Search results for: Bayesian approach Kalman filtering approach

Authors: Kais Hafsaoui

Abstract:

In this paper, we propose to study the synthesis of the vertical dipole antenna over imperfect ground. The synthesis implementation-s method for this type of antenna permits to approach the appropriated radiance-s diagram. The used approach is based on neural network. Our main contribution in this paper is the extension of a synthesis model of this vertical dipole antenna over imperfect ground.

Keywords: Vertical dipole antenna, imperfect ground, neural network.

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Authors: S. S. Nafee, A. K. Al-Ramady, S. A. Shaheen

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The mixed oxide nuclear fuel (MOX) of U and Pu contains several percent of fission products and minor actinides, such as neptunium, americium and curium. It is important to determine accurately the decay heat from Curium isotopes as they contribute significantly in the MOX fuel. This heat generation can cause samples to melt very quickly if excessive quantities of curium are present. In the present paper, we introduce a new approach that can predict the decay heat from curium isotopes. This work is a part of the project funded by King Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, and take place in King Abdulaziz University (KAU), Saudi Arabia. The approach is based on the numerical solution of coupled linear differential equations that describe decays and buildups of many nuclides to calculate the decay heat produced after shutdown. Results show the consistency and reliability of the approach applied.

Keywords: Decay heat, Mixed oxide nuclear fuel, Numerical Solution of Linear Differential Equations, and Curium isotopes

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Authors: Mohamed Al-Badrashiny, Abdelghani Bellaachia

Abstract:

This paper presents a classifier ensemble approach for predicting the survivability of the breast cancer patients using the latest database version of the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute. The system consists of two main components; features selection and classifier ensemble components. The features selection component divides the features in SEER database into four groups. After that it tries to find the most important features among the four groups that maximizes the weighted average F-score of a certain classification algorithm. The ensemble component uses three different classifiers, each of which models different set of features from SEER through the features selection module. On top of them, another classifier is used to give the final decision based on the output decisions and confidence scores from each of the underlying classifiers. Different classification algorithms have been examined; the best setup found is by using the decision tree, Bayesian network, and Na¨ıve Bayes algorithms for the underlying classifiers and Na¨ıve Bayes for the classifier ensemble step. The system outperforms all published systems to date when evaluated against the exact same data of SEER (period of 1973-2002). It gives 87.39% weighted average F-score compared to 85.82% and 81.34% of the other published systems. By increasing the data size to cover the whole database (period of 1973-2014), the overall weighted average F-score jumps to 92.4% on the held out unseen test set.

Keywords: Classifier ensemble, breast cancer survivability, data mining, SEER.

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Authors: Ramin Javadzadeh, Zahra Afsahi, MohammadReza Meybodi

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The hybridization of artificial immune system with cellular automata (CA-AIS) is a novel method. In this hybrid model, the cellular automaton within each cell deploys the artificial immune system algorithm under optimization context in order to increase its fitness by using its neighbor-s efforts. The hybrid model CA-AIS is introduced to fix the standard artificial immune system-s weaknesses. The credibility of the proposed approach is evaluated by simulations and it shows that the proposed approach achieves better results compared to standard artificial immune system.

Keywords: Artificial Immune System, Cellular Automat, neighborhood

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Authors: Shankar Kambhampaty, Venkata Srinivas Modali

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When architecting an application, key nonfunctional requirements such as performance, scalability, availability and security, which influence the architecture of the system, are some times not adequately addressed. Performance of the application may not be looked at until there is a concern. There are several problems with this reactive approach. If the system does not meet its performance objectives, the application is unlikely to be accepted by the stakeholders. This paper suggests an approach for performance modeling for web based J2EE and .Net applications to address performance issues early in the development life cycle. It also includes a Performance Modeling Case Study, with Proof-of-Concept (PoC) and implementation details for .NET and J2EE platforms.

Keywords: Performance Measures, Performance Modeling, Performance Testing, Resource Utilization, Response Time, Throughput.

