Search results for: multirate systems

Authors: Anuraj Singh, Sunita Gakkhar

Abstract:

The three-species food web model proposed and investigated by Gakkhar and Naji is known to have chaotic behaviour for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.

Keywords: Lyapunov Exponent, Bidirectional Coupling, ChaosSynchronization, Synchronization Manifold

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Authors: Chi-Lun Liu

Abstract:

Requirements modeling and analysis are important in successful information systems' maintenance. Unified Modeling Language (UML) class diagrams are useful standards for modeling information systems. To our best knowledge, there is a lack of a systems development methodology described by the organism metaphor. The core concept of this metaphor is adaptation. Using the knowledge representation and reasoning approach and ontologies to adopt new requirements are emergent in recent years. This paper proposes an organic methodology which is based on constructivism theory. This methodology is a knowledge representation and reasoning approach to analyze new requirements in the class diagrams maintenance. The process and rules in the proposed methodology automatically analyze inconsistencies in the class diagram. In the big data era, developing an automatic tool based on the proposed methodology to analyze large amounts of class diagram data is an important research topic in the future.

Keywords: Knowledge representation, reasoning, ontology, class diagram, software engineering.

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Authors: Muhammad Rehan Khalid, Ahmed Farhan Hanif, Adnan Ahmed Khan

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This paper investigates the performance of Multiple- Input Multiple-Output (MIMO) feedback system combined with Orthogonal Frequency Division Multiplexing (OFDM). Two types of codebook based channel feedback techniques are used in this work. The first feedback technique uses a combination of both the long-term and short-term channel state information (CSI) at the transmitter, whereas the second technique uses only the short term CSI. The long-term and short-term CSI at the transmitter is used for efficient channel utilization. OFDM is a powerful technique employed in communication systems suffering from frequency selectivity. Combined with multiple antennas at the transmitter and receiver, OFDM proves to be robust against delay spread. Moreover, it leads to significant data rates with improved bit error performance over links having only a single antenna at both the transmitter and receiver. The effectiveness of these techniques has been demonstrated through the simulation of a MIMO-OFDM feedback system. The results have been evaluated for 4x4 MIMO channels. Simulation results indicate the benefits of the MIMO-OFDM channel feedback system over the one without incorporating OFDM. Performance gain of about 3 dB is observed for MIMO-OFDM feedback system as compared to the one without employing OFDM. Hence MIMO-OFDM becomes an attractive approach for future high speed wireless communication systems.

Keywords: MIMO systems, OFDM, Codebooks, Channel Feedback

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Authors: Beata Czarnacka-Chrobot

Abstract:

Execution of Business Software Systems (BSS) Development and Enhancement Projects (D&EP) is characterized by the exceptionally low effectiveness, leading to considerable financial losses. The general reason for low effectiveness of such projects is that they are inappropriately managed. One of the factors of proper BSS D&EP management is suitable (reliable and objective) method of project work effort estimation since this is what determines correct estimation of its major attributes: project cost and duration. BSS D&EP is usually considered to be accomplished effectively if product of a planned functionality is delivered without cost and time overrun. The goal of this paper is to prove that choosing approach to the BSS D&EP work effort estimation has a considerable influence on the effectiveness of such projects execution.

Keywords: Business software systems, development and enhancement projects, effectiveness, work effort estimation methods, software product size, software product functionality, project duration, project cost.

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Authors: G. Parmar, R. Prasad, S. Mukherjee

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The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

Keywords: Genetic algorithm, Integral square error, Orderreduction, Stability equation method.

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Authors: K. K. Starkov, A. Y. Pogromsky, I. J. B. F. Adan, J. E. Rooda

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In this paper we present our results on the performance analysis of a multi-product manufacturing line. We study the influence of external perturbations, intermediate buffer content and the number of manufacturing stages on the production tracking error of each machine in the multi-product line operated under a surplusbased production control policy. Starting by the analysis of a single machine with multiple production stages (one for each product type), we provide bounds on the production error of each stage. Then, we extend our analysis to a line of multi-stage machines, where similarly, bounds on each production tracking error for each product type, as well as buffer content are obtained. Details on performance of the closed-loop flow line model are illustrated in numerical simulations.

Keywords: Flexible manufacturing systems, tracking systems, discrete time systems, production control, boundary conditions.

