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 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.

n/a

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.

The European Metal sector is at a critical juncture, navigating through the complex landscape of the twin transition towards digitalization and sustainability. This transformative journey, though essential, is fraught with challenges that if not addressed, could undermine the sector's resilience, competitiveness and social equity. The Metallica project emerges as a pivotal initiative in this context, aiming to mitigate these challenges by fostering enhanced worker engagement, participation and conflict resolution.