Search results for: mathematical abilities

Authors: Jose Francisco Ferreira Ribeiro, Alexandre Bevilacqua Leoneti, Andre Lucirton Costa

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This paper presents a mathematical model in binary variables 0/1 to make the assignment of surgical procedures to the operating rooms in a hospital. The proposed mathematical model is based on the generalized assignment problem, which maximizes the sum of preferences for the use of the operating rooms by doctors, respecting the time available in each room. The corresponding program was written in Visual Basic of Microsoft Excel, and tested to schedule surgeries at St. Lydia Hospital in Ribeirao Preto, Brazil.

Keywords: generalized assignment problem, logistics, optimization, scheduling

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Authors: Antonella Poce, Deborah Seid Howes, Maria Rosaria Re, Mara Valente

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The Creative Industries education contexts, Museum Education in particular, generally presents a low emphasis on the use of new digital technologies, digital abilities and transversal skills development. The spread of the Covid-19 pandemic has underlined the importance of these abilities and skills in cultural heritage education contexts: gaining digital skills, museum professionals will improve their career opportunities with access to new distribution markets through internet access and e-commerce, new entrepreneurial tools, or adding new forms of digital expression to their work. However, the use of web, mobile, social, and analytical tools is becoming more and more essential in the Heritage field, and museums, in particular, to face the challenges posed by the current worldwide health emergency. Recent studies highlight the need for stronger partnerships between the cultural and creative sectors, social partners and education and training providers in order to provide these sectors with the combination of skills needed for creative entrepreneurship in a rapidly changing environment. Considering the above conditions, the paper presents different examples of digital learning experiences carried out in Italian and USA contexts with the aim of promoting digital skills in museum professionals. In particular, a quali-quantitative research study has been conducted on two international Postgraduate courses, “Advanced Studies in Museum Education” (2 years) and “Museum Education” (1 year), in order to identify the educational effectiveness of the online learning strategies used (e.g., OBL, Digital Storytelling, peer evaluation) for the development of digital skills and the acquisition of specific content. More than 50 museum professionals participating in the mentioned educational pathways took part in the learning activity, providing evaluation data useful for research purposes.

Keywords: digital skills, museum professionals, technology, education

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: Kayijuka Idrissa

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This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.

Keywords: statistical methods, traffic flow, Poisson distribution, car moving technics

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Authors: Misho Matsankov, Stoyan Petrov

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The paper presents the methodology and the obtained mathematical models for determining the value of the grounding resistance of a disconnected conductor in a three-phase power line, for which the contact voltage is safe, by taking into account the potentials, induced by the non-disconnected phase conductors. The mathematical models have been obtained by implementing the experimental design techniques.

Keywords: contact voltage, experimental design, induced voltage, safety

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Authors: David Glassmeyer

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Quantitative reasoning is necessary to robustly understand mathematical concepts ranging from elementary to university levels. Quantitative reasoning involves identifying and representing quantities and the relationships between these quantities. Without reasoning quantitatively, students often resort to memorizing formulas and procedures, which have negative impacts when they encounter mathematical topics in the future. This study investigated how high school students’ quantitative reasoning could be fostered within a unit on arc measure and angle relationships. Arc measure, or the measure of a central angle that cuts off a portion of a circle’s circumference, is often confused with arclength. In this study, the researcher redesigned an activity to clearly distinguish arc measure and arc length by using a quantitative reasoning framework. Data were collected from high school students to determine if this approach impacted their understanding of these concepts. Initial data indicates the approach was successful in supporting students’ quantitative reasoning of these topics. Implications for the work are that teachers themselves may also benefit from considering mathematical definitions from a quantitative reasoning framework and can use this activity in their own classrooms.

