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2. Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines
- Author
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Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, Göddeke, Dominik, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Garoufallou, Emmanouel, editor, and Sartori, Fabio, editor
- Published
- 2024
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3. Minimizing CO and CO2 Emissions by Modelling the Distribution of Energy Consumed in Industrial Enterprises
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Solnitsev, R. I., Wang, Lei, Förstner, Ulrich, Series Editor, Rulkens, Wim H., Series Editor, Wen, Fushuan, editor, and Zhu, Jizhong, editor
- Published
- 2024
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4. Electronic vs. Paper Textbook Presentations of the Various Aspects of Mathematics
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Usiskin, Zalman
- Abstract
Based in part on our work in adapting existing paper textbooks for secondary schools for a digital format, this paper discusses paper form and the various electronic platforms with regard to the presentation of five aspects of mathematics that have roles in mathematics learning in all the grades kindergarten-12: symbolization, deduction, modeling, algorithms, and representations. In moving to digital platforms, each of these aspects of mathematics presents its own challenges and opportunities for both curriculum and instruction, that is, for the content goals and how they connect with students for learning. A combination of paper and electronic presentations may be an optimal solution but some difficulties with such a complex solution are presented.
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- 2018
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5. Job Scheduling Problem in the Production of Electrical Equipment
- Author
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Aldemir, Aybüke, Pancarcı, Batuhan, Oral, Buse Eylül, Şahin, Helin, Çakır, İbrahim Onur, Şahbaz, Zülfinaz, Öner, Adalet, Erdem, Gamze, Çakır, Çağlar, Chaari, Fakher, Series Editor, Gherardini, Francesco, Series Editor, Ivanov, Vitalii, Series Editor, Cavas-Martínez, Francisco, Editorial Board Member, di Mare, Francesca, Editorial Board Member, Haddar, Mohamed, Editorial Board Member, Kwon, Young W., Editorial Board Member, Trojanowska, Justyna, Editorial Board Member, Xu, Jinyang, Editorial Board Member, Durakbasa, Numan M., editor, and Gençyılmaz, M. Güneş, editor
- Published
- 2023
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6. Mathematical Models for No-Wait Permutation Flowshop Scheduling Problems
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Yüksel, Damla, Kandiller, Levent, Taşgetiren, Mehmet Fatih, Chaari, Fakher, Series Editor, Gherardini, Francesco, Series Editor, Ivanov, Vitalii, Series Editor, Cavas-Martínez, Francisco, Editorial Board Member, di Mare, Francesca, Editorial Board Member, Haddar, Mohamed, Editorial Board Member, Kwon, Young W., Editorial Board Member, Trojanowska, Justyna, Editorial Board Member, Xu, Jinyang, Editorial Board Member, Durakbasa, Numan M., editor, and Gençyılmaz, M. Güneş, editor
- Published
- 2023
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7. Bridging between Real World & Mathematics Ideas through Modelling Task
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Abolfazl Rafiepour
- Abstract
In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the modelling cycle. In this paper after discussion about modelling in more details, two modelling cycles will be elaborated in the context of mathematical tasks that are related to everyday life. Main ideas behind different modelling cycles is starting point that would be from real world situation. Then gradually mathematical elements of real world phenomenon identified and mathematics problem will have shaped in a form that could be solved through mathematical problem solving techniques. Furthermore, it would be important phase that call interpretation of mathematics answer and check it in front of real world situation. This paper will be followed by discussion about learning theories that support the idea of modelling. Finally, two educational challenges (Design good modelling tasks and assessing of students performance) in mathematical modelling activity will be discussed. [For the complete proceedings, see ED655360.]
- Published
- 2023
8. On the Paper by Leonid A. Gavrilov and Natalia S. Gavrilova entitled “Trends in Human Species-Specific Lifespan and Actuarial Aging Rate” Published in Biochemistry (Moscow), Vol. 87, Nos. 12-13, pp. 1622-1633 (2022)
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Mikhalsky, Anatoly I.
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- 2023
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9. Optimal Volume Planning and Scheduling of Paper Production with Smooth Transitions by Product Grades.
