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13 pages, 2275 KB  
Article
Investigating the Mars–van Krevelen Mechanism for CO Capture on the Surface of Carbides
by Naveed Ashraf and Younes Abghoui
Molecules 2025, 30(17), 3637; https://doi.org/10.3390/molecules30173637 (registering DOI) - 6 Sep 2025
Abstract
Electrochemical reduction processes enable the CO to be converted into a useful chemical fuel. Our study employs density functional theory calculations to analyze the (110) facets of the transition metal carbide surfaces for CO capture, incorporating the Mars–van Krevelen (MvK) mechanism. All the [...] Read more.
Electrochemical reduction processes enable the CO to be converted into a useful chemical fuel. Our study employs density functional theory calculations to analyze the (110) facets of the transition metal carbide surfaces for CO capture, incorporating the Mars–van Krevelen (MvK) mechanism. All the possible adsorption sites on the surface, including carbon, metal, and bridge sites, were fully investigated. The findings indicate that the carbon site is more active relative to the other adsorption sites examined. The CO hydrogenation paths have been comprehensively investigated on all the surfaces, and the free energy diagrams have been constructed towards the product. The results conclude that the TiC is the most promising candidate for the formation of methane, exhibiting an onset potential of −0.44 V. The predicted onset potential for CrC, MoC, NbC, VC, WC, ZrC, and HfC are −0.86, −0.61, −0.61, −0.93, −0.87, −0.61, and −0.81 V, respectively. Our calculated results demonstrate that MvK is selectively relevant to methane synthesis. Additionally, we investigated the stability of these surfaces against decomposition and conversion to pure metals concerning thermodynamics and kinetics. It was found that these carbides could remain stable under ambient conditions. The exergonic adsorption of hydrogen on carbon sites, requiring smaller potential values for product formation, and stability against decomposition indicate that these surfaces are highly suitable for CO reduction reactions using the MvK mechanism. Full article
(This article belongs to the Special Issue Carbon-Based Electrochemical Materials for Energy Storage)
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14 pages, 3237 KB  
Article
Dimensional Engineering of 1D/2D Synergistic TiO2 Nanostructures for High-Efficiency Photocatalytic CO2 Reduction
by Xiang Liu, Fujiang Huang, Xiang Shi, Hangmin Xu, Jian Xu and Xingwang Zhu
Materials 2025, 18(17), 4148; https://doi.org/10.3390/ma18174148 - 4 Sep 2025
Abstract
Alongside the gradual progress of industrialization and the continuous development of human society, the problems of environmental pollution and energy crisis have become increasingly prominent. Semiconductor photocatalysis is a promising solution to these challenges. The photocatalytic reduction of CO2 by TiO2 [...] Read more.
Alongside the gradual progress of industrialization and the continuous development of human society, the problems of environmental pollution and energy crisis have become increasingly prominent. Semiconductor photocatalysis is a promising solution to these challenges. The photocatalytic reduction of CO2 by TiO2 to produce carbon monoxide and methane is a process which has been identified as a means of developing clean energy. In this paper, two-dimensional TiO2 (2D-TiO2) was synthesized via a one-step solvothermal method, and one-dimensional TiO2 (1D-TiO2) was obtained through a hydrothermal process. Their photocatalytic CO2 reduction performances were systematically investigated. The results show that 2D-TiO2 exhibits superior catalytic activity compared to 1D-TiO2, which can be attributed to its lamellar structure, larger specific surface area, and improved hydrophilicity, providing more active sites and faster reaction kinetics. To further reveal the reaction mechanism, density functional theory (DFT) calculations were carried out using VASP with the GGA–PBE functional, PAW potentials, and a plane-wave cutoff energy of 520 eV. A 3 × 3 × 1 Monkhorst–Pack grid was used for Brillouin zone integration, and all possible adsorption configurations of CO2*, COOH*, and CO* intermediates on the 2D-TiO2 surface were evaluated. The results confirm that 2D-TiO2 stabilizes key intermediates more effectively, thereby lowering the energy barrier and facilitating CO2 reduction. These findings demonstrate that structural modulation of TiO2 significantly influences its photocatalytic performance and highlight the great potential of 2D-TiO2 for efficient CO2 conversion and clean energy applications. Full article
(This article belongs to the Special Issue Emerging Materials for Photonic and Solar-Driven Applications)
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23 pages, 1946 KB  
Article
Sustainability-Embedded Leadership for Successful Change Management
by Susan Akinwalere, Kirk Chang and Salim Barbhuiya
Sustainability 2025, 17(17), 7973; https://doi.org/10.3390/su17177973 - 4 Sep 2025
Viewed by 7
Abstract
Drawing on Daniel Goleman’s leadership paradigm as well as critically engaging with the Authentic Leadership and Complexity Leadership theories, this article explores how leadership drives change management, specifically in the context of advancing organizational sustainability. While change management has been widely examined in [...] Read more.
