Triassic to Lower Jurassic deposits known as the Silves Group in the Algarve, southern Portugal, have been studied for over 150 years. However, many of this unit’s sedimentological, stratigraphical, and palaeontological aspects remain poorly documented. Here, we present novel observations on sedimentology, stratigraphy, taphonomy, and fauna at the Rocha da Pena site, located in the central part of the Algarve Basin. The investigated sequence is established to correspond to the upper part of the Silves Group. The mudstone, calcrete, and palustrine carbonate facies comprise most of the sequence thickness and are interpreted as having been deposited within coastal alluvial mudflats to palustrine settings under semi-arid and seasonal climates. The overlying siltstone and sandstone facies indicate an environmental shift towards tidally influenced environments, subsequently covered by the latest Triassic to earliest Jurassic volcaniclastics and basaltic lava flows. Furthermore, novel faunal elements, including actinopterygian and unionoid bivalves, are described from mudstone layers. New fossiliferous beds are identified within palustrine facies that yield numerous but poorly preserved materials assigned to cyamodontoid placodonts, hybodont sharks, and actinopterygians. The poor preservation of the remains is attributed to the pedogenetic processes prevalent in the palustrine depositional setting. A distinct faunal composition between the mudstone and palustrine facies is observed. It is preliminarily hypothesized to be likely linked with salinity fluctuations, but sampling bias cannot currently be excluded. The recovered vertebrate fauna aligns most closely with the Carnian and, to a lesser extent, the Norian fossil record. Nonetheless, the precise age of the fossil-bearing levels remains uncertain and can currently be reliably constrained to the upper Carnian–Rhaetian interval. Consequently, this work provides new insights into the palaeoenvironmental evolution of the western Tethys margin during the Late Triassic and highlights the relevance of the Silves Group in reconstructing coastal-continental ecosystem dynamics in southwestern Iberia.Triassic to Lower Jurassic deposits known as the Silves Group in the Algarve, southern Portugal, have been studied for over 150 years. However, many of this unit’s sedimentological, stratigraphical, and palaeontological aspects remain poorly documented. Here, we present novel observations on sedimentology, stratigraphy, taphonomy, and fauna at the Rocha da Pena site, located in the central part of the Algarve Basin. The investigated sequence is established to correspond to the upper part of the Silves Group. The mudstone, calcrete, and palustrine carbonate facies comprise most of the sequence thickness and are interpreted as having been deposited within coastal alluvial mudflats to palustrine settings under semi-arid and seasonal climates. The overlying siltstone and sandstone facies indicate an environmental shift towards tidally influenced environments, subsequently covered by the latest Triassic to earliest Jurassic volcaniclastics and basaltic lava flows. Furthermore, novel faunal elements, including actinopterygian and unionoid bivalves, are described from mudstone layers. New fossiliferous beds are identified within palustrine facies that yield numerous but poorly preserved materials assigned to cyamodontoid placodonts, hybodont sharks, and actinopterygians. The poor preservation of the remains is attributed to the pedogenetic processes prevalent in the palustrine depositional setting. A distinct faunal composition between the mudstone and palustrine facies is observed. It is preliminarily hypothesized to be likely linked with salinity fluctuations, but sampling bias cannot currently be excluded. The recovered vertebrate fauna aligns most closely with the Carnian and, to a lesser extent, the Norian fossil record. Nonetheless, the precise age of the fossil-bearing levels remains uncertain and can currently be reliably constrained to the upper Carnian–Rhaetian interval. Consequently, this work provides new insights into the palaeoenvironmental evolution of the western Tethys margin during the Late Triassic and highlights the relevance of the Silves Group in reconstructing coastal-continental ecosystem dynamics in southwestern Iberia.

In this paper, we study permutations on n elements that are even on every subset of size t. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral. In this context, we define and study monoids that generalize both monoids of order-preserving mappings and monoids of orientation-preserving mappings.

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In this paper, we consider the inverse submonoids AM_n of monotone transformations and AO_n of order-preserving transformations of the alternating inverse monoid AI_n on a chain with n elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of these two submonoids of AI_n.

In this paper, we consider the inverse submonoids AOR_n of oriented transformations and AOP_n of orientation-preserving transformations of the alternating inverse monoid AI_n on a chain with n elements. We compute the cardinalities, describe the Green's structures and the congruences, and calculate the ranks of AOR_n and AOP_n.

Let $\Omega_n$ be a finite chain with $n$ elements $(n\in\mathbb{N})$, and let $\mathcal{POPI}_{n}$ be the semigroup of all injective orientation-preserving partial transformations of $\Omega_n$. In this paper, for any nonempty subset $Y$ of $\Omega_n$, we consider the subsemigroup $\mathcal{POPI}_{n}(Y)$ of $\mathcal{POPI}_{n}$ of all transformations with range contained in $Y$. We describe the Green's relations and study the regularity of $\mathcal{POPI}_{n}(Y)$. Moreover, we calculate the rank of $\mathcal{POPI}_{n}(Y)$ and determine when two semigroups of this type are isomorphic.

