Search results for: mathematical thinking

Authors: M. Tan, N. N. Wan, N. Ramli, N. H. Hassan

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Car drivers would always like to have custom wheel on their car for two reasons; to improve their car's aesthetic beauty and to improve their car handling. As the size of the rims or wheels played an important role in influencing the way of car handles around turns, this paper aims to present the optimality of rim size that drivers should have known while changing their rim. There are three factors that drivers should have considered while changing their rim: rim size, its weight and material of which they are made. Using mathematical analysis, this paper will focus on only one factor, which is rim size. Factors that are considered in calculating the optimum rim size are the vehicle rim radius, tire height and weight, and aspect ratio. This paper has found that there are limitations in percentage change in rim size from the original tire size. Failure to have the right offset size may cause problems in maneuvering the vehicle.

Keywords: mathematical analysis, optimum wheel size, percentage change, custom wheel

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Authors: R. Herscu-Kluska

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The rise of the flipped or inverted classroom meet the conceptual needs of our time. The evidence of increased student satisfaction and course grades improvement promoted the flipped learning approach. Due to the successful outcomes of the inverted classroom, the flipped learning became a pedagogy and educational rising strategy among all education sciences. The aim of this study is to analyze the effect of flipped classroom on higher order learning in chemistry courses since it has been suggested that in higher education courses, class time should focus on knowledge application. The results of this study indicate improving meta-cognitive thinking and learning skills. The students showed better ability to cope with higher order learning assignments during the actual class time, using inverted classroom strategy. These results suggest that flipped learning can be used as an effective pedagogy and educational strategy for developing higher order thinking skills, proved to contribute to building lifelong learning.

Keywords: chemistry education, flipped classroom, flipped learning, inverted classroom, science education

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models. The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces. The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations. In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: eddy current, finite element method, non destructive testing, numerical simulations

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Authors: Maha Ben Salem

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The transformative aspect of emerging adulthood brings about a development of self-processes, including changes in self-esteem and personal goals. Success in this life stage entails the emotional growth necessary to navigate the demands and challenges of college life. Understanding the concept of self-awareness within this particular age group sheds light on emerging adults’ internal world and the transformative aspect of their emotional growth. Uncovering the thoughts' processes that foster or hinder self-awareness is important to the understanding of how emerging adults learn to make themselves positive or negative. However, existing research in self-awareness has explored this phenomenon mostly using quantitative research methodology or through tying an individual’s level of self-awareness to specific actions or outcomes. Little is known about the process of how college students emerging adults notice and monitor their inner thoughts and emotions. Methodology and theoretical orientation: A grounded theory study using in-depth semi-structured interview was utilized. Nine interviews have been conducted. A constructionist framework was employed to generate a theory as for how self-awareness facilitates specific patterns of thinking in emerging adults. The choice of grounded theory emanates from a lack of knowledge regarding underlying thinking procedures and internal states that emerging adult college students navigate in an attempt to make meaning out of the new academic experience and life stage. Findings: Initial data analysis generated the following categories of the theory: (a) a non-judgmental perception of negative thinking and negative emotions that allow for a better understanding of the self; (b) negative state of mind is easy to overcome when it is accepted and acknowledged; (c) knowledge of the actual and desired self-generates an intentional decision to shift to a positive mindset. Preliminary findings indicate that college academic and social environment foster a new understanding of the self that yield a change in mindset and in self-knowledge.

Keywords: college environment, emergent adults, grounded theory, positive mindset, self-awareness

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: Joao Fialho

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The mathematical modelling of idiopathic scoliosis has been studied throughout the years. The models presented on those papers are based on the orthotic stabilization of the idiopathic scoliosis, which are based on a transversal force being applied to the human spine on a continuous form. When considering the ATT (Antalgic-Trak Technology) device, the existent models cannot be used, as the type of forces applied are no longer transversal nor applied in a continuous manner. In this device, vertical traction is applied. In this study we propose to model the idiopathic scoliosis, using the ATT (Antalgic-Trak Technology) device, and with the parameters obtained from the mathematical modeling, set up a case-by-case individualized therapy plan, for each patient.

