数学季刊

Saad A Bedaiwi, 李尚志

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.

无约束全局优化的一个可调参数的填充函数

尚有林, 李晓燕

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.

齐次平衡法和浅水波中WBK方程的精确分析解

夏志

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.

一类非线性广义Euler-Possion-Darboux方程的精确分析解

梁保松, 陈振

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.

关于K₄-同胚图色性的研究

彭燕玲

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.

非线性二元算子方程组的迭代求解方法

张志宏, 李文丰

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.

一类Kdv-Burgers型方程的拟谱逼近

张瑞凤, 杨慧

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.

一些部分差集和相对差集的构造

张习勇, 韩文报

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.

一类含三角形图的伴随多项式的根

冶成福

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.

关于Toeplitz矩阵的某些注记

刘舒强, 张熇铭

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.

E小波乘子的某些应用

李登峰, 程俊芳

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.

关于BCK代数的模型论性质

梁俊奇

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.

双边Prequantale中的Frame核映射

徐少贤, 王顺钦, 马菲菲

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.

非线性林龄结构森林系统的稳定解

王定江, 赵廷芳

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.

广义泰勒余项“中值点”的渐进性

任立顺, 张彩玉

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.

模糊熵：公理化定义和神经网络模型

卿铭, 曹悦, 黄天民

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.

一个特征值问题的非线性化及其生成的经典可积系统

罗满, 李秀丽, 向明森

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).

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