WSEAS CONFERENCES. WSEAS, Unifying the Science

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 Volume 9,  2010
Print ISSN: 1109-2769
E-ISSN: 2224-2880








Issue 1, Volume 9, January 2010

Title of the Paper: Comparison of Spline Approximation with the Modified Likelihoods in the Presence of Nuisance Parameter


Authors: Ahmet Sezer

Abstract: The likelihood functions from independent studies can be easily combined, and the combined likelihood function serves as a meaningful indication of the support the observed data give to the various parameter values. This fact has led many scientists to suggest using the likelihood function as a summary of post-data uncertainty concerning the parameter. Indeed, likelihood functions have several desired properties . They are objective, in that they depend only on the agreed-upon model and the data. They are also flexible, allowing us to combine information about competing models across studies. However, a serious difficulty arises because likelihood functions may not be expressible in a compact, easily-understood mathematical form suitable for communication or publication. For example, likelihood functions in mixture models may only be computable for individual values of the parameters and otherwise cannot be given in ”closed form”. To overcome this difficulty, we propose to approximate loglikelihood functions by using piecewise polynomials governed by a minimal number of parameters

Keywords: Likelihood, Approximation

Title of the Paper: An Application of Fuzzy Time Series to Improve ISE Forecasting


Authors: Memmedaga Memmedli, Ozer Ozdemir

Abstract: The problem of fuzzy time series forecasting plays an important role in many scientific areas such as statistics and neural networks. While forecasting fuzzy time series, most of forecasting applications use the same length of intervals. The determination of length of intervals is significant and critical in fuzzy time series forecasting. The usage of convenient performance measure may also have an important affect for forecasting studies. MSE (Mean squared error) as a performance measure is widely used in many studies. The aim of this paper is to improve fuzzy time series forecasting by using different length of intervals with neural networks according to various performance measures. For this reason, we take ISE (Istanbul stock exchange) national-100 index as a large data set for forecasting. We use various performance measures such as MSE, RMSE (Root mean squared error), MAE (Mean absolute error) and MAPE (Mean absolute percentage error) to compare forecasting performances with different length of intervals. The empirical results show that the most convenient length of intervals can be chosen as 300 by comparing overall performance of MSE, RMSE, MAE and MAPE by using neural networks.

Keywords: Forecasting, Fuzzy time series, Neural networks, ISE national-100 index, Performance measures, Length of intervals

Title of the Paper: The Computation of Abelian Subalgebras in Low-Dimensional Solvable Lie Algebras


Authors: Manuel Ceballos, Juan Nunez, Angel F. Tenorio

Abstract: The main goal of this paper is to compute the maximal abelian dimension of each solvable nondecomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic method which goes ruling out non-valid maximal abelian dimensions until obtaining its exact value. Based on Mubarakzyanov and Turkowsky’s classical classifications of solvable Lie algebras (see [13] and [19]) and the classification of 6-dimensional nilpotent Lie algebras by Goze and Khakimdjanov [7], we have explicitly computed the maximal abelian dimension for the algebras given in those classifications.

Keywords: Solvable Lie algebra, maximal abelian dimension

Title of the Paper: A Note on Skew-Normal Distribution Approximation to the Negative Binomal Distribution


Authors: Jyh-Jiuan Lin, Ching-Hui Chang, Rosemary Jou

Abstract: This article revisits the problem of approximating the negative binomial distribution. Its goal is to show that the skew-normal distribution, another alternative methodology, provides a much better approximation to negative binomial probabilities than the usual normal approximation.

Keywords: Central Limit Theorem, cumulative distribution function (cdf), skew-normal distribution, skew parameter

Title of the Paper: Partial State-Owned Bank Interest Margin, Default Risk, and Structural Breaks: A Model of Financial Engineering


Authors: Jyh-Horng Lin, Ching-Hui Chang, Rosemary Jou

Abstract: Recent reports demonstrate that the grip of nationalism is tightest in banking (Economist, 2009a), and in France and Britain, politicians powering taxpayers’ money into ailing banks are demanding that the cash be lent at home (Economist, 2009b). This paper proposes a call option model for bank interest margin and default risk valuation based on an event-dependent, structural break framework under the return of banking nationalization. The primary feature is the existence of the discontinuity and fat tails of asset returns and risks caused by structural changes. We show that an increase in the structural breaks in mean return discontinuity and volatility fluctuation caused by the increasing degree of the bank’s partial nationalization increases the bank’s interest margin and default risk. We conclude that nationalization may be a high return-volatility structure break.

Keywords: Partial Nationalization, Structural Change, Retail Banking, Interest Margin

Title of the Paper: Descriptor Techniques for Modeling of Swirling Fluid Structures and Stability Analysis


Authors: Diana Alina Bistrian, Florica Ioana Dragomirescu, George Savii

Abstract: In this paper we develop descriptor techniques for modeling swirling hydrodynamic structures. Using the descriptor notation we obtain the generalized eigenvalue formulation for differential-algebraic equations describing the spatial stability of the fluid flow. We describe the general framework for spatial stability investigation of vortex structures in both viscous and inviscid cases. The dispersion relation is analytically investigated and the polynomial eigenvalue problem describing the viscous spatial stability is reduced to a generalized eigenvalue problem in operator formulation using the companion vector technique. A different approach is assessed for spatial inviscid study when the stability model is obtained by means of a class of shifted orthogonal basis and a spectral differentiation matrix is derived to approximate the discrete spatial derivatives. Both schemes applied to a swirling fluid profile provide good results.

Keywords: Hydrodynamic stability, Swirling flow, Descriptor operators, Spectral collocation

Title of the Paper: Uniqueness of Positive Solutions for Degenerate Logistic Neumann Problems in a Half Space


Authors: Wei Dong, Tieguo Ji

Issue 2, Volume 9, February 2010

Title of the Paper: Quintic B-Spline Curve Generation using Given Points and Gradients and Modification based on Specified Radius of Curvature


Authors: Tetsuzo Kuragano

Abstract: A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more unknown control point positions than there are equations. To overcome this problem three methods are described. First, solve the underdetermined system as it stands. Secondly, decrease the number of unknown control point positions in an underdetermined system in order to convert it to a determined system. Third, a method to increase the number of equations is employed to change an underdetermined system to a determined system. In addition to this, another method to generate a quintic B-spline curve using given points with gradients in sequence is described. In this case, a linear system will be either overdetermined, determined or underdetermined. This depends on the number of given points with gradients in sequence. Additionally, a method to modify a quintic B-spline curve is described. The objective is to change an aesthetically unpleasing curve to an aesthetically pleasing curve. Algebraic functions are used to determine an aesthetically pleasing radius of curvature distribution. This is accomplished by minimizing the difference between the quintic B-spline curves radius of curvature and the specified radius of curvature using the least-squares method. Examples of curve generation are given.

Keywords: B-spline curve generation, curvature vector, given points, given points with gradients, underdetermined system, overdetermined system, curve shape modification

Title of the Paper: Image Hiding Based on Circular Moire Fringes


Authors: Minvydas Ragulskis, Algiment Aleksa, Jurate Ragulskiene

Abstract: Circular time-averaging moire technique is exploited to hide an image in a background moire grating. The secret image can be visualized when the encoded image is oscillated around a pre-defined axial point. It is a new visual decoding scheme when the secret image is embedded into a circular moire grating and can be interpreted by a naked eye. The encoded secret image is not shared into components; this is a one image method. Computational examples are used to demonstrate the functionality of the method. The property of the human visual system to average fast dynamical processes being not able to follow rapid oscillatory motions is exploited to decode the secret image.

Keywords: Visual Cryptography, Moire fringes, Bessel Functions

Title of the Paper: Use of Vodcasting in Higher Education to Improve Student Learning


Authors: Javier Bilbao, Eugenio Bravo, Olatz Garcia, Concepcion Varela, Purificacion Gonzalez, Izaskun Baro, Miguel Rodriguez

Abstract: In several countries the curricula for the different degrees of the universities is changing to adapt it to the Anglo-Saxon model of four years. In this context, several degrees must reduce the hours for classroom and this affects in a higher way to some subjects. Some of them can see reduced their teaching hours even to the half. So, it is necessary to adopt some measures in order to maintain the level of the degree (it would be very difficult to increase this level in such situation of reducing a lot of teaching hours) and to take advantage of the change and adapt the subjects to the new century and technologies. One of these measures that we can take is to use the Information and Communication Technologies (ICT) out of the classroom. In this way, we are developing a vodcast. The information in electronic form (as well as the access to this information) has very specific characteristics and the aim of all of us who make use of this information is getting the most out. Simply to prepare a text and place in cyberspace is wasting much of the potential we have at our disposal. To insert static images helps to improve the information. Accompanying text with audio enriches considerably the text. And to produce a combined video image and sound is the most comprehensive offering that can be done to anyone seeking information. Vodcasting can be a powerful tool to use in some subjects. The generalization of this idea is not probed. But we are developing our vodcast for subjects of Mathematics of the first year of Engineering degrees and it seems that the tool is very well accepted by students.

