Mathematical and Computational Applications

184 KiB

Open AccessArticle

Examining of Tetragonal Surface Patches with Their Geometric Properties and Relationships

by A. Caliskan and Y. Yuzcelik

Math. Comput. Appl. 2005, 10(1), 155-163; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010155 - 01 Apr 2005

Viewed by 1040

In this paper, the geometric properties and relationships of the rectangular are applied to a tetragonal surface patch. Then, O. Bonnet integral formula is generalized for the tetragonal surface patchs which are bounded with a curvatural polygon. Full article

329 KiB

Open AccessArticle

Assessment of Optimum Tip Speed Ratio of Wind Turbines

by N. S. Çetin, M. A. Yurdusev, R. Ata and A. Özdamar

Math. Comput. Appl. 2005, 10(1), 147-154; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010147 - 01 Apr 2005

Cited by 59 | Viewed by 3387

Abstract

The first thing to do in wind turbine blade design is to select tip speed ratio. Generally speaking, the speed ratio depends on the profile type used and the number of blades. Various speed ratios could be chosen for different types of profiles [...] Read more.

The first thing to do in wind turbine blade design is to select tip speed ratio. Generally speaking, the speed ratio depends on the profile type used and the number of blades. Various speed ratios could be chosen for different types of profiles with different number of blades. Therefore, an optimization procedure should be applied to find the best ratio since this directly affects the energy generated from the turbine and in turn the investment made. This study presents a procedure to assess the optimum speed ratios for various profile types used in practice with various numbers of blades. Full article

147 KiB

Open AccessArticle

Approximate Symmetries of Hyperbolic Heat Conduction Equation with Temperature Dependent Thermal Properties

by M. Pakdemirli and A. Z. Şahin

Math. Comput. Appl. 2005, 10(1), 139-145; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010139 - 01 Apr 2005

Cited by 4 | Viewed by 1162

Abstract

Hyperbolic heat conduction equation with temperature dependent thermal properties is considered. The thermal conductivity, specific heat and density are assumed to be functions of temperature. The equation is cast into a non-dimensional form suitable for perturbation analysis. By employing a newly developed approximate [...] Read more.

Hyperbolic heat conduction equation with temperature dependent thermal properties is considered. The thermal conductivity, specific heat and density are assumed to be functions of temperature. The equation is cast into a non-dimensional form suitable for perturbation analysis. By employing a newly developed approximate symmetry theory, the approximate symmetries of the equation are calculated for the case of small variations in thermal properties. Various similarity solutions corresponding to the symmetries of first order equations are presented. For second order equations, the method of constructing approximate symmetries and similarity solutions are discussed. A linear functional variation is assumed for the thermal properties and a similarity solution is constructed using one of the first order solutions as an example. Full article

151 KiB

Open AccessArticle

Enlarged Ionization Region and Wiley-McLaren Type Geometry

by Ş. Şentürk

Math. Comput. Appl. 2005, 10(1), 133-138; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010133 - 01 Apr 2005

Cited by 1 | Viewed by 1075

Abstract

The ionization region of the ToF mass spectrometer having the Wiley- McLaren geometry was further enlarged on the basis of the Milani–de Heer criteria. The enlarging limits the use of the spectrometer to small cluster range as a result of mass resolution decrease [...] Read more.

The ionization region of the ToF mass spectrometer having the Wiley- McLaren geometry was further enlarged on the basis of the Milani–de Heer criteria. The enlarging limits the use of the spectrometer to small cluster range as a result of mass resolution decrease at great deal amount. However the spectrometer is promising for the electron-cluster interaction studies. Full article

197 KiB

Open AccessArticle

Dynamic System Modeling Using Rules3 Induction Algorithm

by M. Sabih Aksoy

Math. Comput. Appl. 2005, 10(1), 121-132; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010121 - 01 Apr 2005

Cited by 2 | Viewed by 1108

Abstract

This paper describes the use of a new induction algorithm to derive production rules for modelling dynamic systems. The algorithm, called RULES-3, is an efficient tool for extracting a compact set of IF-THEN rules from a collection of examples to classify objects into [...] Read more.

