Search results for: reliability prediction model

Authors: Boubekeur Dokkar, Nasreddine Chennouf, Noureddine Settou, Belkhir Negrou, Abdesslam Benmhidi

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The optimal operation of proton exchange membrane fuel cell (PEMFC) requires good water management which is presented under two forms vapor and liquid. Moreover, fuel cells have to reach higher output require integration of some accessories which need electrical power. In order to analyze fuel cells operation and different species transport phenomena a biphasic mathematical model is presented by governing equations set. The numerical solution of these conservation equations is calculated by Matlab program. A multi-criteria optimization with weighting between two opposite objectives is used to determine the compromise solutions between maximum output and minimal stack size. The obtained results are in good agreement with available literature data.

Keywords: Biphasic model, PEM fuel cell, optimization, simulation, specie transport.

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Authors: Sachin Kumar, Michael Pecht

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A study was conducted to formally characterize notebook computer performance under various environmental and usage conditions. Software was developed to collect data from the operating system of the computer. An experiment was conducted to evaluate the performance parameters- variations, trends, and correlations, as well as the extreme value they can attain in various usage and environmental conditions. An automated software script was written to simulate user activity. The variability of each performance parameter was addressed by establishing the empirical relationship between performance parameters. These equations were presented as baseline estimates for performance parameters, which can be used to detect system deviations from normal operation and for prognostic assessment. The effect of environmental factors, including different power sources, ambient temperatures, humidity, and usage, on performance parameters of notebooks was studied.

Keywords: Health monitoring, Electronic prognostics, Reliability, Usage monitoring, Notebook computer.

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Authors: Worachat Wannawong, Usa W. HumphriesPrungchan Wongwises, Suphat Vongvisessomjai

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The mathematical modeling of storm surge in sea and coastal regions such as the South China Sea (SCS) and the Gulf of Thailand (GoT) are important to study the typhoon characteristics. The storm surge causes an inundation at a lateral boundary exhibiting in the coastal zones particularly in the GoT and some part of the SCS. The model simulations in the three dimensional primitive equations with a high resolution model are important to protect local properties and human life from the typhoon surges. In the present study, the mathematical modeling is used to simulate the typhoon–induced surges in three case studies of Typhoon Linda 1997. The results of model simulations at the tide gauge stations can describe the characteristics of storm surges at the coastal zones.

Keywords: lateral boundary, mathematical modeling, numericalsimulations, three dimensional primitive equations, storm surge.

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Authors: Majdi M. Alomari, Nafesah I. Alshdaifat, Mohammad S. Widyan

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Different countries have introduced different schemes and policies to counter global warming. The rationale behind the proposed policies and the potential barriers to successful implementation of the policies adopted by the countries were analyzed and estimated based on different models. It is argued that these models enhance the transparency and provide a better understanding to the policy makers. However, these models are underpinned with several structural and baseline assumptions. These assumptions, modeling features and future prediction of emission reductions and other implication such as cost and benefits of a transition to a low-carbon economy and its economy wide impacts were discussed. On the other hand, there are potential barriers in the form political, financial, and cultural and many others that pose a threat to the mitigation options.

Keywords: Economic wide impact, energy models, environmental policy instruments, mitigating CO2 emission.

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Authors: Debashish Panda, Kannan A.

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Equilibrium and rate based models have been applied in the simulation of methyl tertiary-butyl ether (MTBE) synthesis through reactive distillation. Temperature and composition profiles were compared for both the models and found that both the profiles trends, though qualitatively similar are significantly different quantitatively. In the rate based method (RBM), multicomponent mass transfer coefficients have been incorporated to describe interphase mass transfer. MTBE mole fraction in the bottom stream is found to be 0.9914 in the Equilibrium Model (EQM) and only 0.9904 for RBM when the same column configuration was preserved. The individual tray efficiencies were incorporated in the EQM and simulations were carried out. Dynamic simulation have been also carried out for the two column configurations and compared.

Keywords: Aspen Plus, equilibrium stage model, methyl tertiary-butyl ether, rate based model.

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Authors: Tomoaki Hashimoto

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Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints, random dither quantization.

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Authors: Mahesh K. Chudasama, Harit K. Raval

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3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: Analytical modeling, cone frustum, dynamic bending, static bending.

