Search results for: Galerkin finite element method

Authors: Bahare Fatemi, Seyed Mehran Kazemi, Nazanin Mehrasa

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Sudoku is a logic-based combinatorial puzzle game which people in different ages enjoy playing it. The challenging and addictive nature of this game has made it a ubiquitous game. Most magazines, newspapers, puzzle books, etc. publish lots of Sudoku puzzles every day. These puzzles often come in different levels of difficulty so that all people, from beginner to expert, can play the game and enjoy it. Generating puzzles with different levels of difficulty is a major concern of Sudoku designers. There are several works in the literature which propose ways of generating puzzles having a desirable level of difficulty. In this paper, we propose a method based on constraint satisfaction problems to evaluate the difficulty of the Sudoku puzzles. Then we propose a hill climbing method to generate puzzles with different levels of difficulty. Whereas other methods are usually capable of generating puzzles with only few number of difficulty levels, our method can be used to generate puzzles with arbitrary number of different difficulty levels. We test our method by generating puzzles with different levels of difficulty and having a group of 15 people solve all the puzzles and recording the time they spend for each puzzle.

Keywords: Constraint satisfaction problem, generating Sudoku puzzles, hill climbing.

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Authors: Peerapong Uthansakul, Monthippa Uthansakul

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The rapid growth of e-Commerce services is significantly observed in the past decade. However, the method to verify the authenticated users still widely depends on numeric approaches. A new search on other verification methods suitable for online e-Commerce is an interesting issue. In this paper, a new online signature-verification method using angular transformation is presented. Delay shifts existing in online signatures are estimated by the estimation method relying on angle representation. In the proposed signature-verification algorithm, all components of input signature are extracted by considering the discontinuous break points on the stream of angular values. Then the estimated delay shift is captured by comparing with the selected reference signature and the error matching can be computed as a main feature used for verifying process. The threshold offsets are calculated by two types of error characteristics of the signature verification problem, False Rejection Rate (FRR) and False Acceptance Rate (FAR). The level of these two error rates depends on the decision threshold chosen whose value is such as to realize the Equal Error Rate (EER; FAR = FRR). The experimental results show that through the simple programming, employed on Internet for demonstrating e-Commerce services, the proposed method can provide 95.39% correct verifications and 7% better than DP matching based signature-verification method. In addition, the signature verification with extracting components provides more reliable results than using a whole decision making.

Keywords: Online signature verification, e-Commerce services, Angular transformation.

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Authors: Wataru Yamazaki, Hironori Hiraishi, Fumio Mizoguchi

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In this paper, we describe a rule-based message passing method to support developing collaborative applications, in which multiple users share resources in distributed environments. Message communications of applications in collaborative environments tend to be very complex because of the necessity to manage context situations such as sharing events, access controlling of users, and network places. In this paper, we propose a message communications method based on unification of artificial intelligence and logic programming for defining rules of such context information in a procedural object-oriented programming language. We also present an implementation of the method as java classes.

Keywords: agent programming, logic programming, multi-media application, collaborative application.

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Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, fluid systems, observer systems, unscented Kalman filter.

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Authors: Guilherme B. B. Vieira, Rafael M. da Silva, Eliana T. P. Senna, Luiz A. S. Senna, Francisco J. Kliemann Neto

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Given the importance of ports as links in the global supply chains and because they are key elements to induce competitiveness in their hinterlands, the number of studies devoted to port governance, management and operations has increased in the last decades. Some of these studies address the port governance model as an element to improve coordination among the actors of the portlogistics chain and to generate a better port performance. In this context, the present study analyzes the governance of Port of Santos through individual interviews with port managers, based on a conceptual model that considers the key dimensions associated with port governance. The results reinforce the usefulness of the applied model and highlight some existing improvement opportunities in the port studied.

Keywords: Port Governance, Model, Port of Santos, Managers’ Perception.

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Authors: Autcha Araveeporn

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This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.

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Authors: Nursyarizal Mohd Nor, Ramiah Jegatheesan, Perumal Nallagownden

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Newton-Raphson State Estimation method using bus admittance matrix remains as an efficient and most popular method to estimate the state variables. Elements of Jacobian matrix are computed from standard expressions which lack physical significance. In this paper, elements of the state estimation Jacobian matrix are obtained considering the power flow measurements in the network elements. These elements are processed one-by-one and the Jacobian matrix H is updated suitably in a simple manner. The constructed Jacobian matrix H is integrated with Weight Least Square method to estimate the state variables. The suggested procedure is successfully tested on IEEE standard systems.