Drawing on Daniel Goleman’s leadership paradigm as well as critically engaging with the Authentic Leadership and Complexity Leadership theories, this article explores how leadership drives change management, specifically in the context of advancing organizational sustainability. While change management has been widely examined in areas such as technology adoption and restructuring, there is less clarity on how to lead change that directly supports sustainability goals. Therefore, the current research addresses the gap by focusing on leadership strategies that effectively embed sustainability into leadership practices. Using a theory triangulation method, we built an analytic framework that integrates theoretical and empirical perspectives to better understand how sustainability-embedded leadership can support change management for the best possible outcome. Research data are gathered from respected academic sources including ProQuest, JSTOR, and Google Scholar. Research findings reveal that leaders who tailor their leadership to specific situations are more effective at advancing organizational sustainability than those who rely on a single type of leadership. We also create a contrast table to demonstrate the characteristics of eight leadership types, with a focus on how each can contribute to organizational performance and sustainability. The table serves as a managerial guide for aligning leadership strategies with sustainability objectives. The current research contributes to the intersection of leadership and sustainability by identifying how different leadership types affect an organization’s ability to adopt and implement sustainable practices. By clarifying the strengths and limitations of each approach, the current research enhances the understanding of how situation-oriented leadership can support sustainability goals. The findings also have practical implications for how organizations design and implement change management policies aimed at long-term environmental, social, and economic sustainability. Limitations and future research directions are discussed. Full article
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21 pages, 375 KB  
Review
Sherlock Holmes Doesn’t Play Dice: The Mathematics of Uncertain Reasoning When Something May Happen, That You Are Not Even Able to Figure Out
by Guido Fioretti
Entropy 2025, 27(9), 931; https://doi.org/10.3390/e27090931 - 4 Sep 2025
Viewed by 45
Abstract
While Evidence Theory (also known as Dempster–Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its distinctive features. In particular, with this paper [...] Read more.
While Evidence Theory (also known as Dempster–Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its distinctive features. In particular, with this paper I stress that an extended version of Evidence Theory can express the uncertainty deriving from the fear that events may materialize, that one is not even able to figure out. By contrast, Probability Theory must limit itself to the possibilities that a decision-maker is currently envisaging. I compare this extended version of Evidence Theory to cutting-edge extensions of Probability Theory, such as imprecise and sub-additive probabilities, as well as unconventional versions of Information Theory that are employed in data fusion and transmission of cultural information. A possible application to creative usage of Large Language Models is outlined, and further extensions to multi-agent interactions are outlined. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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30 pages, 1729 KB  
Article
FiCT-O: Modelling Fictional Characters in Detective Fiction from the 19th to the 20th Century
by Enrica Bruno, Lorenzo Sabatino and Francesca Tomasi
Humanities 2025, 14(9), 180; https://doi.org/10.3390/h14090180 - 3 Sep 2025
Viewed by 73
Abstract
This paper proposes a formal descriptive model for understanding the evolution of characters in detective fiction from the 19th to the 20th century, using methodologies and technologies from the Semantic Web. The integration of Digital Humanities within the theory of comparative literature opens [...] Read more.
