Table of Content

30 September 2004, Volume 19 Issue 3

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An Investigation on the Parabolic Subgroups of the General Linear Groups by Using GAP

Saad A Bedaiwi, LI Shang-zhi

2004, 19(3):  221-231. 

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A typical example for the algebraic groups is the general linear groups G = GL(n,F),we have  studied the  structure of such groups and paid  special attention to its important substructures,namely the Parabolic subgroups.
For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified,wereport here some investigations on the computed Parabolic subgroups.This has been done with the utility of GAP.


A Filled Function with Adjustable Parameters for Unconstrained Global Optimization

SHANG You-lin, LI Xiao-yan

2004, 19(3):  232-239. 

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A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded  and  closed  domain.This  function  has  two  adjustable  parameters.   We will discuss the properties of the proposed filled function.Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.



Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water

XIA Zhi

2004, 19(3):  240-246. 

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Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan’s, Xie’s and Yan’s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations. 


Asymptotic Behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation

LIANG Bao-song, CHEN Zhen

2004, 19(3):  247-252. 

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 J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.



An Approach to Chromaticity of K₄-homeomorphs

PENG Yan-ling

2004, 19(3):  253-261. 

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We introduce a new method for studying the chromaticity of K₄-homeomorphs, by which some new results are obtained.



Iterative Solution for Systems of Nonlinear Two Binary Operator Equations

ZHANG Zhi-hong, LI Wen-feng

2004, 19(3):  262-266. 

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 Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are improved and generalized.


Pseudo-spectral Approximations for a Class of the Kdv-Burgers Type Equation

ZHANG Rui-feng, YANG Hui

2004, 19(3):  267-272. 

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In this paper, the pseudo-spectral approximations for a class of the Kdv-Burgers type equation is presented. Convergence and stability of the approximation have been proved by Sobolev’s inequalities and the bounded extensive method of the nonlinear function. Finally, the numerical examples are proposed.



A Construction of Relative Difference Set

ZHANG Xi-yong, HAN Wen-baon

2004, 19(3):  273-279. 

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 In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.



The Roots of Adjoint Polynomial of the Graphs Contain Triangles

YE Cheng-fu

2004, 19(3):  280-285. 

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We denote h(G,x) as the adjoint polynomial of graph G. In [5], Ma obtained the interpolation properties of the roots of adjoint polynomial of graphs containing triangles. By the properties, we prove the non-zero root of adjoint polynomial of Dn and Fn are single multiple.



Some Notes for Toeplitz Matrix

LIU Shu-qiang, ZHANG He-ming

2004, 19(3):  286-291. 

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 In this paper,we study real symmetric Toeplitz matrices commutable with tridi-agonal matrices, present more detailed results than those in [1], and extend them to non-symmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.





Some Applications of E-wavelet Multipliers

LI Deng-feng, CHENG Jun-fang

2004, 19(3):  292-299. 

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 Let E=...  measurable function v is called an E- waveletmultiplier if (vψ) is an E-wavelet whenever ψ is an E-wavelet. Some characterizations and applications of E-wavelet multiplier were considered in [1]. In this paper, we give some other applications of E-wavelet multiplier, and prove that the set of all MRA E-wavelets is arcwise connected.


On the Model Properties of BCK Algebras

LIANG Jun-qi

2004, 19(3):  300-305. 

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This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no built-in Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding properties of fuzzy ideals discussed.



A Frame Nucleus on a Two-side Prequantale

XU Shao-xian, WANG Shun-qin, MA Fei-fii

2004, 19(3):  306-308. 

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In this paper, a Frame nucleus and prime elements in a Prequantale are defined. The concrete structure of a Frame prequantic quotient is considered, and the relation between the half-prime element and the Frame nucleus in a two-side Prequantale are obtained.





Stable Solution of Nonlinear Age-structured Forest Evolution System

WANG Ding-jiang, ZHAO Ting-fang

2004, 19(3):  309-313. 

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 This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.



The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

REN Li-shun, ZHANG Cai-yu

2004, 19(3):  314-318. 

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This paper discussed asymptotic property of Taylor remainder "mean value point" in normed Linear space. The asymptotic progerty of "mean value point" is solved when f⁽ⁿ⁺ⁱ⁾(x₀)h⁽ⁿ⁺ⁱ⁾ = 0(i = 1, 2,..., p - 1) and f^(n+p)(x₀)h^(h+p) don’t exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.





Fuzzy Entropy: Axiomatic Definition and Neural Networks Model

QING Ming, CAO Yue, HUANG Tian-min

2004, 19(3):  319-322. 

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The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model. 


Classical Completely Integrable System Generated through Nonlinearization of an Eigenvalue Problem

LUO Man, LI Xiu-li, XIANG Ming-sen

2004, 19(3):  323-330. 

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Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R^2N,dp^dq, H₀=1/2F₀)(F0= (^q,p) + (^p,p) + (p,q)²). While the nonlinearization of the time part leads to its N-involutive system (F_m).