Keywords: State Estimation (SE), Weight Least Square (WLS), Newton-Raphson State Estimation (NRSE), Jacobian matrix H.

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Authors: Takuya Sumi, Syoko Nukaya, Takashi Kaburagi, Hiroshi Tanaka, Kajiro Watanabe, Yosuke Kurihara

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We propose an unconstrained measurement system for scratching motion based on mathematical model of unconstrained bed sensing method which could measure the bed vibrations due to the motion of the person on the bed. In this paper, we construct mathematical model of the unconstrained bed monitoring system; and we apply the unconstrained bed sensing method to the system for detecting scratching motion. The proposed sensors are placed under the three bed feet. When the person is lying on the bed, the output signals from the sensors are proportional to the magnitude of the vibration due to the scratching motion. Hence, we could detect the subject’s scratching motion from the output signals from ceramic sensors. We evaluated two scratching motions using the proposed system in the validity experiment as follows: 1st experiment is the subject’s scratching the right side cheek with his right hand, and; 2nd experiment is the subject’s scratching the shin with another foot. As the results of the experiment, we recognized the scratching signals that enable the determination when the scratching occurred. Furthermore, the difference among the amplitudes of the output signals enabled us to estimate where the subject scratched.

Keywords: Unconstrained bed sensing method, scratching, body movement, itchy, piezoceramics.

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Authors: Noorfakhriah Yaakub, Madzlan Napiah

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Public bus service plays a significant role in our society as people movers and to facilitate travels within towns and districts. The quality of service of public bus is always being regarded as poor, or rather, underestimated as second class means of transportation. Reliability of service, or the ability to deliver service as planned, is one key element in perceiving the quality of bus service and the punctuality index is one of the performance parameters in determining the service reliability. This study concentrates on evaluating the reliability performance of bus operation using punctuality index assessment. A week data for each of six city bus routes is recorded using the on-board methodology to calculate the punctuality index for city bus service in Kota Bharu. The results revealed that the punctuality index for the whole city bus network is 94.25% (LOS B).

Keywords: Punctuality Index, Reliability Performance, Service Performance.

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Authors: Mohammadreza Vafaei, Amirali Moradi, Sophia C. Alih

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The method selected for the design of structures not only can affect their seismic vulnerability but also can affect their construction cost. For the design of steel structures, two distinct methods have been introduced by existing codes, namely allowable stress design (ASD) and load resistant factor design (LRFD). This study investigates the effect of using the aforementioned design methods on the seismic vulnerability and construction cost of steel structures. Specifically, a 20-story building equipped with special moment resisting frame and an eccentrically braced system was selected for this study. The building was designed for three different intensities of peak ground acceleration including 0.2 g, 0.25 g, and 0.3 g using the ASD and LRFD methods. The required sizes of beams, columns, and braces were obtained using response spectrum analysis. Then, the designed frames were subjected to nine natural earthquake records which were scaled to the designed response spectrum. For each frame, the base shear, story shears, and inter-story drifts were calculated and then were compared. Results indicated that the LRFD method led to a more economical design for the frames. In addition, the LRFD method resulted in lower base shears and larger inter-story drifts when compared with the ASD method. It was concluded that the application of the LRFD method not only reduced the weights of structural elements but also provided a higher safety margin against seismic actions when compared with the ASD method.

Keywords: Allowable stress design, load resistant factor design, nonlinear time history analysis, seismic vulnerability, steel structures.

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Authors: Soma Roychowdhury

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This paper deals with a periodic-review substitutable inventory system for a finite and an infinite number of periods. Here an upward substitution structure, a substitution of a more costly item by a less costly one, is assumed, with two products. At the beginning of each period, a stochastic demand comes for the first item only, which is quality-wise better and hence costlier. Whenever an arriving demand finds zero inventory of this product, a fraction of unsatisfied customers goes for its substitutable second item. An optimal ordering policy has been derived for each period. The results are illustrated with numerical examples. A sensitivity analysis has been done to examine how sensitive the optimal solution and the maximum profit are to the values of the discount factor, when there is a large number of periods.

