Search results for: Abdallah Saad
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 337

Search results for: Abdallah Saad

337 Comparison between Classical and New Direct Torque Control Strategies of Induction Machine

Authors: Mouna Essaadi, Mohamed Khafallah, Abdallah Saad, Hamid Chaikhy

Abstract:

This paper presents a comparative analysis between conventional direct torque control (C_DTC), Modified direct torque control (M_DTC) and twelve sectors direct torque control (12_DTC).Those different strategies are compared by simulation in term of torque, flux and stator current performances. Finally, a summary of the comparative analysis is presented.

Keywords: C_DTC, M_DTC, 12_DTC, torque dynamic, stator current, flux, performances

Procedia PDF Downloads 579
336 Effects of Flexible Flat Feet on Electromyographic Activity of Erector Spinae and Multifidus

Authors: Abdallah Mohamed Kamel Mohamed Ali, Samah Saad Zahran, Mohamed Hamed Rashad

Abstract:

Background: Flexible flatfoot (FFF) has been considered as a risk factor for several lower limb injuries and mechanical low back pain. This was attributed to the dysfunction of the lumbopelvic-hip complex musculature. Objective: To investigate the influence of FFF on electromyographic activities of erector spinae and multifidus. Methods: A cross-section study was held between an FFF group (20 subjects) and a normal foot group (20 subjects). A surface electromyography was used to assess the electromyographic activity of erector spinae and multifidus. Group differences were assessed by the T-test. Results: There was a significant increase in EMG activities of erector spinae and multifidus in the FFF group compared with the normal group. Conclusion: There is an increase in EMG activities in erector spinae and multifidus in FFF subjects compared with normal subjects.

Keywords: electromyography, flatfoot, low back pain, paraspinal muscles

Procedia PDF Downloads 180
335 A Blind Three-Dimensional Meshes Watermarking Using the Interquartile Range

Authors: Emad E. Abdallah, Alaa E. Abdallah, Bajes Y. Alskarnah

Abstract:

We introduce a robust three-dimensional watermarking algorithm for copyright protection and indexing. The basic idea behind our technique is to measure the interquartile range or the spread of the 3D model vertices. The algorithm starts by converting all the vertices to spherical coordinate followed by partitioning them into small groups. The proposed algorithm is slightly altering the interquartile range distribution of the small groups based on predefined watermark. The experimental results on several 3D meshes prove perceptual invisibility and the robustness of the proposed technique against the most common attacks including compression, noise, smoothing, scaling, rotation as well as combinations of these attacks.

Keywords: watermarking, three-dimensional models, perceptual invisibility, interquartile range, 3D attacks

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334 Status of Artisanal Fishery in Libya

Authors: Esmail Shakman, Khaled Etyab, Ibraheim Taboni, Mohamed Et-wail, Abdallah Ben Abdallah

Abstract:

This study was carried out along the Libyan coast during the period from 1st February to 31st March 2013. More than 120 landing sites have been visited in order to investigate their status and fishing activities. The study found that more than 91% of the landing sites were permanent and around 8% were seasonal. The type of landing sites were mostly harbors (42.86%), 31.75% protected bays and 25.4% are open beach. However, seven types of fishing boats were observed; flouka type was the largest percentage (70.06%), then 18.14% for mator, 3.28% for lampara, 0.41% for Tarrad, Gayag (0.16%), 5.97 for Daghesa, and 1.98% for batah. Moreover, the majority of them were concentrated in the western region of the country. The most common used fishing gearsare the trammel nets about 80%, which are used by flouka, mator, Tarrad, and batah. The using of trammel nets rely on the fishing season, fishes size and the target fish species. The other fishing gears are also used but occasionally.

Keywords: fishery, South Mediterranean, landing sites, marine biology

Procedia PDF Downloads 486
333 Interlanguage Pragmatics Instruction: Evidence from EFL Teachers

Authors: Asma Ben Abdallah

Abstract:

