World Academy of Science, Engineering and Technology

Authors: Said Laachir, Aziz Laaribi

Abstract:

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

Authors: N. Z. A. Hamid, M. S. M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.

Authors: M.V. Shyla, K.B. Naidu

Abstract:

The objective of this paper is to develop a computational model of human nasal cavity from computed tomography (CT) scans using MIMICS software. Computational fluid dynamic techniques were employed to understand nasal airflow. Gambit and Fluent software was used to perform CFD simulation. Velocity profiles, iteration plots, pressure distribution, streamline and pathline patterns for steady, laminar airflow inside the human nasal cavity of healthy and also infected persons are presented in detail. The implications for olfaction are visualized. Results are validated with the available numerical and experimental data. The graphs reveal that airflow varies with different anatomical nasal structures and only fraction of the inspired air reaches the olfactory region. The Deviations in the results suggest that the treatment of infected volunteers will improve the olfactory function.

Keywords: CFD techniques, Finite Volume Method, Fluid dynamic sniffing, Human nasal cavity.

Authors: Teerayut Chomchuen, Aiyared Iampan

Abstract:

The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

Keywords: Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal.

Authors: M. K. Hasan, Y. H. Ng, J. Sulaiman

Abstract:

This paper present the implementation of a new ordering strategy on Successive Overrelaxation scheme on two dimensional boundary value problems. The strategy involve two directions alternatingly; from top and bottom of the solution domain. The method shows to significantly reduce the iteration number to converge. Four numerical experiments were carried out to examine the performance of the new strategy.

Keywords: Two dimensional boundary value problems, Successive Overrelaxation scheme, Alternating Top-Bottom strategy, fast convergence

Authors: Fares Innal, Yves Dutuit, Mourad Chebila

Abstract:

The object of this work is the probabilistic performance evaluation of safety instrumented systems (SIS), i.e. the average probability of dangerous failure on demand (PFD_avg) and the average frequency of failure (PFH), taking into account the uncertainties related to the different parameters that come into play: failure rate (λ), common cause failure proportion (β), diagnostic coverage (DC)... This leads to an accurate and safe assessment of the safety integrity level (SIL) inherent to the safety function performed by such systems. This aim is in keeping with the requirement of the IEC 61508 standard with respect to handling uncertainty. To do this, we propose an approach that combines (1) Monte Carlo simulation and (2) fuzzy sets. Indeed, the first method is appropriate where representative statistical data are available (using pdf of the relating parameters), while the latter applies in the case characterized by vague and subjective information (using membership function). The proposed approach is fully supported with a suitable computer code.

Keywords: Fuzzy sets, Monte Carlo simulation, Safety instrumented system, Safety integrity level.

Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

Abstract:

This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: Interpolation, Approximate Solution, Collocation, Differential system, Half step, Converges, Block method, Efficiency.

Authors: Jedol Dayou, Jackson Hian Wui Chang, Rubena Yusoff, Ag. Sufiyan Abd. Hamid, Fauziah Sulaiman, Justin Sentian

Abstract:

Aerosols are small particles suspended in air that have wide varying spatial and temporal distributions. The concentration of aerosol in total columnar atmosphere is normally measured using aerosol optical depth (AOD). In long-term monitoring stations, accurate AOD retrieval is often difficult due to the lack of frequent calibration. To overcome this problem, a near-sea-level Langley calibration algorithm is developed using the combination of clear-sky detection model and statistical filter. It attempts to produce a dataset that consists of only homogenous and stable atmospheric condition for the Langley calibration purposes. In this paper, a radiance-based validation method is performed to further investigate the feasibility and consistency of the proposed algorithm at different location, day, and time. The algorithm is validated using SMARTS model based n DNI value. The overall results confirmed that the proposed calibration algorithm feasible and consistent for measurements taken at different sites and weather conditions.

Keywords: Aerosol optical depth, direct normal irradiance, Langley calibration, radiance-based validation, SMARTS.

Authors: Avellino I. Mondlane, Karin Hansson, Oliver Popov

Abstract:

This paper discusses the application of extreme events distribution taking the Limpopo River Basin at Xai-Xai station, in Mozambique, as a case analysis. We analyze the extreme value concepts, namely Gumbel, Fréchet, Weibull and Generalized Extreme Value Distributions and then extrapolate the original data to 1000, 5000 and 10000 figures for further simulations and we compare their outcomes based on these three main distributions.

Keywords: Catastrophes, extreme event, disasters, mathematical models, simulation.

Authors: Jaipong Kasemsuwan

Abstract:

This paper presents the finite difference scheme and the numerical simulation of suspended string. The vibration solutions when the various external forces are taken into account are obtained and compared with the solutions without external force. In addition, we also investigate how the external forces and their powers and coefficients affect the amplitude of vibration.

Keywords: Nonlinear external forces, Numerical simulation, Suspended string equation.

