Search results for: Discrete spatiotemporal systems
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4817

Search results for: Discrete spatiotemporal systems

4457 Noise Reduction in Image Sequences using an Effective Fuzzy Algorithm

Authors: Mahmoud Saeidi, Khadijeh Saeidi, Mahmoud Khaleghi

Abstract:

In this paper, we propose a novel spatiotemporal fuzzy based algorithm for noise filtering of image sequences. Our proposed algorithm uses adaptive weights based on a triangular membership functions. In this algorithm median filter is used to suppress noise. Experimental results show when the images are corrupted by highdensity Salt and Pepper noise, our fuzzy based algorithm for noise filtering of image sequences, are much more effective in suppressing noise and preserving edges than the previously reported algorithms such as [1-7]. Indeed, assigned weights to noisy pixels are very adaptive so that they well make use of correlation of pixels. On the other hand, the motion estimation methods are erroneous and in highdensity noise they may degrade the filter performance. Therefore, our proposed fuzzy algorithm doesn-t need any estimation of motion trajectory. The proposed algorithm admissibly removes noise without having any knowledge of Salt and Pepper noise density.

Keywords: Image Sequences, Noise Reduction, fuzzy algorithm, triangular membership function

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4456 Modelling of Electron States in Quantum -Wire Systems - Influence of Stochastic Effects on the Confining Potential

Authors: Mikhail Vladimirovich Deryabin, Morten Willatzen

Abstract:

In this work, we address theoretically the influence of red and white Gaussian noise for electronic energies and eigenstates of cylindrically shaped quantum dots. The stochastic effect can be imagined as resulting from crystal-growth statistical fluctuations in the quantum-dot material composition. In particular we obtain analytical expressions for the eigenvalue shifts and electronic envelope functions in the k . p formalism due to stochastic variations in the confining band-edge potential. It is shown that white noise in the band-edge potential leaves electronic properties almost unaffected while red noise may lead to changes in state energies and envelopefunction amplitudes of several percentages. In the latter case, the ensemble-averaged envelope function decays as a function of distance. It is also shown that, in a stochastic system, constant ensembleaveraged envelope functions are the only bounded solutions for the infinite quantum-wire problem and the energy spectrum is completely discrete. In other words, the infinite stochastic quantum wire behaves, ensemble-averaged, as an atom.

Keywords: cylindrical quantum dots, electronic eigen energies, red and white Gaussian noise, ensemble averaging effects.

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4455 Finite Time Symplectic Synchronization between Two Different Chaotic Systems

Authors: Chunming Xu

Abstract:

In this paper, the finite-time symplectic synchronization between two different chaotic systems is investigated. Based on the finite-time stability theory, a simple adaptive feedback scheme is proposed to realize finite-time symplectic synchronization for the Lorenz and L¨u systems. Numerical examples are provided to show the effectiveness of the proposed method.

Keywords: Chaotic systems, symplectic synchronization, finite-time synchronization, adaptive controller.

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4454 Flexibility in Modular Furniture Systems in Open Offices, Famagusta, North Cyprus

Authors: E. Farjami, La. Mohammadzadeh Afshar, Li. Mohammadzade Afshar, A. Taran

Abstract:

Nowadays, flexibility introduced as a modern technology in furniture systems especially in interior planning design. According to results, the most important impact of these systems can be seen on open plan design that makes workspaces comfortable and increases the productivity of employees besides making good relationship between them. Briefly, there are some factors along with new systems in furniture design help create inappropriate space to make working better and easier while it has modular planning organization. It brings about some approaches to have a successful space for open offices with modular design and flexible furniture systems. These approaches have been investigated in open and close offices at Eastern Mediterranean University (EMU) in Famagusta, Cyprus, using information extracted from questionnaires.

Keywords: Flexibility, Flexible Furniture, Modular design, Open offices, Modular furniture systems.

