Mathematical and Computational Applications

109 KiB

Open AccessDiscussion

Discussion of "An Approximate Method for Free Vibration Analysis of Multibay Coupled Shear Walls" K. B. Bozdoğan and D. Öztürk, Mathematical and Computational Applications 12, 41-50, 2007"

by Hikmet Hüseyin Çatal

Math. Comput. Appl. 2010, 15(3), 503-505; https://doi.org/10.3390/mca15030503 - 1 Dec 2010

Viewed by 940

Abstract

n/a Full article

473 KiB

Open AccessArticle

Bifurcation and Chaos of Slightly Curved Pipes

by B. Gültekin Sinir

Math. Comput. Appl. 2010, 15(3), 490-502; https://doi.org/10.3390/mca15030490 - 1 Dec 2010

Cited by 49 | Viewed by 1470

Abstract

Non-linear vibrations of slightly curved pipes conveying fluid with constant velocity are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is considered due to the geometry of the pipe itself. The ends of the curved [...] Read more.

Non-linear vibrations of slightly curved pipes conveying fluid with constant velocity are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is considered due to the geometry of the pipe itself. The ends of the curved pipe are assumed to be immovable simple supports. The equations of motion of pipes are derived using Hamilton's principle and solved by Galerkin method. The bifurcation diagrams are presented for various amplitudes of the curvature function and fluid velocity. The periodic and chaotic motions have been observed in the transverse vibrations of slightly curved pipe conveying fluid. Full article

231 KiB

Open AccessArticle

Analytical Aspect of Fourth-Order Parabolic Partial Differential Equations with Variable Coefficients

by Najeeb Alam Khan, Asmat Ara, Muhammad Afzal and Azam Khan

Math. Comput. Appl. 2010, 15(3), 481-489; https://doi.org/10.3390/mca15030481 - 1 Dec 2010

Cited by 11 | Viewed by 1366

Abstract

In this work, the homotopy analysis method (HAM) is applied to solve the fourth-order parabolic partial differential equations. This equation practically arises in the transverse vibration problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Some applications [...] Read more.

In this work, the homotopy analysis method (HAM) is applied to solve the fourth-order parabolic partial differential equations. This equation practically arises in the transverse vibration problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Some applications are given to verify the reliability and efficiency of the method. The convergence control parameter h in the HAM solutions has provided a convenient way of controlling the convergence region of series solutions. It is also shown that the solutions that are obtained by Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the solutions obtained by HAM. Full article

260 KiB

Open AccessArticle

Intrauterine Growth Restriction (IUGR) Risk Decision Based on Support Vector Machines

by Zeynep Zengin, Fikret Gürgen and Füsun Varol

Math. Comput. Appl. 2010, 15(3), 472-480; https://doi.org/10.3390/mca15030472 - 1 Dec 2010

Viewed by 1121

Abstract

This paper studies the risk of intrauterine growth restriction (IUGR) using support vector machines (SVM). A structured and globally optimized SVM system may be preferable procedure in the identification of IUGR fetus at risk. The IUGR risk is estimated in two stages: in [...] Read more.

This paper studies the risk of intrauterine growth restriction (IUGR) using support vector machines (SVM). A structured and globally optimized SVM system may be preferable procedure in the identification of IUGR fetus at risk. The IUGR risk is estimated in two stages: in the first stage, noninvasive Doppler pulsatility index (PI) and resistance index (RI) of umbilical artery (UA), middle cerebral artery (MCA) and ductus venosus (DV) and amniotic fluid index (AFI) are retrospectively analyzed and the Doppler indices are applied to the SVM system to make a diagnosis decision on the fetal wellbeing as ”reactive” or “nonreactive and/or acute fetal distress (AFD)” on the nonstress test (NST) (training data). In the second stage (testing data), the decision is validated by the NST (target value). Experiments are performed on previously collected data. Fortyfour preterm with IUGR and without IUGR pregnancies before 34 weeks gestation are considered.The nonparametric Bayes-risk decision rule, k-nearest neighbor (k-NN), is used for comparison. It is observed that the SVM system is proven to be useful in predicting the expected risk in IUGR cases in this small population study. The PI and RI values of UA, MCA and DV are also effective in distinguishing IUGR at risk. Full article

201 KiB

Open AccessArticle

The Emergence of Spherical Magneto-Gas Dynamic Strong Shock with Radiation near the Surface of a Star with a Rotating , Gravitating, Non-Uniform Atmosphere

by Ashok Ganguly and Pankaj Sharma

Math. Comput. Appl. 2010, 15(3), 461-471; https://doi.org/10.3390/mca15030461 - 1 Dec 2010

Viewed by 1087

Abstract

The propagation of a strong magneto-gas dynamic, rotating and gravitating shock wave originating in a stellar interior is considered, when it approaches the surface of the star. The flow behind the shock wave is assumed to be spatially isothermal rather than adiabatic to [...] Read more.

