Search results for: Desirability Function Approach.

Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: P. Javid, A. Aeenmehr, J. Taghavifar

Abstract:

In this paper, supply air pressure of HVAC system has been modeled with second-order transfer function plus dead-time. In HVAC system, the desired input has step changes, and the output of proposed control system should be able to follow the input reference, so the idea of using model based predictive control is proceeded and designed in this paper. The closed loop control system is implemented in MATLAB software and the simulation results are provided. The simulation results show that the model based predictive control is able to control the plant properly.

Keywords: Air conditioning system, GPC, dead time, Air supply control.

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Authors: Jaroslav Polec, Lenka Krulikovská, Natália Helešová, Tomáš Hirner

Abstract:

In this paper we present a novel approach for face image coding. The proposed method makes a use of the features of video encoders like motion prediction. At first encoder selects appropriate prototype from the database and warps it according to features of encoding face. Warped prototype is placed as first I frame. Encoding face is placed as second frame as P frame type. Information about features positions, color change, selected prototype and data flow of P frame will be sent to decoder. The condition is both encoder and decoder own the same database of prototypes. We have run experiment with H.264 video encoder and obtained results were compared to results achieved by JPEG and JPEG2000. Obtained results show that our approach is able to achieve 3 times lower bitrate and two times higher PSNR in comparison with JPEG. According to comparison with JPEG2000 the bitrate was very similar, but subjective quality achieved by proposed method is better.

Keywords: Triangulation, H.264, Model-based coding, Average face

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Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

Abstract:

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.

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Authors: Rossella Arcucci, Luisa D’Amore, Simone Celestino, Giuseppe Scotti, Giuliano Laccetti

Abstract:

This work is the first dowel in a rather wide research activity in collaboration with Euro Mediterranean Center for Climate Changes, aimed at introducing scalable approaches in Ocean Circulation Models. We discuss designing and implementation of a parallel algorithm for solving the Variational Data Assimilation (DA) problem on Graphics Processing Units (GPUs). The algorithm is based on the fully scalable 3DVar DA model, previously proposed by the authors, which uses a Domain Decomposition approach (we refer to this model as the DD-DA model). We proceed with an incremental porting process consisting of 3 distinct stages: requirements and source code analysis, incremental development of CUDA kernels, testing and optimization. Experiments confirm the theoretic performance analysis based on the so-called scale up factor demonstrating that the DD-DA model can be suitably mapped on GPU architectures.

Keywords: Data Assimilation, Parallel Algorithm, GPU architectures, Ocean Models.

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Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The geometric errors in the manufacturing process can be reduced by optimal positioning of the fixture elements in the fixture to make the workpiece stiff. We propose a new fixture layout optimization method N-3-2-1 for large metal sheets in this paper that combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of the nodal deflection normal to the surface of the workpiece. Two different kinds of case studies are presented, and optimal position of the fixturing element is obtained for different cases.

Keywords: Fixture layout, optimization, fixturing element, genetic algorithm.

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Authors: Le Zhao, Alain Nogaret

Abstract:

We have built universal central pattern generator (CPG) hardware by interconnecting Hodgkin-Huxley neurons with reciprocally inhibitory synapses. We investigate the dynamics of neuron oscillations as a function of the time delay between current steps applied to individual neurons. We demonstrate stimulus dependent switching between spiking polyrhythms and map the phase portraits of the neuron oscillations to reveal the basins of attraction of the system. We experimentally study the dependence of the attraction basins on the network parameters: The neuron response time and the strength of inhibitory connections.

Keywords: Central pattern generator, winnerless competition principle.

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Authors: Benjamin D. Leiby, Darryl K. Ahner

Abstract:

This study demonstrates an alternative stochastic imputation approach for large datasets when preferred commercial packages struggle to iterate due to numerical problems. A large country conflict dataset motivates the search to impute missing values well over a common threshold of 20% missingness. The methodology capitalizes on correlation while using model residuals to provide the uncertainty in estimating unknown values. Examination of the methodology provides insight toward choosing linear or nonlinear modeling terms. Static tolerances common in most packages are replaced with tailorable tolerances that exploit residuals to fit each data element. The methodology evaluation includes observing computation time, model fit, and the comparison of known  values to replaced values created through imputation. Overall, the country conflict dataset illustrates promise with modeling first-order interactions, while presenting a need for further refinement that mimics predictive mean matching.

Keywords: Correlation, country conflict, imputation, stochastic regression.