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4453 FPGA Based Longitudinal and Lateral Controller Implementation for a Small UAV

Authors: Hafiz ul Azad, Dragan V.Lazic, Waqar Shahid

Abstract:

This paper presents implementation of attitude controller for a small UAV using field programmable gate array (FPGA). Due to the small size constrain a miniature more compact and computationally extensive; autopilot platform is needed for such systems. More over UAV autopilot has to deal with extremely adverse situations in the shortest possible time, while accomplishing its mission. FPGAs in the recent past have rendered themselves as fast, parallel, real time, processing devices in a compact size. This work utilizes this fact and implements different attitude controllers for a small UAV in FPGA, using its parallel processing capabilities. Attitude controller is designed in MATLAB/Simulink environment. The discrete version of this controller is implemented using pipelining followed by retiming, to reduce the critical path and thereby clock period of the controller datapath. Pipelined, retimed, parallel PID controller implementation is done using rapidprototyping and testing efficient development tool of “system generator", which has been developed by Xilinx for FPGA implementation. The improved timing performance enables the controller to react abruptly to any changes made to the attitudes of UAV.

Keywords: Field Programmable gate array (FPGA), Hardwaredescriptive Language (HDL), PID, Pipelining, Retiming, XilinxSystem Generator.

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4452 A Functional Framework for Large Scale Application Software Systems

Authors: Han-hua Lu, Shun-yi Zhang, Yong Zheng, Ya-shi Wang, Li-juan Min

Abstract:

From the perspective of system of systems (SoS) and emergent behaviors, this paper describes large scale application software systems, and proposes framework methods to further depict systems- functional and non-functional characteristics. Besides, this paper also specifically discusses some functional frameworks. In the end, the framework-s applications in system disintegrations, system architecture and stable intermediate forms are additionally dealt with in this in building, deployment and maintenance of large scale software applications.

Keywords: application software system, framework methods, system of systems, emergent behaviors

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4451 Finite-Horizon Tracking Control for Repetitive Systems with Uncertain Initial Conditions

Authors: Sung Wook Yun, Yun Jong Choi, Kyong-min Lee, Poogyeon Park*

Abstract:

Repetitive systems stand for a kind of systems that perform a simple task on a fixed pattern repetitively, which are widely spread in industrial fields. Hence, many researchers have been interested in those systems, especially in the field of iterative learning control (ILC). In this paper, we propose a finite-horizon tracking control scheme for linear time-varying repetitive systems with uncertain initial conditions. The scheme is derived both analytically and numerically for state-feedback systems and only numerically for output-feedback systems. Then, it is extended to stable systems with input constraints. All numerical schemes are developed in the forms of linear matrix inequalities (LMIs). A distinguished feature of the proposed scheme from the existing iterative learning control is that the scheme guarantees the tracking performance exactly even under uncertain initial conditions. The simulation results demonstrate the good performance of the proposed scheme.

Keywords: Finite time horizon, linear matrix inequality (LMI), repetitive system, uncertain initial condition.

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4450 The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem

Authors: Jiming Yang

Abstract:

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

Keywords: Singularly perturbed, upwind difference, uniform convergence.

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4449 Contribution of On-Site and Off-Site Processes to Greenhouse Gas (GHG) Emissions by Wastewater Treatment Plants

Authors: Laleh Yerushalmi, Fariborz Haghighat, Maziar Bani Shahabadi

Abstract:

The estimation of overall on-site and off-site greenhouse gas (GHG) emissions by wastewater treatment plants revealed that in anaerobic and hybrid treatment systems greater emissions result from off-site processes compared to on-site processes. However, in aerobic treatment systems, onsite processes make a higher contribution to the overall GHG emissions. The total GHG emissions were estimated to be 1.6, 3.3 and 3.8 kg CO2-e/kg BOD in the aerobic, anaerobic and hybrid treatment systems, respectively. In the aerobic treatment system without the recovery and use of the generated biogas, the off-site GHG emissions were 0.65 kg CO2-e/kg BOD, accounting for 40.2% of the overall GHG emissions. This value changed to 2.3 and 2.6 kg CO2-e/kg BOD, and accounted for 69.9% and 68.1% of the overall GHG emissions in the anaerobic and hybrid treatment systems, respectively. The increased off-site GHG emissions in the anaerobic and hybrid treatment systems are mainly due to material usage and energy demand in these systems. The anaerobic digester can contribute up to 100%, 55% and 60% of the overall energy needs of plants in the aerobic, anaerobic and hybrid treatment systems, respectively.

