Table of Content

30 December 2012, Volume 27 Issue 4

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The Distortion Theorems for k-fold Symmetric Quasi-convex Mappings along a Unit Direction in Cⁿ

LU Jin, LIU Tai-shun, WANG Jian-fei

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.



Two Notes on Numerical Differentiation Formulae

ZHENG Hua-sheng

2012, 27(4):  480-484. 

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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.



Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

ZHOU Zong-fu, ZENC Li, JIA Bao-rui, XU Jian-zhong

2012, 27(4):  485-494. 

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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.



The Orders of the Automorphism Groups of all Groups of Order p⁵

LAN Yong-hong, HUI Min, BAN Gui-ning, SHAO Ming-wen

2012, 27(4):  495-503. 

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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.



A Simple Approach to Estimating the Banach-Mazur Distance between Simplex and Convex Bodies

GUO Qi

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.





Relational Representations of Strongly Algebraic Lattices

XU Guang-hong, RAO San-ping

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.



Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

HAN Ren-ji, GE Jian-sheng, JIANG Wei

2012, 27(4):  516-525. 

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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. 

New Pooling Design Constructed with Pseudo-symplectic Space

ZHAO Xiang-hui, XU Ning, ZHANG Geng-sheng

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.



A New Circulant Preconditioned GMRES Method for Solving Ordinary Differential Equation

ZHU Mu-zheng

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. 


Boundedness of Multilinear Singular Integrals and Their Commutators on Morrey-Herz Spaces with Non-doubling Measures 

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).

On the McShane Integral on Time Scales

LIU De-hua, ZHAO Da-fang.

2012, 27(4):  556-561. 

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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.



Application of Exp-function Method to KdV-Burgers-Kuramoto Equation and Kuramoto-Sivashinsky Equation

CHEN Bo-kui, LIU Yi-ke, WANG Bing-hong

2012, 27(4):  562-571. 

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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.



Some Inequalities for Lp-mixed Affne Surface Area

ZHU Xian-yang

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.





On Isolations for the Brunn-Minkowski Inequality of Quermassintegrals and Dual Quermassintegrals

WANG Wei-dong, QI Chen

2012, 27(4):  582-589. 

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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.



Scheduling and Subcontracting under Parallel Machines

CHEN Rong-jun, TANG Guo-chun

2012, 27(4):  590-597. 

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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.

An Algorithm for Solutions of Nonlinear Difference-differential Equations

XU Li-ping

2012, 27(4):  598-605. 

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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. 

A Note on the Existence of a Specified Number of Interior Points

WEI Xiang-lin, DING Ren

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.





Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals

ZHAO Yan-xia, WANG Deng-yin

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.

A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step

GONG Xiao-yu, HU Zhen-peng, WANG Xian-jia

2012, 27(4):  624-632. 

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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.