Search results for: fractional order systems

Authors: Jozsef Katona, Attila Kovari, Tibor Ujbanyi, Gergely Sziladi

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By the development of IT systems, human-computer interaction is also developing even faster and newer communication methods become available in human-machine interaction. In this article, the application of a hand gesture controlled human-computer interface is being introduced through the example of a mobile robot. The control of the mobile robot is implemented in a realistic virtual environment that is advantageous regarding the aspect of different tests, parallel examinations, so the purchase of expensive equipment is unnecessary. The usability of the implemented hand gesture control has been evaluated by test subjects. According to the opinion of the testing subjects, the system can be well used, and its application would be recommended on other application fields too.

Keywords: Human-machine interface, hand control, mobile robot, virtual environment.

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Authors: Ilya Kavalchuk, Hayrettin Arisoy, Alex Stojcevski, Aman Maun Than Oo

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Electric vehicles are one of the most complicated electric devices to simulate due to the significant number of different processes involved in electrical structure of it. There are concurrent processes of energy consumption and generation with different onboard systems, which make simulation tasks more complicated to perform. More accurate simulation on energy consumption can provide a better understanding of all energy management for electric transport. As a result of all those processes, electric transport can allow for a more sustainable future and become more convenient in relation to the distance range and recharging time. This paper discusses the problems of energy consumption simulations for electric vehicles using different software packages to provide ideas on how to make this process more precise, which can help engineers create better energy management strategies for electric vehicles.

Keywords: Electric Vehicles, EV, Power Consumption, Power Management, Simulation.

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Authors: Randa I. M. Elanwar, Mohsen A. Rashwan, Samia A. Mashali

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In this paper we present the first Arabic sentence dataset for on-line handwriting recognition written on tablet pc. The dataset is natural, simple and clear. Texts are sampled from daily newspapers. To collect naturally written handwriting, forms are dictated to writers. The current version of our dataset includes 154 paragraphs written by 48 writers. It contains more than 3800 words and more than 19,400 characters. Handwritten texts are mainly written by researchers from different research centers. In order to use this dataset in a recognition system word extraction is needed. In this paper a new word extraction technique based on the Arabic handwriting cursive nature is also presented. The technique is applied to this dataset and good results are obtained. The results can be considered as a bench mark for future research to be compared with.

Keywords: Arabic, Handwriting recognition, on-line dataset.

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Authors: Yi Yu, Lin Ma, Yong Sun, Yuantong Gu

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This paper presents a novel method for remaining useful life prediction using the Elliptical Basis Function (EBF) network and a Markov chain. The EBF structure is trained by a modified Expectation-Maximization (EM) algorithm in order to take into account the missing covariate set. No explicit extrapolation is needed for internal covariates while a Markov chain is constructed to represent the evolution of external covariates in the study. The estimated external and the unknown internal covariates constitute an incomplete covariate set which are then used and analyzed by the EBF network to provide survival information of the asset. It is shown in the case study that the method slightly underestimates the remaining useful life of an asset which is a desirable result for early maintenance decision and resource planning.

Keywords: Elliptical Basis Function Network, Markov Chain, Missing Covariates, Remaining Useful Life

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Authors: Turan Erman Erkan

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Business Process Reengineering (BPR) is an essential tool before an information system project implementation. Enterprise Resource Planning (ERP) projects definitely require the standardization and fixation of business processes from customer order to shipment. Therefore, ERP implementations are well proven to be coupled with BPR, although the extend and timing of BPR with respect to ERP implementation differ. This study aims at analyzing the effects of BPR on ERP implementation success. Basing on two Turkish ERP implementations in pharmaceutical sector, a comparative study is performed. One of the ERP implementations took place after a BPR implementation, whereas the other implementation was without a prior BPR application. Both implementations have been realized with the same consultant team, the case with prior BPR implementation going live first. The results of the case study reveal that if business processes are not optimized and improved before an ERP implementation, ERP live system would face with disharmony problems of processes and processes automated by ERP. This suggests a definite precedence relationship between BPR and ERP applications

Keywords: Business Process Reengineering, Enterprise Resource Planning

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Authors: Ruilian Zhao, Ling Lin

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MM-Path, an acronym for Method/Message Path, describes the dynamic interactions between methods in object-oriented systems. This paper discusses the classifications of MM-Path, based on the characteristics of object-oriented software. We categorize it according to the generation reasons, the effect scope and the composition of MM-Path. A formalized representation of MM-Path is also proposed, which has considered the influence of state on response method sequences of messages. .Moreover, an automatic MM-Path generation approach based on UML Statechart diagram has been presented, and the difficulties in identifying and generating MM-Path can be solved. . As a result, it provides a solid foundation for further research on test cases generation based on MM-Path.

