Search results for: Rectified Linear Unit

Authors: Maziyar Nouraee

Abstract:

Electronic markets in recent decades contribute remarkably in business transactions. Many organizations consider traditional ways of trade non-economical and therefore they do trade only through electronic markets. There are different categorizations of electronic markets functions. In one classification, functions of electronic markets are categorized into classes as information, transactions, and value added. In the present paper, effects of the three classes on the two major elements of the supply chain management are measured. The two elements are decrease in the product unit cost and reduction in response time to the customer. The results of the current research show that among nine minor elements related to the three classes of electronic markets functions, six factors and three factors influence on reduction of the product unit cost and reduction of response time to the customer, respectively.

Keywords: Electronic Commerce, Electronic Market, B2B Trade, Supply Chain Management.

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Authors: Yang Luo, Beibei Wang

Abstract:

In this paper, we present a design methodology of lightweight register transfer level (RTL) hardware threat implemented based on a MAX II FPGA platform. The dynamic power consumed by the toggling of the various bit of registers as well as the dynamic power consumed per unit of logic circuits were analyzed. The hardware threat was designed taking advantage of the differences in dynamic power consumed per unit of logic circuits to hide the transfer information. The experiment result shows that the register hardware threat was successfully implemented by using different dynamic power consumed per unit of logic circuits to hide the key information of DES encryption module. It needs more than 100000 sample curves to reduce the background noise by comparing the sample space when it completely meets the time alignment requirement. In additional, an external trigger signal is playing a very important role to detect the hardware threat in this experiment.

Keywords: Side-channel analysis, hardware threat, register transfer level, dynamic power.

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Authors: K. Ganesan

Abstract:

By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.

Keywords: Interval arithmetic, Interval matrix, linear equations.

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Authors: Erol Seke, Kemal Özkan

Abstract:

Linear approximation of point spread function (PSF) is a new method for determining subpixel translations between images. The problem with the actual algorithm is the inability of determining translations larger than 1 pixel. In this paper a multiresolution technique is proposed to deal with the problem. Its performance is evaluated by comparison with two other well known registration method. In the proposed technique the images are downsampled in order to have a wider view. Progressively decreasing the downsampling rate up to the initial resolution and using linear approximation technique at each step, the algorithm is able to determine translations of several pixels in subpixel levels.

Keywords: Point Spread Function, Subpixel translation, Superresolution, Multiresolution approach.

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Authors: Levan Nadareishvili, Roland Bakuradze, Barbara Kilosanidze, Nona Topuridze, Liana Sharashidze, Ineza Pavlenishvili

Abstract:

Some regularities of formation of a new structural state of the thermoplastic polymers - gradually oriented (stretched) state (GOS) are discussed. Transition into GOS is realized by the graded oriented stretching - by action of inhomogeneous mechanical field on the isotropic linear polymers or by zone stretching that is implemented on a standard tensile-testing machine with using a specially designed zone stretching device (ZSD). Both technical approaches (especially zone stretching method) allows to manage the such quantitative parameters of gradually oriented polymers as a range of change in relative elongation/orientation degree, length of this change and profile (linear, hyperbolic, parabolic, logarithmic, etc.). The possibility of obtaining functionally graded materials (FGMs) by graded orientation method is briefly discussed. Uniaxial graded stretching method should be considered as an effective technological solution to create polymer materials with a predetermined gradient of physical properties.

Keywords: Controlled graded stretching, gradually oriented state, linear polymers, zone stretching device.

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Authors: Yash Pal, A.Swarup, Bhim Singh

Abstract:

This paper presents a novel control strategy of a threephase four-wire Unified Power Quality (UPQC) for an improvement in power quality. The UPQC is realized by integration of series and shunt active power filters (APFs) sharing a common dc bus capacitor. The shunt APF is realized using a thee-phase, four leg voltage source inverter (VSI) and the series APF is realized using a three-phase, three leg VSI. A control technique based on unit vector template technique (UTT) is used to get the reference signals for series APF, while instantaneous sequence component theory (ISCT) is used for the control of Shunt APF. The performance of the implemented control algorithm is evaluated in terms of power-factor correction, load balancing, neutral source current mitigation and mitigation of voltage and current harmonics, voltage sag and swell in a three-phase four-wire distribution system for different combination of linear and non-linear loads. In this proposed control scheme of UPQC, the current/voltage control is applied over the fundamental supply currents/voltages instead of fast changing APFs currents/voltages, there by reducing the computational delay and the required sensors. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC.