This paper proposes a formal descriptive model for understanding the evolution of characters in detective fiction from the 19th to the 20th century, using methodologies and technologies from the Semantic Web. The integration of Digital Humanities within the theory of comparative literature opens new paths of study that allow for a digital approach to the understanding of intertextuality through close reading techniques and ontological modelling. In this research area, the variety of possible textual relationships, the levels of analysis required to classify these connections, and the inherently referential nature of certain literary genres demand a structured taxonomy. This taxonomy should account for stylistic elements, narrative structures, and cultural recursiveness that are unique to literary texts. The detective figure, central to modern literature, provides an ideal lens for examining narrative intertextuality across the 19th and 20th centuries. The analysis concentrates on character traits and narrative functions, addressing various methods of rewriting within the evolving cultural and creative context of authorship. Through a comparative examination of a representative sample of detective fiction from the period under scrutiny, the research identifies mechanisms of (meta)narrative recurrence, transformation, and reworking within the canon. The outcome is a formal model for describing narrative structures and techniques, with a specific focus on character development, aimed at uncovering patterns of continuity and variation in diegetic content over time and across different works, adaptable to analogous cases of traditional reworking and narrative fluidity. Full article
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15 pages, 282 KB  
Article
Emotional Skills and Nursing Training: A Study on Italian Students and a TRI-COM-Based Educational Model
by Giulia Savarese, Giovanna Stornaiuolo, Alessandro Vertullo, Carolina Amato and Luna Carpinelli
Brain Sci. 2025, 15(9), 961; https://doi.org/10.3390/brainsci15090961 - 3 Sep 2025
Viewed by 156
Abstract
Background/Objectives: Emotional competence is a crucial skill in nursing education, yet it remains underdeveloped in academic curricula. This study aims to (1) propose and preliminarily apply the TRI-COM model as a conceptual and educational framework to operationalize the definition of emotions within nursing [...] Read more.
Background/Objectives: Emotional competence is a crucial skill in nursing education, yet it remains underdeveloped in academic curricula. This study aims to (1) propose and preliminarily apply the TRI-COM model as a conceptual and educational framework to operationalize the definition of emotions within nursing contexts, and (2) explore the multidimensional structure of emotional competence among nursing students. Methods: A cross-sectional study was conducted with 233 nursing students (M_age = 23.79, SD = 5.19) from various Italian universities, with 82.8% identifying as female. The participants completed an online questionnaire including the Toronto Alexithymia Scale (TAS-20) and the Jefferson Scale of Empathy—Health Profession Student (JSE-HPS) version. Descriptive statistics, t-test, ANOVA, and Pearson’s correlation analyses were performed. Results: The overall mean TAS-20 score was 60.36 (SD = 11.22), which is close to the clinical threshold (cut-off = 61). The EOT subscale showed the highest mean (M = 26.48, SD = 3.16), suggesting a tendency toward externally oriented thinking. The mean JSE-HPS total score was 87.05 (SD = 7.88), with higher scores for Perspective Taking (M = 60.95, SD = 7.42) than Compassionate Care (M = 18.92, SD = 6.40). A significant gender difference was found in Perspective Taking (female: M = 61.54, male: M = 58.10; p = 0.007). The ANOVA results showed no significant differences in empathy across academic years, but the DIF subscale of TAS-20 showed a trend near significance (p = 0.053). Significant negative correlations were observed between age and TAS-20 scores (e.g., age–TAS-20 total: r = −0.23, p < 0.001). Conclusions: The findings suggest a general tendency toward rationalization and emotional detachment among students, possibly as a coping strategy in emotionally demanding contexts. The TRI-COM model—an original pedagogical framework inspired by tripartite theories of emotion—was used as a conceptual lens, providing a preliminary framework to interpret emotional competence in nursing education. Further research is needed to validate its educational relevance and explore practical applications within curricula. Full article
(This article belongs to the Special Issue Defining Emotion: A Collection of Current Models)
30 pages, 403 KB  
Article
The Numerical Solution of Volterra Integral Equations
by Peter Junghanns
Axioms 2025, 14(9), 675; https://doi.org/10.3390/axioms14090675 - 1 Sep 2025
Viewed by 122
Abstract
Recently we studied a collocation–quadrature method in weighted L2 spaces as well as in the space of continuous functions for a Volterra-like integral equation of the form [...] Read more.