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Authors: Parvinder S. Sandhu, Satish Kumar Dhiman, Anmol Goyal

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Fault-proneness of a software module is the probability that the module contains faults. A correlation exists between the fault-proneness of the software and the measurable attributes of the code (i.e. the static metrics) and of the testing (i.e. the dynamic metrics). Early detection of fault-prone software components enables verification experts to concentrate their time and resources on the problem areas of the software system under development. This paper introduces Genetic Algorithm based software fault prediction models with Object-Oriented metrics. The contribution of this paper is that it has used Metric values of JEdit open source software for generation of the rules for the classification of software modules in the categories of Faulty and non faulty modules and thereafter empirically validation is performed. The results shows that Genetic algorithm approach can be used for finding the fault proneness in object oriented software components.

Keywords: Genetic Algorithms, Software Fault, Classification, Object Oriented Metrics.

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Authors: Yang Cui, Yong Qiang Chen

Abstract:

An appropriate project delivery system (PDS) is crucial to the success of a construction projects. Case-based Reasoning (CBR) is a useful support for PDS selection. However, the traditional CBR approach represents cases as attribute-value vectors without taking relations among attributes into consideration, and could not calculate the similarity when the structures of cases are not strictly same. Therefore, this paper solves this problem by adopting the Relational Case-based Reasoning (RCBR) approach for PDS selection, considering both the structural similarity and feature similarity. To develop the feature terms of the construction projects, the criteria and factors governing PDS selection process are first identified. Then feature terms for the construction projects are developed. Finally, the mechanism of similarity calculation and a case study indicate how RCBR works for PDS selection. The adoption of RCBR in PDS selection expands the scope of application of traditional CBR method and improves the accuracy of the PDS selection system.

Keywords: Relational Cased-based Reasoning, Case-based Reasoning, Project delivery system, Selection.

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: Chih-Hung Wu, Chih-Chin Lai, Chun-Yen Chen, Yan-He Chen

Abstract:

Interpretation of aerial images is an important task in various applications. Image segmentation can be viewed as the essential step for extracting information from aerial images. Among many developed segmentation methods, the technique of clustering has been extensively investigated and used. However, determining the number of clusters in an image is inherently a difficult problem, especially when a priori information on the aerial image is unavailable. This study proposes a support vector machine approach for clustering aerial images. Three cluster validity indices, distance-based index, Davies-Bouldin index, and Xie-Beni index, are utilized as quantitative measures of the quality of clustering results. Comparisons on the effectiveness of these indices and various parameters settings on the proposed methods are conducted. Experimental results are provided to illustrate the feasibility of the proposed approach.

Keywords: Aerial imaging, image segmentation, machine learning, support vector machine, cluster validity index

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Authors: A. Derardja

Abstract:

The present work is motivated by the idea that the layer deformation in anisotropic elasticity can be estimated from the theory of interfacial dislocations. In effect, this work which is an extension of a previous approach given by one of the authors determines the anisotropic displacement fields and the critical thickness due to a complex biperiodic network of MDs lying just below the free surface in view of the arrangement of dislocations. The elastic fields of such arrangements observed along interfaces play a crucial part in the improvement of the physical properties of epitaxial systems. New results are proposed in anisotropic elasticity for hexagonal networks of MDs which contain intrinsic and extrinsic stacking faults. We developed, using a previous approach based on the relative interfacial displacement and a Fourier series formulation of the displacement fields, the expressions of elastic fields when there is a possible dissociation of MDs. The numerical investigations in the case of the observed system Si/(111)Si with low twist angles show clearly the effect of the anisotropy and thickness when the misfit networks are dissociated.

Keywords: Angular misfit, dislocation networks, plane interfaces, stacking faults.

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Authors: Wanida Suwunniponth

Abstract:

The objectives of this research paper were to study the influencing factors that contributed to the success of electronic commerce (e-commerce) and to study the approach to enhance the standard of e-commerce for small and medium enterprises (SME). The research paper focused the study on only sole proprietorship SMEs in Bangkok, Thailand. The factors contributed to the success of SME included business management, learning in the organization, business collaboration, and the quality of website. A quantitative and qualitative mixed research methodology was used. In terms of quantitative method, a questionnaire was used to collect data from 251 sole proprietorships. The System Equation Model (SEM) was utilized as the tool for data analysis. In terms of qualitative method, an in-depth interview, a dialogue with experts in the field of ecommerce for SMEs, and content analysis were used. By using the adjusted causal relationship structure model, it was revealed that the factors affecting the success of e-commerce for SMEs were found to be congruent with the empirical data. The hypothesis testing indicated that business management influenced the learning in the organization, the learning in the organization influenced business collaboration and the quality of the website, and these factors, in turn, influenced the success of SMEs. Moreover, the approach to enhance the standard of SMEs revealed that the majority of respondents wanted to enhance the standard of SMEs to a high level in the category of safety of e-commerce system, basic structure of e-commerce, development of staff potentials, assistance of budget and tax reduction, and law improvement regarding the e-commerce respectively.

