Mathematical and Computational Applications

145 KiB

Open AccessArticle

Ranking Decision Making Units with Stochastic Data by Using Coefficient of Variation

by F. Hosseinzadeh Lotfi, N. Nematollahi, M.H. Behzadi and M. Mirbolouki

Math. Comput. Appl. 2010, 15(1), 148-155; https://doi.org/10.3390/mca15010148 - 01 Apr 2010

Cited by 8 | Viewed by 1044

Data Envelopment Analysis (DEA) is a non-parametric technique which is based on mathematical programming for evaluating the efficiency of a set of Decision Making Units (DMUs). Throughout applications, managers encounter with stochastic data and the necessity of having a method that is able [...] Read more.

Data Envelopment Analysis (DEA) is a non-parametric technique which is based on mathematical programming for evaluating the efficiency of a set of Decision Making Units (DMUs). Throughout applications, managers encounter with stochastic data and the necessity of having a method that is able to evaluate efficiency and rank efficient units has been under consideration. In this paper considering the concept of coefficient of variation among efficient DMUs, two ranking methods has been proposed. Within these ranking methods, a DMU will have a higher rank if it's coefficient of variation be smaller. These methods are suitable when managers are able to determine weights on coefficient of variations or on inputs and outputs. At the end we applied these methods on a numerical example. Full article

278 KiB

Open AccessArticle

Prediction of Head, Efficiency, and Power Characteristics in a Semi-Open Impeller

by Mustafa Gölcü, Yasar Pancar, H. Sevil Ergür and Esrah Ö. Göral

Math. Comput. Appl. 2010, 15(1), 137-147; https://doi.org/10.3390/mca15010137 - 01 Apr 2010

Cited by 3 | Viewed by 1169

Abstract

Artificial Neural Network (ANN) was used to predict the effects of splitter blades in a semi-open impeller on centrifugal pump performance. The characteristics of this impeller were compared with those of impellers without splitter blades. Experimental results for lengths of splitter blades in [...] Read more.

Artificial Neural Network (ANN) was used to predict the effects of splitter blades in a semi-open impeller on centrifugal pump performance. The characteristics of this impeller were compared with those of impellers without splitter blades. Experimental results for lengths of splitter blades in ratio of 1/3, 2/3, and 3/3 of the main blade length were evaluated by different ANN training algorithm. Training and test data were obtained from experimental studies. The best training algorithm and number of neurons were determined. The values of head, efficiency, and effective power were estimated in a semi-open impeller with splitter blades in ratio of 3/6 and 5/6 of the main blade length at the best efficiency point (b.e.p.). Here, as the splitter blade length increases; the flow rate and power increases, the efficiency decrease. All of the estimated values of performance in a semi-open impeller with splitter blades indicate the model works in line with expectations. Experimental studies to determine head, efficiency and effective power consumption in different types of pumps are complex, time consuming, and costly. It also requires specific measurement tools to obtain the characteristics values of pump. To overcome these difficulties, an ANN can be used for prediction of pump performance in semi open impeller. Full article

184 KiB

Open AccessArticle

Analysis of B-Spline Curve Using Discrete Fourier Transform

by Ashok Ganguly and Pranjali Arondekar

Math. Comput. Appl. 2010, 15(1), 127-136; https://doi.org/10.3390/mca15010127 - 01 Apr 2010

Cited by 2 | Viewed by 1133

Abstract

We apply the Discrete Fourier Transform to the construction of B-Spline curves to gain more insight into their structure. As a B-Spline curve is determined by its control polygon, this analysis is intimately linked to the Fourier analysis of the control polygon. To [...] Read more.

We apply the Discrete Fourier Transform to the construction of B-Spline curves to gain more insight into their structure. As a B-Spline curve is determined by its control polygon, this analysis is intimately linked to the Fourier analysis of the control polygon. To do this we apply Fast Fourier transform (FFT) algorithm to the structure of B-Spline curve and its rational form. We get inner structure of original B-Spline curve in the transform domain again in the form of B-Spline curve, having control polygon as regular or star polygon. Using the technique mentioned in the paper we get the same curve without change of shape in the transformed case of polygon points. We also extend the idea for the interval form of B-Spline Curve. Full article

204 KiB

Open AccessArticle

Asymptotic Expansions for the Moments of the Boundary Functionals of the Renewal Reward Process with a Discrete Interference of Chance

by Rovshan Aliyev, Nurgul Okur Bekar, Tahir Khaniyev and Ihsan Unver

Math. Comput. Appl. 2010, 15(1), 117-126; https://doi.org/10.3390/mca15010117 - 01 Apr 2010

Cited by 1 | Viewed by 972

Abstract

In this study, two boundary functionals N\(_{1}\) and \(\tau_{1}\) of the renewal reward process with a discrete interference of chance (X(t)) are investigated. A relation between the moment generating function (\(\Psi\)N(z)) of the boundary functional N\(_{1}\) and the Laplace transform (\(\Phi_{\tau}(\mu\))) of the [...] Read more.

