Search results for: differential learning

Authors: Muneer Abbad

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In search of better, traditional learning universities have expanded their ways to deliver knowledge and integrate cost effective e-learning systems. Universities’ use of information and communication technologies has grown tremendously over the last decade. To ensure efficient use of the e-learning system, this project aimed to evaluate the good and bad practices, detect errors and determine areas for further improvements in usage. This project critically evaluated the students’ perception of the e-learning system and recommended changes to improve students’ e-learning usage, through conducting questionnaire given to the students that have experience with e-learning systems. Results of the study indicated that, in general, students have favourable perceptions toward using the e-learning system. They seemed to value the resources tool and its contribution to building their knowledge more than other e-learning tools. However, they seemed to perceive a limited value from the audio or video podcasts. This study has shown that technology acceptance is the most variable, factor that contributes to students’ perception and satisfaction of the e-learning system.

Keywords: e-learning, perception, Jordan, universities

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Authors: Nur Sofi Hidayah, Ratih Tri Purwatiningsih

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Learning is a process attempts person to obtain a new behavior changes as a whole, as a result of his own experience in the interaction with the environment. Learning involves our brain to think, while the ability of the brain to each student's performance is different. To obtain optimal learning results then need time to learn the exact hour that the brain's performance is not too heavy. Referring to the learning system in Finland which apply 45 minutes to learn and a 15-minute break is expected to be the brain work better, with the rest of the brain, the brain will be more focused and lessons can be absorbed well. It can be concluded that learning in this way students learn with brain always fresh and the best possible use of the time, but it can make students not saturated in a lesson.

Keywords: learning, working hours brain, time efficient learning, working hours in the brain receive stimulus.

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Authors: Andy Wang

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Personalized learning refers to an educational approach that tailors instruction to meet the unique needs, interests, and abilities of each learner. This method of learning aims at providing students with a customized learning experience that is more engaging, interactive, and relevant to their personal lives. With generative AI technology, the author has developed a Personal Tutoring Bot (PTB) that supports personalized learning. The author is currently testing PTB in his EE 499 – Microelectronics Metrology course. Virtual Reality (VR) and Augmented Reality (AR) provide interactive and immersive learning environments that can engage student in online learning. This paper presents the rationale of integrating VR/AR tools in PTB and discusses challenges and solutions of incorporating VA/AR into the Personal Tutoring Bot (PTB).

Keywords: personalized learning, online education, hands-on practice, VR/AR tools

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Zenaide Carvalho da Silva, Leandro Rodrigues Ferreira, Andrey Ricardo Pimentel

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Learning styles (LS) refer to the ways and forms that the student prefers to learn in the teaching and learning process. Each student has their own way of receiving and processing information throughout the learning process. Therefore, knowing their LS is important to better understand their individual learning preferences, and also, understand why the use of some teaching methods and techniques give better results with some students, while others it does not. We believe that knowledge of these styles enables the possibility of making propositions for teaching; thus, reorganizing teaching methods and techniques in order to allow learning that is adapted to the individual needs of the student. Adapting learning would be possible through the creation of online educational resources adapted to the style of the student. In this context, this article presents the structure of a learning object interface adaptation based on the LS. The structure created should enable the creation of the adapted learning object according to the student's LS and contributes to the increase of student’s motivation in the use of a learning object as an educational resource.

Keywords: adaptation, interface, learning object, learning style

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee, Yu-Cheng Kuo

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In order to understand whether there is a better than the learning function of learning methods and improve the CAD Courses for enterprise’s design human resource development, this research is applied in learning practical learning computer graphics software. In this study, Revit building information model for learning content, design of two different modes of learning curriculum to learning, learning functions, respectively, and project learning. Via a post-test, questionnaires and student interviews, etc., to study the effectiveness of a comparative analysis of two different modes of learning. Students participate in a period of three weeks after a total of nine-hour course, and finally written and hands-on test. In addition, fill in the questionnaire response by the student learning, a total of fifteen questionnaire title, problem type into the base operating software, application software and software-based concept features three directions. In addition to the questionnaire, and participants were invited to two different learning methods to conduct interviews to learn more about learning students the idea of two different modes. The study found that the ad hoc short-term courses in learning, better learning outcomes. On the other hand, functional style for the whole course students are more satisfied, and the ad hoc style student is difficult to accept the ad hoc style of learning.

