A-扩张Lie Rinehart代数

陈酌, 祁玉海

2007, 22(3): 317-327.

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The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative,associative algebra A.It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group,analogous to the well known relationship of Lie algebras and Lie groups.

基本的局部实心Riesz空间

陈金喜

2007, 22(3): 328-332.

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In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality.From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.

建立在L-凸空间上的截口定理及其应用

金彩云, 程曹宗

2007, 22(3): 333-338.

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In this paper,the author gives a new section theorem in L-convex spaces.And as its applications,the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.

F-调和映照的稳定性

刘建成

2007, 22(3): 339-343.

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In this paper,the author discusses the stable F-harmonic maps,and obtains the Liouville-type theorem for F-harmonic maps intoδ-pinched manifolds,which improves the ones in [3] due to M Ara.

黎曼流形上一类非线性偏微分方程正解的唯一性和不存在性结果

李兴校, 曹林芬

2007, 22(3): 344-351.

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The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold (M,g) with some curvature restriction.The authors try to prove some uniqueness and nonexistent results for the positive solutions of the equations concerned.

秩2修正矩阵的秩

盛兴平, 陈果良

2007, 22(3): 352-358.

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In this paper,the authors discuss the relationship in detail between the rank of M in the modified matrix M=A+BC* and the rank of matrix A.The authors do believe the results are useful tools in the modified matrices.

K_m V K_n的最小直径定向

缪小燕, 孙志人

2007, 22(3): 359-363.

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For a graph G,let D denote an orientation of G having minimum diameter. Define f(G)=diamD.In this paper,we concentrate on exploring the minimum diameter of K_m V K_n(m≥1,n≥1).Some special cases are known: f(K_m V K_n)=∞,2,3, where m=1 and n≥1,m=2 or m≥4 and n=1,m=3 and n=1,respectively. So we only consider the case when m≥2 and n≥2.The following results are obtained. (1) f(K_m V K_n)=3,where m=2,3,n≥2 and m=n=4.(2) f(K_m V K_n)=2, where m≥5 and m is odd,2≤n≤m-m.(3) f(K_m V K_n)=2,where m≥4 and m≡0(mod4),2≤n≤m-(m/2+1).(4) f(K_m V K_n)=2,where m≥6 and m≡2(mod4),2≤n≤m-m/2.(5) f(K_m V K_n)=3,where m≥4,n>m.

二阶问题Adini元的误差估计

高继梅, 李文华

2007, 22(3): 364-369.

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The main aim of this paper is to have an accurate analysis on the famous Adini’s element for the second order problems under to the anisotropic meshes.We firstly show that the interpolation of Adini’s element satisfy the anisotropic property.Then the optimal error estimate is obtained without the regularity assumption on the meshes.

α-Bloch空间到H^∞的加权复合算子

唐笑敏

2007, 22(3): 370-376.

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The article not only presents the boundedness and compactness of the weighted composition operator fromα-Bloch spaces(or littleα-Bloch spaces) to H^∞,but also gives some estimates for the norm of the weighted composition operator.

一种基于Eno-Haar小波变换二维遗传算法

宋锦萍, 赵晨萍, 李登峰

2007, 22(3): 377-383.

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A two-dimensional genetic algorithm of wavelet coefficient is presented by using the ENO wavelet transform and the decomposed characterization of the two-dimensional Haar wavelet.And simulated by the ENO interpolation the article shows the affectivity and the superiority of this algorithm.

退化时滞系统的极点配置

周先锋, 蒋威

2007, 22(3): 384-387.

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This paper deals with the pole placement of the singular system ..., where x∈Rⁿ,u∈R^m,and y∈Rⁿ are its state,control input and measure output respectively;E,A∈R^n×n,B∈R^n×m,and C∈Rr^×n are constant matrices.It is also assumed that rankE<n.The results generalize the results of [1].

各向异性双二次元的自然超收敛性结果

李清善, 孙会霞

2007, 22(3): 388-394.

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The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson’ problem on anisotropic meshes.By detailed analysis,it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element.

带有临界Sobolev指数的奇异双调和问题

胡丽平, 周世国

2007, 22(3): 395-401.