Interlanguage Pragmatics (ILP) Instruction has brought a lot of enlightenment for Foreign Language Teaching and has secured itself a deserved position in SLA research. In the Tunisian context, ILP instruction remains less explored for academics and educational practitioners. In our experience as teachers, both at secondary school and at university levels, the instruction and assessment of pragmatics seem to be contentious. This paper firstly introduces the theoretical models of Interlanguage pragmatics Instruction and focuses on their implications for foreign language teaching. This study builds on the work of Ben Abdallah (2015) that investigated the effects of pragmatic Instruction on Tunisian EFL Learners where pragmatic Instruction has been approached from the perspective of students and their learning strategies. The data for the present study, however, come from Tunisian EFL teachers by investigating their pragmatics practices and their perceptions of pragmatic instruction. The findings indicated that EFL teachers have pragmatic awareness; yet, their reflections revealed that their awareness was mostly on theoretical pragmatic knowledge, and not explicitly brought into practical pragmatic applications. The paper concludes by promoting pragmatics instruction with the suggestion that EFL teachers should teach pragmatics in class.

Keywords: interlanguage pragmatics theory, pragmatics, pragmatic instruction, SLA

Procedia PDF Downloads 246
332 Enhancing the Performance of Bug Reporting System by Handling Duplicate Reporting Reports: Artificial Intelligence Based Mantis

Authors: Afshan Saad, Muhammad Saad, Shah Muhammad Emaduddin

Abstract:

Bug reporting systems are most important tool that guides regarding different maintenance activities in software engineering. Duplicate bug reports which describe the bugs and issues in bug reporting system repository increases processing time of bug triage that monitors all such activities and software programmers who are working and spending time on reports which were assigned by triage. These reports can reveal imperfections and degrade software quality. As there is a number of the potential duplicate bug reports increases, the number of bug reports in bug repository increases. Identifying duplicate bug reports help in decreasing development work load in fixing defects. However, it is difficult to manually identify all possible duplicates because of the huge number of already reported bug reports. In this paper, an artificial intelligence based system using Mantis is proposed to automatically detect duplicate bug reports. When new bugs are submitted to repository triages will mark it with a tag. It will investigate that whether it is a duplicate of an existing bug report by matching or not. Reports with duplicate tags will be eliminated from the repository which not only will improve the performance of the system but can also save cost and effort waste on bug triage and finding the duplicate bug.

Keywords: bug tracking, triager, tool, quality assurance

Procedia PDF Downloads 162
331 Management of Recurrent Temporomandibular Joint True Bony Ankylosis : A Case Report

Authors: Mahmoud A. Amin, Essam Taman, Ahmed Omran, Mahmoud Shawky, Ahmed Mekawy, Abdallah M. Kotkat, Saber Younes, Nehad N. Ghonemy, Amin Saad, Ezz-Aleslam, Abdullah M. Elosh

Abstract:

Introduction: TMJ is a one-of-a-kind, complicated synovial joint that helps with masticatory function by allowing the mandible to open and close the mouth. True ankylosis is a situation in which condylar movement is limited by a mechanical defect in the joint, whereas false ankylosis is a condition in which there is a restriction in mandibular movement due to muscular spasm myositis ossificans, and coronoid process hyperplasia. Ankylosis is characterized by the inability to open the mouth due to fusion of the TMJ condyle to the base of the skull as a result of trauma, infection, or systemic diseases such as rheumatoid arthritis (the most common) and psoraisis. Ankylosis causes facial asymmetry and affects the patient psychologically as well as speech, difficult mastication, poor oral hygiene, malocclusion, and other factors. TMJ is a technically challenging joint; hence TMJ ankylosis management is complicated. Case presentation: this case is a male patient 25 years old reported to our maxillofacial clinic in Damietta faculty of medicine, Al-Azhar University with the inability to open the mouth at all, with a history of difficulty of mouth breathing and eating foods, there was a history of falling from height at 2006, and the patient underwent corrective surgery before with no improvement because the ankylosis was relapsed short period after the previous operations with that done out of our hospital inter-incisor distant ZERO so, this condition need mandatory management. Clinical examination and radiological investigations were done after complete approval from the patient and his brother; tracheostomy was done for our patient before the operation. The patient entered the operation in our hospital and drastic improvement in mouth opening was noticed, helping to restore the physical psychological health of the patient.

Keywords: temporomandibular joint, TMJ, Ankylosis, mouth opening, physiotherapy, condylar plate

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330 Proposal for a Generic Context Meta-Model

Authors: Jaouadi Imen, Ben Djemaa Raoudha, Ben Abdallah Hanene

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The access to relevant information that is adapted to users’ needs, preferences and environment is a challenge in many applications running. That causes an appearance of context-aware systems. To facilitate the development of this class of applications, it is necessary that these applications share a common context meta-model. In this article, we will present our context meta-model that is defined using the OMG Meta Object facility (MOF). This meta-model is based on the analysis and synthesis of context concepts proposed in literature.

