Chinese Quarterly Journal of Mathematics

CHEN Zhuo, QI Yu-hai

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.

Fundamental Locally Solid Riesz Spaces

CHEN Jin-xi

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.

A New Section Theorem in L-convex Spaces and Its Applications

JIN Cai-yun, CHENG Cao-zong

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.

Stability for F-Harmonic Maps

LIU Jian-cheng

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.

The Uniqueness and Nonexistent Results for Some Nonlinear Partial Equations on Riemannian Manifolds

LI Xing-xiao, CAO Lin-fen

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.

The Rank of Rank-2 Modified Matrix

SHENG Xing-ping, CHEN Guo-liang

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.

Minimum Diameter Orientations of K_m V K_n

MIAO Xiao-yan, SUN Zhi-ren

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.

On the Error Estimate of Adini's Element for the Second Order Problems

GAO Ji-mei, LI Wen-hua

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.

Weighted Composition Operators from a-Bloch Spaces to H^∞

TANG Xiao-min

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.

A Two-dimensional Genetic Algorithm Based on the Eno-Haar Wavelet Transform

SONG Jin-ping, ZHAO Chen-pingl, LI Deng-feng

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.

The Pole Placement of a Singular System with Delay

ZHOU Xian-feng, JIANG Wei

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].

Anisotropic Biquadratic Finite Element with Some Natural Superconvergence Results

LI Qing-shan, SUN Hui-zia

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.

On the Singular Biharmonic Problems Involving Critical Sobolev Exponents

HU Li-ping, ZHOU Shi-guo

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.

Properties of Some Kind of Number Theoretical Function (II)

LIYi-jun, LIU Hua-ke

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.

Existence of Multiple Positive Solutions on the Three Point Boundary Value Problems

REN Li-shun, WANG Zhi-guo

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).

An Integral Inequality and Polya-Szego Inequality

ZHU Yong-e, HOU Hai-jun

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.

Cauchy Problem for the Nonlinear Double Dispersive Wave Equation

GUO Ji-feng, LI Hong

2007, 22(3): 415-425.

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A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p²

LIAO Jing-yu, ZHANG Jian-jun, ZHANG Ying-shan

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.

The Spirallike Mapping of Type a and the Generalized Roper-Suffridge Operator

LIU Hao, WU Zhong-lin, LIU Ai-chao

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.

Existence and Nonexistence of the Global Solution on the Quasilinear Parabolic Equation

PANG Jin-sheng, ZHANG Hong-wei

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.

A Mini Max Theorem for the Functionals with Hemicontinuous Gateaux Derivative and the Solution of the Boundary Value Problem for the Nonlinear Wave Equation

HUANG Wen-hua, LU Chuan

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.

On the Property of Cubic Complements

GUO Ya-mef, ZHANG Hong-kui

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.

Asympotic Behavior of Solutions for Landau-Lifshitz Equation

GUO Bo-ling, FAN Ji-shan, ZENG Ming

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.

The Extension of Robinson's Sequential Lemma and Its Application

CHEN Dong-li, MA Chun-hui, LU Zhi-yi

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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