Keywords: arc length, arc measure, quantitative reasoning, student content knowledge

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Authors: A. Giniatoulline

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We consider the internal oscillations of the ocean which are caused by the gravity force and the Coriolis force, for different models with changeable density, heat transfer, and salinity. Traditionally, the mathematical description of the resonance effect is related to the growing amplitude as a result of input vibrations. We offer a different approach: the study of the relation between the spectrum of the internal oscillations and the properties of the limiting amplitude of the solution for the harmonic input vibrations of the external forces. Using the results of the spectral theory of self-adjoint operators in Hilbert functional spaces, we prove that there exists an explicit relation between the localization of the frequency of the external input vibrations with respect to the essential spectrum of proper inner oscillations and the non-uniqueness of the limiting amplitude. The results may find their application in various problems concerning mathematical modeling of turbulent flows in the ocean.

Keywords: computational fluid dynamics, essential spectrum, limiting amplitude, rotating fluid, spectral theory, stratified fluid, the uniqueness of solutions of PDE equations

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Michael Luc Andre, Célia Maintenant

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Theory of mind is a milestone in child development which allows children to understand that others could have different mental states than theirs. Understanding the developmental stages of theory of mind in children leaded researchers on two Connected research problems. In one hand, the link between executive function and theory of mind, and on the other hand, the relationship of theory of mind and syntax processing. These two lines of research involved a great literature, full of important results, despite certain level of disagreement between researchers. For a long time, these two research perspectives continue to grow up separately despite research conclusion suggesting that the three variables should implicate same developmental period. Indeed, our goal was to study the relation between theory of mind, executive function, and language via a unique research question. It supposed that between executive function and language, one of the two variables could play a critical role in the relationship between theory of mind and the other variable. Thus, 112 children aged between three and six years old were recruited for completing a receptive and an expressive vocabulary task, a syntax understanding task, a theory of mind task, and three executive function tasks (inhibition, cognitive flexibility and working memory). The results showed significant correlations between performance on theory of mind task and performance on executive function domain tasks, except for cognitive flexibility task. We also found significant correlations between success on theory of mind task and performance in all language tasks. Multiple regression analysis justified only syntax and general abilities of language as possible predictors of theory of mind performance in our preschool age children sample. The results were discussed in the perspective of a great role of language abilities in theory of mind development. We also discussed possible reasons that could explain the non-significance of executive domains in predicting theory of mind performance, and the meaning of our results for the literature.

Keywords: child development, executive function, general language, syntax, theory of mind

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Authors: Carlos Alberto Carvalho Castro, Nancy Del Ducca Barbedo, Edmilsom Otoni Côrrea

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With increase the production oil and lines transmission gases that are in ample expansion, the industries medium and great transport they had to adapt itself to supply the demand manufacture in this fabrication segment. In this context, two welding processes have been more extensively used: the GMAW (Gas Metal Arc Welding) and the FCAW (Flux Cored Arc Welding). In this work, welds using these processes were carried out in flat position on ASTM A-36 carbon steel plates in order to make a comparative evaluation between them concerning to mechanical and metallurgical properties. A statistical tool based on technical analysis and design of experiments, DOE, from the Minitab software was adopted. For these analyses, the voltage, current, and welding speed, in both processes, were varied. As a result, it was observed that the welds in both processes have different characteristics in relation to the metallurgical properties and performance, but they present good weldability, satisfactory mechanical strength e developed mathematical models.

Keywords: Flux Cored Arc Welding (FCAW), Gas Metal Arc Welding (GMAW), Design of Experiments (DOE), mathematical models

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Authors: Hanifeh Imanian, Morteza Kolahdoozan

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The purpose of this study is to present a mathematical phrase for calculating the dispersion rate of spilled oil in water column under non-breaking waves. In this regard, a multiphase numerical model is applied for which waves and oil phase were computed concurrently, and accuracy of its hydraulic calculations have been proven. More than 200 various scenarios of oil spilling in wave waters were simulated using the multiphase numerical model and its outcome were collected in a database. The recorded results were investigated to identify the major parameters affected vertical oil dispersion and finally 6 parameters were identified as main independent factors. Furthermore, some statistical tests were conducted to identify any relationship between the dependent variable (dispersed oil mass in the water column) and independent variables (water wave specifications containing height, length and wave period and spilled oil characteristics including density, viscosity and spilled oil mass). Finally, a mathematical-statistical relationship is proposed to predict dispersed oil in marine waters. To verify the proposed relationship, a laboratory example available in the literature was selected. Oil mass rate penetrated in water body computed by statistical regression was in accordance with experimental data was predicted. On this occasion, it was necessary to verify the proposed mathematical phrase. In a selected laboratory case available in the literature, mass oil rate penetrated in water body computed by suggested regression. Results showed good agreement with experimental data. The validated mathematical-statistical phrase is a useful tool for oil dispersion prediction in oil spill events in marine areas.

