Search results for: combined sewer systems

Authors: F. Stazi, C. Di Perna, C. Filiaci, A. Stazi

Abstract:

Passive systems were born with the purpose of the greatest exploitation of solar energy in cold climates and high altitudes. They spread themselves until the 80-s all over the world without any attention to the specific climate and the summer behavior; this caused the deactivation of the systems due to a series of problems connected to the summer overheating, the complex management and the rising of the dust. Until today the European regulation limits only the winter consumptions without any attention to the summer behavior but, the recent European EN 15251 underlines the relevance of the indoor comfort, and the necessity of the analytic studies validation by monitoring case studies. In the porpose paper we demonstrate that the solar wall is an efficient system both from thermal comfort and energy saving point of view and it is the most suitable for our temperate climates because it can be used as a passive cooling sistem too. In particular the paper present an experimental and numerical analisys carried out on a case study with nine different solar passive systems in Ancona, Italy. We carried out a detailed study of the lodging provided by the solar wall by the monitoring and the evaluation of the indoor conditions. Analyzing the monitored data, on the base of recognized models of comfort (ISO, ASHRAE, Givoni-s BBCC), is emerged that the solar wall has an optimal behavior in the middle seasons. In winter phase this passive system gives more advantages in terms of energy consumptions than the other systems, because it gives greater heat gain and therefore smaller consumptions. In summer, when outside air temperature return in the mean seasonal value, the indoor comfort is optimal thanks to an efficient transversal ventilation activated from the same wall.

Keywords: Building envelope, energy saving, passive solarwall, thermal comfort.

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Authors: Noura Boudiaf, Allaoua Chaoui

Abstract:

To analyze the behavior of Petri nets, the accessibility graph and Model Checking are widely used. However, if the analyzed Petri net is unbounded then the accessibility graph becomes infinite and Model Checking can not be used even for small Petri nets. ECATNets [2] are a category of algebraic Petri nets. The main feature of ECATNets is their sound and complete semantics based on rewriting logic [8] and its language Maude [9]. ECATNets analysis may be done by using techniques of accessibility analysis and Model Checking defined in Maude. But, these two techniques supported by Maude do not work also with infinite-states systems. As a category of Petri nets, ECATNets can be unbounded and so infinite systems. In order to know if we can apply accessibility analysis and Model Checking of Maude to an ECATNet, we propose in this paper an algorithm allowing the detection if the ECATNet is bounded or not. Moreover, we propose a rewriting logic based tool implementing this algorithm. We show that the development of this tool using the Maude system is facilitated thanks to the reflectivity of the rewriting logic. Indeed, the self-interpretation of this logic allows us both the modelling of an ECATNet and acting on it.

Keywords: ECATNets, Rewriting Logic, Maude, Finite-stateSystems, Infinite-state Systems, Boundness Property Checking.

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Authors: Nelson K. Lujara

Abstract:

The paper presents a practical three-phase PWM inverter suitable for low voltage, low rating energy efficient systems. The work in the paper is conducted with the view to establishing the significance of the loss contribution from the PWM inverter in the determination of the complete losses of a photovoltaic (PV) arraypowered induction motor drive water pumping system. Losses investigated include; conduction and switching loss of the devices and gate drive losses. It is found that the PWM inverter operates at a reasonable variable efficiency that does not fall below 92% depending on the load. The results between the simulated and experimental results for the system with or without a maximum power tracker (MPT) compares very well, within an acceptable range of 2% margin.

Keywords: Energy, Inverter, Losses, Photovoltaic.

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Authors: Miroslav Byrtus

Abstract:

Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM). The MSM enables significant DOF number reduction while keeping the nonlinear behavior of the system in a specific frequency range. Further, the MSM with DOF number reduction is suitable for including detail models of nonlinear couplings (mainly gear and bearing couplings) into the complete gear drive models. Since each subsystem is modeled separately using different FEM systems, it is advantageous to parameterize models of subsystems and to use the parameterization for optimization of chosen design parameters. Final complex model of gear drive is assembled in MATLAB and MATLAB tools are used for dynamical analysis of the nonlinear system. The contribution is further focused on developing of a methodology for investigation of behavior of the system by Nonlinear Normal Modes with combination of the MSM using numerical continuation method. The proposed methodology will be tested using a two-stage gearbox including its housing.