Keywords: idiopathic scoliosis, mathematical modelling, human spine, Antalgic-Trak technology

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Authors: Meryem Kanzari, Rabah Boukhanouf, Hatem G. Ibrahim

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Indirect Evaporative Cooling process has the advantage of supplying cool air at constant moisture content. However, such system can only supply air at temperatures above wet bulb temperature. This paper presents a mathematical model for a sub-wet bulb temperature indirect evaporative cooling arrangement that can overcome this limitation and supply cool air at temperatures approaching dew point and without increasing its moisture content. In addition, the use of porous ceramics as wet media materials offers the advantage of integration into building elements. Results of the computer show that the proposed design is capable of cooling air to temperatures lower than the ambient wet bulb temperature and achieving wet bulb effectiveness of about 1.17.

Keywords: indirect evaporative cooling, porous ceramic, sub-wet bulb temperature, mathematical modeling

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Authors: Endrik Mifta Shaiful, Firman Riyudha

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Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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Authors: Sulafah Basahel

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Nowadays, Higher Education Institutions (HEIs) around the world are attempting to utilize Information and Communication Technologies (ICTs) to enhance learning process and strategies of knowledge delivery for students through Distance Education (DE) system. Stakeholders in DE system face a complex situation of different ill-defined and related issues that influence decision making process. In this study system thinking as a body of knowledge is used to explore the emergent properties that produced from these connections between issues and could have either positive or negative outcomes for the DE development. Checkland Soft System Methodology (SSM) - Mode 2 is employed in a cultural context of Saudi Arabia for more knowledge acquisition purposes among multiple stakeholders in DE rather than solving problems to achieve an overall development of DE system. This paper will discuss some political, cultural issues and connections between them that impact on effectiveness of stakeholders’ activities and relations. This study will significantly contribute to both system thinking and education fields by leading decision makers in DE to reconsider future plans, strategies and right actions for more successful educational practices.

Keywords: distance education, higher education institutions, ill-defined issues, soft system methodology-Mode 2

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Authors: Diane Prorak, Perri Moreno

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University students may have been born in the digital age, but they need to be taught the critical thinking skills to detect misinformation and social media manipulation online. In recent years, librarians have been active in designing instructional methods to help students learn information evaluation skills. At the University of Idaho Library (USA), librarians have developed new teaching methods for these skills. Last academic year, when classes were taught via Zoom, librarians taught these skills to an online session of each first-year rhetoric and composition course. In the Zoom sessions, students were placed in breakout groups where they practiced using an evaluation method known as lateral reading. Online collaborative software was used to give each group an evaluative task and break the task into steps. Groups reported back to the full class. Students learned to look at an information source, then search outside the source to find information about the organization, publisher or author, before evaluating the source itself. Class level pre-and post-test comparison results showed students learned better techniques for evaluation than they knew before instruction.

Keywords: critical thinking, information evaluation, information literacy instruction, lateral reading.

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Authors: Iryna Shevchenko

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The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

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Authors: Nirupma Bhatti

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This empirical study was aimed to compare the effectiveness of Computer Assisted Instruction (CAI) and Conventional Method (CM) in attaining and retaining mathematical concepts. Instructional and measuring tools were developed for five units of Matrix Algebra, two of Calculus and five of Numerical Analysis. Reliability and validity of these tools were also examined in pilot study. Ninety undergraduates participated in this study. Pre-test – post-test equivalent – groups research design was used. SPSS v.16 was used for data analysis. Findings supported CAI as better mode of instruction for attainment and retention of basic mathematical concepts. Administrators should motivate faculty members to develop Computer Assisted Instructional Material (CAIM) in mathematics for higher education.

Keywords: attainment, CAI, CAIM, conventional method, retention

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Authors: Miguel Mariano Rivera Galvan

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The purpose of this research was to create a digital tool by which users can obtain an immediate and accurate solution of the angular characteristics of an irregular quadrilateral. The development of this project arose because of the frequent absence of a polygon’s geometric information in land ownership accreditation documents. The researcher created a mathematical model using a linear approximation iterative method, employing various disciplines and techniques including trigonometry, geometry, algebra, and topography. This mathematical model uses as input data the surface of the quadrilateral, as well as the length of its sides, to obtain its interior angles and make possible its representation in a coordinate system. The results are as accurate and reliable as the user requires, offering the possibility of using this tool as a support to develop future engineering and architecture projects quickly and reliably.