In this study, two boundary functionals N\(_{1}\) and \(\tau_{1}\) of the renewal reward process with a discrete interference of chance (X(t)) are investigated. A relation between the moment generating function (\(\Psi\)N(z)) of the boundary functional N\(_{1}\) and the Laplace transform (\(\Phi_{\tau}(\mu\))) of the boundary functional \(\tau_{1}\) is obtained. Using this relation, the exact formulas for the first four moments of the boundary functional \(\tau_{1}\) are expressed by means of the first four moments of the boundary functional N\(_{1}\). Moreover, the asymptotic expansions for the first four moments of these boundary functionals are established when the random variables \(\{\zeta_{n}\}\), \(n \geq 0\), which describe a discrete interference of chance, have an exponential distribution with parameter \(\lambda > 0\) . Finally, the accuracy of the approximation formulas for the moments (EN\(_{1}^{k}\)) of the boundary functional N\(_{1}\) are tested by Monte Carlo simulation method. Full article

172 KiB

Open AccessArticle

A Design of an Expert System for Selecting Pumps Used in Agricultural Irrigation

by Ali Yavuz Seflek and Kazım Çarman

Math. Comput. Appl. 2010, 15(1), 108-116; https://doi.org/10.3390/mca15010108 - 01 Apr 2010

Cited by 1 | Viewed by 1131

Abstract

The economical development of Turkey depends on agriculture so yield in agricultural production has to be increased for improving Turkey’s economy. Irrigation is also very important factor to increase yield per unit area. Different kinds of pumps such as centrifugal, submersible and deep [...] Read more.

The economical development of Turkey depends on agriculture so yield in agricultural production has to be increased for improving Turkey’s economy. Irrigation is also very important factor to increase yield per unit area. Different kinds of pumps such as centrifugal, submersible and deep well turbines are used according to the system conditions for irrigation of agricultural areas. It is very difficult to find an expert at desired time and desired place for choosing correct pump which are varied in different kinds and models. In this study, this problem was to be tried to solve by designing of an expert system. The choosing of proper pump is very important because of the plant efficiency.
The expert system database was formed by using data obtained from commonly used pumps in Turkey. Flow rate and total manometric head which are important for selecting pump were determined by taking into consideration irrigation area, irrigation methods, water resource, climate, soil properties, crop pattern and well characteristics. The software of expert system was developed for Windows operation system by using Visual Basic Programming Language. In this expert system, when the programme is operated, the trademark/model of pump having the lowest specific energy consumption is determined to be the most suitable pump for the plant at the end of the programme. Full article

310 KiB

Open AccessArticle

Effect of Material Properties on Vibrations of Nonsymmetrical Axially Loaded Thin-Walled Euler-Bernoulli Beams

by Gökhan Altıntas

Math. Comput. Appl. 2010, 15(1), 96-107; https://doi.org/10.3390/mca15010096 - 01 Apr 2010

Cited by 6 | Viewed by 1185

Abstract

This paper focuses on effect of material properties on free vibration characteristics of nonsymmetrical axially loaded thin-walled Euler-Bernoulli beams. Many scientists studied the vibration of coupled systems but adequate consideration has not been given to detailed and parametric studies on the effect of [...] Read more.

This paper focuses on effect of material properties on free vibration characteristics of nonsymmetrical axially loaded thin-walled Euler-Bernoulli beams. Many scientists studied the vibration of coupled systems but adequate consideration has not been given to detailed and parametric studies on the effect of material properties on vibration properties. The current findings of this study show that there have been quite different effects of material properties on the systems without symmetry axis than on the systems with symmetry axis. Material properties are properties affecting the free vibration behavior. Moreover, effect of axial load on natural frequencies was also investigated in this study. Convergence work revealed that the current mathematical model simulated the problem with excellent accuracy. Full article

144 KiB

Open AccessArticle

A New Decomposition Method for Solving System of Nonlinear Equations

by Mustafa Özel

Math. Comput. Appl. 2010, 15(1), 89-95; https://doi.org/10.3390/mca15010089 - 01 Apr 2010

Cited by 6 | Viewed by 1018

Abstract

In this paper, an efficient decomposition method is constructed and used for solving system of nonlinear equations. The method based on the decomposition technique of Noor [M.A.Noor, K.I.Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput. 183(2006), 774-779]. This technique is revised [...] Read more.

