Scholarly

Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems

Year: 2010 Volume: 4 Issue: 7 944 - 951 Pages

Abstract: This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and present a generalized second-order Arnoldi process for constructing an orthonormal basis of the generalized second-order Krylov subspace. Then, by using the projection technique and the refined projection technique, we propose a restarted generalized second-order Arnoldi method and a restarted refined generalized second-order Arnoldi method for computing some eigenpairs of largescale quadratic eigenvalue problems. Some theoretical results are also presented. Some numerical examples are presented to illustrate the effectiveness of the proposed methods.

Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation

Year: 2010 Volume: 4 Issue: 7 940 - 943 Pages

Abstract: By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g t, 0 −τ x(t + s) dα(s) + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

Year: 2010 Volume: 4 Issue: 7 935 - 939 Pages

Authors:
Ahmet Tekcan

Abstract: Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Periodicity for a Semi–Ratio–Dependent Predator–Prey System with Delays on Time Scales

Year: 2010 Volume: 4 Issue: 7 931 - 934 Pages

Authors:
Kejun Zhuang

Abstract: In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.

Certain Conditions for Strongly Starlike and Strongly Convex Functions

Year: 2010 Volume: 4 Issue: 7 928 - 930 Pages

Abstract: In the present paper, we investigate a differential subordination involving multiplier transformation related to a sector in the open unit disk E = {z : |z| < 1}. As special cases to our main result, certain sufficient conditions for strongly starlike and strongly convex functions are obtained.

The Pell Equation x2 − Py2 = Q

Year: 2010 Volume: 4 Issue: 7 924 - 927 Pages

Abstract: Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.

Haar Wavelet Method for Solving Fitz Hugh-Nagumo Equation

Year: 2010 Volume: 4 Issue: 7 919 - 923 Pages

Abstract: In this paper, we develop an accurate and efficient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

An Advanced Stereo Vision Based Obstacle Detection with a Robust Shadow Removal Technique

Year: 2010 Volume: 4 Issue: 7 913 - 918 Pages

Abstract: This paper presents a robust method to detect obstacles in stereo images using shadow removal technique and color information. Stereo vision based obstacle detection is an algorithm that aims to detect and compute obstacle depth using stereo matching and disparity map. The proposed advanced method is divided into three phases, the first phase is detecting obstacles and removing shadows, the second one is matching and the last phase is depth computing. We propose a robust method for detecting obstacles in stereo images using a shadow removal technique based on color information in HIS space, at the first phase. In this paper we use Normalized Cross Correlation (NCC) function matching with a 5 × 5 window and prepare an empty matching table τ and start growing disparity components by drawing a seed s from S which is computed using canny edge detector, and adding it to τ. In this way we achieve higher performance than the previous works [2,17]. A fast stereo matching algorithm is proposed that visits only a small fraction of disparity space in order to find a semi-dense disparity map. It works by growing from a small set of correspondence seeds. The obstacle identified in phase one which appears in the disparity map of phase two enters to the third phase of depth computing. Finally, experimental results are presented to show the effectiveness of the proposed method.

Improved Robust Stability and Stabilization Conditions of Discrete-time Delayed System

Year: 2010 Volume: 4 Issue: 7 906 - 912 Pages

Authors:
Zixin Liu

Abstract: The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

A New Preconditioned AOR Method for Z-matrices

Year: 2010 Volume: 4 Issue: 7 903 - 905 Pages

Abstract: In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices

Year: 2010 Volume: 4 Issue: 7 899 - 902 Pages

Authors:
Yongxin Yuan

Abstract: In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Dynamic-Stochastic Influence Diagrams: Integrating Time-Slices IDs and Discrete Event Systems Modeling

Year: 2010 Volume: 4 Issue: 7 891 - 898 Pages

Abstract: The Influence Diagrams (IDs) is a kind of Probabilistic Belief Networks for graphic modeling. The usage of IDs can improve the communication among field experts, modelers, and decision makers, by showing the issue frame discussed from a high-level point of view. This paper enhances the Time-Sliced Influence Diagrams (TSIDs, or called Dynamic IDs) based formalism from a Discrete Event Systems Modeling and Simulation (DES M&S) perspective, for Exploring Analysis (EA) modeling. The enhancements enable a modeler to specify times occurred of endogenous events dynamically with stochastic sampling as model running and to describe the inter- influences among them with variable nodes in a dynamic situation that the existing TSIDs fails to capture. The new class of model is named Dynamic-Stochastic Influence Diagrams (DSIDs). The paper includes a description of the modeling formalism and the hiberarchy simulators implementing its simulation algorithm, and shows a case study to illustrate its enhancements.

A Hybrid Approach Using Particle Swarm Optimization and Simulated Annealing for N-queen Problem

Year: 2010 Volume: 4 Issue: 7 886 - 890 Pages

Abstract: This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.

Keywords:
PSO
SA
N-queen
CSP

Periodic Solutions for a Delayed Population Model on Time Scales

Year: 2010 Volume: 4 Issue: 7 883 - 885 Pages

Abstract: This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

On the Solution of Fully Fuzzy Linear Systems

Year: 2010 Volume: 4 Issue: 7 878 - 882 Pages

Authors:
Hsuan-Ku Liu

Abstract: A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

Parallel Multisplitting Methods for Singular Linear Systems

Year: 2010 Volume: 4 Issue: 7 874 - 877 Pages

Abstract: In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

On Detour Spectra of Some Graphs

Year: 2010 Volume: 4 Issue: 7 871 - 873 Pages

Abstract: The Detour matrix (DD) of a graph has for its ( i , j) entry the length of the longest path between vertices i and j. The DD-eigenvalues of a connected graph G are the eigenvalues for its detour matrix, and they form the DD-spectrum of G. The DD-energy EDD of the graph G is the sum of the absolute values of its DDeigenvalues. Two connected graphs are said to be DD- equienergetic if they have equal DD-energies. In this paper, the DD- spectra of a variety of graphs and their DD-energies are calculated.

Losses Analysis in TEP Considering Uncertainity in Demand by DPSO

Year: 2010 Volume: 4 Issue: 7 865 - 870 Pages

Abstract: This paper presents a mathematical model and a methodology to analyze the losses in transmission expansion planning (TEP) under uncertainty in demand. The methodology is based on discrete particle swarm optimization (DPSO). DPSO is a useful and powerful stochastic evolutionary algorithm to solve the large-scale, discrete and nonlinear optimization problems like TEP. The effectiveness of the proposed idea is tested on an actual transmission network of the Azerbaijan regional electric company, Iran. The simulation results show that considering the losses even for transmission expansion planning of a network with low load growth is caused that operational costs decreases considerably and the network satisfies the requirement of delivering electric power more reliable to load centers.

Keywords:
DPSO
TEP
Uncertainty

Splitting Modified Donor-Cell Schemes for Spectral Action Balance Equation

Year: 2010 Volume: 4 Issue: 7 856 - 864 Pages

Abstract: The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Haar wavelet Method for Solving Initial and Boundary Value Problems of Bratu-type

Year: 2010 Volume: 4 Issue: 7 852 - 855 Pages

Abstract: In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

International Journal of Engineering, Mathematical and Physical Sciences

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