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Voronov, Roman, Shabaev, Anton, and Prokhorov, Ilya
- Subjects
PRODUCTION scheduling ,GREEDY algorithms ,PAPER mills ,CUTTING stock problem ,MATHEMATICAL models ,SIMPLEX algorithm - Abstract
The article deals with the problem of calculating the volume calendar plan of a paper mill. The presented mathematical model and methods make it possible to schedule paper production orders between several paper machines (PM) to even their loading, devise cutting plans for each winder and arrange the order of their implementation. When forming cutting plans, orders are grouped in accordance with such parameters as grammage, roll diameter, core diameter, product type and number of layers. Deadlines and volumes in customer orders are taken into account. The cutting plans for each winder account for the allowable roll width limits and the maximum number of knives. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives' setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm and the local search procedure. We tested the solution approach on real production data from a paper mill in European Russia and obtained the production sequence that better matches deadlines in customer orders compared to the plan devised manually by production planners. [ABSTRACT FROM AUTHOR]
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- 2023
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10. An Ontology to Structure Biological Data: The Contribution of Mathematical Models
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Inizan, Olivier, Fromion, Vincent, Goelzer, Anne, Saïs, Fatiha, Symeonidou, Danai, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Garoufallou, Emmanouel, editor, Ovalle-Perandones, María-Antonia, editor, and Vlachidis, Andreas, editor
- Published
- 2022
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11. Mathematical modelling of a slow flameless combustion of a two-dimensional paper.
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Fusi, Lorenzo, Calusi, Benedetta, Giovinetto, Antonio, and Panconi, Leonardo
- Subjects
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COMBUSTION , *MATHEMATICAL models , *ADVECTION-diffusion equations , *RAYLEIGH number , *CHEBYSHEV polynomials , *TRANSPORT theory , *AIR flow - Abstract
We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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12. Mapping Teacher Moves When Facilitating Mathematical Modelling
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Mathematics Education Research Group of Australasia (MERGA), Brown, Jill P., and Stillman, Gloria A.
- Abstract
This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video and audio-recorded task implementation. The analytical tools developed, with one teacher and one task early in a three-year project were particularly useful in ascertaining what the teacher moves were as we subsequently sought to determine reasons for these.
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- 2023
13. Monte Carlo simulation of the coffee-ring effect on porous papers.
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Hwang, Youngjin, Kim, Sangkwon, Lee, Chaeyoung, Kwak, Soobin, Lee, Gyeonggyu, and Kim, Junseok
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MATHEMATICAL models , *COMPUTER simulation , *MONTE Carlo method - Abstract
In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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14. Mining Artificially Generated Data to Estimate Competency
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Robson, Robby, Ray, Fritz, Hernandez, Mike, Blake-Plock, Shelly, Casey, Cliff, Hoyt, Will, Owens, Kevin, Hoffman, Michael, and Goldberg, Benjamin
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The context for this paper is the "Synthetic Training Environment Experiential Learning -- Readiness" (STEEL-R) project [1], which aims to estimate individual and team competence using data collected from synthetic, semi-synthetic, and live scenario-based training exercises. In STEEL-R, the "Generalized Intelligent Framework for Tutoring" (GIFT) orchestrates scenario sessions and reports data as experience API (xAPI)statements. These statements are translated into assertions about individual and team competencies by the "Competency and Skills System" (CaSS). Mathematical models use these assertions to estimate the competency states of trainees. This information is displayed in a dashboard that enables users to explore progression over time and informs decisions concerning advancement to the next training phase and which skills to address. To test, tune, and demo STEEL-R, more data was needed than was available from real-world training exercises. Since the raw data used to estimate competencies are captured in xAPI statements, a component called DATASIM was added. DATASIM simulated training sessions by generating xAPI statements that conformed to a STEEL-R "xAPI Profile." This facilitated testing of STEEL-R and was used to create a demo that highlighted the ability to map data from multiple training systems to a single competency framework and to generate a display that team leaders can use to personalize and optimize training across multiple training modalities. This paper gives an overview of STEEL-R, its architecture, and the features that enabled the use of artificial data. The paper explains how xAPI statements are converted to assertions and how these are used to estimate trainee competency. This is followed by a section on xAPI Profiles and on the xAPI Profile used in STEEL-R. The paper then discusses how artificial data were generated and the challenges of modeling longitudinal development and team in these data. The paper ends with a section on future research. [For the full proceedings, see ED623995.]
- Published
- 2022
15. Objective Determination of the Graduating Students’ Competencies Level
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Roshkovan, Kirill, Chaley, Ivan, Latypova, Olga, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Sukhomlin, Vladimir, editor, and Zubareva, Elena, editor
- Published
- 2021
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16. Intelligent System for Generation and Evaluation of e-Learning Tests Using Integer Programming
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Borissova, Daniela, Keremedchiev, Delyan, Barbosa, Simone Diniz Junqueira, Editorial Board Member, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Simian, Dana, editor, and Stoica, Laura Florentina, editor
- Published
- 2020
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17. Teaching Students to Extend Economic Models Using In-Class Scaffolding Assignments
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Lynn Trafton, Tamara
- Abstract
The author discusses how to teach students to extend economic models using in-class scaffolding assignments, supported by discussions and workshops. Methods include discussions of a model's strengths and weaknesses; small group, in-class assignments that provide steps toward model extension; informal presentations of the work resulting from these assignments; and large group, post-presentation discussions in which students critique and build upon each other's work. Students then draw upon what they have learned to take one final step--to write a paper detailing a model extension. Although student model extensions do not reach a professional level of sophistication, students do extend models beyond what they know of them from textbooks and lectures. In doing so, students begin to create knowledge and to participate in economic discourse.