Keywords: digital tool, geometry, mathematical model, quadrilateral, solution

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Authors: E. Koyuncu

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The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling

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Authors: Saleit Ron

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The Mitar program was established to drive a shift in middle school mathematics education, emphasizing the connection of math to real-life situations, exploring mathematical modeling and literacy, and integrating social and emotional learning (SEL) components for enhanced excellence. The program envisions math coordinators as catalysts for change, equipping them to create educational materials, strengthen leadership skills, and develop SEL competencies within coordinator communities. These skills are then employed to lead transformative efforts within their respective schools. The program engaged 90 participants across six math coordinator communities during 2022-2023, involving 30-60 hours of annual learning. The process includes formative and summative evaluations through questionnaires and interviews, revealing participants' high contentment and successful integration of acquired skills into their schools. Reflections from participants highlighted the need for enhanced change leadership processes, often seeking more personalized mentoring to navigate challenges effectively.

Keywords: math coordinators, mathematical literacy, mathematical modeling, SEL competencies

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Authors: Sofya Komarova, Frashia Ndungu, Alessia Gavazzoli, Roberta Mineo

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Modern society requires people to be flexible and to develop innovative solutions to unexpected situations. Creativity refers to the “interaction among aptitude, process, and the environment by which an individual or group produces a perceptible product that is both novel and useful as defined within a social context”. It allows humans to produce novel ideas, generate new solutions, and express themselves uniquely. Only a few scientific studies have examined group dynamics' influence on individuals' creativity. There exist some gaps in the research on creative thinking, such as the fact that collaborative effort frequently results in the enhanced production of new information and knowledge. Therefore, it is critical to evaluate creativity via social settings. The study aimed at exploring the group dynamics of young adults in small group settings and the influence of these dynamics on their creativity. The study included 30 participants aged 20 to 25 who were attending university after completing a bachelor's degree. The participants were divided into groups of three, in gender homogenous and heterogeneous groups. The groups’ creative task was tied to the Lego mosaic created for the Scintillae laboratory at the Reggio Children Foundation. Group dynamics were operationalized into patterns of behaviors classified into three major categories: 1) Social Interactions, 2) Play, and 3) Distraction. Data were collected through audio and video recording and observation. The qualitative data were converted into quantitative data using the observational coding system; then, they were analyzed, revealing correlations between behaviors using median points and averages. For each participant and group, the percentages of represented behavior signals were computed. The findings revealed a link between social interaction, creative thinking, and creative activities. Other findings revealed that the more intense the social interaction, the lower the amount of creativity demonstrated. This study bridges the research gap between group dynamics and creativity. The approach calls for further research on the relationship between creativity and social interaction.

Keywords: group dynamics, creative thinking, creative action, social interactions, group play

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Authors: M. C. A. Leite, B. Chen-Charpentier, F. Agusto

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A long-term goal of sustainable forest management is a relatively stable source of wood and a stable forest age-class structure has become the goal of many forest management practices. In the absence of disturbances, this forest management goal could easily be achieved. However, in the face of recurring insect outbreaks and other disruptive processes forest planning becomes more difficult, requiring knowledge of the effects on the forest of a wide variety of environmental factors (e.g., habitat heterogeneity, fire size and frequency, harvesting, insect outbreaks, and age distributions). The association between distinct forest disturbances and the potential effect on forest dynamics is a complex matter, particularly when evaluated over time and at large scale, and is not well understood. However, gaining knowledge in this area is crucial for a sustainable forest management. Mathematical modeling is a tool that can be used to broader the understanding in this area. In this talk we will introduce mathematical models formulation incorporating the effect of insect outbreaks either as a single disturbance in the forest population dynamics or coupled with other disturbances: either wildfire or harvesting. The results and ecological insights will be discussed.