Recently we studied a collocation–quadrature method in weighted L2 spaces as well as in the space of continuous functions for a Volterra-like integral equation of the form u(x)αx1h(xαy)u(y)dy=f(x),0<x<1, where h(x) (with a possible singularity at x=0) and f(x) are given (in general complex-valued) functions, and α(0,1) is a fixed parameter. Here, we want to investigate the same method for the case when α=1. More precisely, we consider (in general weakly singular) Volterra integral equations of the form u(x)0xh(x,y)(xy)κu(y)dy=f(x),0<x<1, where κ>1, and h:DC is a continuous function, D=(x,y)R2:0<y<x<1. The passage from 0<α<1 to α=1 and the consideration of more general kernel functions h(x,y) make the studies more involved. Moreover, we enhance the family of interpolation operators defining the approximating operators, and, finally, we ask if, in comparison to collocation–quadrature methods, the application of the Nyström method together with the theory of collectively compact operator sequences is possible. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
14 pages, 3639 KB  
Article
Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction
by Kewei Yu, Xinyu Liu, Meiyan Wang and Jingyao Liu
Catalysts 2025, 15(9), 837; https://doi.org/10.3390/catal15090837 - 1 Sep 2025
Viewed by 253
Abstract
Single-atom catalysts supported by two-dimensional materials have been widely used in the electrochemical CO2 reduction reaction (CO2RR). Defects are inevitably generated during the preparation of two-dimensional materials. In this study, six Fe–N4-doped graphene catalysts (CAT1–CAT6) containing single carbon [...] Read more.
Single-atom catalysts supported by two-dimensional materials have been widely used in the electrochemical CO2 reduction reaction (CO2RR). Defects are inevitably generated during the preparation of two-dimensional materials. In this study, six Fe–N4-doped graphene catalysts (CAT1–CAT6) containing single carbon vacancy defects were designed and calculated using density functional theory (DFT) calculations. The stability, catalytic activity and product selectivity of these catalysts for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 were discussed and compared with the defect-free Fe−N4-doped graphene catalyst (CAT0). The results show that CAT1–CAT6 all exhibit excellent thermodynamic and electrochemical stabilities. The possible reaction pathways for CO2 reduction to different C1 products were systematically investigated. The CAT2, CAT3 and CAT6 exhibit high selectivity for HCOOH, whereas the products of CAT1, CAT4 and CAT5 are HCOOH, CH3OH and CH4, the same as those of CAT0. Moreover, these six catalysts more effectively suppress the competing hydrogen evolution reaction (HER) compared to CAT0, indicating that the defect improves the catalytic selectivity of CO2RR. Among all of the catalysts, CAT2 demonstrates the most prominent catalytic activity and selectivity toward the CO2 reduction reaction (CO2RR). The large distortion of Fe−N4 in *HCOO with CAT2 contributes to the lower limiting potential UL. We hope that the finding that the large distortion of Fe−N4 could lower the limiting potential will provide theoretical insights for the design of more efficient CO2RR electrocatalysts. Full article
(This article belongs to the Special Issue Catalysis Accelerating Energy and Environmental Sustainability)
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21 pages, 1005 KB  
Article
Teachers’ Responses to Six-Year-Old Students’ Input: Learning Opportunities in Early Mathematics Education
by Jessica Elofsson and Anna-Lena Ekdahl
Educ. Sci. 2025, 15(9), 1127; https://doi.org/10.3390/educsci15091127 - 30 Aug 2025
Viewed by 289
Abstract
This study explores how teachers in Swedish preschool classes respond to and elaborate on six-year-old students’ input during mathematics teaching. The aim is to understand how different teacher responses offer different learning opportunities related to numbers and number relations. Data were collected through [...] Read more.
This study explores how teachers in Swedish preschool classes respond to and elaborate on six-year-old students’ input during mathematics teaching. The aim is to understand how different teacher responses offer different learning opportunities related to numbers and number relations. Data were collected through classroom observations of 145 teaching episodes across 95 preschool classes. Each episode was analyzed using an adapted version of the Mediating Primary Mathematics framework. Four qualitatively different response categories, predefined within the framework, were used to capture variation in how student input was responded to. Although most teaching episodes involved brief confirmations, only a few episodes included elaborations that offered students opportunities to engage more deeply with mathematical ideas. Two teaching episodes were selected for a closer analysis, using variation theory of learning, with the aim of describing the different learning opportunities offered depending on how the teachers responded to and elaborated on student input. The results show that, in both teaching episodes, students were given opportunities to learn that numbers can be represented in different ways. In one episode, the teacher’s elaboration enabled students to learn how to use units of five to count collections larger than five. In the other episode, although groups of five were represented visually, they were not explicitly used as a strategy for determining the total, and no alternative to counting by single units was offered. The study highlights the importance of how teachers respond to student input and how these responses influence what becomes possible to learn in early mathematics education. Full article
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18 pages, 3139 KB  
Article
A Kinetic Theory Approach to Modeling Counterflow in Pedestrian Social Groups
by Nouamane Bakhdil, Carlo Bianca and Abdelilah Hakim
Mathematics 2025, 13(17), 2788; https://doi.org/10.3390/math13172788 - 30 Aug 2025
Viewed by 311
Abstract
This article focuses on modeling counterflows within pedestrian social groups in a corridor using the kinetic theory approach, specifically when two social groups move in opposite directions. The term social group refers to a set of pedestrians with established social relationships who stay [...] Read more.
