Search results for: mathematical data analysis.

Authors: S. Madhu, V. V. Subba Rao

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In the implementation of Carbon Nanotube Reinforced Polymer matrix Composites in structural applications, deflection and stress analysis are important considerations. In the present study, a multi scale analysis of deflection and stress analysis of carbon nanotube (CNT) reinforced polymer composite plates is presented. A micromechanics model based on the Mori-Tanaka method is developed by introducing straight CNTs aligned in one direction. The effect of volume fraction and diameter of CNTs on plate deflection and the stresses are investigated using classical laminate plate theory (CLPT). The study is primarily conducted with the intention of observing the suitability of CNT reinforced polymer composite plates under static loading for structural applications.

Keywords: Carbon Nanotube, Micromechanics, Composite plate, Multi-scale analysis, Classical Laminate Plate Theory.

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Authors: Gitanjali Devi, Kandarpa Kumar Sarma, Pranayee Datta, Anjana Kakoti Mahanta

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Cosmic showers, during the transit through space, produce sub - products as a result of interactions with the intergalactic or interstellar medium which after entering earth generate secondary particles called Extensive Air Shower (EAS). Detection and analysis of High Energy Particle Showers involve a plethora of theoretical and experimental works with a host of constraints resulting in inaccuracies in measurements. Therefore, there exist a necessity to develop a readily available system based on soft-computational approaches which can be used for EAS analysis. This is due to the fact that soft computational tools such as Artificial Neural Network (ANN)s can be trained as classifiers to adapt and learn the surrounding variations. But single classifiers fail to reach optimality of decision making in many situations for which Multiple Classifier System (MCS) are preferred to enhance the ability of the system to make decisions adjusting to finer variations. This work describes the formation of an MCS using Multi Layer Perceptron (MLP), Recurrent Neural Network (RNN) and Probabilistic Neural Network (PNN) with data inputs from correlation mapping Self Organizing Map (SOM) blocks and the output optimized by another SOM. The results show that the setup can be adopted for real time practical applications for prediction of primary energy and location of EAS from density values captured using detectors in a circular grid.

Keywords: EAS, Shower, Core, ANN, Location.

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Authors: Pragya Paneru

Abstract:

This paper explores altogether 10 primary teachers’ views on gender representation in primary level textbooks. Data were collected from the teachers who taught in private schools in the Kailali and Kathmandu districts. This research uses a semi-structured interview method to obtain information regarding teachers’ attitudes toward gender representations in textbook contents. The interview data were analysed by using critical skills of qualitative research. The findings revealed that most of the teachers were unaware and regarded gender issues as insignificant to discuss in primary-level classes. Most of them responded to the questions personally and claimed that there were no gender issues in their classrooms. Some of the teachers connected gender issues with contexts other than textbook representations such as school discrimination in the distribution of salary among male and female teachers, school practices of awarding girls rather than boys as the most disciplined students, following girls’ first rule in the assembly marching, encouraging only girls in the stage shows, and involving students in gender-specific activities such as decorating works for girls and physical tasks for boys. The interview also revealed teachers’ covert gendered attitudes in their remarks. Nevertheless, most of the teachers accepted that gender-biased contents have an impact on learners and this problem can be solved with more gender-centred research in the education field, discussions, and training to increase awareness regarding gender issues. Agreeing with the suggestion of teachers, this paper recommends proper training and awareness regarding how to confront gender issues in textbooks.

Keywords: Content analysis, gender equality, school education, critical awareness.

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Authors: Ephraim Gower, Thato Tsalaile, Monageng Kgwadi, Malcolm Hawksford.

Abstract:

This paper introduces a new point estimation algorithm, with particular focus on coherent noise suppression, given several measurements of the device under test where it is assumed that 1) the noise is first-order stationery and 2) the device under test is linear and time-invariant. The algorithm exploits the robustness of the Pitman estimator of the Cauchy location parameter through the initial scaling of the test signal by a centred Gaussian variable of predetermined variance. It is illustrated through mathematical derivations and simulation results that the proposed algorithm is more accurate and consistently robust to outliers for different tailed density functions than the conventional methods of sample mean (coherent averaging technique) and sample median search.

Keywords: Central limit theorem, Fisher-Cramer Rao, gamma function, Pitman estimator.

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Authors: M.Somjarod, V. Tanawat, l. Weerawat

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The understanding of knee movement during swing importance for golf swing improving and preventing injury. Thirty male professional and amateur golfers were assigned to swing time by time for 3 times. Data from a vedio-based motion capture were used to compute knee joint movement variables. The results showed that professional and amateur golfers were significantly in left knee flexion angle at the impact point and mid follow through phase. Nevertheless, left knee external rotation in both groups was also significant. The right knee were no significant different in all variable. However, pattern of knee joint movement are also likely between professional and amateur golfers.