Keywords: On-site and off-site greenhouse gas (GHG)emissions, wastewater treatment plants, biogas recovery

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4448 An Optimal Algorithm for Finding (r, Q) Policy in a Price-Dependent Order Quantity Inventory System with Soft Budget Constraint

Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

Abstract:

This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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4447 Modeling and Control of an Acrobot Using MATLAB and Simulink

Authors: Dong Sang Yoo

Abstract:

The problem of finding control laws for underactuated systems has attracted growing attention since these systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled. The acrobot, which is a planar two-link robotic arm in the vertical plane with an actuator at the elbow but no actuator at the shoulder, is a representative in underactuated systems. In this paper, the dynamic model of the acrobot is implemented using Mathworks’ Simscape. And the sliding mode control is constructed using MATLAB and Simulink.

Keywords: Acrobot, MATLAB and Simulink, sliding mode control, underactuated systems.

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4446 Stability Analysis of Fractional Order Systems with Time Delay

Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li

Abstract:

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords: Fractional order systems, Time delay, Characteristic equation.

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4445 RUPSec: An Extension on RUP for Developing Secure Systems - Requirements Discipline

Authors: Mohammad Reza Ayatollahzadeh Shirazi, Pooya Jaferian, Golnaz Elahi, Hamid Baghi, Babak Sadeghian

Abstract:

The world is moving rapidly toward the deployment of information and communication systems. Nowadays, computing systems with their fast growth are found everywhere and one of the main challenges for these systems is increasing attacks and security threats against them. Thus, capturing, analyzing and verifying security requirements becomes a very important activity in development process of computing systems, specially in developing systems such as banking, military and e-business systems. For developing every system, a process model which includes a process, methods and tools is chosen. The Rational Unified Process (RUP) is one of the most popular and complete process models which is used by developers in recent years. This process model should be extended to be used in developing secure software systems. In this paper, the Requirement Discipline of RUP is extended to improve RUP for developing secure software systems. These proposed extensions are adding and integrating a number of Activities, Roles, and Artifacts to RUP in order to capture, document and model threats and security requirements of system. These extensions introduce a group of clear and stepwise activities to developers. By following these activities, developers assure that security requirements are captured and modeled. These models are used in design, implementation and test activitie

Keywords:

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4444 Business Intelligence for N=1 Analytics using Hybrid Intelligent System Approach

Authors: Rajendra M Sonar

Abstract:

The future of business intelligence (BI) is to integrate intelligence into operational systems that works in real-time analyzing small chunks of data based on requirements on continuous basis. This is moving away from traditional approach of doing analysis on ad-hoc basis or sporadically in passive and off-line mode analyzing huge amount data. Various AI techniques such as expert systems, case-based reasoning, neural-networks play important role in building business intelligent systems. Since BI involves various tasks and models various types of problems, hybrid intelligent techniques can be better choice. Intelligent systems accessible through web services make it easier to integrate them into existing operational systems to add intelligence in every business processes. These can be built to be invoked in modular and distributed way to work in real time. Functionality of such systems can be extended to get external inputs compatible with formats like RSS. In this paper, we describe a framework that use effective combinations of these techniques, accessible through web services and work in real-time. We have successfully developed various prototype systems and done few commercial deployments in the area of personalization and recommendation on mobile and websites.

Keywords: Business Intelligence, Customer Relationship Management, Hybrid Intelligent Systems, Personalization and Recommendation (P&R), Recommender Systems.

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4443 Power System Contingency Analysis Using Multiagent Systems

Authors: Anant Oonsivilai, Kenedy A. Greyson

Abstract:

The demand of the energy management systems (EMS) set forth by modern power systems requires fast energy management systems. Contingency analysis is among the functions in EMS which is time consuming. In order to handle this limitation, this paper introduces agent based technology in the contingency analysis. The main function of agents is to speed up the performance. Negotiations process in decision making is explained and the issue set forth is the minimization of the operating costs. The IEEE 14 bus system and its line outage have been used in the research and simulation results are presented.

Keywords: Agents, model, negotiation, optimal dispatch, powersystems.

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4442 A Performance Study of Fixed, Single-Axis and Dual-Axis Photovoltaic Systems in Kuwait

Authors: A. Al-Rashidi, A. El-Hamalawi

Abstract:

In this paper, a performance study was conducted to investigate single and dual-axis PV systems to generate electricity in five different sites in Kuwait. Relevant data were obtained by using two sources for validation purposes. A commercial software, PVsyst, was used to analyse the data, such as metrological data and other input parameters, and compute the performance parameters such as capacity factor (CF) and final yield (YF). The results indicated that single and dual-axis PV systems would be very beneficial to electricity generation in Kuwait as an alternative source to conventional power plants, especially with the increased demand over time. The ranges were also found to be competitive in comparison to leading countries using similar systems. A significant increase in CF and YF values around 24% and 28.8% was achieved related to the use of single and dual systems, respectively.