Keywords: Vibro-impact system, rotating system, gear drive, modal synthesis method, numerical continuation method, periodic solution.

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Authors: Clark Van Dam, Gagan Mirchandani

Abstract:

The Continuously Adaptive Mean-Shift (CamShift) algorithm, incorporating scene depth information is combined with the l1-minimization sparse representation based method to form a hybrid kernel and state space-based tracking algorithm. We take advantage of the increased efficiency of the former with the robustness to occlusion property of the latter. A simple interchange scheme transfers control between algorithms based upon drift and occlusion likelihood. It is quantified by the projection of target candidates onto a depth map of the 2D scene obtained with a low cost stereo vision webcam. Results are improved tracking in terms of drift over each algorithm individually, in a challenging practical outdoor multiple occlusion test case.

Keywords: CamShift, l1-minimization, particle filter, stereo vision, video tracking.

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Authors: S. N. Vijayan, S. Sendhil Kumar

Abstract:

Recent years have an upward trend in the research of renewable energy sector, due to the low availability of resources and huge consumption of conventional energies. Considerable renewable energy can be achieved from the available solar power with the utilization of collecting systems. Parabolic trough concentrating collector systems are mostly used to utilize maximum availability of solar power. This paper reviews the contributing factors for the overall performance of parabolic trough collectors. Its performance depends on the operating parameters such as the type of receiver and the collector material, medium of heat transfer, type of application and various climatic conditions.

Keywords: Solar radiation, parabolic trough collector, thermal analysis, efficiency.

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Authors: Feng Wang, Shencheng Ni, Shuying Han, Shanhong You

Abstract:

With the development of optical communication, optical performance monitoring (OPM) has received more and more attentions. Since optical signal-to-noise ratio (OSNR) is directly related to bit error rate (BER), it is one of the important parameters in optical networks. Recently, artificial neural network (ANN) has been greatly developed. ANN has strong learning and generalization ability. In this paper, a method of OSNR monitoring based on delay-tap sampling (DTS) and ANN has been proposed. DTS technique is used to extract the eigenvalues of the signal. Then, the eigenvalues are input into the ANN to realize the OSNR monitoring. The experiments of 10 Gb/s non-return-to-zero (NRZ) on–off keying (OOK), 20 Gb/s pulse amplitude modulation (PAM4) and 20 Gb/s return-to-zero (RZ) differential phase-shift keying (DPSK) systems are demonstrated for the OSNR monitoring based on the proposed method. The experimental results show that the range of OSNR monitoring is from 15 to 30 dB and the root-mean-square errors (RMSEs) for 10 Gb/s NRZ-OOK, 20 Gb/s PAM4 and 20 Gb/s RZ-DPSK systems are 0.36 dB, 0.45 dB and 0.48 dB respectively. The impact of chromatic dispersion (CD) on the accuracy of OSNR monitoring is also investigated in the three experimental systems mentioned above.

Keywords: Artificial neural network, ANN, chromatic dispersion, delay-tap sampling, optical signal-to-noise ratio, OSNR.

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Authors: Roman Ružarovský, Radovan Holubek, Peter Košťál

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The current trend of increasing quality and demands of the final product is affected by time analysis of the entire manufacturing process. The primary requirement of manufacturing is to produce as many products as soon as possible, at the lowest possible cost, but of course with the highest quality. Such requirements may be satisfied only if all the elements entering and affecting the production cycle are in a fully functional condition. These elements consist of sensory equipment and intelligent control elements that are essential for building intelligent manufacturing systems. The intelligent manufacturing paradigm includes a new approach to production system structure design. Intelligent behaviors are based on the monitoring of important parameters of system and its environment. The flexible reaction to changes. The realization and utilization of this design paradigm as an "intelligent manufacturing system" enables the flexible system reaction to production requirement as soon as environmental changes too. Results of these flexible reactions are a smaller layout space, be decreasing of production and investment costs and be increasing of productivity. Intelligent manufacturing system itself should be a system that can flexibly respond to changes in entering and exiting the process in interaction with the surroundings.