This article focuses on modeling counterflows within pedestrian social groups in a corridor using the kinetic theory approach, specifically when two social groups move in opposite directions. The term social group refers to a set of pedestrians with established social relationships who stay as close as possible to one another and share a common goal or destination, such as friends or family. The model accounts for interactions both within the same social group and between pedestrians from different social groups. Numerical simulations based on a Monte Carlo particle method are performed. A key criterion for evaluating simulation models is their ability to reproduce empirically observed collective motion patterns. One of the most significant emergent behaviors in bidirectional pedestrian flows is lane formation. To analyze this phenomenon, we employ Yamori’s band index to quantify the evolution of lane structures. Full article
(This article belongs to the Section E4: Mathematical Physics)
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16 pages, 310 KB  
Article
Walking Together Differently: Empirical Insights into Emerging Church Communities in Hungary
by Márta Katalin Korpics, Lajos Kovács and Balázs Siba
Religions 2025, 16(9), 1125; https://doi.org/10.3390/rel16091125 - 30 Aug 2025
Viewed by 299
Abstract
This study examines the transformation of communities within Christian churches in late-modern and postmodern social contexts. As a theoretical foundation, it presents changes in the concept of community, with a particular focus on the role of religious communities. Emphasis is placed on community [...] Read more.
This study examines the transformation of communities within Christian churches in late-modern and postmodern social contexts. As a theoretical foundation, it presents changes in the concept of community, with a particular focus on the role of religious communities. Emphasis is placed on community as a social and spiritual resource and on the possibilities for reorganising churches. Three national case studies—an urban Reformed congregation, a small-town Catholic parish, and an ecumenical pilgrimage community—will be used to illustrate the functioning, challenges, and responses of church communities. This research uses both qualitative and quantitative methods, and the results highlight the power of community retention, the importance of personal relationships, and spiritual depth. This study also highlights the theory that the key to church renewal lies in rethinking and consciously building community forms. Digital space, personal networks, and spiritual needs are calling for new models for the church. Full article
(This article belongs to the Section Religions and Theologies)
23 pages, 1573 KB  
Article
The Evolution of Monkeypox Vaccination Acceptance in Romania: A Comparative Analysis (2022–2025), Psychosocial Perceptions, and the Impact of Anti-Vaccination Rhetoric on Societal Security
by Cătălin Peptan, Flavius Cristian Mărcău, Olivia-Roxana Alecsoiu, Dragos Mihai Panagoret, Marian Emanuel Cojoaca, Alina Magdalena Musetescu, Genu Alexandru Căruntu, Alina Georgiana Holt, Ramona Mihaela Nedelcuță and Victor Gheorman
Behav. Sci. 2025, 15(9), 1175; https://doi.org/10.3390/bs15091175 - 29 Aug 2025
Viewed by 231
Abstract
This study examines the evolution of willingness to accept the monkeypox (Mpox) vaccine in Romania between 2022 and 2025. It explores key sociodemographic and behavioral predictors of vaccine acceptance and investigates how public perceptions—particularly concerning disease severity and conspiracy beliefs—have shifted across two [...] Read more.
