Mathematical and Computational Applications

338 KiB

Open AccessArticle

Taiex Index Option Model by Using Nonlinear Differential Equation

by Tsung-Jui Chiang Lin, Meng-Rong Li and Yong Shiuan Lee

Math. Comput. Appl. 2014, 19(1), 78-92; https://doi.org/10.3390/mca19010078 - 01 Apr 2014

Cited by 7 | Viewed by 1330

In this study we treat TXO price as a dynamic system which changes over time and characterize it by differential equations. Our goal is to construct a model more suitable for TXO. We use ―Parabola Approximation‖ proposed by Li et al. (2011) to [...] Read more.

In this study we treat TXO price as a dynamic system which changes over time and characterize it by differential equations. Our goal is to construct a model more suitable for TXO. We use ―Parabola Approximation‖ proposed by Li et al. (2011) to solve the differential equations and try to find the model which fits our data the most. Empirical study shows the model used all produce accurate estimates of TXO prices. Full article

198 KiB

Open AccessArticle

On Characterization of Inextensible Flows of Curves According to Type-2 Bishop Frame E3

by Sezai Kızıltuğ

Math. Comput. Appl. 2014, 19(1), 69-77; https://doi.org/10.3390/mca19010069 - 01 Apr 2014

Cited by 1 | Viewed by 1154

Abstract

In this paper, we study inextensible flows of curves according to type-2 Bishop frame in Euclidean 3-space. Necessary and sufficient conditions for an inextensible curve flow are expressed as a partial differential equation involving the curvature. Full article

793 KiB

Open AccessArticle

Optimizing Hybrid Basis Function Types in Functional Network Design via Cultural Algorithm

by Peigang Guo and Yongquan Zhou

Math. Comput. Appl. 2014, 19(1), 50-68; https://doi.org/10.3390/mca19010050 - 01 Apr 2014

Viewed by 1465

Abstract

In this paper, a novel functional network designing method based on cultural algorithm is proposed. This method can get the hybrid basis function and its parameters with optimal searching achieving the learning between functional network structure and the functional parameters, and each model [...] Read more.

In this paper, a novel functional network designing method based on cultural algorithm is proposed. This method can get the hybrid basis function and its parameters with optimal searching achieving the learning between functional network structure and the functional parameters, and each model of the initial set is evaluated by the adjusted R − squared criterion (R_a²) , to find the optimal basis functions and functional parameters. Finally, the simulation experiments show that the proposed constructive functional network design scheme is feasible, and can obtain better generalization property. Full article

571 KiB

Open AccessArticle

Fault Diagnosis of Shaft- Ball Bearing System Using One-Way Analysis of Variance

by Mustafa Yuzukirmizi and Hakan Arslan

Math. Comput. Appl. 2014, 19(1), 37-49; https://doi.org/10.3390/mca19010037 - 01 Apr 2014

Cited by 2 | Viewed by 1262

Abstract

Roller bearing is one of the most widely used and critical elements in rotating machinery. In consequence, bearing fault diagnosis in machines, as well as to discriminate the different fault conditions have been a great interest. In this study, firstly, analytical model of [...] Read more.

Roller bearing is one of the most widely used and critical elements in rotating machinery. In consequence, bearing fault diagnosis in machines, as well as to discriminate the different fault conditions have been a great interest. In this study, firstly, analytical model of a shaft-ball bearing system is developed. The shaft is assumed to be perfectly rigid and uniform, and supported by two radial ball bearings. Then, the effect of localized defects on bearing running surfaces (i.e. surfaces of inner and outer rings and balls) on the shaft vibrations are obtained using the simulation program. Then, vibration signatures are analyzed by one-way analysis of variance (ANOVA) method. Finally, post-hoc tests are applied to differentiate the ball bearing element's localized defects in shaft-ball bearing simulation model. Full article

683 KiB

Open AccessArticle

Authorship Attribution Using Principal Component Analysis and Competitive Neural Networks

by Mehmet Can

Math. Comput. Appl. 2014, 19(1), 21-36; https://doi.org/10.3390/mca19010021 - 01 Apr 2014

Cited by 8 | Viewed by 1517

Abstract

Feature extraction is a common problem in statistical pattern recognition. It refers to a process whereby a data space is transformed into a feature space that, in theory, has exactly the same dimension as the original data space. However, the transformation is designed [...] Read more.

