Showing papers in "American Journal of Computational and Applied Mathematics in 2012"
TL;DR: A general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy is developed and three altenative measures of a fuzzy system's effectiveness connected to the model are introduced.
Abstract: In the present paper we use princip les of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainty. For this, the main stages of the corresponding process are represented as fuzzy subsets of a set of linguistic labels characterizing the system's performance at each stage. We also introduce three alternative measures of a fuzzy system's effect iveness connected to our general model. These measures include the system's total possibilistic uncertainty, the Shannon's entropy properly modified for use in a fuzzy environment and the "centroid" method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system's performance. The advantages and disadvantages of the above measures are discussed and a comb ined use of them is suggested for achieving a worthy of credit mathemat ical analysis of the corresponding situation. An application is also developed for the Mathematical Modelling process illustrating the use of our results in practice.
23 citations
TL;DR: A comparative study of Finite volume method and finite difference method is presented in this paper, where the finite volume method is also used for solving these governing equations and the comparison of the two methods can be found here.
Abstract: Now-a-days computational fluid mechanics has become very vital area in which obtained governing equations are differential equations. Sometimes, these governing equations cannot be easily solved by existing analytical methods. Due to this reason, we use various numerical techniques to find out approximate solution for such problems. Among these techniques, finite volume method is also being used for solving these governing equations here we are describing comparative study of Finite volume method and finite difference method.
22 citations
TL;DR: In this article, a convolution kernel was used to solve a linear PIDE with a Laplace transform (LT) and an exact solution of the problem was obtained by solving this ODE and applying inverse LT.
Abstract: Partialintegro-differential equations (PIDE) occur naturally in various fields of science, engineering and social sciences. In this article, we propose a most general form of a linear PIDE with a convolution kernel. We convert the proposed PIDE to an ordinary differential equation (ODE) using a Laplace transform (LT). Solving this ODE and applying inverse LT an exact solution of the problem is obtained. It is observed that the LT is a simple and reliable technique for solving such equations. A variety of numerical examples are presented to show the performance and accuracy of the proposed method.
20 citations
TL;DR: In this article, the effects of chemical reaction in two dimensional steady free convective flow of an electrically conducting viscous fluid through a porous medium bounded by vertical surface with slip flow region has been studied.
Abstract: The effects of chemical reaction in two dimensional steady free convective flow of an electrically conducting viscous fluid through a porous medium bounded by vertical surface with slip flow region has been studied. A uniform magnetic field is assumed to be applied transversely in the direction of the flow. . A chemically reactive species is emitted from the vertical surface into the flow field. The governing equations are developed by usual Boussinesq's approximation .The problem is solved by regular perturbation technique. The expressions for the velocity field, temperature field, species concentration, shearing stress and the coefficient of heat transfer (in terms of Nusselt number) at the walls are obtained and their nature has been discussed by means of graphs. The effects of Hartmann number, the rarefaction parameter ,the porous parameter, Schmidt number and chemical reaction parameter on the flow are discussed.
19 citations
TL;DR: In this paper, a modulated soliton solution is presented, which is a mu ltifo rm soliton prototype modulated by the very small parameter of the soliton parameters.
Abstract: We constructed in this work a modulated soliton solution. This solution is a mu ltifo rm soliton prototype modulated by the very small parameter
18 citations
TL;DR: In this paper, the design methods of both proportional integral observers and unknown inputs observers for descriptor multi-models are described in detail, and sufficient conditions of stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs).
Abstract: In this note, the problem of states and unknown inputs estimation of nonlinear descriptor system is considered. The methodology is based on the use of Proportional Integral and Unknown Input Observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. In this paper, the design methods of both proportional integral observers and unknown inputs observers for descriptor multi-models are described in detail. Sufficient conditions of stability analysis and gain matrices determination are per-formed by resolving a set of Linear Matrices Inequalities (LMIs). The design method offers all the degrees of design free-dom, which can be utilized to achieve various desired system specifications and performances and, thus, has great poten-tials in applications. A numerical example is employed to show the design procedure of these two observers and illustrate the effect of the proposed approach.
