数学季刊

An Outline of DaiXu's Mathematical Achievements

王荣彬

1995, 10(3): 1-8.

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This present paper deals with the main methematical achievements of Dai Xu,a fa- mous mathematician of the Qing Dynasty:Dai Shi Series Numbers,Dai Shi Iterative Method, Kai Ji Duo Wei Jiu-Cheng-Fang Method and the Relationship between Exponents and Loga- rithms etc.,which have been ignored by former research workers.The paper also puts forward different understandings from the past research at the following points:the Artificial Loga- rithm,the Formula for Changing Base,the Binomial Theorem and so on.

The Third Order Estimate of Mixed Finite Element for the Navier-Stokes Problem

罗振东

1995, 10(3): 9-12.

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Meromorphic Functions with Two Deficient Values

徐万松

1995, 10(3): 13-16.

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In this paper we deal with the problem of uniqueness of meromorphic functions with two deficient values and obtain a result which is an improvement of that ofF.Gross and Yi Hongxun.

One Class of Hyperbolic Function Equation and Its Application

白凤图

1995, 10(3): 17-22.

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In this paper,one class of transcendental function equation is considered.Using the methods of one-dimensional search,series expansion of function and the property of infinite series,we obtain existence,distribution of solution for this equation,we also discuss it's some application.

Approximation of Generalized Szasz-Mirakjan Operator

程海来

1995, 10(3): 23-28.

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In this paper,the author define a kind of generalized Szász-Mirakjan operator and dis- cuss its convergence and degree of the approximation,extend some results got by J.GrofD]and Z.Ditzian[2].

BCC-Algebras and BCK-Algebras

张小红, 卫宗礼

1995, 10(3): 29-31.

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We investigate some properties of BCC-algebras and prove the following results:(1) any BCC-algebraX has a subalgebra Z(X),where Z(X)={z∈XIV x,y∈X,x(yz)=y(zz)};(2)the dual algebra of Z(X)is a BCK-algebra.

The Relative Properties of Graded Ring R and Smash Product R# G*

魏俊潮, 李立斌

1995, 10(3): 32-36.

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Let G be a group,R be a G-graded ring,jG|-¹∈R,this paper deals with some relative properties of R and smash product R#G.We give out R is graded regular ring,graded rig+SF-ring,graded right V-ring,graded QF-ring if and only if R is regular ring,right SF-r ,right V-ring and QF-ring respectively.

2-Harmonic Totally Real Submanifolds in a Complex Projective Space#br#

孙弘安

1995, 10(3): 37-41.

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In this paper,we discuss the relations between the 2-harmornic totally real submsni fold and the minimal totall real submanifold in the complex projective spsace,and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally.real submanifold in the complex projective space.

The Metapositive Definite Self-Conjugate Solution of the Matrix Equation AXB=C over a Skew Field

王卿文

1995, 10(3): 42-51.

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Let F be the strong p-division ring [4].This paper is sequel to [1].Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented.Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.

Application of the Regularization Method to the Numberical Inversion of a Class of Generalized Radon Transform

蒋慧琴

1995, 10(3): 52-58.

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In the research of bistatic tomography imaging of translating object,we get a class of generalized Radon transformation.In this paper,first we prove the existence and uniguenness of its solution in theory and point out this problem is ill-posed with an especial example Secondly by means of multiplicative interpolation functions to approximate models,we constracted regularizing functional.Fially we simplify calculation by Fourier transformation, get regularizing solutions that converge to accurate solution.

A Fixed Point Theorem for Multi-valued Composite Increasing Operators

李凤友, 刘云生

1995, 10(3): 59-61.

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In this paper,we give a fixed point theorem for multi-valued composite increasing operators,which generalizes the theorem of the paper [1]under not only multi-valued mappings but also single-valued mappings.And we generalizes the corresponding results of [2]~[5].

Existence and Uniqueness of Solution for a Fourth Order Differential-Difference Equation

王培光, 王宗申

1995, 10(3): 62-66.

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Using Schauder's fixed point theorem,the existence and uniqueness theorem for a fourth order differential-difference equation is given.

Solutions to a Class of Differential-fuctional Equations

李泽民

1995, 10(3): 67-71.

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In this paper,we study the solutions to a class of equations such as f(2x)= 2f(z)f(z).Some related problems are discussed.

The Existence of Periodic Orbits for Higher Dimensional Autonomous Systems with Small Perturbations

蒋里强, 周毅, 范晔, 王越

1995, 10(3): 72-77.

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By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations,we discuss the existence of nontrivial periodic orbits for higher dimensional autonomous system with small perturbations.

On a Generalization of Some Restrictive Distribution Theorems

田震 , 张松

1995, 10(3): 78-85.

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This paper is on a distribution question of I type in the combinatorics(see:“Ke Zhao,Wei WanDi,combinatorial theory,science press,1981.").Suppose n distinct balls,m distinct boxes,m=p+q,0≤p,q≤m.The capacity set of every box is ….

Solutions of Schródinger Equations in Gravitational Field

王惠民, 刘书振, 陈书勤

1995, 10(3): 86-90.

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For three cases(rectilinear motion,circular motion and small vibration)the Schrodinger equations in the gravitational field were solved.

The Jacobson and Brown-McCoy Radicals of Certain Group Rings

周永新

1995, 10(3): 91-96.

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In this paper,we determine the Jacobson radicals and Brown-MeCoy radicals of group rings of certain non-abelian groups and generalize some known results.

Global Existence of Positive Solutions for Volterra Integral Equations

王术, 万春林, 张锟

1995, 10(3): 97-101.

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This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations (I) ... Matrix B is called a positive definite one,if all the k-th(k=1,2,3 )principal minors have positive deteminants.By considering theexistence of positivve solutions for algebra equations,it is proved that if I-A is a positive definite matrix, where I is an identity matrix,A=(m;), then (I) has global positive solution;Otherwise,(I) has no continous nondeereasing positive solution.

Symmetry Reductions of the Combined KdV-mKdV Equation

张解放, 许学军, 程德声

1995, 10(3): 102-107.

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In this paper,some similarity reductions of the combined KdV-mKdV equation are given by using both the direct method introduced by Clarkson and Kruskal and the classical Lie aproach by Lakshmanan and Kaliappan.The similarity solutions obtained by the classical Lie approach is only the special case of that obtained by the direct method.

Certain Solutions of Equation f （ z，0，…，0，u_k，0，…，0）＝0

刘光民

1995, 10(3): 108-110.

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