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2012年 第27卷 第4期    刊出日期：2012-12-30

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Cⁿ中k次对称准凸映射在单位多圆柱某方向上的偏差定理

卢金, 刘太顺, 王建飞

2012, 27(4):  475-479. 

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We obtain a distortion theorem of Jacobian matrix J_f(z) for k-fold symmetric quasi-convex / along a unit direction in Cⁿ on the unit polydisc.



关于数值微分公式的两个注记

郑华盛

2012, 27(4):  480-484. 

摘要 ( 24 )   PDF (322KB) ( 28 )  

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Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper. In the first place, several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor’s formula. And then, based on the ideas of algebraic accuracy, several inverse problems of numerical differentiation formulae are given.



一类带分布时滞和离散时滞中立型泛函微分方程的周期解

周宗福, 曾力, 贾宝瑞, 徐建中

2012, 27(4):  485-494. 

摘要 ( 31 )   PDF (575KB) ( 21 )  

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Based on Krasnoselskii’s fixed point theorem, matrix measure and functional analysis methods, some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover, we construct an example to illustrate the feasibility of our results.



所有p⁵阶群的自同构群的阶

蓝永红, 惠敏, 班桂宁, 邵明文

2012, 27(4):  495-503. 

摘要 ( 46 )   PDF (620KB) ( 34 )  

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In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field, completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall’s concept of isoclinism, also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.



一般凸体与单形间Banach-Mazur距离估计的一种简单方法

国起

2012, 27(4):  504-508. 

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We use a simple approach to estimating the Banach-Mazur distance between convex bodies and simplex. As an application of this approach, we provide a purely analytic proof for the known result sup_C∈Kⁿd_BM(C,△)≤n + 2, where d_BM(.,.) denotes the Banach-Mazur distance, △ denotes an n-dimensional simplex and Kⁿ denotes the class of n-dimensional convex sets in Rⁿ.



强代数格的关系表示

许广红, 饶三平

2012, 27(4):  509-515. 

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In this paper, we introduce and investigate the strongly regular relation. Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.



高阶非线性分数阶微分方程三点边值问题正解的存在性

韩仁基, 葛建生, 蒋威

2012, 27(4):  516-525. 

摘要 ( 23 )   PDF (585KB) ( 13 )  

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In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form ... We first transform it into another equivalent boundary value problem. Then, we derive the Green’s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result. 


利用伪辛空间构作的新Pooling设计

赵向会, 徐宁, 张更生

2012, 27(4):  526-534. 

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Pooling design is a mathematical tool in many application areas. In this paper, we give a new construction of pooling design with subspaces of the pseudo-symplectic space and discuss its properties. We define the design parameters of a d^z-disjunct matrix. Then we discuss the change law of the design parameters in our construction along with their variables.



一个新的求解常微分方程的循环预条件GMRES方法

朱睦正

2012, 27(4):  535-544. 

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The preconditioned generalized minimal residual(GMRES) method is a common method for solving non-symmetric, large and sparse linear systems which originated in discrete ordinary differential equations by Boundary value methods. In this paper, we propose a new circulant preconditioner to speed up the convergence rate of the GMRES method, which is a convex linear combination of P-circulant and Strang-type circulant preconditioners. Theoretical and practical arguments are given to show that this preconditioner is feasible and effective in some cases. 


非双倍测度下多线性奇异积分算子及其交换子在Morrey-Herz型空间上的有界性

周娟, 朱月萍

2012, 27(4):  545-555. 

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Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L¹(μ)×…×L¹(μ) to L^1/m,∞(μ).



关于时标上的McShane积分

刘德华, 赵大方

2012, 27(4):  556-561. 

摘要 ( 30 )   PDF (386KB) ( 36 )  

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In this paper, we introduce and study the concept of McShane delta integral on time scales. We discuss the relationship between McShane delta integral and Henstock delta integral, and prove a dominated convergence theorems for the McShane delta integral.



用指数函数法求解KdV-Burgers-Kuramoto方程和Kuramoto-Sivashinsky方程

陈博奎, 刘伊可, 汪秉宏

2012, 27(4):  562-571. 

摘要 ( 33 )   PDF (748KB) ( 49 )  

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This paper focuses on the application of Exp-function method to obtain generalized solutions of the KdV-Burgers-Kuramoto equation and the Kuramoto-Sivashinsky equation. It is demonstrated that the Exp-function method provides a mathematical tool for solving the nonlinear evolution equation in mathematical physics.



关于Lp-混合仿射表面积的不等式

朱先阳

2012, 27(4):  572-581. 

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In this paper, the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced, some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed. Moreover, a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.





关于Brunn-Minkowski不等式的均质积分和对偶均质积分形式的隔离

王卫东, 齐晨

2012, 27(4):  582-589. 

摘要 ( 32 )   PDF (476KB) ( 25 )  

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Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery L_p-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of L_p-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals, respectively.



平行机的排序与转包

陈荣军, 唐国春

2012, 27(4):  590-597. 

摘要 ( 29 )   PDF (573KB) ( 30 )  

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In this paper, we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor. The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted. Furthermore, it needs to determine a  production schedule for jobs to be produced in-house. We discuss five classical scheduling objectives as production costs. For each problem with different objective functions, we give optimality conditions and propose dynamic programming algorithms. 


求解非线性微分差分方程精确解的一个算法

许丽萍

2012, 27(4):  598-605. 

摘要 ( 25 )   PDF (540KB) ( 59 )  

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In this paper, an algorithm is developed for using the G’ /G-expansion method to obtain exact solutions for discrete nonlinear systems. Applying this method, some kinds of travelling wave solutions for AL system and Toda lattice system are derived. These solutions are expressed by hyperbolic function, trigonometric function and rational function with parameters. When the parameters are taken as special values, some known solutions including kink-type solitary wave solution and singular travelling wave solution are recovered. It is shown that the developed algorithm is effective and direct. It also can be used for many other nonlinear differential-difference equations in mathematical physics. 


特定内点个数集合的存在性研究

魏祥林, 丁仁

2012, 27(4):  606-614. 

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An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k>1, let h(k) be the smallest integer such that every set of points in the plane, no three collinear, with at least h(k) interior points, has a subset of points with exactly k or k+1 interior points of P. We prove that h(5) = 11.



单李代数的Borel子代数的保可换理想的非线性映射

赵延霞, 王登银

2012, 27(4):  615-623. 

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Let g be a complex simple Lie algebra of rank I, b the standard Borel subalgebra. An invertible map on b is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of b.



基于全牛顿求解线性互补问题的一种新的不可行内点算法

龚小玉, 胡振鹏, 王先甲

2012, 27(4):  624-632. 

摘要 ( 27 )   PDF (472KB) ( 24 )  

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This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem, which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last, we prove that the algorithm has O(nlog n/ε) polynomial complexity, which coincides with the best known one for the infeasible interior-point algorithm at present.