This paper describes the use of a new induction algorithm to derive production rules for modelling dynamic systems. The algorithm, called RULES-3, is an efficient tool for extracting a compact set of IF-THEN rules from a collection of examples to classify objects into known categories. The paper summarises the operation of RULES-3 and presents the results obtained in the modelling of two linear systems and two non-linear systems. Full article

113 KiB

Open AccessArticle

Pruning Decision Trees using Rules3 Inductive Learning Algorithm

by Mehmet Sabih Aksoy

Math. Comput. Appl. 2005, 10(1), 113-120; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010113 - 01 Apr 2005

Cited by 2 | Viewed by 1342

Abstract

One important disadvantage of decision tree based inductive learning algorithms is that they use some irrelevant values to establish the decision tree. This causes the final rule set to be less general. To overcome with this problem the tree has to be pruned. [...] Read more.

One important disadvantage of decision tree based inductive learning algorithms is that they use some irrelevant values to establish the decision tree. This causes the final rule set to be less general. To overcome with this problem the tree has to be pruned. In this article using the recently developed RULES inductive learning algorithm, pruning of a decision tree is explained. The decision tree is extracted for an example problem using the ID3 algorithm and then is pruned using RULES. The results obtained before and after pruning are compared. This shows that the pruned decision tree is more general. Full article

159 KiB

Open AccessArticle

Null Generalized Helices in L3 and L4, 3 and 4-Dimensional Lorentzian Space

by Ayse Funda Yalınız and H. Hilmi Hacısalihoğlu

Math. Comput. Appl. 2005, 10(1), 105-111; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010105 - 01 Apr 2005

Cited by 2 | Viewed by 1066

Abstract

In this paper we obtain the harmonic curvatures of a null generalized helix in L3 and L4 , 3 and 4-dimensional Lorentzian spaces. Thus we another definitions of null generalized helix in terms of harmonic curvatures. Also we find the relation [...] Read more.

In this paper we obtain the harmonic curvatures of a null generalized helix in L3 and L4 , 3 and 4-dimensional Lorentzian spaces. Thus we another definitions of null generalized helix in terms of harmonic curvatures. Also we find the relation of between Frenet frame, slope axis and curvature functions 1 k , 2 k of null generalized helix. Finally we characterize the null helices thanks to harmonic curvatures in L3 and L4 , 3 and 4- dimensional Lorentzian space. Full article

140 KiB

Open AccessArticle

Formulas for the Exponential of a Semi Skew-Symmetric Matrix of Order 4

by Levent Kula, Murat Kemal Karacan and Yusuf Yaylı

Math. Comput. Appl. 2005, 10(1), 99-104; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010099 - 01 Apr 2005

Cited by 9 | Viewed by 1460

Abstract

In this paper the formula of the exponential matrix e ^A when A is a semi skew-symmetric real matrix of order 4 is derived. The formula is a generalization of the Rodrigues formula for skew-symmetric matrices of order 3 in Minkowski 3-space. Full article

181 KiB

Open AccessArticle

A Comparison of the Stress Analysis of an Unrestored and Restored Tooth with Amalgam and Composite Resin

by Halil Aykul and Mustafa Toparlı

Math. Comput. Appl. 2005, 10(1), 89-98; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010089 - 01 Apr 2005

Cited by 2 | Viewed by 1199

Abstract

Finite element models were developed for an unrestored tooth and restored tooth. The tooth was considered to be in a restored state with amalgam and composite resin on glass-ionomer as the base material. For this study, an axisymmetric model of a maxillary second [...] Read more.

Finite element models were developed for an unrestored tooth and restored tooth. The tooth was considered to be in a restored state with amalgam and composite resin on glass-ionomer as the base material. For this study, an axisymmetric model of a maxillary second premolar that included an alveolar bone was used. A load of 200 N at an angle of 45o to the radial axis was applied on the occlusal margin of the tooth. The tooth was assumed isotropic, homogenous and elastic. The authors using FORTRAN 77 prepared all calculation programs. The distributions of radial axial and shear stresses were plotted with length of radial for some critical points. Full article

179 KiB

Open AccessArticle

The Effects of Duct Shape on the Nusselt Number

by M. Emin Erdoğan and C. Erdem Imrak

Math. Comput. Appl. 2005, 10(1), 79-88; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010079 - 01 Apr 2005

Cited by 3 | Viewed by 1189 | Correction

Abstract

This article considers the effect of duct shape on the Nusselt number. In order to show the effects of duct shape on the Nusselt number, four illustrative examples are given: the heat transfer in a duct of rectangular cross-section, heat transfer in a [...] Read more.

