Search results for: Fuzzy membership functions

Authors: K. V. Geetha, N. R. Mangalambal

Abstract:

Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: N. F. F. Ebecken, G. C. Pereira

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Ecological systems are exposed and are influenced by various natural and anthropogenic disturbances. They produce various effects and states seeking response symmetry to a state of global phase coherence or stability and balance of their food webs. This research project addresses the development of a computational methodology for modeling plankton food webs. The use of algorithms to establish connections, the generation of representative fuzzy multigraphs and application of technical analysis of complex networks provide a set of tools for defining, analyzing and evaluating community structure of coastal aquatic ecosystems, beyond the estimate of possible external impacts to the networks. Thus, this study aims to develop computational systems and data models to assess how these ecological networks are structurally and functionally organized, to analyze the types and degree of compartmentalization and synchronization between oscillatory and interconnected elements network and the influence of disturbances on the overall pattern of rhythmicity of the system.

Keywords: Ecological networks, plankton food webs, fuzzy multigraphs, dynamic of networks.

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Authors: Zhanar Kozhabekova

Abstract:

There are many demonstrations of political interrelation of Turk kaganate and Mongol empire. The article deals with one of the points of Turk-Mongol interrelation as the ceremony of ascending the khan to the throne. It is historically proved that the ascending to the throne ceremony takes origin from Turk kaganate period by comparing the materials, concerning the facts of the history of both states. The function of Turk-Mongol kaganates remained unchangeable for ages.

Keywords: Enthronement, kagan functions, Mongol empire, Turk kaganate.

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Authors: Nakhoon Baek

Abstract:

Stipples are desired for pattern fillings and transparency effects. In contrast, some graphics standards, including OpenGL ES 1.1 and 2.0, omitted this feature. We represent details of providing line stipples and polygon stipples, through combining texture mapping and alpha blending functions. We start from the OpenGL-specified stipple-related API functions. The details of mathematical transformations are explained to get the correct texture coordinates. Then, the overall algorithm is represented, and its implementation results are followed. We accomplished both of line and polygon stipples, and verified its result with conformance test routines.

Keywords: Stipple operation, OpenGL ES, Implementation.

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Authors: Mehdi Nafar, Mohammad Reza Mansouri

Abstract:

The present research presents a direct active and reactive power control (DPC) of a wind energy conversion system (WECS) for the maximum power point tracking (MPPT) based on a doubly fed induction generator (DFIG) connected to electric power grid. The control strategy of the Rotor Side Converter (RSC) is targeted in extracting a maximum of power under fluctuating wind speed. A fuzzy logic speed controller (FLC) has been used to ensure the MPPT. The Grid Side Converter is directed in a way to ensure sinusoidal current in the grid side and a smooth DC voltage. To reduce fluctuations, rotor torque and voltage use of multilevel inverters is a good way to remove the rotor harmony.

Keywords: DFIG, power quality improvement, wind energy conversion system, WECS, fuzzy logic, RSC, GSC, inverter.

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Authors: T. N. Sindhu, M. Aslam

Abstract:

A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.

Keywords: Credible Intervals, Loss Functions, Posterior Predictive Distributions, Predictive Intervals.

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Authors: Robert Gold

Abstract:

Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modeled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyze the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: Control flow graph, graph reduction.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

Abstract:

Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: Naima Ikken, Abdelhadi Bouknadel, Nour-eddine Tariba Ahmed Haddou, Hafsa El Omari

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The operation of grid-connected inverters necessity a single-phase phase locked loop (PLL) is proposed in this article to accurately and quickly estimate and detect the grid phase angle. This article presents the improvement of a method of phase-locked loop. The novelty is to generate a method (PLL) of synchronizing the grid with a Notch filter based on adaptive fuzzy logic for inverter systems connected to the grid. The performance of the proposed method was tested under normal and abnormal operating conditions (amplitude, frequency and phase shift variations). In addition, simulation results with ISPM software are developed to verify the effectiveness of the proposed method strategy. Finally, the experimental test will be used to extract the result and discuss the validity of the proposed algorithm.

Keywords: Phase locked loop, PLL, notch filter, fuzzy logic control.