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Authors: Youngpo Lee, Jaewoo Lee, Seokho Yoon

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This paper proposes a fast code acquisition scheme for optical code division multiple access (O-CDMA) systems. Unlike the conventional scheme, the proposed scheme employs multiple thresholds providing a shorter mean acquisition time (MAT) performance. The simulation results show that the MAT of the proposed scheme is shorter than that of the conventional scheme.

Keywords: Optical CDMA, acquisition, MAT, multiple-shift

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Authors: Hamze Torabian, Mohammad Mehrabioun Mohammadi

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Like many other industries, the payment industry has been affected by digital transformation. The importance of digital transformation in the payment industry is very crucial. Because the payment industry is considered a leading industry in digital and emerging technologies, and the digitalization of other industries such as retail, health, and telecommunication, it also depends on the growth rate of digitalized payment systems. One of the technological innovations in service management is Field Service Management (FSM). Despite the widespread use of FSM in various industries such as petrochemical, health, maintenance, etc., this technology can also be recruited in the payment industry, transforming the payment industry into a more agile and efficient one. Accordingly, the present study pays close attention to the application of FSM in the payment industry. Given the importance of merchants' bargaining power in the payment industry, this study aims to use FSM in the digital transformation initiative with a targeted focus on providing real-time services to merchants. The research method consists of three parts. Firstly, conducting the review of past research, applications of FSM in the payment industry are considered. In the next step, merchants' benefits such as emotional, functional, economic, and social benefits in using FSM are identified using in-depth interviews and content analysis methods. The related business model in helping the payment industry transforming into a more agile and efficient industry is considered in the following step. The results revealed the 10 main pillars required to realize the digital transformation of payment systems using FSM.

Keywords: Digital transformation, field service management, merchant support systems, payment industry.

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Authors: Tom Snir, Eitan Rubin

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Mendelian Disease Genes represent a collection of single points of failure for the various systems they constitute. Such genes have been shown, on average, to encode longer proteins than 'non-disease' proteins. Existing models suggest that this results from the increased likeli-hood of longer genes undergoing mutations. Here, we show that in saturated mutagenesis experiments performed on model organisms, where the likelihood of each gene mutating is one, a similar relationship between length and the probability of a gene being lethal was observed. We thus suggest an extended model demonstrating that the likelihood of a mutated gene to produce a severe phenotype is length-dependent. Using the occurrence of conserved domains, we bring evidence that this dependency results from a correlation between protein length and the number of functions it performs. We propose that protein length thus serves as a proxy for protein cardinality in different networks required for the organism's survival and well-being. We use this example to argue that the collection of Mendelian Disease Genes can, and should, be used to study the rules governing systems vulnerability in living organisms.

Keywords: Systems Biology, Protein Length

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Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

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In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

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Distributed Generation (DG) in the form of renewable power generation systems is currently preferred for clean power generation. It has a significant impact on the distribution systems. This impact may be either positively or negatively depending on the distribution system, distributed generator and load characteristics. In this works, an overview of DG is briefly introduced. The technology of DG is also listed while the technical impacts and economic impacts are explained.

Keywords: Distributed Generation, Technical Impacts, Economic Impacts.

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Authors: Faraj El Dabee, Romeo Marian, Yousef Amer

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Just-In-Time (JIT) is a lean manufacturing tool, which provides the benefits of efficiency, and of minimizing unnecessary costs for many organisations. However, the risks arising from these benefits have been disregarded. These risks impact on system processes disrupting the whole supply chain. This paper proposes an inventory model that can simultaneously reduce costs and risks in JIT systems. This model is developed to ascertain an optimal ordering strategy for procuring raw materials by using regular multi-external and local backup suppliers to reduce the total cost of the products, and at the same time to reduce the risks arising from this cost reduction within production systems. Some results that will be illustrated in the second part of this paper are presented.

Keywords: Lean manufacturing, Just-in-Time (JIT), production system, cost-risk reduction, inventory model, eternal supplier, local backup supplier.