Keywords: context, meta-model, MOF, awareness system

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329 H∞robust Control Law for a Speed Dc Motor in Both Directions of Rotation

Authors: Ben Abdallah Aicha

Abstract:

In this work we show a H∞ synthesis method which enables us to calculate a feedback controller according to considerations of stability robustness and disturbance rejection translated on to the open loop response. However, it may happen that we have an additional specification on the closed loop response relating to tracking of the reference trajectory. The H∞ synthesis has the advantage of offering increased specifications in robustness stability. Implemented for a DC motor, it offers invaluable performance in speed control in both directions of rotation.

Keywords: H∞ synthesis, DC motor, robustness stability, performance conditions

Procedia PDF Downloads 43
328 Adding Business Value in Enterprise Applications through Quality Matrices Using Agile

Authors: Afshan Saad, Muhammad Saad, Shah Muhammad Emaduddin

Abstract:

Nowadays the business condition is so quick paced that enhancing ourselves consistently has turned into a huge factor for the presence of an undertaking. We can check this for structural building and significantly more so in the quick-paced universe of data innovation and programming designing. The lithe philosophies, similar to Scrum, have a devoted advance in the process that objectives the enhancement of the improvement procedure and programming items. Pivotal to process enhancement is to pick up data that grants you to assess the condition of the procedure and its items. From the status data, you can design activities for the upgrade and furthermore assess the accomplishment of those activities. This investigation builds a model that measures the product nature of the improvement procedure. The product quality is dependent on the useful and auxiliary nature of the product items, besides the nature of the advancement procedure is likewise vital to enhance programming quality. Utilitarian quality covers the adherence to client prerequisites, while the auxiliary quality tends to the structure of the product item's source code with reference to its practicality. The procedure quality is identified with the consistency and expectedness of the improvement procedure. The product quality model is connected in a business setting by social occasion the information for the product measurements in the model. To assess the product quality model, we investigate the information and present it to the general population engaged with the light-footed programming improvement process. The outcomes from the application and the client input recommend that the model empowers a reasonable evaluation of the product quality and that it very well may be utilized to help the persistent enhancement of the advancement procedure and programming items.

Keywords: Agile SDLC Tools, Agile Software development, business value, enterprise applications, IBM, IBM Rational Team Concert, RTC, software quality, software metrics

Procedia PDF Downloads 141
327 A Small Signal Model for Resonant Tunneling Diode

Authors: Rania M. Abdallah, Ahmed A. S. Dessouki, Moustafa H. Aly

Abstract:

This paper has presented a new simple small signal model for a resonant tunnelling diode device. The resonant tunnelling diode equivalent circuit elements were calculated and the results led to good agreement between the calculated equivalent circuit elements and the measurement results.

Keywords: resonant tunnelling diode, small signal model, negative differential conductance, electronic engineering

Procedia PDF Downloads 417
326 Cluster Based Ant Colony Routing Algorithm for Mobile Ad-Hoc Networks

Authors: Alaa Eddien Abdallah, Bajes Yousef Alskarnah

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Ant colony based routing algorithms are known to grantee the packet delivery, but they su ffer from the huge overhead of control messages which are needed to discover the route. In this paper we utilize the network nodes positions to group the nodes in connected clusters. We use clusters-heads only on forwarding the route discovery control messages. Our simulations proved that the new algorithm has decreased the overhead dramatically without affecting the delivery rate.

Keywords: ad-hoc network, MANET, ant colony routing, position based routing

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325 Ant System with Acoustic Communication

Authors: Saad Bougrine, Salma Ouchraa, Belaid Ahiod, Abdelhakim Ameur El Imrani

Abstract:

Ant colony optimization is an ant algorithm framework that took inspiration from foraging behaviour of ant colonies. Indeed, ACO algorithms use a chemical communication, represented by pheromone trails, to build good solutions. However, ants involve different communication channels to interact. Thus, this paper introduces the acoustic communication between ants while they are foraging. This process allows fine and local exploration of search space and permits optimal solution to be improved.