Keywords: dispersion, marine environment, mathematical-statistical relationship, oil spill

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

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A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: Xavi Vilajosana Guillen, Emilio José Pérez Salgado

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This document presents experimental results obtained in a realistic environment using an underwater LoRa link. It aims to analyze the behavior of electromagnetic waves underwater and determine this communication capability. With this it has been tried to empirically evaluate the results obtained in the mathematical model using a commercial device with low cost and low consumption that works at frequency 433Mhz. The mathematical results obtained for wireless communication at 433Mhz underwater indicate that a communication of up to 7.5 m is possible, however experimentally 8 m has been achieved.

Keywords: 433Mhz link, internet of things, LoRa link, underwater communication

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Authors: Christopher Thornton, Niina Kolehmainen, Kianoush Nazarpour

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Background: Accelerometers are widely used to measure physical activity behavior, including in children. The traditional method for processing acceleration data uses cut points, relying on calibration studies that relate the quantity of acceleration to energy expenditure. As these relationships do not generalise across diverse populations, they must be parametrised for each subpopulation, including different age groups, which is costly and makes studies across diverse populations difficult. A data-driven approach that allows physical activity intensity states to emerge from the data under study without relying on parameters derived from external populations offers a new perspective on this problem and potentially improved results. We evaluated the data-driven approach in a diverse population with a range of rapidly evolving physical and mental capabilities, namely very young children (9-38 months old), where this new approach may be particularly appropriate. Methods: We applied an unsupervised machine learning approach (a hidden semi-Markov model - HSMM) to segment and cluster the accelerometer data recorded from 275 children with a diverse range of physical and cognitive abilities. The HSMM was configured to identify a maximum of six physical activity intensity states and the output of the model was the time spent by each child in each of the states. For comparison, we also processed the accelerometer data using published cut points with available thresholds for the population. This provided us with time estimates for each child’s sedentary (SED), light physical activity (LPA), and moderate-to-vigorous physical activity (MVPA). Data on the children’s physical and cognitive abilities were collected using the Paediatric Evaluation of Disability Inventory (PEDI-CAT). Results: The HSMM identified two inactive states (INS, comparable to SED), two lightly active long duration states (LAS, comparable to LPA), and two short-duration high-intensity states (HIS, comparable to MVPA). Overall, the children spent on average 237/392 minutes per day in INS/SED, 211/129 minutes per day in LAS/LPA, and 178/168 minutes in HIS/MVPA. We found that INS overlapped with 53% of SED, LAS overlapped with 37% of LPA and HIS overlapped with 60% of MVPA. We also looked at the correlation between the time spent by a child in either HIS or MVPA and their physical and cognitive abilities. We found that HIS was more strongly correlated with physical mobility (R²HIS =0.5, R²MVPA= 0.28), cognitive ability (R²HIS =0.31, R²MVPA= 0.15), and age (R²HIS =0.15, R²MVPA= 0.09), indicating increased sensitivity to key attributes associated with a child’s mobility. Conclusion: An unsupervised machine learning technique can segment and cluster accelerometer data according to the intensity of movement at a given time. It provides a potentially more sensitive, appropriate, and cost-effective approach to analysing physical activity behavior in diverse populations, compared to the current cut points approach. This, in turn, supports research that is more inclusive across diverse populations.