Keywords: development, education, human resource, learning

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Nasser Al-Rawahi

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The study aims at determining self-regulated learning strategies used by Omani physical education candidates to learn sport skills. The data were collected by a self-regulated learning theory questionnaire. The sample of the study comprised of 145 undergraduate physical education students enrolled in the department of physical education at the College of Education, Sultan Qaboos University. The findings of the study revealed that the most commonly used strategies for learning sport skills by Omani physical education candidate are ‘the effort learning strategies, planning learning strategies and evaluation learning strategies’. However, the reflection learning strategies, self-monitoring and self-efficacy learning strategies were revealed as the least used strategies by the PE candidates in learning and acquiring sport skills. Based on these findings, suggestions and recommendations for future research were provided.

Keywords: learning strategies, physical education candidates, self-regulated learning theory, Oman

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: Azli Bin Ariffin, Noor Amy Afiza Binti Mohd Yusof

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This study aims to identify effect of social network usage on the self-learning method in teaching and learning at Sultan Idris Education University. The study involved 270 respondents consisting of students in the pre-graduate and post-graduate levels from nine fields of study offered. Assessment instrument used is questionnaire which measures respondent’s background includes level of study, years of study and field of study. Also measured the extent to which social pages used for self-learning and effect received when using social network for self-learning in learning process. The results of the study showed that students always visit Facebook more than other social sites. But, it is not for the purpose of self-learning. Analyzed data showed that 45.5% students not sure about using social sites for self-learning. But they realize the positive effect that they will received when use social sites for self-learning to improve teaching and learning process when 72.7% respondent agreed with all the statements provided.

Keywords: facebook, self-learning, social network, teaching, learning

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Authors: Chloe L. Southern

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If play is deemed to fulfill children’s social, emotional, and physical domains, as well as satisfy their natural curiosity and promote self-reflexivity, it is difficult to understand why play is not prioritized to the same extent for older children. This paper explores and discusses the importance of play-based learning as well as the preliminary implications beyond the realm of kindergarten. To further extend the inquiry, discussions pertaining to play-based learning are looked at through the lens of relevant methodologies and theories. Different education systems are looked at in certain areas of the world that lead to curiosities not only towards their play-based practices and curriculum but what ideologies they have that set them apart.

Keywords: 21ˢᵗ century learning, play-based learning, student-centered learning, transformative learning

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Authors: Jonathan H. Westover, Jacque P. Westover, Maureen S. Andrade

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Though learning theories vary in complexity and usefulness, a thorough understanding of foundational learning theories is a necessity in today’s educational environment. Additionally, learning theories lead to approaches in instruction that can affect student motivation and learning. The combination of a learning theory and elements to enhance student motivation can create a learning context where the student can thrive in their educational pursuits. This paper will provide an overview of three main learning theories: (1) Behavioral Theory, (2) Cognitive Theory, and (3) Constructivist Theory and explore their connection to elements of student learning motivation. Finally, we apply these learning theories and elements of student motivation to the following two context: (1) The FastStart Program at the Community College of Denver, and (2) An Online Academic English Language Course. We discussed potential of the program and course to have success in increasing student success outcomes.

Keywords: learning theory, student motivation, inclusive pedagogy, developmental education

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: H. van Rensburg, B. Adcock, B. Al Mansouri

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This paper discusses the impact of pedagogical and learning differences on Arabic international students’ (AIS) learning when they come to study in Australia. It describes the difference in teaching and learning methods between the students’ home countries in the Arabic world and Australia. There are many research papers that discuss the general experiences of international students in the western learning systems, including Australia. However, there is little research conducted specifically about AIS learning in Australia. Therefore, the data was collected through in-depth, semi-structured interviews with AIS who are learning at an Australian regional university in Queensland. For that reason, this paper contributes to fill a gap by reporting on the learning experiences of AIS in Australia and, more specifically, on the AIS’ pedagogical experiences. Not only discussing the learning experiences of AIS, but also discussing the cultural adaptation using the Oberg’s cultural adaptation model. This paper suggests some learning strategies that may benefit AIS and academic lecturers when teaching students from a completely different culture and language.

