Search results for: transfer learning

Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

Abstract:

Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The control volume finite element method (CVFEM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the CVFEM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 2-D cylindrical geometries were considered. In order to establish the suitability of the LBM, the energy equation of the present problem was also solved using the the finite difference method (FDM) of the computational fluid dynamics. The CVFEM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FDM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the CVFEM for the radiative information, results were analyzed for the effects of various parameters such as the boundary emissivity. The results of the LBMCVFEM combination were found to be in excellent agreement with the FDM-CVFEM combination. The number of iterations and the steady state temperature in both of the combinations were found comparable. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature distribution.

Keywords: heat generation, cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

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Authors: Tomáš Brabenec

Abstract:

Cost contribution arrangements (CCAs) and Cost sharing agreements (CCAs) belong to the tools of modern finance management. Costs spend by associated enterprises on developing producing or obtaining assets, services or rights (in general - benefits) are used for tax optimizing too. The main purpose of joint research and development, producing or obtaining benefits is to lower these costs as much as possible or to maximize the benefits. In this article is mentioned the problematic of transfer pricing and arm's length principle with connection of CCAs, CSAs. Next, there is mentioned how to settle participation shares of the total cost and benefits contributions with respect to the OECD Transfer pricing for MNEs Guidelines and with respect to other significant regulations.

Keywords: Arm's length principle, Cost contribution arrangements, Cost sharing agreements, Reasonable anticipated benefits, Relevant costs, Transfer prices.

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Authors: Yueming Wang, Zenghui Zhang, Rendong Ying, Peilin Liu

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Sparse representation has long been studied and several dictionary learning methods have been proposed. The dictionary learning methods are widely used because they are adaptive. In this paper, a new dictionary learning method for audio is proposed. Signals are at first decomposed into different degrees of Intrinsic Mode Functions (IMF) using Empirical Mode Decomposition (EMD) technique. Then these IMFs form a learned dictionary. To reduce the size of the dictionary, the K-means method is applied to the dictionary to generate a K-EMD dictionary. Compared to K-SVD algorithm, the K-EMD dictionary decomposes audio signals into structured components, thus the sparsity of the representation is increased by 34.4% and the SNR of the recovered audio signals is increased by 20.9%.

Keywords: Dictionary Learning, EMD, K-means Method, Sparse Representation.

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Authors: Trevor E. Davis, Isaac Cassar, Yi-Kai Lo, Wentai Liu

Abstract:

This study models the use of transcutaneous electrical nerve stimulation on skin with a disk electrode in order to simulate tissue damage. The current density distribution above a disk electrode is known to be a dynamic and non-uniform quantity that is intensified at the edges of the disk. The non-uniformity is subject to change through using various electrode geometries or stimulation methods. One of these methods known as edge-retarded stimulation has shown to reduce this edge enhancement. Though progress has been made in modeling the behavior of a disk electrode, little has been done to test the validity of these models in simulating the actual heat transfer from the electrode. This simulation uses finite element software to couple the injection of current from a disk electrode to heat transfer described by the Pennesbioheat transfer equation. An example application of this model is studying an experimental form of stimulation, known as edge-retarded stimulation. The edge-retarded stimulation method will reduce the current density at the edges of the electrode. It is hypothesized that reducing the current density edge enhancement effect will, in turn, reduce temperature change and tissue damage at the edges of these electrodes. This study tests this hypothesis as a demonstration of the capabilities of this model. The edge-retarded stimulation proved to be safer after this simulation. It is shown that temperature change and the fraction of tissue necrosis is much greater in the square wave stimulation. These results bring implications for changes of procedures in transcutaneous electrical nerve stimulation and transcutaneous spinal cord stimulation as well.

Keywords: Bioheat transfer, Electrode, Neuroprosthetics, TENS, Transcutaneous stimulation.