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Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: R. Saraçoğlu, N. Allahverdi

Abstract:

Searching similar documents and document management subjects have important place in text mining. One of the most important parts of similar document research studies is the process of classifying or clustering the documents. In this study, a similar document search approach that includes discussion of out the case of belonging to multiple categories (multiple categories problem) has been carried. The proposed method that based on Fuzzy Similarity Classification (FSC) has been compared with Rocchio algorithm and naive Bayes method which are widely used in text mining. Empirical results show that the proposed method is quite successful and can be applied effectively. For the second stage, multiple categories vector method based on information of categories regarding to frequency of being seen together has been used. Empirical results show that achievement is increased almost two times, when proposed method is compared with classical approach.

Keywords: Document similarity, Fuzzy classification, Multiple categories, Text mining.

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Authors: Y. Sabzehmeidani, M. Mailah, M. Hussein, A. R. Tavakolpour

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In this paper, a worm-like micro robot designed for inpipe application with intelligent active force control (AFC) capability is modelled and simulated. The motion of the micro robot is based on an impact drive mechanism (IDM) that is actuated using piezoelectric device. The trajectory tracking performance of the modelled micro robot is initially experimented via a conventional proportionalintegral- derivative (PID) controller in which the dynamic response of the robot system subjected to different input excitations is investigated. Subsequently, a robust intelligent method known as active force control with fuzzy logic (AFCFL) is later incorporated into the PID scheme to enhance the system performance by compensating the unwanted disturbances due to the interaction of the robot with its environment. Results show that the proposed AFCFL scheme is far superior than the PID control counterpart in terms of the system-s tracking capability in the wake of the disturbances.

Keywords: Active Force Control, Micro Robot, Fuzzy Logic, In-pipe Application.

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Authors: Sadaf Sahar, Usman Qamar, Sadaf Ayaz

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In the software development lifecycle, the quality prediction techniques hold a prime importance in order to minimize future design errors and expensive maintenance. There are many techniques proposed by various researchers, but with the increasing complexity of the software lifecycle model, it is crucial to develop a flexible system which can cater for the factors which in result have an impact on the quality of the end product. These factors include properties of the software development process and the product along with its operation conditions. In this paper, a neural network (perceptron) based software quality prediction technique is proposed. Using this technique, the stakeholders can predict the quality of the resulting software during the early phases of the lifecycle saving time and resources on future elimination of design errors and costly maintenance. This technique can be brought into practical use using successful training.

Keywords: Software quality, fuzzy logic, perceptron, prediction.

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Authors: Anna Lower, Michal Lower, Robert Masztalski, Agnieszka Szumilas

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The paper presents a method in which the expert knowledge is applied to fuzzy inference model. Even a less experienced person could benefit from the use of such a system, e.g. urban planners, officials. The analysis result is obtained in a very short time, so a large number of the proposed locations can also be verified in a short time. The proposed method is intended for testing of locations of car parks in a city. The paper shows selected examples of locations of the P&R facilities in cities planning to introduce the P&R. The analyses of existing objects are also shown in the paper and they are confronted with the opinions of the system users, with particular emphasis on unpopular locations. The results of the analyses are compared to expert analysis of the P&R facilities location that was outsourced by the city and the opinions about existing facilities users that were expressed on social networking sites. The obtained results are consistent with actual users’ feedback. The proposed method proves to be good, but does not require the involvement of a large experts team and large financial contributions for complicated research. The method also provides an opportunity to show the alternative location of P&R facilities. Although the results of the method are approximate, they are not worse than results of analysis of employed experts. The advantage of this method is ease of use, which simplifies the professional expert analysis. The ability of analyzing a large number of alternative locations gives a broader view on the problem. It is valuable that the arduous analysis of the team of people can be replaced by the model's calculation. According to the authors, the proposed method is also suitable for implementation on a GIS platform.

Keywords: Fuzzy logic inference, P&R facilities, P&R location.