Keywords: MM-Path, Message Sequence, Object-Oriented Integration Testing, Response Method Sequence, UML Statechart Diagram.

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Authors: Atul Krishna Banik

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Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.

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Authors: R. Nedunchezhian, K. Anbumani

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A big organization may have multiple branches spread across different locations. Processing of data from these branches becomes a huge task when innumerable transactions take place. Also, branches may be reluctant to forward their data for centralized processing but are ready to pass their association rules. Local mining may also generate a large amount of rules. Further, it is not practically possible for all local data sources to be of the same size. A model is proposed for discovering valid rules from different sized data sources where the valid rules are high weighted rules. These rules can be obtained from the high frequency rules generated from each of the data sources. A data source selection procedure is considered in order to efficiently synthesize rules. Support Equalization is another method proposed which focuses on eliminating low frequency rules at the local sites itself thus reducing the rules by a significant amount.

Keywords: Association rules, multiple data stores, synthesizing, valid rules.

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Authors: Thorben Kuprat, Julian Becker, Jonas Mayer, Peter Nyhuis

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For years now, it has been recognized that logistic performance capability contributes enormously to a production enterprise’s competitiveness and as such is a critical control lever. In doing so, the orientation on customer wishes (e.g. delivery dates) represents a key parameter not only in the value-adding production but also in product regeneration. Since production and regeneration processes have different characteristics, production planning and control measures cannot be directly transferred to regeneration processes. As part of a special research project, the Institute of Production Systems and Logistics Hannover is focused on increasing the logistic performance capability of regeneration processes for complex capital goods. The aim is to ensure logistic targets are met by implementing a model specifically designed to align the capacities and load in regeneration processes.

Keywords: Capacity planning, complex capital goods, logistic performance, regeneration process.

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Authors: Supachai Tangwongsan, Labhidhorn Pangphuthipong

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This research work proposes a model of network security systems aiming to prevent production system in a data center from being attacked by intrusions. Conceptually, we introduce a decoy system as a part of the security system for luring intrusions, and apply network intrusion detection (NIDS), coupled with the decoy system to perform intrusion prevention. When NIDS detects an activity of intrusions, it will signal a redirection module to redirect all malicious traffics to attack the decoy system instead, and hence the production system is protected and safe. However, in a normal situation, traffic will be simply forwarded to the production system as usual. Furthermore, we assess the performance of the model with various bandwidths, packet sizes and inter-attack intervals (attacking frequencies).

Keywords: Intrusion detection, Decoy, Snort, Intrusion prevention.

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Authors: Dan Ohev Zion, Alon Cohen

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In recent years, the presence of short-range millimeter-wave radar in civil application has increased significantly. Autonomous driving, security, 3D imaging and high data rate communication systems are a few examples. The next challenge is the integration inside small form-factor devices, such as smartphones (e.g. gesture recognition). The main challenge is implementation of a truly low-power, low-complexity high-resolution radar. The most popular approach is the Frequency Modulated Continuous Wave (FMCW) radar, with an analog multiplication front-end. In this paper, we present an approach for adaptive estimation and correction of impairments of such front-end, specifically implemented using the Six-Port Device (SPD) as the multiplier element. The proposed algorithm was simulated and implemented on a 60 GHz radar lab prototype.

Keywords: Radar, millimeter-wave, six-port, FMCW Radar, IQ mismatch.

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Authors: Z. Soleymani, M. Amirzadeh

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Quality Function Deployment (QFD) was developed in 1960 in Japan and introduced in 1983 in America and Europe. The paper presents a real application of this technique in a way that the method of applying QFD in design and production aero fuel pumps has been considered. While designing a product and in order to apply system engineering process, the first step is identification customer needs then its transition to engineering parameters. Since each change in deign after production process leads to extra human costs and also increase in products quality risk, QFD can make benefits in sale by meeting customer expectations. Since the needs identified as well, the use of QFD tool can lead to increase in communications and less deviation in design and production phases, finally it leads to produce the products with defined technical attributes.

Keywords: Customer voice, engineering parameters, QFD, gear pump.

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Authors: Sara Felloni, Giuliano Strini

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We explore entanglement in composite quantum systems and how its peculiar properties are exploited in quantum information and communication protocols by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for Bell states generation, measurements and projections, for dense coding and quantum teleportation, for probabilistic quantum machines designed to perform approximate quantum cloning and universal NOT and, finally, for quantum privacy amplification based on entanglement purification. Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.