Keywords: physical activity, machine learning, under 5s, disability, accelerometer

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Authors: Hui-Yi Wang, Shu-Mei Chen, Mei-Fang Liu

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Background and purpose: Providing clinical experience in medical education is an important discipline method where students can gradually apply their academic knowledge to clinical situations. The purpose of this study was to establish self-assessment questionnaires for students to assess their learning outcomes for two fields of physical therapy, orthopedic physical therapy, and pediatric physical therapy, in a clinical fieldwork course. Methods: The questionnaires were developed based on the core competence dimensions of the course. The content validity of the questionnaires was evaluated and established by expert meetings. Among the third-year undergraduate students who took the clinical fieldwork course, there were 49 students participated in this study. Teachers arranged for the students to study two professional fields, and each professional field conducted a three-week clinical lesson. The students filled out the self-assessment questionnaires before and after each three-week lesson. Results: The self-assessment questionnaires were established by expert meetings that there were six core competency dimensions in each of the two fields, with 20 and 21 item-questions, respectively. After each three-week clinical fieldwork, the self-rating scores in each core competency dimension were higher when compared to those before the course, indicating having better clinical abilities after the lessons. The best self-rating scores were the dimension of attitude and humanistic literacy, and the two lower scores were the dimensions of professional knowledge and skills and problem-solving critical thinking. Conclusions: This study developed questionnaires for clinical fieldwork courses to reflect students' learning outcomes, including the performance of professional knowledge, practice skills, and professional attitudes. The use of self-assessment of learning performance can help students build up their reflective competencies. Teachers can guide students to pay attention to the performance of abilities in each core dimension to enhance the effectiveness of learning through self-reflection and improvement.

Keywords: physical therapy, clinical fieldwork course, learning outcomes assessment, medical education, self-reflection ability

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: Abdelkhalek Bakkari

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Image segmentation is a critical step in image processing and pattern recognition. In this paper, we proposed a new robust automatic image classification based on a dynamic fuzzy c-means algorithm and mathematical morphology. The proposed segmentation algorithm (DFCM_MM) has been applied to MR perfusion images. The obtained results show the validity and robustness of the proposed approach.

Keywords: segmentation, classification, dynamic, fuzzy c-means, MR image

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Authors: Divya Palaniappan

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Early Childhood assessment tools must measure the quality and the appropriateness of a curriculum with respect to culture and age of the children. Preschool assessment tools lack psychometric properties and were developed to measure only few areas of development such as specific skills in music, art and adaptive behavior. Existing preschool assessment tools in India are predominantly informal and are fraught with judgmental bias of observers. The World of Discovery TM curriculum focuses on accelerating the physical, cognitive, language, social and emotional development of pre-schoolers in India through various activities. The curriculum caters to every child irrespective of their dominant intelligence as per Gardner’s Theory of Multiple Intelligence which concluded "even students as young as four years old present quite distinctive sets and configurations of intelligences". The curriculum introduces a new theme every week where, concepts are explained through various activities so that children with different dominant intelligences could understand it. For example: The ‘Insects’ theme is explained through rhymes, craft and counting corner, and hence children with one of these dominant intelligences: Musical, bodily-kinesthetic and logical-mathematical could grasp the concept. The child’s progress is evaluated using an assessment tool that measures a cluster of inter-dependent developmental areas: physical, cognitive, language, social and emotional development, which for the first time renders a multi-domain approach. The assessment tool is a 5-point rating scale that measures these Developmental aspects: Cognitive, Language, Physical, Social and Emotional. Each activity strengthens one or more of the developmental aspects. During cognitive corner, the child’s perceptual reasoning, pre-math abilities, hand-eye co-ordination and fine motor skills could be observed and evaluated. The tool differs from traditional assessment methodologies by providing a framework that allows teachers to assess a child’s continuous development with respect to specific activities in real time objectively. A pilot study of the tool was done with a sample data of 100 children in the age group 2.5 to 3.5 years. The data was collected over a period of 3 months across 10 centers in Chennai, India, scored by the class teacher once a week. The teachers were trained by psychologists on age-appropriate developmental milestones to minimize observer’s bias. The norms were calculated from the mean and standard deviation of the observed data. The results indicated high internal consistency among parameters and that cognitive development improved with physical development. A significant positive relationship between physical and cognitive development has been observed among children in a study conducted by Sibley and Etnier. In Children, the ‘Comprehension’ ability was found to be greater than ‘Reasoning’ and pre-math abilities as indicated by the preoperational stage of Piaget’s theory of cognitive development. The average scores of various parameters obtained through the tool corroborates the psychological theories on child development, offering strong face validity. The study provides a comprehensive mechanism to assess a child’s development and differentiate high performers from the rest. Based on the average scores, the difficulty level of activities could be increased or decreased to nurture the development of pre-schoolers and also appropriate teaching methodologies could be devised.