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- 2019
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18. Mathematical modelling, multi-objective optimization, and compliance reliability of paper-derived eco-composites.
- Author
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Adewale Akinwande, Abayomi, Folorunso, Davies Oludayo, Balogun, Oluwatosin Abiodun, and Romanovski, Valentin
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CONSTRUCTION materials ,WASTE paper ,PAPER pulp ,MATHEMATICAL models ,BENDING strength ,SULFATE pulping process ,CEMENT ,PULPING - Abstract
The quest for cost-effective and thermal efficient structural materials onto beating the high cost of construction is gaining more attention among researchers. This study focused on the blending of cement and sand with waste paper pulp into cost-effective structural materials. The composites were prepared in four mix groups with each containing a fixed amount of sand at 5, 10, 15, and 20 wt.% (by weight of pulp). Cement was varied at 10, 20, 30, and 40 wt.% in each group, and curing was done for 28 days. Properties evaluated are compressive, bending, and splitting strengths. It was observed that increasing cement and sand contents enhanced strengths; howbeit, the blend of 30 wt.% cement/15 wt.% sand resulted in a reduction in bending strength even as 30 wt.% cement/20 wt.% sand engendered a decrease in bending and splitting strength. The microstructural features showed that inherent fibers of the pulp were well bonded with hydration products and sand content yielding good performance in the composites. The optimization procedure carried out depicted a combination of 35.27% cement and 20% sand as the optimum composition. Experimental outcomes were modelled for the purpose of prediction of responses. The models were confirmed statistically fit showing how varying cement content affected strength responses at fixed sand proportion. ANOVA affirmed the significant contribution of cement and sand on the strength responses. Compliance reliability was observed to be dependent on the interactive pattern between cement and sand. Going by the standard prescription for the strength properties, cement and sand content of 35.27 and sand 20 wt.% satisfied all strength requirements for low-cost construction having a compliance reliability of 1.31. [ABSTRACT FROM AUTHOR]
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- 2022
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19. A Disposition to Attend to Relationships: A Key Shift in the Development of Multiplicative Thinking. Key Shifts in Thinking in the Development of Mathematical Reasoning. [Symposium]
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Mathematics Education Research Group of Australasia (MERGA) and Siemon, Dianne
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This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment Framework for multiplicative thinking, it has been difficult to move students through Zone 4 at the same rate. A closer examination of item responses at this level reveal that a disposition to notice and work with relationships between quantities may explain this phenomenon.
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- 2022
20. A Typology for Instructional Enablers of Mathematical Modelling
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Mathematics Education Research Group of Australasia (MERGA), Geiger, Vince, Galbraith, Peter, Niss, Mogens, and Holland-Twining, Ben
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Competency with mathematical modelling is increasingly important for career and informed and engaged participation in personal, civic and work life. In this paper we report on an aspect of a three-year longitudinal study that aimed to identify and describe enablers of mathematical modelling. Teacher interview data has been drawn upon to exemplify key features of a typology for instructional enablers of mathematical modelling. Findings highlight the importance of the didactical contract and socio-mathematical norms in promoting students' mathematical modelling competency, as well as teachers' anticipatory capabilities.
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- 2022
21. Promoting Covariational Reasoning with the Aid of Digital Technology = Promoviendo el razonamiento covariacional con apoyo de la Tecnología digital
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Pérez Martínez, Helen Mariel, Cuevas-Vallejo, Carlos A., Islas Ortiz, Erasmo, and Orozco-Santiago, José
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In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning Trajectory supported by digital technology and elements of Cuevas-Pluvinage didactics. The activities were evaluated according to the levels of covariation proposed by Carlson and colleagues, categorizing students' achievements and difficulties for each level of understanding. The results show that the activities favor students' progress by moving from the context situation to the different representations, establishing the relationship between the variables, and identifying their functional dependence. [For the complete proceedings, see ED630210.]
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- 2022
22. Leveraging Equity and Civic Empathy through Community-Based Mathematical Modeling
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Aguirre, Julia M., Suh, Jennifer, Tate, Holly, Carlson, Mary Alice, Fulton, Elizabeth, and Turner, Erin E.
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This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy, and elevating justice. We illustrate how these goals work together to advance equity and cultivate civic empathy through classroom vignettes of community-based modeling lessons. Through this theoretical synthesis, implications for community-based mathematical modeling instruction will be discussed. [For the complete proceedings, see ED630210.]
