Search results for: matrix means

Authors: Federico Pérez González, Iñaki Goirizelaia Ordorika, Pedro Iriondo Bengoa

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In this work a new method for low complexity image coding is presented, that permits different settings and great scalability in the generation of the final bit stream. This coding presents a continuous-tone still image compression system that groups loss and lossless compression making use of finite arithmetic reversible transforms. Both transformation in the space of color and wavelet transformation are reversible. The transformed coefficients are coded by means of a coding system in depending on a subdivision into smaller components (CFDS) similar to the bit importance codification. The subcomponents so obtained are reordered by means of a highly configure alignment system depending on the application that makes possible the re-configure of the elements of the image and obtaining different importance levels from which the bit stream will be generated. The subcomponents of each importance level are coded using a variable length entropy coding system (VBLm) that permits the generation of an embedded bit stream. This bit stream supposes itself a bit stream that codes a compressed still image. However, the use of a packing system on the bit stream after the VBLm allows the realization of a final highly scalable bit stream from a basic image level and one or several improvement levels.

Keywords: Image compression, wavelet transform, highly scalable, reversible transform, embedded, subcomponents.

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Authors: A. Samraj, S. Sayeed, J. E. Raja., J. Hossen, A. Rahman

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Monitoring the tool flank wear without affecting the throughput is considered as the prudent method in production technology. The examination has to be done without affecting the machining process. In this paper we proposed a novel work that is used to determine tool flank wear by observing the sound signals emitted during the turning process. The work-piece material we used here is steel and aluminum and the cutting insert was carbide material. Two different cutting speeds were used in this work. The feed rate and the cutting depth were constant whereas the flank wear was a variable. The emitted sound signal of a fresh tool (0 mm flank wear) a slightly worn tool (0.2 -0.25 mm flank wear) and a severely worn tool (0.4mm and above flank wear) during turning process were recorded separately using a high sensitive microphone. Analysis using Singular Value Decomposition was done on these sound signals to extract the feature sound components. Observation of the results showed that an increase in tool flank wear correlates with an increase in the values of SVD features produced out of the sound signals for both the materials. Hence it can be concluded that wear monitoring of tool flank during turning process using SVD features with the Fuzzy C means classification on the emitted sound signal is a potential and relatively simple method.

Keywords: Fuzzy c means, Microphone, Singular ValueDecomposition, Tool Flank Wear.

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Authors: Josef Fládr, Jiří Němeček, Veronika Koudelková, Petr Bílý

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Mechanical parameters of cementitious composites differ quite significantly based on the composition of cement matrix. They are also influenced by mixing times and procedure. The research presented in this paper was aimed at identification of differences in microstructure of normal strength (NSC) and differently mixed high strength (HSC) cementitious composites. Scanning electron microscopy (SEM) investigation together with energy dispersive X-ray spectroscopy (EDX) phase analysis of NSC and HSC samples was conducted. Evaluation of interfacial transition zone (ITZ) between the aggregate and cement matrix was performed. Volume share, thickness, porosity and composition of ITZ were studied. In case of HSC, samples obtained by several different mixing procedures were compared in order to find the most suitable procedure. In case of NSC, ITZ was identified around 40-50% of aggregate grains and its thickness typically ranged between 10 and 40 µm. Higher porosity and lower share of clinker was observed in this area as a result of increased water-to-cement ratio (w/c) and the lack of fine particles improving the grading curve of the aggregate. Typical ITZ with lower content of Ca was observed only in one HSC sample, where it was developed around less than 15% of aggregate grains. The typical thickness of ITZ in this sample was similar to ITZ in NSC (between 5 and 40 µm). In the remaining four HSC samples, no ITZ was observed. In general, the share of ITZ in HSC samples was found to be significantly smaller than in NSC samples. As ITZ is the weakest part of the material, this result explains to large extent the improved mechanical properties of HSC compared to NSC. Based on the comparison of characteristics of ITZ in HSC samples prepared by different mixing procedures, the most suitable mixing procedure from the point of view of properties of ITZ was identified.

Keywords: Energy dispersive X-ray spectroscopy, high strength concrete, interfacial transition zone, mixing procedure, normal strength concrete, scanning electron microscopy.