Keywords: Vodcasting, higher education, video podcast, vodcast, learning, educational innovation, information in electronic form, knowledge

Title of the Paper: Comparison of the Results of Factorial Experiments, Fractional Factorial Experiments, Regression Trees and MARS for Fuel Consumption Data


Authors: Betul Kan, Berna Yazici

Abstract: In this study effects that are significant on the fuel consumption of F-4 aircrafts are analyzed by using different statistical methods and the results of those different methods are compared. The response variable of every possible combination of factors and interactions are analyzed to provide information about main effect(s) and interaction effect(s). MARS is applied in order to find the relationship and a tree model in order to summarize the relationship of main effects and the interactions on a plot. Also a 25 factorial experiment with 4 replications is performed to determine the significant main effects and interactions. The analysis is repeated for one-half fractional factorial experiment. A comparison of performance of the methods is made in order to investigate their applicability.

Keywords: Regression trees, MARS, factorial experiments, fractional factorial experiments, basis function, GCV (Generalized Cross Validation), recursive partitioning, AID (Automatic Interaction Detection)

Title of the Paper: Stochastic Optimal Control for Small Noise Intensities: The Discrete-Time Case


Authors: Hugo Cruz-Suarez, Rocio Ilhuicatzi-Roldan

Abstract: This paper deals with Markov Decision Processes (MDPs) on Borel spaces with an infinite horizon and a discounted total cost. It will be considered a stochastic optimal control problem which arises by perturbing the transition law of a deterministic control problem, through an additive random noise term with coefficient epsilon. In the paper, we will analyze the behavior of the optimal solution (optimal value function and optimal policy) of the stochastic system, when the coefficient epsilon goes to zero. Specifically, conditions given in the paper guarantee the uniform on compact sets convergence of both the optimal value function and the optimal policy of the stochastic system to the optimal value function and the optimal policy of the deterministic one, when epsilon goes to zero, respectively. Finally, two examples which illustrate the developed theory are presented.

Keywords: Stochastic Optimization, Markov Decision Process, Dynamic Programming, Total Discounted Cost, Deterministic Approximation, Inventory/Production System

Title of the Paper: Optimization of Stepped Shells


Authors: J. Lellep, E. Puman, L. Roots, E. Tungel

Abstract: Problems of analysis and optimization of axisymmetric shells of piece wise constant thickness are studied. The cases of quasistatic and dynamic loading are considered separately whereas the shells may be manufactured from both, elastic and inelastic materials. Minimum weight designs of inelastic shells of piece wise constant thickness are established under the condition that the limit load is fixed. Also the designs of maximum load carrying capacity are determined for given weight (material volume) of the shell. Necessary optimality conditions are derived with the aid of variational methods of the theory of optimal control. Particular cases of maximization of the load carrying capacity of spherical caps and conical shells are studied in a greater detail in the cases of von Mises and Hill’s materials.

Keywords: Optimization, optimal control, inelastic material, crack, conical shell, spherical shell, cylindrical shell

Title of the Paper: Generalized Concentration/Inequality Indices of Economic Systems Evolving in Time


Authors: Guglielmo D'Amico, Giuseppe Di Biase

Abstract: In this paper time evolving indices are defined and studied through the introduction of a population structure chancing during the time. These indices are useful to describe the concentration (or inequality) of the wealth in a stochastic model of the wealth evolution. Here some static indices usually used in literature are generalized. In particular the paper shows how it is possible to generalize the Herfindahl-Hirschman and Gini indices and the Theil’s entropy. These indices become stochastic processes of which the moments and the asymptotic behavior is provided. A computation of such indices and their asymptotic behavior in different economical scenarios concludes the paper.

Keywords: Population dynamic, Herfindahl-Hirschman index, Gini index, Theil’s entropy, Rewards

Issue 3, Volume 9, March 2010

Title of the Paper: When are the Value Iteration Maximizers Close to an Optimal Stationary Policy of a Discounted Markov Decision Process? Closing the Gap between the Borel Space Theory and Actual Computations


Authors: Raul Montes-De-Oca, Enrique Lemus-Rodriguez

Abstract: Markov Decision Processes [MDPs] have been repeteadly used in Economy and Engineering but apparently are still far from achieving its full potential due to the computational difficulties inherent to the subject due to the usual impossibility of finding explicit optimal solutions. Value iteration is an elegant, theoretical method of approximating an optimal solution, frequently mentioned in Economy when MDPs are used. To extend its use and benefits, improved understanding of its convergence is needed still even if it would appear not to be the case. For instance, the corresponding convergence properties of the policies is still not well understood. In this paper we further analyze this issue: using Value Iteration, if a stationary policy fN is obtained in th N-th iteration, such that the optimal discounted rewards of f and fN are close, we would like to know whether are the corresponding actions f (x) and fN(x) necessarily close for each state x? To our knowledge this question is still largely open. In this paper it is studied when it is possible to stop the value iteration algorithm so that the corresponding maximizer stationary policy fN approximates an optimal policy both in the total discounted reward and in the action space (uniformly over the state space). In this article the action space is assumed to be a compact set and the reward function bounded. An ergodicity condition on the transition probability law and a structural condition on the reward function are needed. Under these conditions, an upper bound on the number of steps needed in the value iteration algorithm, such that its corresponding maximizer is a uniform approximation of the optimal policy, is obtained.

Keywords: Markov decision process, compact action space, bounded reward, expected total discounted reward, approximation of optimal policies by means of value iteration policies

Title of the Paper: Numerical Solutions for a Class of Nonlinear Systems and Application to Stochastic Resonance


Authors: Romeo Negrea, Andrei Eckstein, Florin Alexa

Abstract: We study a nonlinear system under regime switching and subject to an environmental noise. The stochastic differential equations with Markovian switching (SDEwMSs), one of the important classes of hybrid systems, have been used to model many physical systems that are subject to frequent unpredictable structural changes. The research in this area has been both theoretical and applied. Most of SDEwMSs do not have explicit solutions so it is important to have numerical solutions. It is surprising that there are not any numerical methods established for SDEwMSs yet, although the numerical methods for stochastic differential equations (SDEs) have been well studied. We will considered some more general conditions for the coefficient functions and prove a result on the existence using the Schauder’s fixed point theorem extended some similarly results on linear systems. The most important results in this paper is to develop a numerical scheme for SDEwMSs and estimate the error between the numerical and exact solutions. Also, we study the application of these system to control the electronic circuits using the benefit of stochastic resonance

Keywords: Stochastic differential equation with Markovian switching, pathwise uniqueness, fixed point technique, numerical solution, Euler-Maruyama method, stopping times, stochastic resonance

Title of the Paper: Traveling Wave Solutions for the Fifth-Order Sawada-Kotera Equation and the General Gardner Equation by (G'/G)-Expansion Method


Authors: Qinghua Feng, Bin Zheng

Abstract: In this paper, a generalized (G'/G)-expansion method is used to seek more general exact solutions of the fifth-order Sawada-Kotera equation and the general Gardner equation. As a result, the traveling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. The method appears to be easier and faster by means of some mathematical software.

Keywords: (G'/G)-expansion method, Traveling wave solutions, fifth-order Sawada-Kotera equation, general Gardner equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: Traveling Wave Solution for the BBM Equation with any Order by (G'/G)-Expansion Method


Authors: Qinghua Feng, Bin Zheng

Abstract: In this paper, we will try to construct the travelling wave solutions of the BBM equation with any order by using a generalized (G'/G)-expansion method. The BBM equation is reduced to a nonlinear ordinary differential equations (ODE) by using a simple transformation. As a result, the traveling wave solutions of the BBM equation are expressed in three forms: hyperbolic function solutions, trigonometric function solutions and rational solutions.

Keywords: (G'/G)-expansion method, Traveling wave solutions, BBM equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: Traveling Wave Solutions for the Variant Boussinseq Equation and the (2+1)-Dimensional Nizhnik-Novikov-Veselov (NNV) System By (G'/G)-Expansion Method


Authors: Qinghua Feng, Bin Zheng

Abstract: In this paper, using the generalized (G'/G)-expansion method, new explicit travelling wave solutions for the variant Boussinseq equation and the (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) system are obtained with the aid of Mathematica.

Keywords: (G'/G)-expansion method, Traveling wave solutions, (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) system, variant Boussinseq equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: Traveling Wave Solutions for the Fifth-Order Kdv Equation and the BBM Equation by (G'/G)-Expansion Method


Authors: Qinghua Feng, Bin Zheng

Abstract: In this paper, we demonstrate the effectiveness of the (G'/G)-expansion method by seeking more exact solutions of the fifth-order Kdv equation and the BBM equation. By the method, the two nonlinear evolution equations are separately reduced to non-linear ordinary differential equations (ODE) by using a simple transformation. As a result, the traveling wave solutions are obtained in three arbitrary functions including hyperbolic function solutions, trigonometric function solutions and rational solutions. When the parameters are taken as special values, we also obtain the soliton solutions of the fifth-order Kdv equation. The method appears to be easier and faster by means of a symbolic computation system.