Keywords: arabic international students, cultural adaption, learning differences, learning systems

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Authors: M. Sarrab, M. Elbasir

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Most of mobile learning applications currently available are developed for the formal education and learning environment. Those applications are characterized by the improvement of the interaction process between instructors and learners to provide more collaboration and flexibility in the learning process. Despite the long history and large amount of research on Instruction design model and mobile learning there is no complete and well defined set of steps to follow in designing mobile learning applications. Based on this scenario, this paper focuses on identifying instruction design phases considerations and influencing factors in developing mobile learning application. This set of instruction design steps includes analysis, design, development, implementation, evaluation and continuous has been built from a literature study with focus on standards for learning and mobile application software quality and guidelines. The effort is part of an Omani-funded research project investigating the development, adoption and dissemination of mobile learning in Oman.

Keywords: instruction design, mobile learning, mobile application

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Authors: Eric Agrie Ambele

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The norms and models for learning pronunciation in relation to the teaching and learning of English pronunciation are key issues nowadays in English Language Teaching in ESL contexts. This paper discusses these issues based on a study on the attitudes of some Francophone university students in Cameroon towards three English accents spoken in Cameroon: Cameroon Francophone English (CamFE), Cameroon English (CamE), and Hyperlectal Cameroon English (near standard British English). With the desire to know more about the treatment that these English accents receive among these students, an aspect that had hitherto received little attention in the literature, a language attitude questionnaire, and the matched-guise technique was used to investigate this phenomenon. Two methods of data analysis were employed: (1) the percentage count procedure, and (2) the semantic differential scale. The findings reveal that the participants’ attitudes towards the selected accents vary in degree. Though Hyperlectal CamE emerged first, CamE second and CamFE third, no accent, on average, received a negative evaluation. It can be deduced from this findings that, first, CamE is gaining more and more recognition and can stand as an autonomous accent; second, that the participants all rated Hyperlectal CamE higher than CamE implies that they would be less motivated in a context where CamE is the learning model. By implication, in the teaching of English pronunciation to francophone learners learning English in Cameroon, Hyperlectal Cameroon English should be the model.

Keywords: teaching pronunciation, English accents, Francophone learners, attitudes

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Authors: Silmy A. Humaira'

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There is an issue about Asian students including Indonesian students that tend to behave passively in the classroom and depend on the teachers’ instruction. Regarding this statement, this study attempts to address the Indonesian high school students’ attitudes on whether they have initiative and be responsible for their learning out of the classroom and if so, why. Therefore, 30 high school students were asked to fill out the questionnaires and interviewed in order to figure out their attitudes towards self-directed learning. The descriptive qualitative research analysis adapted Knowles’s theory (1975) about Self-directed learning (SDL) to analyze the data. The findings show that the students have a potential to possess self-directed learning through ICT, but they have difficulties in choosing appropriate learning strategy, doing self-assessment and conducting self-reflection. Therefore, this study supports the teacher to promote self-directed learning instruction for successful learning by assisting students in dealing with those aforementioned problems. Furthermore, it is expected to be a beneficial reference which gives new insights on the self-directed learning practice in specific context.

Keywords: ICT, learning autonomy, students’ attitudes, self-directed learning

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Authors: Ibraheem Alzahrani

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This paper seeks to discover the relationship between both the social constructivist learning theory and the collaborative learning environment. This relationship can be identified through given an example of the learning environment. Due to wiki characteristics, wiki can be used to understand the relationship between constructivist learning theory and collaborative learning environment. However, several evidences will come in this paper to support the idea of why wiki is the suitable method to explore the relationship between social constructivist theory and the collaborative learning and their role in learning. Moreover, learning activities in wiki classroom will be discussed in this paper to find out the result of the learners' interaction in the classroom groups, which will be through two types of communication; synchronous and asynchronous.

Keywords: social constructivist, collaborative, environment, wiki, activities

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Authors: Razieh Khalafi

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The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli.