Keywords: Multi-period model, inventory, random demand, upward substitution.

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Authors: Mahanijah Md Kamal., Dingli Yu

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This paper presents a new method of fault detection and isolation (FDI) for polymer electrolyte membrane (PEM) fuel cell (FC) dynamic systems under an open-loop scheme. This method uses a radial basis function (RBF) neural network to perform fault identification, classification and isolation. The novelty is that the RBF model of independent mode is used to predict the future outputs of the FC stack. One actuator fault, one component fault and three sensor faults have been introduced to the PEMFC systems experience faults between -7% to +10% of fault size in real-time operation. To validate the results, a benchmark model developed by Michigan University is used in the simulation to investigate the effect of these five faults. The developed independent RBF model is tested on MATLAB R2009a/Simulink environment. The simulation results confirm the effectiveness of the proposed method for FDI under an open-loop condition. By using this method, the RBF networks able to detect and isolate all five faults accordingly and accurately.

Keywords: Polymer electrolyte membrane fuel cell, radial basis function neural networks, fault detection, fault isolation.

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Authors: M. N. Moschakis, I. G. Andritsos, V. V. Dafopoulos, J. M. Prousalidis, E. S. Karapidakis

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This paper deals with the evaluation of different detection strategies used in power electronic devices as a critical element for an effective mitigation of voltage disturbances. The effectiveness of those detection schemes in the mitigation of disturbances such as voltage sags by a Solid-State Transfer Switch is evaluated through simulations. All critical parameters affecting their performance is analytically described and presented. Moreover, the effect of fast detection of sags on the overall performance of STS is analyzed and investigated.

Keywords: Faults (short-circuits), industrial engineering, power electronics, power quality, static transfer switch, voltage sags (or dips).

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Authors: Nicolae Bold, Daniel Nijloveanu

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The idea of cropping-system is a method used by farmers. It is an environmentally-friendly method, protecting the natural resources (soil, water, air, nutritive substances) and increase the production at the same time, taking into account some crop particularities. The combination of this powerful method with the concepts of genetic algorithms results into a possibility of generating sequences of crops in order to form a rotation. The usage of this type of algorithms has been efficient in solving problems related to optimization and their polynomial complexity allows them to be used at solving more difficult and various problems. In our case, the optimization consists in finding the most profitable rotation of cultures. One of the expected results is to optimize the usage of the resources, in order to minimize the costs and maximize the profit. In order to achieve these goals, a genetic algorithm was designed. This algorithm ensures the finding of several optimized solutions of cropping-systems possibilities which have the highest profit and, thus, which minimize the costs. The algorithm uses genetic-based methods (mutation, crossover) and structures (genes, chromosomes). A cropping-system possibility will be considered a chromosome and a crop within the rotation is a gene within a chromosome. Results about the efficiency of this method will be presented in a special section. The implementation of this method would bring benefits into the activity of the farmers by giving them hints and helping them to use the resources efficiently.

Keywords: Genetic algorithm, chromosomes, genes, cropping, agriculture.

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Authors: Ahcene Habbi, Yassine Boudouaoui

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This paper deals with the problem of automatic rule generation for fuzzy systems design. The proposed approach is based on hybrid artificial bee colony (ABC) optimization and weighted least squares (LS) method and aims to find the structure and parameters of fuzzy systems simultaneously. More precisely, two ABC based fuzzy modeling strategies are presented and compared. The first strategy uses global optimization to learn fuzzy models, the second one hybridizes ABC and weighted least squares estimate method. The performances of the proposed ABC and ABC-LS fuzzy modeling strategies are evaluated on complex modeling problems and compared to other advanced modeling methods.

Keywords: Automatic design, learning, fuzzy rules, hybrid, swarm optimization.

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Authors: Katsumi Hirata

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To develop the useful acoustic environmental recognition system, the method of estimating 3D-position of a stationary random acoustic source using bispectral analysis of 4-point detected signals is proposed. The method uses information about amplitude attenuation and propagation delay extracted from amplitude ratios and angles of auto- and cross-bispectra of the detected signals. It is expected that using bispectral analysis affects less influence of Gaussian noises than using conventional power spectral one. In this paper, the basic principle of the method is mentioned first, and its validity and features are considered from results of the fundamental experiments assumed ideal circumstances.