In this paper, an efficient decomposition method is constructed and used for solving system of nonlinear equations. The method based on the decomposition technique of Noor [M.A.Noor, K.I.Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput. 183(2006), 774-779]. This technique is revised to solve the system of nonlinear equations. Some illustrative examples have been presented, to demonstrate the proposed method and the results are compared with those derived from the previous methods. All test problems reveals the accuracy and fast convergence of the suggested method. Full article

192 KiB

Open AccessArticle

The Investigation of Even-Even ^114-120Xe Isotopes by the Framework of IBA

by Ismail Maras, Ramazan Gümüs and Nurettin Türkan

Math. Comput. Appl. 2010, 15(1), 79-88; https://doi.org/10.3390/mca15010079 - 01 Apr 2010

Cited by 3 | Viewed by 1313

Abstract

In this work, the ground state, quasi beta and quasi gamma band energies of ^{114,116,118,120}Xe isotopes have been investigated by using the both (IBM-1 and IBM-2) versions of interacting boson model (IBM). In calculations, the theoretical energy levels have been obtained by [...] Read more.

In this work, the ground state, quasi beta and quasi gamma band energies of ^{114,116,118,120}Xe isotopes have been investigated by using the both (IBM-1 and IBM-2) versions of interacting boson model (IBM). In calculations, the theoretical energy levels have been obtained by using PHINT and NP-BOS program codes. The presented results are compared with the experimental data in respective tables and figures. At the end, it was seen that the obtained theoretical results are in good agreement with the experimental data. Full article

268 KiB

Open AccessArticle

Neural Network Model for Moment-Curvature Relationship of Reinforced Concrete Sections

by Muhiddin Bağcı

Math. Comput. Appl. 2010, 15(1), 66-78; https://doi.org/10.3390/mca15010066 - 01 Apr 2010

Cited by 4 | Viewed by 1129

Abstract

The analysis of moment-curvature relationship of reinforced concrete sections is complex due to large number of variables as well as non-linear material behavior involved. Artificial Neural Networks (ANNs) are found to be a tool capable of solving such problems. This has led to [...] Read more.

The analysis of moment-curvature relationship of reinforced concrete sections is complex due to large number of variables as well as non-linear material behavior involved. Artificial Neural Networks (ANNs) are found to be a tool capable of solving such problems. This has led to increasing use of ANN for analyzing the behavior of reinforced concrete sections. This paper reports the details of a study conducted using ANN for predicting moment-curvature relationship of a reinforced concrete section. Using data generated based on the analytical solutions, the ANN model was trained. The trained model was tested for a different set of input parameters and the output values were compared with the values based on analytical results. The agreement was found to be good. Full article

226 KiB

Open AccessArticle

Free Vibration Analysis of Carbon Nanotubes Based on Shear Deformable Beam Theory by Discrete Singular Convolution Technique

by Çiğdem Demir, Ömer Civalek and Bekir Akgöz

Math. Comput. Appl. 2010, 15(1), 57-65; https://doi.org/10.3390/mca15010057 - 01 Apr 2010

Cited by 89 | Viewed by 1860

Abstract

In this study, free vibration analysis of carbon nanotubes is investigated based on Timoshenko beam theory. Discrete singular convolution (DSC) method is used for free vibration problem of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in [...] Read more.

In this study, free vibration analysis of carbon nanotubes is investigated based on Timoshenko beam theory. Discrete singular convolution (DSC) method is used for free vibration problem of numerical solution of carbon nanotubes. Numerical results are presented and compared with that available in the literature. It is shown that reasonable accurate results are obtained. Full article

289 KiB

Open AccessArticle

Approximate Solution of Higher Order Linear Differential Equations by Means of a New Rational Chebyshev Collocation Method

by Salih Yalçınbas, Nesrin Özsoy and Mehmet Sezer

Math. Comput. Appl. 2010, 15(1), 45-56; https://doi.org/10.3390/mca15010045 - 01 Apr 2010

Cited by 7 | Viewed by 1275

Abstract

In this paper, a new approximate method for solving higher-order linear ordinary differential equations with variable coefficients under the mixed conditions is presented. The method is based on the rational Chebyshev (RC) Tau, Chebyshev and Taylor collocation methods. The solution is obtained in [...] Read more.

In this paper, a new approximate method for solving higher-order linear ordinary differential equations with variable coefficients under the mixed conditions is presented. The method is based on the rational Chebyshev (RC) Tau, Chebyshev and Taylor collocation methods. The solution is obtained in terms of rational Chebyshev (RC) functions. Also, illustrative examples are given to demonstrate the validity and applicability of the method. Full article

501 KiB

Open AccessArticle

Tibial Rotation Assessment Using Artificial Neural Networks

by B. Gültekin Çetiner and Murat Sarı

Math. Comput. Appl. 2010, 15(1), 34-44; https://doi.org/10.3390/mca15010034 - 01 Apr 2010

Cited by 5 | Viewed by 1364

Abstract

Assessment of the tibial rotations by the conventional approaches is generally difficult. An investigation has been made in this study to assess the tibial motions based on the prediction of the effects of physical factors as well as a portion of tibial measurements [...] Read more.