Authors: Dong Hoon Lim

Abstract:

A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented via a singular value decomposition(SVD), is useful for analysis of microarray data. For application of PCA using SVD we use the DNA microarray data for the small round blue cell tumors(SRBCT) of childhood by Khan et al.(2001). To decide the number of components which account for sufficient amount of information we draw scree plot. Biplot, a graphic display associated with PCA, reveals important features that exhibit relationship between variables and also the relationship of variables with observations.

Keywords: Principal component analysis, singular value decomposition, microarray data, SRBCT

Authors: Kannanut Chamsri

Abstract:

Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

Authors: Thawatchai Khumprapussorn

Abstract:

We introduced the notions of (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule as a generalization of prime ideal and jointly prime (R, S)-submodule, respectively. We provide a relationship between (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule. Characterizations of (1, k)-jointly prime (R, S)- submodules are also given.

Keywords: R, S)-module, (1, k)-prime ideal, (1, k)-jointly prime (R, S)-submodule.

Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

Authors: Sa-aat Niwitpong, Rada Somkhuean, Suparat Niwitpong

Abstract:

This paper presents the generalized p-values for testing the Behrens-Fisher problem when one variance is unknown. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Keywords: Generalized p-value, hypothesis testing, upper bound.

Authors: Rada Somkhuean, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

This paper presents the generalized p-values for testing the Behrens-Fisher problem when a ratio of variance is known. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Keywords: Generalized p-value, hypothesis testing, ratio of variances, upper bound.

Authors: Jeerapa Sappakitkamjorn, Sa-aat Niwitpong

Abstract:

In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.  

Keywords: Bounded parameters, coefficient of variation, confidence interval, Monte Carlo simulation.

Authors: Arunee Wongkha, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

Keywords: The inverse of a normal mean, confidence interval, generalized confidence intervals, known coefficient of variation.

Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Keywords: Food chain system, periodic solution, time scales, coincidence degree.

Authors: Lazim Abdullah, Nurhakimah Ab. Rahman

Abstract:

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Keywords: Fuzzy linear systems, Jacobi, Jacobi Over- Relaxation, Refinement of Jacobi, Refinement of Jacobi Over- Relaxation.

Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

Authors: Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

Abstract:

As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Keywords: periodic solution, neutral Rayleigh equation, variable sign, Deviating argument, p-Laplacian, Mawhin’s continuation.

Authors: Mario Mastriani, Marcelo Naiouf

Abstract:

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for signal and image processing applications.

Keywords: Digital filters, digital signal and image processing, Gram-Schmidt Process, orthonormalization.

Authors: Min Sun, Jing Liu

Abstract:

In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Keywords: structured variational inequalities, proximal point method, global convergence

Authors: N. Feroze, M. Aslam

Abstract:

The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.

Keywords: Fisher information matrix, confidence intervals, censoring.

Authors: Sharif E. Guseynov, Jekaterina V. Aleksejeva, Janis S. Rimshans

Abstract:

A filtering problem of almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain is studied. In this work general approaches to the solution of twodimensional filtering problems in ananisotropic, inhomogeneous and multilayered medium are developed, and on the basis of the obtained results mathematical models are constructed (according to Ollendorff method) for studying the certain engineering and technical problem of filtering the almost incompressible liquid chemical compound in the porous inhomogeneous 3D domain. For some of the formulated mathematical problems with additional requirements for the structure of the porous inhomogeneous medium, namely, its isotropy, spatial periodicity of its permeability coefficient, solution algorithms are proposed. Continuation of the current work titled ”On one mathematical model for filtration of weakly compressible chemical compound in the porous heterogeneous 3D medium. Part II: Determination of the reference directions of anisotropy and permeabilities on these directions” will be prepared in the shortest terms by the authors.

Keywords: Porous media, filtering, permeability, elliptic PDE.

Authors: Pandaba Patro, Brundaban Patro

Abstract:

The numerical simulation of fully developed gas–solid flow in a horizontal pipe is done using the eulerian-eulerian approach, also known as two fluids modeling as both phases are treated as continuum and inter-penetrating continua. The solid phase stresses are modeled using kinetic theory of granular flow (KTGF). The computed results for velocity profiles and pressure drop are compared with the experimental data. We observe that the convection and diffusion terms in the granular temperature cannot be neglected in gas solid flow simulation along a horizontal pipe. The particle-wall collision and lift also play important role in eulerian modeling. We also investigated the effect of flow parameters like gas velocity, particle properties and particle loading on pressure drop prediction in different pipe diameters. Pressure drop increases with gas velocity and particle loading. The gas velocity has the same effect ((proportional toU2 ) as single phase flow on pressure drop prediction. With respect to particle diameter, pressure drop first increases, reaches a peak and then decreases. The peak is a strong function of pipe bore.

Keywords: CFD, Eulerian modeling, gas solid flow, KTGF.

Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.