Reflexivity of Banach C(K)-modules via the reflexivity of Banach lattices

We extend the well known criteria of reflexivity of Banach lattices due to Lozanovsky and Lotz to the class of finitely generated Banach \(C(K)\) -modules. Namely we prove that a finitely generated Banach \(C(K)\) -module is reflexive if and only if it does not contain any subspace isomorphic to either \(l^{1}\) or \(c_{0}\) .     

Spectrum of weighted composition operators part VI: essential spectra of d-endomorphisms of Banach C(K)-modules

Positivity - We investigate properties of essential spectra of disjointness preserving operators acting on Banach C(K)-modules. In particular, we prove that under some very mild conditions the...     

Mechanisms of postsynthesis doping of boron nitride nanostructures with carbon from first-principles simulations

Electron-beam-mediated postsynthesis doping of boron-nitride nanostructures with carbon atoms [Nature (London) 464, 571 (2010); J. Am. Chem. Soc. 132, 13?692 (2010)] was recently demonstrated, thus opening a new way to control the electronic properties of these systems. Using density-functional theory static and dynamic calculations, we show that the substitution process is governed not only by the response of such systems to irradiation, but also by the energetics of the atomic configurations, especially when the system is electrically charged. We suggest using spatially localized electron irradiation for making carbon islands and ribbons embedded into BN sheets. We further study the magnetic and electronic properties of such hybrid nanostructures and show that triangular carbon islands embedded into BN sheets possess magnetic moments, which can be switched on and off by electrically charging the structure.     

Cross-couplings of alkyl halides with heteroaromatic halides, in water at room temperature

Zn-mediated, Pd-catalyzed cross-coupling reactions between heteroaromatic and alkyl halides can be done at room temperature in pure water using a commercially available Pd catalyst and PTS, a nanomicelle-forming amphiphile. Notably, zinc metal inserts selectively into a carbon sp³-halide bond, while palladium adds oxidatively to a carbon sp²-bond.     

Generalized detection of a turbulent front generated by an oscillating grid

This report presents experimental results on the propagation of a turbulent front induced by an oscillating grid starting from rest. The purpose of this preliminary investigation is to implement and validate detection methods of the turbulent/non-turbulent interface, which are based on flow measurements (velocity and vorticity) and scalar intensity, for oscillating grid turbulence. This is done using particle image velocimetry (PIV) and fluorescent dye visualization, separately. The results of both techniques describe the spreading of the turbulent front, confirming the known dependency of the front location, H, on time, t. It is demonstrated, that the level-based detection of a turbulent front can be applied to an unsteady flow, such as grid turbulence advancing into a fluid at rest.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.