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- 2022
23. Research on the Evaluation of Teachers' Teaching Quality Based on [delta]S Equation
- Author
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Hongnan Wan
- Abstract
The teaching quality evaluation of college teachers is an important indicator of school evaluation, performance assessment and teacher promotion. However, the existing evaluation methods are only limited to the formal evaluation of teaching behavior, and have not achieved objective, reasonable and scientific evaluation results. The purpose of this paper is to propose a [delta]S equation of the state of the teaching system from the point of view of the teaching system's operation process. On this basis, a Markov process evaluation method for teachers' teaching quality is established. The research results show that the application of the [delta]S equation of the teaching system to the evaluation of teaching behavior and teaching effect has its own characteristics, and the key lies in the reasonable selection of the [delta]S equation and the the combination of Markov analysis can effectively achieve the evaluation goal of teachers' teaching quality. [For the full proceedings, see ED638044.]
- Published
- 2022
24. Authenticity of elementary teacher designed and implemented mathematical modeling tasks.
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Turner, Erin E., Bennett, Amy Been, Granillo, Monica, Ponnuru, Nishaan, Roth Mcduffie, Amy, Foote, Mary Q., Aguirre, Julia M., and McVicar, Elzena
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MATHEMATICAL models , *WASTE paper , *TEACHERS , *SCHOOL lunchrooms, cafeterias, etc. , *STEM education , *PUBLIC spaces , *PLASTIC scrap , *SCHOOL health services - Abstract
Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Perspectives on Deriving Mathematical Models in Pulp and Paper Science.
- Author
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Kerekes, Richard, McDonald, David, and Joe Zha
- Subjects
- *
PAPER pulp , *MATHEMATICAL models , *CAUSAL models , *FORECASTING - Abstract
Mathematical modelling is a powerful tool in science. Causal mathematical models based on a clear picture of how key variables interact enable a deeper understanding of a given situation and provide reliable predictions. This is a classic approach in science. Unfortunately, this approach is declining in pulp and paper-related research in favour of simply reporting experimental data. The lack of a framework provided by a model diminishes the value of much experimental work. Therefore, the increased use of mathematical models is encouraged, and this approach is illustrated via several practical examples from our work. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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26. The VNS Approach for a Consistent Capacitated Vehicle Routing Problem Under the Shift Length Constraints
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Kulachenko, Igor, Kononova, Polina, Barbosa, Simone Diniz Junqueira, Editorial Board Member, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Kotenko, Igor, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Bykadorov, Igor, editor, Strusevich, Vitaly, editor, and Tchemisova, Tatiana, editor
- Published
- 2019
- Full Text
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27. Data Analytics for Trajectory Selection and Preference-Model Extrapolation in the European Airspace
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Lancia, Carlo, Giovanni, Luigi De, Lulli, Guglielmo, Fortz, Bernard, editor, and Labbé, Martine, editor
- Published
- 2019
- Full Text
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28. Possibilities of Raster Mathematical Algorithmic Models Utilization as an Information Support of Military Decision Making Process
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Nohel, Jan, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, and Mazal, Jan, editor
- Published
- 2019
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29. Real-Time AI-Driven Assessment & Scaffolding That Improves Students' Mathematical Modeling during Science Inquiry
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Adair, Amy, Segan, Ellie, Gobert, Janice, and Sao Pedro, Michael
- Abstract
Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative performance-based assessments designed to elicit fine-grained data about students' competencies on these practices can be leveraged to develop embedded AI scaffolds to support students' learning. In this paper, we present the design and initial classroom test of virtual labs that automatically assess fine-grained sub-components of students' mathematical modeling competencies based on their actions within the learning environment. We describe how we leveraged underlying machine-learned and knowledge-engineered algorithms to trigger scaffolds, delivered proactively by a pedagogical agent, that address students' individual difficulties as they work. Results show that the students who received automated scaffolds for a given practice on their first virtual lab improved on that practice for the next virtual lab on the same science topic in a different scenario (a near-transfer task). These findings suggest that real-time automated scaffolds based on fine-grained assessment can foster students' mathematical modeling competencies related to the NGSS.
