A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Counter-examples to non-noetherian Elkik's approximation theorem

Elkik established a remarkable theorem that can be applied for any noetherian henselian ring. For algebraic equations with a formal solution (restricted by some smoothness assumption), this theorem provides a solution adically close to the formal one in the base ring. In this paper, we show that the theorem would fail for some non-noetherian henselian rings. These rings do not satisfy several conditions weaker than noetherianness, such as weak proregularity (due to Grothendieck et al.) of the defining ideal. We describe the resulting pathologies.     

Densely defined non‐closable curl on carpet‐like metric measure spaces

The paper deals with the possibly degenerate behaviour of the exterior derivative operator defined on 1‐forms on metric measure spaces. The main examples we consider are the non self‐similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. Although topologically one‐dimensional, they may have positive two‐dimensional Lebesgue measure and carry nontrivial 2‐forms. We prove that in this case the curl operator (and therefore also the exterior derivative on 1‐forms) is not closable, and that its adjoint operator has a trivial domain. We also formulate a similar more abstract result. It states that for spaces that are, in a certain way, structurally similar to Sierpinski carpets, the exterior derivative operator taking 1‐forms into 2‐forms cannot be closable if the martingale dimension is larger than one.     

Divagations about the periodic table: Boolean hypercube and quantum similarity connections

In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc.     

An efficient approach for the total synthesis of balticolid

An efficient stereoselective total synthesis of balticolid has been accomplished starting from known aldehyde. The key steps involved in this synthesis are Sharpless asymmetric epoxidation, Wittig olefination, alkylation of 1,3-dithiane and Yamaguchi macrolactonization.     

New Transition Metal Oxo‐Thiostannate: Synthesis,Characterization, and Investigation of its Photocatalytic Properties

The new transition metal oxo‐thiostannate {[Ni(cyclen)]₆[Sn₆S₁₂O₂(OH)₆]} · 2(ClO₄) · 19H₂O ( 1 ) was prepared under hydrothermal conditions using Na₄SnS₄ · 14H₂O and [Ni(cyclen)](ClO₄)₂ as reactants. In the crystal structure the rare [Sn₆S₁₂O₂(OH)₆]^10– anion is observed, which is composed of SnS₂O(OH)₃ and SnS₄O₂ octahedra, and SnS₄ tetrahedra sharing edges and corners. The anion is expanded by six Ni²⁺ centered complexes via Ni–S and Ni–OH bonds. The photocatalytic properties for the visible light driven hydrogen evolution reaction shows that 26.6 mmol · g^–1 H₂ were evolved after 3 h.     

Mechanistic studies on the reaction between glutathionylcobalamin and selenocysteine

Abstract

The reaction between glutathionylcobalamin (GSCbl), a complex of Co(III)-cobalamin with glutathione, and selenocysteine (Sec) was investigated using ultraviolet-visible (UV–vis) spectroscopy. The interaction results in the formation of cob(II)alamin and proceeds via two pathways: (i) a rapid formation of complex between GSCbl and Sec followed by the rate-determining substitution of glutathionyl-ligand by Sec and rapid electron-transfer from Se-atom to Co(III)-ion and (ii) a nucleophilic attack of Co(III)-S bond by Sec.     

CuI/Fe3O4 NPs@Biimidazole IL‐KCC‐1 as a leach proof nanocatalyst for the synthesis of imidazo[1,2‐a]pyridines in aqueous medium

In the present work, an innovative leach proof nanocatalyst based on dendritic fibrous nanosilica (DFNS) modified with ionic liquid loaded Fe₃O₄ NPs and CuI salts was designed and applied for the rapid synthesis of imidazo[1,2‐a]pyridines from the reaction of phenyl acetylene, 2‐aminopyridine, and aldehydes in aqueous medium. The structure of the synthesized nanocatalyst was studied by field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), Fourier transform infrared (FT‐IR), flame atomic absorption spectroscopy (FAAS), energy‐dispersive X‐ray (EDX), and X‐ray diffraction (XRD), vapor–liquid–solid (VLS), and adsorption/desorption analysis (Brunauer–Emmett–Teller [BET] equation) instrumental techniques. CuI/Fe₃O₄NPs@IL‐KCC‐1 with high surface area (225 m² g^?1) and porous structure not only exhibited excellent catalytic activity in aqueous media but also, with its good stability, simply recovered by an external magnet and recycled for eight cycles without significant loss in its intrinsic activity. Higher catalytic activity of CuI/Fe₃O₄NPs@IL‐KCC‐1 is due to exceptional dendritic fibrous structure of KCC‐1 and the ionic liquid groups that perform as strong anchors to the loaded magnetic nanoparticles (MNPs) and avoid leaching them from the pore of the nanocatalyst. Green reaction media, shorter reaction times, higher yields (71–97%), easy workup, and no need to use the chromatographic column are the advantages of the reported synthetic method.