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Authors: Sunitha Ramanujam, Hany El Yamany, Miriam A. M. Capretz

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Software reliability, defined as the probability of a software system or application functioning without failure or errors over a defined period of time, has been an important area of research for over three decades. Several research efforts aimed at developing models to improve reliability are currently underway. One of the most popular approaches to software reliability adopted by some of these research efforts involves the use of operational profiles to predict how software applications will be used. Operational profiles are a quantification of usage patterns for a software application. The research presented in this paper investigates an innovative multiagent framework for automatic creation and management of operational profiles for generic distributed systems after their release into the market. The architecture of the proposed Operational Profile MAS (Multi-Agent System) is presented along with detailed descriptions of the various models arrived at following the analysis and design phases of the proposed system. The operational profile in this paper is extended to comprise seven different profiles. Further, the criticality of operations is defined using a new composed metrics in order to organize the testing process as well as to decrease the time and cost involved in this process. A prototype implementation of the proposed MAS is included as proof-of-concept and the framework is considered as a step towards making distributed systems intelligent and self-managing.

Keywords: Software reliability, Software testing, Metrics, Distributed systems, Multi-agent systems

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Authors: Md. Mahbubur Rahim

Abstract:

B2E portals represent a new class of web-based information technologies which many organisations are introducing in recent years to stay in touch with their distributed workforces and enable them to perform value added activities for organisations. However, actual usage of these emerging systems (measured using suitable instruments) has not been reported in the contemporary scholarly literature. We argue that many of the instruments to measure usage of various types of IT-enabled information systems are not directly applicable for B2E portals because they were developed for the context of traditional mainframe and PC-based information systems. It is therefore important to develop a new instrument for web-based portal technologies aimed at employees. In this article, we report on the development and initial qualitative evaluation of an instrument that seeks to operationaise a set of independent factors affecting the usage of portals by employees. The proposed instrument is useful to IT/e-commerce researchers and practitioners alike as it enhances their confidence in predicting employee usage of portals in organisations.

Keywords: Portal, business-to-employees, instrument, evaluation, qualitative research.

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Authors: Justinian Anatory, N. Theethayi, R. Thottappillil, C. Mwase, N.H. Mvungi

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Power-line networks are widely used today for broadband data transmission. However, due to multipaths within the broadband power line communication (BPLC) systems owing to stochastic changes in the network load impedances, branches, etc., network or channel capacity performances are affected. This paper attempts to investigate the performance of typical medium voltage channels that uses Orthogonal Frequency Division Multiplexing (OFDM) techniques with Quadrature Amplitude Modulation (QAM) sub carriers. It has been observed that when the load impedances are different from line characteristic impedance channel performance decreases. Also as the number of branches in the link between the transmitter and receiver increases a loss of 4dB/branch is found in the signal to noise ratio (SNR). The information presented in the paper could be useful for an appropriate design of the BPLC systems.

Keywords: Communication channel model, Power-line communication, Transfer function, Multipath, Branched network, OFDM, QAM, performance evaluation

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Authors: Mohammad Ali Tabarzad, Caro Lucas, Ali Hamzeh

Abstract:

Generalization is one of the most challenging issues of Learning Classifier Systems. This feature depends on the representation method which the system used. Considering the proposed representation schemes for Learning Classifier System, it can be concluded that many of them are designed to describe the shape of the region which the environmental states belong and the other relations of the environmental state with that region was ignored. In this paper, we propose a new representation scheme which is designed to show various relationships between the environmental state and the region that is specified with a particular classifier.

Keywords: Classifier Systems, Reinforcement Learning, Relational Representation, XCSF.

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: Chaos theory, GMM estimator, Lyapunov Exponent, Monetary System, Taylor Rule.

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Authors: A. Pedram, M. R. Jamali, T. Pedram, S. M. Fakhraie, C. Lucas

Abstract:

Local Linear Neuro-Fuzzy Models (LLNFM) like other neuro- fuzzy systems are adaptive networks and provide robust learning capabilities and are widely utilized in various applications such as pattern recognition, system identification, image processing and prediction. Local linear model tree (LOLIMOT) is a type of Takagi-Sugeno-Kang neuro fuzzy algorithm which has proven its efficiency compared with other neuro fuzzy networks in learning the nonlinear systems and pattern recognition. In this paper, a dedicated reconfigurable and parallel processing hardware for LOLIMOT algorithm and its applications are presented. This hardware realizes on-chip learning which gives it the capability to work as a standalone device in a system. The synthesis results on FPGA platforms show its potential to improve the speed at least 250 of times faster than software implemented algorithms.

Keywords: LOLIMOT, hardware, neurofuzzy systems, reconfigurable, parallel.