- Published
- 2023
30. Modelling and Simulation of Intelligent English Paper Generating Based on SSA-GA.
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Han, Limin, Gao, Hong, and Zhai, Rongjie
- Subjects
GENETIC algorithms ,SEARCH algorithms ,MATHEMATICAL models ,SIMULATION methods & models - Abstract
To enhance the quality and efficiency of computer-enabled generation of papers for Test for English Majors Band 8 (TEM-8), a paper generation model supported by sparrow search algorithm-genetic algorithm was studied. First, a simplified test paper generation mathematical model was set up after analyzing and studying types and characteristics of TEM-8 tasks. In the model, quantity, type, difficulty, discrimination degree, scores, exposure, and answering time of test questions were taken into consideration. To enhance the optimizing effect of the genetic algorithm for searching test questions, the traditional genetic algorithm was improved by introducing the sparrow search algorithm into the model to achieve a better crossover rate, variance rate, optimization precision, and speed of the genetic algorithm. A new sparrow search-genetic algorithm (SSA-GA) was designed, and the optimizing effect of SSA-GA was verified to be ideal through optimizing six standard test functions. Then, SSA-GA was applied to conduct experimentation with test paper generation, and comparison with traditional genetic algorithms was also made. The values of best and average fitness of SSA-GA were better than those of the traditional genetic algorithm (GA) in the paper generation. Exposure rate and success rate in TEM-8 paper generation of SSA-GA were higher than those of traditional GA in TEM-8 paper generation. Results showed that the studied SSA-GA could implement test paper generation with higher speed and better quality. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Paper Lifetime Mathematical Modelling based on Multi Pre-Exponential Factors for Oil-Immersed Transformer.
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Saleh, Najiyah, Azis, Norhafiz, Jasni, Jasronita, Ab Kadir, Mohd Zainal Abidin, and Talib, Mohd Aizam
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MATHEMATICAL models ,ARRHENIUS equation ,MOISTURE - Abstract
This work examines the impact of multi pre-exponential factors on the lifetime modelling of the paper in oil-immersed transformers. First, the corresponding pre-exponential factor was determined based on the concentrations of the three parameters known as oxygen, moisture and acid. Next, the pre-exponential factor for each of the parameters at different concentrations was combined based on the summative approach to obtain the overall impact on the lifetime of the paper. It is found that the expected life of the paper for overall multi pre-exponential factors is higher than either single or double pre-exponential factors. For a single pre-exponential factor, the expected life of the paper decreases by a factor of 59.8 as the oxygen concentration increases from 15,000 ppm to 210,000 ppm. Moisture can decrease the expected life of the paper by a factor of 34 as it increases from 0.5% to 5%. Low molecular weight acid (LMA) has a higher impact than high molecular weight acid (HMA), whereby its impact is further enhanced through multi pre-exponential factor effect whereby the expected life of the paper decreases by a factor of 7.9 as the moisture content increases from 0.5% to 5% and oxygen increases from 300 ppm to 20,000 ppm. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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32. An Operations Research-Based Teaching Unit for Grade 11: The ROAR Experience, Part II
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Gabriella Colajanni, Alessandro Gobbi, Marinella Picchi, Alice Raffaele, and Eugenia Taranto
- Abstract
In this paper, we continue describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students' interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation.
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- 2024
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33. Mathematical Modelling Using Scenarios, Case Studies and Projects in Early Undergraduate Classes
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G. R. Fulford
- Abstract
Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a "Classroom Note": modelling the dynastic cycles in Chinese history.
- Published
- 2024
- Full Text
- View/download PDF
34. What Does Mathematical Modelling Have to Offer Mathematics Education? Insights from Students' Perspectives on Mathematical Modelling
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Kerri Spooner
- Abstract
The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience.
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- 2024
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35. Fostering Students' Modelling and Problem-Solving Skills through Operations Research, Digital Technologies and Collaborative Learning
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E. Taranto, G. Colajanni, A. Gobbi, M. Picchi, and A. Raffaele
- Abstract
Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically included in most curricula of higher secondary schools (i.e. Grades 9-12), but it is usually presented mainly at university level. To show how OR could be significant for these school students' education, the authors of this paper developed an educational project consisting of three teaching units. In this paper, we share the result of the teaching experiment related to the first unit, addressed to Grade 10. Qualitative and quantitative analyses show how it is appropriate to include OR and its typology of problems in regular school mathematics lectures. Second, these data also show how modelling and problem-solving skills, developed working with OR, can be fostered by implementing a collaborative way of working, also by making use of digital technologies. Last but not least, we demonstrate the positive impact such activities have on students' appreciation of OR.
- Published
- 2024
- Full Text
- View/download PDF
36. An Introduction to Modelling through a Microbial Interaction Application
- Author
-
Fabiana Zama
- Abstract
This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms.
- Published
- 2024
- Full Text
- View/download PDF
37. Fuzzy Linguistic Variables in Mathematical Activities in Kindergarten
- Author
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Jankovic, Branka and Magzan, Maša
- Abstract
In this paper, the application of fuzzy logic in mathematical education is viewed from the perspective of pre- school education. The aim of the paper is to give a brief overview of examples from the literature related to fuzzy logic and to point out the presence of fuzzy linguistic variables in the everyday life of a preschool child, as well as the importance of developing and respecting the approximate reasoning of preschool children. Although crisp mathematics requires crisp arguments that characterize our cognitive development, preschoolers start from common argumentation and use vague words. Fuzzy logic is an excellent tool for supporting such approximate reasoning which allows preschoolers to model real-life situations using vague words.
