Existence of maximizers for Sobolev–Strichartz inequalities

We prove the existence of maximizers of Sobolev–Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrödinger flows.     

Syntheses,structure, and reactivity of acyclic enetriyne and enetetrayne derivatives

Sonogashira coupling of buta-1,3-diynylbenzene with ((2-iodophenyl)ethynyl)trimethylsilane and 1,2-diiodobenzene led to the novel enetriyne, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene, and enetetrayne, 1,2-bis(phenylbuta-1,3-diynyl)benzene, respectively. Solid state structural and thermal analyses are also described. In solution, 1-ethynyl-2-(phenylbuta-1,3-diynyl)benzene was found to undergo thermal Bergman cyclization to afford 2-(phenylethynyl)naphthalene.     

On circular–linear one-factorizations of the complete graph

In Korchmáros et al. (2018)one-factorizations of the complete graph $K_n$ are constructed for $n=q+1$ with any odd prime power $q$ such that either $q\equiv 1(mod4)$ or $q=2^h?1$. The arithmetic restriction $n=q+1$ is due to the fact that the vertices of $K_n$ in the construction are the points of a conic $\Omega$ in the finite plane of order $q$. Here we work on the Euclidean plane and describe an analogous construction where the role of $\Omega$ is taken by a regular $n$-gon. This allows us to remove the above constraints and construct one-factorizations of $K_n$ for every even $n\ge 6$.     

Exploring the Phase-Selective,Green, Hydrothermal Synthesis of Upconverting Doped Sodium Yttrium Fluoride: Effects of Temperature,Time, and Precursors

The aim of this work was i) to develop a hydrothermal, low-temperature synthesis protocol affording the upconverting hexagonal phase NaYF₄ with suitable dopants while adhering to the “green chemistry” standards and ii) to explore the effect that different parameters have on the products. In optimizing the synthesis protocol, short reaction times and low temperatures (below 150 °C) were considered. Yb³⁺ and Er³⁺ ions were chosen as dopants for the NaYF₄ material. Within the context of the second goal, parameters including nature of the precursors, treatment temperature, and treatment time were investigated to afford a pure hexagonal crystalline phase, both in the doped and undoped materials. To fully explore the synthesis results, the prepared materials were characterized from a structural (XRD), compositional (XPS, ICP-MS), and morphological (SEM) point of view. The upconverting properties of the compounds were confirmed by photoluminescence measurements.     

A Matter of Philosophers and Spheres: Medieval Glosses on Artephius’s Key of Wisdom

The article examines the two Latin versions of Artephius's Clavis sapientiae (Key of Wisdom) that have been preserved in early modern collections of alchemical texts. A comparative analysis of the two versions shows that one of them has undergone a process of textual manipulation. In particular, an interpolation of short philosophical passages concerning the doctrine of prime matter has relevant interpretative implications. These additions appear to be grounded in the early thirteenth-century philosophical debate on cosmology and the first Latinate reception of Aristotle’s metaphysics.     

Effect of nematic ordering on the elasticity and yielding in disordered polymeric solids

The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τ_Y/G between the shear yield strength τ_Y and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τ_Y/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769