In this paper, we consider the monoid PIO_n, of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIO_n^- of order-decreasing transformations. Our main aim is to give presentations for PIO_n^- and PIO_n. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.

In this paper, we consider the monoids of all partial endomorphisms, of all partial weak endomorphisms, of all injective partial endomorphisms, of all partial strong endomorphisms and of all partial strong weak endomorphisms of a star graph with a finite number of vertices. Our main objective is to exhibit a presentation for each of them.

The integration of digital technology to promote mathematical learning remains challenging for teachers. The continuous difficulty in fully achieving technology’s potential highlights the need to further examine and develop models addressing teachers’ knowledge in relation to technology. In this Research Forum, we analyse existing technology-related knowledge models, exploring similarities and differences. We also consider how these models have been used in research, highlighting tensions driven by emerging technologies, and resulting extensions of the models. Finally, we discuss possible integrations across frameworks and the potential to include dimensions beyond knowledge. This discussion aims to deepen understanding of current models and suggest directions and a research agenda for future development.

Polysaccharides in plant cell walls serve as a rich carbon and energy source, yet their structural complexity presents a barrier to efficient degradation. To address this, anaerobic microorganisms like R. flavefaciens have developed sophisticated multi-enzyme complexes known as cellulosomes, which enable the efficient breakdown of these recalcitrant polysaccharides. These complexes are assembled through high-affinity interactions between cohesin (Coh) modules in scaffoldin proteins and dockerin (Doc) modules in cellulosomal enzymes. R. flavefaciens FD-1 harbors one of the most intricate cellulosomes described to date, comprising over 200 Doc-containing proteins encoded in its genome. Despite substantial research on this cellulosome, the role of a group of truncated but functional dockerins, known as group-2 Docs, remains unclear. In this study, we present a detailed structural and binding analysis of a Coh-Doc complex involving the cohesin from the cell-anchoring scaffoldin ScaE and a group-2 Doc that bears only one of the two Ca+2-coordinating loops that characterise the canonical Docs. Our findings reveal a novel tripartite binding mechanism, in which the cohesin can simultaneously bind two distinct dockerin units in three alternative conformations. This discovery provides new insights into the modular versatility of the R. flavefaciens cellulosome and sheds light on the mechanisms that enhance its efficiency in polysaccharide degradation.

Incorporating technologies with Generative Artificial Intelligence (GenAI) into education requires a shift in teaching methodologies. However, little is known about how pre-service teachers perceive the relevance and challenges of this incorporation, particularly in mathematics education. This study investigates pre-service teachers’ interactions with GenAI, addressing the relevance and challenges of integrating it in mathematics teaching and discussing possible implications for their knowledge and professional development. Specifically, it intends to understand: How does the pre-service teachers’ interaction with GenAI during the design and implementation of teaching activities relate to their professional knowledge? And how does this relation impact the relevance they ascribe to GenAI? In this qualitative and interpretative study, involving seven pre-service mathematics teachers, we analyse the interplay between participants’ knowledge and use of a GenAI (in this case, ChatGPT), guided by KTMT – Knowledge for Teaching Mathematics with Technology model. The main conclusions revealed a landscape characterised by promise and challenge, where GenAI can be a valuable educational
tool when used to facilitate discussion and promote critical thinking, highlighting the relevance and development of KTMT. The ability to evaluate and reflect on AI-generated responses can promote professional development, preparing pre-service teachers for an increasing presence of technology in educational environments.

In this note, we consider the monoid PIM_n of all partial monotone transformations on a chain with n elements whose domains and ranges are intervals and its submonoid IM_n constituted by the full transformations. For both of these monoids, our aim is to determine their cardinalities and ranks and define them by means of presentations. We also calculate the number of nilpotent elements of PIM_n.

In this paper, we consider the monoids of all endomorphisms, of all weak endomorphisms, of all strong endomorphisms and of all strong weak endomorphisms of a star graph with a finite number of vertices. Our main objective is to exhibit a presentation for each of them.

In this work, fully patterned zinc tin oxide (ZTO) memristors are introduced using inkjet printing. By targeting a scalable, solution-based fabrication approach, highly stable devices with excellent reproducibility and minimal variability are achieved, using ZTO as the active layer, silver (Ag) as the top electrode, and molybdenum as the bottom electrode. The use of sustainable materials like ZTO enhances scalability and environmental compatibility, paving the way for next-generation, low-power neuromorphic computing. The devices successfully fulfill the fundamental criteria for in materia implementation of physical reservoir computing (PRC), including nonlinearity and fading memory property. The devices are successfully trained for classification tasks with MNIST handwritten dataset, achieving 89.4% accuracy and 86.5% by processing 4-bit and 5-bit input temporal sequences. The integration of printed memristors into hardware-based PRC architecture simplifies training complexity, making them particularly advantageous for energy-efficient, wearable AI systems.