Some notes on convex sets

In [1] Tukey proves that if A and B are closed convex subsets in a Banach space, so that A is bounded and A-B is dense in the open unit ball U then A-BU. We shall give here a more general result than the former one which contains the Banach's isomorphism theorem as particular case. Other results over convex sets are also given.The author is indebted to the referee for the several very valuable comments.     

Combating small molecule environmental contaminants: detection and sequestration using functional nucleic acids

Small molecule contaminants pose a significant threat to the environment and human health. While regulations are in place for allowed limits in many countries, detection and remediation of contaminants in more resource-limited settings and everyday environmental sources remains a challenge. Functional nucleic acids, including aptamers and DNA enzymes, have emerged as powerful options for addressing this challenge due to their ability to non-covalently interact with small molecule targets. The goal of this perspective is to outline recent efforts toward the selection of aptamers for small molecules and describe their subsequent implementation for environmental applications. Finally, we provide an outlook that addresses barriers that hinder these technologies from being widely adopted in field friendly settings and propose a path forward toward addressing these challenges.

Small molecule contaminants pose a significant threat to the environment and human health.     

Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

Dimethyl Sulfoxide: A Bio-Friendly or Bio-Hazard Chemical? The Effect of DMSO in Human Fibroblast-like Synoviocytes

The effect of dimethyl sulfoxide (DMSO) in rheumatoid arthritis (RA) human fibroblast-like synoviocytes (FLSs) has been studied on five different samples harvested from the joints (fingers, hands and pelvis) of five women with RA. At high concentrations (>5%), the presence of DMSO induces the cleavage of caspase-3 and PARP-1, two phenomena associated with the cell death mechanism. Even at a 0.5% concentration of DMSO, MTT assays show a strong toxicity after 24 h exposure (≈25% cell death). Therefore, to ensure a minimum impact of DMSO on RA FLSs, our study shows that the concentration of DMSO has to be below 0.05% to be considered safe.     

Comparative Effect of UV,UV/H2O2 and UV/H2O2/Fe on Terbuthylazine Degradation in Natural and Ultrapure Water

Different advanced oxidation processes (AOPs) (ultraviolet radiation, hydrogen peroxide photolysis and photo-Fenton) were applied to test the degradation of terbuthylazine in three types of water: (a) ultrapure water, (b) surface water from the Gaditana area (Los Hurones reservoir, Cádiz, Spain) and (c) groundwater from the Tempul spring in Jerez de la Frontera (Cádiz, Spain). The experiments were carried out on a laboratory scale, using two different types of reactors, batch and semi-continuous. In batch reactors, the most efficient process for the experiments carried out with both ultrapure water and underground groundwater was ultraviolet radiation, whereas for surface water from the Gaditana area, the process that obtained the best results was the photolysis of hydrogen peroxide with 2.5 mg L⁻¹ of H₂O₂. In semi-continuous reactors, the most efficient process was the photolysis of hydrogen peroxide with 2.5 mg L⁻¹ of H₂O₂ for all the matrices studied. In both types of reactors, terbuthylazine degradation percentages higher than 90% were achieved; the main difference was in the reaction time, which varied from minutes in the batch reactor to seconds in the semi-continuous reactor. In all the applied AOPs, N-terbutyl-6-hydroxy-N′ethyl-1,3,5-triazine-2,4-diamine (TBA-212) was generated as a reaction intermediate.     

A brief review of the methods used to evaluate vapour pressures and sublimation enthalpies

A brief review of the experimental methods used to evaluate vapour pressures and sublimation enthalpies is presented. The methods discussed have been used for determining the results of several substituted benzenes that were collected in a database, with the main purpose of developing new estimation methods of these thermodynamic properties. A critical evaluation of the two most used calorimetric techniques for determining enthalpies of sublimation is also addressed.     

Unexpected reactivity of trifluoromethylated olefins with indole: a mechanistic investigation

Several trifluoromethylated compounds were reacted with indole sodium salt, leading to monofluorinated compounds. The unexpected products formation was rationalized by DFT calculations.