Assessment of the tibial rotations by the conventional approaches is generally difficult. An investigation has been made in this study to assess the tibial motions based on the prediction of the effects of physical factors as well as a portion of tibial measurements by making use of Artificial Neural Networks (ANN). Therefore, this study aimed at the prediction of the relations between several physical factors and tibial motion measurements in terms of Artificial Neural Networks. These factors include gender, age, weight, and height. Data collected for 484 healthy subjects have been analyzed by Artificial Neural Networks. Promising results showed that the ANN has been found to be appropriate for modeling and simulation in the data assessments. The paper gives detailed results regarding the use of ANN for modeling tibial rotations in terms of physical factors. The study shows the feasibility of ANN to predict the behaviour of knee joints. Full article

151 KiB

Open AccessArticle

Determining Spot Price and Economic Dispatch in Deregulated Power Systems

by Abdullah Urkmez and Nurettin Cetinkaya

Math. Comput. Appl. 2010, 15(1), 25-33; https://doi.org/10.3390/mca15010025 - 01 Apr 2010

Cited by 2 | Viewed by 1075

Abstract

This paper presents a new formula for determining spot price and a new algorithm for economic dispatch in deregulated power systems. According to participant’s biddings, an independent system operator (ISO) manages deregulated power systems (DPS) and decides transaction between participants. ISO aims to [...] Read more.

This paper presents a new formula for determining spot price and a new algorithm for economic dispatch in deregulated power systems. According to participant’s biddings, an independent system operator (ISO) manages deregulated power systems (DPS) and decides transaction between participants. ISO aims to obtain minimum cost for entire power system. However each participant aims to work with minimum cost for only themselves. Each participant in DPS shares expensive operating and upkeep costs. Energy sources are used more efficient. Energy prices are determined according to the costs. The proposed algorithm considers price / power bids, generating / demand balance and generating units’ constraints. The results are shown on the IEEE 30 bus standart test system. Full article

1542 KiB

Open AccessArticle

A Study for Boronizing Process within Nonextensive Thermostatistics

by Özhan Kayacan, Salim Sahin and Filiz Tastan

Math. Comput. Appl. 2010, 15(1), 14-24; https://doi.org/10.3390/mca15010014 - 01 Apr 2010

Cited by 6 | Viewed by 1143

Abstract

In this study, diffusion mechanism of the boronizing process of AISI 1040 has been investigated. A nonlinear diffusion equation, which was proposed earlier, has been employed and compared with the experimental data. An interesting property of the diffusion equation used here is that [...] Read more.

In this study, diffusion mechanism of the boronizing process of AISI 1040 has been investigated. A nonlinear diffusion equation, which was proposed earlier, has been employed and compared with the experimental data. An interesting property of the diffusion equation used here is that it establishes a connection between the diffusion process and nonextensivity. The theoretical model also exhibits a possible connection between the exponents appeared in the differential equation and the entropic index. In this manner, the possible effects of nonextensivity on the boronizing process have been shown theoretically. We believe that a diffusion equation based on the nonextensive formalism is first applied to the boronizing process in literature. Full article

1330 KiB

Open AccessArticle

Strength of Wheat and Barley Stems and Design of New Beam/Columns

by Gözde Değer, Mehmet Pakdemirli, Feyza Candan, Selda Akgün and Hakan Boyacı

Math. Comput. Appl. 2010, 15(1), 1-13; https://doi.org/10.3390/mca15010001 - 01 Apr 2010

Viewed by 1167

Abstract

In this study, physical and mechanical properties of wheat and barley stems are examined. Transverse sections of the stems are magnified by a microscope and the material structure in the transverse sections are analysed with image processing programs. Geometric properties such as inner, [...] Read more.

In this study, physical and mechanical properties of wheat and barley stems are examined. Transverse sections of the stems are magnified by a microscope and the material structure in the transverse sections are analysed with image processing programs. Geometric properties such as inner, outer radius, stem wall thickness and density variation of the material along the radius are measured and density variations are approximated by a mathematical model. Moment of inertia of the cross-sectional area which plays a vital role in resistance against bending and buckling is calculated approximately. Using the material density variations of the wheat (Triticum sativum L.) stems, new beam/columns are designed. Stress distributions in this new design and conventional designs of equivalent weight are compared using ANSYS program. It is found that stresses are more uniformly distributed in the new design with maximum stresses being lower than the conventional designs. Full article

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Math. Comput. Appl., Volume 15, Issue 1 (April 2010) – 15 articles , Pages 1-155

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