Keywords: Sensory equipment, intelligent manufacturing systems, manufacturing process, control system, smart automation.

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Authors: M. Mordjaoui, B. Boudjema, M. Chabane, R. Daira

Abstract:

In determining the electromagnetic properties of magnetic materials, hysteresis modeling is of high importance. Many models are available to investigate those characteristics but they tend to be complex and difficult to implement. In this paper a new qualitative hysteresis model for ferromagnetic core is presented, based on the function approximation capabilities of adaptive neuro fuzzy inference system (ANFIS). The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach can restored the hysteresis curve with a little RMS error. The model accuracy is good and can be easily adapted to the requirements of the application by extending or reducing the network training set and thus the required amount of measurement data.

Keywords: ANFIS modeling technique, magnetic hysteresis, Jiles-Atherton model, ferromagnetic core.

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Authors: May Thant Zin, Josephine Borja, Hirofumi Hinode, Winarto Kurniawan

Abstract:

Nanotechnology has multiple and enormous advantages for all application. Therefore, this research is carried out to synthesize and characterize bimetallic iron with copper nanoparticles. After synthesizing nano zero valent iron by reduction of ferric chloride by sodium borohydride under nitrogen purging environment, bimetallic iron with copper nanoparticles are synthesized by varying different loads of copper chloride. Due to different standard potential (E⁰) values of copper and iron, copper is coupled with iron at (Cu to Fe ratio of 1:5, 1:6.7, 1:10, 1:20). It is found that the resulted bimetallic Fe/Cu nanoparticles are composing phases of iron and copper. According to the diffraction patterns indicating the state of chemical combination of the bimetallic nanoparticles, the particles are well-combined and crystalline sizes are less than 1000A^o (or 100nm). Specifically, particle sizes of synthesized bimetallic Fe/Cu nanoparticles are ranging from 44.583 nm to 85.149 nm.

Keywords: Bimetallic Fe/Cu nanoparticles, Loading ratio, Synthesis.

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Authors: Mohammed Abdalla Osman Mukhtar, Azween Abdullah, Alan Giffin Downe

Abstract:

Model mapping and transformation are important processes in high level system abstractions, and form the cornerstone of model-driven architecture (MDA) techniques. Considerable research in this field has devoted attention to static system abstraction, despite the fact that most systems are dynamic with high frequency changes in behavior. In this paper we provide an overview of work that has been done with regard to behavior model mapping and transformation, based on: (1) the completeness of the platform independent model (PIM); (2) semantics of behavioral models; (3) languages supporting behavior model transformation processes; and (4) an evaluation of model composition to effect the best approach to describing large systems with high complexity.

Keywords: MDA; PIM, PSM, QVT, Model Transformation

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Authors: Manoj Kumar, A.K. Verma, A. Srividya

Abstract:

Time varying network induced delays in networked control systems (NCS) are known for degrading control system-s quality of performance (QoP) and causing stability problems. In literature, a control method employing modeling of communication delays as probability distribution, proves to be a better method. This paper focuses on modeling of network induced delays as probability distribution. CAN and MIL-STD-1553B are extensively used to carry periodic control and monitoring data in networked control systems. In literature, methods to estimate only the worst-case delays for these networks are available. In this paper probabilistic network delay model for CAN and MIL-STD-1553B networks are given. A systematic method to estimate values to model parameters from network parameters is given. A method to predict network delay in next cycle based on the present network delay is presented. Effect of active network redundancy and redundancy at node level on network delay and system response-time is also analyzed.

Keywords: NCS (networked control system), delay analysis, response-time distribution, worst-case delay, CAN, MIL-STD-1553B, redundancy

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Authors: Xueting Liu, Daojin Song, Chuandai Dong, Hongkui Li

Abstract:

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.

Keywords: High-resolution MAP image, Reconstruction, Image interpolation, Motion Estimation, Hermitian positive definite solutions.