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Let Ω be a smooth bounded domain such that 0∈Ω, N≥5, 2*:=(2N)/(N-4) is the critical Sobolev exponent, and f(x) is a given function. By using the variational methods, the paper proves the existence of solutions for the singular critical in the homogeneous problem Δ^u-μu/(|x|4)=|u|^2*-2u+f(x) with Dirichlet boundary condition on Ω under some assumptions on f(x) and μ.

一类数论函数的性质(Ⅱ)

李怡君, 刘华柯

2007, 22(3): 402-405.

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For any given positive integer n≥1,the Euler function φ(n) is defined to be the number of positive integers not exceeding n,which is relatively prime to n.ω(n) is defined to be the number of different prime divisors of n.In order to know the solvability of the function of φ(φ(φ(n)))=2(ω(n)),properties of the number theoretical function φ(φ(n)) is studied in the paper.

关于二阶三点边值的多个正解存在性

任立顺, 王治国

2007, 22(3): 406-411.

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In this paper,using fixed theorem in cones,the authors obtain the existence of multiple positive solutions on the following boundary value problem u"+α(t)f(u)=0,t∈[0,1], u(0)=0,αu(η)·=u(1).

积分不等式与Pólya-Szego不等式

朱永娥, 侯海军

2007, 22(3): 412-414.

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The paper brings an important integral inequality,which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.

一类双色散波方程的Cauchy问题

郭基风, 李红

2007, 22(3): 415-425.

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This paper concerns with the Cauchy problem for the nonlinear double dispersive wave equation.By the priori estimates and the method in [9],It proves that the Cauchy problem admits a unique global classical solution.And by the concave method,we give sufficient conditions on the blowup of the global solution for the Cauchy problem.

一类试验次数为4p²的非对称正交表的构造

廖靖宇, 张建军, 张应山

2007, 22(3): 426-435.

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Nowadays orthogonal arrays play important roles in statistics,computer science, coding theory and cryptography.The usual difference matrices are essential for the con- struction of many mixed orthogonal arrays.But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices.In order to construct these asymmetrical orthogonal arrays,a class of special matrices,so-called generalized difference matrices,were discovered by Zhang(1989,1990, 1993) by the orthogonal decompositions of projective matrices.In this article,an interesting equivalent relationship between the orthogonal arrays and the generalized difference matri- ces is presented.As an application,a family of orthogonal arrays of run sizes 4p²,such as L36(6134210),are constructed.

α型螺形映照与Roper-suffridge算子

刘浩, 吴中林, 刘爱超

2007, 22(3): 436-443.

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In this paper,we get the fact that generalized Roper-Suffridge operators act on spirallike mapping of typeαon different domains is invariable,these results include some results known.

拟线性抛物方程整体解的存在性和不存在性

庞进生, 张宏伟

2007, 22(3): 444-450.

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The paper studies the existence,the exponential decay and the nonexistence of global solution for a class of quasilinear parabolic equations.

一个具有半连续Gateaux导数的泛函的Mini Max定理和非线性波动方程的边值问题的解

黄文华, 陆川

2007, 22(3): 451-458.

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In this paper,a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem.

关于立方幂补数倒数的性质

郭亚梅, 张洪奎

2007, 22(3): 459-464.

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Let n be any positive integer,and S(n) be the cubic complements of n.The main purpose of this paper is to study the asymptotic of sum from (n≤x) (n/(S(n)))k (k≥1).And by using the elementary methods,it intends to give two sharper asymptotic formulas,and thus extends the related conclusious.

Landau-Lifshitz方程解的渐进性质

郭柏灵, 樊继山, 曾明

2007, 22(3): 465-470.

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The paper considers the existence of the global solution for Landau-Lifshitz equation and discusses its asympotic behavior.

罗宾逊序列引理的推广及其应用

陈东立, 马春晖, 卢志义

2007, 22(3): 471-474.

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A.Robinson’s sequential lemma is extended to nets in general topological space, and obviously the case of nets in *R is its corollary.As its application,the paper proves a property about topology of uniform convergence.
基金资助： the Basic Research Foundation of Xi’an University Architecture Technology(JC0620)； the Youth Science and Technology Foundation of Xi’an University of Architecture and Technology(QN0736)；

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一种基于Eno-Haar小波变换二维遗传算法