Keywords: Golfer, Knee joint, Movement, Swing

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Authors: Sandeep Sharma, Sarabjit Singh, Meenakshi Sharma

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Load balancing is the process of improving the performance of a parallel and distributed system through a redistribution of load among the processors [1] [5]. In this paper we present the performance analysis of various load balancing algorithms based on different parameters, considering two typical load balancing approaches static and dynamic. The analysis indicates that static and dynamic both types of algorithm can have advancements as well as weaknesses over each other. Deciding type of algorithm to be implemented will be based on type of parallel applications to solve. The main purpose of this paper is to help in design of new algorithms in future by studying the behavior of various existing algorithms.

Keywords: Load balancing (LB), workload, distributed systems, Static Load balancing, Dynamic Load Balancing

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: Distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor.

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Authors: Jing Lu, Malcolm Keech, Weiru Chen

Abstract:

Web usage mining is an interesting application of data mining which provides insight into customer behaviour on the Internet. An important technique to discover user access and navigation trails is based on sequential patterns mining. One of the key challenges for web access patterns mining is tackling the problem of mining richly structured patterns. This paper proposes a novel model called Web Access Patterns Graph (WAP-Graph) to represent all of the access patterns from web mining graphically. WAP-Graph also motivates the search for new structural relation patterns, i.e. Concurrent Access Patterns (CAP), to identify and predict more complex web page requests. Corresponding CAP mining and modelling methods are proposed and shown to be effective in the search for and representation of concurrency between access patterns on the web. From experiments conducted on large-scale synthetic sequence data as well as real web access data, it is demonstrated that CAP mining provides a powerful method for structural knowledge discovery, which can be visualised through the CAP-Graph model.

Keywords: concurrent access patterns (CAP), CAP mining and modelling, CAP-Graph, web access patterns (WAP), WAP-Graph, Web usage mining.

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Authors: Santanu Santra, Utpal Roy

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The most important mathematical operation for any computing system is addition. An efficient adder can be of greater assistance in designing of any arithmetic circuits. Quantum-dot Cellular Automata (QCA) is a promising nanotechnology to create electronic circuits for computing devices and suitable candidate for next generation of computing systems. The article presents a modest approach to implement a novel XOR gate. The gate is simple in structure and powerful in terms of implementing digital circuits. By applying the XOR gate, the hardware requirement for a QCA circuit can be decrease and circuits can be simpler in level, clock phase and cell count. In order to verify the functionality of the proposed device some implementation of Half Adder (HA) and Full Adder (FA) is checked by means of computer simulations using QCA-Designer tool. Simulation results and physical relations confirm its usefulness in implementing every digital circuit.

Keywords: Clock, Computing system, Majority gate, QCA, QCA Designer.

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Authors: Thomas Jin-Chee Liu

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The numerical simulation of the crack welding process is reported in this paper. The thermo-electro-structural coupled-field finite element analysis is adopted to investigate the welding process of crack surfaces. In the simulation, the pressure-dependent and temperature-dependent electrical contact conditions are considered. From the results, the crack surfaces can melt and weld together under the compressive load and electric current. The contact pressure effect must be considered in the finite element analysis to obtain more practical results.

Keywords: Crack welding, contact pressure, Joule heating, finite element, coupled-field.

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Authors: Rosmini Yanti, Safira Aviolita, Marsetio

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Indonesia has several straits that are very important as a shipping lane, including the Sunda Strait and the Lombok Strait, which are the part of the Indonesian Archipelagic Sea Lane (IASL). An increase in traffic on the Marine Archipelago makes the task of monitoring sea routes increasingly difficult. Indonesia has proposed the establishment of a Traffic Separation Scheme (TSS) in the Sunda Strait and the Lombok Strait and the country now has the right to be able to conceptualize the TSS as well as the obligation to regulate it. Indonesia has the right to maintain national safety and sovereignty. In setting the TSS, Indonesia needs to issue national regulations that are in accordance with international law and the general provisions of the IMO (International Maritime Organization) can then be used as guidelines for maritime safety and security in the Sunda Strait and the Lombok Strait. The research method used is a qualitative method with the concept of linguistic and visual data collection. The source of the data is the analysis of documents and regulations. The results show that the determination of TSS was justified by International Law, in accordance with article 22, article 41, and article 53 of the United Nations Convention on the Law of the Sea (UNCLOS) 1982. The determination of TSS by the Indonesian government would be in accordance with COLREG (International Convention on Preventing Collisions at Sea) 10, which has been designed to follow IASL. Thus, TSS can provide a function as a safety and monitoring medium to minimize ship accidents or collisions, including the warship and aircraft of other countries that cross the IASL.