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Authors: Wiem Daoud Ben Amor, Luis Martínez López, Jr., Hela Moalla Frikha

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Most of the multi-criteria group decision making (MCGDM) problems dealing with qualitative criteria require consideration of the large background of expert information. It is common that experts have different degrees of knowledge for giving their alternative assessments according to criteria. So, it seems logical that they use different evaluation scales to express their judgment, i.e., multi granular linguistic scales. In this context, we propose the extension of the classical additive ratio assessment (ARAS) method to the case of a hierarchical linguistics term for managing multi granular linguistic scales in uncertain context where uncertainty is modeled by means in linguistic information. The proposed approach is called the extended hierarchical linguistics-ARAS method (ELH-ARAS). Within the ELH-ARAS approach, the decision maker (DMs) can diagnose the results (the ranking of the alternatives) in a decomposed style i.e., not only at one level of the hierarchy but also at the intermediate ones. Also, the developed approach allows a feedback transformation i.e., the collective final results of all experts are able to be transformed at any level of the extended linguistic hierarchy that each expert has previously used. Therefore, the ELH-ARAS technique makes it easier for decision-makers to understand the results. Finally, an MCGDM case study is given to illustrate the proposed approach.

Keywords: Additive ratio assessment, extended hierarchical linguistic, multi-criteria group decision making problems, multi granular linguistic contexts.

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Authors: Vultchan T. Gueorgiev, Racho M. Ivanov, Ivan S. Yatchev, Krastyo L. Hinov

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An approach for experimental measurement of the dynamic characteristics of linear electromagnet actuators is presented. It uses accelerometer sensor to register the armature acceleration. The velocity and displacement of the moving parts can be obtained by integration of the acceleration results. The armature movement of permanent magnet linear actuator is acquired using this technique. The results are analyzed and the performance of the supposed approach is compared with the most commonly used experimental setup where the displacement of the armature vs. time is measured instead of its acceleration.

Keywords: Dynamic characteristics, dynamic simulation, linearactuators.

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IPprotocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: Quality of communication, IP-telephony, Fuzzy set, Fuzzy implication, Neural network.

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Authors: Alireza Tavakolinia

Abstract:

In order to understand the role of the injured party's fault in dividing liability, we studied its historical background. In common law, the traditional contributory negligence rule was a complete defense. Then the legislature and judicial procedure modified that rule to one of apportionment. In Islamic law, too, the Action rule was at first used when the injured party was the sole cause, but jurists expanded the scope of this rule, so this rule was used in cases where both the injured party's fault and that of the other party are involved. There are some popular approaches for apportionment of damages. Some common law countries like Britain had chosen ‘the causal potency approach’ and ‘fixed apportionment’. Islamic countries like Iran have chosen both ‘the relative blameworthiness’ and ‘equal apportionment’ approaches. The article concludes that both common law and Islamic law believe in the division of responsibility between a wrongdoer claimant and the defendant. In contrast, in the apportionment of responsibility, Islamic law mostly believes in equal apportionment that is way easier and saves time and money, but common law legal systems have chosen the causal potency approach which is more complicated than the rival approach but is fairer.

Keywords: Contributory negligence, common law, Islamic Law, Tort Law.

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Authors: Jahan Zeb, Muhammad Younus Javed, Usman Qayyum

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This research paper deals with the implementation of face recognition using neural network (recognition classifier) on low-resolution images. The proposed system contains two parts, preprocessing and face classification. The preprocessing part converts original images into blurry image using average filter and equalizes the histogram of those image (lighting normalization). The bi-cubic interpolation function is applied onto equalized image to get resized image. The resized image is actually low-resolution image providing faster processing for training and testing. The preprocessed image becomes the input to neural network classifier, which uses back-propagation algorithm to recognize the familiar faces. The crux of proposed algorithm is its beauty to use single neural network as classifier, which produces straightforward approach towards face recognition. The single neural network consists of three layers with Log sigmoid, Hyperbolic tangent sigmoid and Linear transfer function respectively. The training function, which is incorporated in our work, is Gradient descent with momentum (adaptive learning rate) back propagation. The proposed algorithm was trained on ORL (Olivetti Research Laboratory) database with 5 training images. The empirical results provide the accuracy of 94.50%, 93.00% and 90.25% for 20, 30 and 40 subjects respectively, with time delay of 0.0934 sec per image.

Keywords: Average filtering, Bicubic Interpolation, Neurons, vectorization.

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Authors: Bagher Rahimpour Cami, Hamid Hassanpour, Hoda Mashayekhi

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Nowadays websites provide a vast number of resources for users. Recommender systems have been developed as an essential element of these websites to provide a personalized environment for users. They help users to retrieve interested resources from large sets of available resources. Due to the dynamic feature of user preference, constructing an appropriate model to estimate the user preference is the major task of recommender systems. Profile matching and latent factors are two main approaches to identify user preference. In this paper, we employed the latent factor and profile matching to cluster the user profile and identify user preference, respectively. The method uses the Distance Dependent Chines Restaurant Process as a Bayesian nonparametric framework to extract the latent factors from the user profile. These latent factors are mapped to user interests and a weighted distribution is used to identify user preferences. We evaluate the proposed method using a real-world data-set that contains news tweets of a news agency (BBC). The experimental results and comparisons show the superior recommendation accuracy of the proposed approach related to existing methods, and its ability to effectively evolve over time.

