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Editorial Board

Prof. Metin Demiralp (Turkey),

Prof. A.Kuri-Morales (Mexico),

Prof. V.Mladenov (Bulgaria),

Prof. G.Bognar (Hyngary),

Prof. Lotfi A. Zadeh (USA),

Prof. Leonid Kazovsky (USA),

Prof. T.Kaczorek (Poland),

Prof. L.Chua (USA),

Prof. O.Martin (Romania),

Prof. C.Udriste (Romania),

Prof. N.Mastorakis (Greece),

Prof. D.Bertsekas (USA),

Prof. R.Yager (USA),

Prof. Anping Xu (China),  

Prof. M. A. Breuer (USA),

Prof. M.Wasfy (USA)


All aspects of classic and modern applied mathematics are covered including algebra, differential equations, probability, statistics, operational research, optimization, algorthms theory, computational complexity, control . It appears quarterly.  Special Issues are specially encouraged.


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Issue 1, Volume 6, 2012

Risk Software Application Using a Credit Scoring Model

by Gabriela Mircea, Marilen Pirtea, Mihaela Neamtu, Sandra Bazavan

Abstract: The purpose of this paper is to define a specific credit score model, based on the discriminant analysis in order to complete financial diagnoses on particular predefined classes. The model is built based on a set of observations for which the classes are known. The classes in this paper are made of companies with certain characteristics which reflect the creditworthiness of that entity.
Credit scoring, discriminant analysis, dicriminant indicators, risk assessment, discriminant analysis algorithm
Full Paper, pp. 1-8


Effects of Aircraft Preventive Maintenance on Reliability

by E. Kiyak

Abstract: Preventive maintenance can be described as maintenance of equipment or systems before fault occurs. The main goal of maintenance is to avoid or mitigate the consequences of failure of equipment. It also improves reliability, decreases cost of replacement and system downtime. Preventive maintenance helps provide high level of availability of system function and obtains great return on investments of hardware and software. However, very frequent application of preventive maintenance is not economical though. In order to obtain optimum benefit, this maintenance should be done at proper times. This study aims at explaining the importance of preventive maintenance mathematically. The mean time to failure (MTTF) or the mean time between failures (MTBF) is taken as the reliability criteria. The reliability values obtained when preventive maintenance is applied and not applied are compared to the MTTF.
Mean time to failure, Preventive maintenance, Reliability, Strategic decision making
Full Paper, pp. 9-16


A Fundamental Conception to Formulate Image Data Hiding Scheme Based on Error Diffusion from Stochastic Viewpoint

by Masakazu Higuchi, Shuji Kawasaki, Jonah Gamba, Atsushi Koike, Hitomi Murakami

Abstract: Image data hiding schemes are techniques to embed secret image data into several images. The embedded data can be extracted with some procedure. On the other hand, visual cryptographic techniques break up a secret image into several shares so that only someone with all shares can decrypt the secret image by superposing all shares together. Image data hiding schemes based on error diffusion have the feature of visual cryptography with respect to extracting of embedded data. They embed secret image data into several halftone images without affecting their perceptual qualities and the embedded data can be restored with apparently high quality when the halftone images are overlaid without any special electronic calculation. In this paper, we consider to formulate an image data hiding scheme based on error diffusion. We propose a formulation for the scheme in the view of a stochastic analysis. The idea is very basic, but theoretical studies by formulating is important trial in this field.
Image data hiding, Visual cryptography, Halftoning, Error diffusion, Probability theory
Full Paper, pp. 17-24


Trap-Decoding of Reed-Solomon Codes and Its Burst-Error-Correcting Performance Evaluation

by Dunwei Xue, Liuguo Yin

Abstract: The communication and storage systems may be corrupted by bursts of noise. These bursts may be long in duration, resulting in a significant degradation for the system performance. Reed-Solomon (RS) codes are proven to be very effective in correcting burst errors. According to the Singleton bound, the maximum length of burst errors that can be corrected by an (n, k) RS code is (n-k)/2 symbols. However, it turns out that, if correlation between erroneous symbols within bursts is considered and well used, variables for burst locations will be decreased and, accordingly, decoding capability may be enhanced with increased length of correctable bursts. As such, we propose a new trap-decoding algorithm for RS codes in this paper. It is shown that, for (n, k) RS codes, this algorithm can correct continuous burst errors with length that approaches to n-k symbols with fairly low miscorrection probability, achieving a good performance over long-burst channels. Moreover, we will further show that the complexity of the proposed algorithm is fairly lower, and the decoding delay is much less than those of existing burst-error-correcting algorithms.
Reed-Solomon (RS) code, burst errors, trap decoding algorithms, burst-error-correcting capability
Full Paper, pp. 25-32


Using Factor Analysis on Survey Study of Factors Affecting Students’ Learning Styles

by Suriani Hassan, Norlita Ismail, Wan Yonsharlinawati Wan Jaafar, Khadizah Ghazali, Kamsia Budin, Darmesah Gabda, Asmar Shahira Abdul Samad

