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中文
Table of Content
30 September 1995, Volume 10 Issue 3
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An Outline
of Dai
Xu's Mathematical A
chievements
Wang Rongbin
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
Luo Zhendong
1995, 10(3): 9-12.
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Meromorphic Functions
with
Two Deficient
Values
Xu Wansong
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
Bai Fengtu
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
Cheng Hailai
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
Zhang Xiaohong, Wei Zongli
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*
Wei Junchao, Li Libin
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#
Sun Hongan
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
Wang Qingwen
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
Jiang Huiqin
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
Li Fengyou, Liu Yunshen
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
Wang Peiguang, Wang Zongsheng
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
Li Zemin
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
Jiang Liqing, Zhou Yi, Fan Ye, Wang Yue
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 G
eneralization of
Some Restrictive
Distribution
Theorems
Tian Zhen, Zhang Song
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
Wang Huimin, Liu Shuzhen, Chen Shuqin
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
Zhou Yongxin
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
Wang Shu, Wan Chunlin, Zhang Kun
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
Zhang Jiefang, Xu Xuejun, Cheng Desheng
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
Liu Guangmin
1995, 10(3): 108-110.
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