- Published
- 2020
38. Modeling in Mathematics and History as Teaching and Learning Approaches to Pandemics
- Author
-
Papadopoulou, Maria, Argyri, Panagiota, and Smyrnaiou, Zacharoula
- Abstract
The integration of innovative interdisciplinary approaches to the ?-12 Curriculum aims to deepen students' knowledge and help them develop transversal skills. Applying an interdisciplinary lens, with a focus on pandemics, can help shape attitudes by means of inculcating the values of responsible global citizenship, and a high sense of personal and social responsibility. In the midst of the current lock-down due to Covid-19, a teaching approach to pandemics is presented, as an interdisciplinary connection between history and mathematics, based on the methodology of modeling in mathematics and the humanities. The main research questions posed: a) can modeling, as analyzed in the scientific literature, be used to interpret pandemics, e.g. in the case of the 'plague of Athens' (430 B.C.), as analyzed in the primary sources? b) Can the mathematical tools of statistical analysis be used to understand prevention measures through the centuries? Taking a longue durée perspective on history, students were asked to work on additional cases of pandemics across time and space, mobilizing both their mathematical and historical knowledge: process numerical data from primary sources, study maps, combine and compare elements of the past and the present using mathematical epidemiological models and real numerical data to study and predict the spread of infectious diseases. This paper presents the assessment of the effectiveness of this approach, conducted by means of closed and open questionnaires, administered in two phases (pre- and post-teaching) to a sample of 40 students aged 16-17 years. The results highlight statistics as a key tool for understanding real-world situations, and record the strengthening of students' knowledge in history, the raising of their critical thinking skills, as well as their enhanced ability to tackle real-world problems and understand responsible decision-making processes. Finally, the paper suggests that such good practices can prepare students for the complexity of globalized knowledge. [For the full proceedings, see ED626375.]
- Published
- 2020
39. Diffusion Mechanism of Furfural in Transformer Oil–Paper Insulation Under Moisture Effect.
- Author
-
Geng, Chuhan, Liu, Jiefeng, Zhang, Heng, Liu, Chuying, Luo, Yiwen, and Zhang, Yiyi
- Subjects
TRANSFORMER insulation ,FURFURAL ,MOLECULAR dynamics ,MOISTURE ,PETROLEUM - Abstract
The generation and distribution of furfural are significantly affected by moisture content in the insulating paper. However, the diffusion mechanism of furfural under moisture effect is not clear, hence, this study investigates the effect of moisture on the diffusion characteristics of furfural by combining macro experiment and micro molecular dynamics simulation. The simulation results demonstrate that the increased moisture content in paper accelerates the diffusion of furfural from paper to oil, which is also proved by the experimental data. Then, the results of interaction energy analysis indicate that the increase of moisture enhances the van der Waals force between oil and furfural. The present findings are expected to improve the theoretical level of furfural analysis, which will facilitate the aging evaluation of the transformer insulating paper based on furfural. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. Two level deacidification mathematical model for the description of transport of solid alkaline particles and diffusion of ions in a treated acid paper.
- Author
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Danielik, Vladimír, Králik, Milan, Ambrová, Marta, Jurišová, Jana, Jablonský, Michal, Vizárová, Katarína, and Vajová, Izabela
- Subjects
MATHEMATICAL models ,SOLIDS ,IONS ,NINETEENTH century ,DISSOLUTION (Chemistry) ,PAPERMAKING - Abstract
Industrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO
4 )2 ) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
41. Assessing Students' Competencies with Mathematical Models in Virtual Science Inquiry Investigations
- Author
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Adair, Amy, Sao Pedro, Michael, Gobert, Janice, and Owens, Jessica A.
- Abstract
Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating" mathematical models in science inquiry contexts aligned with the NGSS (2013). Results show that model development and evaluation competencies are correlated, but students who demonstrate proficiency with model development often struggle with evaluation. Nuanced data illustrate how components of modeling competencies differ and how they may be related.
- Published
- 2023
42. Overconsumption as a function of how individuals make choices: A paper in honor of Howard Rachlin's contributions to psychology.
- Author
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Heyman, Gene M.