Keywords: acoustic communication, ant colony optimization, local search, traveling salesman problem

Procedia PDF Downloads 559
324 Natural Convection between Two Parallel Wavy Plates

Authors: Si Abdallah Mayouf

Abstract:

In this work, the effects of the wavy surface on free convection heat transfer boundary layer flow between two parallel wavy plates have been studied numerically. The two plates are considered at a constant temperature. The equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm. The important parameters in this problem are the amplitude of the wavy surfaces and the distance between the two wavy plates. Results are presented as velocity profiles, temperature profiles and local Nusselt number according to the important parameters.

Keywords: free convection, wavy surface, parallel plates, fluid dynamics

Procedia PDF Downloads 274
323 In vitro Culture of Flowers of Maerua crassiflia

Authors: Abobkar Abrahem Mohamed Saad, Asma Abud Alsalam

Abstract:

Closed flowers of Maerua crassifolia were cultured on Murashige and Skoog medium supplemented with benzyl amino purine BA (1.0 mg/l). The colour of flowers changed from green to pale brown after one week. They opened after two weeks. The anthers became clear which was observed after 3 weeks. Calluses are induced from sepals after one month. 19 anthers were observed with average length of 1.9 cm. The amount of calluses increased after 40 days. These calluses were fragmented and subcultured on MS+ 2-4D (1.0 mg/l) in order to increase growth.

Keywords: in vitro, Maerua, flowers, culture

Procedia PDF Downloads 352
322 Waiting Time Reduction in a Government Hospital Emergency Department: A Case Study on AlAdan Hospital, Kuwait

Authors: Bashayer AlRobayaan, Munira Saad, Alaa AlBawab, Fatma AlHamad, Sara AlAwadhi, Sherif Fahmy

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This paper addresses the problem of long waiting times in government hospitals emergency departments (ED). It aims at finding feasible and simple ways of reducing waiting times that do not require a lot of resources and/or expenses. AlAdan Hospital in Kuwait was chosen to be understudy to further understand and capture the problem.

Keywords: healthcare, hospital, Kuwait, waiting times, emergency department

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321 Moisturising Prepared Lip Balm Behavior in Dynamic States

Authors: Fatiha Boudjema, Samia Boudergua, Abdallah Elhirtsi Nour El Houda, Ahmed Mbarek Kaouther

Abstract:

The main objective of our work is to prepare and characterize a moisturizing lip balm based on natural ingredients such as waxes, vegetable oils, and shea butter. First, the vegetable and essential oils were extracted, and then lip balm was prepared. The extracted oils and the lip balm were submitted to many tests in order to guarantee their quality and effectiveness. These tests show that our balm has a shear thinning behavior with a melting point of 58 °C and that it spreads easily on the skin without showing an allergic reaction. The balm showed a moisturising effect and stability over the two-month period at storage room temperature condition.

Keywords: lip balm, natural products, rheological study, antioxydant activity

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320 High Voltage Magnetic Pulse Generation Using Capacitor Discharge Technique

Authors: Mohamed Adel Abdallah

Abstract:

A high voltage magnetic pulse is designed by applying an electrical pulse to the coil. Capacitor banks are developed to generate a pulse current. Switching circuit consisting of DPDT switches, thyristor, and triggering circuit is built and tested. The coil current is measured using a Hall-effect current sensor. The magnetic pulse created is measured and tabulated in the graph. Simulation using FEMM is done to compare the results obtained between experiment and simulation. This technology can be applied to area such as medical equipment, measuring instrument, and military equipment.

Keywords: high voltage, magnetic pulse, capacitor discharge, coil

Procedia PDF Downloads 644
319 The Role of Emotional Intelligence on Job Performance and Job Satisfaction: An Empirical Investigation of the Jordanian Universities

Authors: Alfalah Tasneem, Abdallah Bataineh, Falah Jannat, Alfalah Salsabeel

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The term emotional intelligence has been unnoticed by a number of scholars in the early 1990s, which was then a major factor that many business managers became interested in understanding its meaning, functions and how it could be integrated in their business life, emotional intelligence is very important for the top managers, to operate in emotionally intelligence way to meet the needs of their employees. Speaking of emotional intelligence success is influenced by personal qualities such as self-awareness, motivation, empathy and relationship skills. The aim of this research is to critically evaluate the potential contribution of emotional intelligence for the Jordanian universities on the level of job satisfaction and the performance of faculty as well as its positive impact on the educational standards.