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Authors: Farah Mahmoud Attallah, Sara El-Deeb

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The non-profit sector has been heavily rising with the rise of sustainable development in developed and developing countries. Most economies are putting high pressure on this sector, believing that nongovernmental organizations (NGOs) are one of the main rescues during crises worldwide. However, with the rising number of those NGOs comes their incapability of sustaining their performance and fundraising. Additionally, donors who are considered the key partners for those organizations have become knowledgeable about this sector which made them more demanding, putting high pressure on those organizations to believe that there must be a valuable return for the economy in order to donate. This research aims to study the impact of a sustainable strategic planning model on raising loyal donors; the proposed model of this research presents several independent variables determining their impact on donors' intention to become loyal.

Keywords: Non-profit sector, non-governmental organizations, strategic planning, sustainable business model.

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Authors: Juan Li, Jiawen Qiu, Yuchuan Chu, Tianping Zhang, Wei Meng, Yanhui Jia, Xiaohui Liu

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This article developed an ion thruster optic system sputter erosion depth numerical 3D model by IFE-PIC (Immersed Finite Element-Particle-in-Cell) and Mont Carlo method, and calculated the downstream surface sputter erosion rate of accelerator grid; compared with LIPS-200 life test data. The results of the numerical model are in reasonable agreement with the measured data. Finally, we predicted the lifetime of the 20cm diameter ion thruster via the erosion data obtained with the model. The ultimate result demonstrated that under normal operating condition, the erosion rate of the grooves wears on the downstream surface of the accelerator grid is 34.6μm⁄1000h, which means the conservative lifetime until structural failure occurring on the accelerator grid is 11500 hours.

Keywords: Ion thruster, accelerator gird, sputter erosion, lifetime assessment.

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Authors: Yaoxin Zhang, Yafei Jia, Sam S.Y. Wang

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A multi-block algorithm and its implementation in two-dimensional finite element numerical model CCHE2D are presented. In addition to a conventional Lagrangian Interpolation Method (LIM), a novel interpolation method, called Consistent Interpolation Method (CIM), is proposed for more accurate information transfer across the interfaces. The consistent interpolation solves the governing equations over the auxiliary elements constructed around the interpolation nodes using the same numerical scheme used for the internal computational nodes. With the CIM, the momentum conservation can be maintained as well as the mass conservation. An imbalance correction scheme is used to enforce the conservation laws (mass and momentum) across the interfaces. Comparisons of the LIM and the CIM are made using several flow simulation examples. It is shown that the proposed CIM is physically more accurate and produces satisfactory results efficiently.

Keywords: Multi-block algorithm, conservation, interpolation, numerical model, flow simulation.

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Authors: Miled Amel, Ben Maad Hatem, Askri Faouzi, Ben Nasrallah Sassi

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Metal hydride water pumping system uses hydrogen as working fluid to pump water for low head and high discharge. The principal operation of this pump is based on the desorption of hydrogen at high pressure and its absorption at low pressure by a metal hydride. This work is devoted to study a concept of the dynamic behavior of a metal hydride pump using unsteady model and LaNi5 as hydriding alloy. This study shows that with MHP, it is possible to pump 340l/kg-cycle of water in 15 000s using 1 Kg of LaNi5 at a desorption temperature of 360 K, a pumping head equal to 5 m and a desorption gear ratio equal to 33. This study reveals also that the error given by the steady model, using LaNi5 is about 2%.A dimensional mathematical model and the governing equations of the pump were presented to predict the coupled heat and mass transfer within the MHP. Then, a numerical simulation is carried out to present the time evolution of the specific water discharge and to test the effect of different parameters (desorption temperature, absorption temperature, desorption gear ratio) on the performance of the water pumping system (specific water discharge, pumping efficiency and pumping time). In addition, a comparison between results obtained with steady and unsteady model is performed with different hydride mass. Finally, a geometric configuration of the reactor is simulated to optimize the pumping time.

Keywords: Dynamic behavior, unsteady model, LaNi5, performance of the water pumping system.