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Authors: Varun

Abstract:

Solar energy is a good option among renewable energy resources due to its easy availability and abundance. The simplest and most efficient way to utilize solar energy is to convert it into thermal energy and this can be done with the help of solar collectors. The thermal performance of such collectors is poor due to less heat transfer from the collector surface to air. In this work, experimental investigations of single pass solar air heater having triangular duct and provided with roughness element on the underside of the absorber plate. V-shaped ribs are used for investigation having three different values of relative roughness pitch (p/e) ranges from 4- 16 for a fixed value of angle of attack (α), relative roughness height (e/Dh) and a relative gap distance (d/x) values are 60°, 0.044 and 0.60 respectively. Result shows that considerable augmentation in heat transfer has been obtained by providing roughness.

Keywords: Artificial roughness, Solar Air heater, Triangular duct, V-Shaped Ribs.

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Authors: A. Schuchter, M. Promegger

Abstract:

The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: Flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning.

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Authors: D. J. Smith, M. A. Qayyum

Abstract:

The use of information tools is a common activity for students of any educational stage when they encounter online learning activities. Finding the relevant information for particular learning tasks is the topic of this paper as it investigates the use of information tools for a group of student participants. The paper describes and discusses the results with particular implications for use in higher education, and the findings suggest that improvement in assessment design and subsequent student learning may be achieved by structuring the purposefulness of information tools usage and online reading behaviors of university students.

Keywords: Information tools, assessment, online learning.

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Authors: Susana Lemos, Neuza Pedro

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Thepurpose of the research is to characterize the levels of satisfaction of the students in e-learning post-graduate courses, taking into account specific dimensions of the course which were considered as benchmarks for the quality of this type of online learning initiative, as well as the levels of satisfaction towards each specific indicator identified in each dimension. It was also an aim of this study to understand how thesedimensions relate to one another. Using a quantitative research approach in the collection and analysis of the data, the study involves the participation of the students who attended on e-learning course in 2010/2011. The conclusions of this study suggest that online students present relatively high levels of satisfaction, which points towards a positive experience during the course. It is possible to note that there is a correlation between the different dimensions studied, consequently leading to different improvement strategies. Ultimately, this investigation aims to contribute to the promotion of quality and the success of e-learning initiatives in Higher Education.

Keywords: e-learning, higher education, quality, students satisfaction

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Authors: Philippe A. Martin

Abstract:

This article first summarizes reasons why current approaches supporting Open Learning and Distance Education need to be complemented by tools permitting lecturers, researchers and students to cooperatively organize the semantic content of Learning related materials (courses, discussions, etc.) into a fine-grained shared semantic network. This first part of the article also quickly describes the approach adopted to permit such a collaborative work. Then, examples of such semantic networks are presented. Finally, an evaluation of the approach by students is provided and analyzed.

Keywords: knowledge sharing, knowledge evaluation, e-learning

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Authors: Kun Lei, Hongfang Ma, Haitao Zhang, Weiyong Ying, Dingye Fang

Abstract:

This paper reported an experimental research of steady-state heat transfer behaviour of a gas flowing through a fixed bed under the different operating conditions. Studies had been carried out in a fixed-bed packed methanol synthesis catalyst percolated by air at appropriate flow rate. Both radial and axial direction temperature distribution had been investigated under the different operating conditions. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on temperature distribution was investigated and the experimental results showed that a higher inlet air temperature was conducive to uniform temperature distribution in the fixed bed. A large temperature drop existed at the radial direction, and the temperature drop increased with the heating pipe temperature increasing under the experimental conditions; the temperature profile of the vicinity of the heating pipe was strongly affected by the heating pipe temperature. A higher air flow rate can improve the heat transfer in the fixed bed. Based on the thermal distribution, heat transfer models of the fixed bed could be established, and the characteristics of the temperature distribution in the fixed bed could be finely described, that had an important practical significance.

Keywords: Thermal distribution, heat transfer, axial-flow, fixed bed.

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Authors: Kai-Long Hsiao

Abstract:

In this study, an analysis has been performed for free convection with radiation effect over a thermal forming nonlinearly stretching sheet. Parameters n, k0, Pr, G represent the dominance of the nonlinearly effect, radiation effect, heat transfer and free convection effects which have been presented in governing equations, respectively. The similarity transformation and the finite-difference methods have been used to analyze the present problem. From the results, we find that the effects of parameters n, k0, Pr, Ec and G to the nonlinearly stretching sheet. The increase of Prandtl number Pr, free convection parameter G or radiation parameter k0 resulting in the increase of heat transfer effects, but increase of the viscous dissipation number Ec will decrease of heat transfer effect.

