Mathematical and Computational Applications

154 KiB

Open AccessArticle

Biquaternionic Description of the Schrödinger Equation

by Murat TANIŞLI and Süleyman DEMİR

Math. Comput. Appl. 2012, 17(2), 176-181; https://doi.org/10.3390/mca17020176 - 1 Aug 2012

Viewed by 1256

This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are currently popular in particle physics and condensed-matter physics, has been re-written by [...] Read more.

This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are currently popular in particle physics and condensed-matter physics, has been re-written by biquaternions. The newly biquaternionic Schrödinger equation, which is defined with various assumptions and approaches, also includes the biquaternionic generalized momentum in Hamiltonian. Full article

635 KiB

Open AccessArticle

Vibration Analysis of Rotor Blades of a Farm Wind-Power Plant

by K. Turgut Gürsel, Tufan Çoban and Aydogan Özdamar

Math. Comput. Appl. 2012, 17(2), 164-175; https://doi.org/10.3390/mca17020164 - 1 Aug 2012

Cited by 5 | Viewed by 1447

Abstract

In wind-power plants like in all engineering structures, vibrations are taken into consideration in design phases in order to avoid resonance. This condition occurs when the frequency of the exciting force coincides with one of the natural frequencies of system, which causes dangerously [...] Read more.

In wind-power plants like in all engineering structures, vibrations are taken into consideration in design phases in order to avoid resonance. This condition occurs when the frequency of the exciting force coincides with one of the natural frequencies of system, which causes dangerously large amplitudes. In the present study, natural frequencies of the Rotor blades of NACA (National Advisory Committee for Aeronautics) 4415 and NASA/Langley LS(1) 421MOD series of wind-power plants that deliver energy to be consumed by a farm family with four persons are calculated. Therefore, after designing the rotors, their natural frequencies are determined first by Rayleigh’s Method and next by finite element method. Further for both rotor blades, resonance analysis is carried out by the found excitation of external forces. Full article

184 KiB

Open AccessArticle

A Proposed Model for Candidate Selection Process in Political Parties Based on Fuzzy Logic Methodology

by Yılmaz Gökşen, Onur Doğan and Mete Eminağaoğlu

Math. Comput. Appl. 2012, 17(2), 152-163; https://doi.org/10.3390/mca17020152 - 1 Aug 2012

Cited by 1 | Viewed by 1261

Abstract

Classical logic and classical set theorems are not sufficient enough when it is necessary to deal with complex decision making problems which also involve human experiences. Some researches suggest that senior management usually makes intuitive decisions in the process of selecting the candidates [...] Read more.

Classical logic and classical set theorems are not sufficient enough when it is necessary to deal with complex decision making problems which also involve human experiences. Some researches suggest that senior management usually makes intuitive decisions in the process of selecting the candidates in political parties which brings out the need to derive a new efficient, robust and applicable method. In this study, the qualitative characteristics and their significance level which could be used for the candidate selection process in political parties are determined. The candidate selection process consisting vague inputs is analyzed by fuzzy logic methodology and a quantitative final score has been determined for the candidate. It has been shown that the model provided some realistic and promising results which could enable fur Full article

214 KiB

Open AccessArticle

On the Numerical Solution of Fractional Partial Differential Equations

by Solat Karimi Vanani and Azim Aminataei

Math. Comput. Appl. 2012, 17(2), 140-151; https://doi.org/10.3390/mca17020140 - 1 Aug 2012

Cited by 12 | Viewed by 1940

Abstract

In this paper, a technique generally known as meshless method is presented for solving fractional partial differential equations (FPDEs). Some physical linear and nonlinear experiments such as time-fractional convective-diffusion equation, timefractional wave equation and nonlinear space-fractional Fisher's equation are considered. We present the [...] Read more.

In this paper, a technique generally known as meshless method is presented for solving fractional partial differential equations (FPDEs). Some physical linear and nonlinear experiments such as time-fractional convective-diffusion equation, timefractional wave equation and nonlinear space-fractional Fisher's equation are considered. We present the advantages of using the radial basis functions (RBFs) especially wherein the data points are scattered. Comparing between the numerical results obtained from our method and the other methods confirms the good accuracy of the presented scheme. Full article

59 KiB

Open AccessArticle

Symmetry Reductions and Exact Solutions of a Variable Coefficient (2+1)-Zakharov-Kuznetsov Equation

by L. D. Moleleki, A. G. Johnpillai and C. M. Khalique

Math. Comput. Appl. 2012, 17(2), 132-139; https://doi.org/10.3390/mca17020132 - 1 Aug 2012

Cited by 5 | Viewed by 1371

Abstract

We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to [...] Read more.