Feature extraction is a common problem in statistical pattern recognition. It refers to a process whereby a data space is transformed into a feature space that, in theory, has exactly the same dimension as the original data space. However, the transformation is designed in such a way that the data set may be represented by a reduced number of "effective" features and yet retain most of the intrinsic information content of the data; in other words, the data set undergoes a dimensionality reduction. Principal component analysis is one of these processes. In this paper the data collected by counting selected syntactic characteristics in around a thousand paragraphs of each of the sample books underwent a principal component analysis. Authors of texts identified by the competitive neural networks, which use these effective features. Full article

390 KiB

Open AccessArticle

A Proposal for a Distinction in Belief Functions I

by Mehmet Nebioğlu, Tarık Çakar and Raşit Köker

Math. Comput. Appl. 2014, 19(1), 12-20; https://doi.org/10.3390/mca19010012 - 01 Apr 2014

Viewed by 1199

Abstract

This study proposes a distinction between the belief function and the credibility function in mind design – a section of artificial intelligence. We show the distinction between the credibility and belief measures first. Then we evaluate the possibility of these measures in case [...] Read more.

This study proposes a distinction between the belief function and the credibility function in mind design – a section of artificial intelligence. We show the distinction between the credibility and belief measures first. Then we evaluate the possibility of these measures in case studies and consider the credibility and belief values of each case. This is a novel method for the evaluation of belief functions and it is shown that they satisfy the rules of current belief function axioms. Full article

347 KiB

Open AccessArticle

Chance Constrained Data Envelopment Analysis for Efficiency Analysis: An Application to Turkish Manufacture of Iron and Steel Sector

by Hakan Gedik, Hasan Bal and Mahmut İzciler

Math. Comput. Appl. 2014, 19(1), 1-11; https://doi.org/10.3390/mca19010001 - 01 Apr 2014

Viewed by 1347

Abstract

This study aims to determine the technical efficiency levels of the enterprises active in the “Manufacture of Basic Iron and Steel and of Ferro-Alloys” sector in Turkey. The inputs and outputs are deterministic in classical Data Envelopment Analysis, so the changes in exchange [...] Read more.

This study aims to determine the technical efficiency levels of the enterprises active in the “Manufacture of Basic Iron and Steel and of Ferro-Alloys” sector in Turkey. The inputs and outputs are deterministic in classical Data Envelopment Analysis, so the changes in exchange rate, inflation rate, etc. aren’t considered, and the precautions for future inconsistencies are not foreseen. This leads to critics of deterministic Data Envelopment Analysis models. In this paper, the additive model developed depending on the Banker, Charnes and Cooper (BCC) model was extended by chance constrained programming formulations in order to overcome the insufficiencies in deterministic Data Envelopment Analysis, and the technical analysis of “Manufacture of Basic Iron and Steel and of Ferro-Alloys” sector was performed. Full article

403 KiB

Open AccessArticle

Comparative Study of Algorithms for Response Surface Optimization

by Özgür Yeniay

Math. Comput. Appl. 2014, 19(1), 93-104; https://doi.org/10.3390/mca19010093 - 01 Jan 2014

Cited by 19 | Viewed by 1295

Abstract

Response Surface Methodology (RSM) is a method that uses a combination of statistical techniques and experimental design for modelling and optimization problems. Many researchers have studied the integration of heuristic methods and RSM in recent years. The purpose of this study is to [...] Read more.

Response Surface Methodology (RSM) is a method that uses a combination of statistical techniques and experimental design for modelling and optimization problems. Many researchers have studied the integration of heuristic methods and RSM in recent years. The purpose of this study is to compare two popular heuristic methods, namely Genetic Algorithms (GA) and Simulated Annealing (SA), with two commonly used gradient-based methods, namely Sequential Quadratic Programming (SQP) and Generalized Reduced Gradient (GRG), to obtain optimal conditions. Moreoever, real quadratic and cubic response surface models are selected from literature and used in this study. The comparison results indicate that the heuristic methods outperform the traditional methods on majority of the problems. Full article

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Math. Comput. Appl., Volume 19, Issue 1 (April 2014) – 8 articles , Pages 1-104

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