Keywords: Archipelago State, maritime law, maritime security, traffic separation scheme.

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Authors: Bita Mashayekhi, Mohammad Ara

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The purpose of this study is to provide some empirical evidence about implementing Activity-Based Costing (ABC) in the hospitality industry in Iran. For this purpose, we consider the Tabriz International Hotel as our sample hotel and then gather the relevant data from its cost accounting system in 2012. Then, we use ABC as our costing method and compare the cost of each service unit with that cost which had been extracted for the traditional costing method. The results show a different cost per unit for two methods. Also, because of its more precise and detailed provided information, an ABC system facilitates the decision-making process for managers on decisions related to profitability analysis, budgeting, pricing, and so on.

Keywords: Activity-based costing, activity, cost driver, hospitality industry.

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Authors: Mariyam Arif, Ye Liu, Israr Ul Haq, Ahsan Ashfaq

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High cost of fossil fuels and intensifying installations of alternate energy generation sources are intimidating main challenges in power systems. Making accurate load forecasting an important and challenging task for optimal energy planning and management at both distribution and generation side. There are many techniques to forecast load but each technique comes with its own limitation and requires data to accurately predict the forecast load. Artificial Neural Network (ANN) is one such technique to efficiently forecast the load. Comparison between two different ranges of input datasets has been applied to dynamic ANN technique using MATLAB Neural Network Toolbox. It has been observed that selection of input data on training of a network has significant effects on forecasted results. Day-wise input data forecasted the load accurately as compared to year-wise input data. The forecasted load is then distributed among the six generators by using the linear programming to get the optimal point of generation. The algorithm is then verified by comparing the results of each generator with their respective generation limits.

Keywords: Artificial neural networks, demand-side management, economic dispatch, linear programming, power generation dispatch.

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Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

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The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: Curved beam, dynamic analysis, elastic foundation, finite element method.

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Authors: Roman Kalvin, Anam Nadeem, Saba Arif

Abstract:

Turbocharger is a device that is driven by the turbine and increases efficiency and power output of the engine by forcing external air into the combustion chamber. This study focused on the distribution of stress on the turbine blades and total deformation that may occur during its working along with turbocharger to carry out its static structural analysis of turbine blades. Structural steel was selected as the material for turbocharger. Assembly of turbocharger and turbine blades was designed on PRO ENGINEER. Furthermore, the structural analysis is performed by using ANSYS. This research concluded that by using structural steel, the efficiency of engine is improved and by increasing number of turbine blades, more waste heat from combustion chamber is emitted.

Keywords: Turbocharger, turbine blades, structural steel, ANSYS.

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Authors: Andreas Theissler, Ian Dear

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The one-class support vector machine “support vector data description” (SVDD) is an ideal approach for anomaly or outlier detection. However, for the applicability of SVDD in real-world applications, the ease of use is crucial. The results of SVDD are massively determined by the choice of the regularisation parameter C and the kernel parameter  of the widely used RBF kernel. While for two-class SVMs the parameters can be tuned using cross-validation based on the confusion matrix, for a one-class SVM this is not possible, because only true positives and false negatives can occur during training. This paper proposes an approach to find the optimal set of parameters for SVDD solely based on a training set from one class and without any user parameterisation. Results on artificial and real data sets are presented, underpinning the usefulness of the approach.

Keywords: Support vector data description, anomaly detection, one-class classification, parameter tuning.

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Authors: R. Behmanesh, I. Rahimi

Abstract:

recurrent neural network (RNN) is an efficient tool for modeling production control process as well as modeling services. In this paper one RNN was combined with regression model and were employed in order to be checked whether the obtained data by the model in comparison with actual data, are valid for variable process control chart. Therefore, one maintenance process in workshop of Esfahan Oil Refining Co. (EORC) was taken for illustration of models. First, the regression was made for predicting the response time of process based upon determined factors, and then the error between actual and predicted response time as output and also the same factors as input were used in RNN. Finally, according to predicted data from combined model, it is scrutinized for test values in statistical process control whether forecasting efficiency is acceptable. Meanwhile, in training process of RNN, design of experiments was set so as to optimize the RNN.

Keywords: RNN, DOE, regression, control chart.