This study examines the evolution of willingness to accept the monkeypox (Mpox) vaccine in Romania between 2022 and 2025. It explores key sociodemographic and behavioral predictors of vaccine acceptance and investigates how public perceptions—particularly concerning disease severity and conspiracy beliefs—have shifted across two independent cross-sectional samples. Two nationally distributed surveys were conducted in July 2022 (n = 820) and January–February 2025 (n = 1029), targeting Romanian residents aged 18 and above. Data were analyzed using descriptive statistics, Chi-square tests, Kolmogorov–Smirnov tests, and a Random Forest classification model to assess the relative importance of predictors of vaccine acceptance. Between 2022 and 2025, vaccine acceptance increased modestly, particularly among individuals aged 36–65 and those with prior experience of voluntary or COVID-19 vaccination. Random Forest analysis identified behavioral factors as the strongest predictors of acceptance in both years, while the influence of education and gender varied over time. Belief in conspiracy theories slightly declined and lost predictive relevance by 2025. Perceptions of pandemic potential and fear of infection also decreased, suggesting reduced risk salience and possible pandemic fatigue. Despite a slight upward trend, overall Mpox vaccine acceptance in Romania remains among the lowest in Europe. These findings highlight the need for targeted public health communication, particularly toward skeptical or demographically vulnerable groups. Prior vaccination behavior emerged as a key driver of acceptance, indicating that trust-building strategies should capitalize on existing pro-vaccination habits. Future research should adopt qualitative and longitudinal approaches to better capture the evolving psychosocial dynamics of vaccine hesitancy. Full article
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27 pages, 3818 KB  
Article
A Novel Master Curve Formulation with Explicitly Incorporated Temperature Dependence for Asphalt Mixtures: A Model Proposal with a Case Study
by Gilberto Martinez-Arguelles, Diego Casas, Rita Peñabaena-Niebles, Oswaldo Guerrero-Bustamante and Rodrigo Polo-Mendoza
Infrastructures 2025, 10(9), 227; https://doi.org/10.3390/infrastructures10090227 - 28 Aug 2025
Viewed by 271
Abstract
Accurately modelling and simulating the stiffness modulus of asphalt mixtures is essential for reliable pavement design and performance prediction under varying environmental and loading conditions. The preceding is commonly achieved through master curves, which relate stiffness to loading frequency at a reference temperature. [...] Read more.
Accurately modelling and simulating the stiffness modulus of asphalt mixtures is essential for reliable pavement design and performance prediction under varying environmental and loading conditions. The preceding is commonly achieved through master curves, which relate stiffness to loading frequency at a reference temperature. However, conventional master curves face two primary limitations. Firstly, temperature is not treated as a state variable; instead, its effect is indirectly considered through shift factors, which can introduce inaccuracies due to their lack of thermodynamic consistency across the entire range of possible temperatures. Secondly, conventional master curves often encounter convergence difficulties when calibrated with experimental data constrained to a narrow frequency spectrum. In order to address these shortcomings, this investigation proposes a novel formulation known as the Thermo-Stiffness Integration (TSI) model, which explicitly incorporates both temperature and frequency as state variables to predict the stiffness modulus directly, without relying on supplementary expressions such as shift factors. The TSI model is built on thermodynamics-based principles (such as Eyring’s rate theory and activation free energy) and leverages the time–temperature superposition principle to create a physically consistent representation of the mechanical behaviour of asphalt mixtures. This manuscript presents the development of the TSI model along with its application in a case study involving eight asphalt mixtures, including four hot-mix asphalts and four warm-mix asphalts. Each type of mixture contains recycled concrete aggregates at replacement levels of 0%, 15%, 30%, and 45% as partial substitutes for coarse natural aggregates. This diverse set of materials enables a robust evaluation of the model’s performance, even under non-traditional mixture designs. For this case study, the TSI model enhances computational stability by approximately 4 to 45 times compared to conventional master curves. Thus, the main contribution of this research lies in establishing a valuable mathematical tool for both scientists and practitioners aiming to improve the design and performance assessment of asphalt mixtures in a more physically realistic and computationally stable approach. Full article
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16 pages, 570 KB  
Article
A Novel Approach to the Collatz Conjecture with Petri Nets
by David Mailland and Iwona Grobelna
Information 2025, 16(9), 745; https://doi.org/10.3390/info16090745 - 28 Aug 2025
Viewed by 450
Abstract
The Collatz conjecture is a famous unsolved problem in mathematics, known for its deceptively simple rules that generate complex, unpredictable behaviour. It can be efficiently modelled using a Petri net that represents its inverse graph, where each place corresponds to an integer and [...] Read more.
