Composition Operators on the Lipschitz Space of a Tree

The Lipschitz space ${\mathcal{L}}$ of an infinite tree T rooted at o is defined as the space consisting of the functions ${f : T \rightarrow \mathbb{C}}$ such that $$\beta_f = {\rm sup}\{|f(v) - f(v^-)| : v \in T\backslash\{o\}, \,v^- {\rm parent \, of \,} v\}$$ is finite. Under the norm ${\|f\|_\mathcal{L} = |f(o)|+\beta_f,\mathcal{L}}$ is a Banach space. In this article, the functions φ mapping T into itself whose induced composition operator ${C_{\varphi} : f \mapsto f \circ \varphi}$ on the Lipschitz space is bounded, compact, or an isometry, are characterized. Specifically, it is shown that the symbols of the bounded composition operators are the Lipschitz maps of T into itself viewed as a metric space under the edge-counting distance. The symbols inducing compact operators have finite range while those inducing isometries on ${\mathcal{L}}$ are precisely the onto maps fixing the root and whose images of neighboring vertices coincide or are themselves neighboring vertices. Finally, the spectrum of the operators ${C_\varphi}$ that are isometries is studied in detail.     

Minimum sum set coloring of trees and line graphs of trees

In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.     

Preparation and characterization of boron-based bioglass by sol−gel process

45S5 bioglass has been widely studied in the last few decades because of its bioactivity and promising applications in the biomedical field. Boron, even few studied, represents a potential element to improve the properties of the 45S5 bioglass derivatives. The bioglasses are conventionally prepared by heat treatment of oxides and silicon. Here, the sol?gel method is proposed for the preparation of the boron-based 45S5 bioglass (45S5B) and the classical 45S5 bioglass (45S5), using water-soluble salts as raw materials. The bioglasses were characterized by FTIR, XRD, and SEM, indicating the success of the sol?gel method for preparation of the samples. The bioglasses were also tested in vitro for bioactivity in biological conditions and cytotoxicity against eukaryotic cells. The bioactivity of 45S5B was similar to the bioactivity of 45S5 bioglass, indicated by the deposition of hydroxyapatite crystals at the surface of the pristine bioglasses. The results of cytotoxicity tests revealed that the IC₅₀ of 45S5B (IC₅₀?=?7.56?mg?mL^?1) was similar to the IC₅₀ of 45S5 (IC₅₀?=?8.15?mg?mL^?1), indicating its safety for application in the biomedical field.

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Antiproliferative and Antimicrobial Effects of Rosmarinus officinalis L. Loaded Liposomes

Rosmarinus officinalis L. is a species that is widely known for its culinary and medicinal uses. The purpose of the present study consisted of the evaluation of the antiproliferative and antimicrobial effects of R. officinalis-loaded liposomes (L-R). Characterization of the liposomes was performed by establishing specific parameters. The load of the obtained liposomes was analyzed using an LC-MS method, and antiproliferative assays evaluated the cell viability on a liver adenocarcinoma cell line and on a human hepatic stellate cell line. Antimicrobial assays were performed by agar–well diffusion and by broth microdilution assays. The obtained liposomes showed high encapsulation efficiency, suitable particle size, and good stability. High amounts of caffeic (81.07 ± 0.76), chlorogenic (14.10 ± 0.12), carnosic (20.03 ± 0.16), rosmarinic (39.81 ± 0.35), and ellagic (880.02 ± 0.14) acids were found in their composition, together with other polyphenols. Viability and apoptosis assays showed an intense effect on the cancerous cell line and a totally different pattern on the normal cells, indicating a selective toxicity towards the cancerous ones and an anti-proliferative mechanism. Antimicrobial potential was noticed against all tested bacteria, with a better efficacy towards Gram-positive species. These results further confirm the biological activities of R. officinalis leaf extract, and proposes and characterizes novel delivery systems for their encapsulation, enhancing the biological activities of polyphenols, and overcoming their limitations.     

Ionic liquids as recycling solvents for the synthesis of magnetic nanoparticles

This work describes an easy synthesis (one pot) of MFe(2)O(4) (M = Co, Fe, Mn, and Ni) magnetic nanoparticles MNPs by the thermal decomposition of Fe(Acac)(3)/M(Acac)(2) by using BMI·NTf(2) (1-n-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) or BMI·PF(6) (1-n-butyl-3-methylimidazolium hexafluorophosphate) ionic liquids (ILs) as recycling solvents and oleylamine as the reducing and surface modifier agent. The effects of reaction temperature and reaction time on the features of the magnetic nanomaterials (size and magnetic properties) were investigated. The growth of the MNPs is easily controlled in the IL by adjusting the reaction temperature and time, as inferred from Fe(3)O(4) MNPs obtained at 150 °C, 200 °C and 250 °C with mean diameters of 8, 10 and 15 nm, respectively. However, the thermal decomposition of Fe(Acac)(3) performed in a conventional high boiling point solvent (diphenyl ether, bp 259 °C), under a similar Fe to oleylamine molar ratio used in the IL synthesis, does not follow the same growth mechanism and rendered only smaller NPs of 5 nm mean diameter. All MNPs are covered by at least one monolayer of oleylamine making them readily dispersible in non-polar solvents. Besides the influence on the nanoparticles growth, which is important for the preparation of highly crystalline MNPs, the IL was easily recycled and has been used in at least 20 successive syntheses.     

Chemical basis of peptidoglycan discrimination by PrkC, a key kinase involved in bacterial resuscitation from dormancy

Bacterial Ser/Thr kinases modulate a wide number of cellular processes. In Bacillus subtilis , the Ser/Thr kinase PrkC has been shown to induce germination of bacterial spores in response to DAP-type but not Lys-type cell wall muropeptides. Muropeptides are a clear molecular signal that growing conditions are promising, since they are produced during cell wall peptidoglycan remodeling associated with cell growth and division of neighboring bacteria. However, whether muropeptides are able to bind the protein physically and how the extracellular region is able to distinguish the two types of muropeptides remains unclear. Here we tackled the important question of how the extracellular region of PrkC (EC-PrkC) senses muropeptides. By coupling NMR techniques and protein mutagenesis, we exploited the structural requirements necessary for recognition and binding and proved that muropeptides physically bind to EC-PrkC through DAP-moiety-mediated interactions with an arginine residue, Arg500, belonging to the protein C-terminal PASTA domain. Notably, mutation of this arginine completely suppresses muropeptide binding. Our data provide the first molecular clues into the mechanism of sensing of muropeptides by PrkC.     

Carbon Nano-Flakes Produced by an Inductively Coupled Thermal Plasma System for Catalyst Applications

Carbon material was produced using an inductively coupled thermal plasma torch system of 35 kW and a conical shape reactor. The carbon nanopowders were obtained by plasma decomposition of methane at various flow rates and show a uniform microstructure throughout the reactor. The product has a crystalline graphitic structure, with a stacking of between 6 and 16 planes and a nano-flake morphology with particles dimensions of approximately 100 nm long, 50 nm wide and 5 nm thick. Nitrogen was also introduced in some synthesis experiments along with the methane precursor using flow rates of 0.1 and 0.2 slpm. The resulting product has the same structural properties and the nitrogen is incorporated into the graphitic structure through pyridinic type bonds.