- Subjects
- *
FISCAL policy , *MATHEMATICAL models , *CONSUMPTION (Economics) , *CONSUMERS , *SELF-control - Abstract
Howard Rachlin's widely influential behavioral economic approach to self‐control and related issues provides the model for this submission. The topic is overconsumption. Current human consumption levels are unsustainable. Explanations typically focus on societal factors, such as the seductive power of advertising and/or misguided tax policies. However, the effectiveness of these factors depends on the degree to which individuals are susceptible to the message: "consume more." Humans are not blank slates. This paper argues that how individuals frame their choices establishes the susceptibility to overconsume. According to economic theory, consumers frame their options as bundles, composed of different combinations of the available items and activities. This leads to maximizing. In experiments, participants tend to frame their options as "either‐or" choices. This leads to the matching law. Mathematical models of concurrent schedule choice procedures show that (1) the matching law implies overconsumption of the most preferred option and (2) that individuals will persist in preferring their favorite option even when doing so reduces overall reward rates. Given that the matching law better describes how individuals choose than does maximizing, the mathematical models of widely used choice procedures help explain why efforts to increase consumption have been more influential than efforts to control consumption. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Prediction Model of Bubble Formation in Oil-Paper Insulation Based on the ITBE Envelope.
- Author
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Yang, Chaojie, Zhao, Tao, Liu, Yunpeng, Zhu, Wenbing, and Gu, Zhaoliang
- Subjects
- *
HENRY'S law , *PREDICTION models , *POWER transformers , *DIELECTRIC strength , *TEMPERATURE effect , *SILICONE rubber , *BUBBLES - Abstract
Due to rapid temperature rise and insulation moisture, bubbles can generate in the oil-paper insulation of oil-immersed power transformers, which can reduce the dielectric strength of oil-paper insulation and even bring about the risk of insulation breakdown. In order to accurately evaluate the conditions of bubble formation, the physical process of bubble formation in oil-paper insulation is studied in this article. Considering the effects of water vaporization, gas dissolution in oil, and moisture migration on bubble formation, a bubble formation prediction model is constructed. Based on Henry’s law, the dissolution equilibrium of gas in oil is taken into consideration and the upper boundary of the initial temperature of bubble effect (ITBE) envelope is obtained in this model. Based on the moisture equilibrium in oil-paper insulation, the bubble formation process caused by the emergence and rapid evaporation of free water is analyzed, and then, the lower boundary of the ITBE envelope is obtained in this model. The model results show that the moisture content of the pressboard and the presence of free water have a great impact on ITBE. Specifically, the higher the moisture content, the lower the ITBE value. In addition, with the further increase of moisture content, the upper and lower boundaries of the ITBE envelope gradually tend to be the same. However, once free water is present on the surface of cellulose, ITBE decreases rapidly to below 120 °C. The model built in this article is of great significance to study the temperature limit of the power transformer. Hence the ITBE envelope can provide an important theoretical reference for reducing the risk of bubble formation during power transformer operation. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
44. On the comparison of inventory replenishment policies with time-varying stochastic demand for the paper industry.
- Author
-
Escuín, David, Polo, Lorena, and Ciprés, David
- Subjects
- *
TIME-varying systems , *PAPER industry , *MATHEMATICAL models , *MAKE-to-order (Manufacturing) , *VENDOR-managed inventory , *PRODUCTION planning - Abstract
The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
45. Study on Space Charge Characteristics of Transformer Insulating Paper Under Different Working Conditions.
- Author
-
Zhang, Yiyi, Wang, Gang, Zhang, Xingtuo, Zhong, Wenbo, Su, Zhicheng, Xu, Chuqi, Wang, Running, Mao, Xinyang, and Liu, Jiefeng
- Subjects
SPACE charge ,ELECTRIC charge ,ELECTRIC distortion ,DYNAMIC balance (Mechanics) ,TRANSFORMER insulation - Abstract
The space charge effect of transformer insulating paper will distort its internal electric field, and its space charge effect will be more prominent under extremely complex working conditions. At present, the micromechanism of charge transport and electric field distortion characteristics of paperboard are not clear under complex working conditions. So in this article, based on the bipolar carrier transport (BCT) model and the dynamic carrier balance model, the effects of high temperature, aging degree, moisture content, and bent degree on charges accumulation in paperboard are studied under dc high voltage by numerical simulation and the measured data needed for simulation. The results show that the higher temperature strengthens the carrier migration, deepens the injection depth of the charge, and aggravates the distortion of electric field intensity in paperboard. The more extended the aging time of paperboard, the greater the internal trap density and the deeper the trap depth, which lead to charges migration difficultly. Increasing water content in the paperboard will accelerate space charges to reach a steady state, while further increasing it will slow down this process, which is related to the shallow trap getting deeper. When the critical part of paperboard is extruded, many traps are introduced, resulting in charges accumulation seriously. The research results can reference the design of paperboard and the maintenance of transformer insulation system. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
46. Quantitative Reasoning and Covariational Reasoning as the Basis for Mathematical Structure for Real-World Situations
- Author
-
Kularajan, Sindura Subanemy and Czocher, Jennifer A.
