International Journal of Engineering, Mathematical and Physical Sciences

(λ, μ)-Intuitionistic Fuzzy Subgroups of Groups with Operators

Year: 2016 Volume: 10 Issue: 9 456 - 462 Pages

Abstract: The aim of this paper is to introduce the concepts of the (λ, μ)-intuitionistic fuzzy subgroups and (λ, μ)-intuitionistic fuzzy normal subgroups of groups with operators, and to investigate their properties and characterizations based on M-group homomorphism.

Semilocal Convergence of a Three Step Fifth Order Iterative Method under Höolder Continuity Condition in Banach Spaces

Year: 2016 Volume: 10 Issue: 11 574 - 578 Pages

Abstract: In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Investigating the Efficiency of Stratified Double Median Ranked Set Sample for Estimating the Population Mean

Year: 2016 Volume: 10 Issue: 11 568 - 573 Pages

Authors:
Mahmoud I. Syam

Abstract: Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.

Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides

Year: 2016 Volume: 10 Issue: 11 560 - 567 Pages

Abstract: This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As2S3 chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

An Experimental Study of Structural, Optical and Magnetic Properties of Lithium Ferrite

Year: 2016 Volume: 10 Issue: 8 409 - 412 Pages

Abstract: Nanomaterials ferrites have applications in making permanent magnets, high density information devices, color imaging etc. In the present examination, lithium ferrite is synthesized by sol-gel process. The x-ray diffraction (XRD) result shows that the structure of lithium ferrite is monoclinic structure. The average particle size 22 nm is calculated by Scherer formula. The lattice parameters and dislocation density (δ) are calculated from XRD data. Strain (ε) values are evaluated from Williamson – hall plot. The FT-IR study reveals the formation of ferrites showing the significant absorption bands. The VU-VIS spectroscopic data is used to calculate direct and indirect optical band gap (Eg) of 1.57eV and 1.01eV respectively for lithium ferrite by using Tauc plot at the edge of the absorption band. The energy dispersive x-ray analysis spectra showed that the expected elements exist in the material. The magnetic behaviour of the materials studied using vibrating sample magnetometer (VSM).

A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

Year: 2016 Volume: 10 Issue: 11 551 - 559 Pages

Abstract: In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces

Year: 2016 Volume: 10 Issue: 11 543 - 550 Pages

Abstract: The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Characterization of an Extrapolation Chamber for Dosimetry of Low Energy X-Ray Beams

Year: 2016 Volume: 10 Issue: 10 517 - 520 Pages

Abstract: Extrapolation chambers were designed to be used as primary standard dosimeter for measuring absorbed dose in a medium in beta radiation and low energy x-rays. The International Organization for Standardization established series of reference x-radiation for calibrating and determining the energy dependence of dosimeters that are to be reproduced in metrology laboratories. Standardization of the low energy x-ray beams with tube potential lower than 30 kV may be affected by the instrument used for dosimetry. In this work, parameters of a 23392 model PTW extrapolation chamber were determined aiming its use in low energy x-ray beams as a reference instrument.

Variogram Fitting Based on the Wilcoxon Norm

Year: 2016 Volume: 10 Issue: 9 449 - 455 Pages

Abstract: Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

On Quasi Conformally Flat LP-Sasakian Manifolds with a Coefficient α

Year: 2016 Volume: 10 Issue: 9 445 - 448 Pages

Authors:
Jay Prakash Singh

Abstract: The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method

Year: 2016 Volume: 10 Issue: 10 512 - 516 Pages

Authors:
M. K. Balyan

Abstract: The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Solutions to Probabilistic Constrained Optimal Control Problems Using Concentration Inequalities

Year: 2016 Volume: 10 Issue: 10 506 - 511 Pages

Authors:
Tomoaki Hashimoto

Abstract: Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.

A Lagrangian Hamiltonian Computational Method for Hyper-Elastic Structural Dynamics

Year: 2016 Volume: 10 Issue: 10 500 - 505 Pages

Abstract: Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

Year: 2016 Volume: 10 Issue: 10 492 - 499 Pages

Abstract: In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Study on Optimal Control Strategy of PM2.5 in Wuhan, China

Year: 2016 Volume: 10 Issue: 8 405 - 408 Pages

Abstract: In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

A Comparative Study of High Order Rotated Group Iterative Schemes on Helmholtz Equation

Year: 2016 Volume: 10 Issue: 10 486 - 491 Pages

Abstract: In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

A Statistical Model for the Dynamics of Single Cathode Spot in Vacuum Cylindrical Cathode

Year: 2016 Volume: 10 Issue: 10 482 - 485 Pages

Abstract: Dynamics of cathode spot has become a major part of vacuum arc discharge with its high academic interest and wide application potential. In this article, using a three-dimensional statistical model, we simulate the distribution of the ignition probability of a new cathode spot occurring in different magnetic pressure on old cathode spot surface and at different arcing time. This model for the ignition probability of a new cathode spot was proposed in two typical situations, one by the pure isotropic random walk in the absence of an external magnetic field, other by the retrograde motion in external magnetic field, in parallel with the cathode surface. We mainly focus on developed relationship between the ignition probability density distribution of a new cathode spot and the external magnetic field.

On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid

Year: 2016 Volume: 10 Issue: 10 475 - 481 Pages

Authors:
A. Giniatoulline

Abstract: A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Module and Comodule Structures on Path Space

Year: 2016 Volume: 10 Issue: 3 151 - 155 Pages

Authors:
Lili Chen
Chao Yuan

Abstract: On path space kQ, there is a trivial kQa-module structure determined by the multiplication of path algebra kQa and a trivial kQc-comodule structure determined by the comultiplication of path coalgebra kQc. In this paper, on path space kQ, a nontrivial kQa-module structure is defined, and it is proved that this nontrivial left kQa-module structure is isomorphic to the dual module structure of trivial right kQc-comodule. Dually, on path space kQ, a nontrivial kQc-comodule structure is defined, and it is proved that this nontrivial right kQc-comodule structure is isomorphic to the dual comodule structure of trivial left kQa-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule.

An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

Year: 2016 Volume: 10 Issue: 9 441 - 444 Pages

Authors:
Autcha Araveeporn

Abstract: This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.