Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

“(Diphosphine)Nickel”‐Catalyzed Negishi Cross‐Coupling: An Experimental and Theoretical Study

The use of a strongly donating “(bis‐dialkylphosphine)Ni” fragment promotes the catalytic coupling of a large range of ArCl and ArZnCl derivatives under mild conditions. Stoichiometric mechanistic investigations and DFT calculations prove that a Ni⁰/Ni^II cycle is operative in this system.     

N‐(2‐Ethylhexyl)carbazole: A New Fluorophore Highly Suitable as a Monomolecular Liquid Scintillator

The synthesis, photophysical properties, and applications in scintillation counting of N‐(2‐ethylhexyl)carbazole (EHCz) are reported. This molecule displays all of the required characteristics for an efficient liquid scintillator (emission wavelength, scintillation yield), and can be used without any extra fluorophores. Thus, its scintillation properties are discussed, as well as its fast neutron/gamma discrimination. For the latter application, the material is compared with the traditional liquid scintillator BC‐501 A, and other liquid fluorescent molecules classically used as scintillation solvents, such as xylene, pseudocumene (PC), linear alkylbenzenes (LAB), diisopropylnaphthalene (DIN), 1‐methylnaphthalene (1‐MeNapht), and 4‐isopropylbiphenyl (iPrBiph). For the first time, an excimeric form of a molecule has been advantageously used in scintillation counting. A moderate discrimination between fast neutrons and gamma rays was observed in bulk EHCz, with an apparent neutron/gamma discrimination potential half of that of BC‐501 A.     

The Reductive Dehydration of Cellulose by Solid/Gas Reaction with TiCl4 at Low Temperature: A Cheap,Simple, and Green Process for Preparing Anatase Nanoplates and TiO2/C Composites

Metal oxides and metal oxide/carbon composites are entering the development of new technologies and should therefore to be prepared by sustainable chemistry processes. Therefore, a new aspect of the reactivity of cellulose is presented through its solid/gas reaction with vapour of titanium(IV) chloride in anhydrous conditions at low temperature (80 °C). This reaction leads to two transformations both for cellulose and titanium(IV) chloride. A reductive dehydration of cellulose is seen at the lowest temperature ever reported and results in the formation of a carbonaceous fibrous solid as the only carbon‐containing product. Simultaneously, the in situ generation of water leads to the formation of titanium dioxide with an unexpected nanoplate morphology (ca. 50 nm thickness) and a high photocatalytic activity. We present the evidence showing the evolution of the cellulose and the TiO₂ nanostructure formation, along with its photocatalytic activity. This low‐temperature process avoids any other reagents and is among the greenest processes for the preparation of anatase and also for TiO₂/carbon composites. The anisotropic morphology of TiO₂ questions the role of the cellulose on the growing process of these nanoparticles.     

Markov-modulated Brownian motions perturbed by catastrophes

ABSTRACT

We consider a one-sided Markov-modulated Brownian motion perturbed by catastrophes that occur at some rates depending on the modulating process. When a catastrophe occurs, the level drops to zero for a random recovery period. Then the process evolves normally until the next catastrophe. We use a semi-regenerative approach to obtain the stationary distribution of this perturbed MMBM. Next, we determine the stationary distribution of two extensions: we consider the case of a temporary change of regime after each recovery period and the case where the catastrophes can only happen above a fixed threshold. We provide some simple numerical illustrations.     

Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature

We investigate the singular limit, as ${\varepsilon \to 0}$ , of the Allen-Cahn equation ${u^\varepsilon_t=\Delta u^\varepsilon+\varepsilon^{-2}f(u^\varepsilon)}$ , with f a balanced bistable nonlinearity. We consider rather general initial data u ₀ that is independent of ${{\varepsilon}}$ . It is known that this equation converges to the generalized motion by mean curvature ?? in the sense of viscosity solutions??defined by Evans, Spruck and Chen, Giga, Goto. However, the convergence rate has not been known. We prove that the transition layers of the solutions ${u^{\varepsilon}}$ are sandwiched between two sharp ??interfaces?? moving by mean curvature, provided that these ??interfaces?? sandwich at t?=?0 an ${\mathcal O({\varepsilon}|\,{\rm ln}\,{\varepsilon}|)}$ neighborhood of the initial layer. In some special cases, which allow both extinction and pinches off phenomenon, this enables to obtain an ${\mathcal O({\varepsilon}|\,{\rm ln}\,{\varepsilon}|)}$ estimate of the location and the thickness measured in space-time of the transition layers. A result on the regularity of the generalized motion by mean curvature is also provided in the Appendix.