Chinese Quarterly Journal of Mathematics

The Approximation Properties of Certain Interpolation Operators of Entire Exponential Type （Ⅱ）

Tian Jishan, Liu Jiufen

1995, 10(2): 1-7.

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In this paper,the authers studied the saturation problem for certain entire exponential type interploation operators in C(R)or L,(R).

The U* -property of Orlicz Spaces

Wang Tingfu, Ji Donghai

1995, 10(2): 8-15.

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For Orlicz spaces,the criteria of U*-property are given.

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

Gui Qingming

1995, 10(2): 16-22.

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In response to some perceived deficiency with the BLUE of the regression parameter matrix in the growth curve model,this paper proposes a class of linear biased estimators,which is called a class of universal ridge ones(URE),based on the recent development theory of biased estimation on the classical regression model.By appropriate choices of the included biased parameters, many interesting and practical linear biased estimators maybe obtained.Some important properties are also discussed.With the UR estimators,the estimation methods used in the growth curve model will be greatly enriched.

Covering Spaces of Graphlike Manifolds

Liu Yaxing

1995, 10(2): 23-23.

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Graphlike Manifold with Torus as Bockstein

Liu Yaxing

1995, 10(2): 24-25.

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The Periodic Solutions of Partial Variables for An Class of Linear Periodic Systems

Wang Hui, Lu Menglin

1995, 10(2): 26-28.

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In this paper,we consider the following linear periodic systems and ... First,we give some definitions about the periodic solutions of partial variables.Then we establish some criterions about existence.

Some Examples of Metrics with Positive Curvature and Negative Curvature on Rⁿ

Zhu Daxin, Hou Wenhua, Song Qingfang

1995, 10(2): 29-32.

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From the class of conformally flat metric of g=f(lxl²)δ,defined on R",where f:[0,0]→(0,0)is a C²function,we find one class of metrics with positive curvature and two classes of complete metrics with negative curvature.

Variational Inequality and Complementarity Problem for Set－Valued Mapping with Application

Zhang Congjun

1995, 10(2): 33-39.

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The purpose of this paper is to study the variational inequality and complementarity problem for set-valued mapping in Banach spaces.The results presented in this paper generalize and improve some recent results on finite dimensional spaces,Hiblert spaces,single-valued mapping. As applications,we utilize our results to study saddle point problems and two programming problems in infinite dimensional spaces.

On Projective Maps of Volume-Decreasing

Cai Kairen

1995, 10(2): 40-44.

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Given a projective map F:M→N of a complete Riemannian manifold to a Riemannian manifold with the sectional curvature bounded above by a negative constant,we prove that f de- creases volume up to a constant depending only on the curvatures of M and N.This generalizes the result due to Har'el.

A Characterization of Exponential Distributions through Conditional Independence

Huang Renyan, Shou Jilun

1995, 10(2): 45-47.

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Let Y₁,Y₂,…Y,be mutually independant non-negative random variables having an aboolutely continuous distribution function F₁(y)over its support 10,∞)and the corresponding density function f;(y)>0 for y>0.Let a denote the event that Y:-Y+1>0 for all i=1,2, … n-1.Then we show that,conditional on the event A,Y;-Yi+1and Yi+1are independent for all i=1,2,…k if and only if Y;(i=1,2,…k)are exponentially distributed random variables, wbere 1≤E≤n.We not that the k exponential distributions can have different scale parameters.

Structure of Stability Subalgebra W（V₁，V₂，…，V_m） Concerning Directionsof Vectors V₁，V₂，…，V_m

Tian Zhen

1995, 10(2): 48-51.

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In order to study structure of the generalized stochastic matrices algebra SL,in[1],the author defined the subalgebra W（V₁，V₂，…，V_m）concerning directions of vectors V₁，V₂，…，V_m.§1 of this paper,we study structure of W（V₁，V₂，…，V_m). And in §2,we research doubly stability subalgebra concerning directions of vectors,and prove a structure theorem of it. Final,we get:The generalized doubly stochastic matrices algebra is a semi-simple algebra.

A Judging Method for Normal Family

Zhu Zhenxing

1995, 10(2): 52-58.

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In 1964,Hayman,W.K.predicated method of judging a function family to be normal variety.This result was proved in 1985.Here,we give a method that judges a function family to be normal variety by using of higher derivative It is a generalization of previous result.

Several Inequalities of Matrix Traces

Chen Hongqing

1995, 10(2): 59-66.

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This paper has made the result of generalization and the answer according to the result of question raised in [1].
Especially we cancel the strong factors(A·B=B·A)in Theorerm 4 in [2]. We get the result to the same as the result of the inequality of Cauchy-Schwarz and Holder in the matrix. Finally,the paper also is a refinement of these two inequalities.It inserts the continuous integral value into the inequalities of matrix mean,and it becomes the inequality of integral form of continuous measure.

A Kind of the ASN' Extreme Value forMeasuring Double Sampling Plan

Han Zhilong

1995, 10(2): 67-71.

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In double sampling plan,the average sample number(called ASN for short)is a very important basis of selecting the plan.For the situation of totality obeyed Weibull distribution,this paper gives the ASN's extreme value for measuring double sampling plan,which is helpful to understand the ASN's characteristics of double sampling plan in Weibull distribution.

Fuzzy-valued Propositional Logic FP* （X）

Qin Keyun

1995, 10(2): 72-76.

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In this paper,we take [0,1],the set of fuzzy subsets of [0,1],as the set oftruth val- ues to establish a fuzzy-valued propositional logic system.

The Quotient Ring of Algebraic Interger Ring

Ding Ruixiang, Liu Guangliang

1995, 10(2): 77-80.

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In this paper,we discuss on the algebraic interger ring of the quadratic field of Q.The form of the quotient ring of the algebraic interger ring with respect to the order ideal is presented.

A Sufficient and Necessary Condition for Subellipticity of Left Invariant Differential Operators on Nilpotent Left Group G^2n＋k

Zheng Zhujun, Zhang Zhiping

1995, 10(2): 81-84.

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In this paper,we use the representation of nilpotent Lie group method to give a suffi- cient and necessary condition for subelipticity of Left invarient differental operators on nilpotent Lie group G²n+*.

A Nonlinear Degenerate Parabolic Equation

Jiang Yingjie

1995, 10(2): 85-88.

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In this paper we study a nonliner degenerate parabolic equation for the second boundary value problem,using the method of regularity we prove the existence and uniqueness of weak solution.

A Mathematical Model for Economic Risk

Xu Zegui

1995, 10(2): 89-93.

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Based on the analysis for economic activity of businesses,in this paper the author set up a mathematical model to evaluate the economic risk,and explain its application in a case.

On the Construction of Globally Asymptotically Stable Liapunov Functions of a Type of Third－order Systems with Nonseparable Variables

Li Qing , Wang Hua, Wang Chuanlong

1995, 10(2): 94-105.

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In the paper,we discuss the global asymptotic stability of a type of nonlinear third-order systems with nonseparable variables by using method of Liapunov functions. By means of the analogism and the improved Barbashin-Krasovskii theorem,we give some sufficient conditions which have not been reported.

The Elementary Proof of an Important Propertyfor B_λ Condition

Li Li

1995, 10(2): 106-108.

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The elementary proof that “W∈B_a(μ)” implies “W∈B_a-8(μ)” which is an important property for B_Acondition is given in this paper.

Separation Properties of Bitopological Space

Tian Liqin

1995, 10(2): 109-110.

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In this paper we study a bitopological space with a fuzzy topological space,and examine the relation between various fuzzy and bitopological separation axioms.

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