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6th International Conference on Dynamics of Information Systems, DIS 2023

作者： Almeida, Ricardo Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal

ISBN: (纸本)9783031503191

The aim of this paper is to present an approximation formula for the Caputo fractional derivative of variable order, with dependence on an arbitrary kernel. For special cases of this kernel function, or the fractional order being constant, we recover some known formulas. This numerical method involves only integer-order derivatives, so any fractional problem can be approximated by an integer-order problem. Some numerical simulations end the paper, showing the effectiveness of our procedure. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Numerical methods

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Discrete pseudo-differential operators in hypercomplex analysis

Discrete pseudo-differential operators in hypercomplex analy...

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作者： Cerejeiras, Paula Kaehler, Uwe Lucas, Simão CIDMA - Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal

In this paper we discuss discrete pseudo-differential operators in the context of hypercomplex analysis. We will provide the definitions and establish the necessary calculus which will be used to discuss questions like boundedness and compactness of operators. In the end, we will discuss well-known examples from hypercomplex analysis as well as give new examples including discrete Dirac operators with non-constant coefficients. © 2021 John Wiley & Sons, Ltd.

关键词： Mathematical operators

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PLAY2ESCAPE - A DIGITAL ESCAPE ROOM IN MATH CLASSES FOR UNDERGRADUATE TOURISM STUDENTS - CASE STUDY 18

PLAY2ESCAPE - A DIGITAL ESCAPE ROOM IN MATH CLASSES FOR UNDE...

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18th International Conference on e-Learning and Digital Learning, ELDL 2024 and 12th International Conference on Sustainability, Technology and Education, STE 2024, Part of the 18th Multi Conference on Computer Science and Information Systems 2024, MCCSIS 2024

作者： Pais, Sónia Sousa, Ana Elisa Lopes, Maria Sofia CIDMA - Center for Research and Development in Mathematics and Applications University of Aveiro Portugal CITUR - Centre for Tourism Research Development and Innovation Polytechnic of Leiria Portugal

ISBN: (纸本)9789898704573

The younger generation, particularly those born in the late 20th and early 21st centuries known as "Generation Z," are deeply integrated with technologies in their daily live. Developing a better understanding of how such technologies influence learning is important to pedagogical approaches designed to co-opt technological applications in novel strategies for teaching and self-learning. Educational technology offers numerous advantages, including: enhancing students' learning experiences, increasing motivation and ultimately, improving student performance. Recognising these advantages, an educational resource was developed, where students explore their problem-solving skill in digital escape room. This paper presents a case study of first-year undergraduate students from a Portuguese higher education institution using a math-related digital escape room intended to increase students' interest and motivation. The aim of the study is to assess how the escape rooms contributes to student motivation, interest and the consolidation of learning. Assessment of students’ perception was based on a quantitative survey and on the results of an evaluation test. Our findings suggest that Escape Room represent an effective educational approach that increases student interest and helps consolidate learning. © 2024 e-Learning and Digital Learning. All Rights Reserved.

关键词： Contrastive Learning

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Constructions of Non-catastrophic MDS Convolutional Codes of Rate 1/2 16th

Constructions of Non-catastrophic MDS Convolutional Codes o...

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16th APCA International Conference on Automatic Control and Soft Computing, CONTROLO 2024

作者： Abreu, Zita Pinto, Raquel Simões, Rita CIDMA – Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal

ISBN: (纸本)9783031817236

As maximum distance separable convolutional codes are known for their ability to achieve the generalized Singleton bound, they are highly suitable for correcting errors. Nevertheless, until now, these codes have primarily been constructed over fields of large size. This paper introduces a distinctive approach for constructing non-catastrophic MDS convolutional codes with rate 1/2 and degree 5 over the fields F11 and F13. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： convolutional codes free distance generalized Singleton bound maximum distance separable (MDS) codes non-catastrophic

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MDS Multidimensional Convolutional Codes 16th

MDS Multidimensional Convolutional Codes

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16th APCA International Conference on Automatic Control and Soft Computing, CONTROLO 2024

作者： Abreu, Zita Pinto, Raquel Simões, Rita CIDMA – Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal

ISBN: (纸本)9783031817236

In this paper mD convolutional codes with finite support are considered, which are convolutional codes whose codewords have compact support indexed in Nm and take values in Fn, where F is a finite field. We establish a natural upper bound on the distance of an mD convolutional code of rate k/n and degree δ, which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. We then present a particular construction of 3D convolutional codes with finite support of rate 1/n and degree δ≤2 that achieve such bound and hence have the maximum distance among all 3D convolutional codes with the same rate and degree. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Convolution

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A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis

A Sturm-Liouville equation on the crossroads of continuous a...

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作者： Cação, Isabel Falcão, M. Irene Malonek, Helmuth R. Tomaz, Graça University of Aveiro Center for Research and Development in Mathematics and Applications Aveiro Portugal University of Minho Centre of Mathematics Braga Portugal Polytechnic of Guarda Research Unit for Inland Development Guarda Portugal

The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences (Formula presented.), first encountered as a special sequence (corresponding to (Formula presented.)) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for (Formula presented.), and we derive an exponential generating function of (Formula presented.) expressed by Kummer's confluent hypergeometric function. © 2021 John Wiley & Sons, Ltd.

关键词： Polynomials

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Comparison of Feature Selection Methods in Regression Modeling: A Simulation Study 23rd

Comparison of Feature Selection Methods in Regression Modeli...