18 citations
TL;DR: In this paper, the authors apply the multiple exp-function method to construct the exact multiple wave solutions of the (2 + 1)- and the (3+ 1)-dimensional breaking soliton equations.
Abstract: The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of the (2 + 1)- and the (3 + 1)-dimensional breaking soliton equations. By this application, we obtain one-wave, two-wave and three-wave solutions for these equations.
15 citations
TL;DR: The proposed GSPN is a pro mising tool that can be conveniently used to model and analyze any co-plex systems and the superiority of this approach over others such as network, fault tree and Markov analysis are outlined.
Abstract: A very high level of availab ility is crucial to the economic operation of modern power plants, in view of the huge expenditure associated with their failures. Th is paper deals with the availab ility analysis of a Lube oil system used in a combined cycle power plant. The system is modeled as a Generalized Stochastic Petri Net (GSPN) taking into consideration of partial failures of their subsystems and common-cause failures; analyzed using Monte Carlo Simu lation approach. The major benefit of GSPN approach is hardware, software and human behavior can be modeled using the same language and hence more suitable to model co mplex system like power p lants. The superiority of this approach over others such as network, fault tree and Markov analysis are outlined. The numerical estimates of availability, failure criticality index o f various subsystems, co mponents causing unavailability of lube oil system are brought out. The proposed GSPN is a pro mising tool that can be conveniently used to model and analyze any co mplex systems.
11 citations
TL;DR: In this article, a four-point derivative-free sixteenth-order iterative method for solving nonlinear equations is con- structed and it is proved that these methods have the convergence order of sixteen requiring only five function evaluations per iteration.
Abstract: New four-point derivative-free sixteenth-order iterative methods for solving nonlinear equations are con- structed. It is proved that these methods have the convergence order of sixteen requiring only five function evaluations per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations, could achieve optimal convergence order 1 2. n− Thus, we present new derivative-free methods which agree with the Kung and Traub conjecture for 5. n = Numerical comparisons are made with other existing methods to show the performance of the presented methods.
11 citations
TL;DR: In this paper, a Bernoulli matrix approach is presented for solving hyperbolic partial differential equations with three variables and constant coefficients, and the efficiency of the proposed approach is evaluated with one exampl e.
Abstract: The purpose of this study is to give a Bernoulli polynomial appro ximat ion for thesolution of hyperbolic partial differential equations with three variables and constant coefficients. For this purpose, a Bernoulli matrix approach is intro- duced. This method is based on taking the truncated Bernoulli expansions of the functions in the partial d ifferential equations. After replacing the approximations of functions in the basic equation, we deal with a linear algebraic equation. Hence, the result matrix equation can be solved and the unknown Bernoulli coefficients can be found approximately. The efficiency of the proposed approach is dem onstrated with one exampl e.
8 citations
TL;DR: Differential Quadrature Method (DQM) as mentioned in this paper is an efficient descriti- zation technique in solving initial and/or boundary value problems accurately using a considerably small number of grid points.
Abstract: In this paper, we have presented the Differential Quadrature Method (DQM) for finding the numerical solution of boundary-value problems for a singularly perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Such problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The Differential Quadrature Method is an efficient descriti- zation technique in solving initial and/or boundary value problems accurately using a considerably small number of grid points. To demonstrate the applicability of the method, we have solved the model examples and compared the computational results with the exact solutions. Comparisons showed that the method is capable of achieving high accuracy and efficiency.
TL;DR: In this paper, it was shown that for any measurable admissible control ( ) w ⋅ and for any 0 e > there exists piecewise constant admissible controlling ( ) such that for set solutions of control set system are e -neighbouring.
Abstract: In this article we prove that for any measurable admissible control ( ) w ⋅ and for any 0 e > there exists piecewise constant admissible control ( ) w ⋅ such that for set solutions of control set system are e -neighbouring.
TL;DR: In this article, the authors extend variational iteration method (VIM) for deriving approximate analytical solution to seventh-order differential equations with specified initial conditions, also in this paper they applied a modified method to identification of Lagrange multiplier.
Abstract: In this paper, we extend variational iteration method (VIM) for deriving approximate analytical solution to seventh-order differential equations with specified initial conditions, also in this paper we applied a modified method to identification of Lagrange multiplier .By providing some examples, we illustrate the capability and reliability of the method.