Keywords: Nonlinearly stretching sheet, Free convection, Finite-difference, Radiation effect.

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Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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Authors: Konstantinos C. Giotopoulos, Christos E. Alexakos, Grigorios N. Beligiannis, Spiridon D.Likothanassis

Abstract:

In this contribution a newly developed elearning environment is presented, which incorporates Intelligent Agents and Computational Intelligence Techniques. The new e-learning environment is constituted by three parts, the E-learning platform Front-End, the Student Questioner Reasoning and the Student Model Agent. These parts are distributed geographically in dispersed computer servers, with main focus on the design and development of these subsystems through the use of new and emerging technologies. These parts are interconnected in an interoperable way, using web services for the integration of the subsystems, in order to enhance the user modelling procedure and achieve the goals of the learning process.

Keywords: E-learning environments, intelligent agents, user modeling, Bayesian Networks, computational intelligence.

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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Authors: Mohammad Najafi, Hossein Roghani-Mamaqani, Mehdi Salami-Kalajahi, Vahid Haddadi-Asl

Abstract:

A high-performance Monte Carlo simulation, which simultaneously takes diffusion-controlled and chain-length-dependent bimolecular termination reactions into account, is developed to simulate atom transfer radical copolymerization of styrene and nbutyl acrylate. As expected, increasing initial feed fraction of styrene raises the fraction of styrene-styrene dyads (fAA) and reduces that of n-butyl acrylate dyads (fBB). The trend of variation in randomness parameter (fAB) during the copolymerization also varies significantly. Also, there is a drift in copolymer heterogeneity and the highest drift occurs in the initial feeds containing lower percentages of styrene, i.e. 20% and 5%.

Keywords: Atom Transfer Radical Copolymerization, MonteCarlo Simulation, Copolymer Heterogeneity, Styrene n-ButylAcrylate

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Authors: Xia Lin

Abstract:

Concept maps can be generated manually or automatically. It is important to recognize differences of the two types of concept maps. The automatically generated concept maps are dynamic, interactive, and full of associations between the terms on the maps and the underlying documents. Through a specific concept mapping system, Visual Concept Explorer (VCE), this paper discusses how automatically generated concept maps are different from manually generated concept maps and how different applications and learning opportunities might be created with the automatically generated concept maps. The paper presents several examples of learning strategies that take advantages of the automatically generated concept maps for concept learning and exploration.

Keywords: Concept maps, Dynamic concept representation, learning strategies, visual interface, Visual Concept Explorer.

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Authors: Hy Dang, Bo Mei

Abstract:

The development of machine learning methods and techniques has opened doors for investigation in many areas such as medicines, economics, finance, etc. One active research area involving machine learning is stock market prediction. This research paper tries to consider multiple techniques and methods for stock movement prediction using historical price or price factors. The paper explores the effectiveness of some deep learning frameworks for forecasting stock. Moreover, an architecture (TimeStock) is proposed which takes the representation of time into account apart from the price information itself. Our model achieves a promising result that shows a potential approach for the stock movement prediction problem.

Keywords: Classification, machine learning, time representation, stock prediction.

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Authors: F. Roger, A. Traidia, B. Reynier

Abstract:

Arc welding creates a weld pool to realize continuity between pieces of assembly. The thermal history of the weld is dependent on heat transfer and fluid flow in the weld pool. The metallurgical transformation during welding and cooling are modeled in the literature only at solid state neglecting the fluid flow. In the present paper we associate a heat transfer – fluid flow and metallurgical model for the 16MnD5 steel. The metallurgical transformation model is based on Leblond model for the diffusion kinetics and on the Koistinen-Marburger equation for Marteniste transformation. The predicted thermal history and metallurgical transformations are compared to a simulation without fluid phase. This comparison shows the great importance of the fluid flow modeling.