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Authors: N. Tadrisi Parsa, A. R. Vali, R. Ghasemi

Abstract:

Diabetes is a growing health problem in worldwide. Especially, the patients with Type 1 diabetes need strict glycemic control because they have deficiency of insulin production. This paper attempts to control blood glucose based on body mathematical body model. The Bergman minimal mathematical model is used to develop the nonlinear controller. A novel back-stepping based sliding mode control (B-SMC) strategy is proposed as a solution that guarantees practical tracking of a desired glucose concentration. In order to show the performance of the proposed design, it is compared with conventional linear and fuzzy controllers which have been done in previous researches. The numerical simulation result shows the advantages of sliding mode back stepping controller design to linear and fuzzy controllers.

Keywords: Back stepping, Bergman Model, Nonlinear control, Sliding mode control.

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Authors: Bogdan Walek, Cyril Klimes

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This paper focuses on testing database of existing information system. At the beginning we describe the basic problems of implemented databases, such as data redundancy, poor design of database logical structure or inappropriate data types in columns of database tables. These problems are often the result of incorrect understanding of the primary requirements for a database of an information system. Then we propose an algorithm to compare the conceptual model created from vague requirements for a database with a conceptual model reconstructed from implemented database. An algorithm also suggests steps leading to optimization of implemented database. The proposed algorithm is verified by an implemented prototype. The paper also describes a fuzzy system which works with the vague requirements for a database of an information system, procedure for creating conceptual from vague requirements and an algorithm for reconstructing a conceptual model from implemented database.

Keywords: testing, database, relational database, information system, conceptual model, fuzzy, uncertain information, database testing, reconstruction, requirements, optimization

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Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan

Abstract:

Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.

Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.

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Authors: C. Ardil

Abstract:

Fuzzy set theory and its extensions (intuitionistic fuzzy sets, picture fuzzy sets, and neutrosophic sets) have been widely used to address imprecision and uncertainty in complex decision-making. However, they may struggle with inherent indeterminacy and inconsistency in real-world situations. This study introduces uncertainty sets as a promising alternative, offering a structured framework for incorporating both types of uncertainty into decision-making processes.This work explores the theoretical foundations and applications of uncertainty sets. A novel decision-making algorithm based on uncertainty set-based proximity measures is developed and demonstrated through a practical application: selecting the most suitable stealth combat aircraft.

The results highlight the effectiveness of uncertainty sets in ranking alternatives under uncertainty. Uncertainty sets offer several advantages, including structured uncertainty representation, robust ranking mechanisms, and enhanced decision-making capabilities due to their ability to account for ambiguity.Future research directions are also outlined, including comparative analysis with existing MCDM methods under uncertainty, sensitivity analysis to assess the robustness of rankings,and broader application to various MCDM problems with diverse complexities. By exploring these avenues, uncertainty sets can be further established as a valuable tool for navigating uncertainty in complex decision-making scenarios.

Keywords: Uncertainty set, stealth combat aircraft selection multiple criteria decision-making analysis, MCDM, uncertainty proximity analysis

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Authors: Raghad Alhusari, Farag Omar, Moustafa Fadel

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A traditional greenhouse is a metal frame agricultural building used for cultivation plants in a controlled environment isolated from external climatic changes. Using greenhouses in agriculture is an efficient way to reduce the water consumption, where agriculture field is considered the biggest water consumer world widely. Controlling greenhouse environment yields better productivity of plants but demands an increase of electric power. Although various control approaches have been used towards greenhouse automation, most of them are applied to traditional greenhouses with ventilation fans and/or evaporation cooling system. Such approaches are still demanding high energy and water consumption. The aim of this research is to develop a fuzzy control system that minimizes water and energy consumption by utilizing outside weather conditions and underground heat exchanger to maintain the optimum climate of the greenhouse. The proposed control system is implemented on an experimental model of thermally isolated greenhouse structure with dimensions of 6x5x2.8 meters. It uses fans for extracting heat from the ground heat exchanger system, motors for automatic open/close of the greenhouse windows and LED as lighting system. The controller is integrated also with environmental condition sensors. It was found that using the air-to-air horizontal ground heat exchanger with 90 mm diameter and 2 mm thickness placed 2.5 m below the ground surface results in decreasing the greenhouse temperature of 3.28 ˚C which saves around 3 kW of consumed energy. It also eliminated the water consumption needed in evaporation cooling systems which are traditionally used for cooling the greenhouse environment.

Keywords: Automation, earth-to-air heat exchangers, fuzzy control, greenhouse, sustainable buildings.

