Chinese Quarterly Journal of Mathematics

On the Extension of PM-Ring

Zhu Yuansen

1994, 9(2): 1-7.

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A ring is called PM ring every primitive ideal is a intersection of its some maximal ideals.In this paper,the property of PM-ring is discussed and the necessary and sufficient condition are given for the polynomial,centralizing,strongly normal extensions of PM-ring to be PM-rings.We also get some applications of the extensjon of PM-ring in group ring.

Some Test Problems on Applications of Wu＇s Method in Nonlinear Programming Problems

Wu Tianjiao

1994, 9(2): 8-17.

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The nonlinear programming problems are important in mathematics applications.They are usually solved by various kinds of numerical methods.This will give solutions in the form of local extremal values but not necessarily global .optimal ones.The present paper shows how to solve the nonlinear programming problems by the MM-method(Mathematics-Mechanization method)or Wu's method.Wu's method s different from the numerical method in that the computations are symbolic instead of numerical ones.Theoretically it is based on computer algebra and algebraic geometry.The author uses the computer to get complete global solutions of some practical test problems in the nonlinear programming.The computations shows that Wu's mehtod is concise for solving the nonlinear programming problems,and is also quite efficient.

Blow－Up and Mass Concentration of Solutions to the Cauchy Problem for Nonlinear Schrodinger Equations

Qin Yuming

1994, 9(2): 18-24.

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We prove in this paper the blow-up theorem of the generalized solution.and ts L²mass concentration theorem on the set of blow-up points near the blow-up time of the Cauchy problem fr nonlinear Schrodinger equations and give the structure of the set of the blow-up points and the estimates on the blow-up time.Furthermore we extend and improve some results in [2] and [5].

Generalized Stirling Numbers and its Properties

Zhang Zhizheng, Wei Zongli, Jiao Dongwu

1994, 9(2): 25-28.

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This paper gives a common generalization of generalized stirling number in [1]-[9],namely and obtains some properties.

On the Distribution of Weakly Composite Numbers

Wang Tianze, Li Guoqiang

1994, 9(2): 29-33.

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Some asymptotic formulas related to the weakly composite numbers are given in this paper.

How to Reach the Equilibrium of Labor Market by Using of Utility Function

Sun Lianzhi, Zhao Qinglin

1994, 9(2): 34-36.

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In the condiction of certain labor supply function,this paper deals with the constraction of labor demmand curve by making use of the utility function ,therefore obtains the equilibration of labor market in a new way.

On a Conjecture of Shapiro's

Chen Zhiguo

1994, 9(2): 37-39.

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This problem was put forward by H.S.Shapiro on Bull.London Math.Soc.16(1984)490 -517,numbered 6.88[1].The original description likes following: ... The equation is met whenf is and only is identical.

Estimates for the Upper Bounds of the First Eigenvalue on Submanifolds

Qi Feng, Yu Linquan, Luo Qiuming

1994, 9(2): 40-43.

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In the article the authors extend B.Y.Chen's inequality to other ambient spaces by the Nash imbedding theorem,obtain some meaningful results about the upper bounds of 2:for the Laplace operator on submanifolds.

On the Involutive Solutions of Solition Hierarchy

Qiao Zhijun

1994, 9(2): 44-53.

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The involutive solutions of soliton hierarchy are given in this paper.Through the nonlinearization of the lax system for solition hierarchy,it is proven that the involutive solution of compatible systems(H)(spatial part)and(F)(time part)is mapped into the soliton of solutin hierarohyby the mappingfwhich is determined by the constraint relation u=f(φ)between potentials and eigenfunotions.

A Characterization of Geometric Distributions Through Conditional Independence

Huang Renyan

1994, 9(2): 54-59.

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Let Y₁,Y₂,…,Y be mutually independent taking random yariables of positive integer value.A denote the event that Y,-Y,i>0 for all z=1,2,…,n-1.Then we show that,under condition A,Y, -Y+i and Y..are independent,for t=1,2,….K and only if Y,(z=1,2,…,K)accords with geometric distribution.Here in I≤K≤n-1.Note:the K geometric distributions can have diffrent scale parameters.

Isomorphism on Hypergroups

Zhong YuBin

1994, 9(2): 60-63.

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This paper gives some further research on the basic of paper[2],The theorem of paper [2]is improved and proved here.considering the limitations of this theorem,we prove isomorphic theotem of structure of hypergroup with no condition.At last,we show some of its application through some examples.

The Stationary Distribution of a Continuous-Time Random Graph Process

Han Dong

1994, 9(2): 64-68.

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A continous-time random graph process with state space consisting of the simple and directed graphs on N vertices is introduced.We obtain the stationary distribution of the process under different couaitions and prove that the stationary distribution is unique.

Support Points of Harmonic Typically-Real Functions

Gong Guifu

1994, 9(2): 69-72.

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It is obtained the set f support points of the closed convex hull of harmonic typically-real functions.

The New Series of LA-Groups (Ⅰ)

Ban Guining, Li Shiyu, Zhang Jinsong

1994, 9(2): 73-76.

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This paper shows that prime power groups which are cyclic extensions of elementary abelian groups are all LA-groups.

The Convergences of Bivariate Integral Jackson Interpolating Operators in Orlicz Spaces

Shang Zengke, Wang Youyi, Sheng Baohuai

1994, 9(2): 77-86.

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This paper introduces a kind ofbivariate integral trigonometrical interpolating polynomials, proves its boundedness in orlicz spaces and gives the quantative estimate degree of approximation in orlicz norm,As application,the degree of approximation by a kind of bivariate integral Hermite-Fejer interpolating operatorsi given in the veight orlicz spaces.

Weighted Restriction Theorems for the Fourier Transform on a Kind of Surfaces

Chen Liyuan

1994, 9(2): 87-92.

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Let 0<k<n,and k-dinensional object SCR°.Also,S will come with a nonnegative Radon measure u on R"such that suppu=S.Define the Fourier restriction operator T by ... ,holds for all f∈C(R")and some redial weighted funcion vifS is a bounded surface and u∈4.Here 1 ≤p<0.Our reslut generalizes those in [6] to some extent.

The Derivation Algebra of Lie Algebra H（n，m） of Cartan Type of Characteristic p＝2

Wang Ying, Zhang Yongzheng

1994, 9(2): 93-101.

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Abstract In this paper,we determine the derivation algebra of non-restricted Lie algebra H(n,m) of Cartan type in characteristic p=2.The main reault is following: ... .

A Correction on the Paper of ＜A Extension of the Mitrinovit－Djokovie Inequality＞

Feng Cihuang

1994, 9(2): 102-103.

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The Asymptotics Stability of Solutions of Some Fourth Order Differential Equation

Fang Xinhua

1994, 9(2): 104-105.

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Some Results About λ-Property

Ma Yumei, Zhang Yibin

1994, 9(2): 106-110.

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In this paper we have proved a open problem of [1].

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