Keywords: (G'/G)-expansion method, Traveling wave solutions, BBM equation, fifth-order Kdv equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: Iterative Strategies for Obstacle Avoidance of a Redundant Manipulator


Authors: Cornel Secara, Luigi Vladareanu

Abstract: This paper presents four different iterative strategies for obstacle avoidance of a redundant manipulator. The end-effector task consists in generating the references along the contour of a curve. The proposed strategies are iterative in the sense that the joint configuration computed in the previous step represents the current point around which the methods provide the next joint configuration corresponding to the imposed end-effector posture. The objective of the strategies is to simultaneously minimize the endeffector location error and the manipulator total joint displacement while the collision with the obstacle is avoided. The strategies are implemented using the Matlab software and the comparative simulation results are obtained for a planar redundant manipulator with four degrees of freedom and with its end-effector following the contour of a circle, whose surface is considered to be restrictive for all elements of the manipulator.

Keywords: Redundancy resolution, iterative strategy, obstacle avoidance, multiple criteria

Issue 4, Volume 9, April 2010

Title of the Paper: Producer's Replenishment Policy for an EPQ Model with Rework and Machine Failure Taking Place in Backorder Reloading Time


Authors: Kuang-Ku Chen, Yuan-Shyi Peter Chiu, Chia-Kuan Ting

Abstract: This paper studies the optimal producer?s replenishment policy for an economic production quantity (EPQ) model with rework and breakdown taking place in backorder replenishing time. A recent published article has studied the lot-sizing problem on an imperfect quality EPQ model. However, another reliability factor - random machine breakdown is inevitable in most real-life production systems. To deal with stochastic machine failures, production planners must practically calculate the mean time between failures (MTBF) and establish the robust plan accordingly, in terms of the optimal production run time that minimizes total production-inventory costs for such an unreliable system. This study extends Chiu’s work and assumes that a machine failure takes place in the backorder replenishing stage. Mathematical modeling and cost analysis are employed. The renewal reward theorem is used to cope with variable cycle length. Convexity of the long-run average cost function is proved and an optimal manufacturing lot-size that minimizes the expected overall costs for such an imperfect system is derived. Numerical example is provided to demonstrate its practical usages.

Keywords: Optimization, Lot size, Breakdown, Backorder, Production run time, Rework, Inventory

Title of the Paper: Applying the New Primer on Prime Numbers


Authors: Ernest G. Hibbs

Abstract: We have a new model for understanding the behavior of prime numbers that considers the increments as sums of second derivatives. We use the perfectly alternating double-threaded helix prime number growth structure that dominated the first 500 prime numbers after a modulo 6 operation. The multiples of 6 influence the two threads in a 3-D manner. Electromagnetic reversal patterns between the threads and the thread bonds indicate a coordinated 3-D multi-physics growth rate of the prime numbers. The harmonic patterns of a newly mapped 10-step model are also introduced. This new concept is presented as a framework to help apply approaches to understanding and solving our hardest multi-physics and Millennium problems. The last sections of this paper suggest how to apply, adapt, or correlate this framework to with WSEAS research. An exciting electromagnetic multidirectional vector model is the result of applying this framework by forcing a 90-degree molecular bond concept.

Keywords: Prime Numbers, Double Helix, Riemann Hypothesis, Second Derivative, Millennium Problems

Title of the Paper: On the Eigenstructures of Functional K-Potent Matrices and their Integral Forms


Authors: Yan Wu, Daniel F. Linder

Abstract: In this paper, a functional k-potent matrix satisfies the equation, where k and r are positive integers, and are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.

Keywords: Nilpotent, Idempotent, Involutary, Unipotent, Skewed k-potent Matrix, Diagonalizability, Image Encryption

Title of the Paper: Exact Solutions through Symmetry Reductions for a New Integrable Equation


Authors: Maria Luz Gandarias, Maria Santos Bruzon

Abstract: In this work we study a new completely integrable equation from the point of view of the theory of symmetry reductions in partial differential equations. This equation has been proposed by Qiao and Liu in [24] and it possesses peak solitons. We obtain the classical symmetries and the classical symmetries of the associated potential system admitted, then, we use the transformations groups to reduce the equations to ordinary differential equations. Physical interpretation of these reductions and some exact solutions are also provided. Among them we obtain a travelling wave with decaying velocity and an smooth soliton solution.

Keywords: Symmetries, partial differential equation, exact solutions

Title of the Paper: Major Issues in Designing an Undergraduate Program in Nanotechnology: The Mexican Case


Authors: Armando Barranon, Antonio Juanico

Abstract: Major Issues for developing an Undergraduate Program in Nanotechnology are hereby described. Nanotechnology Courses are designed so that students may apply the Nanosciences, Biotechnology and Information Sciences convergence model to develop new materials and applications Nanotechnology. Infrastructure and Human Resources turn out to be crucial for establishing a successful Nanotechnology Undergraduate Program. Several Mexican National Nanotechnology Labs will be cooperating for student internships and students may continue doing postgraduate studies at those centers of research. Societal and Environmental impacts of Nanotechnology are also addressed in the Undergraduate Program in Nanotechnology proposed in this article. Women participation is expected, considering recent statistics of women participation in undergraduate engineering programs related to Nanotechnology. Mexican government has been funding to the federal and state level the university where this program will be launched, as part of a national effort to provide universities all along the Mexican territory.

Keywords: Undergraduate Program in Nanotechnology, PROMEP scholarships, PRONABES scholarships, NBI model, Nanotechnology faculty, Mexico

Title of the Paper: Classical Potential Symmetries of the K(m, n) Equation with Generalized Evolution Term


Authors: Maria S. Bruzon, Maria L. Gandarias

Abstract: We consider a K(m, n) equation with generalized evolution term which is of considerable interest in mathematical physics. We classify the nonlocal symmetries, which are known as potential symmetries, for this equation. It turns out that potential symmetries exist only if the parameters n, m and l satisfy certain relationship.

Keywords: Potential symmetries, Partial differential equation, Exact Solutions

Issue 5, Volume 9, May 2010

Title of the Paper: The Numerical Solution of Obstacle Problem by Self Adaptive Finite Element Method


Authors: Lian Xue, Minghui Wu

Abstract: In this paper, the bisection of the local mesh refinement in self adaptive finite element is applied to the obstacle problem of elliptic variational inequalities .We try to find the approximated region of the contact in the obstacle problem efficiently .Numerical examples are given for the obstacle problem.

Keywords: Obstacle problem, variational inequalities, self adaptive finite element, bisection, triangulation refinement

Title of the Paper: Multidimensional Unreplicated Linear Functional Relationship Model with Single Slope and Its Coefficient of Determination


Authors: Chang Yun Fah, Omar Mohd Rijal, Syed Abdul Rahman Abu Bakar

Abstract: Multidimensional unreplicated linear functional relationship model (MULFR) with single slope is considered where p-dimensional measurement errors are introduced. When the ratio of error variances is known, the parameters’ estimation can be considered as a generalization of the unreplicated linear functional relationship model. However, investigation on unbiased property of the estimators are not strict-forward. Taylor approximation is applied to show the intercept and slope estimators are approximately unbiased. The consistency property is discussed using Fisher Information Matrix. The coefficient of determination for MULFR model and its properties are also studied. A simulation study is carried out to evaluate the proposed estimators of the intercept and slope, and the coefficient of determination. This coefficient of determination provides a useful analysis tool for many image processing applications. A numerical example for JPEG compressed image quality assessment is explained.

Keywords: Coefficient of determination; Image quality; JPEG compression; Measurement errors; Unreplicated linear functional relationship

Title of the Paper: Elastic-Plastic Analysis of a Thin Rotating Disk of Exponentially Variable Thickness with Inclusion


Authors: Sanjeev Sharama, Manoj Sahni, Ravindra Kumar

Abstract: Transition theory has been used to derive the elastic-plastic and transitional stresses. Results obtained have been discussed numerically and depicted graphically. It has been observed that for disc with exponentially varying thickness (k=2), high angular speed is required for initial yielding at internal surface as compared to the flat disc and exponentially varying thickness for k=4 onwards. Thus we can conclude that flat disc (C=0.75) is on the safer side of the design as it requires high percentage increase in angular speed to become fully plastic as compared to the flat disc with the compressible factors (C=0,0.25,etc.).

Keywords: Elastic, plastic, compressibility, transitional stresses, isotropic, rotating disk

Title of the Paper: Running Damage Extraction Technique for Identifying Fatigue Damaging Events


Authors: Z. M. Nopiah, M. N. Baharin, S. Abdullah, M. I. Khairir, A. Ariffin

Abstract: This paper presents the development of a new fatigue data editing technique, called Running Damage Extraction (RDE), for summarising long records of fatigue data. This technique is used to extract fatigue damaging events in the record that cause the majority of fatigue damage, whilst preserving the load cycle sequence. In this study, fatigue damaging events are identified from the characteristic of abrupt changes that exist in the fatigue data. Then, these events are combined to produce a mission signal which has equivalent statistics and fatigue damage to the original signal. The objective of this study is to observe the capability of RDE technique for summarising long records of fatigue data. For the purpose of this study, a collection of nonstationary data that exhibits random behavior was used. This random data was measured in the unit of microstrain on the lower suspension arm of a car. Experimentally, the data was collected for 60 seconds at a sampling rate of 500 Hz, which gave 30,000 discrete data points. Global signal statistical value indicated that the data were non Gaussian distribution in nature. The result of the study indicates that this technique is applicable in detecting and extracts fatigue damaging events that exist in fatigue data.