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Authors: Guangbin Wang, Fuping Tan

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In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: Seok Hyoung Lee, Vladimir Shin

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An optimal mean-square fusion formulas with scalar and matrix weights are presented. The relationship between them is established. The fusion formulas are compared on the continuous-time filtering problem. The basic differential equation for cross-covariance of the local errors being the key quantity for distributed fusion is derived. It is shown that the fusion filters are effective for multi-sensor systems containing different types of sensors. An example demonstrating the reasonable good accuracy of the proposed filters is given.

Keywords: Kalman filtering, fusion formula, multi-sensor, mean-square error.

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Authors: O. Khalaj, B. Mašek, H. Jirková, J. Svoboda

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By using a combination of new technologies together with an unconventional use of different types of materials, specific mechanical properties and structures of the material can be achieved. Some possibilities are enabled by a combination of powder metallurgy in the preparation of a metal matrix with dispersed stable particles achieved by mechanical alloying and hot consolidation. This paper explains the thermomechanical properties of new generation of Oxide Dispersion Strengthened alloys (ODS) within three ranges of temperature with specified deformation profiles. The results show that the mechanical properties of new ODS alloys are significantly affected by the thermomechanical treatment.

Keywords: Hot forming, ODS, alloys, thermomechanical, Fe-Al, Al2O3.

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Authors: Xiuqin Ma, Norrozila Binti Sulaiman, Hongwu Qin

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In the research field of Rough Set, few papers concern the significance of attribute set. However, there is important relation between the significance of single attribute and that of attribute set, which should not be ignored. In this paper, we draw conclusions by case analysis that (1) the attribute set including single attributes with high significance is certainly significant, while, (2)the attribute set which consists of single attributes with low significance possibly has high significance. We validate the conclusions on discernibility matrix and the results demonstrate the contribution of our conclusions.

Keywords: relation, attribute set, single attribute, rough set, significance

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

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In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.

Keywords: Hopfield Neural Networks, Exponential stability.

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Authors: Dimitrios E. Kontaxis, George Litainas, Dimitrios P. Ptochos, Vaggelis P. Ptochos, Sotirios P. Ptochos, Dimitrios Beletsis, Konstantinos Kritikakis, Milan Sunaric

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Real-time monitoring of the supply chain conditions and procedures is a critical element for the optimal coordination and safety of the deliveries, as well as for the minimization of the delivery time and cost. Real time monitoring requires IoT data streams, which are related to the conditions of the products and the means of transport (e.g., location, temperature/humidity conditions, kinematic state, ambient light conditions, etc.). These streams are generated by battery-based IoT tracking devices, equipped with appropriate sensors, and are transmitted to a cloud-based back-end system. Proper handling and processing of the IoT data streams, using predictive and artificial intelligence algorithms, can provide significant and useful results, which can be exploited by the supply chain stakeholders in order to enhance their financial benefits, as well as the efficiency, security, transparency, coordination and sustainability of the supply chain procedures. The technology, the features and the characteristics of a complete, proprietary system, including hardware, firmware and software tools - developed in the context of a co-funded R&D program - are addressed and presented in this paper. 

Keywords: IoT embedded electronics, real-time monitoring, tracking device, sensor platform

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Authors: Fetah Eren, Ismail Sahin, Ismail Celik, Ahmet Oguz Akturk

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The aim of this study is to discover secondary school students’ perceptions related to information technologies and the connections between concepts in their cognitive structures. A word association test consisting of six concepts related to information technologies is used to collect data from 244 secondary school students. Concept maps that present students’ cognitive structures are drawn with the help of frequency data. Data are analyzed and interpreted according to the connections obtained as a result of the concept maps. It is determined students associate most with these concepts—computer, Internet, and communication of the given concepts, and associate least with these concepts—computer-assisted education and information technologies. These results show the concepts, Internet, communication, and computer, are an important part of students’ cognitive structures. In addition, students mostly answer computer, phone, game, Internet and Facebook as the key concepts. These answers show students regard information technologies as a means for entertainment and free time activity, not as a means for education.

Keywords: Word association test, cognitive structure, information technology, secondary school.

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Authors: Ilia Marchevsky, Victoriya Moreva

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The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: Farzad Abdous

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Fuel cell's system requires regulating circuit for voltage and current in order to control power in case of connecting to other generative devices or load. In this paper Fuel cell system and convertor, which is a multi-variable system, are controlled using sliding mode method. Use of weighting matrix in design procedure made it possible to regulate speed of control. Simulation results show the robustness and accuracy of proposed controller for controlling desired of outputs.