The propagation of a strong magneto-gas dynamic, rotating and gravitating shock wave originating in a stellar interior is considered, when it approaches the surface of the star. The flow behind the shock wave is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. It has been observed that gravitation and rotation have important impact upon the emergence of shock at the surface of the star. Full article

251 KiB

Open AccessArticle

High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation

by Murat Sari, Gürhan Gürarslan and Asuman Zeytinoğlu

Math. Comput. Appl. 2010, 15(3), 449-460; https://doi.org/10.3390/mca15030449 - 1 Dec 2010

Cited by 40 | Viewed by 1951

Abstract

Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order [...] Read more.

Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. The methods are implemented to solve two problems having exact solutions. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the current methods. The techniques are seen to be very accurate in solving the advection-diffusion equation for Pe ≤ 5 . The produced results are also seen to be more accurate than some available results given in the literature. Full article

187 KiB

Open AccessArticle

On Some Double Lacunary Sequence Spaces of Fuzzy Numbers

by Ekrem Savas

Math. Comput. Appl. 2010, 15(3), 439-448; https://doi.org/10.3390/mca15030439 - 1 Dec 2010

Cited by 14 | Viewed by 1087

Abstract

In this paper we introduce a new concept for lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space of fuzzy numbers. We also show that if a sequence is lacunary strong Pconvergence with respect [...] Read more.

In this paper we introduce a new concept for lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space of fuzzy numbers. We also show that if a sequence is lacunary strong Pconvergence with respect to an Orlicz function then it is S _{θ _{r s}}(F) -convergent. Full article

192 KiB

Open AccessArticle

E(5) Behaviour of the Ge Isotopes

by Nureddin Turkan and Ismail Maras

Math. Comput. Appl. 2010, 15(3), 428-438; https://doi.org/10.3390/mca15030428 - 1 Dec 2010

Cited by 4 | Viewed by 1124

Abstract

The sufficient aspects of model leading to the E(5) symmetry have been proved by presenting E(5) characteristic of the transitional nuclei 64-80Ge. The positive parity states of even-mass Ge nuclei within the framework of Interacting Boson Model have been calculated and compared with [...] Read more.

The sufficient aspects of model leading to the E(5) symmetry have been proved by presenting E(5) characteristic of the transitional nuclei 64-80Ge. The positive parity states of even-mass Ge nuclei within the framework of Interacting Boson Model have been calculated and compared with the Davidson potential predictions along with the experimental data. It can be said that the set of parameters used in an calculations is the best approximation that has been carried out so far. Hence, Interacting Boson Approximation (IBA) is fairly reliable for the calculation of spectra in such set of Ge isotopes. Full article

564 KiB

Open AccessArticle

Application of Image Processing in Unsteady Flows to Investigate Bed Load Transport

by Gökçen Bombar, M. Sükrü Güney and Mustafa S. Altınakar

Math. Comput. Appl. 2010, 15(3), 420-427; https://doi.org/10.3390/mca15030420 - 1 Dec 2010

Cited by 3 | Viewed by 1099

Abstract

Image processing is a promising technique to investigate bed load characteristics and its movement which has been applied in steady flow conditions for the last few decades. In this study, it is aimed to perform experiments in unsteady flows through generating a hydrograph [...] Read more.

Image processing is a promising technique to investigate bed load characteristics and its movement which has been applied in steady flow conditions for the last few decades. In this study, it is aimed to perform experiments in unsteady flows through generating a hydrograph to apply this technique and calculate the bed load transport. The sediment motion is recorded by a video recorder. The video records are analyzed by image processing techniques to determine the number and area of active grains moving at any instant as well as the average velocity of the grains. A bed load transport formula is introduced particularly used by the digital video analysis in which the time variation of the bed load due to the hydrograph could be precisely determined. It is revealed that the bed load determined at two sections of the flume is in accord and the bed load – time curve has a fluctuating character. Full article

212 KiB

Open AccessArticle

Existence and Uniqueness of Solution of an Uncertain Characteristic Cauchy Reaction-Diffusion Equation by Adomian Decomposition Method

by H. Rouhparvar, S. Abbasbandy and T. Allahviranloo

Math. Comput. Appl. 2010, 15(3), 404-419; https://doi.org/10.3390/mca15030404 - 1 Dec 2010

Cited by 4 | Viewed by 1180

Abstract

In this paper, the existence and uniqueness theorems for a solution to an uncertain characteristic Cauchy reaction-diffusion problem is studied by Adomian decomposition method. Sufficient conditions are presented for uniform convergence of the proposed method. Also, some illustrative examples are given for solving [...] Read more.

