Discrete Kakeya-type problems and small bases

A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erdős and Newman on bases for sets of integers, and to obtain several extensions for other groups.     

Influence of Drug Load on the Printability and Solid-State Properties of 3D-Printed Naproxen-Based Amorphous Solid Dispersion

Fused deposition modelling-based 3D printing of pharmaceutical products is facing challenges like brittleness and printability of the drug-loaded hot-melt extruded filament feedstock and stabilization of the solid-state form of the drug in the final product. The aim of this study was to investigate the influence of the drug load on printability and physical stability. The poor glass former naproxen (NAP) was hot-melt extruded with Kollidon^® VA 64 at 10–30% w/w drug load. The extrudates (filaments) were characterised using differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and thermogravimetric analysis (TGA). It was confirmed that an amorphous solid dispersion was formed. A temperature profile was developed based on the results from TGA, DSC, and DMA and temperatures used for 3D printing were selected from the profile. The 3D-printed tablets were characterised using DSC, X-ray computer microtomography (XµCT), and X-ray powder diffraction (XRPD). From the DSC and XRPD analysis, it was found that the drug in the 3D-printed tablets (20 and 30% NAP) was amorphous and remained amorphous after 23 weeks of storage (room temperature (RT), 37% relative humidity (RH)). This shows that adjusting the drug ratio can modulate the brittleness and improve printability without compromising the physical stability of the amorphous solid dispersion.     

Cover Feature: Effects of Microhydration on the Mechanisms of Hydrolysis and Cl− Substitution in Reactions of N2O5 and Seawater (ChemPhysChem 5/2023)

The reaction of N₂O₅ at atmospheric interfaces has recently received considerable attention due to its importance in atmospheric chemistry. N₂O₅ reacts preferentially with Cl⁻ to form ClNO₂/NO₃⁻ (Cl⁻ substitution), but can also react with H₂O to form 2HNO₃ (hydrolysis). In this paper, we explore these competing reactions in a theoretical study of the clusters N₂O₅/Cl⁻/nH₂O (n=2–5), resulting in the identification of three reaction motifs. First, we uncovered an S_N2-type Cl⁻ substitution reaction of N₂O₅ that occurs very quickly due to low barriers to reaction. Second, we found a low-lying pathway to hydrolysis via a ClNO₂ intermediate (two-step hydrolysis). Finally, we found a direct hydrolysis pathway where H₂O attacks N₂O₅ (one-step hydrolysis). We find that Cl⁻ substitution is the fastest reaction in every cluster. Between one-step and two-step hydrolysis, we find that one-step hydrolysis barriers are lower, making two-step hydrolysis (via ClNO₂ intermediate) likely only when concentrations of Cl⁻ are high.