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Authors: J. E. Ortiz, P. Plaza, J. Herrero, I. Cabria, J. L. Blanco, J. Gavilanes, J. I. Escavy, I. López-Cilla, V. Yagüe, C. Pérez, S. Rodríguez, J. Rico, C. Serrano, J. Bernat

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The development of Artificial Intelligence services in mining processes, specifically in aggregate quarries, is facilitating automation and improving numerous aspects of operations. Ultimately, AI is transforming the mining industry by improving efficiency, safety and sustainability. With the ability to analyze large amounts of data and make autonomous decisions, AI offers great opportunities to optimize mining operations and maximize the economic and social benefits of this vital industry. Within the framework of the European DIGIECOQUARRY project, various services were developed for the identification of material quality, production estimation, detection of anomalies and prediction of consumption and production automatically with good results.

Keywords: Aggregates, artificial intelligence, automatization, mining operations.

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Authors: Youn-Sung Kim, Jin-Ho Jo, Mi-Sung Kim, Jae-Kun Lee

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Accelerated life cycle test is applied to various products or components in order to reduce the time of life cycle test in industry. It must be considered for many test conditions according to the product characteristics for the test and the selection of acceleration parameter is especially very important. We have carried out the general life cycle test and the accelerated life cycle test by applying the acceleration factor (AF) considering the characteristics of brushless DC (BLDC) motor for washing machine. The final purpose of this study is to verify the validity by analyzing the results of the general life cycle test and the accelerated life cycle test. It will make it possible to reduce the life test time through the reasonable accelerated life cycle test.

Keywords: Accelerated life cycle test, reliability test, motor for washing machine, brushless dc motor test.

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Authors: Peifei Zhu, Zisheng Li, Yasuki Kakishita, Mayumi Suzuki, Tomoaki Chono

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Segmentation of left ventricle (LV) from cardiac ultrasound images provides a quantitative functional analysis of the heart to diagnose disease. Active Shape Model (ASM) is widely used for LV segmentation, but it suffers from the drawback that initialization of the shape model is not sufficiently close to the target, especially when dealing with abnormal shapes in disease. In this work, a two-step framework is improved to achieve a fast and efficient LV segmentation. First, a robust and efficient detection based on Hough forest localizes cardiac feature points. Such feature points are used to predict the initial fitting of the LV shape model. Second, ASM is applied to further fit the LV shape model to the cardiac ultrasound image. With the robust initialization, ASM is able to achieve more accurate segmentation. The performance of the proposed method is evaluated on a dataset of 810 cardiac ultrasound images that are mostly abnormal shapes. This proposed method is compared with several combinations of ASM and existing initialization methods. Our experiment results demonstrate that accuracy of the proposed method for feature point detection for initialization was 40% higher than the existing methods. Moreover, the proposed method significantly reduces the number of necessary ASM fitting loops and thus speeds up the whole segmentation process. Therefore, the proposed method is able to achieve more accurate and efficient segmentation results and is applicable to unusual shapes of heart with cardiac diseases, such as left atrial enlargement.

Keywords: Hough forest, active shape model, segmentation, cardiac left ventricle.

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Authors: Pascal Mwenge, Tumisang Seodigeng

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The combination of world population and the third industrial revolution led to high demand for fuels. On the other hand, the decrease of global fossil 8fuels deposits and the environmental air pollution caused by these fuels has compounded the challenges the world faces due to its need for energy. Therefore, new forms of environmentally friendly and renewable fuels such as biodiesel are needed. The primary analytical techniques for methanolysis yield monitoring have been chromatography and spectroscopy, these methods have been proven reliable but are more demanding, costly and do not provide real-time monitoring. In this work, the in situ monitoring of biodiesel from sunflower oil using FTIR (Fourier Transform Infrared) has been studied; the study was performed using EasyMax Mettler Toledo reactor equipped with a DiComp (Diamond) probe. The quantitative monitoring of methanolysis was performed by building a quantitative model with multivariate calibration using iC Quant module from iC IR 7.0 software. 15 samples of known concentrations were used for the modelling which were taken in duplicate for model calibration and cross-validation, data were pre-processed using mean centering and variance scale, spectrum math square root and solvent subtraction. These pre-processing methods improved the performance indexes from 7.98 to 0.0096, 11.2 to 3.41, 6.32 to 2.72, 0.9416 to 0.9999, RMSEC, RMSECV, RMSEP and R2Cum, respectively. The R² value of 1 (training), 0.9918 (test), 0.9946 (cross-validation) indicated the fitness of the model built. The model was tested against univariate model; small discrepancies were observed at low concentration due to unmodelled intermediates but were quite close at concentrations above 18%. The software eliminated the complexity of the Partial Least Square (PLS) chemometrics. It was concluded that the model obtained could be used to monitor methanol of sunflower oil at industrial and lab scale.