In this paper, the existence and uniqueness theorems for a solution to an uncertain characteristic Cauchy reaction-diffusion problem is studied by Adomian decomposition method. Sufficient conditions are presented for uniform convergence of the proposed method. Also, some illustrative examples are given for solving the problem. Full article

168 KiB

Open AccessArticle

Method for Multiple Attribute Decision-Making with Continuous Random Variable under Risk Based on Projection Model

by Fang Jin, Xin Zhang and Peide Liu

Math. Comput. Appl. 2010, 15(3), 394-403; https://doi.org/10.3390/mca15030394 - 1 Dec 2010

Cited by 10 | Viewed by 1271

Abstract

A rank approach based on projection model is proposed to deal with multiple attribute decision-making[MADM] problems under risk and with attribute value as continuous random variable on bounded intervals. Firstly, risk decision matrix is normalized by density function, and weights of attributes are [...] Read more.

A rank approach based on projection model is proposed to deal with multiple attribute decision-making[MADM] problems under risk and with attribute value as continuous random variable on bounded intervals. Firstly, risk decision matrix is normalized by density function, and weights of attributes are calculated based on exception value of random variable by using projection pursuit model and genetic algorithm. Next, through calculating weighted correlation coefficients between alternatives and ideal solutions, weighted grey correlation projection models on ideal solutions are developed by grey correlation projection method for every alternative. Furthermore, alternatives are ranked by grey correlation projection value. Finally, an MADM example with interval numbers is provided to demonstrate the steps and effectiveness of the proposed approach. Full article

344 KiB

Open AccessArticle

Reduced Differential Transform Method for Generalized KdV Equations

by Yıldıray Keskin and Galip Oturanç

Math. Comput. Appl. 2010, 15(3), 382-393; https://doi.org/10.3390/mca15030382 - 1 Dec 2010

Cited by 55 | Viewed by 1754

Abstract

In this paper, a general framework of the reduced differential transform method is presented for solving the generalized Korteweg–de Vries equations. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology with [...] Read more.

In this paper, a general framework of the reduced differential transform method is presented for solving the generalized Korteweg–de Vries equations. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. In addition, three test problems of mathematical physics are discussed to illustrate the effectiveness and the performance of the reduced differential transform method. Full article

193 KiB

Open AccessArticle

Legendre Series Solutions of Fredholm Integral Equations

by Salih Yalçınbas, Müge Aynigül and Tuğçe Akkaya

Math. Comput. Appl. 2010, 15(3), 371-381; https://doi.org/10.3390/mca15030371 - 1 Dec 2010

Cited by 10 | Viewed by 1536

Abstract

A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then [...] Read more.

A matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Legendre coefficients. In addition, some equations considered by other authors are solved in terms of Legendre polynomials and the results are compared. Full article

152 KiB

Open AccessArticle

An Algebraic Approach for Determining the Optimal Lot Size for EPQ Model with Rework Process

by Singa Wang Chiu, Chi-Bin Cheng, Mei-Fang Wu and Jyh-Chau Yang

Math. Comput. Appl. 2010, 15(3), 364-370; https://doi.org/10.3390/mca15030364 - 1 Dec 2010

Cited by 12 | Viewed by 1295

Abstract

This paper presents a simple algebraic approach for deriving the optimal lot size for economic production quantity (EPQ) model with rework process. Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the [...] Read more.

This paper presents a simple algebraic approach for deriving the optimal lot size for economic production quantity (EPQ) model with rework process. Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. A few recent articles proposed the algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This paper extends it to an EPQ model with reworking of defective items. We demonstrate that optimal lot size and optimal production-inventory cost for such an imperfect EPQ model can be derived without derivatives. As a result, it may enable the practitioners or students who with little knowledge of calculus to understand or handle with ease the realistic production systems. Full article

253 KiB

Open AccessArticle

MHD Flow of a Second Order/Grade Fluid Due to Noncoaxial Rotation of a Porous Disk and the Fluid at Infinity

by H. Volkan Ersoy

Math. Comput. Appl. 2010, 15(3), 354-363; https://doi.org/10.3390/mca15030354 - 1 Dec 2010

Cited by 7 | Viewed by 1316

Abstract

The magnetohydrodynamic (MHD) flow of an electrically conducting second order/grade fluid past a porous disk is studied when the disk and the fluid at infinity rotate with the same angular velocity about non-coincident axes. It is found that the existence of solutions is [...] Read more.