This article considers the effect of duct shape on the Nusselt number. In order to show the effects of duct shape on the Nusselt number, four illustrative examples are given: the heat transfer in a duct of rectangular cross-section, heat transfer in a duct of semicircular cross-section, the heat transfer in a duct of circular crosssection and heat transfer between two parallel plates. The method used in this paper is general and it can be applied al flows. It is not necessary to use thin plate analogy, first, the velocity distribution is obtained and then the temperature distribution is found. It is shown that the Nusselt numbers calculated for the four examples cited depend not only on duct shape but also on wall friction. Full article

145 KiB

Open AccessArticle

Modified LSM for Calibration of Measuring Apparatus

by Chingiz Hajiyev

Math. Comput. Appl. 2005, 10(1), 71-77; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010071 - 01 Apr 2005

Viewed by 1085

Abstract

Modified least squares method (LSM) is developed that take into account errors in input standard signals for calibration of measuring devices. Calibration of the differential pressure gage by the standard control-point setting mechanisms is demonstrated in the paper as an example. The accuracy [...] Read more.

Modified least squares method (LSM) is developed that take into account errors in input standard signals for calibration of measuring devices. Calibration of the differential pressure gage by the standard control-point setting mechanisms is demonstrated in the paper as an example. The accuracy of the coefficient estimates changes when the errors of the control-point setting mechanisms are taken into account. Using the LSM in the classic form for the mentioned case gives wrong estimation errors in the final estimations of calibration curve coefficients. Therefore, for estimation of errors, characteristics of fractional errors are proposed use and as a variance of estimations errors guarantee the stability of the final estimation values. Full article

270 KiB

Open AccessArticle

Neural Network Classification of EEG Signals by Using AR with MLE Preprocessing for Epileptic Seizure Detection

by Abdulhamit Subasi, M. Kemal Kiymik, Ahmet Alkan and Etem Koklukaya

Math. Comput. Appl. 2005, 10(1), 57-70; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010057 - 01 Apr 2005

Cited by 45 | Viewed by 1876

Abstract

The purpose of the work described in this paper is to investigate the use of autoregressive (AR) model by using maximum likelihood estimation (MLE) also interpretation and performance of this method to extract classifiable features from human electroencephalogram (EEG) by using Artificial Neural [...] Read more.

The purpose of the work described in this paper is to investigate the use of autoregressive (AR) model by using maximum likelihood estimation (MLE) also interpretation and performance of this method to extract classifiable features from human electroencephalogram (EEG) by using Artificial Neural Networks (ANNs). ANNs are evaluated for accuracy, specificity, and sensitivity on classification of each patient into the correct two-group categorization: epileptic seizure or non-epileptic seizure. It is observed that, ANN classification of EEG signals with AR gives better results and these results can also be used for detecting epileptic seizure. Full article

164 KiB

Open AccessArticle

Penalty Function Methods for Constrained Optimization with Genetic Algorithms

by Özgür Yeniay

Math. Comput. Appl. 2005, 10(1), 45-56; https://doi.org/10.3390/mca10010045 - 01 Apr 2005

Cited by 510 | Viewed by 9715

Abstract

Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use [...] Read more.

Genetic Algorithms are most directly suited to unconstrained optimization. Application of Genetic Algorithms to constrained optimization problems is often a challenging effort. Several methods have been proposed for handling constraints. The most common method in Genetic Algorithms to handle constraints is to use penalty functions. In this paper, we present these penalty-based methods and discuss their strengths and weaknesses. Full article

153 KiB

Open AccessArticle

An Investigation for Semi-Rigid Frames by Different Connection Models

by Ali Uğur Öztürk and Mutlu Seçer

Math. Comput. Appl. 2005, 10(1), 35-44; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010035 - 01 Apr 2005

Cited by 8 | Viewed by 1095

Abstract

A review is made of the development of models used to examine the dynamic response of semi-rigid frames. The connection flexibility is modeled by linear elastic rotational springs. The reducing coefficients and the lateral rigidity values are determined by using a computer program. [...] Read more.