TL;DR: In this paper, the weighted goal program is reformulated as a lexicographic goal program with two main goals, the first goal is to minimize the maximum weighted undesired normalized deviation, and the second goal, having the second priority, minimizes the sum of the undesirable normalized deviations.
Abstract: In this paper, the weighted goal program is reformulated as a lexicographic goal program with two main goals. The first goal, which has the first priority, seeks to minimize the maximum weighted undesired normalized deviation. The second goal, having the second priority, minimizes the sum of the undesired normalized deviations. This approach provides a solution that is consistent with the weighting scheme. The suggested approach is illustrated by numerical example.
TL;DR: A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations and shows that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameters greater than unity.
Abstract: This paper examines the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus (HCV) disease with Acute and Chronic stages. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However the disease becomes more endemic due to the presence of infected immigrants in the community. It is also shown that in the presence of treatment, the rate of infected immigrants (acute and chronic) decreases and consequently the treated in- fected individuals decreases continuously. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and infected immigrants on the spread of the disease with acute and chronic stages.
TL;DR: In this article, the authors applied the variational iterative method to solve the problem of the two-dimensional incompressi-ble laminar boundary layer flow over a flat plat also called the Blasius problem.
Abstract: This paper applied the variational iterative method to solve the problem of the two-dimensional incompressi- ble laminar boundary layer flow over a flat plat also called the Blasius problem. The problem is governed by the Na- vier-Stokes and continuity equations which were first transformed into an ordinary differential equation using similarity transforms and the resulting problem solved using variational iterative method. The results obtained for the similarity stream function and velocity were tabulated and were highly comparable in terms of accuracy with that obtained by Ganji et al. (2009) who studied the same problem using the homotopy perturbation technique and results obtained by Blasius. The results were found to be very accurate especially for η ≤ 4 when using the variational iterative method. The method is con- venient as it greatly reduces the amount of computational work.
TL;DR: In this article, a numerical algorithm using fifth degree quintic B-spline for fourth order singular per- turbation problem has been developed, which is applied directly to the problem without transforming the problem into an equivalent system.
Abstract: In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular per- turbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spline is applied directly to the problem without transforming the problem into an equivalent system. The method uses values of fifth degree B-spline function and its derivatives up to the order four at nodal points. Resulting system of equations is solved to get the required quintic B-spline solution. Since perturbed problems contain boundary layers, the strategy of fitted mesh is used which assigns more mesh points in the boundary layer regions. The algorithm is tested on two problems to demonstrate the practical usefulness and superiority of the approach.
TL;DR: A new and fast method for matching and recognition of characters in Arabic license plate images and developing a system architecture combining statistical and structural recognition methods is provided.
Abstract: This paper provides a new and fast method for matching and recognition of characters in Arabic license plate images. For this purpose, various methods have been proposed in literature. However, most of them suffer from: sensitivity to non-uniform illumination distribution, existence of shade in license plate, license plate color and the need for receiving an exact image of the license plate. The main contributions of our work include (I) chain code use to bounded the shape and distinguishing similar characters by local structural features. The moving window matching algorithm has been implemented. The distance measure (squared Euclidean distance) technique has been used for measuring the similarities between the moving window and the plate image. (2) Developing a system architecture combining statistical and structural recognition methods. We tested the method with 300 of plate images captured in different environments from real applications. The result yield 93.93% recognition accuracy.
TL;DR: In this article, a general analysis has been developed to study the combined effect of the free convective heat and mass trans- fer on the unsteady two-dimensional boundary layer flow over a stretching vertical plate.
Abstract: A general analysis has been developed to study the combined effect of the free convective heat and mass trans- fer on the unsteady two-dimensional boundary layer flow over a stretching vertical plate. The flow is subject to magnetic field normal to the plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl num- ber Pr and Schmidt number Sc are examined on the velocity, temperature and concentration profiles. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions.
TL;DR: In this article, a modified variational iterative method (MVIM) for the solution of a differential equation of Bratu-type is presented, which converges to the exact solution after an iteration.