Keywords: Electronic Commerce, Influencing Factors, Small and Medium Enterprises.

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Authors: F. Gökgöz, M. E. Atmaca

Abstract:

Electricity has an indispensable role in human daily life, technological development and economy. It is a special product or service that should be instantaneously generated and consumed. Sources of the world are limited so that effective and efficient use of them is very important not only for human life and environment but also for technological and economic development. Competitive electricity market is one of the important way that provides suitable platform for effective and efficient use of electricity. Besides benefits, it brings along some risks that should be carefully managed by a market player like Electricity Generation Company. Risk management is an essential part in market players’ decision making. In this paper, risk management through diversification is applied with the help of Value at Risk methods for case studies. Performance of optimal electricity sale solutions are measured and the portfolio performance has been evaluated via Sharpe-Ratio, and compared with conventional approach. Biennial historical electricity price data of Turkish Day Ahead Market are used to demonstrate the approach.

Keywords: Electricity market, portfolio optimization, risk management, Sharpe ratio, value at risk.

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Authors: Yu T. Tsai, Jin H. Huang

Abstract:

In this paper, the specific sound Transmission Loss (TL) of the Laminated Composite Plate (LCP) with different material properties in each layer is investigated. The numerical method to obtain the TL of the LCP is proposed by using elastic plate theory. The transfer matrix approach is novelty presented for computational efficiency in solving the numerous layers of dynamic stiffness matrix (D-matrix) of the LCP. Besides the numerical simulations for calculating the TL of the LCP, the material properties inverse method is presented for the design of a laminated composite plate analogous to a metallic plate with a specified TL. As a result, it demonstrates that the proposed computational algorithm exhibits high efficiency with a small number of iterations for achieving the goal. This method can be effectively employed to design and develop tailor-made materials for various applications.

Keywords: Sound transmission loss, laminated composite plate, transfer matrix approach, inverse problem, elastic plate theory, material properties.

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Authors: C. Ketviriyakit, W. Kongnun, C. Chanapromma, P. Silapan

Abstract:

This article proposes a voltage-mode multifunction filter using differential voltage current controllable current conveyor transconductance amplifier (DV-CCCCTA). The features of the circuit are that: the quality factor and pole frequency can be tuned independently via the values of capacitors: the circuit description is very simple, consisting of merely 1 DV-CCCCTA, and 2 capacitors. Without any component matching conditions, the proposed circuit is very appropriate to further develop into an integrated circuit. Additionally, each function response can be selected by suitably selecting input signals with digital method. The PSpice simulation results are depicted. The given results agree well with the theoretical anticipation.

Keywords: DV-CCCCTA, Voltage-mode, Multifunction filter

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Authors: F. Achouri, K. Chouicha

Abstract:

The main parameters affecting the workability are the water content, particle size, and the total surface of the grains, as long as the mixing water begins by wetting the surface of the grains and then fills the voids between the grains to form entrapped water, the quantity of water remaining is called free water. The aim of this study is to undertake a fractal approach through the relationship between the concrete formulation parameters and workability. To develop this approach a series of concrete taken from the literature was investigated by varying formulation parameters such as G/S, the quantity of cement C and the quantity of water W. We also call another model as the model of water layer thickness and model of paste layer thickness to judge their relevance, hence the following results: the relevance of the water layer thickness model is considered as a relevant when there is a variation in the water quantity. The model of the paste layer thickness is only applicable if we considered that the paste is made with the grain value Dmax = 2.85: value from which we see a stability of the model.

Keywords: Concrete, fractal method, paste layer thickness, water layer thickness, workability.

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Authors: Shiraz Ahmad, Zhe-Ming Lu

Abstract:

An effective visual error concealment method has been presented by employing a robust rotation, scale, and translation (RST) invariant partial patch matching model (RSTI-PPMM) and exemplar-based inpainting. While the proposed robust and inherently feature-enhanced texture synthesis approach ensures the generation of excellent and perceptually plausible visual error concealment results, the outlier pruning property guarantees the significant quality improvements, both quantitatively and qualitatively. No intermediate user-interaction is required for the pre-segmented media and the presented method follows a bootstrapping approach for an automatic visual loss recovery and the image and video error concealment.