Keywords: Abrupt changes, fatigue data, global statistics, nonstationary data, RDE technique

Title of the Paper: Time Complexity Estimation and Optimisation of the Genetic Algorithm Clustering Method


Authors: Z. M. Nopiah, M. I. Khairir, S. Abdullah, M. N. Baharin, A. Arifin

Abstract: This paper presents the time complexity estimation and optimisation of the genetic algorithm clustering method. The tested feature in the clustering algorithm is the population limit function. For the purpose of the study, segmental kurtosis analysis was done on several segmented fatigue time series data, which are then represented in two-dimensional heteroscaled datasets. These datasets are then clustered using the genetic algorithm clustering method and the runtime of the algorithm is measured against the number of iterations. Polynomial fitting is used on the runtime data to determine the time complexity of the algorithm. Analysis is repeated with the inclusion of the population limit in the clustering algorithm. The results of the analysis will be used to determine the significance of including the population limit function in the algorithm for optimal performance.

Keywords: Genetic algorithms, fatigue damage, clustering, time complexity, big-O notation, algorithm efficiency

Title of the Paper: The Morlet Wavelet Analysis for Fatigue Feature Clustering


Authors: S. Abdullah, T. E. Putra, M. Z. Nuawi, Z. M. Nopiah, A. Arifin, L. Abdullah

Abstract: This paper presents clustering of fatigue features resulted from the segmentation of SAESUS time series data. The segmentation process was based on the Morlet wavelet coefficient amplitude level which produced 49 segments that each has overall fatigue damage. Observation of the fatigue damage and the wavelet coefficients was made on each segment. At the end of the process, the segments were clustered into three in order to identify any improvements in the data scattering for fatigue data clustering prospects. This algorithm produced a more reliable and suitable method of segment by segment analysis for fatigue strain signal segmentation. According to the findings, the higher Morlet wavelet coefficient presented damaging segment, otherwise, it was non-damaging segment. This indicated that the relationship between the Morlet wavelet coefficient and the fatigue damage was strong and parallel.

Keywords: Fatigue strain signal, segmentation, fatigue damage, Morlet wavelet coefficient, clustering

Title of the Paper: Towards a Mathematical Theory of Unconscious Adaptation and Emotions


Authors: Alin Gilbert Sumedrea

Abstract: The psychological adaptability is realized through the conscious and the unconscious mechanisms. Even though the functionality of the mechanisms involved emphasizes different approaches, the main reason for these - approaches - is the obtaining of the maximum adaptability which has to protect the person at the conscious level. The invisible unconscious mechanisms have a major role in the process of psychological adaptation. The unconscious contribution does not eliminate completely the danger of psychological collapse, and this accredits the idea of the existence of a psychological guarantee only for proper inquirer stimuli. The incapacity of the consciousness filters to mediate the transactions of unconscious offers changes the adaptability process in an approach which is not entirely controllable. The uncontrollable part validates the approach of the imposing of own unconscious offers in the environment. The emotion analyzed at the conscious level translates the uncertainty of the validation of the transactions of unconscious offers with the environment as tensional state. The mathematical approach of this paper describes the need for psychological stimulation as a facet of adaptability and the emotional mechanisms as devices of the preserving of tensional states.

Keywords: Coordinate systems, Dynamics, Emotion, Group theory, Mechanism, Symmetry group, Unconscious adaptability

Title of the Paper: MHD Viscous Flow and Heat Transfer Induced by a Permeable Shrinking Sheet with Prescribed Surface Heat Flux


Authors: Fadzilah Md Ali, Roslinda Nazar, Norihan Md Arifin

Abstract: The problem of magnetohydrodynamic (MHD) boundary layer flow and heat transfer due to a permeable shrinking sheet with prescribed surface heat flux is studied. The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected. The transformed nonlinear ordinary differential equations are solved numerically via the implicit finite-difference scheme known as the Keller-box method. Both two-dimensional and axisymmetric cases are considered. The results for the skin friction coefficient and the wall temperature, as well as the velocity and temperature profiles are presented and discussed for various parameters. Dual solutions exist for certain range of the suction parameter and Hartmann number. It is found that the boundary layer separation is delayed with Hartmann number.

Keywords: Boundary layer, Heat transfer, Magnetohydrodynamic, Shrinking sheet, Suction, Surface heat flux

Title of the Paper: Thermal and Solutal Marangoni Mixed Convection Boundary Layer Flow


Authors: Norihan Md. Arifin, Fadzilah Md. Ali, Roslinda Nazar, Ioan Pop

Abstract: An analysis is performed for mixed convection thermal and solute concentration Marangoni boundary layer that can be formed along the surface, which separates two immiscible fluids in surface tension flows. Similarity equations for the case in which an external pressure gradient is imposed are derived. The dimensionless governing equations of the flow field are solved numerically using the shooting method. The effect of flow parameters on the velocity, temperature and concentration are computed and presented in tables and figures.

Keywords: Marangoni flow, Thermosolutal, Mixed convection, Boundary layer

Title of the Paper: Modeling Put-Option Margin and Default Risk when Labor has a Voice in Bank Governance Mechanism


Authors: Chuen-Ping Chang, Jyh-Jiuan Lin, Jeng-Yan Tsai

Abstract: Although considerable research effort has been put toward modeling governance mechanisms for the purpose of valuing investment decisions written on them, little attention has been paid to the effects of governance mechanisms by labor voice on bank operations management. Like entrenched operations management, entrenched labor cannot be gotten rid of easily. This paper demonstrates how labor voice determines the optimal bank interest margin and default risk decisions. Our model is based on a regime giving corporate governance power to current labor and then labor’s objective is equivalent to minimizing the equity value of the put option. We show that the governance voice pushes bank interest margin determination toward shareholder value maximization. However, an opportunity cost of bank governance from listening labor voice is increasing the bank’s default risk in equity returns.

Keywords: Bank Interest Margin, Default Risk, Labor Voice, Put Option

Issue 6, Volume 9, June 2010

Title of the Paper: Estimating Bias and RMSE of Indirect Effects using Escaled Residual Bootstrap in Mediation Analysis


Authors: Anwar Fitrianto, Habshah Midi

Abstract: It is a common practice to estimate the parameters of mediation model by using the Ordinary Least Squares (OLS) method. The construction of T statistics and confidence interval estimates for making inferences on the parameters of a mediation model, particularly the indirect effect, is usually are based on the assumption that the estimates are normally distributed. Nonetheless, in practice many estimates are not normal and have a heavy tailed distribution which may be the results of having outliers in the data. An alternative approach is to use bootstrap method which does not rely on the normality assumption. In this paper, we proposed a new bootstrap procedure of indirect effect in mediation model which is resistant to outliers. The proposed approach was based on residual bootstrap which incorporated rescaled studentized residuals, namely the Rescaled Studentized Residual Bootstrap using Least Squares (ReSRB). The Monte Carlo simulations showed that the ReSRB is more efficient than some existing methods in the presence of outliers.

Keywords: Mediation analysis, outliers, bootstrap, studentized residuals, indirect effect

Title of the Paper: Duality, Barycentric Coordinates and Intersection Computation in Projective Space with GPU support


Authors: Vaclav Skala

Abstract: This paper presents solution of selected problems using principle of duality and projective space representation. It will be shown that alternative formulation in the projective space offers quite surprisingly simple solutions that lead to more robust and faster algorithms which are convenient for use within parallel architectures as GPU (Graphical Processor Units-NVIDIA-TESLA/Fermi) or SCC (Intel-Single-chip Cloud Computing), which can speed up solutions of numerical problems in magnitude of 10-100. There are many geometric algorithms based on computation of intersection of lines, planes etc. Sometimes, very complex mathematical notations are used to express simple mathematical solutions, even if their formulation in the projective space offers much more simple solution. It is shown that a solution of a system of linear equations is equivalent to generalized cross product, which leads with the duality principle to new algorithms. This is presented on a new formulation of a line in 3D given as intersection of two planes which is robust and fast, based on duality of Plucker coordinates. The presented approach can be used also for reformulation of barycentric coordinates computations on parallel architectures. The presented approach for intersection computation is well suited especially for applications where robustness is required, e.g. large GIS/CAD/CAM systems etc.

Keywords: Computer graphics, homogeneous coordinates, Plucker coordinates, principle of duality, line and plane intersections computation, projective geometry, barycentric coordinates.

Title of the Paper: Lattice Boltzmann Numerical Scheme for the Simulation of Natural Convection in an Inclined Square Cavity


Authors: C. S. Nor Azwadi, N. I. Nik Izual

Abstract: In this paper, a mesoscale numerical method was applied to solve two dimensional, incompressible, thermal fluid flow problem. This study presents numerical prediction of natural convection heat transfer inside an inclined square cavity with perfectly conducting boundary conditions for the top and bottom walls. The lattice Boltzmann scheme with uniform mesh resolution was applied as a numerical research tool. The inclination angels were varied from 20° to 160° with 20° intervals. The results were presented in terms of streamlines and isotherms plots, and average Nusselt number in the system. We found that the flow structure together with the heat transfer mechanism are significantly dependence on the magnitude of the inclination angles. Good agreements were obtained when compared with the results published by other researchers in previous studies.