Keywords: DC-DC converter, Fuel cell, PEM, Slides mode control.

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Authors: Peter Podbreznik, Božidar Potocnik

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The camera parameters are changed due to temperature variations, which directly influence calibrated cameras accuracy. Robustness of calibration methods were measured and their accuracy was tested. An error ratio due to camera parameters change with respect to total error originated during calibration process was determined. It pointed out that influence of temperature variations decrease by increasing distance of observed objects from cameras.

Keywords: camera calibration, perspective projection matrix, epipolar geometry, temperature variation.

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Authors: Congo Tak Shing Ching, Hong-Sheng Chen, Tai-Ping Sun, Hsiu-Li Shieh

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Nuclear matrix protein 22 (NMP22) is a FDA approved biomarker for bladder cancer. The objective of this study is to develop a simple NMP22 immumosensor (NMP22-IMS) for accurate measurement of NMP22. The NMP22-IMS was constructed with NMP22 antibody immobilized on screen-printed carbon electrodes. The construction procedures and antibody immobilization are simple. Results showed that the NMP22-IMS has an excellent (r2³0.95) response range (20 – 100 ng/mL). In conclusion, a simple and reliable NMP22-IMS was developed, capable of precisely determining urine NMP22 level.

Keywords: Bladder Cancer, Immunosensor, Impedance, NMP22

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Authors: A. T. Asutosh, J. Woo, M. Kouhirostami, M. Sam, A. Khantawang, C. Cuales, W. Ryor, C. Kibert

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Climate change and global warming vortex have grown to alarming proportions. Therefore, the need for a shift in the conceptualization of energy production is paramount. Energy practices have been created in the current situation. Fossil fuels continue their prominence, at the expense of renewable sources. Despite this abundance, a large percentage of the world population still has no access to electricity but there have been encouraging signs in global movement from nonrenewable to renewable energy but means to reverse climate change have been elusive. Worldwide, organizations have put tremendous effort into innovation. Conferences and exhibitions act as a platform that allows a broad exchange of information regarding trends in the renewable energy field. The Solar Power International (SPI) conference and exhibition is a gathering of concerned activists, and probably the largest convention of its kind. This study investigates current development in the renewable energy field, analyzing means by which industry is being applied to the issue. In reviewing the 2019 SPI conference, it was found innovations in recycling and assessing the environmental impacts of the solar products that need critical attention. There is a huge movement in the electrical storage but there exists a large gap in the development of security systems. This research will focus on solar energy, but impacts will be relevant to the entire renewable energy market.

Keywords: Climate change, renewable energy, solar, trends, research, SPI.

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Authors: Volker Koch

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This paper deals with the education of purchasing professionals in Austria. In this education, equivalent and measurable criteria are collected in order to create a comparison. The comparison shows the problem. To make the aforementioned comparison possible, methodologies such as KODE-Competence Atlas or presentations in a matrix form are used. The result shows the content taught and whether there are any similarities or interesting differences in the current Austrian purchasers’ formations. Purchasing professionals learning competencies are also illustrated in the study result.

Keywords: Competencies, education, purchasing professional, technological-oriented.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

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This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Supriya Gupta, Paresh Chokshi

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Polymer-particle interactions can be effectively utilized to produce composites that possess physicochemical properties superior to that of neat polymer. The incorporation of fillers with dimensions comparable to polymer chain size produces composites with extra-ordinary properties owing to very high surface to volume ratio. The dispersion of nanoparticles is achieved by inducing steric repulsion realized by grafting particles with polymeric chains. A comprehensive understanding of the interparticle interaction between these functionalized nanoparticles plays an important role in the synthesis of a stable polymer nanocomposite. With the focus on incorporation of clay sheets in a polymer matrix, we theoretically construct the polymer mediated interparticle potential for two nanosheets grafted with polymeric chains. The self-consistent field theory (SCFT) is employed to obtain the inhomogeneous composition field under equilibrium. Unlike the continuum models, SCFT is built from the microscopic description taking in to account the molecular interactions contributed by both intra- and inter-chain potentials. We present the results of SCFT calculations of the interaction potential curve for two grafted nanosheets immersed in the matrix of polymeric chains of dissimilar chemistry to that of the grafted chains. The interaction potential is repulsive at short separation and shows depletion attraction for moderate separations induced by high grafting density. It is found that the strength of attraction well can be tuned by altering the compatibility between the grafted and the mobile chains. Further, we construct the interaction potential between two nanosheets grafted with diblock copolymers with one of the blocks being chemically identical to the free polymeric chains. The interplay between the enthalpic interaction between the dissimilar species and the entropy of the free chains gives rise to a rich behavior in interaction potential curve obtained for two separate cases of free chains being chemically similar to either the grafted block or the free block of the grafted diblock chains.

