweg－de Vires－Burgers Equation

Jiang Weilin, Zhang Jiefang

1994, 9(3): 102-103.

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The exact soliton wave solution for the two-dimensional Korteweg-de Vires-Burgers equation is obtaind via introducing nonlinear transformations.This method,which is different from reference [1],here is very concise and primary.The metiod in this letter can be aprlied to other nonlinear equations.

Completeness of the Metric Space Induced by Finite Measur

Yu Jianli, Jin Jiaqi, Wang Wei

1994, 9(3): 104-106.

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In this paper,the metric space induced by finite measure space(X,A) is introduced completeness and researched.

Finite π-Quasisurpersolvable Groups

Yu Yuehua

1994, 9(3): 107-110.

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In this paper we have extended the notion of finite surpersolvable groups to π- quasisurpersolvable groups,and have shawed series of properties of group of this sort and have extended theorem 9 in [1] and two main results in [2].

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