Keywords: Double population, lattice Boltzmann, distribution function, BGK collision, natural convection

Title of the Paper: Estimations and Predictions using Record Statistics from the Modified Weibull Model


Authors: Vasile Preda, Eugenia Panaitescu, Alina Constantinescu, Supian Sudradjat

Abstract: This paper develops Bayesian and non-Bayesian analysis in the context of record statistics values from the modified Weibull distribution. We obtained non-Bayes estimators using MLE and Bayes estimators using the general entropy loss functions. This was done with respect to the conjugate prior for the shape parameter. Finally, Bayesian predictive density function, which is necessary to obtain bounds for predictive interval of future record, is derived. The results may be of interest in a situation where only record values are stored.

Keywords: Bayesian and non-Bayesian estimation, Bayesian prediction, Entropy loss function, Modified Weibull distribution, Record values, Record statistics

Title of the Paper: Binary Response Modeling and Validation of its Predictive Ability


Authors: Habshah Midi, Sohel Rana, S. K. Sarkar

Abstract: Assessment of the quality of the logistic regression model is central to the conclusion. Application of logistic regression modeling techniques without subsequent performance analysis regarding predictive ability of the fitted model can result in poorly fitting results that inaccurately predict outcomes on new subjects. It is not unusual for statisticians to check fitted model with validation. Validation of predictions from logistic regression models is of paramount importance. Model validation is possibly the most important step in the model building sequence. Model validity refers to the stability and reasonableness of the logistic regression coefficients, the plausibility and usability of the fitted logistic regression function, and the ability to generalize inferences drawn from the analysis. The aim of this study is to evaluate and measure how effectively the fitted logistic regression model describes the outcome variable both in the sample and in the population. A straightforward and fairly popular split-sample approach has been used here to validate the model. The present study have dealt with how to measure the quality of the fit of a given model and how to evaluate its performance regarding the predictive ability in order to avoid poorly fitted model. Different summary measures of goodness-of-fit and other supplementary indices of predictive ability of the fitted model indicate that the fitted binary logistic regression model can be used to predict the new subjects.

Keywords: Validation, training sample, deviance, prediction error rate, ROC curve

Title of the Paper: Application of the (G'/G)-Expansion Method for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota Equation


Authors: Bin Zheng

Abstract: In this paper, a generalized (G'/G)-expansion method is used to seek more general exact solutions of the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation. As a result, the traveling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. The method appears to be easier and faster by means of some mathematical software.

Keywords: (G'/G)-expansion method, Traveling wave solutions, integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation, nonlinear heat conduction equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: Exact Solutions for Two Non-linear Equations


Authors: Bin Zheng

Abstract: In this paper, we test the validity and reliability of the (G'/G)-expansion method by applying it to get the exact traveling wave solutions of the (2+1) dimensional Boussinesq and Kadomtsev-Petviashvili equation and the nonlinear heat conduction equation. The traveling wave solutions are obtained in three forms. Being concise and less restrictive, the method can also be applied to many other nonlinear partial differential equations.

Keywords: (G'/G)-expansion method, Traveling wave solutions, (2+1) dimensional Boussinesq and Kadomtsev-Petviashvili equation, nonlinear heat conduction equation, exact solution, evolution equation, nonlinear equation

Title of the Paper: New Exact Traveling Wave Solutions for Some Non-linear Evolution Equations by (G'/G)-Expansion Method


Authors: Bin Zheng

Abstract: In this paper, we study the application of the known generalized (G'/G)-expansion method for seeking more exact traveling solutions solutions and soliton solutions of the ZK-MEW equation and the (2+1) dimensional Boiti-Leon-Pempinelli equation. As a result, we come to the conclusion that the traveling wave solutions for the two non-linear equations are obtained in three arbitrary functions including hyperbolic function solutions,trigonometric function solutions and rational solutions. The method appears to be easier and faster by means of some mathematical software.

Keywords: (G'/G)-expansion method,Traveling wave solutions,ZK-MEW equation, (2+1) dimensional Boiti-Leon-Pempinelli equation,exact solution, evolution equation, nonlinear equation

Title of the Paper: A Note for Plane Laplace's Exterior Boundary Value Problems


Authors: Yaoming Zhang, Wenzhen Qu, Bin Zheng

Abstract: The solution of conventional boundary integral equations (CBIEs) sometimes does not exist or is not unique, which has been demonstrated in a large number of numerical experiments. According to the authors’ opinion, there exist two reasons which can lead to this phenomenon. One reason is that the solution of the CBIEs can not describe the behavior of the solution of the corresponding boundary value problem at infinity accurately; the other one is that the form of exterior boundary value problem has deficiency, which is still a problem to be solved but has not attracted adequate attention. In this paper, a sufficient and necessary condition with respect to the Dirichlet exterior boundary value problem, which can ensure the existence and uniqueness of the solution, is provided and fully proved. Based on the proposed condition, equivalent boundary integral equations (EBIEs) for exterior problems are established. In addition, an extremum principle on the exterior domain is introduced in this paper.

Keywords: Laplace equation, exterior boundary value problem, BEM, Equivalent boundary integral equations, Extremum principle , Numerical method

Title of the Paper: Equivalent Boundary Integral Equations for Plane Poisson's Exterior Boundary Value Problems


Authors: Yaoming Zhang, Wenzhen Qu, Bin Zheng

Abstract: The solution of conventional boundary integral equations (CBIEs) sometimes does not exist or is not unique, which has been demonstrated in a large number of numerical experiments. According to the authors’ opinion, there exist two reasons which can lead to this phenomenon. One reason is that the solution of the CBIEs can not describe the behavior of the solution of the corresponding boundary value problem at infinity accurately; the other one is that the form of exterior boundary value problem has deficiency, which is still a problem to be olved but has not attracted adequate attention. Many examples illustrate that CBIEs are not equivalent to the Poisson’s exterior boundary value problem. In this paper, the equivalent boundary integral equations (EBIEs) for Poisson’s exterior boundary value problems are established.

Keywords: Poisson equation, exterior boundary value problem, BEM, EBIEs, Equivalent boundary integral equations, Extremum principle

Issue 7, Volume 9, July 2010

Title of the Paper: Robust Individuals Control Chart for Change Point Model


Authors: Ng Kooi Huat, Habshah Midi

Abstract: Control charts are used to monitor for changes in a process by distinguishing between common and special causes of variability. When a control chart signals, process engineers must initiate a search for the special cause of the process disturbance. Identifying which combination of the many process variables is responsible for a change in the process allows engineers to improve quality by preventing or avoiding changes in those variables which lead to poor quality. We examine a process-monitoring tool that not only provides speedy detection regardless of the magnitude of the process shift, but also provides useful change point statistics. Robustness against assignable causes of variation appears to be important and a likelihood ratio method is used to develop test statistics for step change shifts. The performance of the proposed methodology is demonstrated with numerical example and simulation studies.

Keywords: Change Point Estimation, Statistical Process Control, In-Control, Out-of-Control, Outlier, Maximum-Type

Title of the Paper: Wavelets Modelling of Water, Energy and Electricity Consumption in Spain


Authors: C. Gonzalez-Concepcion, M. C. Gil-Farina, C. Pestano-Gabino

Abstract: Wavelet techniques possess many desirable properties, some of which are useful in economics and finance, but many of which are not. In this paper we use wavelets to reveal the different cycles that are hidden by the data. So, we consider some of the advantages and drawbacks of this time series multiresolution analysis technique for the purpose of obtaining simultaneous time and frequency information in determining the periodicity and the modelling of the water consumption in Santa Cruz de Tenerife (Canary Islands, Spain), energy and electricity consumption in Spain.

Keywords: Wavelets, Time series, Scale domain, Water, energy and electricity consumption

Title of the Paper: Optimal Conditions for the Control Problem Associated to an Economic Growth Process Exposed to a Risk Factor


Authors: Olivia Bundau, Adina Juratoni

Abstract: The aim of this paper is to extend the study done by [6]. Here two different research lines have been joined together: the one studying an endogenous economical growth model in the case of which the occurrence of a disaster is possible, and the one analyzing the same model but with logistic population growth and the Cobb- Douglas production function. First economical growth model leads to an optimal control problem with an infinite horizon. For this problem we will prove that the solution of the optimal control problem verifies Euler-Lagrange’s equation. Using these necessary conditions we will determine the consumption evolution equation. Also, we will prove a necessary optimality condition in terms of value function. In the second model we will analyze an economic growth process with logistic population growth and the Cobb-Douglas production function. The model is a version of the Ramsey model in the case of which the occurrence of a disaster is possible. Mathematical modeling of this economical growth process leads to an optimal control problem with an infinite horizon. The necessary conditions for optimality are given.

Keywords: Mathematical models applied in economies, endogenous growth, natural disaster,logistic population

Title of the Paper: Study on Feature Extraction and Classification of Ultrasonic Flaw Signals


Authors: Yanhua Zhang, Lu Yang, Jianping Fan

Abstract: One of the most important techniques of ultrasonic flaw classification is feature extraction of flaw signals,which directly affects the accuracy and reliability of flaw classification.Based on the non-stationary characteristic of ultrasonic flaw signals, a new feature extraction method of ultrasonic signals based on empirical mode decomposition (EMD) is put forward in the paper. Firstly, the original ultrasonic flaw signals are decomposed into a finite number of stationary intrinsic mode functions (IMFs) by EMD, and the Fourier transformation of IMF is made. The next step is to find a set of classification values from time domain and frequency domain of IMFs relating to flaw information, and to analyze these classification values and construct vector as signal eigenvector for identification. According to specific characteristics of ultrasonic echo signal, identification defect diagnosis system for ultrasonic echo signal based on BP is built up, and the specific structure of BP neural network is designed. Finally BP neural network is made as decision-making classifier, signal eigenvector is inputted and flaw type is outputted. Experimental results show that the method has better performance in detecting ultrasonic flaw signals.