Keywords: Clay nanosheets, polymer brush, polymer nanocomposites, self-consistent field theory.

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Authors: Blandína Šramová, Gabriel Bianchi, Barbara Lášticová, Katarína Fichnová, Anežka Hamranová

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The contribution deals with analysis of identity style at adolescents (N=463) at the age from 16 to 19 (the average age is 17,7 years). We used the Identity Style Inventory by Berzonsky, distinguishing three basic, measured identity styles: informational, normative, diffuse-avoidant identity style and also commitment. The informational identity style influencing on personal adaptability, coping strategies, quality of life and the normative identity style, it means the style in which an individual takes on models of authorities at self-defining were found to have the highest representation in the studied group of adolescents by higher scores at girls in comparison with boys. The normative identity style positively correlates with the informational identity style. The diffuse-avoidant identity style was found to be positively associated with maladaptive decisional strategies, neuroticism and depressive reactions. There is the style, in which the individual shifts aside defining his personality. In our research sample the lowest score represents it and negatively correlates with commitment, it means with coping strategies, thrust in oneself and the surrounding world. The age of adolescents did not significantly differentiate representation of identity style. We were finding the model, in which informational and normative identity style had positive relationship and the informational and diffuseavoidant style had negative relationship, which were determinated with commitment. In the same time the commitment is influenced with other outside factors.

Keywords: Identity Style Inventory, Informational IdentityStyle, Normative Identity Style, Diffuse-Avoidant Style, IdentityCommitment.

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Authors: Arup K. Sarma, Jayshree Hazarika

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The North-eastern part of India, which receives heavier rainfall than other parts of the subcontinent, is of great concern now-a-days with regard to climate change. High intensity rainfall for short duration and longer dry spell, occurring due to impact of climate change, affects river morphology too. In the present study, an attempt is made to delineate the North-eastern region of India into some homogeneous clusters based on the Fuzzy Clustering concept and to compare the resulting clusters obtained by using conventional methods and nonconventional methods of clustering. The concept of clustering is adapted in view of the fact that, impact of climate change can be studied in a homogeneous region without much variation, which can be helpful in studies related to water resources planning and management. 10 IMD (Indian Meteorological Department) stations, situated in various regions of the North-east, have been selected for making the clusters. The results of the Fuzzy C-Means (FCM) analysis show different clustering patterns for different conditions. From the analysis and comparison it can be concluded that nonconventional method of using GCM data is somehow giving better results than the others. However, further analysis can be done by taking daily data instead of monthly means to reduce the effect of standardization.

Keywords: Climate change, conventional and nonconventional methods of clustering, FCM analysis, homogeneous regions.

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Authors: Rui Wu, Tapani Ristaniemi

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In this paper, we propose a new algorithm for joint time-delay and direction-of-arrival (DOA) estimation, here called two-dimensional code acquisition, in an asynchronous directsequence code-division multiple-access (DS-CDMA) array system. This algorithm depends on eigenvector-eigenvalue decomposition of sample correlation matrix, and requires to know desired user-s training sequence. The performance of the algorithm is analyzed both analytically and numerically in uncorrelated and coherent multipath environment. Numerical examples show that the algorithm is robust with unknown number of coherent signals.

Keywords: Two-Dimensional Code Acquisition, EV-t, DSCDMA

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Authors: M. Ezkurra, J. A. Esnaola, M. Martinez-Agirre, U. Etxeberria, U. Lertxundi, L. Colomo, M. Begiristain, I. Zurutuza

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Butterfly valves are widely used industrial piping components as on-off and flow controlling devices. The main challenge in the design process of this type of valves is the correct dimensioning to ensure proper mechanical performance as well as to minimise flow losses that affect the efficiency of the system. Butterfly valves are typically dimensioned in a closed position based on mechanical approaches considering uniform hydrostatic pressure, whereas the flow losses are analysed by means of CFD simulations. The main limitation of these approaches is that they do not consider either the influence of the dynamics of the manoeuvring stage or coupled phenomena. Recent works have included the influence of the flow on the mechanical behaviour for different opening angles by means of one-way FSI approach. However, these works consider steady-state flow for the selected angles, not capturing the effect of the transient flow evolution during the manoeuvring stage. Two-way FSI modelling approach could allow overcoming such limitations providing more accurate results. Nevertheless, the use of this technique is limited due to the increase in the computational cost. In the present work, the applicability of FSI one-way and two-way approaches is evaluated for the analysis of butterfly valves, showing that not considering fluid-structure coupling involves not capturing the most critical situation for the valve disc.

