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.     

Selected Species of the Cucurbitaceae Family Used in Mexico for the Treatment of Diabetes Mellitus

In Mexico, Diabetes mellitus (DM) is a serious health problem, and although the current pharmacological treatments for DM such as insulin and oral hypoglycemics are available, the Mexican population continues to use medicinal plants in the treatment of DM. The antidiabetic properties of the plant species that belong to the Cucurbitaceae family has already been recognized worldwide. Since Mexico is one of the most important centers of diversity of Cucurbitaceae, the present work contributes to the review of the most used species of Cucurbitaceae in the treatment of DM in Mexico. The reviewed species (Cucurbita ficifolia, C. maxima, C. moschata, C. pepo, Ibervillea sonorae, Sechium edule, Citrullus lanatus, Cucumis melo, and C. sativus) revealed that the antidiabetic effects exerted are effective in a number of mechanisms involved in the complex pathogenesis of DM: hypoglycemic, antioxidant, anti-inflammatory, anti-obesity, protective effects on diverse organs and cells, as well as in the control of dyslipidemias; furthermore, the select species of the Cucurbitaceae family could also be essential components of diets for the control of DM in patients with the disease. Thus, the Cucurbitaceae species selected in the present work represent a source of antidiabetic agents that perhaps establish the bases for novel clinical treatments.     

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.     

XANES speciation of mercury in three mining districts – Almadén,Asturias (Spain), Idria (Slovenia)

The mobility, bioavailability and toxicity of mercury in the environment strongly depend on the chemical species in which it is present in soil, sediments, water or air. In mining districts, differences in mobility and bioavailability of mercury mainly arise from the different type of mineralization and ore processing. In this work, synchrotron‐based X‐ray absorption near‐edge spectroscopy (XANES) has been taken advantage of to study the speciation of mercury in geological samples from three of the largest European mercury mining districts: Almadén (Spain), Idria (Slovenia) and Asturias (Spain). XANES has been complemented with a single extraction protocol for the determination of Hg mobility. Ore, calcines, dump material, soil, sediment and suspended particles from the three sites have been considered in the study. In the three sites, rather insoluble sulfide compounds (cinnabar and metacinnabar) were found to predominate. Minor amounts of more soluble mercury compounds (chlorides and sulfates) were also identified in some samples. Single extraction procedures have put forward a strong dependence of the mobility with the concentration of chlorides and sulfates. Differences in efficiency of roasting furnaces from the three sites have been found.     

Water flows induced by microwave electric fields in microsystems

AC electric fields are of increasing importance for the generation of fluid flows in microsystems. We analyse numerically the use of AC electric fields at microwave frequencies for electro-thermal actuation of water in microdevices. Water is heated because of its significant dielectric loss at microwave frequencies. Buoyancy and dielectric forces actuate in the liquid bulk, and the relative importance between them is studied. The microwave liquid actuation can be used for pure water as well as for water saline solutions, such as bio-fluids. Therefore, it is of interest for the Lab-on-a-Chip technology.     

Complexation and Transport of Alkali and Alkaline Earth Metal Cations by p-tert-Butyldihomooxacalix[4]arene Tetraketone Derivatives

The binding properties of three p-tert-butyldihomooxacalix[4]arene tetraketone derivatives (tert-butyl 2b, adamantyl 2c and phenyl 2d) in the cone conformation and one derivative (methyl 2a) in a partial cone conformation, towards alkali and alkaline earth metal cations have been established by extraction studies of metal picrates from water into dichloromethane, stability constant measurements in methanol and acetonitrile, and by ¹H NMR spectrometry. Transport experiments of metal picrates through a dichloromethane membrane were also performed. The results are compared to those obtained with closely-related calix[n]arene derivatives (n = 4 and 5) and discussed in terms of the substituents, size and conformational effects. Methylketone 2a is a poor binder for all the cations studied, due to its partial cone conformation. Ketones 2b, 2c and 2d show high extraction and complexation levels for the alkali cations, with similar profiles and preference for K⁺ and Na⁺ (plateau selectivity). Towards alkaline earth cations, these ketones show a strong peak selectivity for Ba²⁺ in extraction, but a plateau selectivity for Ca²⁺, Sr²⁺ and Ba²⁺ in complexation. The nature of the substituent attached to the ketone function has some influence on their binding properties, with phenylketone 2d being a slightly weaker binder than ketones 2b and 2c. ¹H NMR titrations confirm the formation of 1:1 complexes between the ketones and the cations studied, also indicating that they should be located inside the cavity defined by the phenoxy and carbonyl oxygen atoms. Ketones 2b, 2c and 2d show transport rates that do not follow, in general, the same trends observed in extraction and complexation.     

Onset of Chiral Adenine Surface Growth

The structure and stability of adenine crystals and thin layers has been studied by using scanning tunneling microscopy, X‐ray diffraction, and density functional theory calculations. We have found that adenine crystals can be grown in two phases that are energetically quasi‐degenerate, the structure of which can be described as a pile‐up of 2D adenine planes. In each plane, the structure can be described as an aggregation of adenine dimers. Under certain conditions, kinetic effects can favor the growth of the less stable phase. These results have been used to understand the growth of adenine thin films on gold under ultra‐high vacuum conditions. We have found that the grown phase corresponds to the α‐phase, which is composed of stacked prochiral planes. In this way, the adenine nanocrystals exhibit a surface that is enantiopure. These results could open new insight into the applications of adenine in biological, medical, and enantioselective or pharmaceutical fields.