Keywords: Content-based recommender systems, dynamic user modeling, extracting user interests, predicting user preference.

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Authors: Nishant Rodrigues, Nicole Spanedda, Chilukuri K. Mohan, Arindam Chakraborty

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A crucial objective in quantum chemistry is the computation of the energy levels of chemical systems. This task requires electron-repulsion integrals as inputs and the steep computational cost of evaluating these integrals poses a major numerical challenge in efficient implementation of quantum chemical software. This work presents a moment-based machine learning approach for the efficient evaluation of electron-repulsion integrals. These integrals were approximated using linear combinations of a small number of moments. Machine learning algorithms were applied to estimate the coefficients in the linear combination. A random forest approach was used to identify promising features using a recursive feature elimination approach, which performed best for learning the sign of each coefficient, but not the magnitude. A neural network with two hidden layers was then used to learn the coefficient magnitudes, along with an iterative feature masking approach to perform input vector compression, identifying a small subset of orbitals whose coefficients are sufficient for the quantum state energy computation. Finally, a small ensemble of neural networks (with a median rule for decision fusion) was shown to improve results when compared to a single network.

Keywords: Quantum energy calculations, atomic orbitals, electron-repulsion integrals, ensemble machine learning, random forests, neural networks, feature extraction.

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Authors: Parviz Fattahi

Abstract:

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it quit difficult to achieve an optimal solution to this problem with traditional optimization approaches owing to the high computational complexity. The combining of several optimization criteria induces additional complexity and new problems. In this paper, a Pareto approach to solve the multi objective flexible job shop scheduling problems is proposed. The objectives considered are to minimize the overall completion time (makespan) and total weighted tardiness (TWT). An effective simulated annealing algorithm based on the proposed approach is presented to solve multi objective flexible job shop scheduling problem. An external memory of non-dominated solutions is considered to save and update the non-dominated solutions during the solution process. Numerical examples are used to evaluate and study the performance of the proposed algorithm. The proposed algorithm can be applied easily in real factory conditions and for large size problems. It should thus be useful to both practitioners and researchers.

Keywords: Flexible job shop, Scheduling, Hierarchical approach, simulated annealing, tabu search, multi objective.

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Authors: Neeta Awasthy, J.P.Saini, D.S.Chauhan

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ICA which is generally used for blind source separation problem has been tested for feature extraction in Speech recognition system to replace the phoneme based approach of MFCC. Applying the Cepstral coefficients generated to ICA as preprocessing has developed a new signal processing approach. This gives much better results against MFCC and ICA separately, both for word and speaker recognition. The mixing matrix A is different before and after MFCC as expected. As Mel is a nonlinear scale. However, cepstrals generated from Linear Predictive Coefficient being independent prove to be the right candidate for ICA. Matlab is the tool used for all comparisons. The database used is samples of ISOLET.

Keywords: Cepstral Coefficient, Distance measures, Independent Component Analysis, Linear Predictive Coefficients.

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Authors: F. Z. Eddoug, J. Benhra, R. Benabbou

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Excellence and Success are the ultimate goal for any project and in order to achieve it, every project manager looks for the convenient tools and methods. This work proposes a framework that seeks an efficient management of general project through a lean and agile approach. In order to get this objective, the article was divided in two stages, the first one was emphasized on exploring and analyzing the existing project management models and then in the second one the desired framework was created, beginning by focusing on seven existing models and then proposing for each phase of the framework the convenient lean and agile tools.

Keywords: Agility, hybrid project management, lean, scrum.

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Authors: Mohamed Asaad Abdelrazek, Amir Taher El-Sheikh, M. Zayan, A.M. Elhady

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The successful realization of complex systems is dependent not only on the technology issues and the process for implementing them, but on the management issues as well. Managing the systems development lifecycle requires technical management. Systems engineering management is the technical management. Systems engineering management is accomplished by incorporating many activities. The three major activities are development phasing, systems engineering process and lifecycle integration. Systems engineering management activities are performed across the system development lifecycle. Due to the ever-increasing complexity of systems as well the difficulty of managing and tracking the development activities, new ways to achieve systems engineering management activities are required. This paper presents a systematic approach used as a design management tool applied across systems engineering management roles. In this approach, Transdisciplinary System Development Lifecycle (TSDL) Model has been modified and integrated with Quality Function Deployment. Hereinafter, the name of the systematic approach is the Transdisciplinary Quality System Development Lifecycle (TQSDL) Model. The QFD translates the voice of customers (VOC) into measurable technical characteristics. The modified TSDL model is based on Axiomatic Design developed by Suh which is applicable to all designs: products, processes, systems and organizations. The TQSDL model aims to provide a robust structure and systematic thinking to support the implementation of systems engineering management roles. This approach ensures that the customer requirements are fulfilled as well as satisfies all the systems engineering manager roles and activities.

