Journal of Applied Mathematics and Computing

article

A numerical investigation on the structure of the roots of q-Genocchi polynomials

Cheon Seoung Ryoo

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 325-332

One purpose of this paper is to introduce the q-Genocchi polynomials, G _n,q(x). Next we display the shape of q-Genocchi polynomials. Finally, we investigate the zeros of the q-Genocchi polynomials.

article

Li-Yorke chaos in 2D discrete systems

Chuanjun Tian, Guanrong Chen

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 503-515

This paper is concerned with chaos of 2D discrete systems of the form $$x_{m+1,n}=f(x_{m,n},x_{m,n+1}),$$ where f:I ²→I is a function on a bounded subset I of R and m,n∈N ₀={0,1,2,…}. A new and illustrative example, different from the coupled map lattice, is shown for such a system to be chaotic in the sense of Li-Yorke.

article

Block SOR methods for fuzzy linear systems

Shu-Xin Miao, Bing Zheng, Ke Wang

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 201-218

In this paper, the block SOR iterative methods are studied for n×n fuzzy linear systems and the corresponding convergence theorems are also given out. We know that the coefficient matrix S of the augmented system SX=Y is consistently ordered when S ₁ is nonsingular, and in this case the optimal parameter ω of the block SOR method is obtained. Numerical examples are presented to illustrate the theory...

article

Global convergence of a memory gradient method without line search

Zhensheng Yu

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 545-553

In this paper, we develop a memory gradient method for unconstrained optimization. The main characteristic of this method is that we obtain the next iteration without any line search. Under certain conditions, we obtain the strong global convergence of the proposed method.

article

Methods for knowledge reduction in inconsistent ordered information systems

Wei-Hua Xu, Wen-Xiu Zhang

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 313-323

Knowledge reduction is one of the most important problems in the study of rough set theory. However, in real-world, most of information systems are based on dominance relations in stead of the classical equivalence relation because of various factors. The ordering of properties of attributes plays a crucial role in those systems. To acquire brief decision rules from the systems, knowledge reductions...

article

Flow shop scheduling with effects of learning and deterioration

Ji-Bo Wang, Lin Lin, Feng Shan

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 367-379

In this paper we consider the flow shop scheduling problems with the effects of learning and deterioration. In this model the processing times of a job is defined as a function of its starting time and position in a sequence. The scheduling objective functions are makespan and total completion time. We prove that even with the introduction of learning effect and deteriorating jobs to job processing...

article

Sub-quadratic convergence of a smoothing Newton method for second-order cone programming

Xiaoni Chi, Sanyang Liu

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 489-502

In this paper, we present a smoothing Newton method for solving the second-order cone programming (SOCP) based on the Chen–Harker–Kanzow–Smale (CHKS) smoothing function. Our smoothing method reformulates SOCP as a nonlinear system of equations and then applies Newton’s method to the system. The proposed method solves only one linear system of equations and performs only one line search at each iteration...

article

On 9- and 10-decomposable finite groups

Ali Reza Ashrafi, Wujie Shi

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 169-182

A finite group G is called n-decomposable if every proper non-trivial normal subgroup of G is a union of n distinct conjugacy classes of G. In some research papers, the question of finding all positive integer n such that there is an n-decomposable finite group was posed. In this paper, we investigate the structure of 9- and 10-decomposable non-perfect finite groups. We prove that a non-perfect...

article

Optimal L ^∞ error estimates for finite element Galerkin methods for nonlinear evolution equations

Khaled Omrani

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 247-262

Finite element Galerkin solutions for three classes of nonlinear evolution equations are considered. The existence, uniqueness and convergence of the fully discrete Crank-Nicolson scheme are discussed. At last a linearized Galerkin approximation is presented, which is also second order accurate in time fully discrete scheme.

article

Representations for the weighted Drazin inverse of a sum of matrices

Zhaoliang Xu, Jianbiao Chen

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 517-533

Three representations for the W-weighted Drazin inverse of a matrix A−CWB have been developed under some conditions where A,B,C∈ℂ^m×n, and W∈ℂ^n×m. The results of this paper not only extend the earlier works about the Drazin inverse and group inverse, but also weaken the assumed condition of a result of the Drazin inverse to the case where Γ_d ZZ _g=ZZ _gΓ_d is substituted with C(Γ_d ZZ _g...

article

The parameterization of 2-channel orthogonal multifilter banks with some symmetry

Xiaoxia Feng, Zhongpeng Yang, Zhengxing Cheng

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 151-168

For the 2-channel orthogonal multiwavelet systems with symmetric center γ/2, we give the parameterization of the associated multifilter banks, whether γ is odd or even. When γ is odd, we obtain the similar results to Jiang’s, for the case that γ is even, we transform the parameterization of the multifilter banks into the one of the case that γ is odd, then by the previous results and inverse transforms,...