Keywords: Single-axis and dual-axis photovoltaic systems, capacity factor, final yield, renewable energy, Kuwait.

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4441 A Modification on Newton's Method for Solving Systems of Nonlinear Equations

Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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4440 Managing User Expectations in Information Systems Development

Authors: Linda, Sau-ling Lai

Abstract:

This paper provides new ways to explore the old problem of failure of information systems development in an organisation. Based on the theory of cognitive dissonance, information systems (IS) failure is defined as a gap between what the users expect from an information system and how well these expectations are met by the perceived performance of the delivered system. Bridging the expectation-perception gap requires that IS professionals make a radical change from being the proprietor of information systems and products to being service providers. In order to deliver systems and services that IS users perceive as valuable, IS people must become expert in determining and assessing users- expectations and perceptions. It is also suggested that the IS community, in general, has given relatively little attention to the front-end process of requirements specification for IS development. There is a simplistic belief that requirements are obtainable from users, they are then translatable into a formal specification. The process of information needs analysis is problematic and worthy of investigation.

Keywords: Information Systems Development, Cognitive Dissonance, Expectation-Perception Gap, Requirements Analysis.

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4439 Review, Analysis and Simulation of Advanced Technology Solutions of Selected Components in Power Electronics Systems (PES) of More Electric Aircraft

Authors: Lucjan Setlak, Emil Ruda

Abstract:

The subject of this paper is to review, comparative analysis and simulation of selected components of power electronic systems (PES), consistent with the concept of a more electric aircraft (MEA). Comparative analysis and simulation in software environment MATLAB / Simulink were carried out on the base of a group of representatives of civil aircraft (B-787, A-380) and military (F-22 Raptor, F-35) in the context of multi-pulse converters used in them (6- and 12-pulse, and 18- and 24-pulse), which are key components of high-tech electronics on-board power systems of autonomous power systems (ASE) of modern aircraft (airplanes of the future).

Keywords: Converters, electrical machinery, more electric aircraft, MEA, power electronics systems, PES.

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4438 A Soft Systems Methodology Perspective on Data Warehousing Education Improvement

Authors: R. Goede, E. Taylor

Abstract:

This paper demonstrates how the soft systems methodology can be used to improve the delivery of a module in data warehousing for fourth year information technology students. Graduates in information technology needs to have academic skills but also needs to have good practical skills to meet the skills requirements of the information technology industry. In developing and improving current data warehousing education modules one has to find a balance in meeting the expectations of various role players such as the students themselves, industry and academia. The soft systems methodology, developed by Peter Checkland, provides a methodology for facilitating problem understanding from different world views. In this paper it is demonstrated how the soft systems methodology can be used to plan the improvement of data warehousing education for fourth year information technology students.

Keywords: Data warehousing, education, soft systems methodology, stakeholders, systems thinking.

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4437 Standardization and Adaption Requirements in Production System Transplants

Authors: G. Schuh, T. Potente, D. Kupke, S. Ivanescu

Abstract:

As German companies roll out their standardized production systems to offshore manufacturing plants, they face the challenge of implementing them in different cultural environments. Studies show that the local adaptation is one of the key factors for a successful implementation. Thus the question arises of where the line between standardization and adaptation can be drawn. To answer this question the influence of culture on production systems is analysed in this paper. The culturally contingent components of production systems are identified. Also the contingency factors are classified according to their impact on the necessary adaptation changes and implementation effort. Culturally specific decision making, coordination, communication and motivation patterns require one-time changes in organizational and process design. The attitude towards rules requires more intense coaching and controlling. Lastly a framework is developed to depict standardization and adaption needs when transplanting production systems into different cultural environments.

Keywords: Culture, influence of national culture on production systems, lean production, production systems.