Keywords: Exemplar-based image and video inpainting, outlierpruning, RST-invariant partial patch matching model (RSTI-PPMM), visual error concealment.

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Authors: S. Sarumathi, M. Vaishnavi, S. Geetha, P. Ranjetha

Abstract:

Machine learning is a new and exciting area of artificial intelligence nowadays. Machine learning is the most valuable, time, supervised, and cost-effective approach. It is not a narrow learning approach; it also includes a wide range of methods and techniques that can be applied to a wide range of complex realworld problems and time domains. Biological image classification, adaptive testing, computer vision, natural language processing, object detection, cancer detection, face recognition, handwriting recognition, speech recognition, and many other applications of machine learning are widely used in research, industry, and government. Every day, more data are generated, and conventional machine learning techniques are becoming obsolete as users move to distributed and real-time operations. By providing fundamental knowledge of machine learning tools and research opportunities in the field, the aim of this article is to serve as both a comprehensive overview and a guide. A diverse set of machine learning resources is demonstrated and contrasted with the key features in this survey.

Keywords: Artificial intelligence, machine learning, deep learning, machine learning algorithms, machine learning tools.

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Authors: F. Bendahma, S. Bentata, S. Cherid, A. Zitouni, S. Terkhi, T. Lantri, Y. Sefir, Z. F. Meghoufel

Abstract:

We examine the electronic transport properties in Al_xGa_1-xAs/GaAs superlattices. Using the transfer-matrix technique and the exact Airy function formalism, we investigate theoretically the effect of structural parameters on the electronic energy spectra of trimer thickness barrier (TTB). Our numerical calculations showed that the localization length of the states becomes more extended when the disorder is correlated (trimer case). We have also found that the resonant tunneling time (RTT) is of the order of several femtoseconds.

Keywords: Electronic transport properties, structural parameters, superlattice, transfer-matrix technique.

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Authors: K. Nirmala Devi, V. Murali Bhaskaran

Abstract:

Traditional document representation for classification follows Bag of Words (BoW) approach to represent the term weights. The conventional method uses the Vector Space Model (VSM) to exploit the statistical information of terms in the documents and they fail to address the semantic information as well as order of the terms present in the documents. Although, the phrase based approach follows the order of the terms present in the documents rather than semantics behind the word. Therefore, a semantic concept based approach is used in this paper for enhancing the semantics by incorporating the ontology information. In this paper a novel method is proposed to forecast the intraday stock market price directional movement based on the sentiments from Twitter and money control news articles. The stock market forecasting is a very difficult and highly complicated task because it is affected by many factors such as economic conditions, political events and investor’s sentiment etc. The stock market series are generally dynamic, nonparametric, noisy and chaotic by nature. The sentiment analysis along with wisdom of crowds can automatically compute the collective intelligence of future performance in many areas like stock market, box office sales and election outcomes. The proposed method utilizes collective sentiments for stock market to predict the stock price directional movements. The collective sentiments in the above social media have powerful prediction on the stock price directional movements as up/down by using Granger Causality test.

Keywords: Bag of Words, Collective Sentiments, Ontology, Semantic relations, Sentiments, Social media, Stock Prediction, Twitter, Vector Space Model and wisdom of crowds.

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Authors: Mohammadreza Nezamirad, Sepideh Amirahmadian, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

Abstract:

Cavitation inside a diesel injector nozzle is investigated numerically in this study. The Reynolds Stress Navier Stokes set of equations (RANS) are utilized to investigate flow behavior inside the nozzle numerically. Moreover, K-ε turbulent model is found to be a better approach comparing to K-ω turbulent model. The Winklhofer rectangular shape nozzle is also simulated in order to verify the current numerical scheme, and with the mass flow rate approach, the current solution is verified. Afterward, a six-hole real size nozzle was simulated and it was found that among the different fuels used in this study with the same condition, diesel fuel provides the largest length of cavitation. Also, it was found that at the same boundary condition, rapeseed methyl ester (RME) fuel leads to the highest value of discharge coefficient and mass flow rate.