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Authors: Andrea Tundis, Carlos García Cordero, Rolf Egert, Alfredo Garro, Max Mühlhäuser

Abstract:

Resilience is an important system property that relies on the ability of a system to automatically recover from a degraded state so as to continue providing its services. Resilient systems have the means of detecting faults and failures with the added capability of automatically restoring their normal operations. Mastering resilience in the domain of Cyber-Physical Systems is challenging due to the interdependence of hybrid hardware and software components, along with physical limitations, laws, regulations and standards, among others. In order to overcome these challenges, this paper presents a modeling approach, based on the concept of Dynamic Cells, tailored to the management of Smart Grids. Additionally, a heuristic algorithm that works on top of the proposed modeling approach, to find resilient configurations, has been defined and implemented. More specifically, the model supports a flexible representation of Smart Grids and the algorithm is able to manage, at different abstraction levels, the resource consumption of individual grid elements on the presence of failures and faults. Finally, the proposal is evaluated in a test scenario where the effectiveness of such approach, when dealing with complex scenarios where adequate solutions are difficult to find, is shown.

Keywords: Cyber-physical systems, energy management, optimization, smart grids, self-healing, resilience, security.

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Authors: Cyrille Lambert, Tatiana Kalganova, Emanuele Stomeo

Abstract:

Since 1992, year where Hugo de Garis has published the first paper on Evolvable Hardware (EHW), a period of intense creativity has followed. It has been actively researched, developed and applied to various problems. Different approaches have been proposed that created three main classifications: extrinsic, mixtrinsic and intrinsic EHW. Each of these solutions has a real interest. Nevertheless, although the extrinsic evolution generates some excellent results, the intrinsic systems are not so advanced. This paper suggests 3 possible solutions to implement the run-time configuration intrinsic EHW system: FPGA-based Run-Time Configuration system, JBits-based Run-Time Configuration system and Multi-board functional-level Run-Time Configuration system. The main characteristic of the proposed architectures is that they are implemented on Field Programmable Gate Array. A comparison of proposed solutions demonstrates that multi-board functional-level run-time configuration is superior in terms of scalability, flexibility and the implementation easiness.

Keywords: Evolvable hardware, evolutionary computation, FPGA systems.

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Authors: Jung-Hyun Kim, Jihyung Kim, Kwangjae Lim, Dong Seung Kwon

Abstract:

Network coding has recently attracted attention as an efficient technique in multicast/broadcast services. The problem of finding the optimal network coding mechanism maximizing the bandwidth efficiency is hard to solve and hard to approximate. Lots of network coding-based schemes have been suggested in the literature to improve the bandwidth efficiency, especially network coding-based automatic repeat request (NCARQ) schemes. However, existing schemes have several limitations which cause the performance degradation in resource limited systems. To improve the performance in resource limited systems, we propose NCARQ with overlapping selection (OS-NCARQ) scheme. The advantages of OS-NCARQ scheme over the traditional ARQ scheme and existing NCARQ schemes are shown through the analysis and simulations.

Keywords: ARQ, Network coding, Multicast/Broadcast services, Packet-based systems.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

Abstract:

The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach is represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in form of prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: C-OTDR-system, guaranteed estimates, nonparametric estimation, sequential confidence estimation, multichannel monitoring systems.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

Abstract:

To minimize power losses, it is important to determine the location and size of local generators to be placed in unbalanced power distribution systems. On account of some inherent features of unbalanced distribution systems, such as radial structure, large number of nodes, a wide range of X/R ratios, the conventional techniques developed for the transmission systems generally fail on the determination of optimum size and location of distributed generators (DGs). This paper presents a simple method for investigating the problem of contemporaneously choosing best location and size of DG in three-phase unbalanced radial distribution system (URDS) for power loss minimization and to improve the voltage profile of the system. Best location of the DG is determined by using voltage index analysis and size of DG is computed by variational technique algorithm according to available standard size of DGs. This paper presents the results of simulations for 25-bus and IEEE 37- bus Unbalanced Radial Distribution system.

Keywords: Distributed generator, unbalanced radial distributionsystem, voltage index analysis, variational algorithm.

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Authors: G. Parmar, S. Mukherjee, R. Prasad

Abstract:

The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing the integral square error in between the transient responses of original and reduced order models using particle swarm optimization technique, pertaining to a unit step input. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The algorithm is illustrated with the help of two numerical examples and the results are compared with the other existing techniques.

Keywords: Eigen spectrum, Integral square error, Orderreduction, Particle swarm optimization, Stability.