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Authors: S. Kherchaoui, A. Houacine

Abstract:

This paper presents a facial expression recognition system. It performs identification and classification of the seven basic expressions; happy, surprise, fear, disgust, sadness, anger, and neutral states. It consists of three main parts. The first one is the detection of a face and the corresponding facial features to extract the most expressive portion of the face, followed by a normalization of the region of interest. Then calculus of curvelet coefficients is performed with dimensionality reduction through principal component analysis. The resulting coefficients are combined with two ratios; mouth ratio and face edge ratio to constitute the whole feature vector. The third step is the classification of the emotional state using the SVM method in the feature space.

Keywords: Facial expression identification, curvelet coefficients, support vector machine (SVM).

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Authors: Nizar Bouguerra, Ahmed Khabou, Sébastien Poncet, Saïd Elkoun

Abstract:

The present work focuses on the preparation and the stabilization of Al₂O₃-water based nanofluids. Though they have been widely considered in the past, to the best of our knowledge, there is no clear consensus about a proper way to prepare and stabilize them by the appropriate surfactant. In this paper, a careful experimental investigation is performed to quantify the combined influence of pH and the surfactant on the stability of Al₂O₃-water based nanofluids. Two volume concentrations of nanoparticles and three nanoparticle sizes have been considered. The good preparation and stability of these nanofluids are evaluated through thermal conductivity measurements. The results show that the optimum value for the thermal conductivity is obtained mainly by controlling the pH of the mixture and surfactants are not necessary to stabilize the solution.

Keywords: Nanofluid, thermal conductivity, pH, transient hot wire, surfactant, Al2O3, stability, dispersion, preparation.

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

Abstract:

This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: Object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation.

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Authors: James D. Clark, Bernard H. Stark

Abstract:

The paper presents a modelling methodology for small scale multi-source renewable energy systems. Using historical site-specific weather data, the relationships of cost, availability and energy form are visualised as a function of the sizing of photovoltaic arrays, wind turbines, and battery capacity. The specific dependency of each site on its own particular weather patterns show that unique solutions exist for each site. It is shown that in certain cases the capital component cost can be halved if the desired theoretical demand availability is reduced from 100% to 99%.

Keywords: Energy Analysis, Forecasting, Distributed powergeneration.

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Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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Authors: Masrour Dowlatabadi, Jalil Shirazi

Abstract:

In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: Z. Nougrara

Abstract:

In this paper we propose a novel methodology for extracting a road network and its nodes from satellite images of Algeria country. This developed technique is a progress of our previous research works. It is founded on the information theory and the mathematical morphology; the information theory and the mathematical morphology are combined together to extract and link the road segments to form a road network and its nodes. We therefore have to define objects as sets of pixels and to study the shape of these objects and the relations that exist between them. In this approach, geometric and radiometric features of roads are integrated by a cost function and a set of selected points of a crossing road. Its performances were tested on satellite images of Algeria country.

Keywords: Satellite image, road network, nodes.

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Authors: Tomáš Seidler, Marek Mihola, Denisa Cihlarova

Abstract:

The article presents analysis results of maps of expected subsidence in undermined areas for road repair management. The analysis was done in the area of Karvina district in the Czech Republic, including undermined areas with ongoing deep mining activities or finished deep mining in years 2003 - 2009. The article discusses the possibilities of local road maintenance authorities to determine areas that will need most repairs in the future with limited data available. Using the expected subsidence maps new map of surface curvature was calculated. Combined with road maps and historical data about repairs the result came for five main categories of undermined areas, proving very simple tool for management.

Keywords: GIS, Map of Subsidence, Road, Undermined Area

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Authors: Mostafa A. Shokshok, Omran Ali Abu Krais

Abstract:

This paper describes the collection and analysis of data obtained from face-to-face interviews conducted in selected Libyan industrial companies. The objectives of the interviews are to enhance understanding, and generate explanations of current issues in culture and quality management systems in Libyan companies. The method used in analyzing the questions, as well as the main finding of each question are explained. The interviews probed areas identify national and organizational culture, quality management systems, current methods, effects, barriers and other factors affecting the success of quality management implementation. Eleven questions are prepared and been discussed with the interviewees.

