Pseudopeptide‐Based Hydrogels Trapping Methylene Blue and Eosin Y

We present herein the preparation of four different hydrogels based on the pseudopeptide gelator Fmoc‐l ‐Phe‐d ‐Oxd‐OH (Fmoc=fluorenylmethyloxycarbonyl), either by changing the gelator concentration or adding graphene oxide (GO) to the water solution. The hydrogels have been analysed by rheological studies that demonstrated that pure hydrogels are slightly stronger compared to GO‐loaded hydrogels. Then the hydrogels efficiency to trap the cationic methylene blue (MB) and anionic eosin Y (EY) dyes has been analyzed. MB is efficiently trapped by both the pure hydrogel and the GO‐loaded hydrogel through π–π interactions and electrostatic interactions. In contrast, the removal of the anionic EY is achieved in less satisfactory yields, due to the unfavourable electrostatic interactions between the dye, the gelator and GO.     

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 $n\ge 6$.