On the reactions of methyl radicals with nitrilotris(methylenephosphonic-acid) complexes in aqueous solutions

Abstract

The reactions of methyl radicals with M^II-(ntp)(H₂O)₂ complexes were studied. The formation of an unstable intermediate (ntp)(H₂O)M^III-CH₃ is observed. This reaction is an equilibrium process, i.e. the M^III-C bond decomposes via homolysis. The (ntp)(H₂O)M^III-CH₃ complexes isomerize to a more stable form. The results compared to those obtained in analogous reactions of the M^II-(nta)(H₂O)₂ complexes were shown to be similar with one exception – for the nta complexes no isomerization process is observed.     

Turing invariant sets and the perfect set property

We show that $\text{◂...▸}\mathsf{ZF}+\mathsf{DC}+\text{“all}\text{Turing}\text{invariant}\text{sets}\text{of}\text{reals}\text{have}\text{the}\text{perfect}\text{set}\text{property”}$ implies that all sets of reals have the perfect set property. We also show that this result generalizes to all countable analytic equivalence relations.     

Adsorption-Inhibition of Clathrate Hydrates by Self-Assembled Nanostructures

The mechanism by which safranine O (SFO), an ice growth inhibitor, halts the growth of single crystal tetrahydrofuran (THF) clathrate hydrates was explored using microfluidics coupled with cold stages and fluorescence microscopy. THF hydrates grown in SFO solutions exhibited morphology changes and were shaped as truncated octahedrons or hexagons. Fluorescence microscopy and microfluidics demonstrated that SFO binds to the surface of THF hydrates on specific crystal planes. Cryo-TEM experiments of aqueous solutions containing millimolar concentrations of SFO exhibited the formation of bilayered lamellae with an average thickness of 4.2±0.2 nm covering several μm². Altogether, these results indicate that SFO forms supramolecular lamellae in solution, which might bind to the surface of the hydrate and inhibit further growth. As an ice and hydrate inhibitor, SFO may bind to the surface of these crystals via ordered water molecules near its amine and methyl groups, similar to some antifreeze proteins.     

BMO‐Type Norms Related to the Perimeter of Sets

In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc.     

Spatiotemporal model for the progression of transgressive dunes

Transgressive dune fields, which are active sand areas surrounded by vegetation, exist on many coasts. In some regions like in Fraser Island in Australia, small dunes shrink while large ones grow, although both experience the same climatic conditions. We propose a general mathematical model for the spatiotemporal dynamics of vegetation cover on sand dunes and focus on the dynamics of transgressive dunes. Among other possibilities, the model predicts growth parallel to the wind with shrinkage perpendicular to the wind, where, depending on geometry and size, a transgressive dune can initially grow although eventually shrink. The larger is the initial area the slower its stabilization process. The model’s predictions are supported by field observations from Fraser Island in Australia.     

Generator Coalgebras are not Necessarily Quasi-coFrobenius

We study the problem of whether a coalgebra that generates its category of left (right) comodules is left (right) quasi-coFrobenius or not. We prove it does not hold in general, by giving a method of constructing counterexamples. This gives a negative answer to a question stated in Nastasescu et al. (Algebr Represent Theory 11(2):179–190, 2008). We also prove it is true for monomial pointed coalgebras and we characterize the quivers Q such that \mathbbkQ\mathbb{k}Q admits a monomial subcoalgebra that is left (right) quasi-coFrobenius.