Keywords: emotional intelligence, higher education, job performance, job satisfaction

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318 Employing Operations Research at Universities to Build Management Systems

Authors: Abdallah A. Hlayel

Abstract:

Operations research science (OR) deals with good success in developing and applying scientific methods for problem solving and decision-making. However, by using OR techniques, we can enhance the use of computer decision support systems to achieve optimal management for institutions. OR applies comprehensive analysis including all factors that affect on it and builds mathematical modeling to solve business or organizational problems. In addition, it improves decision-making and uses available resources efficiently. The adoption of OR by universities would definitely contributes to the development and enhancement of the performance of OR techniques. This paper provides an understanding of the structures, approaches and models of OR in problem solving and decision-making.

Keywords: best candidates' method, decision making, decision support system, operations research

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317 Calculation of Lungs Physiological Lung Motion in External Lung Irradiation

Authors: Yousif Mohamed Y. Abdallah, Khalid H. Eltom

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This is an experimental study deals with measurement of the periodic physiological organ motion during lung external irradiation in order to reduce the exposure of healthy tissue during radiation treatments. The results showed for left lung displacement reading (4.52+1.99 mm) and right lung is (8.21+3.77 mm) which the radiotherapy physician should take suitable countermeasures in case of significant errors. The motion ranged between 2.13 mm and 12.2 mm (low and high). In conclusion, the calculation of tumour mobility can improve the accuracy of target areas definition in patients undergo Sterostatic RT for stage I, II and III lung cancer (NSCLC). Definition of the target volume based on a high resolution CT scan with a margin of 3-5 mm is appropriate.

Keywords: physiological motion, lung, external irradiation, radiation medicine

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316 A New Protocol Ensuring Users' Privacy in Pervasive Environment

Authors: Mohammed Nadir Djedid, Abdallah Chouarfia

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Transparency of the system and its integration into the natural environment of the user are some of the important features of pervasive computing. But these characteristics that are considered as the strongest points of pervasive systems are also their weak points in terms of the user’s privacy. The privacy in pervasive systems involves more than the confidentiality of communications and concealing the identity of virtual users. The physical presence and behavior of the user in the pervasive space cannot be completely hidden and can reveal the secret of his/her identity and affect his/her privacy. This paper shows that the application of major techniques for protecting the user’s privacy still insufficient. A new solution named Shadow Protocol is proposed, which allows the users to authenticate and interact with the surrounding devices within an ubiquitous computing environment while preserving their privacy.

Keywords: pervasive systems, identification, authentication, privacy

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315 Comparison between LQR and ANN Active Anti-Roll Control of a Single Unit Heavy Vehicle

Authors: Babesse Saad, Ameddah Djemeleddine

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In this paper, a learning algorithm using neuronal networks to improve the roll stability and prevent the rollover in a single unit heavy vehicle is proposed. First, LQR control to keep balanced normalized rollovers, between front and rear axles, below the unity, then a data collected from this controller is used as a training basis of a neuronal regulator. The ANN controller is thereafter applied for the nonlinear side force model, and gives satisfactory results than the LQR one.

Keywords: rollover, single unit heavy vehicle, neural networks, nonlinear side force

Procedia PDF Downloads 441
314 Dynamic Synthesis of a Flexible Multibody System

Authors: Mohamed Amine Ben Abdallah, Imed Khemili, Nizar Aifaoui

Abstract:

This work denotes an insight into dynamic synthesis of multibody systems. A set of mechanism parameters design variable are synthetized based on a desired mechanism response, such as, velocity, acceleration and bodies deformations. Moreover, knowing the work space, for a robot, and mechanism response allow defining optimal parameters mechanism handling with the desired target response. To this end, evolutionary genetic algorithm has been deployed. A demonstrative example for imperfect mechanism has been treated, mainly, a slider crank mechanism with a flexible connecting rod. The transversal deflection of the connecting rod has been chosen as response to identify the mechanism design parameters.

Keywords: dynamic response, evolutionary genetic algorithm, flexible bodies, optimization

Procedia PDF Downloads 286
313 Numerical Modeling of Various Support Systems to Stabilize Deep Excavations

Authors: M. Abdallah

Abstract:

Urban development requires deep excavations near buildings and other structures. Deep excavation has become more a necessity for better utilization of space as the population of the world has dramatically increased. In Lebanon, some urban areas are very crowded and lack spaces for new buildings and underground projects, which makes the usage of underground space indispensable. In this paper, a numerical modeling is performed using the finite element method to study the deep excavation-diaphragm wall soil-structure interaction in the case of nonlinear soil behavior. The study is focused on a comparison of the results obtained using different support systems. Furthermore, a parametric study is performed according to the remoteness of the structure.

