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.

How snow leopard gradually adapted to the extreme environments in Tibet remains unexplored due to the scanty fossil record in Tibet. Here, we recognize five valid outside-Tibet records of the snow leopard lineage. Our results suggest that the snow leopard dispersed out of the Tibetan Plateau multiple times during the Quaternary. The osteological anatomy of the modern snow leopard shows adaptation to the steep slope and, to a lesser extent, cold/high-altitude environment. Fossils and phylogeny suggest that the snow leopard experienced a gradual strengthening of such adaptation, especially since the Middle Pleistocene ( 0.8 million years). Species distribution modeling suggests that the locations of the fossil sites are not within most suitable area, and we argue that local landscape features are more influential factors than temperature and altitude alone. Our study underscores the importance of integrating morphology, fossil records, and species distribution modeling, to comprehensively understand the evolution, ecology, and inform conservation strategies for endangered species. Integrated morphology, fossil records, and SDM reveal the evolution and adaptation in the snow leopard lineage.

Open-cell foams based on hydroxyapatite (HAp) can mimic the extracellular matrix (ECM) to better replace damaged hard tissues and assist in their regeneration processes. Aerogels of HAp nanowires (NW) with barium titanate (BT) particles were produced and characterized regarding their physical and chemical properties, bioactivity, and in vitro cytotoxicity. Considering the role of piezoelectricity (mainly due to collagen) and surface charges in bone remodeling, all BT particles, of size 280 nm and 2 and 3 µm, contained BaTiO3 in their piezoelectric tetragonal phase. The synthesized nanowires were verified to be AB-type carbonated hydroxyapatite. The aerogels showed high porosity and relatively homogeneous distribution of the BT particles. Barium titanate proved to be non-cytotoxic while all the aerogels produced were cytotoxic for an extract concentration of 1 mg/mL but became non-cytotoxic at concentrations of 0.5 mg/mL and below. It is possible that these results were affected by the higher surface area and quicker dissolution rate of the aerogels. In the bioactivity assays, SEM/EDS, it was not easy to differentiate between the apatite deposition and the surface of the HAp wires. However, a quantitative EDS analysis shows a possible CaP deposition/dissolution cycle taking place.

The introduction of exoskeletons by many companies has often resulted in potential users not wanting to wear them. Evaluations of the exoskeleton reveal benefits of use, including ergonomic advantages and a reduction of work-related musculoskeletal disorders. How can this contradiction be explained? By searching the available literature, we can identify the methods used to develop these devices and the methods employed to evaluate their acceptance and benefit. By looking at the product from different viewpoints and involving different disciplines, we will get to the root of this discrepancy. Our findings indicate that the product definition, development focus, and evaluation methods do not sufficiently and adequately address the primary goal of exoskeletons. The development of such devices should be prioritized not only for the delivery of support but also for the motivation of the user. Finally, we put forward the proposal to discuss the establishment of a novel development method for the prospective elaboration of exoskeletons.

Shock absorbers have been widely used in the automotive and aeronautical industries for many years. Inspired on these devices, the paper presents an analytical and numerical assessment of a high performance protective system for building structures against blast loads, which is composed of a shielding element connected to the main structure, at the floor levels, through ductile Energy Absorbing Connectors (EACs). The EACs exploit the external tube inversion mechanism to absorb a significant part of the imparted kinetic energy from the blast wave. While the system prototype has been developed in laboratory, it was characterized and tested in a full-scale blast testing campaign. A validated finite element model was used next to analyze its performance in a more demanding design scenario. The introduction of EACs notably reduces the peak horizontal loads and the kinetic energy transferred to the protected structure, being expected a significant reduction of the stresses in the supporting vertical elements, in addition to the protection of structural and non-structural members. These results encourage further studies of the presented protective system that can be potentially employed for a large variety of blast threat scenarios, especially when increasing the stand-off is not a possible/viable option and sensitive facilities have to be protected.

In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the semigroup of all monotone partial permutations of a finite chain.