Keywords: Power Quality, UPQC, Harmonics, Load Balancing, Power Factor Correction, voltage harmonic mitigation, currentharmonic mitigation, voltage sag, swell

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Authors: P. K. Singhal, R. Naresh, V. Sharma

Abstract:

This paper presents the three optimization models, namely New Binary Artificial Bee Colony (NBABC) algorithm, NBABC with Local Search (NBABC-LS), and NBABC with Genetic Crossover (NBABC-GC) for solving the Wind-Thermal Unit Commitment (WTUC) problem. The uncertain nature of the wind power is incorporated using the Weibull probability density function, which is used to calculate the overestimation and underestimation costs associated with the wind power fluctuation. The NBABC algorithm utilizes a mechanism based on the dissimilarity measure between binary strings for generating the binary solutions in WTUC problem. In NBABC algorithm, an intelligent scout bee phase is proposed that replaces the abandoned solution with the global best solution. The local search operator exploits the neighboring region of the current solutions, whereas the integration of genetic crossover with the NBABC algorithm increases the diversity in the search space and thus avoids the problem of local trappings encountered with the NBABC algorithm. These models are then used to decide the units on/off status, whereas the lambda iteration method is used to dispatch the hourly load demand among the committed units. The effectiveness of the proposed models is validated on an IEEE 10-unit thermal system combined with a wind farm over the planning period of 24 hours.

Keywords: Artificial bee colony algorithm, economic dispatch, unit commitment, wind power.

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Authors: P. K. Singhal, R. Naresh, V. Sharma

Abstract:

This paper presents the three optimization models, namely New Binary Artificial Bee Colony (NBABC) algorithm, NBABC with Local Search (NBABC-LS), and NBABC with Genetic Crossover (NBABC-GC) for solving the Wind-Thermal Unit Commitment (WTUC) problem. The uncertain nature of the wind power is incorporated using the Weibull probability density function, which is used to calculate the overestimation and underestimation costs associated with the wind power fluctuation. The NBABC algorithm utilizes a mechanism based on the dissimilarity measure between binary strings for generating the binary solutions in WTUC problem. In NBABC algorithm, an intelligent scout bee phase is proposed that replaces the abandoned solution with the global best solution. The local search operator exploits the neighboring region of the current solutions, whereas the integration of genetic crossover with the NBABC algorithm increases the diversity in the search space and thus avoids the problem of local trappings encountered with the NBABC algorithm. These models are then used to decide the units on/off status, whereas the lambda iteration method is used to dispatch the hourly load demand among the committed units. The effectiveness of the proposed models is validated on an IEEE 10-unit thermal system combined with a wind farm over the planning period of 24 hours.

Keywords: Artificial bee colony algorithm, economic dispatch, unit commitment, wind power.

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Authors: Ε. Giovanis

Abstract:

In this paper we apply an Adaptive Network-Based Fuzzy Inference System (ANFIS) with one input, the dependent variable with one lag, for the forecasting of four macroeconomic variables of US economy, the Gross Domestic Product, the inflation rate, six monthly treasury bills interest rates and unemployment rate. We compare the forecasting performance of ANFIS with those of the widely used linear autoregressive and nonlinear smoothing transition autoregressive (STAR) models. The results are greatly in favour of ANFIS indicating that is an effective tool for macroeconomic forecasting used in academic research and in research and application by the governmental and other institutions

Keywords: Linear models, Macroeconomics, Neuro-Fuzzy, Non-Linear models

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Authors: Randhir Singh Baghel, Govind Shay Sharma

Abstract:

In this paper, we explore an ecosystem that contains a three-species food chain. The first and second species are in competition with one another for resources. However, the third species plays an important role in providing non-linear Crowley-Martin functional support for the first species. Additionally, the third species consumes the second species in a linear fashion, taking advantage of the available resources. This intricate balance ensures the survival of all three species in the ecosystem. A set of non-linear isolated first-order differential equations establish this model. We examine the system's stability at all potential equilibrium locations using the perturbed technique. Furthermore, by spending a lot of time observing the species in their natural habitat, the numerical illustrations at suitable parameter values for the model are shown.

Keywords: Competition, predator, response function, local stability, numerical simulations.

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Authors: A. Brouri, F. Giri, A. Mkhida, F. Z. Chaoui, A. Elkarkri, M. L. Chhibat

Abstract:

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

Keywords: Nonlinear system identification, Hammerstein systems, Wiener systems, frequency identification.

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Authors: Taiki Baba, Tomoaki Hashimoto

Abstract:

The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: Model predictive control, stochastic systems, probabilistic constraints, random dither quantization.

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Authors: Subir Das, Tuhin Subhra Sarkar, Badal Chakraborty

Abstract:

Differing from the structure of traditional parallel plate capacitive sensor a semi cylindrical capacitive sensor has been introduced in this present work to measure the soil moisture conveniently. Here, the numerical analysis method to evaluate the capacitance from the semi-cylindrical capacitive sensor is analyzed and discussed. The changes of capacitance with the variation of soil moisture obtained linear in the nano farad range (nF) and which converted into voltage variation by using proper signal conditioning circuit. Experimental results depict the satisfactory performance of the sensor for measurement of soil moisture in the range of 0 to 70%. We investigated the linearity of 4% of FSO and sensitivity of 70 mV/unit percentage changes in soil moisture level (DB).