Keywords: cavitation, diesel fuel, CFD, real size nozzle, discharge coefficient

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Authors: Marco Picco, Mahmood Alam

Abstract:

Improving the energy performance of existing buildings can be challenging, particularly when facades cannot be modified, and the only available option is internal insulation. In such cases, the choice of the most suitable material becomes increasingly complex, as in addition to thermal transmittance and capital cost, the designer needs to account for the impact of the intervention on the internal spaces, and in particular the loss of usable space due to the additional layers of materials installed. This paper explores this issue by analyzing a case study of an average office building needing to go through a refurbishment in order to reach the limits imposed by current regulations to achieve energy efficiency in buildings. The building is simulated through dynamic performance simulation under three different climate conditions in order to evaluate its energy needs. The use of Vacuum Insulated Panels as an option for energy refurbishment is compared to traditional insulation materials (XPS, Mineral Wool). For each scenario, energy consumptions are calculated and, in combination with their expected capital costs, used to perform a financial feasibility analysis. A holistic approach is proposed, taking into account the impact of the intervention on internal space by quantifying the value of the lost usable space and used in the financial feasibility analysis. The proposed approach highlights how taking into account different drivers will lead to the choice of different insulation materials, showing how accounting for the economic value of space can make VIPs an attractive solution for energy retrofitting under various climate conditions.

Keywords: Vacuum insulated panels, building performance simulation, payback period, building energy retrofit.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: H∞ control, Takagi-Sugeno (TS) fuzzy model, Linear Matrix Inequalities (LMIs), Descriptor systems.

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Authors: Mahdi Hamzeh, Sied Mehdi Fakhraie, Caro Lucas

Abstract:

All practical real-time scheduling algorithms in multiprocessor systems present a trade-off between their computational complexity and performance. In real-time systems, tasks have to be performed correctly and timely. Finding minimal schedule in multiprocessor systems with real-time constraints is shown to be NP-hard. Although some optimal algorithms have been employed in uni-processor systems, they fail when they are applied in multiprocessor systems. The practical scheduling algorithms in real-time systems have not deterministic response time. Deterministic timing behavior is an important parameter for system robustness analysis. The intrinsic uncertainty in dynamic real-time systems increases the difficulties of scheduling problem. To alleviate these difficulties, we have proposed a fuzzy scheduling approach to arrange real-time periodic and non-periodic tasks in multiprocessor systems. Static and dynamic optimal scheduling algorithms fail with non-critical overload. In contrast, our approach balances task loads of the processors successfully while consider starvation prevention and fairness which cause higher priority tasks have higher running probability. A simulation is conducted to evaluate the performance of the proposed approach. Experimental results have shown that the proposed fuzzy scheduler creates feasible schedules for homogeneous and heterogeneous tasks. It also and considers tasks priorities which cause higher system utilization and lowers deadline miss time. According to the results, it performs very close to optimal schedule of uni-processor systems.

Keywords: Computational complexity, Deadline, Feasible scheduling, Fuzzy scheduling, Priority, Real-time multiprocessor systems, Robustness, System utilization.

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Authors: A. V. Sai Balasubramanian, N. Ravi Shankar, S. Subbaraman, R. Rengaraj

Abstract:

One of the major cause of eye strain and other problems caused while watching television is the relative illumination between the screen and its surrounding. This can be overcome by adjusting the brightness of the screen with respect to the surrounding light. A controller based on fuzzy logic is proposed in this paper. The fuzzy controller takes in the intensity of light surrounding the screen and the present brightness of the screen as input. The output of the fuzzy controller is the grid voltage corresponding to the required brightness. This voltage is given to CRT and brightness is controller dynamically. For the given test system data, different de-fuzzifier methods have been implemented and the results are compared. In order to validate the effectiveness of the proposed approach, a fuzzy controller has been designed by obtaining a test data from a real time system. The simulations are performed in MATLAB and are verified with standard system data. The proposed approach can be implemented for real time applications.

Keywords: Fuzzy controller, Grid voltage

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Authors: K. Daud, A. F. Abidin, N. Hamzah, H. S. Nagindar Singh

Abstract:

This paper produces a new approach for power quality analysis using a windowing technique based on Continuous S-transform (CST). This half-cycle window technique approach can detect almost correctly for initial detection of disturbances i.e. voltage sags, swells, and transients. Samples in half cycle window has been analyzed based continuous S-transform for entire disturbance waveform. The modified parameter has been produced by MATLAB programming m-file based on continuous s-transform. CST has better time frequency and localization property than traditional and also has ability to detect the disturbance under noisy condition correctly. The excellent time-frequency resolution characteristic of the CST makes it the most an attractive candidate for analysis of power system disturbances signals.

Keywords: Power quality disturbances, initial detection, half cycle windowing, continuous S-transform.

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Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: Chromatic Polynomial, Chromatically Equivalent, Chromatically Unique, Wheel.

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Authors: Jong-Jy Shyu, Soo-Chang Pei, Min-Han Chang

Abstract:

In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method.

Keywords: Differentiator, variable fractional-delay filter, FIR filter, least-squares method, Farrow structure.

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