Keywords: deep excavation, ground anchors, interaction soil-structure, struts

Procedia PDF Downloads 375
312 Knowledge and Attitude of Final Year Undergraduate Nursing Students towards Prevention of Cervical Cancer

Authors: Afaf Abdallah, Moawia Elsadig

Abstract:

Background: Cervical cancer is the second most common women cancer among worldwide; representing 13% of female cancers. In Sudan, it ranks as the second most frequent cancer among women as other developing countries. Aim: Is to study awareness, attitude of nursing students towards cervical cancer prevention. The results: Most of the students were not aware of other screening methods than Pap smear test. However, half of the respondents showed positive attitudes towards HPV vaccination. More than two-thirds of respondents exhibited a positive attitude and were willing to undergo Pap smear in the future. Conclusion: The study shows that the majority of the participants have poor information, education would motivate nurses to participate actively in awareness raising, screening, and management.

Keywords: cervical cancer, knowledge, attitude, screening

Procedia PDF Downloads 413
311 Comparative Study between Direct Torque Control and Sliding Mode Control of Sensorless Induction Machine

Authors: Fouad Berrabah, Saad Salah, Zaamouche Fares

Abstract:

In this paper, the Direct Torque Control (DTC) Control and the Sliding Mode Control for induction motor are presented and compared. The performance of the two control schemes is evaluated in terms of torque and current ripple, and transient response to variations of the torque , speed and robustness, trajectory tracking. In order to identify the more suitable solution for any application, both techniques are analyzed mathematically and simulation results are compared which advantages and drawbacks are discussed.

Keywords: induction motor, DTC- MRAS control, sliding mode control, robustness, trajectory tracking

Procedia PDF Downloads 561
310 Using Gene Expression Programming in Learning Process of Rough Neural Networks

Authors: Sanaa Rashed Abdallah, Yasser F. Hassan

Abstract:

The paper will introduce an approach where a rough sets, gene expression programming and rough neural networks are used cooperatively for learning and classification support. The Objective of gene expression programming rough neural networks (GEP-RNN) approach is to obtain new classified data with minimum error in training and testing process. Starting point of gene expression programming rough neural networks (GEP-RNN) approach is an information system and the output from this approach is a structure of rough neural networks which is including the weights and thresholds with minimum classification error.

Keywords: rough sets, gene expression programming, rough neural networks, classification

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309 Sliding Mode Control of an Internet Teleoperated PUMA 600 Robot

Authors: Abdallah Ghoul, Bachir Ouamri, Ismail Khalil Bousserhane

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In this paper, we have developed a sliding mode controller for PUMA 600 manipulator robot, to control the remote robot a teleoperation system was developed. This system includes two sites, local and remote. The sliding mode controller is installed at the remote site. The client asks for a position through an interface and receives the real positions after running of the task by the remote robot. Both sites are interconnected via the Internet. In order to verify the effectiveness of the sliding mode controller, that is compared with a classic PID controller. The developed approach is tested on a virtual robot. The results confirmed the high performance of this approach.

Keywords: internet, manipulator robot, PID controller, remote control, sliding mode, teleoperation

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308 Asymptotic Expansion of Double Oscillatory Integrals: Contribution of Non Stationary Critical Points of the Second Kind

Authors: Abdallah Benaissa

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In this paper, we consider the problem of asymptotics of double oscillatory integrals in the case of critical points of the second kind, the order of contact between the boundary and a level curve of the phase being even, the situation when the order of contact is odd will be studied in other occasions. Complete asymptotic expansions will be derived and the coefficient of the leading term will be computed in terms of the original data of the problem. A multitude of people have studied this problem using a variety of methods, but only in a special case when the order of contact is minimal: the more cited papers are a paper of Jones and Kline and an other one of Chako. These integrals are encountered in many areas of science, especially in problems of diffraction of optics.

Keywords: asymptotic expansion, double oscillatory integral, critical point of the second kind, optics diffraction

Procedia PDF Downloads 320