The magnetohydrodynamic (MHD) flow of an electrically conducting second order/grade fluid past a porous disk is studied when the disk and the fluid at infinity rotate with the same angular velocity about non-coincident axes. It is found that the existence of solutions is in connection with the sign of the material modulus α₁ for both suction and blowing cases. The effects of all the parameters on the flow are carefully examined. Full article

166 KiB

Open AccessArticle

Proposing a New Model on Data Envelopment Analysis by Considering Non Discretionary Factors and a Review on Previous Models

by G.R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, A.Gholam Abri, M. Fallah Jelodar and Kamran Jamali Firouzabadi

Math. Comput. Appl. 2010, 15(3), 344-353; https://doi.org/10.3390/mca15030344 - 1 Dec 2010

Cited by 9 | Viewed by 1169

Abstract

Discretionary models of data envelopment analysis (DEA) assume that all inputs and outputs are discretionary, i.e., controlled by the management of each decision making unit (DMU) and varied at its discretion. In any realistic situation, however, there may exist exogenously fixed or non-discretionary [...] Read more.

Discretionary models of data envelopment analysis (DEA) assume that all inputs and outputs are discretionary, i.e., controlled by the management of each decision making unit (DMU) and varied at its discretion. In any realistic situation, however, there may exist exogenously fixed or non-discretionary inputs or outputs that are beyond the control of a DMU's management. There are some models that incorporate non-discretionary inputs into DEA models. This paper reviews these approaches, providing a discussion of strengths and weaknesses and highlighting potential limitations. Moreover, a new method is developed that overcomes existing weaknesses. Full article

1307 KiB

Open AccessArticle

Application of Taylor Matrix Method to the Solution of Longitudinal Vibration of Rods

by Mehmet Çevik

Math. Comput. Appl. 2010, 15(3), 334-343; https://doi.org/10.3390/mca15030334 - 1 Dec 2010

Cited by 4 | Viewed by 1287

Abstract

The present study introduces a novel and simple matrix method for the solution of longitudinal vibration of rods in terms of Taylor polynomials. The proposed method converts the governing partial differential equation of the system into a matrix equation, which corresponds to a [...] Read more.

The present study introduces a novel and simple matrix method for the solution of longitudinal vibration of rods in terms of Taylor polynomials. The proposed method converts the governing partial differential equation of the system into a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Then the solution is obtained easily by solving these matrix equations. Both free and forced vibrations of the system are studied; particular and general solutions are determined. The method is demonstrated by an illustrative example using symbolic computation. Comparison of the numerical solution obtained in this study with the exact solution is quite good. Full article

148 KiB

Open AccessArticle

Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System

by Ben Muatjetjeja and Chaudry Masood Khalique

Math. Comput. Appl. 2010, 15(3), 325-333; https://doi.org/10.3390/mca15030325 - 1 Dec 2010

Cited by 18 | Viewed by 1334

Abstract

Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden [...] Read more.

Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obtained for the Lane-Emden system under consideration. We show that the first integrals for both the Noether and partial Noether operators are the same. However, the gauge function is different in certain cases. Full article

128 KiB

Open AccessArticle

RULES3-EXT Improvements on RULES-3 Induction Algorithm

by Hassan I. Mathkour

Math. Comput. Appl. 2010, 15(3), 318-324; https://doi.org/10.3390/mca15030318 - 1 Dec 2010

Cited by 4 | Viewed by 1174

Abstract

This paper describes RULES3-EXT, a new algorithm for inductive learning. It has been developed to cope with some drawbacks of RULES-3 induction algorithm. The extra features of RULES3-EXT are (1) The number of required files to extract a knowledge base (a set of [...] Read more.

This paper describes RULES3-EXT, a new algorithm for inductive learning. It has been developed to cope with some drawbacks of RULES-3 induction algorithm. The extra features of RULES3-EXT are (1) The number of required files to extract a knowledge base (a set of rules) is reduced to 2 from 3 (2) The repeated examples are eliminated, (3) The users are able to change the order of attributes and (4) The system is able to fire rule(s) partially if any of the extracted rules cannot fully be satisfied by an unseen example. The new algorithm has been tested on well known data sets and the efficiency found to be superior to that of RULES-3. Full article

162 KiB

Open AccessArticle

Modified Variational Iteration Method for Schrodinger Equations

by Syed Tauseef Mohyud-Din, Muhammad Aslam Noor and Khalida Inayat Noor

Math. Comput. Appl. 2010, 15(3), 309-317; https://doi.org/10.3390/mca15030309 - 1 Dec 2010

Cited by 7 | Viewed by 1317

Abstract

In this paper, we apply the modified variational iteration method (MVIM) for solving Schrödinger equations. The proposed modification is made by introducing He’s polynomials in the correction functional of variational iteration method (VIM). The suggested iterative scheme finds the solution without any discretization, [...] Read more.

In this paper, we apply the modified variational iteration method (MVIM) for solving Schrödinger equations. The proposed modification is made by introducing He’s polynomials in the correction functional of variational iteration method (VIM). The suggested iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The use of Lagrange multiplier coupled with He’s polynomials are the clear advantages of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed algorithm. Full article

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Math. Comput. Appl., Volume 15, Issue 3 (December 2010) – 20 articles , Pages 309-505

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