Keywords: age-structured forest population, disturbances interaction, harvesting insects outbreak dynamics, mathematical modeling

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Authors: Małgorzata Osowiecka

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Negative emotions are rather seen as creativity inhibitor. On the other hand, it is worth noting that negative emotions may be good for our functioning. Negative emotions enhance cognitive resources and improve evaluative processes. Moreover maintaining a negative emotional state allow for cognitive reinterpretation of the emotional stimuli, what is good for our creativity, especially cognitive flexibility. Writing a diary or writing about difficult emotional experiences in general can be the way to not only improve psychical health, but also – enhance creative behaviors. Thanks to translating difficult emotions to the verbal level and giving them ‘a name’ or ‘a label’, we can get easier access to both emotional content of an experience and to the semantic content, without the need of speaking out loud. Expressive writing improves academic results and the efficiency of working memory. The classical method of writing about emotions consists in a long-term process of describing negative experiences. Present research demonstrate the efficiency of this process over a shorter period of time - one writing session, on school children sample. Participants performed writing task. Writing task had two different topics: emotions connected with their negative emotions (expressive writing) and content not connected with negative emotional state (writing about one’s typical day). Creativity was measured by Guilford’s Alternative Uses Task. Results have shown that writing about negative emotions results in the higher level of divergent thinking in all three parameters: fluency, flexibility and originality. After the writing task mood of expressive writing participants remained negative more than the mood of the controls. Taking an expressive action after a difficult emotional experience can support functioning, which can be observed in enhancement of divergent thinking. Writing about emotions connected with negative experience makes one more creative, than writing about something unrelated with difficult emotional moments. Research has shown that young people should not demonize negative emotions. Sometimes, properly applied, negative emotions can be the basis of creation. Preparation was supported by a The Young Scientist University grant titled ‘Dynamics of emotions in the creative process’ from The Polish Ministry of Science and Higher Education.

Keywords: creativity, divergent thinking, emotions, expressive writing

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Authors: Nadezda Kobzeva

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Under the current trend of globalization, economic and technological dynamics information and the means by which it is delivered and renewed becomes out-of-date rapidly. Thus, educational systems as well as higher education are being seriously tested. New strategies’ developing that is supported by Information and Communication Technology is urgently required. The essential educators’ mission is to meet the demands of the future by preparing our young learners with proper knowledge, skills and innovation capabilities necessary to advance our competitiveness globally. In response to the modern society and future demands, the oldest Siberian Tomsk Polytechnic University has wisely proposed several initiatives to promote the integration of Information and Communication Technology (ICT) in education, and increase the competitiveness of graduates by emphasizing inquiry-based learning, higher order thinking and problem solving. This paper gives a brief overview of how Web Quest as ICT device is being used for language teaching and describes its use advantages for teaching English as a Foreign Language (EFL), in particular business writing skills. This study proposes to use Web Quest to promote higher order thinking and ICT integration in the process of engineers training in Tomsk Polytechnic University, Russia.

Keywords: web quest, web quest in pedagogy, resume (CVs) and cover letter writing skills, ICT integration

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Authors: Dominic Roulx

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Many scholars have in the past decade emphasized the relevance of Adorno’s criticism of the rationalized domination of nature (Naturbeherrschung) for thinking the environmental crisis. Beyond the intersubjective critical models of thinkers such as Habermas and Honneth, Adorno’s critical theory has the benefit, according to them, of disclosing the entwinement of social and natural domination in a critically productive way. The author will be arguing in this paper that Adorno’s model of critical theory displays a theoretical framework that is both original and relevant for thinking the ins and outs of the currentenvironmental crisis. To do so, he first construe Adorno’s understanding of the historical domination of nature and argue that Adorno’s method for its criticizing is immanent critique. He puts emphasis on how his understanding of the domination of nature implicitly implies an account of thedialectical relationship between reason and nature. In doing so, he presents a naturalistic understanding of his idea of the primacy of the object. Second, regarding Adorno’s concept of nature, he discusses what he sees as the shortcomings of many commentators’ understanding of the concept of nature in Adorno. He contends that they tend to fall short of Adorno’s concept of nature in failing to make sense of its thoroughly negative signification, thereby falling into an uncritical and fetichized comprehension of “nature. Third, he discusses the prospect for a possible “reconciliation” (Versöhnung) of nature with society. Highlighting how the domination of nature proves to produce the necessary conditions for its own overcoming, he contends that reconciliation with nature relies mainly on the subject’s capacity for critical self-reflection.