Keywords: 4-point detection, a stationary random acoustic source, auto- and cross-bispectra, estimation of 3D-position.

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Authors: G. L. C. Yap

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Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.

Keywords: Long-memory, Gaussian process, Whittle estimator, normalization, volatility, value-at-risk.

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Authors: Binyamin Yusoff, Imran Taib, Lazim Abdullah, Abd Fatah Wahab

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Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems.

Keywords: Intuitionistic fuzzy sets, similarity measures, multicriteriadecision making.

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Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

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This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm² and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.

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Authors: Salam Khalifa, Naveed Ahmed

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We present a new method to reconstruct a temporally coherent 3D animation from single or multi-view RGB-D video data using unbiased feature point sampling. Given RGB-D video data, in form of a 3D point cloud sequence, our method first extracts feature points using both color and depth information. In the subsequent steps, these feature points are used to match two 3D point clouds in consecutive frames independent of their resolution. Our new motion vectors based dynamic alignement method then fully reconstruct a spatio-temporally coherent 3D animation. We perform extensive quantitative validation using novel error functions to analyze the results. We show that despite the limiting factors of temporal and spatial noise associated to RGB-D data, it is possible to extract temporal coherence to faithfully reconstruct a temporally coherent 3D animation from RGB-D video data.

Keywords: 3D video, 3D animation, RGB-D video, Temporally Coherent 3D Animation.

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Authors: M. Tahmasebi, R.A. Rahman, M. Mailah, M. Gohari

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The control of sprayer boom undesired vibrations pose a great challenge to investigators due to various disturbances and conditions. Sprayer boom movements lead to reduce of spread efficiency and crop yield. This paper describes the design of a novel control method for an active suspension system applying proportional-integral-derivative (PID) controller with an active force control (AFC) scheme integration of an iterative learning algorithm employed to a sprayer boom. The iterative learning as an intelligent method is principally used as a method to calculate the best value of the estimated inertia of the sprayer boom needed for the AFC loop. Results show that the proposed AFC-based scheme performs much better than the standard PID control technique. Also, this shows that the system is more robust and accurate.

Keywords: Active force control, sprayer boom, active suspension, iterative learning.

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Authors: Xu Zhao

Abstract:

Text categorization techniques are widely used to many Information Retrieval (IR) applications. In this paper, we proposed a simple but efficient method that can automatically find the relationship between any pair of terms and documents, also an indexing matrix is established for text categorization. We call this method Indexing Matrix Categorization Machine (IMCM). Several experiments are conducted to show the efficiency and robust of our algorithm.

Keywords: Text categorization, Sub-space learning, Latent Semantic Space

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Authors: M. Behbahani-Nejad, Y. Shekari

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A reduced order modeling approach for natural gas transient flow in pipelines is presented. The Euler equations are considered as the governing equations and solved numerically using the implicit Steger-Warming flux vector splitting method. Next, the linearized form of the equations is derived and the corresponding eigensystem is obtained. Then, a few dominant flow eigenmodes are used to construct an efficient reduced-order model. A well-known test case is presented to demonstrate the accuracy and the computational efficiency of the proposed method. The results obtained are in good agreement with those of the direct numerical method and field data. Moreover, it is shown that the present reduced-order model is more efficient than the conventional numerical techniques for transient flow analysis of natural gas in pipelines.

Keywords: Eigenmode, Natural Gas, Reduced Order Modeling, Transient Flow.

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Authors: Matías Micheletto, Rodrigo Santos, Sergio F. Ochoa

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In developing countries, most roads in rural areas are dirt road. They require frequent maintenance since they are affected by erosive events, such as rain or wind, and the transit of heavy-weight trucks and machinery. Early detection of damages on the road condition is a key aspect, since it allows to reduce the maintenance time and cost, and also the limitations for other vehicles to travel through. Most proposals that help address this problem require the explicit participation of drivers, a permanent internet connection, or important instrumentation in vehicles or roads. These constraints limit the suitability of these proposals when applied into developing regions, like Latin America. This paper proposes an alternative method, based on unattended crowdsensing, to determine the quality of dirt roads in rural areas. This method involves the use of a mobile application that complements the road condition surveys carried out by organizations in charge of the road network maintenance, giving them early warnings about road areas that could be requiring maintenance. Drivers can also take advantage of the early warnings while they move through these roads. The method was evaluated using information from a public dataset. Although they are preliminary, the results indicate the proposal is potentially suitable to provide awareness about dirt roads condition to drivers, transportation authority and road maintenance companies.