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Authors: Abdalla Kablan, Joseph Falzon

Abstract:

This paper is motivated by the aspect of uncertainty in financial decision making, and how artificial intelligence and soft computing, with its uncertainty reducing aspects can be used for algorithmic trading applications that trade in high frequency. This paper presents an optimized high frequency trading system that has been combined with various moving averages to produce a hybrid system that outperforms trading systems that rely solely on moving averages. The paper optimizes an adaptive neuro-fuzzy inference system that takes both the price and its moving average as input, learns to predict price movements from training data consisting of intraday data, dynamically switches between the best performing moving averages, and performs decision making of when to buy or sell a certain currency in high frequency.

Keywords: Financial decision making, High frequency trading, Adaprive neuro-fuzzy systems, moving average strategy.

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Authors: D. Garg, S. Luthra, A. Haleem

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Reverse logistics (RL) is supposed to be a systematic procedure that helps in improving the environmental hazards and maintain business sustainability for industries. Industries in Indian are now opting for adoption of RL techniques in business. But, RL practices are not popular in Indian industries because of many barriers for its successful implementation. Therefore, need arises to identify and evaluate the barriers to implement RL practices by taking an Indian industries perspective. Literature review approach and case study approach have been adapted to identify relevant barriers to implement RL practices. Further, Fuzzy Decision Making Trial and Evaluation Laboratory methodology has been brought into use for evaluating causal relationships among the barriers to implement RL practices. Seven barriers out of ten barriers have been categorized into the cause group and remaining into effect group. This research will help Indian industries to manage these barriers towards effective implementing RL practices.

Keywords: Barriers, decision making trial and evaluation laboratory, fuzzy set theory, Indian industries, reverse logistics.

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Authors: M. Padmavathi, R. M. Suresh

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Every machine plays roles of client and server simultaneously in a peer-to-peer (P2P) network. Though a P2P network has many advantages over traditional client-server models regarding efficiency and fault-tolerance, it also faces additional security threats. Users/IT administrators should be aware of risks from malicious code propagation, downloaded content legality, and P2P software’s vulnerabilities. Security and preventative measures are a must to protect networks from potential sensitive information leakage and security breaches. Bit Torrent is a popular and scalable P2P file distribution mechanism which successfully distributes large files quickly and efficiently without problems for origin server. Bit Torrent achieved excellent upload utilization according to measurement studies, but it also raised many questions as regards utilization in settings, than those measuring, fairness, and Bit Torrent’s mechanisms choice. This work proposed a block selection technique using Fuzzy ACO with optimal rules selected using ACO.

Keywords: Ant Colony Optimization (ACO), Bit Torrent, Download time, Peer-to-Peer (P2P) network, Performance.

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Authors: Anupama Pande, Vishik Goel

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A complex valued neural network is a neural network, which consists of complex valued input and/or weights and/or thresholds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in image and vision processing. In Neural networks, radial basis functions are often used for interpolation in multidimensional space. A Radial Basis function is a function, which has built into it a distance criterion with respect to a centre. Radial basis functions have often been applied in the area of neural networks where they may be used as a replacement for the sigmoid hidden layer transfer characteristic in multi-layer perceptron. This paper aims to present exhaustive results of using RBF units in a complex-valued neural network model that uses the back-propagation algorithm (called 'Complex-BP') for learning. Our experiments results demonstrate the effectiveness of a Radial basis function in a complex valued neural network in image recognition over a real valued neural network. We have studied and stated various observations like effect of learning rates, ranges of the initial weights randomly selected, error functions used and number of iterations for the convergence of error on a neural network model with RBF units. Some inherent properties of this complex back propagation algorithm are also studied and discussed.

Keywords: Complex valued neural network, Radial BasisFunction, Image recognition.

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Authors: Anusua Ghosh, Andrew Nafalski, Jeffery Tweedale, Maureen Dollard

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This paper presents anapproach of hybridizing two or more artificial intelligence (AI) techniques which arebeing used to fuzzify the workstress level ranking and categorize the rating accordingly. The use of two or more techniques (hybrid approach) has been considered in this case, as combining different techniques may lead to neutralizing each other-s weaknesses generating a superior hybrid solution. Recent researches have shown that there is a need for a more valid and reliable tools, for assessing work stress. Thus artificial intelligence techniques have been applied in this instance to provide a solution to a psychological application. An overview about the novel and autonomous interactive model for analysing work-stress that has been developedusing multi-agent systems is also presented in this paper. The establishment of the intelligent multi-agent decision analyser (IMADA) using hybridized technique of neural networks and fuzzy logic within the multi-agent based framework is also described.