Keywords: child development, early childhood assessment, early childhood curriculum, quantitative assessment of preschool curriculum

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Authors: Sarwat Jahan, Asker Rajin Rahman

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Management of offtake of any fluvial river is very sensitive in terms of long-term sustainability where the variation of water flow and sediment transport range are wide enough throughout a hydrological year. The Gorai River is a major distributary of the Ganges River in Bangladesh and is termed as a primary source of fresh water for the South-West part of the country. Every year, significant siltation of the Gorai offtake disconnects it from the Ganges during the dry season. As a result, the socio-economic and environmental condition of the downstream areas has been deteriorating for a few decades. To improve the overall situation of the Gorai offtake and its dependent areas, a study has been conducted by the Institute of Water Modelling, Bangladesh, in 2022. Using the mathematical morphological modeling tool MIKE 21C of DHI Water & Environment, Denmark, simulated results revealed the need for dredging/river training structures for offtake management at the Gorai offtake to ensure significant dry season flow towards the downstream. The dry season flow is found to increase significantly with the proposed river interventions, which also improves the environmental conditions in terms of salinity of the South-West zone of the country. This paper summarizes the primary findings of the analyzed results of the developed mathematical model for improving the existing condition of the Gorai River.

Keywords: Gorai river, mathematical modelling, offtake, siltation, salinity

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.

Keywords: algebra, grade 7 math, math anxiety, math misconceptions

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Authors: Atara Shriki, Ilana Lavy

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Teaching for the first time an online course dealing with the history of mathematics, we were struggling with questions related to the design of a proper learning environment (LE). Thirteen high school mathematics teachers, M.Ed. students, attended the course. The teachers were engaged in independent reading of mathematical texts, a task that is recognized as complex due to the unique characteristics of such texts. In order to support the learning processes and develop skills that are essential for succeeding in learning online (e.g. self-regulated learning skills, meta-cognitive skills, reflective ability, and self-assessment skills), the LE comprised of three components aimed at “scaffolding” the learning: (1) An online "self-feedback" questionnaires that included drill-and-practice questions. Subsequent to responding the questions the online system provided a grade and the teachers were entitled to correct their answers; (2) Open-ended questions aimed at stimulating critical thinking about the mathematical contents; (3) Reflective questionnaires designed to assist the teachers in steering their learning. Using a mixed-method methodology, an inquiry study examined the learning processes, the learners' difficulties in reading the mathematical texts and on the unique contribution of each component of the LE to the ability of teachers to comprehend the mathematical contents, and support the development of their learning skills. The results indicate that the teachers found the online feedback as most helpful in developing self-regulated learning skills and ability to reflect on deficiencies in knowledge. Lacking previous experience in expressing opinion on mathematical ideas, the teachers had troubles in responding open-ended questions; however, they perceived this assignment as nurturing cognitive and meta-cognitive skills. The teachers also attested that the reflective questionnaires were useful for steering the learning. Although in general the teachers found the LE as supportive, most of them indicated the need to strengthen instructor-learners and learners-learners interactions. They suggested to generate an online forum to enable them receive direct feedback from the instructor, share ideas with other learners, and consult with them about solutions. Apparently, within online LE, supporting learning merely with respect to cognitive aspects is not sufficient. Leaners also need an emotional support and sense a social presence.