Keywords: Semi cylindrical Capacitive Sensor, Capacitance to Voltage converter Circuit, Soil Moisture.

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Authors: Kyogun Chang, Yoon Bok Lee

Abstract:

Fault detection determines faultexistence and detecting time. This paper discusses two layered fault detection methods to enhance the reliability and safety. Two layered fault detection methods consist of fault detection methods of component level controllers and system level controllers. Component level controllers detect faults by using limit checking, model-based detection, and data-driven detection and system level controllers execute detection by stability analysis which can detect unknown changes. System level controllers compare detection results via stability with fault signals from lower level controllers. This paper addresses fault detection methods via stability and suggests fault detection criteria in nonlinear systems. The fault detection method applies tothe hybrid control unit of a military hybrid electric vehicleso that the hybrid control unit can detect faults of the traction motor.

Keywords: Two Layered Fault Detection, Stability Analysis, Fault-Tolerant Control

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Authors: A. Sherif, A. El Zafarany, R. Arafa

Abstract:

Hospitals, everywhere, are considered heavy energy consumers. Hospital Intensive Care Unit spaces pose a special challenge, where design guidelines requires the provision of external windows for daylighting and external view. Window protection strategies could be employed to reduce energy loads without detriment effect on comfort or health care. This paper addresses the effectiveness of using various window strategies on the annual cooling, heating and lighting energy use of a typical Hospital Intensive Unit space. Series of experiments were performed using the EnergyPlus simulation software for a typical Intensive Care Unit (ICU) space in Cairo, located in the Egyptian desert. This study concluded that the use of shading systems is more effective in conserving energy in comparison with glazing of different types, in the Cairo ICUs. The highest energy savings in the West and South orientations were accomplished by external perforated solar screens, followed by overhangs positioned at a protection angle of 45°.

Keywords: Energy, Hospital, Intensive Care Units, Shading.

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: Saad Mutashar, M. A. Hannan, S. A. Samad, A. Hussain

Abstract:

This paper deals with the modified wireless power transmission system for biomedical implanted devices. The system consists of efficient class-E power amplifier and inductive power links based on spiral circular transmitter and receiver coils. The model of the class-E power amplifier operated with 13.56 MHz is designed, discussed and analyzed in which it is achieved 87.2% of efficiency. The inductive coupling method is used to achieve link efficiency up to 73% depending on the electronic remote system resistance. The improved system powered with 3.3 DC supply and the voltage across the transmitter side is 40 V whereas, cross the receiver side is 12 V which is rectified to meet the implanted micro-system circuit requirements. The system designed and simulated by NI MULTISIM 11.02.

Keywords: Wireless Transmission, inductive coupling, implanted devices, class-E power amplifier, coils design.

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Authors: Ender Bulgun, Arzu Vuruskan

Abstract:

Apparel product development is an important stage in the life cycle of a product. Shortening this stage will help to reduce the costs of a garment. The aim of this study is to examine the production parameters in knitwear apparel companies by defining the unit costs, and developing a software to calculate the unit costs of garments and make the cost estimates. In this study, with the help of a questionnaire, different companies- systems of unit cost estimating and cost calculating were tried to be analyzed. Within the scope of the questionnaire, the importance of cost estimating process for apparel companies and the expectations from a new cost estimating program were investigated. According to the results of the questionnaire, it was seen that the majority of companies which participated to the questionnaire use manual cost calculating methods or simple Microsoft Excel spreadsheets to make cost estimates. Furthermore, it was discovered that many companies meet with difficulties in archiving the cost data for future use and as a solution to that problem, it is thought that prior to making a cost estimate, sub units of garment costs which are fabric, accessory and the labor costs should be analyzed and added to the database of the programme beforehand. Another specification of the cost estimating unit prepared in this study is that the programme was designed to consist of two main units, one of which makes the product specification and the other makes the cost calculation. The programme is prepared as a web-based application in order that the supplier, the manufacturer and the customer can have the opportunity to communicate through the same platform.

Keywords: Apparel, cost estimating, design archive.

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Authors: N. Z. A. Hamid, M. S. M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly Ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: Chaotic approach, phase space, Cao method, local linear approximation method.

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Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss

Abstract:

This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.

Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)

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Authors: Punit Kumar, Niraj Kumar

Abstract:

The traction behavior of lubricants with the linear pressure-viscosity response in EHL line contacts is investigated numerically for smooth as well as rough surfaces. The analysis involves the simultaneous solution of Reynolds, elasticity and energy equations along with the computation of lubricant properties and surface temperatures. The temperature modified Doolittle-Tait equations are used to calculate viscosity and density as functions of fluid pressure and temperature, while Carreau model is used to describe the lubricant rheology. The surface roughness is assumed to be sinusoidal and it is present on the nearly stationary surface in near-pure sliding EHL conjunction. The linear P-V oil is found to yield much lower traction coefficients and slightly thicker EHL films as compared to the synthetic oil for a given set of dimensionless speed and load parameters. Besides, the increase in traction coefficient attributed to surface roughness is much lower for the former case. The present analysis emphasizes the importance of employing realistic pressure-viscosity response for accurate prediction of EHL traction.

Keywords: EHL, linear pressure-viscosity, surface roughness, traction, water/glycol.

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Authors: Ahmed N. Shmroukh, Gamal Tag Abdel-Jaber, Rashed D. Aldughpassi

Abstract:

The feasibility of improving the performance of the proposed solar still unit which operated in very hot climate is investigated numerically and verified with experimental data. This solar desalination unit with proposed auxiliary device as seawater preheating system using petrol based textherm oil was used to produce pure fresh water from seawater. The effective evaporation area of basin is about 1 m². The unit was tested in two main operation modes which are normal and with seawater preheating system. The results showed that, there is good agreement between the theoretical data and the experimental data; this means that the numerical model can be accurately dependable for predicting the proposed solar still performance and design parameters. The results also showed that the fresh water productivity of the solar still in the modified preheating case which is higher than normal case, leads to an increase in productivity of 42%.

Keywords: Improving productivity, seawater desalination, solar stills, theoretical model.

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Authors: Changchun Shen, Shouming Zhong

Abstract:

This paper investigates the problem of absolute stability and robust stability of a class of Lur-e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the considered systems. To obtain less conservative stability conditions, an operator is defined to construct the Lyapunov functional. Also, the free weighting matrices approach combining a matrix inequality technique is used to reduce the entailed conservativeness. Numerical examples are given to indicate significant improvements over some existing results.

Keywords: Lur'e system, linear matrix inequalities, Lyapunov, stability.

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Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: D. Vijayakumar, R. K. Nema

Abstract:

Over Current Relays (OCRs) and Directional Over Current Relays (DOCRs) are widely used for the radial protection and ring sub transmission protection systems and for distribution systems. All previous work formulates the DOCR coordination problem either as a Non-Linear Programming (NLP) for TDS and Ip or as a Linear Programming (LP) for TDS using recently a social behavior (Particle Swarm Optimization techniques) introduced to the work. In this paper, a Modified Particle Swarm Optimization (MPSO) technique is discussed for the optimal settings of DOCRs in power systems as a Non-Linear Programming problem for finding Ip values of the relays and for finding the TDS setting as a linear programming problem. The calculation of the Time Dial Setting (TDS) and the pickup current (Ip) setting of the relays is the core of the coordination study. PSO technique is considered as realistic and powerful solution schemes to obtain the global or quasi global optimum in optimization problem.

Keywords: Directional over current relays, Optimization techniques, Particle swarm optimization, Power system protection.

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: Joseph Oh, Bo-Hyun Kim, Jae-Yong Baek

Abstract:

This study suggests how an order-receiving company can avoid disclosing schedule information on unit tasks to the order-placing company when carrying out a collaborative project on the value chain in an order-oriented industry. Specifically, it suggests methods for keeping schedule information confidential, and categorizes potential situations by inter-task dependency. Lastly, an approach to select the most optimal non-disclosure method is discussed. With the methods for not disclosing work-related information suggested in the study, order-receiving companies can logically deal with political issues relating to the question of whether or not to disclose information upon the execution of a collaborative project in cooperation with an order-placing firm. Moreover, order-placing companies can monitor undistorted information, while respecting the legitimate rights of an order-receiving company. Therefore, it is fair to say that the suggestions made in this study will contribute to the smooth operation of collaborative intercompany projects.

Keywords: collaborative project, dependency, schedule management, unit task.

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Authors: A. Zare Bazghaleh, M. R. Naghashan, H. Mahmoudimanesh, M. R. Meshkatoddini

Abstract:

Linear induction motors are used in various industries but they have some specific phenomena which are the causes for some problems. The most important phenomenon is called end effect. End effect decreases efficiency, power factor and output force and unbalances the phase currents. This phenomenon is more important in medium and high speeds machines. In this paper a factor, EEF , is obtained by an accurate equivalent circuit model, to determine the end effect intensity. In this way, all of effective design parameters on end effect is described. Accuracy of this equivalent circuit model is evaluated by two dimensional finite-element analysis using ANSYS. The results show the accuracy of the equivalent circuit model.

Keywords: Linear induction motor, end effect, equivalent circuitmodel, finite-element method.

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