Keywords: Axiomatic design, quality function deployment, systems engineering management, system development lifecycle.

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Authors: Kar Foo Chong, Pradeep K. Gopalakrishnan, T. Hui Teo

Abstract:

There are multiple ways to implement a decimator filter. This paper addresses usage of CIC (cascaded-integrator-comb) filter and HB (half band) filter as the decimator filter to reduce the frequency sample rate by factor of 64 and detail of the implementation step to realize this design in hardware. Low power design approach for CIC filter and half band filter will be discussed. The filter design is implemented through MATLAB system modeling, ASIC (application specific integrated circuit) design flow and verified using a FPGA (field programmable gate array) board and MATLAB analysis.

Keywords: CIC filter, decimation filter, half-band filter, lowpower.

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Authors: Yue Wang

Abstract:

Five years after the newest English curriculum, reform policy was enacted in China and hand-wringing spread among teachers who accused that this is another “wearing new shoes to walk the old road” policy. This paper provides a thoroughly philosophical policy analysis of serious efforts that had been made to support this reform and revealed the hindrances that bridled the reform to yield the desired effect. Blame could be easily put on teachers for their insufficient pedagogical content knowledge, conservative resistance, and the handicaps of large class sizes and limited teaching times and so on. However, the underlying causes for this implementation failure are the interrelated factors in the NCEE-centred education system, such as the reluctance from students, the lack of school and education bureau support and insufficient teacher training. A further discussion of the 2017 to 2020’s NCEE reform on English prompts new possibilities for the authentic pedagogical approach reform in secondary English classes. In all, the pedagogical approach reform at the secondary level is heading towards a brighter future with the initiation of new NCEE reform.

Keywords: English curriculum, failure, NCEE, new possibilities, pedagogical, policy analysis, reform.

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Authors: George Karkavitsas, Maria Rangoussi

Abstract:

We present a genetic algorithm application to the problem of object registration (i.e., object detection, localization and recognition) in a class of medical images containing various types of blood cells. The genetic algorithm approach taken here is seen to be most appropriate for this type of image, due to the characteristics of the objects. Successful cell registration results on real life microscope images of blood cells show the potential of the proposed approach.

Keywords: Genetic algorithms, object registration, pattern recognition, blood cell microscope images.

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Authors: Maithem Al-Saadi, Min An

Abstract:

During airport planning and design stages, the major issues of capacity and safety in construction and operation of an airport need to be taken into consideration. The airside of an airport is a major and critical infrastructure that usually consists of runway(s), taxiway system, and apron(s) etc., which have to be designed according to the international standards and recommendations, and local limitations to accommodate the forecasted demands. However, in many cases, airport airsides are suffering from unexpected risks that occurred during airport operations. Therefore, safety risk assessment should be applied in the planning and design of airsides to cope with the probability of risks and their consequences, and to make decisions to reduce the risks to as low as reasonably practicable (ALARP) based on safety risk assessment. This paper presents a combination approach of Failure Modes, Effect, and Criticality Analysis (FMECA), Fuzzy Reasoning Approach (FRA), and Fuzzy Analytic Hierarchy Process (FAHP) to develop a risk analysis model for safety risk assessment. An illustrated example is used to the demonstrate risk assessment process on how the design of an airside in an airport can be analysed by using the proposed safety design risk assessment model.

Keywords: Airport airside planning and design, design for safety, fuzzy reasoning approach, fuzzy AHP, risk assessment.

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Authors: G. Reinhart, J. Pohl

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Manufacturing companies are facing a broad variety of challenges caused by a dynamic production environment. To succeed in such an environment, it is crucial to minimize the loss of time required to trigger the adaptation process of a company-s production structures. This paper presents an approach for the continuous monitoring of production structures by neurologic principles. It enhances classical monitoring concepts, which are principally focused on reactive strategies, and enables companies to act proactively. Thereby, strategic aspects regarding the harmonization of certain life cycles are integrated into the decision making process for triggering the reconfiguration process of the production structure.