Keywords: cognitive and meta-cognitive skills, independent reading of mathematical texts, online learning environment, self-regulated learning skills

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Authors: A. A. Okafor, C. H. Achebe, J. L. Chukwuneke, C. G. Ozoegwu

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The performance of an engine whose basic design parameters are known can be predicted with the assistance of simulation programs into the less time, cost and near value of actual. This paper presents a comprehensive mathematical model of the performance parameters of four stroke spark ignition engine. The essence of this research work is to develop a mathematical model for the analysis of engine performance parameters of four stroke spark ignition engine before embarking on full scale construction, this will ensure that only optimal parameters are in the design and development of an engine and also allow to check and develop the design of the engine and it’s operation alternatives in an inexpensive way and less time, instead of using experimental method which requires costly research test beds. To achieve this, equations were derived which describe the performance parameters (sfc, thermal efficiency, mep and A/F). The equations were used to simulate and optimize the engine performance of the model for various engine speeds. The optimal values obtained for the developed bivariate mathematical models are: sfc is 0.2833kg/kwh, efficiency is 28.77% and a/f is 20.75.

Keywords: bivariate models, engine performance, injector engine, optimization, performance parameters, simulation, spark ignition

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Authors: Vangmayee V. Subban, Suzan Deelan. Pinto, Somashekara Haralakatta Shivananjappa, Shwetha Prabhu, Jayashree S. Bhat

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Introduction and Need: During early years of schooling, the instruction in the schools mainly focus on children’s word decoding abilities. However, the skilled readers should master all the components of reading such as word decoding, reading fluency and comprehension. Nevertheless, the relationship between each component during the process of learning to read is less clear. The studies conducted in alphabetical languages have mixed opinion on relative contribution of word decoding and reading fluency on reading comprehension. However, the scenarios in alphasyllabary languages are unexplored. Aim and Objectives: The aim of the study was to explore the role of word decoding, reading fluency on reading comprehension abilities in children learning to read Kannada between the age ranges of 5.6 to 8.6 years. Method: In this cross sectional study, a total of 60 typically developing children, 20 each from Grade I, Grade II, Grade III maintaining equal gender ratio between the age range of 5.6 to 6.6 years, 6.7 to 7.6 years and 7.7 to 8.6 years respectively were selected from Kannada medium schools. The reading fluency and reading comprehension abilities of the children were assessed using Grade level passages selected from the Kannada text book of children core curriculum. All the passages consist of five questions to assess reading comprehension. The pseudoword decoding skills were assessed using 40 pseudowords with varying syllable length and their Akshara composition. Pseudowords are formed by interchanging the syllables within the meaningful word while maintaining the phonotactic constraints of Kannada language. The assessment material was subjected to content validation and reliability measures before collecting the data on the study samples. The data were collected individually, and reading fluency was assessed for words correctly read per minute. Pseudoword decoding was scored for the accuracy of reading. Results: The descriptive statistics indicated that the mean pseudoword reading, reading comprehension, words accurately read per minute increased with the Grades. The performance of Grade III children found to be higher, Grade I lower and Grade II remained intermediate of Grade III and Grade I. The trend indicated that reading skills gradually improve with the Grades. Pearson’s correlation co-efficient showed moderate and highly significant (p=0.00) positive co-relation between the variables, indicating the interdependency of all the three components required for reading. The hierarchical regression analysis revealed 37% variance in reading comprehension was explained by pseudoword decoding and was highly significant. Subsequent entry of reading fluency measure, there was no significant change in R-square and was only change 3%. Therefore, pseudoword-decoding evolved as a single most significant predictor of reading comprehension during early Grades of reading acquisition. Conclusion: The present study concludes that the pseudoword decoding skills contribute significantly to reading comprehension than reading fluency during initial years of schooling in children learning to read Kannada language.