Keywords: Diagrams of states, entanglement, quantum circuits, quantum information.

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Authors: Ilya Kavalchuk, Mehdi Seyedmahmoudian, Ben Horan, Aman Than Oo, Alex Stojcevski

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The power electronic components within Electric Vehicles (EV) need to operate in several important modes. Some modes directly influence safety, while others influence vehicle performance. Given the variety of functions and operational modes required of the power electronics, it needs to meet efficiency requirements to minimize power losses. Another challenge in the control and construction of such systems is the ability to support bidirectional power flow. This paper considers the construction, operation, and feasibility of available converters for electric vehicles with feasible configurations of electrical buses and loads. This paper describes logic and control signals for the converters for different operations conditions based on the efficiency and energy usage bases.

Keywords: Electric Vehicles, Electrical Machines Control, Power Electronics, Powerflow Regulations.

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Authors: Viet-Hung Truong, Seung-Eock Kim

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This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: Advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame.

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Authors: V. Chahal, A. Nagpal, Y. B. Pakade, J. K. Katnoria

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Soil is a complex physical and biological system that provides support, water, nutrients and oxygen to the plants. Apart from these, it acts as a connecting link between inorganic, organic and living components of the ecosystem. In recent years, presence of xenobiotics, alterations in the natural soil environment, application of pesticides/inorganic fertilizers, percolation of contaminated surface water as well as leachates from landfills to subsurface strata and direct discharge of industrial wastes to the land have resulted in soil pollution which in turn has posed severe threats to human health especially in terms of causing carcinogenicity by direct DNA damage. The present review is an attempt to summarize literature on sources of soil pollution, characterization of pollutants and their consequences in different living systems.

Keywords: Soil Pollution, Contaminants, Heavy metals, Pesticides, Bioassays.

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Authors: Christina Volioti, Sotiris Manitsaris, Eleni Katsouli, Vasiliki Tsekouropoulou, Leontios J. Hadjileontiadis

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The piano sonatas of Beethoven represent part of the Intangible Cultural Heritage. The aims of this research were to further explore this intangibility by placing emphasis on defining emotional normative ratings for the “Waldstein” (Op. 53) and “Tempest” (Op. 31) Sonatas of Beethoven. To this end, a musicological analysis was conducted on these particular sonatas and referential patterns in these works of Beethoven were defined. Appropriate interactive questionnaires were designed in order to create a statistical normative rating that describes the emotional status when an individual listens to these musical excerpts. Based on these ratings, it is possible for emotional annotations for these same referential patterns to be created and integrated into the music score.

Keywords: Emotional annotations, intangible cultural heritage, musicological analysis, normative ratings.

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Authors: J. Fernandez, R. Fernandez de Canete, J. Perea-Paizal, J. C. Ramos-Diaz

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The high prevalence of cardiovascular diseases has provoked a raising interest in the development of mathematical models in order to evaluate the cardiovascular function both under physiological and pathological conditions. In this paper, a physical model of the cardiovascular system with intrinsic regulation is presented and implemented by using the object-oriented Modelica simulation software tools.  For this task, a multi-compartmental system previously validated with physiological data has been built, based on the interconnection of cardiovascular elements such as resistances, capacitances and pumping among others, by following an electrohydraulic analogy. The results obtained under both physiological and pathological scenarios provide an easy interpretative key to analyze the hemodynamic behavior of the patient. The described approach represents a valuable tool in the teaching of physiology for graduate medical and nursing students among others.

Keywords: Cardiovascular system, Modelica simulation software, physical modeling, teaching tool.

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Authors: S.Shokri, S.Zahedi, M.Ahmadi Marvast, B. Baloochi, H.Ganji

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In this research, a systematic investigation was carried out to determine the optimum conditions of HDS reactor. Moreover, a suitable model was developed for a rigorous RTO (real time optimization) loop of HDS (Hydro desulfurization) process. A systematic experimental series was designed based on CCD (Central Composite design) and carried out in the related pilot plant to tune the develop model. The designed variables in the experiments were Temperature, LHSV and pressure. However, the hydrogen over fresh feed ratio was remained constant. The ranges of these variables were respectively equal to 320-380ºC, 1- 21/hr and 50-55 bar. a power law kinetic model was also developed for our further research in the future .The rate order and activation energy , power of reactant concentration and frequency factor of this model was respectively equal to 1.4, 92.66 kJ/mol and k0=2.7*109 .