Keywords: Interviews, quality, culture, Libyan industrial companies.

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Authors: Imen Sfaihi, Noureddine Hamdi

Abstract:

In this paper, we investigate the study of techniques for scheduling users for resource allocation in the case of multiple input and multiple output (MIMO) packet transmission systems. In these systems, transmit antennas are assigned to one user or dynamically to different users using spatial multiplexing. The allocation of all transmit antennas to one user cannot take full advantages of multi-user diversity. Therefore, we developed the case when resources are allocated dynamically. At each time slot users have to feed back their channel information on an uplink feedback channel. Channel information considered available in the schedulers is the zero forcing (ZF) post detection signal to interference plus noise ratio. Our analysis study concerns the round robin and the opportunistic schemes. In this paper, we present an overview and a complete capacity analysis of these schemes. The main results in our study are to give an analytical form of system capacity using the ZF receiver at the user terminal. Simulations have been carried out to validate all proposed analytical solutions and to compare the performance of these schemes.

Keywords: MIMO, scheduling, ZF receiver, spatial multiplexing, round robin scheduling, opportunistic.

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Authors: Zixin Liu, Jian Yu, Daoyun Xu

Abstract:

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.

Keywords: Game networks, zero-sum game, delayed singular system, nonlinear perturbation, time delay.

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Authors: Wassila Kiamouche, Malek Benslama

Abstract:

In order to derive important parameters concerning mobile subscriber MS with ongoing calls in Low Earth Orbit Mobile Satellite Systems LEO MSSs, a positioning system had to be integrated into MSS in order to localize mobile subscribers MSs and track them during the connection. Such integration is regarded as a complex implementation. We propose in this paper a novel method based on advantages of mobility model of Low Earth Orbit Mobile Satellite System LEO MSS called Evaluation Parameters Method EPM which allows for such systems the evaluation of different information concerning a MS with a call in progress even if its location is unknown.

Keywords: Cellular layout, LEO mobile satellite system, mobilitymodel, positioning system.

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Authors: Abhijit Mitra

Abstract:

An effective approach for extracting document images from a noisy background is introduced. The entire scheme is divided into three sub- stechniques – the initial preprocessing operations for noise cluster tightening, introduction of a new thresholding method by maximizing the ratio of stan- dard deviations of the combined effect on the image to the sum of weighted classes and finally the image restoration phase by image binarization utiliz- ing the proposed optimum threshold level. The proposed method is found to be efficient compared to the existing schemes in terms of computational complexity as well as speed with better noise rejection.

Keywords: Document image extraction, Preprocessing, Ratio of stan-dard deviations, Bi-level adaptive thresholding.

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

Abstract:

In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Mohammed Fethi Khalfi, Malika Kandouci

Abstract:

Over the past decade, mobile has experienced a revolution that will ultimately change the way we communicate.All these technologies have a common denominator exploitation of computer information systems, but their operation can be tedious because of problems with heterogeneous data sources.To overcome the problems of heterogeneous data sources, we propose to use a technique of adding an extra layer interfacing applications of management or supervision at the different data sources.This layer will be materialized by the implementation of a mediator between different host applications and information systems frequently used hierarchical and relational manner such that the heterogeneity is completely transparent to the VoIP platform.

Keywords: TOIP, Data Integration, Mediation, informationcomputer system, heterogeneous data sources

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Authors: Kang-Hung Yang, Jin-Yuan Hsu

Abstract:

In recent years, several severe large-scale influenza outbreaks happened in many countries, such as SARS in 2005 or H1N1 in 2009. Those influenza Epidemics have greatly impacts not only on people-s life and health, but medical systems in different countries. Although severe diseases are more experienced, they are not fully controlled. Governments have different policies to control the spreads of diseases. However, those policies have both positive and negative social or economical influence on people and society. Therefore, it is necessary and essential to develop an appropriate model for evaluations of policies. Consequently, a proper measure can be implemented to confront the diseases. The main goal of this study is to develop a SIR-based model for the further evaluations of the candidate policies during the influenza outbreaks.

Keywords: SIR, influenza, systems dynamic model, H1N1

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: Collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation.

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