World Academy of Science, Engineering and Technology

Authors: Pakkinee Chitsakul

Abstract:

In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: Cut locus, flat torus, geodesics.

Authors: P. Pongsumpun

Abstract:

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

Keywords: Age structural model, Herpes zoster, local stability, Numerical solution.

Authors: Amel Abdoullah Ahmed Dghais, Mohd Tahir Ismail

Abstract:

In this paper the core objective is to apply discrete wavelet transform and maximal overlap discrete wavelet transform functions namely Haar, Daubechies2, Symmlet4, Coiflet2 and discrete approximation of the Meyer wavelets in non stationary financial time series data from Dow Jones index (DJIA30) of US stock market. The data consists of 2048 daily data of closing index from December 17, 2004 to October 23, 2012. Unit root test affirms that the data is non stationary in the level. A comparison between the results to transform non stationary data to stationary data using aforesaid transforms is given which clearly shows that the decomposition stock market index by discrete wavelet transform is better than maximal overlap discrete wavelet transform for original data.

Keywords: Discrete wavelet transform, maximal overlap discrete wavelet transform, stationarity, autocorrelation function.

Authors: Xing-Jian Li, Shen Qu

Abstract:

The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.

Keywords: Elementary row transformation, Euler function, Matrix decomposition, Smith arithmetic determinant.

Authors: Yilun Shang

Abstract:

In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

Keywords: Stochastic matrix, ergodicity coefficient, partition.

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: Md. Alal Hosen

Abstract:

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^1/3 force nonlinear oscillator but it is also useful for many other nonlinear problems.

Keywords: Approximate solutions, Harmonic balance method, Nonlinear oscillator, Perturbation.

Authors: Chao Wang, Ting-Zhu Huang, Chen Jia

Abstract:

In this paper, we present a simplified higher-order Markov chain model for multiple categorical data sequences also called as simplified higher-order multivariate Markov chain model.

Keywords: Higher-order multivariate Markov chain model, Categorical data sequences, Multivariate Markov chain.

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: 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: 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: 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: 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: 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: 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: 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: 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: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

Authors: Xin Luo, Jin Huang, Pan Cheng

Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

Authors: Xun Ge, Jianhua Gong

Abstract:

ankings for output of Chinese main agricultural commodity in the world for 1978, 1980, 1990, 2000, 2006, 2007 and 2008 have been released in United Nations FAO Database. Unfortunately, where the ranking of output of Chinese cotton lint in the world for 2008 was missed. This paper uses sequential data mining methods with decision rules filling this gap. This new data mining method will be help to give a further improvement for United Nations FAO Database.

Keywords: Ranking, output of the main agricultural commodity, gross domestic product, decision table, information system, data mining, decision rule

Authors: D. A. Farinde

Abstract:

In this paper, two-sided uniformly normal distribution techniques were used in the derivation of monotone likelihood ratio. The approach mainly employed the parameters of the distribution for a class of all size a. The derivation technique is fast, direct and less burdensome when compared to some existing methods.

Keywords: Neyman-Pearson Lemma, Normal distribution