Keywords: Ultrasonic signal; empirical mode decomposition (EMD); intrinsic mode function; feature extraction; neural network; eigenvector

Title of the Paper: Bayes Estimators of Modified-Weibull Distribution Parameters using Lindley's Approximation


Authors: Vasile Preda, Eugenia Panaitescu, Alina Constantinescu

Abstract: For Modified-Weibull distribution we have obtained the Bayes Estimators of scale and shape parameters using Lindley's approximation (L-approximation) under various loss functions. The proposed estimators have been compared with the corresponding MLE for their risks based on corresponding simulated samples.

Keywords: Bayesian estimation, Lindley's approximation, Maximum likelihood estimates, Modified Weibull distribution, Monte Carlo simulation

Title of the Paper: Diagonally Implicit Runge-Kutta Nystrom General Method Order Five for Solving Second Order IVPs


Authors: Fudziah Ismail

Abstract: A diagonally implicit Runge-Kutta-Nystrom General (SDIRKNG) method of fifth order with an explicit first stage for the integration of second-order IVPs is presented. A standard set of test problems are tested upon and the numerical results are compared when the same set of test problems are reduced to first-order system and solved using existing fifth order singly diagonally implicit Runge-Kutta method. The time taken to solve each problem over all the stepsizes are also compared. The results suggest the superiority of the new method.

Keywords: Diagonally implicit, Runge-Kutta-Nystrom, Second-order IVPs

Title of the Paper: Diffusion and Semi-Convexity of Fuzzy Set Multifunctions


Authors: Alina Gavrilut, Anca Croitoru, Nikos E. Mastorakis

Abstract: We present some properties regarding diffusion and semi-convexity for fuzzy set multifunctions defined on a ring of subsets of an abstract nonvoid space and taking values in the family of all nonvoid closed subsets of a real normed space.

Keywords: Diffused, semi-convex, fuzzy set multifunction, non-atomicity, Darboux property, regular, multimeasure, null-additive

Title of the Paper: Stochastic, Fuzzy and Hybrid Monetary Models with Delay


Authors: G. Mircea, M. Pirtea, M. Neamtu, D. Opris

Abstract: This paper addresses an autonomous stochastic system with delay and associated fuzzy and hybrid models, which describe a monetary system involving interest rate, investment demand and price index. We analyze the deterministic model and the stochastic model with perturbation. For the stochastic system with delay we identify the differential equations for the mean values as well as for the mean square value. The last part of the paper includes numerical simulations and conclusions.

Keywords: Monetary system, deterministic model with delay, stochastic delay system, fuzzy, hybrid system

Title of the Paper: Stochastic, Fuzzy, Hybrid Delayed Dynamics Heterogeneous Competitions with Product Differentiation


Authors: Mihaela Neamtu, Marilen Pirtea, Gabriela Mircea, Dumitru Opris

Abstract: In this paper, we study the heterogeneous duopoly with product differentiation, in which one firm is quantity setter and the other is price setter. The deterministic and stochastic models with delay are presented and fuzzy and hybrid models, as well. For the stochastic disturbance model with delay, sufficient conditions are done so that the steady state is asymptotically stable in mean and in mean square. Using programs in Maple 13 we make some numerical simulations that verify the theoretical results.

Keywords: Delay dynamics, stochastic differential equations, heterogeneous duopoly competition, product differentiation, fuzzy model, hybrid model, fixed time delay

Issue 8, Volume 9, August 2010

Title of the Paper: Effect of Rotation and Magnetic Field on Thermal Instability of a Viscoelastic Fluid Permeated with Suspended Particles


Authors: A. K. Aggarwal, Anushri Verma

Abstract: The effect of rotation and magnetic field on the thermal instability of Walters’ (model ) viscoelastic fluid permeated with suspended particles is considered. For stationary convection, Walters’ viscoelastic fluid behaves like a Newtonian fluid. It is found that, for the case of stationary convection, the rotation and magnetic field have stabilizing effect whereas the suspended particles has destabilizing effect on the system. The principle of exchange of stabilities is satisfied in the absence of magnetic field. The magnetic field, viscoelasticity and rotation introduce oscillatory modes in the systems which were non-existent in their absence.

Keywords: Rotation, magnetic field, thermal instability, viscoelasticity, suspended particles

Title of the Paper: The Haar Wavelets used how Expansion Function in the Method of the Moments in the Solution of Some Electrostatic Problems


Authors: Aldo Artur Belardi, Jose Roberto Cardoso, Carlos A. Franca Sartori

Abstract: This work presents the methodology from the determination the charge superficial density and electrical fields, in three simple structures to a finite straight wire, square plane plates and the capacitance between to plane plate, all finite and submitted to a constant potential. That involves the method of the moments using as expansion function the Haar wavelets instead of the pulse function, in order to reach a good precision and reducing the computational execution time. We also intend to take advantages of the wavelets application through the Cholesky decomposition, talking about formation of scattered matrixes, and the detection of nulls values.

Keywords: Moments, Wavelets, Electrostatic

Title of the Paper: Deterministic and Stochastic Cournot Duopoly Games with Tax Evasion


Authors: Mihaela Neamtu

Abstract: In this paper the static model of the Cournot duopoly with tax evasion is analyzed. A study for the local stability of the stationary states is carried out in the case of the dynamic model with tax evasion and delay. Also, the stochastic approach is taken into consideration. Numerical simulations are performed for the above mentioned processes. Finally, conclusions regarding the economic processes are provided.

Keywords: Cournot competition, rent seeking games, stochastic differential equations, product differentiation, time delay, Hopf bifurcation, tax evasion

Title of the Paper: Using CPSO for the Engineering Optimization Problems


Authors: Ching-Long Su, Shutan Hsieh

Abstract: The aim of this study is to solve the optimization problems of different engineering designs by using nonlinear mixed integer programming mode. In the past, this type of engineering design optimization problem has been widely studied and discussed. They are usually solved through mathematical programming method or heuristics. However, there are more constraints and more constraints that cannot be satisfied. In solving this type of problems, we used a penalty guided cooperative particle swarm optimization to avoid the disadvantage of decreased efficiency from the increase of search spatial dimension and to raise the efficiency. In resolving some engineering design problems, the results shows that the solutions found by cooperative particle swarm optimization are equal or better than the best-known solutions from past literature. Thus, the results of this study indicate that cooperative particle swarm optimization is another effective method to find solutions to optimization problems.

Keywords: Engineering optimization, Nonlinear mixed integer programming, Cooperative particle swarm optimization

Title of the Paper: Deterministic, Uncertainty and Stochastic Models of Kaldor-Kalecki Model of Business Cycles


Authors: Gabriela Mircea, Mihaela Neamtu, Dumitru Opris

Abstract: This paper presents the Kaldor-Kalecki nonlinear business cycle model of the income. It will take into consideration the investment demand in the form suggested by Rodano. We will analyze the deterministic, uncertainty and stochastic Kaldor-Kalecki models. The dynamics of the mean values and the square mean values of the model’s variables are set. Numerical examples are given in the end, to illustrate our theoretical results.

Keywords: Business cycle model, deterministic model with delay, Kaldor-Kalecki model, uncertain system, stochastic system

Title of the Paper: The Analysis of Mathematical Models Associated to Some Economic Growth Processes with Endogenous Population


Authors: Olivia Bundau, Mihaela Neamtu

Abstract: The aim of this paper is to extend the study done by [5]. Here, we will analyze two mathematical models associated to some economic growth processes with endogenous population depending on the current fertility. The first model is a version of the Ramsey model in continuous and infinite time with the Cobb-Douglas production function. In the second model we consider the AK production function. The mathematical models of these economical growth processes lead to two optimal control problems with an infinite horizon. The necessary conditions for optimality are given for both economic problems. Using the optimality conditions we prove the existence, the uniqueness and the stability of the steady states.

Keywords: Mathematical models applied in economies, endogenous growth, endogenous population, optimization problems

Title of the Paper: Evaluation of Steady State Vector of Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 of an Incineration Process


Authors: Sumarni Abu Bakar, Tahir Ahmad, Sabariah Baharun

Abstract: Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theory. This paper employs Markov chain to the evaluation of steady state of an incineration process. Novel definition of transition probability matrix of FACS is presented. Steady state vector of Markov chain for incineration process is determined and graph of convergence of its norm difference is presented. This study led to some relation of Markov process and Perron-Frobenius Theorem.