Keywords: Dirt roads automatic quality assessment, collaborative system, unattended crowdsensing method, roads quality awareness provision.

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Authors: H. Sajjadi, M. Gorji, GH.R. Kefayati, D. D. Ganji, M. Shayan nia

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In this paper effects of inclination angle on natural convection flow in an open cavity has been analyzed with Lattice Boltzmann Method (LBM).The angle of inclination varied from θ= - 45° to 45° with 15° intervals. Study has been conducted for Rayleigh numbers (Ra) 104 to 106. The comparisons show that the average Nusselt number increases with growth of Rayleigh number and the average Nusselt number increase as inclination angles increases at Ra=104.At Ra=105 and Ra=106 the average Nusselt number enhance as inclination angels varied from θ= -45° to θ= 0° and decrease as inclination angels increase in θ= 0° to θ= 45°.

Keywords: Lattice Boltzmann Method, Inclination angle, Opencavity, Natural convection

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Authors: Behnaz Zohouri, Mahdi Zowghiand, Mohsen haghighi

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In this paper, a method for decision making in fuzzy environment is presented.A new subjective and objective integrated approach is introduced that used to assign weight attributes in fuzzy multiple attribute decision making (FMADM) problems and alternatives and fmally ranked by proposed method.

Keywords: Multiple Attribute Decision Making, Triangular fuzzy numbers, ranking index, Fuzzy Entropy.

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Authors: G. Revathi, P. Saikrishnan

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In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

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Authors: A. O. Oladele

Abstract:

The purpose of this study was to find out the effectiveness of neurological impress method and repeated reading technique on reading fluency of children with learning disabilities. Thirty primary four pupils in three public primary schools participated in the study. There were two experimental groups and a control. This research employed a 3 by 2 factorial matrix and the participants were taught for one session. Two hypotheses were formulated to guide the research. T-test was used to analyse the data gathered, and data analysis revealed that pupils exposed to the two treatment strategies had improvement in their reading fluency. It was recommended that the two strategies used in the study can be used to intervene in reading fluency problems in children with learning disabilities.

Keywords: Learning disabilities, neurological impress method, repeated reading, reading fluency.

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Authors: S. Jeyarajan

Abstract:

Concept of knowledge is discovered from conducted study for successive Competition in Sri Lankan Non-State Higher Educational Institutes. The Concept discovered out of collected Knowledge Management Practices from Emerald inside likewise reputed literatures and of Non-State Higher Educational sector. A test is conducted to reveal existences and its reason behind of these collected practices in Sri Lankan Non-State Higher Education Institutes. Further, unavailability of such study and uncertain on number of participants for data collection in the Sri Lankan context contributed selection of research method as qualitative method, which used attributes of Delphi Method to manage those likewise uncertainty. Data are collected under Dramaturgical Method, which contributes efficient usage of the Delphi method. Grounded theory is selected as data analysis techniques, which is conducted in intermixed discourse to manage different perspectives of data that are collected systematically through perspective and modified snowball sampling techniques. Data are then analysed using Grounded Theory Development Techniques in Intermix discourses to manage differences in Data. Consequently, Agreement in the results of Grounded theories and of finding in the Foreign Study is discovered in the analysis whereas present study conducted as Qualitative Research and The Foreign Study conducted as Quantitative Research. As such, the Present study widens the discovery in the Foreign Study. Further, having discovered reason behind of the existences, the Present result shows Concept for Knowledge from Sri Lankan Non-State sector to manage higher educational Institutes in successful manner.

Keywords: Adherence of snowball sampling into perspective sampling, Delphi method in qualitative method, grounded theory development in intermix discourses of analysis, knowledge management for success of higher educational institutes.

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Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

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The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T)^p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λ_c whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q<0)  the surface heat transfer rate decreases with increasing p but increases with parameters Q and s when the sheet is either stretched or shrunk.

Keywords: Magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet.

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