Keywords: german philosophy, adorno, nature, environmental crisis

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Authors: Nurcihan Kiris

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Restricted sleep is common in young adults and adolescents. The results of a few objective studies of sleep deprivation on cognitive performance were not clarified. In particular, the effect of sleep deprivation on the cognitive functions associated with frontal lobe such as attention, executive functions, working memory is not well known. The aim of this study is to investigate the effect of partial sleep deprivation experimentally in adolescents on the cognitive tasks of frontal lobe including working memory, strategic thinking, simple attention, continuous attention, executive functions, and cognitive flexibility. Subjects of the study were recruited from voluntary students of Cukurova University. Eighteen adolescents underwent four consecutive nights of monitored sleep restriction (6–6.5 hr/night) and four nights of sleep extension (10–10.5 hr/night), in counterbalanced order, and separated by a washout period. Following each sleep period, cognitive performance was assessed, at a fixed morning time, using a computerized neuropsychological battery based on frontal lobe functions task, a timed test providing both accuracy and reaction time outcome measures. Only the spatial working memory performance of cognitive tasks was found to be statistically lower in a restricted sleep condition than the extended sleep condition. On the other hand, there was no significant difference in the performance of cognitive tasks evaluating simple attention, constant attention, executive functions, and cognitive flexibility. It is thought that especially the spatial working memory and strategic thinking skills of adolescents may be susceptible to sleep deprivation. On the other hand, adolescents are predicted to be optimally successful in ideal sleep conditions, especially in the circumstances requiring for the short term storage of visual information, processing of stored information, and strategic thinking. The findings of this study may also be associated with possible negative functional effects on the processing of academic social and emotional inputs in adolescents for partial sleep deprivation. Acknowledgment: This research was supported by Cukurova University Scientific Research Projects Unit.

Keywords: attention, cognitive functions, sleep deprivation, working memory

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Authors: Raluca Ionela Maxim

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Designing a gender responsive Science, Technology, Engineering and Mathematics (STEM) mobile game based learning solution (mGBL) is a challenge in terms of content, gamification level and equal engagement of girls and boys. The goal of this case study was to research and create a high-fidelity prototype design of a mobile game that contains role-models as avatars that guide and expose girls and boys to STEM learning content. For this research purpose it was applied the methodology of design sprint with five-phase process that combines design thinking principles. The technique of this methodology comprises smart interviews with STEM experts, mind-map creation, sketching, prototyping and usability testing of the interactive prototype of the gender responsive STEM mGBL. The results have shown that the effect of the avatar/role model had a positive impact. Therefore, by exposing students (boys and girls) to STEM role models in an mGBL tool is helpful for the decreasing of the gender inequalities in STEM fields.

Keywords: design thinking, design sprint, gender-responsive STEM education, mobile game based learning, role-models

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Authors: Yuan-Jye Tseng, Shin-Han Lin

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In this research, a mathematical model for integrated evaluation of green design and green manufacturing processes is presented. To design a product, there can be alternative options to design the detailed components to fulfill the same product requirement. In the design alternative cases, the components of the product can be designed with different materials and detailed specifications. If several design alternative cases are proposed, the different materials and specifications can affect the manufacturing processes. In this paper, a new concept for integrating green design and green manufacturing processes is presented. A green design can be determined based the manufacturing processes of the designed product by evaluating the green criteria including energy usage and environmental impact, in addition to the traditional criteria of manufacturing cost. With this concept, a mathematical model is developed to find the green design and the associated green manufacturing processes. In the mathematical model, the cost items include material cost, manufacturing cost, and green related cost. The green related cost items include energy cost and environmental cost. The objective is to find the decisions of green design and green manufacturing processes to achieve the minimized total cost. In practical applications, the decision-making can be made to select a good green design case and its green manufacturing processes. In this presentation, an example product is illustrated. It shows that the model is practical and useful for integrated evaluation of green design and green manufacturing processes.

Keywords: supply chain management, green supply chain, green design, green manufacturing, mathematical model

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Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

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Authors: Nilson Barbieri, Bruno Matos Martins, Gabriel de Sant'Anna Vitor Barbieri

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In more complex systems, such as automotive gearbox, a rigorous treatment of the data is necessary because there are several moving parts (gears, bearings, shafts, etc.), and in this way, there are several possible sources of errors and also noise. The basic objective of this work is the detection of damage in automotive gearbox. The detection methods used are the wavelet method, the bispectrum; advanced filtering techniques (selective filtering) of vibrational signals and mathematical morphology. Gearbox vibration tests were performed (gearboxes in good condition and with defects) of a production line of a large vehicle assembler. The vibration signals are obtained using five accelerometers in different positions of the sample. The results obtained using the kurtosis, bispectrum, wavelet and mathematical morphology showed that it is possible to identify the existence of defects in automotive gearboxes.