Keywords: Biodiesel, calibration, chemometrics, FTIR, methanolysis, multivariate analysis, transesterification.

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Authors: Abhilash Narayan, S. Panneerselvam

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Dual bell nozzle is a promising one among the altitude adaptation nozzle concepts, which offer increased nozzle performance in rocket engines. Its advantage is the simplicity it offers due to the absence of any additional mechanical device or movable parts. Hence it offers reliability along with improved nozzle performance as demanded by future launch vehicles. Among other issues, the flow transition to the extension nozzle of a dual bell nozzle is one of the major issues being studied in the development of dual bell nozzle. A parameter named over-expansion factor, which controls the value of the wall inflection angle, has been reported to have substantial influence in this transition process. This paper studies, through CFD and cold flow experiments, the effect of overexpansion factor on flow transition in dual bell nozzles.

Keywords: Altitude adaptation, Dual bell nozzle, Nozzle pressure ratio, Over-expansion factor

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Authors: M.R. Mansoujian, N. Hedayat, M. Mashal, H, Kiamanesh

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Analytical investigation of the sedimentation processes in the river engineering and hydraulic structures is of vital importance as this can affect water supply for the cultivating lands in the command area. The reason being that gradual sediment formation behind the reservoir can reduce the nominal capacity of these dams. The aim of the present paper is to analytically investigate sedimentation process along the river course and behind the storage reservoirs in general and the Eastern Intake of the Dez Diversion weir in particular using the SHARC software. Results of the model indicated the water level at 115.97m whereas the real time measurement from the river cross section was 115.98 m which suggests a significantly close relation between them. The average transported sediment load in the river was measured at 0.25mm , from which it can be concluded that nearly 100% of the suspended loads in river are moving which suggests no sediment settling but indicates that almost all sediment loads enters into the intake. It was further showed the average sediment diameter entering the intake to be 0.293 mm which in turn suggests that about 85% of suspended sediments in the river entre the intake. Comparison of the results from the SHARC model with those obtained form the SSIIM software suggests quite similar outputs but distinguishing the SHARC model as more appropriate for the analysis of simpler problems than other model.

Keywords: SHARC, Eastern Intake, Dez Diversion Weir.

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Authors: Turgay Temel, John Hallam

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An improved processing description to be employed in biosonar signal processing in a cochlea model is proposed and examined. It is compared to conventional models using a modified discrimination analysis and both are tested. Their performances are evaluated with echo data captured from natural targets (trees).Results indicate that the phase characteristics of low-pass filters employed in the echo processing have a significant effect on class separability for this data.

Keywords: Cochlea model, discriminant analysis, neurospikecoding, classification.

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Authors: Hussam Elias, Ninovic Perez, Holger Hirsch

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The completion of the EMC regulations worldwide is growing steadily as the usage of electronics in our daily lives is increasing more than ever. In this paper, we present a method to perform the final phase of Electromagnetic Compatibility (EMC) measurement and to reduce the required test time according to the norm EN 55032 by using a developed tool and the Conventional Neural Network (CNN). The neural network was trained using real EMC measurements which were performed in the Semi Anechoic Chamber (SAC) by CETECOM GmbH in Essen Germany. To implement our proposed method, we wrote software to perform the radiated electromagnetic interference (EMI) measurements and use the CNN to predict and determine the position of the turntable that meet the maximum radiation value.

Keywords: Conventional neural network, electromagnetic compatibility measurement, mean absolute error, position error.