Abstract: In this paper, a Modified Variational Iterat ion Method (MVIM) for the solution of a differential equation of Bratu-type is presented. The method converges to the exact solution after an iteration. This shows that the method is efficient for this class of init ial and boundary value problems.
TL;DR: In this article, a sinecosine method is used to construct many periodic and solitary wave solutions to Kadomtsev-Petviashvili equation with power law nonlinearity.
Abstract: In this paper, a sine-cosine method is used to construct many periodic and solitary wave solutions to Kadomtsev-Petviashvili equation with power law nonlinearity. Many new families of exact traveling wave solutions of the Kadomtsev-Petviashvili equation with power law nonlinearity are successfully obtained.
TL;DR: In this paper, the slider bearing of various shapes stator pad surfaces (e.g., inclined plane, expo- nential, secant, convex, and parallel) including combined effects of porosity at both the ends, anisotropic permeability, slip velocity, and squeeze velocity was discussed.
Abstract: This paper discusses about the slider bearing of various shapes stator pad surfaces (e.g. inclined plane, expo- nential, secant, convex, and parallel) including combined effects of porosity at both the ends, anisotropic permeability, slip velocity, and squeeze velocity. Expression for load capacity is obtained in general and discussed for various cases of stator pad surface to explore its possible effects on the above system for different permeabilities at both the ends. Various sizes of the porous matrix at both the ends are also discussed for the possible optimization of bearing performance. From the study we conclude that better load capacity is obtained when the thickness of both the porous plates are small, and also when both the porous plates are of same size rather than different size.
TL;DR: In this article, the authors used the finite element method to derive the equation of motion for an elastic circular plate element under the influence of exponential impulse forces, and the effects of transverse shear deformation and rotatory inertia were included.
Abstract: The result of the study of dynamic response of an elastic circular plate to blast load is presented in this research work. Finite element method is used to derive the equation of motion for the circular plate element under the influence of exponential impulse forces. System stiffness and mass matrices were drive. The effects of transverse shear deformation and rotatory inertia were included. From the numerically simulated results it is observed that the amplitude dies out quickly due to the effect of damping. The pulse duration ���� ���� is also one of the most important parameter because it gives serious influence to the vibration amplitude. It gives rise to the vibration amplitude on any small decrease on the pulse duration. It is also observed that the exponential blast loading brings faster rate of amplitude decay than those of triangular and sinusoidal blast loading.
TL;DR: The mathematical model of processes of electro-magnetic fields' effects on thin conducting plates by complex form is proposed, calculating algorithm mining by the joint using variation method and analytical method RFM and software for this algorithm and so calculating experiment are given.
Abstract: In this work the mathematical model of processes of electro-magnetic fields’ effects on thin conducting plates by complex form, calculating algorithm mining by the joint using variation method and analytical method RFM and software for this algorithm and so calculating experiment are given
TL;DR: In this paper, the effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration, and the efficiency of generalized differential quadrature method for the natural frequency of vibrat ion of monoclinic rectangular p lates has been examined.
Abstract: Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Levy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations C-C, C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been carried out for four decimal exactitude. Mode shapes for all the three plates have been presented. The efficiency of generalized differential quadrature method for the natural frequencies of vibrat ion of monoclin ic rectangular p lates has been examined.
TL;DR: The optimal BPNN training has been used successfully to tackle uncertain of h idden layer's parameters structure and it has ten times better MSE achievement than NN machine expert.
Abstract: Previous research works tried to optimize the architectures of Back Propagation Neural Netwo rks (BPNN) in order to enhance their performance. However, the using of appropriate method to perform this task still needs expanding knowledge. The paper studies the effect and the benefit of using Taguchi method to optimize the architecture o f BPNN car body design system. The paper started with literatures review to define factors and level of BPNN parameters for number of hidden layer, nu mber of neurons, learn ing algorithm, and etc. Then the BPNN arch itecture is optimized by Taguchi method with Mean Square Error (MSE) indicator. The Signal to No ise (S/N) ratio, analysis of variance (ANOVA) and analysis of means (ANOM) have been employed to identify the Taguchi results. The optimal BPNN training has been used successfully to tackle uncertain of h idden layer's parameters structure. It has faster iterations to reach the convergent condition and it has ten times better MSE achievement than NN machine expert. The paper still shows how to use the informat ion of car body shapes, car speed, vibration, noise, and fuel consumption of the car body database in BPNN training and validation.
