数学季刊

石东洋, 王彩霞

2006, 21(2): 159-165.

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It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini’s element’s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.

用统一方法研究双全纯映射的一些子族

徐庆华, 刘太顺

2006, 21(2): 166-175.

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Let Ω∈Cⁿ be a bounded starlike circular domain with 0∈Ω. In this paper, we introduce a class of holomorphic mappings M_g onΩ. Let f(z) be a normalized locally biholomorphic mapping onΩsuch that J_f^-1(z)f(z)∈M_g and z=0 is the zero of order k + 1 of f(z)-z. We obtain the growth and covering theorems for f(z). Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.

中立型脉冲双曲型方程的振动准则

朱先阳, 李永昆, 卢玲红

2006, 21(2): 176-184.

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Oscillation properties of the solutions of impulsive hyperbolic equations are investigated by the method of differential inequalities.

有限时区非线性系统的最优切换控制

慕小武, 刘海军

2006, 21(2): 185-195.

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This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities(the appropriate generalization of the Hamilton-Jacobi equation in this context) and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.

四零点辅助函数在除X₁X₂X₃X₄外其余为非主特征条件下的估值

李怡君

2006, 21(2): 196-201.

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To obtain a better Vinogradov’s bound, assistant function with two or three zeros and all Dirichlet’s characters has been evaluated. Assistant function g(X₁,X₂,X₃,X₄) with four zeros and all nonprincipal characters but X₁X₂X₃X₄ is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.

固定设计下一类半参数回归模型估计的强相合性

田萍, 薛留根

2006, 21(2): 202-209.

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In this paper, we consider the following semiparametric regression model under fixed design: y_i=x_i¹β+g(x_i)+e_i. The estimators of β, g(·) and σ²are obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.

含k-Brocard距离的一类几何不等式

文家金, 柯睿, 吕涛

2006, 21(2): 210-219.

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Let P be an inner point of a convex N-gon Γ_N:A₁A₂…A_NA₁(N≥3), and let di,k denote the distance from the point A_i+k, to the line PA_i(i=1,2,…,N,A_i=A_ji=j(modN)), which is called the k-Brocard distance for P of Γ_N. We have proved the following double-inequality: If P∈Γ_N, and then ... .

一族与薛定谔型谱问题相联系的新的孤子方程及其相应的有限维可积系统

邢秀芝, 吴景珠, 耿献国

2006, 21(2): 220-228.

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By introducing a Schrodinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.

一个四阶方程组在全直线上的整体吸引子

赵才地, 李用声

2006, 21(2): 229-235.

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This paper studies the long time behavior of the following Cauchy problem The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.

三系数有限元向量尺度函数的构造

李锐

2006, 21(2): 236-241.

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The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.

正态分布参数函数的最小最大估计

孟红玲, 亢金轩, 张开广

2006, 21(2): 242-245.

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The estimation of the functionθ=exp{αμ+bσ²} of parameters (μ,σ²) in normal distribution N(μ,σ²) is discussed. And when the prior distributions of μ and σ² are independent, under the loss function L(θ,δ)=(θ^-1×δ-1)², the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.

L-型模糊格蕴涵代数

宋庆龙, 李春瑞, 赵光峰

2006, 21(2): 246-251.

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This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.

关于0-F-逆半群的一个注记

陈历敏

2006, 21(2): 252-254.

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In this paper, we introduce 0-F-inverse semigroups and characterize 0-F-inverse categorical semigroups by using their minimal primitive congruenceβ.

广义抽象进化算法的性质分析

薛明志, 马云苓

2006, 21(2): 255-260.

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There has been a growing interest in mathematical models to character the evo- lutionary algorithms.The best-known one of such models is the axiomatic model called the abstract evolutionary algorithm(AEA),which unifies most of the currently known evolu- tionary algorithms and describes the evolution as an abstract stochastic process composed of two fundamental abstract operators:abstract selection and evolution operators.In this paper,we first introduce the definitions of the generalized abstract selection and evolution operators.Then we discuss the characterizatlon of some parameters related to generalized abstract selection and evolution operators.Based on these operators,we finally give the strong convergence of the generalized abstract evolutionary algorithm. The present work provides a big step toward the establishment of a unified theory of evolutionary computa- tion.

第二类Stirling数的一个公式

杜春雨, 张建国

2006, 21(2): 261-263.

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In this paper, we propose and prove the following equation, where is a Stirling number of the second kind, when n≥3 is given.

K_m,n和C_n的联图的全色数

李光荣, 张利民

2006, 21(2): 264-270.

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The total chromatic number XT(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no adjacent or incident pair of elements receive the same color. G is called Type 1 if XT(G)=Δ(G) + 1. In this paper we prove that the join of a complete bipartite graph K_m,n and a cycle C_n is of Type 1.

具非线性中立项的二阶时滞微分方程的振动性质

徐志庭, 金楚华

2006, 21(2): 271-277.

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By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.

关于积和式差的一点注记

侯谦民, 刘修生

2006, 21(2): 278-282.

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It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖_Fmax(‖A‖_F,‖B‖_F)^n-1 or ... holds for where A^Hdenotes the conjuagte transpose of the matrix A=(a_ij)_n×n.

奇异离散线性系统的开关切换控制

郭晓丽, 李蔚, 慕小武

2006, 21(2): 283-287.

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In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.

类奇异积分和交换子在广义Morrey空间上的有界性

王月山, 王学敏

2006, 21(2): 288-292.

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The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO.

广义非均匀Cantor集的Hausdorff测度存在的充要条件的证明

曾超益

2006, 21(2): 293-296.

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The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1):S_i(x)=a_ix+b_i,x∈[0,1], i=1, 2,…,m, where 0<a_i< 1, i=1, 2,…, m; b_i+a_i>0, i=1, 2,…, m-1, b1=0 and a_m+b_m=1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.

关于亚纯函数微分多项式的值分布

刘孝书

2006, 21(2): 297-300.

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Let f(z) be a meromorphic function and Ψ be the differential polynomial of f which satisfies the condition of N(r, f) + N (r, 1/f) = S(r, f). We obtain several results about the zero point of the Ψ and those results extend and improve the results of Yang and Yi in this paper.

格值命题逻辑系统LP(X)的语法扩张

郑逢斌, 李庆玉, 王学芳, 徐扬

2006, 21(2): 301-308.

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We have given a semantic extension of lattice-valued propositional logic LP(X) in [6]. In this paper, we investigate its corresponding syntactic extension of LP(X) and give the relations between these two extensions.

利用分层抽样数据中完全辅助信息的模型校正方法

伍长春, 张润楚

2006, 21(2): 309-316.

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In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).

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