Chinese Quarterly Journal of Mathematics

Remark on Some Classes of P-valent Functions

Liu Mingsheng

1999, 14(1): 1-4.

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Recently，Aouf and Darwish^［1］proved some estimates in relation to the real part of function ... for f (z) ∈R（1，k，p ，α）．In this paper we improve their results and obtain the sharp estimation．

Correlation Wavelet and its Applications

Xu Changfa, Cai Chao, Pi Minghong, Zhu Chunxi, Li Guokuan

1999, 14(1): 5-9.

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Many types of wavelets have been constructed for adapting to different applications．In this paper，we have got a new family of wavelets using the auto-correlation functions of Daubechies wavelets，then discussed its some properties and applications．

Global Asymptotic Stability for a Class of Nonlinear Populations Model

Zhou Lun, Qi Chuanda

1999, 14(1): 10-15.

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This paper discussed the stability of model of an age structured population systems， proved that the equilibrium solution systems is globally asymptotically stable．

Solution and Application of the Matrix Equation Ax=b

Sun Jianping, Zhang Yane, Wang Xizhao

1999, 14(1): 16-21.

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In this paper,we first give the solution concept of the fuzzy matrix equation Ax=b. Secondly,we discuss the property of the solution and give the method of solving the fuzzy matrix equation Ax=b. Finally,we present an application of solving fuzzy matrix equation Ax=b to the fuzzy linear regression analysis,establish a new model of fuzzy linear regression,and introduce a new method of estimating parameters.

Probabilistic Norm of Operators and Continuity of Bounded Operators

Xiao Jianzhong, Zhu Xinghua

1999, 14(1): 22-25.

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In this paper,the equivalence for continuity and boundedness of the linear operators on a general PN space is proved by means of their probabilistic norm,and the corresponding result in [1] is improved.

A Property of Solutions for Elliptic Equation with Nonstandard Growth Conditions in Unbounded Domain

Qiu Zihua, Ye Ruifen

1999, 14(1): 26-34.

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In this paper the author proves that the Phragmen Lindelof principle holds for solutions of elliptic equation (1) with nonstandard growth conditions.

The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

Wen Guochu, Huang Sha

1999, 14(1): 35-42.

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This paper deals with the existence theorem and Riemann Hilbert boundary value problem for general nonlinear elliptic complex equations of fourth order. Firstly we give the representation and existence theorem of solutions for the complex equations. Moreover,we propose the Riemann Hilbert problem and its well posedness,and then we give the representation of solutions for the modified boundary value problem and prove its solvsbility,and finally derive solvability conditions of the original Riemann Hilbert problem.

A Remark on the Positive Definite Problem of a Binary Quartic Form

Ling Shengzhi

1999, 14(1): 43-46.

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In this paper，we discussed the positive definite problem of binary quartic forms and obtained a necessary and sufficient conditions．

On the Moments of Sup_n||S_n/(nφ（n）)^1/p || in p-type Space

Guo Qiuli, Yang Changsen, Liu Hongxing

1999, 14(1): 47-51.

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Let B be a p-type Banach space （1＜p ＜2），φ（ x ） be some slow increasing functions on ［0，＋∞），if ｛X ，

X_n，n≥1｝is a sequence of i．i．d B-valued random variables，then we obtain a necessary and sufficient condition for the moments of Sup_n||S_n/(nφ（n）)^1/p || being bounded．

A Note of Spirallike Mappings in Cⁿ

Li Xiaoshen

1999, 14(1): 52-54.

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In this paper,the Growth and covering Theorems for a kind of spirallike mapping are given.

Analysis and Forecast on the Car Market of Our Country

Li Rui, Liang Qingwen

1999, 14(1): 55-61.

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This paper is intended to forecast the demand of the car market and the quantity of car possession in our country in 2000 by means of two statistics methods, i.e. tendency inference and regression analysis, and then its future growth tendency and market demand in our country are analyzed, according to the strategy requirement and the actual facts of our car industry development.

On Spirallike Mappings in Several Complex Variables

Liu Hao

1999, 14(1): 62-72.

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In this paper,the parametric representation of a kind of spirallike mappings is given. As a direct application,the growth Theorem is set up. Moreover,a character of starlike mappings and a kind of spirallike mappings is obtained.

The Pell Equations x²-8y²=1 and y²-Dz²=1

Pan Jiayu, Zhang Yuping, Zou Rong

1999, 14(1): 73-77.

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In this paper，we have proved that if one of the following conditions is satisfed，then the equations in title has no positive integer solution：... D≠5*7，29*41*239．

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

Zhang Chengyi, Dang Pingʾan

1999, 14(1): 78-81.

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In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

Two Dimensional Submanifolds in Four Manifolds with Boundary

Gao Hongzhu, Yu Dazhe

1999, 14(1): 82-87.

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A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In this paper,we consider this problem for four manifold with boundary.

Gamma Functions and Siegel Integrals on Nonselfdual Cones

Zhao Xiaoxia, Lin Ping, Yin Weiping

1999, 14(1): 88-101.

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In this paper，we will define Gamma functions and Siegel integrals on nonselfdual cones and give some applications．

A Probe Method of Gradient Projection Type

Zhu Jianqing, Jin Lili

1999, 14(1): 102-110.

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In this paper,a probe method for nonlinear programming wiht equality and inequality is given. Its iterative directions at an arbitrary point x can be obtained through solving a liear system. The terminate conditions and choices of the parameters are given. The global convergence of the method is proved. Further more,some well known gradient projection type algorithms [1-15] and new gradient projection type algorithms from the linear system are given in this paper.

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