Keywords: Fuzzy logic, intelligent agent, multi-agent systems, neural network, workplace stress.

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Authors: Chunshien Li, Jhao-Wun Hu, Tai-Wei Chiang, Tsunghan Wu

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Time series forecasting is an important and widely popular topic in the research of system modeling. This paper describes how to use the hybrid PSO-RLSE neuro-fuzzy learning approach to the problem of time series forecasting. The PSO algorithm is used to update the premise parameters of the proposed prediction system, and the RLSE is used to update the consequence parameters. Thanks to the hybrid learning (HL) approach for the neuro-fuzzy system, the prediction performance is excellent and the speed of learning convergence is much faster than other compared approaches. In the experiments, we use the well-known Mackey-Glass chaos time series. According to the experimental results, the prediction performance and accuracy in time series forecasting by the proposed approach is much better than other compared approaches, as shown in Table IV. Excellent prediction performance by the proposed approach has been observed.

Keywords: forecasting, hybrid learning (HL), Neuro-FuzzySystem (NFS), particle swarm optimization (PSO), recursiveleast-squares estimator (RLSE), time series

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine

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This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Keywords: Gauss-Legendre, Clenshaw-Curtis, quadrature, Peano kernel, irregular sampling.

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Authors: Mohamed M. M. Elnasharty, Azhar M. Elwan

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Irradiation deposits energy through ionisation changing the bio-system’s net dipole, allowing the use of dielectric parameters and thermodynamic state functions related to these parameters as biophysical detectors to electrical inhomogeneity within the biosystem. This part is concerned with the effect of Moringa leaves extract, natural supplement, on the response of the biosystem to two different dose rates of irradiation. Having Hb molecule as a representative to the biosystem to be least invasive to the biosystem, dielectric measurements were used to extract the relaxation time of certain process found in the Hb spectrum within the indicated frequency window and the interrelated thermodynamic state functions were calculated from the deduced relaxation time. The results showed that relaxation time was decreased for both dose rates indicating a strong influence of Moringa on the response of biosystem and consequently Hb molecule. This influence was presented in the relaxation time and other parameters as well.

Keywords: Activation energy, DC conductivity, dielectric relaxation, enthalpy change, moringa leaves extract, relaxation time.

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Authors: Grouz Faten, Sbita Lassaâd

Abstract:

In this paper, Speed Sensorless Indirect Field Oriented Control (IFOC) of a Permanent Magnet Synchronous machine (PMSM) is studied. The closed loop scheme of the drive system utilizes fuzzy speed and current controllers. Due to the well known drawbacks of the speed sensor, an algorithm is proposed in this paper to eliminate it. In fact, based on the model of the PMSM, the stator currents and rotor speed are estimated simultaneously using adaptive Luenberger observer for currents and MRAS (Model Reference Adaptive System) observer for rotor speed. To overcome the sensivity of this algorithm against parameter variation, adaptive for on line stator resistance tuning is proposed. The validity of the proposed method is verified by an extensive simulation work.

Keywords: PMSM, Indirect Field Oriented Control, fuzzy speed and currents controllers, Adaptive Luenberger observer, MRAS.

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Authors: Verónica Diaz Quezada

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This research examines the teaching models used by secondary math teachers when teaching logarithmic, quadratic and exponential functions. For this, descriptive case studies have been carried out on 5 secondary teachers. These teachers have been chosen from 3 scientific-humanistic and technical schools, in Chile. Data have been obtained through non-participant class observation and the application of a questionnaire and a rubric to teachers. According to the results, the didactic model that prevails is the one that starts with an interactive strategy, moves to a more content-based structure, and ends with a reinforcement stage. Nonetheless, there is always influence from teachers, their methods, and the group of students.

Keywords: Teaching models, math teachers, functions, secondary education.

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