The Collatz conjecture is a famous unsolved problem in mathematics, known for its deceptively simple rules that generate complex, unpredictable behaviour. It can be efficiently modelled using a Petri net that represents its inverse graph, where each place corresponds to an integer and each transition encodes an inverse rule. The net, constructed up to a bound n, reveals the tree-like structure of predecessors and highlights properties such as recurrence, reachability, and liveness. Token flows simulate possible trajectories towards 1. This formal approach enables the investigation of the problem through discrete event systems theory and opens perspectives for parametric or inductive extensions beyond the bounded domain. The model proposed provides a structured framework for visualising and analysing the inverse dynamics of the conjecture. Some key numerical results highlight the challenges of working within a finite domain: for nmax=1000, the constructed Petri net comprises 1000 places and 667 transitions, including 417 source nodes (no predecessors), 333 sink nodes (no successors), and 218 isolated orphans, i.e., nodes only reachable via Div2 transitions with no incoming 3n+1 edge. Full article
(This article belongs to the Special Issue Intelligent Information Technology, 2nd Edition)
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38 pages, 12981 KB  
Article
Development and Analysis of an Exoskeleton for Upper Limb Elbow Joint Rehabilitation Using EEG Signals
by Christian Armando Castro-Moncada, Alan Francisco Pérez-Vidal, Gerardo Ortiz-Torres, Felipe De Jesús Sorcia-Vázquez, Jesse Yoe Rumbo-Morales, José-Antonio Cervantes, Carmen Elvira Hernández-Magaña, María Dolores Figueroa-Jiménez, Jorge Aurelio Brizuela-Mendoza and Julio César Rodríguez-Cerda
Appl. Syst. Innov. 2025, 8(5), 126; https://doi.org/10.3390/asi8050126 - 28 Aug 2025
Viewed by 1076
Abstract
Motor impairments significantly affect individuals’ ability to perform activities of daily living, reducing autonomy and quality of life. In response to this, robot-assisted rehabilitation has emerged as an effective and practical solution, enabling controlled limb movements and supporting functional recovery. This study presents [...] Read more.
Motor impairments significantly affect individuals’ ability to perform activities of daily living, reducing autonomy and quality of life. In response to this, robot-assisted rehabilitation has emerged as an effective and practical solution, enabling controlled limb movements and supporting functional recovery. This study presents the development of an upper-limb exoskeleton designed to assist rehabilitation by integrating neurophysiological signal processing and real-time control strategies. The system incorporates a proportional–derivative (PD) controller to execute cyclic flexion and extension movements based on a sinusoidal reference signal, providing repeatability and precision in motion. The exoskeleton integrates a brain–computer interface (BCI) that utilizes electroencephalographic signals for therapy selection and engagement enabling user-driven interaction. The EEG data extraction was possible by using the UltraCortex Mark IV headset, with electrodes positioned according to the international 10–20 system, targeting alpha-band activity in channels O1, O2, P3, P4, Fp1, and Fp2. These channels correspond to occipital (O1, O2), parietal (P3, P4), and frontal pole (Fp1, Fp2) regions, associated with visual processing, sensorimotor integration, and attention-related activity, respectively. This approach enables a more adaptive and personalized rehabilitation experience by allowing the user to influence therapy mode selection through real-time feedback. Experimental evaluation across five subjects showed an overall mean accuracy of 86.25% in alpha wave detection for EEG-based therapy selection. The PD control strategy achieved smooth trajectory tracking with a mean angular error of approximately 1.70°, confirming both the reliability of intention detection and the mechanical precision of the exoskeleton. Also, our core contributions in this research are compared with similar studies inspired by the rehabilitation needs of stroke patients. In this research, the proposed system demonstrates the potential of integrating robotic systems, control theory, and EEG data processing to improve rehabilitation outcomes for individuals with upper-limb motor deficits, particularly post-stroke patients. By focusing the exoskeleton on a single degree of freedom and employing low-cost manufacturing through 3D printing, the system remains affordable across a wide range of economic contexts. This design choice enables deployment in diverse clinical settings, both public and private. Full article
(This article belongs to the Section Medical Informatics and Healthcare Engineering)
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