Table of Content

30 March 2005, Volume 20 Issue 1

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Oscillation Theorems for Second Order Damped Nonlinear Differential Equations

HE Wan-sheng, LI Wan-tong

2005, 20(1):  1-9. 

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Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y’(t))^σ]’ +p(t)(y’(t))^σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t₀, ∞), and f∈C¹ (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.


Analysis of Singularity for Reducible Quasi-linear Hyperbolic Systems

WANG Li-zhen

2005, 20(1):  10-20. 

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In this paper we investigate the formation of singularities of hyperbolic systems. Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.



The Generalization of a Converse of Matrix Inequality

FENG Xiao-xia, YANG Zhong-peng

2005, 20(1):  21-27. 

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We prove that the inequality ... holds, when a m ×n real matrix X = (x_ij) whose entries are not all equal to 0 satisfies ... . Therefore we not only generalize the results of Horst Alzer [2] from non-negative matrix to real matrix, but also complete a result of E R van Dam [1], which indicated that the best possible upper bound is equal to 1 for real matrix.


Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

LING Neng-xiang, DU Xue-qiao

2005, 20(1):  28-33. 

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In this paper, we study the strong consistency for partitioning estimation of regression function under samples that are (?)-mixing sequences with identically distribution.



Study on the Grey Polynomial Geometric Programming

LUO Dang

2005, 20(1):  34-41. 

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In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory, and using some analysis strategies, a model of grey polynomial geometric programming, a model of θpositioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem. This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm. 


Uniqueness Problems for Meromorphic Functions that Share Three Values

WANG Jian-ping

2005, 20(1):  42-46. 

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This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.



Multipliers on Generalized Bergman Spaces

YUE Xiu-kui

2005, 20(1):  47-53. 

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In this paper,we characterize the multipliers of generalized Bergman spaces A^p,q,α with 0<p≤1,0<q, α<∞into some analytic function spaces and into sequence spaces, and show that the multipliers of A^p,q,α(0 <p≤1,0<q,α<∞) into a given space are the same as those of A^p,α(0 < p≤1, α>0) in almost every case considered. The corollaries on multipliers of the spaces A^p,q,α extend some related results.


Generalizations of Euler Numbers and Euler Numbers of Higher Order

LUO Qiu-ming, QI Feng

2005, 20(1):  54-58. 

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The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.


Existence and Uniqueness of Nested Regular Quadrilateral Central Configurations

LIU Xue-fei

2005, 20(1):  59-64. 

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Two cases of the nested configurations in R3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = ... must be satisfied in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (6) of masses. 

Estimates of the Dilatation Function of Beurling-Ahlfors Extension

ZHENG Xue-liang, WANG Jian-ping

2005, 20(1):  65-71. 

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In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.

Periodic Wave Solutions for Konopelchenko-Dubrovsky Equation

ZHANG Jin-liang, ZHANG Ling-yuan, WANG Ming-liang

2005, 20(1):  72-78. 

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By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.


On p-ω-hyponormal Operators

YANG Chang-sen, LI Hai-ying

2005, 20(1):  79-84. 

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In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.



Remarks on a Real Viscous Heat-conducting Flow with Shear Viscosity

ZHANG Zhi-ping, WANG Xiu-qin, DENG Shu-xian

2005, 20(1):  85-89. 

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This paper is concerned with the global existence and exponential stability of solutions with large initial date in H1 for real viscous heat-conducting flow with shear viscosity.


Global Solutions for a Strongly-coupled Parabolic System with Initial Boundary Values

XU Zhi-fen, CHEN Bin

2005, 20(1):  90-100. 

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In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincare inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.


Another Approach to Multiobjective Programming Problems with V-invex Functions

LIU San-ming, FENG En-min, LI Xiao-shen)

2005, 20(1):  101-110. 

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In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, a (α,η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.