On a refinement of Craig’s lattices

Let p be an odd prime. A family of (p−1)-dimensional over-lattices yielding new record packings for several values of p in the interval [149…3001] is presented. The result is obtained by modifying Craig’s construction and considering conveniently chosen Z-submodules of Q(ζ), where ζ is a primitive pth root of unity. For p≥59, it is shown that the center density of the (p−1)-dimensional lattice in the new family is at least twice the center density of the (p−1)-dimensional Craig lattice.     

A note on geodesic connectedness of Gödel type spacetimes

In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former.     

Domination problems for strictly singular operators and other related classes

We survey recent results on domination properties of strictly singular operators and related operator ideals, as well as Banach–Saks operators, Narrow operators and p-summing operators.     

Solvato Modulation of the Magnetic Memory in Isotopically Enriched Erbium Polyoxometalate

Single-Molecule Magnet (SMM) property is by essence molecular, while commonly measured in solid crystalline state. Solvent crystallization molecules are usually neglected in the analysis and interpretation of solid-state properties. The solvation/desolvation process in the polyoxometalate(POM)-based Na₉[Er(W₅O₁₈)₂] ⋅ 35 H₂O SMM demonstrates that the dehydrated form relaxes more than 1000 times faster than the initial state, while the rehydration process allows the quasi complete recovering of the initial magnetic behaviour. This dehydration process is monitored by thermogravimetric analysis (TGA) and temperature-dependent X-ray powder diffraction, and rationalized by periodic quantum chemical calculations evidencing the tremendous role of the labile water molecules in the stability of the edifice. Ab-initio calculations highlight that sodium ions localization in the structure drive the magnetic responses. Isotopic enrichment with nuclear spin free (¹⁶⁶Er, I=0) Er^III ions shows that the relaxation dynamics in the quantum regime depends on the nuclear spin.     

Macrocystis pyrifera Extract Residual as Nutrient Source for the Production of Sophorolipids Compounds by Marine Yeast Rhodotorula rubra

Seaweed processing generates liquid fraction residual that could be used as a low-cost nutrient source for microbial production of metabolites. The Rhodotorula strain is able to produce antimicrobial compounds known as sophorolipids. Our aim was to evaluate sophorolipid production, with antibacterial activity, by marine Rhodotorula rubra using liquid fraction residual (LFR) from the brown seaweed Macrocystis pyrifera as the nutrient source. LFR having a composition of 32% w/w carbohydrate, 1% w/w lipids, 15% w/w protein and 52% w/w ash. The best culture condition for sophorolipid production was LFR 40% v/v, without yeast extract, artificial seawater 80% v/v at 15 °C by 3 growth days, with the antibacterial activity of 24.4 ± 3.1 % on Escherichia coli and 21.1 ± 3.8 % on Staphylococcus aureus. It was possible to identify mono-acetylated acidic and methyl ester acidic sophorolipid. These compounds possess potential as pathogen controllers for application in the food industry.     

Combination of radon and stable isotope analysis as a tool for decision support concerning the remediation of NAPL-contaminated sites

The non-aqueous phase-liquid (NAPL)-contaminated aquifer at a major refinery site in Mexico was investigated. Owing to the depth of the contaminated aquifer section (NAPL source zone) of over 100 m below the surface, the actual aquifer material was not accessible for sampling. Information on the residual NAPL contamination of the aquifer could only be obtained indirectly by analysing groundwater samples from a few wells available at the site. To tackle the problem, an approach alternative to conventional groundwater analysis for dissolved NAPL was chosen. For evaluating the recent contamination and estimating its probable future development, the radioisotope radon-222 and the stable isotopes 13C, 34S and 18O were used as naturally occurring contamination tracers and process indicators. Radon was used as partitioning tracer for the approximate localization and semi-quantitative assessment of the NAPL source zone. The stable isotopes were used as indicators for naturally occurring biodegradation processes, which might potentially be implemented into future remediation schemes.     

An NMR study of merocyanine-type dyes derived from barbituric acid

The 13C NMR of two solvatochromic dyes derived from a barbituric acid acceptor and dimethylaminophenyl donor fragments, compound 1 and the related merocyanine 2, were recorded in various solvents. The observed chemical-shift variations were used to interpret their structural differences and solvatochromic behavior in solution.