TL;DR: In this paper, a fourth order finite difference method is developed for solving singularly perturbed boundary value problems with small delay parameter, where the term containing delay lies on nodal points after discretization.
Abstract: This paper deals with the singularly perturbed boundary value problem for a linear second order differen- tial-difference equation of the convection-diffusion type with small delay parameter. A fourth order finite difference method is developed for solving singularly perturbed differential difference equations. To handle the delay argument, we construct a special type of mesh, so that the term containing delay lies on nodal points after discretization. The proposed finite difference method works nicely when the delay parameter is smaller or bigger to perturbation parameter. The trunca- tion error of the finite difference method is calculated. On the basis of truncation error, as well as the results of number of computational examples, it is concluded that the present method offers significant advantage for the linear problems.
TL;DR: The analysis of records of Accident and Emergency patients admitted into AE unit between 1995 and 2006 showed that patient's admission peaked in May and minimal in November, and Seasonal index showed that the peak of number of patients admitted was observed in the last quarter of every year.
Abstract: Mortality resulting from accidents and late admission of patients into modern health facility constitute a high proportion of all deaths in the developing countries. Information on patterns of admission of Accident and Emergency (AE) patients is valuable to caregivers in AE department in meeting patients' seasonal needs. This retrospective study used gen- der-classified records of 79990 patients admitted into the AE unit between 1995 and 2006 in University College Hospital (UCH), Ibadan. We examined seasonal variation using trigonometric regression and moving average models. There exists significant difference in number of admission between males (���� � = 306.63,����= 69.56) and females (���� � = 248.85,����= 65.27).The analysis further showed that patient's admission peaked in May and minimal in November. Seasonal index showed that the peak of number of patients admitted was observed in the last quarter of every year. This is an indication that admission occurs mostly during the festive periods where people travel home to celebrate with their love ones. The projected quarterly admissions for 2011 are (Q1=1488, Q2=1497, Q3=1632, Q4=1634) and for 2012 are (Q1=1490, Q2=1499, Q3=1634, Q4=1635). The hospital management should engage more caregivers and make available more resus- citating medical equipments during last quarter of each year and peak periods.
TL;DR: In this paper, a reduced differential transform method is presented to solve the MEW equation, its variant and nonhomogeneous Burgers' equation, which is capable of reducing the size of calculation and easily overcoming the difficulty of the perturbation technique or Adomain polynomials.
Abstract: The modified equal width equation and its variant are investigated. We have presented a reduced differential transform method to solve the MEW equation, its variant and non-homogeneous Burgers' equation. This method is an alternative approach to overcome the demerit of complex calculation of differential transform method, capable of reducing the size of calculation and easily overcoming the difficulty of the perturbation technique or Adomain polynomials. The approximate analytical solutions of the equations are calculated in the form of series with easily computable components. Numerical results are derived and the obtained results are found in good agreement with the exact solutions.
TL;DR: A hybrid technique for classification of fingerprint identification has been developed to decrease the matching time and a Support Vector Machine and a Multi-Layered Perceptron network are described and used.
Abstract: In this work a hybrid technique for classification of fingerprint identification has been developed to decrease the matching time. For classification, a Support Vector Machine (SVM) and a Multi-Layered Perceptron (MLP) network are described and used. Automatic Fingerprint Identification Systems (AFIS) are widely used today, and it is therefore necessary to find a classification system that is less time-consuming. The fingerprint patterns generated are based on minu- tiae extraction from a thinned fingerprint image. The given fingerprint database is decomposed into four different sub- classes. Two different classification regimes are used to train the systems to do correct classification. The classification rate has been estimated to about 87.0 % and 88.8% of unseen fingerprints for SVM and MLP classification respectively. The classification rate of both systems is only differing marginally.A benchmark test has been done for both systems. The matching time is estimated to decrease with a factor of about 3.7 compared to a brute force approach.