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Authors: Puntani Pongsumpun, I-Ming Tang

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The incidences of dengue hemorrhagic disease (DHF) over the long term exhibit a seasonal behavior. It has been hypothesized that these behaviors are due to the seasonal climate changes which in turn induce a seasonal variation in the incubation period of the virus while it is developing the mosquito. The standard dynamic analysis is applied for analysis the Susceptible-Exposed- Infectious-Recovered (SEIR) model which includes an annual variation in the length of the extrinsic incubation period (EIP). The presence of both asymptomatic and symptomatic infections is allowed in the present model. We found that dynamic behavior of the endemic state changes as the influence of the seasonal variation of the EIP becomes stronger. As the influence is further increased, the trajectory exhibits sustained oscillations when it leaves the chaotic region.

Keywords: Chaotic behavior, dengue hemorrhagic fever, extrinsic incubation period, SEIR model.

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Authors: Sidhartha Panda, Narayana Prasad Padhy

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This paper presents a systematic procedure for modelling and simulation of a power system installed with a power system stabilizer (PSS) and a flexible ac transmission system (FACTS)-based controller. For the design purpose, the model of example power system which is a single-machine infinite-bus power system installed with the proposed controllers is developed in MATLAB/SIMULINK. In the developed model synchronous generator is represented by model 1.1. which includes both the generator main field winding and the damper winding in q-axis so as to evaluate the impact of PSS and FACTS-based controller on power system stability. The model can be can be used for teaching the power system stability phenomena, and also for research works especially to develop generator controllers using advanced technologies. Further, to avoid adverse interactions, PSS and FACTS-based controller are simultaneously designed employing genetic algorithm (GA). The non-linear simulation results are presented for the example power system under various disturbance conditions to validate the effectiveness of the proposed modelling and simultaneous design approach.

Keywords: Genetic algorithm, modelling and simulation, MATLAB/SIMULINK, power system stabilizer, thyristor controlledseries compensator, simultaneous design, power system stability.

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Authors: Geeta Sikka, Arvinder Kaur Takkar, Moin Uddin

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Missing data is a persistent problem in almost all areas of empirical research. The missing data must be treated very carefully, as data plays a fundamental role in every analysis. Improper treatment can distort the analysis or generate biased results. In this paper, we compare and contrast various imputation techniques on missing data sets and make an empirical evaluation of these methods so as to construct quality software models. Our empirical study is based on NASA-s two public dataset. KC4 and KC1. The actual data sets of 125 cases and 2107 cases respectively, without any missing values were considered. The data set is used to create Missing at Random (MAR) data Listwise Deletion(LD), Mean Substitution(MS), Interpolation, Regression with an error term and Expectation-Maximization (EM) approaches were used to compare the effects of the various techniques.

Keywords: Missing data, Imputation, Missing Data Techniques.

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Authors: Sobhy Fathy A. Hashesh

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This study aimed at investigating the effect of Andalus Knowledge Phases and Times (ANPT) model of learning and the effect of 'Intel Education Contribution in ANPT' on the development of students’ academic performance and emotional quotient. The society of the study composed of Andalus Private Schools, elementary school students (N=700), while the sample of the study composed of four randomly assigned groups (N=80) with one experimental group and one control group to study "ANPT" effect and the "Intel Contribution in ANPT" effect respectively. The study followed the quantitative and qualitative approaches in collecting and analyzing data to answer the study questions. Results of the study revealed that there were significant statistical differences between students’ academic performances and emotional quotients for the favor of the experimental groups. The study recommended applying this model on different educational variables and on other age groups to generate more data leading to more educational results for the favor of students’ learning outcomes.

Keywords: ANPT, Flipped Classroom, 5Es learning Model, Kagan structures.

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Authors: Thanawit Buafai, Siyathorn Khunon

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This paper aims to explore the satisfaction levels of tourism product components on the island of Samui by studying the cultural dimension relationships of Hofsted’s classic theory. Both the six Hofsted cultural dimensions and tourism production satisfaction measures have been of interest worldwide. Therefore, the challenge of this study is to re-confirm previous research results in the ever-changing current contexts of the modern globalized business era. Self-rated questionnaires were employed to collect data from six nationalities of tourists in Samui, totaling 386 samples. The reliability of this research methodology was 0.967. Correlation was applied to analyze the relationships. The results indicate that Masculinity is significantly related to tourism destination satisfaction for every factor, while the other five cultural dimensions are related to some factors of tourism satisfaction. Surprisingly, tourist satisfaction toward the bar/restaurant factor is significantly correlated with all six cultural dimensions.