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Authors: Ebrahim Panah, Muhammad Yasir Babar

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Thanks to the development of online technology and social networks, people are able to communicate as well as learn. WhatsApp is a popular social network which is growingly gaining popularity. This app can be used for communication as well as education. It can be used for instructor-learner, learner-learner, and learner-content interactions; however, very little knowledge is available on these potentials of WhatsApp. The current study was undertaken to investigate university students’ perceptions of WhatsApp used as a tool for instructor-learner dialogue, learner-content dialogue, and learner-learner dialogue. The study adopted a survey approach and distributed the questionnaire developed by Google Forms to 54 (11 males and 43 females) university students. The obtained data were analyzed using SPSS version 20. The result of data analysis indicates that students have positive attitudes towards WhatsApp as a tool for Instructor-Learner Dialogue: it easy to reach the lecturer (4.07), the instructor gives me valuable feedback on my assignment (4.02), the instructor is supportive during course discussion and offers continuous support with the class (4.00). Learner-Content Dialogue: WhatsApp allows me to academically engage with lecturers anytime, anywhere (4.00), it helps to send graphics such as pictures or charts directly to the students (3.98), it also provides out of class, extra learning materials and homework (3.96), and Learner-Learner Dialogue: WhatsApp is a good tool for sharing knowledge with others (4.09), WhatsApp allows me to academically engage with peers anytime, anywhere (4.07), and we can interact with others through the use of group discussion (4.02). It was also found that there are significant positive correlations between students’ perceptions of Instructor-Learner Dialogue (ILD), Learner-Content Dialogue (LCD), Learner-Learner Dialogue (LLD) and WhatsApp Application in classroom. The findings of the study have implications for lectures, policy makers and curriculum developers.

Keywords: Instructor-learner dialogue, learners-contents dialogue, learner-learner dialogue, WhatsApp.

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Authors: Amalia Suzianti

Abstract:

This research elaborates decision models for product innovation in the early phases, focusing on one of the most widely implemented method in marketing research: conjoint analysis and the related conjoint-based models with special focus on heuristics programming techniques for the development of optimal product innovation. The concept, potential, requirements and limitations of conjoint analysis and its conjoint-based heuristics successors are analysed and the development of conceptual framework of Genetic Algorithm (GA) as one of the most widely implemented heuristic methods for developing product innovations are discussed.

Keywords: Product Innovation, Conjoint Analysis, Heuristic Model, Genetic Algorithm

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Authors: H. Aghayan, F. A. Hashemi, R. Yavari, S. Zolghadri

Abstract:

In this work, a new composite adsorbent based on a mesoporous silica SBA-15 with platelet morphology and tin salt of tungstomolybdophosphoric (TWMP) acid was synthesized and applied for uranium adsorption from aqueous solution. The sample was characterized by X-ray diffraction, Fourier transfer infra-red, and N₂ adsorption-desorption analysis, and then, effect of various parameters such as concentration of metal ions and contact time on adsorption behavior was examined. The experimental result showed that the adsorption process was explained by the Langmuir isotherm model very well, and predominant reaction mechanism is physisorption. Kinetic data of adsorption suggest that the adsorption process can be described by the pseudo second-order reaction rate model.

Keywords: Platelet SBA-15, tungstomolybdophosphoric acid, adsorption, uranium ion.

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Authors: Lucjan Setlak, Emil Ruda

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The subject of this paper is to review, comparative analysis and simulation of selected components of power electronic systems (PES), consistent with the concept of a more electric aircraft (MEA). Comparative analysis and simulation in software environment MATLAB / Simulink were carried out on the base of a group of representatives of civil aircraft (B-787, A-380) and military (F-22 Raptor, F-35) in the context of multi-pulse converters used in them (6- and 12-pulse, and 18- and 24-pulse), which are key components of high-tech electronics on-board power systems of autonomous power systems (ASE) of modern aircraft (airplanes of the future).

Keywords: Converters, electrical machinery, more electric aircraft, MEA, power electronics systems, PES.

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Authors: T.R. Sahroni, S. Sulaiman, I. Romli, M.R. Salleh, H.A. Ariff

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The thermal expansion behaviour of silicon carbide (SCS-2) fibre reinforced 6061 aluminium matrix composite subjected to the influenced thermal mechanical cycling (TMC) process were investigated. The thermal stress has important effect on the longitudinal thermal expansion coefficient of the composites. The present paper used experimental data of the thermal expansion behaviour of a SiC/Al composite for temperatures up to 370°C, in which their data was used for carrying out modelling of theoretical predictions.