Keywords: brain, stimuli, partial differential equation, response, EEG signal

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Authors: Dorottya Horváth, Tímea Harmath-Tánczos

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Attention deficit hyperactivity disorder (ADHD) and learning disabilities are common neurocognitive disorders that can have a significant impact on a child's academic performance. ADHD is characterized by inattention, hyperactivity, and impulsivity, while learning disabilities are characterized by difficulty with specific academic skills, such as reading, writing, or math. The aim of this study was to investigate the working memory, executive, and attention functions of neurotypical children and children with ADHD and learning disabilities in order to fill the gaps in the Hungarian mean test scores of these cognitive functions in children with neurocognitive disorders. Another aim was to specify the neuropsychological differential diagnostic toolkit in terms of the relationships and peculiarities between these cognitive functions. The research question addressed in this study was: How do the working memory, executive, and attention functions of neurotypical children compare to those of children with ADHD and learning disabilities? A self-administered test battery was used as a research tool. Working memory was measured with the Non-Word Repetition Test, the Listening Span Test, the Digit Span Test, and the Reverse Digit Span Test; executive function with the Letter Fluency, Semantic Fluency, and Verb Fluency Tests; and attentional concentration with the d2-R Test. The data for this study was collected from 115 children aged 9-14 years. The children were divided into three groups: neurotypical children (n = 44), children with ADHD without learning disabilities (n = 23), and children with ADHD with learning disabilities (n = 48). The data was analyzed using a variety of statistical methods, including t-tests, ANOVAs, and correlational analyses. The results showed that the performance of children with neurocognitive involvement in working memory, executive functions, and attention was significantly lower than the performance of neurotypical children. However, the results of children with ADHD and ADHD with learning disabilities did not show a significant difference. The findings of this study are important because they provide new insights into the cognitive profiles of children with ADHD and learning disabilities and suggest that working memory, executive functions, and attention are all impaired in children with neurocognitive involvement, regardless of whether they have ADHD or learning disabilities. This information can be used to develop more effective diagnostic and treatment strategies for these disorders.

Keywords: ADHD, attention functions, executive functions, learning disabilities, working memory

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Authors: Roman Kalvin, Anam Nadeem, Shahab Khushnood

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Differential is an integral part of four wheeled vehicle, and its main function is to transmit power from drive shaft to wheels. Differential assembly allows both rear wheels to turn at different speed along curved paths. It consists of four gears which are assembled together namely pinion, ring, spider and bevel gears. This research focused on the spider gear and its static structural analysis using ANSYS. The main aim was to evaluate the distribution of stresses on the teeth of the spider gear. This study also analyzed total deformation that may occur during its working along with bevel gear that is meshed with spider gear. Structural steel was chosen for spider gear in this research. Modeling and assembling were done on SolidWorks for both spider and bevel gear. They were assembled exactly same as in a differential assembly. This assembly was then imported to ANSYS. After observing results that maximum amount of stress and deformation was produced in the spider gear, it was concluded that structural steel material for spider gear possesses greater amount of strength to bear maximum stress.

Keywords: ANSYS, differential, spider gear, structural steel

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Authors: Farouk Lawan Gambo

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Data compression shrinks files into fewer bits then their original presentation. It has more advantage on internet because the smaller a file, the faster it can be transferred but learning most of the concepts in data compression are abstract in nature therefore making them difficult to digest by some students (Engineers in particular). To determine the best approach toward learning data compression technique, this paper first study the learning preference of engineering students who tend to have strong active, sensing, visual and sequential learning preferences, the paper also study the advantage that mobility of learning have experienced; Learning at the point of interest, efficiency, connection, and many more. A survey is carried out with some reasonable number of students, through random sampling to see whether considering the learning preference and advantages in mobility of learning will give a promising improvement over the traditional way of learning. Evidence from data analysis using Ms-Excel as a point of concern for error-free findings shows that there is significance different in the students after using learning content provided on smart phone, also the result of the findings presented in, bar charts and pie charts interpret that mobile learning has to be promising feature of learning.

Keywords: data analysis, compression techniques, learning content, traditional learning approach

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Kirill D. Kapustin, Mikhail B. Krasilnikov, Anatoly A. Kudryavtsev

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Physical formation mechanisms of differential electron fluxes is high pressure positive column gas discharge are discussed. It is shown that the spatial differential fluxes of the electrons are directed both inward and outward depending on the energy relaxation law. In some cases the direction of energy differential flux at intermediate energies (5-10eV) in whole volume, except region near the wall, appeared to be down directed, so electron in this region dissipate more energy than gain from axial electric field. Paradoxical behaviour of electron flux in spatial-energy space is presented.

Keywords: plasma kinetics, electron distribution function, excitation and radiation rates, local and nonlocal EDF

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

Procedia PDF Downloads 443