OPTIMAL MAPS IN NON BRANCHING SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

We prove existence of optimal maps in non branching spaces with Ricci curvature bounded from below. The approach we adopt makes no use of Kantorovich potentials.     

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.     

Ice‐Templated Scaffolds with Microridged Pores Direct DRG Neurite Growth

Successful spinal cord repair is thought to be promoted with hierarchically structured scaffolds. These should combine aligned porosity with additional linear features on the micrometer scale to guide axons across multiple length scales. Such scaffolds are generated through the carefully controlled directional solidification of an aqueous biopolymer solution, followed by lyophilization. Under specific freezing conditions this yields a highly regular and aligned lamellar architecture. This architecture exhibits uniform ridges of controlled height and width on the lamellar surface. These ridges run parallel to the pore axis, serving as secondary guidance features. The ridges are capable of linearly aligning 62.4% of chick dorsal root ganglia neurites to within ±10° of the ridge direction. Notably, neurites sprouting perpendicular to the ridge are guided into alignment with these microridged features.     

Reversible Fragmentation and Self‐Assembling of Nematic Liquid Crystal Droplets on Functionalized Pyroelectric Substrates

Investigation on the behavior of nematic liquid crystals on functionalized polar dielectric crystal substrates is accomplished. Very interesting effects can be observed in maneuvering liquid crystal droplets on the substrate surface, driven by electric fields generated by pyroelectric effect. Reversible drops fragmentation and self‐assembling in different configurations can be achieved. The dynamics of the observed phenomena is studied and the repeatability of the process is full assessed.     

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.