Keywords: automotive gearbox, mathematical morphology, wavelet, bispectrum

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Authors: Mechlouch Ridha Fethi

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This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

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Authors: Emily S. M. Chow

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The word ‘utopia’ was coined by Thomas More in Utopia (1516). Its Greek roots ‘ou’ means ‘not’ and ‘topos’ means ‘place.’ In other words, it literally refers to ‘no-place.’ However, the possibility of having an alternative and better future society has always been appealing. In fact, at the core of every utopianism is the search for a future alternative state with the anticipation of a better life. Nonetheless, the practicalities of such ideas have never ceased to be questioned. At times, building a utopia presents itself as a divisive act. In addition to the violence that must be employed to sweep away the old regime in order to make space for the new, all utopias carry within them the potential for bringing catastrophic consequences to human life. After all, every utopia seeks to remodel the individual in a very particular way for the benefit of the masses. In this sense, utopian thinking has the potential both to create and destroy the future. While writing during a traumatic transitional period in Zimbabwe’s history, Dambudzo Marechera witnessed an age of upheavals in which different parties battled for power over Zimbabwe. Being aware of the fact that all institutionalized narratives, be they originated from the governance of the UK, Ian Smith’s white minority regime or Zimbabwe’s revolutionary parties, revealed themselves to be nothing more than fiction, Marechera realized the impossibility of determining reality absolutely. As such, this thesis concerns the writing of the Zimbabwean maverick, Dambudzo Marechera. It argues that Marechera writes a unique vision of utopia. In short, for Marechera utopia is not a static entity but a moment of perpetual change. He rethinks utopia in the sense that he phrases it as an event that ceaselessly contests institutionalized and naturalized narratives of a post-colonial self and its relationship to society. Marechera writes towards a vision of an alternative future of the country. Yet, it is a vision that does not constitute a fully rounded sense of utopia. Being cautious about the world and the operation of power upon the people, rather than imposing his own utopian ideals, Marechera chooses to instead peeling away the narrative constitution of the self in relation to society in order to turn towards a truly radical utopian thinking that empowers the individual.

Keywords: African literature, Marechera, post-colonial literature, utopian studies

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Chen-Ya Juan

Abstract:

Problem-Based Learning uses vague questions to guide student thinking and enhance their self-learning and collaboration. Most teachers implement PBL in a physical classroom, where teachers can monitor and evaluate students’ learning progress and guide them to search resources for answers. However, the prevalence of the Covid-19 in the world had changed from physical teaching to distance teaching. This instruction used many cases and applied Problem-Based Learning combined on the distance teaching via the internet for college students. This study involved an experimental group with PBL and a control group without PBL. The teacher divided all students in PBL class into eight groups, and 7~8 students in each group. The teacher assigned different cases for each group of the PBL class. Three stages of instruction were developed, including background knowledge of Learning, case analysis, and solving problems for each case. This study used a quantitative research method, a two-sample t-test, to find a significant difference in groups with PBL and without PBL. Findings indicated that PBL incased the average score of special education knowledge. The average score was improved by 20.46% in the PBL group and 15.4% without PBL. Results didn’t show significant differences (0.589>0.05) in special education professional knowledge. However, the feedback of the PBL students implied learning more about the application, problem-solving skills, and critical thinking. PBL students were more likely to apply professional knowledge on the actual case, find questions, resources, and answers. Most of them understood the importance of collaboration, working as a team, and communicating with other team members. The suggestions of this study included that (a) different web-based teaching instruments influenced student’s Learning; (b) it is difficult to monitor online PBL progress; (c) online PBL should be implemented flexible and multi-oriented; (d) although PBL did not show a significant difference on the group with PBL and without PBL, it did increase student’s problem-solving skills and critical thinking.

Keywords: problem-based learning, college students, distance learning, case analysis, problem-solving

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