Keywords: alphasyllabary, pseudo-word decoding, reading comprehension, reading fluency

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Authors: Hau-Wei Lee, Yu-Chi Liu, Chien-Hung Liu

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A mathematical model is presented for a system that measures rotational errors in a shaft using a ball lens. The geometric optical characteristics of the ball lens mounted on the shaft allows the measurement of rotation axis errors in both the radial and axial directions. The equipment used includes two quadrant detectors (QD), two laser diodes and a ball lens that is mounted on the rotating shaft to be evaluated. Rotational errors in the shaft cause changes in the optical geometry of the ball lens. The resulting deflection of the laser beams is detected by the QDs and their output signals are used to determine rotational errors. The radial and the axial rotational errors can be calculated as explained by the mathematical model. Results from system calibration show that the measurement error is within ±1 m and resolution is about 20 nm. Using a direct drive motor (DD motor) as an example, experimental results show a rotational error of less than 20 m. The most important features of this system are that it does not require the use of expensive optical components, it is small, very easy to set up, and measurements are highly accurate.

Keywords: ball lens, quadrant detector, axial error, radial error

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Authors: Tsao Jui-Jung

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Previous research findings have shown that most students do not fully utilize the written corrective feedback provided by teachers (Stone, 2014). This common phenomenon results in the ineffective utilization of teachers' written corrective feedback. As Ellis (2010) points out, the effectiveness of written corrective feedback depends on the level of student engagement with it. Therefore, it is crucial to understand how students utilize the written corrective feedback from their teachers. Previous studies have confirmed the positive impact of teacher-student writing conferences on students' engagement in the writing process and their writing abilities (Hum, 2021; Nosratinia & Nikpanjeh, 2019; Wong, 1996; Yeh, 2016, 2019). However, due to practical constraints such as time limitations, this instructional activity is not fully utilized in writing classrooms (Alfalagg, 2020). Therefore, to address this research gap, the purpose of this study was to explore several aspects of teacher-student writing conferences, including the frequency of meaning negotiation (i.e., comprehension checks, confirmation checks, and clarification checks) and teacher scaffolding techniques (i.e., feedback, prompts, guidance, explanations, and demonstrations) in teacher-student writing conferences, examining students’ self-assessment of their writing strengths and weaknesses in post-conference journals and their experiences with teacher-student writing conferences (i.e., interaction styles, communication levels, how teachers addressed errors, and overall perspectives on the conferences), and gathering insights from their responses to open-ended questions in the final stage of the study (i.e., their preferences and reasons for different written corrective feedback techniques used by teachers and their perspectives and suggestions on teacher-student writing conferences). Data collection methods included transcripts of audio recordings of teacher-student writing conferences, students’ post-conference journals, and open-ended questionnaires. The participants of this study were sophomore students enrolled in an English writing course for a duration of one school year. Key research findings are as follows: Firstly, in terms of meaning negotiation, students attempted to clearly understand the corrective feedback provided by the teacher-researcher twice as often as the teacher-researcher attempted to clearly understand the students' writing content. Secondly, the most commonly used scaffolding technique in the conferences was prompting (indirect feedback). Thirdly, the majority of participants believed that teacher-student writing conferences had a positive impact on their writing abilities. Fourthly, most students preferred direct feedback from the teacher-research as it directly pointed out their errors and saved them time in revision. However, some students still preferred indirect feedback, as they believed it encouraged them to think and self-correct. Based on the research findings, this study proposes effective teaching recommendations for English writing instruction aimed at optimizing teaching strategies and enhancing students' writing abilities.

Keywords: written corrective feedback, student engagement, teacher-student writing conferences, action research

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Authors: Marko Kolakovic, Mihaela Mikic, Martina Taborin