Keywords: Arc welding, Weld pool, Fluid flow, Metallurgical transformations.

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Authors: G. Kumaravelan, R. Sivakumar

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Modeling the behavior of the dialogue management in the design of a spoken dialogue system using statistical methodologies is currently a growing research area. This paper presents a work on developing an adaptive learning approach to optimize dialogue strategy. At the core of our system is a method formalizing dialogue management as a sequential decision making under uncertainty whose underlying probabilistic structure has a Markov Chain. Researchers have mostly focused on model-free algorithms for automating the design of dialogue management using machine learning techniques such as reinforcement learning. But in model-free algorithms there exist a dilemma in engaging the type of exploration versus exploitation. Hence we present a model-based online policy learning algorithm using interconnected learning automata for optimizing dialogue strategy. The proposed algorithm is capable of deriving an optimal policy that prescribes what action should be taken in various states of conversation so as to maximize the expected total reward to attain the goal and incorporates good exploration and exploitation in its updates to improve the naturalness of humancomputer interaction. We test the proposed approach using the most sophisticated evaluation framework PARADISE for accessing to the railway information system.

Keywords: Dialogue management, Learning automata, Reinforcement learning, Spoken dialogue system

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Authors: A. Ghafouri, A. Falavand Jozaei, M. Salari

Abstract:

In this paper, effects of using Alumina-water nanofluid on the rate of heat transfer have been investigated numerically. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the Richardson number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are presented by isotherms lines, average Nusselt number and normalized Nusselt number in different range of φ and Ri for forced, combined and natural convection dominated regime. It is found that higher heat transfer rate is predicted when the effects of nanoparticle is taken into account.

Keywords: Nanofluid, Heat Transfer Enhancement, Square Enclosure, Nusselt number.

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Authors: Saeed Mohammed Baneamoon, Rosalina Abdul Salam, Abdullah Zawawi Hj. Talib

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Designing a simulated system and training it to optimize its tasks in simulated environment helps the designers to avoid problems that may appear when designing the system directly in real world. These problems are: time consuming, high cost, high errors percentage and low efficiency and accuracy of the system. The proposed system will investigate and improve the efficiency and accuracy of a simulated robot to choose correct behavior to perform its task. In this paper, machine learning, which uses genetic algorithm, is adopted. This type of machine learning is called genetic-based machine learning in which a distributed classifier system is used to improve the efficiency and accuracy of the robot. Consequently, it helps the robot to achieve optimal action.

Keywords: Machine Learning, Genetic-Based MachineLearning, Learning Classifier System, Behaviors.

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Authors: YuLung Wu, YuTien Wu, ShuMey Yu

Abstract:

Game-based learning can enhance the learning motivation of students and provide a means for them to learn through playing games. This study used augmented reality technology to develop an interactive card game as a game-based teaching aid for delivering elementary school science course content with the aim of enhancing student learning processes and outcomes. Through playing the proposed card game, students can familiarize themselves with appearance, features, and foraging behaviors of insects. The system records the actions of students, enabling teachers to determine their students’ learning progress. In this study, 37 students participated in an assessment experiment and provided feedback through questionnaires. Their responses indicated that they were significantly more motivated to learn after playing the game, and their feedback was mostly positive.

Keywords: Game-based learning, learning motivation, teaching aid, augmented reality.

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Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: Statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization.

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Authors: Asfar Ali Khan

Abstract:

Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.

Keywords: Power Transfer, PV Curve, Voltage Stability.

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Authors: Subramaniam Chandran

Abstract:

This paper explains how mobile learning assures sustainable e-education for multicultural group of students. This paper reports the impact of mobile learning on distance education in multicultural environment. The emergence of learning technologies through CD, internet, and mobile is increasingly adopted by distance institutes for quick delivery and cost-effective purposes. Their sustainability is conditioned by the structure of learners as well as the teaching community. The experimental study was conducted among the distant learners of Vinayaka Missions University located at Salem in India. Students were drawn from multicultural environment based on different languages, religions, class and communities. During the mobile learning sessions, the students, who are divided on language, religion, class and community, were dominated by play impulse rather than study anxiety or cultural inhibitions. This study confirmed that mobile learning improved the performance of the students despite their division based on region, language or culture. In other words, technology was able to transcend the relative deprivation in the multicultural groups. It also confirms sustainable e-education through mobile learning and cost-effective system of instruction. Mobile learning appropriates the self-motivation and play impulse of the young learners in providing sustainable e-education to multicultural social groups of students.