Keywords: Fuzzy Autocatalytic Set, Fuzzy Graph, Incineration Process, Perron-Frobenius Theorem, Transition Probability Matrix, Markov process

Issue 9, Volume 9, September 2010

Title of the Paper: Transformation of Fuzzy State Space Model of a Boiler System: A Graph Theoretic Approach


Authors: Noor Ainy Harish, Razidah Ismail, Tahir Ahmad

Abstract: Graph theory has many real-world applications and is rich in theoretical results, especially for studying interconnection among elements in natural and man-made systems. In recent studies of complex control system, directed graph was introduced to define and interpret the interconnection structure underlying the dynamics of the interacting subsystems. Similarly, Fuzzy State Space Model (FSSM) was developed for solving inverse problem in multivariable control system. Thus, this paper aims to describe the transformation of FSSM of a Boiler system using a graph theoretic approach. The main subsystems of the Boiler system are furnace, superheater, drum, riser and reheater. These subsystems are transformed into vertices whereas the interconnections between subsystems are associated with edges of the graph. Here, the Autocatalytic Set (ACS) is a subgraph, whereby each of the nodes has at least one incoming link from a node belonging to the same subgraph. The concept of ACS is integrated to reveal some properties of the new graphical representation of FSSM such that irreducible graph, adjacency matrix and the relationship of an ACS to Perron Frobenius Eigenvector. These properties indicate initial findings that will lead to further exploration in Fuzzy Graphical representation.

Keywords: Combined Cycle Power Plant, State Space, Multi-connected System, Adjacency Matrix

Title of the Paper: A New Diagonally Implicit Runge-Kutta-Nystrom Method for Periodic IVPs


Authors: Norazak Senu, Mohamed Suleiman, Fudziah Ismail, Mohamed Othman

Abstract: A new diagonally implicit Runge-Kutta-Nystrom (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-order with dispersive order six and 'small' principal local truncation error terms and dissipation constant. The analysis of phase-lag, dissipation and stability of the method are also given. This new method is more efficient when compared with current methods of similar type for the numerical integration of second-order differential equations with periodic solutions, using constant step size.

Keywords: Runge-Kutta-Nystrom methods; Diagonally implicit; Phase-lag; Oscillatory solutions

Title of the Paper: Vibrations of Cylindrical Shells with Circumferential Cracks


Authors: Jaan Lellep, Larissa Roots

Abstract: An approximate method for the vibration analysis of stepped shells accounting for the influence of cracks located at re-entrant corners of steps is presented. Introducing the additional compliance function it is shown that the flexibility of the shell near cracks can be prescribed by means of the compliance of the structure. The latter is coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. Theoretical analysis is developed for circular cylindrical shells, provided the shell wall has an arbitrary number of steps and circular cracks of constant depth. Various combinations of end conditions are considered.

Keywords: Crack, cylinder, free vibration, elasticity, axisymmetric response, stepped shell

Title of the Paper: About Three Important Transformations Groups


Authors: Monica A. P. Purcaru, Mirela Tarnoveanu, Laura Ciupala

Abstract: In the present paper we introduce the concepts of conformal metrical d-structure and of conformal metrical N-linear connection with respect to the conformal metrical d-structure, corresponding to an 1-form on a generalized Hamilton space. We determine the set of all conformal metrical N-linear connections in the case when the nonlinear connection is arbitrary and we find important examples and particular cases. We find the transformations group of these connections. We study the role of the torsion d-tensor fields Tijk, Sijk and Sijk in this theory, especially in the determination of the set of all semisymmetric conformal metrical N-linear connections with respect to the conformal metrical d-structure, corresponding to the same nonlinear connection N. We give the transformations group of these connections and other two important groups and we find their remarkable invariants. Finally we determine the set of all metrical N-linear connections in the case when the nonlinear connection is arbitrary, we give important examples and particular cases and for the case when the nonlinear connection is fixed we find the transformations group of these connections.

Keywords: Second order cotangent bundle, nonlinear connection, N-linear connection, metrical d-structure, conformal metrical d-structure, conformal metrical N-linear connection, semisymmetric conformal metrical N-linear connection

Title of the Paper: Spectral Techniques for Solving PDE Stability Model of Vortex Rope


Authors: Diana Alina Bistrian

Abstract: In this paper spectral methods are applied to investigate the hydrodynamic instability of swirling flow with application to Francis hydraulic turbine. Spectral methods imply representing the problem solution as truncated series of smooth global functions. An 2 L - projection and the collocation methods are developed assessing both analytically methodology and computational techniques using symbolic and numerical conversions. Remarks concerning the efficiency and the accuracy of each method in this case are presented. The model of the trailing vortex is used to validate the numerical algorithms with existing results in the literature. All the results are compared to existing ones and they prove to agree quite well. The advantages of using this methods in flow control problems are pointed out.

Keywords: Hydrodynamic instability, swirling flow, projection algorithm, spectral collocation, vortex hydrodynamics, vortex rope

Title of the Paper: Blow-up Solutions of Degenerate Parabolic Problems


Authors: P. Sawangtong, W. Jumpen

Abstract: In this article, we study the degenerate parabolic problem, q ( ) q ( ), t x x x u ? xβ u = x f u satisfying the Dirichlet boundary condition and a nonnegative initial condition where q and β are given constants and f is a suitable function. We show that under certain conditions the degenerate parabolic problem has a blow-up solution and the blow-up set of such a blow-up solution is the whole domain of x. Furthermore, we give the sufficient condition to blow-up in finite time. Finally, we generalize the degenerate parabolic problem into the general form, ( ) ( ( ) ) ( ) ( ). t x x k x u ? p x u = k x f u Under appropriate assumptions on functions k, p and f , we still obtain the same results as the previous problem.

Keywords: Degenerate parabolic problems, Finite time blow-up, Blow-up set, Blow-up solution

Title of the Paper: Quantum Theory of Fields from Planck to Cosmic Scales


Authors: Siavash H. Sohrab

Abstract: A scale invariant model of statistical mechanics is applied to describe a modified statistical theory of turbulence and its quantum mechanical foundations. Hierarchies of statistical fields from cosmic to Planck scales are described. Energy spectrum of equilibrium isotropic turbulence is shown to follow Planck law. Predicted velocity profiles of turbulent boundary layer over a flat plate at four consecutive scales of LED, LCD, LMD, and LAD are shown to be in close agreement with the experimental observations in the literature. The physical and quantum nature of time is described and a scale-invariant definition of time is presented and its relativistic behavior is examined. New paradigms for physical foundations of quantum mechanics as well as derivation of Dirac relativistic wave equation are introduced.

Keywords: Theory of turbulence, Quantum mechanics, Relativity, Dirac and Schrodinger equations, TOE

Issue 10, Volume 9, October 2010

Title of the Paper: The Effect of Time Scales on SIS Epidemic Model


Authors: Wichuta Sae-Jie, Kornkanok Bunwong, Elvin J. Moore

Abstract: The distribution of diseases is one of the most interesting real-world phenomena which can be systematically studied through a mathematical model. A well-known simple epidemic model with surprising dynamics is the SIS model. Usually, the time domains that are widely used in mathematical models are limited to real numbers for the case of continuous time or to integers for the case of discrete time. However, a disease pandemic such as an influenza pandemic regularly disappears from a population and then recurs after a period of time. Additionally, collecting actual data continuously is time-consuming, relatively expensive, and really impractical. It seems that using a continuous-time model to describe observed data may not always be possible due to time domain conflict. The purpose of this paper is, therefore, to study the qualitative behavior of SIS models on continuous, discrete, and mixed continuous-discrete time scales. We investigate their dynamic behavior and examine how this behavior changes in the different time scale domains. We show that the dynamic behavior can change in a systematic manner from simple stable steady-state solutions for the continuous time domain to complicated chaotic solutions for the discrete-time domain.

Keywords: Bifurcation, Chaos, Limit cycles, Period doubling, SIS epidemic model, Time scales calculus

Title of the Paper: A New Approach to Pair Approximation Method for Spatial Model in Ecology


Authors: Kornkanok Bunwong

Abstract: A mathematical model using either mean-field approximation or pair approximation has both advantage and limitation. Mean-field approximation is suitable for describing behaviors of a large system; however, it neglects the scale of individual interaction. On the other hand, pair approximation is suitable for studying local interaction especially singles and pairs; however, the mathematical formulas are still limited. Thus, choosing the right model for the right purpose is recommended. The objective of this paper is to develop the techniques of pair approximation by using probability averaged value based on probability distribution; for example, multinomial distribution and Poisson distribution. These extended formulas are suitable for a model composed of individuals whose event rates are additionally affected by their nearby neighbor. Finally, we apply these tools to a simple SIS epidemic model.

Keywords: Multinomial distribution, Poisson distribution, Pair approximation, Spatial interaction, Lattice model, Ecology, Epidemiology

Title of the Paper: A Simulation Approach: Improving Patient Waiting Time for Multiphase Patient Flow of Obstetrics and Gynecology Department (O&G Department) in Local Specialist Centre


Authors: A. F. Najmuddin, I. M. Ibrahim, S. R. Ismail

Abstract: An outpatient clinic is a very complex department to manage. The management of the outpatient department should given greater emphasis on its medical facilities in order to ensure the services provided are in high quality, which conforms to customer or patient satisfaction. Long waiting time for treatment at the department is always the main problem faced by the management, and even worst the consultation time is tremendously shorter than the waiting time. This situation has been a common complaint by the patients and remains to occur even though an appointment system is implemented. The implementation of inefficient appointment and inconsistent service time contributes to the dissatisfaction among patients as well as giving a huge impact to the healthcare’s overall operations. Therefore, the purpose of this study is to analyze the multiphase patient flow system in Obstetrics and Gynecology Department (O&G Department) of a specialist centre by developing a simulation model that illustrates the actual patient flow in the department. The Arena 7.0 software package is used to develop the simulation model in order to examine the patient flow, especially the waiting time involved. In addition, 120 questionnaires were distributed to patients to gather direct responds and opinions towards the services provided. The information gathered was used to aid the model improvement process. The result obtained from the simulation model shows that a long waiting time does exist in the system. Based on the developed simulation model, two proposed experimentation are being done to find the right solutions to reduce the patients’ waiting time and at the same time enhanced the quality of services of the O&G Department. The proposed experimentation model can be effective to the system and is possible to be implemented in the department.