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Women entrepreneurship is often regarded as the unused economical potential in many countries, including Republic of Croatia. Although women represent a majority in the population, they are still a minority in the field of entrepreneurship and face many challenges in fulfilling their entrepreneurship potential. The reasons are often hided in historical distorted perceptions about value, credibility, competitiveness, responsibility and knowledge which women have, or can have. This is significant for at least two reasons. First, in terms of global economic crisis, the economy needs more quality, more skilled and educated people willing to face entrepreneurial challenges and create new jobs, new opportunities and higher living standards. Second, in the entrepreneurial activity, women finally have a chance to highlight their own abilities, such as knowledge, relentless work, organizational skills, communication and negotiation skills, responsibility, flexibility, etc., in order to insure their economic independence, for a better social position, and to increase confidence and faith in their own abilities. This paper empirically analyses characteristics of women entrepreneurship in Croatia and conducted policies for it improvement. An empirical research was conducted with the goal of discovering real life experiences and attitudes of Croatian women entrepreneurs. Results show that Croatian women entrepreneurs are usually highly educated, have previous work experience and operate in service sector, due to lower need for start-up capital. The biggest obstacle on their entrepreneurial path represents government bureaucracy. Although the number of women entrepreneurs is rising today and the gap between male and women entrepreneurs in Croatia, as well as women entrepreneurship levels lower than the European average, we believe that there is still a long way to reach potential and successful women entrepreneurship development. Research showed that by breaking down the barriers as access to finance, education investments, knowledge, skills and confidence development, women will be able to accomplish more significant and more efficient entrepreneurial outcome.

Keywords: Croatia, policy, SMEs, women entrepreneurial strategy, women entrepreneurship

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Ozgul Kartal, Wade Tillett, Lyn D. English

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Despite its global significance in curricula, mathematical modeling encounters persistent disparities in recognition and emphasis within regular mathematics classrooms and teacher education across countries with diverse educational and cultural traditions, including variations in the perceived role of mathematical modeling. Over the past two decades, increased attention has been given to the integration of mathematical modeling into national curriculum standards in the U.S. and other countries. Therefore, the mathematics education research community has dedicated significant efforts to investigate various aspects associated with the teaching and learning of mathematical modeling, primarily focusing on exploring the applicability of modeling in schools and assessing students', teachers', and preservice teachers' (PTs) competencies and engagement in modeling cycles and processes. However, limited attention has been directed toward examining potential resistance hindering teachers and PTs from effectively implementing mathematical modeling. This study focuses on how PTs, without prior modeling experience, resist and/or embrace mathematical modeling and its pedagogy as they learn about models and modeling perspectives, navigate the modeling process, design and implement their modeling activities and lesson plans, and experience the pedagogy enabling modeling. Model eliciting activities (MEAs) were employed due to their high potential to support the development of mathematical modeling pedagogy. The mathematical modeling module was integrated into a mathematics methods course to explore how PTs embraced or resisted mathematical modeling and its pedagogy. The module design included reading, reflecting, engaging in modeling, assessing models, creating a modeling task (MEA), and designing a modeling lesson employing an MEA. Twelve senior undergraduate students participated, and data collection involved video recordings, written prompts, lesson plans, and reflections. An open coding analysis revealed acceptance and resistance toward teaching mathematical modeling. The study identified four overarching themes, including both acceptance and resistance: pedagogy, affordance of modeling (tasks), modeling actions, and adjusting modeling. In the category of pedagogy, PTs displayed acceptance based on potential pedagogical benefits and resistance due to various concerns. The affordance of modeling (tasks) category emerged from instances when PTs showed acceptance or resistance while discussing the nature and quality of modeling tasks, often debating whether modeling is considered mathematics. PTs demonstrated both acceptance and resistance in their modeling actions, engaging in modeling cycles as students and designing/implementing MEAs as teachers. The adjusting modeling category captured instances where PTs accepted or resisted maintaining the qualities and nature of the modeling experience or converted modeling into a typical structured mathematics experience for students. While PTs displayed a mix of acceptance and resistance in their modeling actions, limitations were observed in embracing complexity and adhering to model principles. The study provides valuable insights into the challenges and opportunities of integrating mathematical modeling into teacher education, emphasizing the importance of addressing pedagogical concerns and providing support for effective implementation. In conclusion, this research offers a comprehensive understanding of PTs' engagement with modeling, advocating for a more focused discussion on the distinct nature and significance of mathematical modeling in the broader curriculum to establish a foundation for effective teacher education programs.

Keywords: mathematical modeling, model eliciting activities, modeling pedagogy, secondary teacher education

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

Procedia PDF Downloads 122