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23rd International Conference on Computational Science and Its applications, ICCSA 2023

作者： Afreixo, Vera Cabral, Jorge Macedo, Pedro CIDMA – Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

ISBN: (纸本)9783031371288

This simulation study explores the impact of different undesirable scenarios (e.g., collinearity, Simpson’s paradox, variable interaction, Freedman’s paradox) on feature selection and coefficients’ estimation using traditional methodologies, such as automatic selection (e.g., stepwise using Akaike information criterion and Bayesian information criterion) and penalized regression (e.g., least absolute shrinkage and selection operator (LASSO), elastic net, relaxed LASSO, adaptive LASSO, minimax concave penalty and smoothly clipped absolute deviation penalty, penalized regression with second-generation p-values). Specifically, we compare wrapper and embedded methods regarding the feature selection, coefficients’ estimation and models’ performance. Our results show that the choice of the methodology can affect the number and the type of selected features, as well as accuracy and precision of coefficients’ estimates. Furthermore, we find that the performance can also depend on the characteristics of the data. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Feature Selection

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When Games get in the way: Gamification Approach for Teaching Maths – A Case Study With Undergraduate Tourism Students 18

When Games get in the way: Gamification Approach for Teachin...

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18th European Conference on Games Based Learning, ECGBL 2024

作者： Pais, Sónia Hall, Andreia CIDMA Center for Research and Development in Mathematics and Applications University of Aveiro Aveiro Portugal CITUR – Centre for Tourism Research Development and Innovation Polytechnic Institute of Leiria Leiria Portugal

ISBN: (纸本)9781917204194

Planning more dynamic and motivating lessons for students is the goal of any teacher, especially maths teachers, a subject where the lack of interest and motivation to learn is so evident and a major concern. Several studies highlight the positive impact of the adoption of gamification strategies in teaching/learning, both in student motivation and in the development of soft skills (teamwork, creativity, decision-making, leadership, communication, and critical thinking). Game-based learning thus promotes students' interest and involves them in this process. In this sense, one of the authors of this study chose to use several (non-digital) games to support the teaching-learning process in her classes. The games used were developed by the authors and have been thoroughly designed to address specific maths topics. The games took various forms, including card games, board games and other hands-on activities. The participants in the study are first-year undergraduate students from a Portuguese higher education institution and encompassed the course of "Quantitative Methods". The aim of the study is to investigate students’ perceptions of the use of gamification in the maths teaching-learning process. To gather information about students’ insights on the use of games in math classes a quantitative survey was conducted. Similar studies have shown that higher education students are usually receptive to the use of games, finding it useful to increase their motivation and consider game-based learning can positively impact learning. Our findings are in line with those studies. © 2024 Dechema e.V.. All rights reserved.

关键词： Students

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Gradient Mittag-Leffler and strong stabilizability of time fractional diffusion processes

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Journal of Mathematical Sciences (United States) 2025年 1-12页

作者： Zitane, Hanaa Torres, Delfim F. M. Department of Mathematics Faculty of Sciences University of Abdelmalek Essaadi Tetouan B.P. 2121 Morocco Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics University of Aveiro Aveiro 3810-193 Portugal

This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use a direct method based essentially on the spectral properties of the system dynamic. Moreover, we consider a class of linear and distributed feedback controls that Mittag-Leffler and strongly stabilize the state gradient. The proposed results lead to an algorithm that allows us to gradient stabilize the state of the fractional systems under consideration. Finally, we illustrate the effectiveness of the developed algorithm by a numerical example and simulations. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： Decomposition approach Distributed controls Fractional diffusion systems Gradient stability Gradient stabilization Partial differential equations

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Fun and Functional: Using Non-Digital Games to Promote Maths Engagement in Pre-service Teachers 18

Fun and Functional: Using Non-Digital Games to Promote Maths...

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18th European Conference on Games Based Learning, ECGBL 2024

作者： Hall, Andreia Pais, Sónia Morando, Paola Spreafico, Maria Luisa Sonia CIDMA Center for Research and Development in Mathematics and Applications University of Aveiro Aveiro Portugal CITUR – Centre for Tourism Research Development and Innovation Polytechnic Institute of Leiria Leiria Portugal DISAA Università degli Studi di Milano Milano Italy

ISBN: (纸本)9781917204194

Humans naturally engage in playful activities throughout their lives and play serves as a fundamental mechanism for cognitive development as well as the development of essential soft skills such as teamwork, decision-making, leadership, and communication. Recognizing this innate predisposition for play, educators are increasingly embracing gamification strategies into their classrooms. More attention has been driven to digital tools such as platforms Kahoot! and Duolingo which gained popularity and demonstrated the potential of game-based learning to increase engagement and knowledge retention. However, concerns about digital screen time fuelled a renewed interest in non-digital activities, including educational games. Non-digital games are often more accessible and affordable, making them suitable for schools with limited resources. research suggests that non-digital games can effectively promote collaboration, communication, and critical thinking skills. In addition, they offer flexibility to teachers to adapt rules and scenarios to specific learning objectives and student needs. Recognizing the benefits of employing games as a pedagogical strategy, the first author of this study opted to incorporate game-based learning strategies into her classes, on a regular basis. Throughout the semester, various non-digital games were implemented, inspired on well-known classics such as memory card games, Monopoly and Pictionary. These games were carefully designed to address specific mathematics topics identified as either the most relevant or those where students revealed more difficulties. The participants in this study were pre-service pre- and primary school teachers enrolled in a maths undergraduate course. Since these students are future educators, the games served a dual purpose: improving current learning experiences and providing teaching resources for their future classrooms. At the end of the semester, a survey was conducted to evaluate students’ perceptions towar

关键词： Gamification

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