We study the generalized (2+1)-Zakharov-Kuznetsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. The Lie point symmetry generators of a special form of the class of equations are derived. We classify the Lie point symmetry generators to obtain the optimal system of onedimensional subalgebras of the Lie symmetry algebras. These subalgebras are then used to construct a number of symmetry reductions and exact group-invariant solutions to the underlying equation. Full article

94 KiB

Open AccessArticle

A Collocation Method for a Class of Nonlinear Singular Integral Equations with a Carleman Shift

by Mohamed M. Allan

Math. Comput. Appl. 2012, 17(2), 121-131; https://doi.org/10.3390/mca17020121 - 1 Aug 2012

Viewed by 1111

Abstract

The paper is concerned with the applicability of the collocation method to a class of nonlinear singular integral equations with a Carleman shift preserving orientation on simple closed smooth Jordan curve in the generalized Holder space H_φ(L). Full article

138 KiB

Open AccessArticle

Discrimination Ability of Time-Domain Features and Rules for Arrhythmia Classification

by Umut Arıkan and Fikret Gürgen

Math. Comput. Appl. 2012, 17(2), 111-120; https://doi.org/10.3390/mca17020111 - 1 Aug 2012

Cited by 3 | Viewed by 1312

Abstract

This study investigates relevant diagnosis information for arrhythmia classification from previously collected cardiac data. Discrimination ability of various time-domain attributes and rules were discussed for automatic diagnosis of arrythmia using electrocardiogram (ECG) signals. Naive Bayes, C4.5, multilayer perceptron (MLP) and support vector machines [...] Read more.

This study investigates relevant diagnosis information for arrhythmia classification from previously collected cardiac data. Discrimination ability of various time-domain attributes and rules were discussed for automatic diagnosis of arrythmia using electrocardiogram (ECG) signals. Naive Bayes, C4.5, multilayer perceptron (MLP) and support vector machines (SVM) algorithms were tested on a number of the input features selected by correlative feature selection (CFS) method. Hot Spot algorithm was employed to extract a number of rules that is useful in diagnosing cardiac problems from ECG signal. 257 time domain features of 452 cases from a cardiac arrhythmia database [1] were used. Various testing configurations and performance measures such as accuracy, TP and FP rates, precision, recall and AUC were considered. The discrimination ability of selected-features and the extracted-rules were demonstrated. Full article

137 KiB

Open AccessArticle

Numerical Elastic Plastic Stress Analysis in a Woven Steel Reinforced Composite Thermoplastic Cantilever Beam

by Semih Benli, Onur Sayman, Metin Sayer and Mustafa Karamolla

Math. Comput. Appl. 2012, 17(2), 100-110; https://doi.org/10.3390/mca17020100 - 1 Aug 2012

Cited by 1 | Viewed by 1273

Abstract

In this study, an elastic-plastic stress analysis has been carried out in a thermoplastic composite cantilever beam. The thermoplastic composite beam was reinforced by steel woven fibers. The beam was loaded uniformly. The orientation angles were chosen as 0°, 15°, 30° and 45°. [...] Read more.

In this study, an elastic-plastic stress analysis has been carried out in a thermoplastic composite cantilever beam. The thermoplastic composite beam was reinforced by steel woven fibers. The beam was loaded uniformly. The orientation angles were chosen as 0°, 15°, 30° and 45°. The finite element models of the beams were developed by using ANSYS software. The obtained results from the nonlinear analyses show that the residual stress component of σ_x is the highest at the fixed end at the upper and lower edges for the 0° orientation. However, it is the highest on or around the elastic plastic boundaries for the 15°, 30° and 45° orientations. The magnitude of the residual stress component of Τ_xy is found to be the highest at or around the axis of the beam at the fixed end. 30° orientation produces the highest stress component of Τ_xy around the axis of the beam. Also, it is found that the magnitude of the residual stress component of σ_xis higher that that of the Τ_xy. Full article

137 KiB

Open AccessArticle

On Strongly Almost Convergent Sequence Spaces of Fuzzy Numbers

by Ekrem Savaş

Math. Comput. Appl. 2012, 17(2), 92-99; https://doi.org/10.3390/mca17020092 - 1 Aug 2012

Viewed by 1191

Abstract

In this paper we define some new almost convergent sequence spaces of fuzzy numbers through a non- negative regular matrix and we also examine some topological properties and some inclusion relations for these new sequence spaces. Full article

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Math. Comput. Appl., Volume 17, Issue 2 (August 2012) – 9 articles , Pages 92-181

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