Scholarly

A Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations

Year: 2011 Volume: 5 Issue: 7 1099 - 1105 Pages

Abstract: In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Strongly Screenableness and its Tychonoff Products

Year: 2011 Volume: 5 Issue: 7 1094 - 1098 Pages

Abstract: In this paper, we prove that if X is regular strongly screenable DC-like (C-scattered), then X ×Y is strongly screenable for every strongly screenable space Y . We also show that the product i∈ω Yi is strongly screenable if every Yi is a regular strongly screenable DC-like space. Finally, we present that the strongly screenableness are poorly behaved with its Tychonoff products.

Compton Scattering of Annihilation Photons as a Short Range Quantum Key Distribution Mechanism

Year: 2011 Volume: 5 Issue: 7 1087 - 1093 Pages

Abstract: The angular distribution of Compton scattering of two quanta originating in the annihilation of a positron with an electron is investigated as a quantum key distribution (QKD) mechanism in the gamma spectral range. The geometry of coincident Compton scattering is observed on the two sides as a way to obtain partially correlated readings on the quantum channel. We derive the noise probability density function of a conceptually equivalent prepare and measure quantum channel in order to evaluate the limits of the concept in terms of the device secrecy capacity and estimate it at roughly 1.9 bits per 1 000 annihilation events. The high error rate is well above the tolerable error rates of the common reconciliation protocols; therefore, the proposed key agreement protocol by public discussion requires key reconciliation using classical error-correcting codes. We constructed a prototype device based on the readily available monolithic detectors in the least complex setup.

Some Constructions of Non-Commutative Latin Squares of Order n

Year: 2011 Volume: 5 Issue: 7 1084 - 1086 Pages

Abstract: Let n be an integer. We show the existence of at least three non-isomorphic non-commutative Latin squares of order n which are embeddable in groups when n ≥ 5 is odd. By using a similar construction for the case when n ≥ 4 is even, we show that certain non-commutative Latin squares of order n are not embeddable in groups.

Sensitivity Computations of Time Relaxation Model with an Application in Cavity Computation

Year: 2011 Volume: 5 Issue: 7 1080 - 1083 Pages

Abstract: We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems

Year: 2011 Volume: 5 Issue: 7 1075 - 1079 Pages

Abstract: We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.

Study of Water on the Surface of Nano-Silica Material: An NMR Study

Year: 2011 Volume: 5 Issue: 7 1070 - 1074 Pages

Authors:
J. Hassan

Abstract: Water 2H NMR signal on the surface of nano-silica material, MCM-41, consists of two overlapping resonances. The 2H water spectrum shows a superposition of a Lorentzian line shape and the familiar NMR powder pattern line shape, indicating the existence of two spin components. Chemical exchange occurs between these two groups. Decomposition of the two signals is a crucial starting point for study the exchange process. In this article we have determined these spin component populations along with other important parameters for the 2H water NMR signal over a temperature range between 223 K and 343 K.

An Asymptotic Solution for the Free Boundary Parabolic Equations

Year: 2011 Volume: 5 Issue: 7 1063 - 1069 Pages

Abstract: In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Performance Comparison and Analysis of Different Schemes and Limiters

Year: 2011 Volume: 5 Issue: 7 1057 - 1062 Pages

Abstract: Eight difference schemes and five limiters are applied to numerical computation of Riemann problem. The resolution of discontinuities of each scheme produced is compared. Numerical dissipation and its estimation are discussed. The result shows that the numerical dissipation of each scheme is vital to improve scheme-s accuracy and stability. MUSCL methodology is an effective approach to increase computational efficiency and resolution. Limiter should be selected appropriately by balancing compressive and diffusive performance.

Inference of Stress-Strength Model for a Lomax Distribution

Year: 2011 Volume: 5 Issue: 7 1053 - 1056 Pages

Authors:
H. Panahi
S. Asadi

Abstract: In this paper, the estimation of the stress-strength parameter R = P(Y < X), when X and Y are independent and both are Lomax distributions with the common scale parameters but different shape parameters is studied. The maximum likelihood estimator of R is derived. Assuming that the common scale parameter is known, the bayes estimator and exact confidence interval of R are discussed. Simulation study to investigate performance of the different proposed methods has been carried out.

Iterative solutions to the linear matrix equation AXB + CXTD = E

Year: 2011 Volume: 5 Issue: 7 1049 - 1052 Pages

Abstract: In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXTD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Some Exact Solutions of the (2+1)-Dimensional Breaking Soliton Equation using the Three-wave Method

Year: 2011 Volume: 5 Issue: 7 1045 - 1048 Pages

Abstract: This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

Year: 2011 Volume: 5 Issue: 7 1039 - 1044 Pages

Abstract: In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Mathematical Modeling for the Processes of Strain Hardening in Heterophase Materials with Nanoparticles

Year: 2011 Volume: 5 Issue: 7 1033 - 1038 Pages

Abstract: An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.

Continuous Threshold Prey Harvesting in Predator-Prey Models

Year: 2011 Volume: 5 Issue: 7 1025 - 1032 Pages

Abstract: The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well as some heteroclinic orbits are computed.

The Direct Updating of Damping and Gyroscopic Matrices using Incomplete Complex Test Data

Year: 2011 Volume: 5 Issue: 7 1021 - 1024 Pages

Abstract: In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords:
Model updating
damped gyroscopic system
partially prescribed spectral information.

A Numerical Study of a Droplet Impinging on a Liquid Surface

Year: 2011 Volume: 5 Issue: 7 1016 - 1020 Pages

Authors:
S.Asadi
H.Panahi

Abstract: The Navier–Stokes equations for unsteady, incompressible, viscous fluids in the axisymmetric coordinate system are solved using a control volume method. The volume-of-fluid (VOF) technique is used to track the free-surface of the liquid. Model predictions are in good agreement with experimental measurements. It is found that the dynamic processes after impact are sensitive to the initial droplet velocity and the liquid pool depth. The time evolution of the crown height and diameter are obtained by numerical simulation. The critical We number for splashing (Wecr) is studied for Oh (Ohnesorge) numbers in the range of 0.01~0.1; the results compares well with those of the experiments.

Simulation of Sloshing behavior using Moving Grid and Body Force Methods

Year: 2011 Volume: 5 Issue: 7 1011 - 1015 Pages

Authors:
Tadashi Watanabe

Abstract: The flow field and the motion of the free surface in an oscillating container are simulated numerically to assess the numerical approach for studying two-phase flows under oscillating conditions. Two numerical methods are compared: one is to model the oscillating container directly using the moving grid of the ALE method, and the other is to simulate the effect of container motion using the oscillating body force acting on the fluid in the stationary container. The two-phase flow field in the container is simulated using the level set method in both cases. It is found that the calculated results by the body force method coinsides with those by the moving grid method and the sloshing behavior is predicted well by both the methods. Theoretical back ground and limitation of the body force method are discussed, and the effects of oscillation amplitude and frequency are shown.

A New Quadrature Rule Derived from Spline Interpolation with Error Analysis

Year: 2011 Volume: 5 Issue: 7 1005 - 1010 Pages

Authors:
Hadi Taghvafard

Abstract: We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

More on Gaussian Quadratures for Fuzzy Functions

Year: 2011 Volume: 5 Issue: 7 1000 - 1004 Pages

Authors:
Shu-Xin Miao

Abstract: In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

International Journal of Engineering, Mathematical and Physical Sciences

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