Keywords: Statistical model, Multiphase Reactors, Gas oil, Hydrodesulfurization, Optimization, Kinetics

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Authors: Hazem M. El-Bakry, Ahmed A. Saleh, Taghreed T. Asfour

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Adaptive e-learning today gives the student a central role in his own learning process. It allows learners to try things out, participate in courses like never before, and get more out of learning than before. In this paper, an adaptive e-learning model for logic design, simplification of Boolean functions and related fields is presented. Such model presents suitable courses for each student in a dynamic and adaptive manner using existing database and workflow technologies. The main objective of this research work is to provide an adaptive e-learning model based learners' personality using explicit and implicit feedback. To recognize the learner-s, we develop dimensions to decide each individual learning style in order to accommodate different abilities of the users and to develop vital skills. Thus, the proposed model becomes more powerful, user friendly and easy to use and interpret. Finally, it suggests a learning strategy and appropriate electronic media that match the learner-s preference.

Keywords: Adaptive learning, Learning styles, Teaching strategies.

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Authors: Maidul Islam, Dibakar Roy Chowdhury, Gagan Kumar

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We investigate sensing capabilities of a planar plasmonic THz waveguide. The waveguide is comprised of one dimensional array of periodically arranged sub wavelength scale corrugations in the form of rectangular dimples in order to ensure the plasmonic response. The THz waveguide transmission is observed for polyimide (as thin film) substance filling the dimples. The refractive index of the polyimide film is varied to examine various sensing parameters such as frequency shift, sensitivity and Figure of Merit (FoM) of the fundamental plasmonic resonance supported by the waveguide. In efforts to improve sensing characteristics, we also examine sensing capabilities of a plasmonic waveguide having V shaped corrugations and compare results with that of rectangular dimples. The proposed study could be significant in developing new terahertz sensors with improved sensitivity utilizing the plasmonic waveguides.

Keywords: Terahertz, plasmonic, sensor, sub-wavelength structures.

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: All-or-none, computational modelling, mathematical model, transmembrane voltage, action potential.

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Authors: Khaled M. Khader, Mamdouh I. Elimy, Omayma A. Nada

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Sustainable development is the nominal goal of most countries at present. In general, fossil fuels are the development mainstay of most world countries. Regrettably, the fossil fuel consumption rate is very high, and the world is facing the problem of conventional fuels depletion soon. In addition, there are many problems of environmental pollution resulting from the emission of harmful gases and vapors during fuel burning. Thus, clean, renewable energy became the main concern of most countries for filling the gap between available energy resources and their growing needs. There are many renewable energy sources such as wind, solar and wave energy. Energy can be obtained from the motion of sea waves almost all the time. However, power generation from solar or wind energy is highly restricted to sunny periods or the availability of suitable wind speeds. Moreover, energy produced from sea wave motion is one of the cheapest types of clean energy. In addition, renewable energy usage of sea waves guarantees safe environmental conditions. Cheap electricity can be generated from wave energy using different systems such as oscillating bodies' system, pendulum gate system, ocean wave dragon system and oscillating water column device. In this paper, a multi-criteria model has been developed using Analytic Hierarchy Process (AHP) to support the decision of selecting the most effective system for generating power from sea waves. This paper provides a widespread overview of the different design alternatives for sea wave energy converter systems. The considered design alternatives have been evaluated using the developed AHP model. The multi-criteria assessment reveals that the off-shore Oscillating Water Column (OWC) system is the most appropriate system for generating power from sea waves. The OWC system consists of a suitable hollow chamber at the shore which is completely closed except at its base which has an open area for gathering moving sea waves. Sea wave's motion pushes the air up and down passing through a suitable well turbine for generating power. Improving the power generation capability of the OWC system is one of the main objectives of this research. After investigating the effect of some design modifications, it has been concluded that selecting the appropriate settings of some effective design parameters such as the number of layers of Wells turbine fans and the intermediate distance between the fans can result in significant improvements. Moreover, simple dynamic analysis of the Wells turbine is introduced. Furthermore, this paper strives for comparing the theoretical and experimental results of the built experimental prototype.

Keywords: Renewable energy, oscillating water column, multi-criteria selection, wells turbine.