A review is made of the development of models used to examine the dynamic response of semi-rigid frames. The connection flexibility is modeled by linear elastic rotational springs. The reducing coefficients and the lateral rigidity values are determined by using a computer program. Response characteristics of frames are compared with reference to their modal attributes. Full article

139 KiB

Open AccessArticle

Special Two Parameter Motion

by Murat Kemal Karacan and Yusuf Yaylı

Math. Comput. Appl. 2005, 10(1), 27-34; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010027 - 01 Apr 2005

Cited by 2 | Viewed by 1034

Abstract

In this study all one parameter motions obtained from two parameters motion on the plane, are investigated. It is shown that the pole points which on fixed and moving plane at any position of (λ,μ) are on a line [...] Read more.

In this study all one parameter motions obtained from two parameters motion on the plane, are investigated. It is shown that the pole points which on fixed and moving plane at any position of (λ,μ) are on a line. It is also shown that the velocity vector lengths of these axis are the same. Moreover, the locus of any Hodograph of any point, and accelaration poles of the motion are investigated. Full article

175 KiB

Open AccessArticle

Monte Carlo Simulation for Electron Dynamics in Semiconductor Devices

by Mustafa Akarsu and Ömer Özbaş

Math. Comput. Appl. 2005, 10(1), 19-26; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010019 - 01 Apr 2005

Cited by 9 | Viewed by 1419

Abstract

The single-particle Monte Carlo simulation for the electron transport in semiconductor devices is presented. The Monte Carlo method is briefly compared with alternative theoretical techniques. Flowchart of the simulation program is given and selections of free flight time, scattering mechanism and electron wave [...] Read more.

The single-particle Monte Carlo simulation for the electron transport in semiconductor devices is presented. The Monte Carlo method is briefly compared with alternative theoretical techniques. Flowchart of the simulation program is given and selections of free flight time, scattering mechanism and electron wave vector are explained. Determination of mean electron velocity and energy is presented. Full article

209 KiB

Open AccessArticle

IBM-1 Calculations on the Even-Even 122-128Te Isotopes

by Atalay Küçükbursa, Kaan Manisa, Mehmet Çiftçi, Tahsin Babacan and İsmail Maraş

Math. Comput. Appl. 2005, 10(1), 9-17; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010009 - 01 Apr 2005

Cited by 9 | Viewed by 1154

Abstract

The ^122-128Te isotopes in O(6)- SU(5) transition region were investigated. For these nuclei, the energy levels, B(E2) transition probabilities, and d(E2/M1) mixing ratios were calculated within framework of the Interacting Boson Model (IBM-1). The results are compared with the experimental data and [...] Read more.

The ^122-128Te isotopes in O(6)- SU(5) transition region were investigated. For these nuclei, the energy levels, B(E2) transition probabilities, and d(E2/M1) mixing ratios were calculated within framework of the Interacting Boson Model (IBM-1). The results are compared with the experimental data and the previous calculations. It is shown that there is a good agreement between the results found and especially with the experimental ones. Full article

151 KiB

Open AccessArticle

Dynamic Analysis of Semi-Rigid Frames

by Ali Ugur Ozturk and Hikmet H. Catal

Math. Comput. Appl. 2005, 10(1), 1-8; https://0-doi-org.brum.beds.ac.uk/10.3390/mca10010001 - 01 Apr 2005

Cited by 13 | Viewed by 1631

Abstract

The dynamic response of semi-rigid frames is studied by using a computer program. The connection flexibility is modeled by linear elastic rotational springs. Having the same geometry and cross-section; semi-rigid frames, with different spring coefficients, are examined. The reducing coefficients and lateral rigidity [...] Read more.

The dynamic response of semi-rigid frames is studied by using a computer program. The connection flexibility is modeled by linear elastic rotational springs. Having the same geometry and cross-section; semi-rigid frames, with different spring coefficients, are examined. The reducing coefficients and lateral rigidity values, representing the real behavior of frames, are determined for each frame. To represent the real behavior, all deformations of a frame are accounted for a dynamic analysis. Response characteristics of five different multistory frames are compared with reference to their modal attributes. The study indicates that connection flexibility tends to increase vibration periods, especially in lower modes, while it causes vibration frequencies decrease. Full article

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Math. Comput. Appl., Volume 10, Issue 1 (April 2005) – 18 articles , Pages 1-163

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