Keywords: Cultural dimensions, tourism products, Samui, Thailand.

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Authors: Omar Gaci, Stefan Balev

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In this paper we introduce the notion of protein interaction network. This is a graph whose vertices are the protein-s amino acids and whose edges are the interactions between them. Using a graph theory approach, we identify a number of properties of these networks. We compare them to the general small-world network model and we analyze their hierarchical structure.

Keywords: interaction network, protein structure, small-world network.

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Authors: Jun Liu, Feihang Zhou, Gungyi Wang

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This paper expounds on the direct-driven PMSG wind power system control strategy, and analyses the stability conditions of the system. The direct-driven PMSG wind power system may generate the intense mechanical vibration, when wind speed changes dramatically. This paper proposes a new type of torque control strategy, which increases the system damping effectively, mitigates mechanical vibration of the system, and enhances the stability conditions of the system. The simulation results verify the reliability of the new torque control strategy.

Keywords: Damping, direct-driven PMSG wind power system, mechanical vibration, torque control.

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Authors: Mohamed Bendahmane, Brahim Elfalaki, Mohammed Benattou

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One of the major sources of learners' professional difficulties is their heterogeneity. Whether on cognitive, social, cultural or emotional level, learners being part of the same group have many differences. These differences do not allow to apply the same learning process at all learners. Thus, an optimal learning path for one, is not necessarily the same for the other. We present in this paper a model-oriented service to offer to each learner a personalized learning path to acquire the targeted skills.

Keywords: Service-oriented architecture, learning path, web service, personalization, trace analysis.

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Authors: Arijit Roy

Abstract:

Occurrence of popcorn in IC packages while assembling them onto the PCB is a well known moisture sensitive reliability issues, especially for surface mount packages. Commonly reflow soldering simulation process is conducted to assess the impact of assembling IC package onto PCB. A strain gauge-based instrumentation is developed to investigate the popcorn effect in surface mount packages during reflow soldering process. The instrument is capable of providing real-time quantitative information of the occurrence popcorn phenomenon in IC packages. It is found that the popcorn occur temperatures between 218 to 241°C depending on moisture soak condition, but not at the peak temperature of the reflow process. The presence of popcorn and delamination are further confirmed by scanning acoustic tomography as a failure analysis.

Keywords: Instrumentation, Popcorn, Real-time, Solder Reflow, Strain Gauge.

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Authors: Shamim Ahmed Koichi Nishigaki

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Genome profiling (GP), a genotype based technology, which exploits random PCR and temperature gradient gel electrophoresis, has been successful in identification/classification of organisms. In this technology, spiddos (Species identification dots) and PaSS (Pattern similarity score) were employed for measuring the closeness (or distance) between genomes. Based on the closeness (PaSS), we can buildup phylogenetic trees of the organisms. We noticed that the topology of the tree is rather robust against the experimental fluctuation conveyed by spiddos. This fact was confirmed quantitatively in this study by computer-simulation, providing the limit of the reliability of this highly powerful methodology. As a result, we could demonstrate the effectiveness of the GP approach for identification/classification of organisms.

Keywords: Fluctuation, Genome profiling (GP), Pattern similarity score (PaSS), Robustness, Spiddos-shift.

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Authors: Alexander Urbach, Mukharbij Banov, Vladislav Turko

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Fatigue tests of specimen-s with numerous holes are presented. The tests were made up till fatigue cracks have been created on both sides of the hole. Their extension was stopping with pressed plastic deformation at the mouth of the detected crack. It is shown that the moments of occurrence of cracks on holes are stochastically dependent. This dependence has positive and negative correlation relations. Shown that the positive correlation is formed across of the applied force, while negative one – along it. The negative relationship extends over a greater distance. The mathematical model of dependence area formation is represented as well as the estimating of model parameters. The positive correlation of fatigue cracks origination can be considered as an extension of one main crack. With negative correlation the first crack locates the place of its origin, leading to the appearance of multiple cracks; do not merge with each other.

Keywords: Correlation analysis, fatigue damage accumulation, local area, mathematical model.

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