Keywords: Butterfly valves, fluid-structure interaction, one-way approach, two-way approach.

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Authors: Ahmed Abbas Helmy, M. R. M. Rizk, Mohamed El-Sayed

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A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

Keywords: Adaptive control, model predictive control, dynamic matrix control, online model identification

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Authors: Filiz Ersoz, Taner Ersoz, Tugrul Bayraktar

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Renewable energy is referred to as "clean energy" and common popular support for the use of renewable energy (RE) is to provide electricity with zero carbon dioxide emissions. This study provides useful insight into the European Union (EU) RE, especially, into electricity generation obtained from renewables, and their targets. The objective of this study is to identify groups of European countries, using multivariate statistical analysis and selected indicators. The hierarchical clustering method is used to decide the number of clusters for EU countries. The conducted statistical hierarchical cluster analysis is based on the Ward’s clustering method and squared Euclidean distances. Hierarchical cluster analysis identified eight distinct clusters of European countries. Then, non-hierarchical clustering (k-means) method was applied. Discriminant analysis was used to determine the validity of the results with data normalized by Z score transformation. To explore the relationship between the selected indicators, correlation coefficients were computed. The results of the study reveal the current situation of RE in European Union Member States.

Keywords: Share of electricity generation, CO2 emission, targets, multivariate methods, hierarchical clustering, K-means clustering, discriminant analyzed, correlation, EU member countries.

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Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

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In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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Authors: Bozena Dohnalkova

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This paper presents a part of the project solving which is dedicated to the identification of the hazardous waste with the most critical production within the Czech Republic with the aim to study and find the optimal composition of the cement matrix that will ensure maximum content disposal of chosen hazardous waste. In the first stage of project solving – which represents this paper – a specific hazardous waste was chosen, its properties were identified and suitable solidification agents were chosen. Consequently solidification formulas and testing methodology was proposed.

Keywords: Cementation, solidification, waste, binder.

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Authors: Meng Hu, Lili Wang

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In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

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

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

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Authors: Sheroz Khan, A. F. Salami, W. A. Lawal, AHM Zahirul Alam, Shihab Abdel Hameed, M. J. E.Salami

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In this paper, a multi-branch power line is modeled using ABCD matrix to show its worth as a communication channel. The model is simulated using MATLAB in an effort to investigate the effects of multiple loading, multipath, and those as a result of load mismatching. The channel transfer function is obtained and investigated using different cable lengths, and different number of bridge taps under given loading conditions.

Keywords: Power line Communication, Transfer Function, Channel Modeling, Signal Transmission.

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Authors: Rachid Ait daoud, Abdellah Amine, Belaid Bouikhalene, Rachid Lbibb

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Given the increase in the number of e-commerce sites, the number of competitors has become very important. This means that companies have to take appropriate decisions in order to meet the expectations of their customers and satisfy their needs. In this paper, we present a case study of applying LRFM (length, recency, frequency and monetary) model and clustering techniques in the sector of electronic commerce with a view to evaluating customers’ values of the Moroccan e-commerce websites and then developing effective marketing strategies. To achieve these objectives, we adopt LRFM model by applying a two-stage clustering method. In the first stage, the self-organizing maps method is used to determine the best number of clusters and the initial centroid. In the second stage, kmeans method is applied to segment 730 customers into nine clusters according to their L, R, F and M values. The results show that the cluster 6 is the most important cluster because the average values of L, R, F and M are higher than the overall average value. In addition, this study has considered another variable that describes the mode of payment used by customers to improve and strengthen clusters’ analysis. The clusters’ analysis demonstrates that the payment method is one of the key indicators of a new index which allows to assess the level of customers’ confidence in the company's Website.

Keywords: Customer value, LRFM model, Cluster analysis, Self-Organizing Maps method (SOM), K-means algorithm, loyalty.

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