Abstract: This study focused on the statistical technique using the factor analysis on constructing the new factors affecting students’ learning styles of the survey done among university students. In addition, comparison means using the Kruskal-Wallis test were done to analyze the demographic differences on the new factors affecting students’ learning styles. The data were collected using survey questionnaires. The number of respondents was 189 students. The methodologies used were descriptive statistics, factor analysis and non-parametric technique using the Kruskal-Wallis test. The results showed seven new factors were successfully constructed using factor analysis and assigned as the factors affecting the learning styles; which are 1) students' attitude before and after attending class, 2) strategies used to comprehend the lecture, 3) the importance of lecture, 4) class size and its condition, 5) efforts outside class, 6) classroom convenient and 7) importance on listening to lecture. The Kruskal-Wallis test results showed there was a significant mean difference between gender on students' efforts outside class (factor 5) while there was no significant mean difference between genders on the other factors of students’ learning style. As for years of study, Kruskal-Wallis test showed that students’ attitude before and after attending class influenced learning style. The result from Kruskal-Wallis test showed different in score for science and non-science stream students. Non-science students have a better comprehend strategy as their field could be practiced outside classroom and do not merely based on theory. On the other hand, science students satisfy with their class size and its condition as compared to non-science students. The result shows that CGPA is only influenced by the importance of class size and its condition and the importance of lecture. Students with CGPA 2.00-2.49 indicated that attending lecture is crucial and satisfy with classroom size and its condition as compared to students with other group of CGPA.
Factor analysis, Demographic factors, Learning styles, Kruskal-Wallis
Full Paper, pp. 33-40


Complex Valued Open Recurrent Neural Network for Power Transformer Modeling

by A. Minin, Yu. Chistyakov, E. Kholodova, H.-G. Zimmermann, A. Knoll

Abstract: Application of artificial Neural Networks (NN) for power equipment modeling has been outlined in many papers, but conventional NN deal only real valued numbers. Complex Valued Open Recurrent Neural Networks (CVORNN) is significant expansion of NN application due to complex numbers usage, which is natural form of data in electrical engineering. Dealing with complex values is very useful in Wide Area Measurement Systems. Power transformer modeling using CVORNN is presented in this paper as it is one of the most common elements of power grid which has nonlinear behavior. Considering paper consists of two main parts: conventional modeling for getting transformer data and CVORNN application for studied transformer. First part of the paper describes nonlinearities which take place in transformer model: nonlinear magnetizing system, ambient temperature influence on windings and OLTC voltage stabilization. Typical day-long load curve is used for load simulation. The second part devoted to CVORNN basics and application. CVORNN is trained and tested using received in the first part data. Obtained results show that CVORNN is promising and convenient method for modeling in electrical engineering.
Complex Valued Open Recurrent neural network, Transformer modeling, Power equipment modeling, On-load tap changer, Complex Valued Back Propagation
Full Paper, pp. 41-48


Application of the Multi Segment Function in Hydraulic Systems

by Claude Ziad Bayeh

Abstract: The Multi Segment function is a mathematical function developed by the author in order to describe the continuity of non derivable linear functions. The form of this function is as its name indicate, it is composed of many linear segments connected together to form a single function. The main goal of developing this function is to be applied in the hydraulic systems and in the design of pipelines for pressurized water supply distributions underground. The Multi segment function is very important in the hydraulic systems in which the pipelines can be run parallel to the earth surface in a way to minimize the depth of the path way of the pipeline under the ground. Moreover, one can get the total length of the pipeline by using a simple formula developed in this paper. This function can be simply programmed using software as Matlab, Microsoft Excel or any other software.
Multi Segment Function, hydraulic application, programmable function
Full Paper, pp. 49-56


Rating and Ranking Criteria for Selected Islands Using Fuzzy Analytic Hierarchy Process (FAHP)

by Noraida Haji Ali, Ily Amalina Ahmad Sabri, Noor Maizura Mohamad Noor, Fathilah Ismail

Abstract: Destination choice is one of decision making problems which should carefully be investigated in order to choose the best alternative among popular alternatives. The structure in modeling decision making may influencing the decision made and different decision making models impose different objectives with the result may not be variant. Therefore island evaluation has become one of important components in the selections. Multi-criteria decision making (MCDM) is a possible evaluation scale for many characters or quantities of decision makers’ evaluation. It could be determined by advantage or ranking. This study presents fuzzy AHP as a proposed method for dealing with decision making in ten (10) social attributes. Fuzzy analytic hierarchy process (FAHP) is employed to calculate the weights of these criteria and sub-criteria, so as to build the fuzzy multi-criteria model of island evaluation. FAHP performed better than domain experts in tourism when the size of criteria and sub-criteria set increase. A detailed numerical example, illustrating the application of our approach to criteria evaluation is given.
Fuzzy Analytic Hierarchy Process (FAHP), Island Tourism, Multi-Criteria Decision Making (MCDM), Social Attributes
Full Paper, pp. 57-65