Keywords: Arena, multiphase patient flow, simulation model, simulation technique, lengthy waiting time, service time

Title of the Paper: Statistical Analysis and Evaluation of Hurst Coefficient for Annual and Monthly Precipitation Time Series


Authors: Alina Barbulescu, Cristina Serban, Carmen Maftei

Abstract: A major issue in time series analysis and particularly in the study of meteorological time series is to model and to predict their behaviour. The first step to reach this goal is the data analysis. It is what we shall do in this article, focusing on the long range dependence (LRD) property. Various estimators of LRD have been proposed. Their accuracy have been generally tested using simulated time series since sometimes only their asymptotic property are known, or worse, no asymptotic property have been proved. For ten annual and monthly data series collected in Dobrudja region, for 41 years, we did the statistical analysis and we compare the results.

Keywords: Normality, homoscedasticity, long – range dependence, Hurst coefficient

Title of the Paper: Implementation of MPI Environment for Solving Large Systems of ODEs using Block Method


Authors: Z. A. Majid, S. Mehrkanoon, K. I. Othman, M. Suleiman

Abstract: Parallel 2-point and 3-point block method will simultaneously compute the numerical solutions at two and three points respectively are suitable for solving large system of first order ordinary differential equations (ODEs) using variable step size. The Gauss Seidel iteration will be implemented for the block methods. The parallelism across the system is considered for the parallelization of the proposed methods using the Message Passing Interface (MPI) communication environment which runs on High Performance Computing (HPC). Numerical examples are given to illustrate the efficiency of the parallel implementation of the proposed method using 2, 4 and 6 processors with respect to the sequential one.

Keywords: 2-point block, 3-point block, ODEs, parallel method, block method, parallelism

Title of the Paper: A Study of the Impact of the Initial Energy in a Close Approach of a Cloud of Particles


Authors: Vivian Martins Gomes, Antonio F. B. A. Prado

Abstract: In this paper we perform a study of the effects of a close approach in the three-dimensional space between a planet and a cloud of particles, with the goal of understanding the dispersion of this cloud in terms of the variations of velocity, energy, angular momentum and inclination. It is assumed that the cloud is formed at the periapsis and the particles differ only by the magnitude of the velocity at this point. In this research we use the three-dimensional circular restricted three-body problem as the basic model for this close approach. A numerical algorithm is developed and implemented to study this problem and then it is applied to a cloud of particles, based in an analytical description of the close approach maneuver in the three-dimensional space. Analytical equations based in the patched conics approximation are used to calculate the variation in velocity, angular momentum, energy and inclination of the spacecraft that performs this maneuver.

Keywords: Astrodynamics, artificial satellites, orbital dynamics, swing-by

Issue 11, Volume 9, November 2010

Title of the Paper: Demonic Fuzzy Operators


Authors: Huda Alrashidi, Fairouz Tchier

Abstract: We deal with a relational algebra model to define a refinement fuzzy ordering (demonic fuzzy inclusion) and also the associated fuzzy operations which are fuzzy demonic join (tfuz), fuzzy demonic meet (ufuz) and fuzzy demonic composition ( 2 fuz). We give also some properties of these operations and illustrate them with simple examples. Our formalism is the relational algebra.

Keywords: Fuzzy sets, demonic operators, demonic fuzzy operators, demonic fuzzy ordering

Title of the Paper: Analysis of Chain Reaction Between Two Stock Indices Fluctuations by Statistical Physics Systems


Authors: Jiguang Shao, Jun Wang

Abstract: In this paper, we consider the statistical properties of chain reaction of stock indices. The theory of interacting systems and statistical physics are applied to describe and study the fluctuations of two stock indices in a stock market, and the properties of the interacting reaction of the two indices are investigated in the present paper. In this work, stochastic analysis and the two random paths model are used to study the probability distribution for the chain reaction of stock indices, further we show the asymptotical behavior of probability measures of the fluctuations for the two stock indices model. In the last part, we discuss the convergence of the finite dimensional probability distributions for the financial model.

Keywords: Stock Index, Chain Reaction, Statistical Analysis, Fluctuation, Statistical Physics, Gibbs Probability Measure

Title of the Paper: Matrix Nonstandard Numerical Schemes for Epidemic Models


Authors: Gilberto Gonzalez-Parra, Rafael J. Villanueva, Abraham J. Arenas

Abstract: This paper is concerned with the construction and developing of several nonstandard finite difference (NSFD) schemes in matrix form in order to obtain numerical solutions of epidemic models. In particular, we deal with a classical SIR epidemic model and a seasonal model associated with the evolution of the transmission of respiratory syncytial virus RSV in the human population. The first model is an autonomous differential equation system, and the second one is a nonautonomous one which generally is more difficult to be solved. The numerical schemes developed here can be used in other general epidemic models based on ordinary differential equations. One advantage of the developed methodology is that can be used easily by the scientific community without special knowledge. In addition, these NSFD schemes which are based on the the nonstandard finite difference methods developed by Mickens solve numerically systems describing epidemics with less computational effort. Finally, with these matrix NSFD schemes it can be exploited more easily matrix operations advantages.

Keywords: Matrix difference scheme, Nonstandard schemes, Matrix computation, Numerical solution, Epidemic model

Title of the Paper: A Study of Vehicle Characteristics of Signalized Intersection based on Queuing Theory


Authors: Lian Xue, Minghui Wu, Hui Yan

Abstract: This paper uses queuing theory to study the features of the vehicle’s arriving and passing of the signalized intersection. The first part of this paper presents the background, purpose and meaning. In the second part, the arrival process and serving process are studied, especially the delay process is mainly analyzed including the dispersion vehicle headway time distribution and vehicle delay at signalized intersections is analyzed. In the third part, time series, cubic spline difference and gray prediction, RBF neural network are used to get the number of vehicles arrived outside of next 18 cycles. Based on the queuing theory, the forth part introduces a predict model on the vehicle’s arrival. It predicts a certain intersections’ average length, average waiting time and average length of stay in the next 18 cycles. The fifth part optimizes the intersection signal timing and gets the best signal cycle time. Scientific model and more complete analysis are founded in the paper. These methods have a good reference value to the relevant departments.

Keywords: Signalized intersection, vehicle characteristics, queuing theory, RBF neural network, forecast, timing optimization

Issue 12, Volume 9, December 2010

Title of the Paper: On a Degenerate Parabolic Equation from Finance


Authors: Huashui Zhan

Abstract: Consider the degenerate parabolic equation , which comes from mathematics finance, and in which u(t, x) is the utility function of a agent’s decision under risk. By Oleinik’s line method, the existence and the uniqueness of the local classical solution for the initial boundary problem of the equation are got. Also, the global entropy solution of the Cauchy problem is discussed.

Keywords: Degenerate parabolic equation, existence, uniqueness, initial boundary problem, global entropy solution

Title of the Paper: Locating Zeros of Polynomials Associated with Daubechies Orthogonal Wavelets


Authors: Jalal Karam

Abstract: In the last decade, Daubechies orthogonal wavelets have been successfully used and proved their practicality in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, the low pass and high pass filters that generate a Daubechies mother wavelet are considered. From these filters, a new set of high pass and low pass filters are derived by using the ”Alternating Flip” techniques. The new set of filters maintain perfect reconstruction status of an input signal, thus allowing the construction of a new mother wavelet and a new scaling function that are reflective to those of the originals. Illustration are given and new reflective wavelets are derived. Also, a subclass of polynomials is derived from this construction process by considering the ratios of consecutive binomial polynomials’ coefficients. A mathematical proof of the residency of the roots of this class of polynomials inside the unit circle is presented along with an illustration for db6, a member of the Daubechies orthogonal wavelets family. The Kakeya-Enestrom theorem is discussed along with some of its generalizations. Finally, a ?-dependent difference among the coefficients of the new set of polynomials is examined and optimized locations of the roots are derived.

Keywords: Zeros, Polynomials, Daubechies Orthogonal Wavelets, Reflective Wavelets, Kakeya-Enestrom Theorem

Title of the Paper: Improvements of Preconditioned SOR Iterative Method for L-Matrices


Authors: Shi-Liang Wu, Cui-Xia Li, Ting-Zhu Huang

Abstract: In this paper, we present some comparison theorems on preconditioned iterative method for solving L-matrices linear systems. Comparison results and numerical examples show that the rate of convergence of the preconditioned Gauss-Seidel iterative method is faster than the rate of convergence of the preconditioned SOR iterative method.

Keywords: Preconditioner; L-matrix; SOR method; Gauss-Seidel method; Spectral radius; Iteration

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