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Authors: Lu Yanhui, Wang Chunming, Yin Changchuan, Yue Guangxin

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In this paper, we address the problem of adaptive radio resource allocation (RRA) and packet scheduling in the downlink of a cellular OFDMA system, and propose a downlink multi-carrier proportional fair (MPF) scheduler and its joint with adaptive RRA algorithm to distribute radio resources among multiple users according to their individual QoS requirements. The allocation and scheduling objective is to maximize the total throughput, while at the same time maintaining the fairness among users. The simulation results demonstrate that the methods presented provide for user more explicit fairness relative to RRA algorithm, but the joint scheme achieves the higher sum-rate capacity with flexible parameters setting compared with MPF scheduler.

Keywords: OFDMA, adaptive radio resource allocation, scheduling, QoS.

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Authors: Nebu Tom John, N. Dhinakaran

Abstract:

Multiparty voice over IP (MVoIP) systems allows a group of people to freely communicate each other via the internet, which have many applications such as online gaming, teleconferencing, online stock trading etc. Peertalk is a peer to peer multiparty voice over IP system (MVoIP) which is more feasible than existing approaches such as p2p overlay multicast and coupled distributed processing. Since the stream mixing and distribution are done by the peers, it is vulnerable to major security threats like nodes misbehavior, eavesdropping, Sybil attacks, Denial of Service (DoS), call tampering, Man in the Middle attacks etc. To thwart the security threats, a security framework called PEERTS (PEEred Reputed Trustworthy System for peertalk) is implemented so that efficient and secure communication can be carried out between peers.

Keywords: Key management system, peer-to-peer voice streaming, reputed trust management system, voice-over-IP.

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Authors: S. Avdakovic, A. Lukac, A. Nuhanovic, M. Music

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Renewable energy systems are becoming a topic of great interest and investment in the world. In recent years wind power generation has experienced a very fast development in the whole world. For planning and successful implementations of good wind power plant projects, wind potential measurements are required. In these projects, of great importance is the effective choice of the micro location for wind potential measurements, installation of the measurement station with the appropriate measuring equipment, its maintenance and analysis of the gained data on wind potential characteristics. In this paper, a wavelet transform has been applied to analyze the wind speed data in the context of insight in the characteristics of the wind and the selection of suitable locations that could be the subject of a wind farm construction. This approach shows that it can be a useful tool in investigation of wind potential.

Keywords: Wind potential, Wind speed data, Wavelettransform.

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Authors: Nasser Mohamed Ramli, Nurul Izzati Zulkifli

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Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.

Keywords: Fuzzy, sump, level, controller.

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Authors: Magdi M. E. Zumrawi

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It is quite essential to investigate the causes of pavement deterioration in order to select the proper maintenance technique. The objective of this study was to identify factors cause deterioration of recently constructed roads in Khartoum state. A comprehensive literature concerning the factors of road deterioration, common road defects and their causes were reviewed. Three major road projects with different deterioration reasons were selected for this study. The investigation involved field survey and laboratory testing on those projects to examine the existing pavement conditions. The results revealed that the roads investigated experienced severe failures in the forms of cracks, potholes, and rutting in the wheel path. The causes of those failures were found mainly linked to poor drainage, traffic overloading, expansive subgrade soils, and the use of low quality materials in construction. Based on the results, recommendations were provided to help highway engineers in selecting the most effective repair techniques for specific kinds of distresses.

Keywords: Pavement, deterioration, causes, failures.

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Authors: Teerapun Saeheaw, Nivit Charoenchai, Wichai Chattinnawat

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Simulation model is an easy way to build up models to represent real life scenarios, to identify bottlenecks and to enhance system performance. Using a valid simulation model may give several advantages in creating better manufacturing design in order to improve the system performances. This paper presents result of implementing a simulation model to design hard disk drive manufacturing process by applying line balancing to improve both productivity and quality of hard disk drive process. The line balance efficiency showed 86% decrease in work in process, output was increased by an average of 80%, average time in the system was decreased 86% and waiting time was decreased 90%.

Keywords: line balancing, arena, hard disk drive process, simulation, work in process (WIP)

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Authors: Sagaren Pillay

Abstract:

This study empirically examines the long run equilibrium relationship between South Africa’s exports and imports using quarterly data from 1985 to 2012. The theoretical framework used for the study is based on Johansen’s Maximum Likelihood cointegration technique which tests for both the existence and number of cointegration vectors that exists. The study finds that both the series are integrated of order one and are cointegrated. A statistically significant cointegrating relationship is found to exist between exports and imports. The study models this unique linear and lagged relationship using a Vector Error Correction Model (VECM). The findings of the study confirm the existence of a long run equilibrium relationship between exports and imports.

Keywords: Cointegration lagged, linear, maximum likelihood, vector error correction model.

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