Keywords: Continuous Factory Planning, Production Structure, Production Management.

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Authors: Dmitry K. Shaytan, Georgy D. Laptev

Abstract:

In our research we aimed to test a managerial approach for the fuzzy front end (FFE) of innovation by creating controlled experiment/ business case in a breakthrough innovation development. The experiment was in the sport industry and covered all aspects of the customer discovery stage from ideation to prototyping followed by patent application. In the paper we describe and analyze mile stones, tasks, management challenges, decisions made to create the break through innovation, evaluate overall managerial efficiency that was at the considered FFE stage. We set managerial outcome of the FFE stage as a valid product concept in hand. In our paper we introduce hypothetical construct “Q-factor” that helps us in the experiment to distinguish quality of FFE outcomes. The experiment simulated for entrepreneur the FFE of innovation and put on his shoulders responsibility for the outcome of valid product concept. While developing managerial approach to reach the outcome there was a decision to look on product concept from the cognitive psychology and cognitive science point of view. This view helped us to develop the profile of a person whose projection (mental representation) of a new product could optimize for a manager or entrepreneur FFE activities. In the experiment this profile was tested to develop breakthrough innovation for swimmers. Following the managerial approach the product concept was created to help swimmers to feel/sense water. The working prototype was developed to estimate the product concept validity and value added effect for customers. Based on feedback from coachers and swimmers there were strong positive effect that gave high value for customers, and for the experiment – the valid product concept being developed by proposed managerial approach for the FFE. In conclusions there is a suggestion of managerial approach that was derived from experiment.

Keywords: Concept development, concept testing, customer discovery, entrepreneurship, entrepreneurial management, idea generation, idea screening, startup management.

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Authors: A. Bennassar, A. Abbou, M. Akherraz, M. Barara

Abstract:

In this paper, we propose a sensorless backstepping control of induction motor (IM) associated with three levels neutral clamped (NPC) inverter. First, the backstepping approach is designed to steer the flux and speed variables to theirs references and to compensate the uncertainties. A Lyapunov theory is used and it demonstrates that the dynamic trajectories tracking are asymptotically stable. Second, we estimate the rotor flux and speed by using the adaptive Luenberger observer (ALO). Simulation results are provided to illustrate the performance of the proposed approach in high and low speeds and load torque disturbance.

Keywords: Sensorless backstepping, IM, Three levels NPC inverter, Lyapunov theory, ALO.

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Authors: Petra Horváthová, Irena Durdová

Abstract:

The article is aimed at bringing information on the scope and the level of use of talent management by organizations in one of the Czech Republic regions, in the Moravian-Silesian Region. On the basis of data acquired by a questionnaire survey it has been found out that organizations in the above-mentioned region are implementing the system of talent management on a small scale: this approach is used by 3.8 % of organizations only that is 9 from 237 (100 %) of the approached respondents. The main reasons why this approach is not used is either that organizations have no knowledge of it or there is lack of financial and personnel resources. In the article recommendations suggested by the author can be found for a wider application of talent management in the Czech practice.

Keywords: Talent, talent management, use, mind map of talent management.

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Authors: Bogdan Walek, Cyril Klimes

Abstract:

Current tools for data migration between documentoriented and relational databases have several disadvantages. We propose a new approach for data migration between documentoriented and relational databases. During data migration the relational schema of the target (relational database) is automatically created from collection of XML documents. Proposed approach is verified on data migration between document-oriented database IBM Lotus/ Notes Domino and relational database implemented in relational database management system (RDBMS) MySQL.

Keywords: data migration, database, document-oriented database, XML, relational schema

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Authors: Atman Jbari, Abdellah Adib, Driss Aboutajdine

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This paper addresses the problem of blind source separation (BSS). To recover original signals, from linear instantaneous mixtures, we propose a new contrast function based on the use of a double referenced system. Our approach assumes statistical independence sources. The reference vectors will be incrusted in the cumulant to evaluate the independence. The estimation of the separating matrix will be performed in two steps: whitening observations and joint diagonalization of a set of referenced cumulant matrices. Computer simulations are presented to demonstrate the effectiveness of the suggested approach.

Keywords: Blind source separation, Referenced Cumulant, Contrast, Joint Diagonalization.

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Authors: M. Rodionov, N. Sharapova, Z. Dedovets

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The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

Keywords: Computer-oriented approach, traditional approach, future teachers, mathematics, lesson, students, education.

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

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This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Sameena Tarannum, S. Pranesh

Abstract:

The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: Gravity modulation, Oldroyd-B liquid, triple diffusive convection, Venezian approach.

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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