- Abstract
In this paper we address the question, how do quantitative reasoning and covariational reasoning present as students build structural conceptions of real-world situations. We use data from an exploratory teaching experiment with an undergraduate STEM major to illustrate the explanatory roles quantitative reasoning and covariational reasoning play in, (a) coordinating more than two interdependent quantities, (b) conceiving of real-world situations in more than one way, (c) constructing networks of quantitative relationships, and (d) creating a mathematical expression. We make the case that looking at mathematical model construction through the lens of quantitative reasoning and covariational reasoning may provide insights into students' mathematical decisions as they structure complex real-world scenarios. [For the complete proceedings, see ED630060.]
- Published
- 2021
47. Basic Mathematical Modelling Competencies for Non-STEM Higher Education
- Author
-
Marchisio, Marina, Roman, Fabio, and Sacchet, Matteo
- Abstract
The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in facing a problem belong to the study programs of secondary schools, and should thus be familiar also to students without a specific background in Mathematics. Difficulties can arise in various phases of modelling: in the comprehension of the problem, in the translation into mathematical formulas, in the resolution process or even in the interpretation of the results. In this paper, we give an analysis of an online test taken by 75 non-STEM students. The 10 questions of the test focused on specific items in mathematical modelling. During the test, students had to write down the reason why they chose a specific answer. The test allowed us to find and categorize the common errors students make and the phase in which it happens, suggesting actions in order to prevent them. Results show percentages of errors and discuss students' arguments. [For the full proceedings, see ED621892.]
- Published
- 2021
48. Temperature dependence of methanol and the tensile strength of insulation paper: kinetics of the changes of mechanical properties during ageing.
- Author
-
Arroyo, Oscar, Jalbert, Jocelyn, Fofana, Issouf, and Ryadi, Mohamed
- Subjects
METHANOL ,INSULATING paper ,TENSILE strength ,TEMPERATURE effect ,DYNAMICS ,MATHEMATICAL models ,MECHANICAL behavior of materials ,STATISTICAL correlation ,DEPOLYMERIZATION - Abstract
This paper reports the temperature-dependence of methanol generation and the tensile index under ageing conditions for two paper/oil systems: one consisting of a standard wood Kraft paper and the other of a thermally-upgraded Kraft paper (TUK). A linear correlation between methanol and the tensile index for these paper/oil systems was observed in a previous study at 170 °C. In the current study, the correlation was extended to a large range of temperatures (150-190 °C). The experimental data were fitted with a modified Calvini's kinetic model, while the Arrhenius equation was used to model the kinetic of changes of the paper's mechanical properties during ageing. Good agreement with the temperature ( lnk vs. 1/ T) was observed for the rate constants of the chain-end group production, methanol formation, and the decrease of mechanical properties. The Arrhenius equation applied to this data grouping showed activation energy of 130 ± 29 kJ/mol for the decrease in mechanical strength of the standard Kraft paper, while the value was 118 ± 55 kJ/mol for the TUK paper. These values are of the same order of magnitude as those obtained in this study and in the literature for the depolymerization of cellulose and the generation of methanol that was reported. This confirmed the close relationship between cellulose depolymerization, methanol generation and the reduction of the paper's mechanical strength during ageing, dominated by the acid hydrolysis mechanism. The results, which can be seen as a benchmark and pave the way to further research, provide an opportunity for applying the proposed correlations to estimate the insulation condition in operating transformers. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
49. Multiple-choice knapsack-based heuristic algorithm for the two-stage two-dimensional cutting stock problem in the paper industry.
- Author
-
Kim, Kyungdoc, Kim, Byung-In, and Cho, Hyunbo
- Subjects
CUTTING stock problem ,MATHEMATICAL optimization ,MATHEMATICAL models ,HEURISTIC algorithms ,KNAPSACK problems ,PAPER mills - Abstract
This study examines a two-stage two-dimensional cutting stock problem encountered by a paper mill company. The problem includes various machine-related and operational constraints based on real-world situations. Paper products are manufactured using two major cutting processes. Each cutting machine has a specific minimum and maximum width for input and output rolls and is limited by the maximum number of rolls it can cut at the same time. A mathematical model is presented to formally address the problem and an efficient multiple-choice knapsack-based heuristic algorithm is proposed to solve the problem. To demonstrate the efficiency of the proposed heuristic algorithm, computational experiments are conducted on test data-set generated from real-world data provided by a large paper mill company in the Republic of Korea. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
- View/download PDF
50. Inclusive Playground Design
- Author
-
Holly Tate, Samantha Anstett, Beth Cooke, Merrie Joy Hrabak, and Jennifer Suh
- Abstract
The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground access, through community-based mathematical modeling (CBMM). This article highlights how third- and fourth-grade teachers, a math coach, and a university professor (also authors of this paper) collaboratively and thoughtfully engaged in the CBMM cycle.
- Published
- 2024
- Full Text
- View/download PDF
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