Keywords: Nonlinear, thermal, fibre reinforced, metal matrixcomposites

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Authors: Cesar H. Ortega Jimenez, Ignacio Eguia Salinas, Pedro Garrido Vega, Jose A. Dominguez Machuca

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The aim of this study is to identify the conditions of implementation for reconfigurability in summarizing past flexible manufacturing systems (FMS) research by drawing overall conclusions from many separate High Performance Manufacturing (HPM) studies. Meta-analysis will be applied to links between HPM programs and their practices related to FMS and manufacturing performance with particular reference to responsiveness performance. More specifically, an application of meta-analysis will be made with reference to two of the main steps towards the development of an empirically-tested theory: testing the adequacy of the measurement of variables and testing the linkages between the variables.

Keywords: FMS (flexible manufacturing system), HPM (highperformance manufacturing), reconfigurability, RMS (reconfigurablemanufacturing system), responsiveness

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Authors: Lilac Al Safadi, Rana Abu Nafesa, Regina Garcia

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Motivated by Microsoft Co. Academic Program initiative, the department of Information Technology in King Saud University has adopted Microsoft products in three courses. The initiative aimed at enhancing the abilities of the university graduates and equipping them with skills that would help them in the job market. A number of methods of collecting assessment data were used to evaluate the course adoption initiative. Assessment data indicated that the goal of the course adoption is being achieved and that the students were much better prepared to design applications and administrate networks.

Keywords: course adoption, assessment, programming, technologies

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Authors: Vladimira Hornackova, Jana Kottasova, Zuzana Vanova, Anna Jungrova

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Present study deals with drama education in preschool education. The research made in this field brings a qualitative comparative survey with the aim to find out the use of methods and techniques of drama education in preschool education at university or secondary school graduate preschool teachers. The research uses a content analysis and an unstandardized questionnaire for preschool teachers and obtained data are processed with the help of descriptive methods and correlations. The results allow a comparison of aspects applied through drama in preschool education. The research brings impulses for education improvement in kindergartens and inspiration for university study programs of drama education in the professional training of preschool teachers.

Keywords: Drama education, preschool education, preschool teacher, research.

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Authors: Mohammad A. Khasawneh

Abstract:

Asphalt concrete pavements gradually lose their skid resistance causing safety problems especially under wet conditions and high driving speeds. In order to enact the actual field polishing and wearing process of asphalt pavement surfaces in a laboratory setting, several laboratory-scale accelerated polishing devices were developed by different agencies. To mimic the actual process, friction and texture measuring devices are needed to quantify surface deterioration at different polishing intervals that reflect different stages of the pavement life. The test could still be considered lengthy and to some extent labor-intensive. Therefore, there is a need to come up with another method that can assist in investigating the bituminous pavement surface characteristics in a practical and time-efficient test procedure.

The purpose of this paper is to utilize a well-developed image analysis technique to characterize asphalt pavement surfaces without the need to use conventional friction and texture measuring devices in an attempt to shorten and simplify the polishing procedure in the lab.

Promising findings showed the possibility of using image analysis in lieu of the labor-sensitive-variable-in-nature friction and texture measurements. It was found that the exposed aggregate surface area of asphalt specimens made from limestone and gravel aggregates produced solid evidence of the validity of this method in describing asphalt pavement surfaces. Image analysis results correlated well with the British Pendulum Numbers (BPN), Polish Values (PV) and Mean Texture Depth (MTD) values.

Keywords: Friction, Image Analysis, Polishing, Statistical Analysis, Texture.

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Authors: Tsai-Hsiu Lin

Abstract:

Dan C. Lortie’s Schoolteacher: A sociological study is one of the best works on the sociology of teaching since W. Waller’s classic study. It is a book worthy of review. Following the tradition of symbolic interactionists, Lortie demonstrated the qualities who studied the occupation of teaching. Using several methods to gather effective data, Lortie has portrayed the ethos of the teaching profession. Therefore, the work is an important book on the teaching profession and teacher culture. Though outstanding, Lortie’s work is also flawed in that his perspectives and methodology were adopted largely from symbolic interactionism. First, Lortie in his work analyzed many points regarding teacher culture; for example, he was interested in exploring “sentiment,” “cathexis,” and “ethos.” Thus, he was more a psychologist than a sociologist. Second, symbolic interactionism led him to discern the teacher culture from a micro view, thereby missing the structural aspects. For example, he did not fully discuss the issue of gender and he ignored the issue of race. Finally, following the qualitative sociological tradition, Lortie employed many qualitative methods to gather data but only foucused on obtaining and presenting interview data. Moreover, he used measurement methods that were too simplistic for analyzing quantitative data fully.

Keywords: Lortie’s Schooltacher, Symbolic interactionism, teacher culture, teaching profession.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Neil Bar, Andrew Heweston

Abstract:

Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

Keywords: Probability of failure, point estimate method, Monte-Carlo simulations, sensitivity analysis, slope stability.

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