Given two graphs G and H, an H-decomposition of G is a partition of the
edge set of G such that each part is either a single edge or forms a graph
isomorphic to H. Let f(n;H) be the smallest number  such that any graph
G of order n admits an H-decomposition with at most f(n;H)  parts. Pikhurko and
Sousa conjectured that f(n;H) = ex(n;H) for (H)  3 and all sufficiently
large n, where ex(n;H) denotes the maximum number of edges in a graph on n vertices not containing H as a subgraph. Their conjecture has been veried by
Ozkahya and Person for all edge-critical graphs H. In this article, the conjecture
is veried for the k-fan graph. The k-fan graph, denoted by F_k, is the graph on
2k + 1 vertices consisting of k triangles which intersect in exactly one common
vertex called the centre of the k-fan.

ABSTRACTIn this article, we study stability properties for two-dimensional non-Newtonian fluids. More precisely, we consider stochastic perturbations of the second grade fluid equations, with Navier slip boundary condition, and analyse the asymptotic behaviour of the solutions as t→+∞. We prove that the strong solutions (in the probability sense) of the stochastic evolutionary equation converge exponentially to the stationary solution in the mean square and almost surely. In addition, we study the stabilization of the deterministic model by introducing a suitable stochastic noise.

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.

Abstract One of the unresolved aspects of cellulose-based liquid crystalline phases is their chirality. Although cellulose is intrinsically chiral, both left-handed (LH) and right-handed (RH) chiral nematic phases are reported in cellulose derivatives under different conditions. The origin of these discrepancies?and whether LH and RH twisted structures coexist within a single material?has remained unclear. Here, the first direct evidence of hierarchical LH and RH twisted structures coexisting in a solvent-free, thermotropic cellulose derivative at room temperature is provided. Free-standing cholesteric films exhibit distinct LH and RH twisted domains, whose pitches respond oppositely to uniaxial mechanical strain: the LH pitch increases, while the RH pitch decreases with increasing strain. This contrasting response results from the coexistence of intertwined LH and RH twisted structures, whose optical axes are oriented differently relative to the strain direction. Notably, after stretching beyond their elastic limit, the films spontaneously recover their original shape within minutes. During this recovery, circular dichroism (CD) measurements reveal an increase in RH pitch and a decrease in LH pitch, evidencing reversible, strain-responsive behavior. Multiscale structural characterization confirms the hierarchical chiral organization and its mechanoresponsive nature, providing new insights into the origin of chirality in cellulose-based liquid crystalline materials.

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.

The study "Innovating Social Dialogue and Collective Bargaining Toward Artificial Intelligence in the MET Industries" explores the integration of AI in the metal, engineering, and technology-based (MET) sectors, emphasizing the role of social dialogue and collective bargaining in ensuring ethical, transparent, and worker-centric AI adoption. The research highlights the collaborative efforts of European social partners — Ceemet and IndustriAll Europe — to develop conclusions addressing AI’s impact on occupational health and safety (OHS), human resources management (HRM), data protection, and skills development. Key findings reveal that while AI offers benefits such as increased efficiency and automation of repetitive tasks, it also poses risks like job displacement, privacy concerns, and algorithmic bias. The study underscores the necessity of involving workers and trade unions in AI implementation to safeguard rights, autonomy, and well-being. Social partners from non EU countries advocate for a comparable regulatory frameworks as EU members, such as the EU AI Act, to balance productivity gains with fundamental labor rights. The research identifies the need for practices in collective agreements which address digital rights, the right to disconnect, and transparency in AI-based decision-making. Recommendations include establishing a European database on AI applications in the MET sector, conducting critical case studies, and fostering further social dialogue to ensure AI contributes positively to both workers and industry competitiveness. The study concludes that proactive collaboration among social partners is essential for harnessing AI’s potential while mitigating its risks.

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 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.