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4436 Automatic Vehicle Location Systems

Authors: S.A. Mahdavifar, G.R. Sotudeh., K. Heydari

Abstract:

In this article, a single application is suggested to determine the position of vehicles using Geographical Information Systems (GIS) and Geographical Position Systems (GPS). The part of the article material included mapping three dimensional coordinates to two dimensional coordinates using UTM or LAMBERT geographical methods, and the algorithm of conversion of GPS information into GIS maps is studied. Also, suggestions are given in order to implement this system based on web (called web based systems). To apply this system in IRAN, related official in this case are introduced and their duties are explained. Finally, economy analyzed is assisted according to IRAN communicational system.

Keywords: GIS-GPS-UTM-LAMBERT.

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4435 Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

Keywords: Impulsive systems, switched systems, quadratic stabilization, robust stabilization.

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4434 Software Industrialization in Systems Integration

Authors: Matthias Minich, B. Harriehausen-Muehlbauer, C. Wentzel

Abstract:

Today-s economy is in a permanent change, causing merger and acquisitions and co operations between enterprises. As a consequence, process adaptations and realignments result in systems integration and software development projects. Processes and procedures to execute such projects are still reliant on craftsman-ship of highly skilled workers. A generally accepted, industrialized production, characterized by high efficiency and quality, seems inevitable. In spite of this, current concepts of software industrialization are aimed at traditional software engineering and do not consider the characteristics of systems integration. The present work points out these particularities and discusses the applicability of existing industrial concepts in the systems integration domain. Consequently it defines further areas of research necessary to bring the field of systems integration closer to an industrialized production, allowing a higher efficiency, quality and return on investment.

Keywords: Software Industrialization, Systems Integration, Software Product Lines, Component Based Development, Model Driven Development.

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4433 Software Model for a Computer Based Training for an HVDC Control Desk Simulator

Authors: José R. G. Braga, Joice B. Mendes, Guilherme H. Caponetto, Alexandre C. B. Ramos

Abstract:

With major technological advances and to reduce the cost of training apprentices for real-time critical systems, it was necessary the development of Intelligent Tutoring Systems for training apprentices in these systems. These systems, in general, have interactive features so that the learning is actually more efficient, making the learner more familiar with the mechanism in question. In the home stage of learning, tests are performed to obtain the student's income, a measure on their use. The aim of this paper is to present a framework to model an Intelligent Tutoring Systems using the UML language. The various steps of the analysis are considered the diagrams required to build a general model, whose purpose is to present the different perspectives of its development.

Keywords: Computer based training, Hypermedia, Software modeling.

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4432 An Approach of Control System for Automated Storage and Retrieval System (AS/RS)

Authors: M. Soyaslan, A. Fenercioglu, C. Kozkurt

Abstract:

Automated storage and retrieval systems (AS/RS) become frequently used systems in warehouses. There has been a transition from human based forklift applications to fast and safe AS/RS applications in firm-s warehouse systems. In this study, basic components and automation systems of the AS/RS are examined. Proposed system's automation components and their tasks in the system control algorithm were stated. According to this control algorithm the control system structure was obtained.

Keywords: AS/RS, Automatic Storage and Retrieval System, Warehouse Control System

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4431 Comparative Analysis of Photovoltaic Systems

Authors: Irtaza M. Syed, Kaamran Raahemifar

Abstract:

This paper presents comparative analysis of photovoltaic systems (PVS) and propose practical techniques to improve operational efficiency of the PVS. The best engineering and construction practices for PVS are identified and field oriented recommendation are made. Comparative analysis of central and string inverter based, as well as 600 and 1000VDC PVS are performed. In addition, direct current (DC) and alternating current (AC) photovoltaic (PV) module based systems are compared. Comparison shows that 1000V DC String Inverters based PVS is the best choice.

Keywords: Photovoltaic module, photovoltaic systems, operational efficiency improvement, comparative analysis.

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4430 Cryptography over Sextic Extension with Cubic Subfield

Authors: A. Chillali, M. Sahmoudi

Abstract:

In this paper, we will give a cryptographic application over the integral closure O_Lof sextic extension L, namely L is an extension of Q of degree 6 in the form Q(a,b), which is a rational quadratic and monogenic extension over a pure monogenic cubic subfield K generated by a who is a root of monic irreducible polynomial of degree 2 andb is a root of irreducible polynomial of degree 3.

Keywords: Integral bases, Cryptography, Discrete logarithm problem.

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4429 Robust H State-Feedback Control for Uncertain Fuzzy Markovian Jump Systems: LMI-Based Design

Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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4428 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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