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Authors: Zoaib Mirza

Abstract:

Half of the Muslim countries in the world have declared Islam the state religion in their constitutions. Yet, none of these countries have implemented authentic Islamic laws in line with the Quran (Holy Book), practices of Prophet Mohammad (P.B.U.H) called the Sunnah, and his four successors known as the Rightly Guided - Khalifa. Since their independence, these countries have adopted different government systems like Democracy, Dictatorship, Republic, Communism, and Monarchy. Instead of benefiting the people, these government systems have put these countries into political, social, and economic crises. These Islamic countries do not have equal representation and membership in worldwide political forums. Western countries lead these forums. Therefore, it is now imperative for the Muslim leaders of all these countries to collaborate, reset, and implement the original Islamic form of government, which led to the prosperity and success of people, including non-Muslims, 1400 years ago. They should unite as one nation under Khalifat, which means establishing the authority of Allah (SWT) and following the divine commandments related to the social, political, and economic systems. As they have declared Islam in their constitution, they should work together to apply the divine framework of the governance revealed by Allah (SWT) and implemented by Prophet Mohammad (P.B.U.H) and his four successors called Khalifas. This paper provides an overview of the downfall and the end of the Khalifat system by 1924, the ways in which the West caused political, social, and economic crises in the Muslim countries, and finally, a summary of the social, political, and economic systems implemented by the Prophet Mohammad (P.B.U.H) and his successors, Khalifas, called the Rightly Guided – Hazrat Abu Bakr (RA), Hazrat Omar (RA), Hazrat Usman (RA), and Hazrat Ali (RA).

Keywords: Khalifat, Khilafat-e-Rashida, The Rightly Guided, colonization, capitalism, neocolonization, government systems.

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Authors: Mohamed Omar

Abstract:

Steel bracing members are widely used in steel  structures to reduce lateral displacement and dissipate energy during  earthquake motions. Concentric steel bracing provide an excellent  approach for strengthening and stiffening steel buildings. Using these  braces the designer can hardly adjust the stiffness together with  ductility as needed because of buckling of braces in compression. In  this study the use of SMA bracing and steel bracing (Mega) utilized  in steel frames are investigated. The effectiveness of these two  systems in rehabilitating a mid-rise eight-storey steel frames were  examined using time-history nonlinear analysis utilizing seismostruct  software. Results show that both systems improve the strength and  stiffness of the original structure but due to excellent behavior of  SMA in nonlinear phase and under compressive forces this system  shows much better performance than the rehabilitation system of  Mega bracing.

 

Keywords: Finite element analysis, seismic response, shapes memory alloy, steel frame, mega bracing.

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Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: K. Sudprasert, M. Precharattana, N. Nuttavut, D. Triampo, B. Pattanasiri, Y. Lenbury, W. Triampo

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The study of non-equilibrium systems has attracted increasing interest in recent years, mainly due to the lack of theoretical frameworks, unlike their equilibrium counterparts. Studying the steady state and/or simple systems is thus one of the main interests. Hence in this work we have focused our attention on the driven lattice gas model (DLG model) consisting of interacting particles subject to an external field E. The dynamics of the system are given by hopping of particles to nearby empty sites with rates biased for jumps in the direction of E. Having used small two dimensional systems of DLG model, the stochastic properties at nonequilibrium steady state were analytically studied. To understand the non-equilibrium phenomena, we have applied the analytic approach via master equation to calculate probability function and analyze violation of detailed balance in term of the fluctuation-dissipation theorem. Monte Carlo simulations have been performed to validate the analytic results.

Keywords: Non-equilibrium, lattice gas, stochastic process

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Authors: Ł. Kiedrowski, H. Gierszal, W. Hołubowicz

Abstract:

This paper presents the H-ARQ techniques comparison for OFDM systems with a new family of non-binary LDPC codes which has been developed within the EU FP7 DAVINCI project. The punctured NB-LDPC codes have been used in a simulated model of the transmission system. The link level performance has been evaluated in terms of spectral efficiency, codeword error rate and average number of retransmissions. The NB-LDPC codes can be easily and effective implemented with different methods of the retransmission needed if correct decoding of a codeword failed. Here the Optimal Symbol Selection method is proposed as a Chase Combining technique.

Keywords: H-ARQ, LDPC, Non-Binary, Punctured Codes.

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