article

AOR iterative methods for rank deficient least squares problems

Yanli Huang, Yongzhong Song

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 105-124

In this paper we study the semiconvergence of accelerated overrelaxation (AOR) iterative methods for the least squares solution of minimal norm of rank deficient linear systems. Necessary and sufficient conditions for the semiconvergence of the AOR and JOR iterative methods are given. The optimum parameters and the associated convergence factor are derived.

article

Approximating common fixed points of non-self asymptotically nonexpansive mapping in Banach spaces

Xiaolong Qin, Yongfu Su, Meijuan Shang

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 233-246

In this paper, we consider a composite iterative algorithm with errors for approximating a common fixed points of non-self asymptotically nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend Chidume et al. (J. Math. Anal. Appl. 280:364–374, [2003]), Shahzad (Nonlinear Anal. 61:1031–1039, [2005]), Su and Qin (J. Appl. Math. Comput. 24:437–448, [2007]) and many others...

article

On the study of multilevel difference methods

Jin Wang

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 381-396

Multilevel finite difference methods can achieve high-order accuracy by using compact stencils and they are preferred in numerical simulation of wave advections when high accuracy in both the amplitude and phase is needed. Based on the modified equation theory, we present two general approaches that can effectively design highly accurate multilevel difference schemes. Numerical experiments are performed...

article

Effect of environmental fluctuation on a detritus based ecosystem

Malay Bandyopadhyay

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 433-450

Present paper deals with the stochastic perturbation analysis on a detritus based three dimensional food-chain in presence of gestation delays and recycling delay. We have perturbed some demographic parameters by white noise and coloured noise and then extensive numerical simulations are performed to understand the effect of fluctuating environment on the dynamics of the model system for different...

article

Sensitivity analysis for cocoercively monotone variational inclusions and (A,η)-maximal monotonicity

Ram N. Mohapatra, Ram U. Verma

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 281-293

Sensitivity analysis for cocoercively monotone variational inclusions based on the generalized resolvent operator technique is discussed. The notion of the cocoercive monotonicity unifies most of the existing notions, such as cocoercivity, strong monotonicity, relaxed monotonicity, relaxed cocoercivity, and others. As a result, the obtained results are general in nature.

article

The existence of solutions for a second-order discrete Neumann problem with a p-Laplacian

Yu Tian, Weigao Ge

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 333-340

In this paper, we investigate the solutions of second-order discrete Neumann boundary value problem with a p-Laplacian. By using critical point theory the existence results are obtained.

article

C ^*-algebras generated by partial isometries

Ilwoo Cho, Palle Jorgensen

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 1-48

We study the interconnection between directed graphs and operators on a Hilbert space. The intuition supporting this link is the following feature shared by partial isometries (as operators on a Hilbert space) on the one hand and edges in directed graphs on the other. A partial isometry a is an operator in a Hilbert space H, i.e., a:H→H which maps a (closed) subspace in H isometrically onto a generally...

article

A stage-structured predator-prey model with Beddington-DeAngelis functional response

Liming Cai, Jingyuan Yu, Guangtian Zhu

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 85-103

In this paper, a stage-structured predator-prey model with Beddington-DeAngelis functional response is proposed and analyzed. It is assumed in the model that the individuals in each specie may belong to one of two classes: the immature and the mature, the age of maturity is represented by a time delay. By using the persistence theory for infinite dimensional systems, necessary and sufficient conditions...

article

ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation

S. Chen, F. Liu

Journal of Applied Mathematics and Computing > 2008 > 26 > 1-2 > 295-311

In this paper, a two-dimensional fractional advection-dispersion equation (2D-FADE) with variable coefficients on a finite domain is considered. We use a new technique of combination of the Alternating Directions Implicit-Euler method (ADI-Euler), the unshifted Grünwald formula for the advection term, the right-shifted Grünwald formula for the diffusion term, and a Richardson extrapolation to establish...

INFONA - science communication portal

Journal of Applied Mathematics and Computing

A numerical investigation on the structure of the roots of q-Genocchi polynomials

Li-Yorke chaos in 2D discrete systems

Block SOR methods for fuzzy linear systems

Global convergence of a memory gradient method without line search

Methods for knowledge reduction in inconsistent ordered information systems

Flow shop scheduling with effects of learning and deterioration

Sub-quadratic convergence of a smoothing Newton method for second-order cone programming

On 9- and 10-decomposable finite groups

Optimal L ^∞ error estimates for finite element Galerkin methods for nonlinear evolution equations

Representations for the weighted Drazin inverse of a sum of matrices

The parameterization of 2-channel orthogonal multifilter banks with some symmetry

AOR iterative methods for rank deficient least squares problems

Approximating common fixed points of non-self asymptotically nonexpansive mapping in Banach spaces

On the study of multilevel difference methods

Effect of environmental fluctuation on a detritus based ecosystem

Sensitivity analysis for cocoercively monotone variational inclusions and (A,η)-maximal monotonicity

The existence of solutions for a second-order discrete Neumann problem with a p-Laplacian

C ^*-algebras generated by partial isometries

A stage-structured predator-prey model with Beddington-DeAngelis functional response

ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation

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