Keywords: E-Education, mobile learning, multiculturalism.

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Authors: O. Boe, A. Langaard Jensen

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The Norwegian Military Academy (Army) has been using a tactical simulator for the last two years. During this time there has been some discussion concerning how to use the simulator most efficiently and what type of learning one achieves by using the simulator. The problem that is addressed in this paper is how simulators can be used as a learning resource for students concerned with developing their military profession. The aim of this article is to create a wider consciousness regarding the use of a simulator while educating officers in a military profession. The article discusses the use of simulators from two different perspectives. The first perspective deals with using the simulator as a computer game, and the second perspective looks at the simulator as a socio-cultural artefact. Furthermore the article discusses four different ways the simulator can be looked upon as a useful learning resource when educating students of a military profession.

Keywords: Learning, military, profession, simulator.

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Authors: Sahilu Wendeson Sahilu, Wan Fatimah Wan Ahmad, Nazleeni Samiha Haron

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Mobile learning (M-learning) integrates mobile devices and wireless computing technology to enhance the current conventional learning system. However, there are constraints which are affecting the implementation of platform and device independent M-learning. The main aim of this research is to fulfill the following main objectives: to develop platform independent mobile learning tool (M-LT) for structured programming course, and evaluate its effectiveness and usability using ADDIE instructional design model (ISD) as M-LT life cycle. J2ME (Java 2 micro edition) and XML (Extensible Markup Language) were used to develop platform independent M-LT. It has two modules lecture materials and quizzes. This study used Quasi experimental design to measure effectiveness of the tool. Meanwhile, questionnaire is used to evaluate the usability of the tool. Finally, the results show that the system was effective and also usability evaluation was positive.

Keywords: ADDIE, Conventional learning, ISD, J2ME, Mlearning, Quasi Experiment, Wireless Technology, XML

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Authors: May George

Abstract:

Inference plays an important role in the learning process and it can lead to a rapid acquisition of a second language. When learning a non-native language i.e., a critical language like Arabic, the students depend on the teacher’s support most of the time to learn new concepts. The students focus on memorizing the new vocabulary and stress on learning all the grammatical rules. Hence, the students became mechanical and cannot produce the language easily. As a result, they are unable to predicate the meaning of words in the context by relying heavily on the teacher, in that they cannot link their prior knowledge or even identify the meaning of the words without the support of the teacher. This study explores how the teacher guides students learning during the inference process and what are the processes of learning that can direct student’s inference.

Keywords: Inference, Reading, Arabic, and Language Acquisition.

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Authors: Sang Hoon Lee, Tae Il Lee, Su Jeong Lee, Jae Min Myoung

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In order to manufacture short gap single Si nanowire (NW) field effect transistor (FET) by imprinting and transferring method, we introduce the method using Al2O3 sacrificial layer. The diameters of cylindrical Si NW addressed between Au electrodes by dielectrophoretic (DEP) alignment method are controlled to 106, 128, and 148 nm. After imprinting and transfer process, cylindrical Si NW is embedded in PVP adhesive and dielectric layer. By curing transferred cylindrical Si NW and Au electrodes on PVP-coated p++ Si substrate with 200nm-thick SiO2, 3μm gap Si NW FET fabrication was completed. As the diameter of embedded Si NW increases, the mobility of FET increases from 80.51 to 121.24 cm2/V·s and the threshold voltage moves from –7.17 to –2.44 V because the ratio of surface to volume gets reduced.

Keywords: Al2O3 Sacrificial transfer layer, cylindrical silicon nanowires, Dielectrophorestic alignment, Field effect transistor.

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Authors: Gilbert Makanda, Roelf Sypkens

Abstract:

A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.

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