Liquid–liquid extraction of copper(II) with substituted salicylideneanilines from sulfate media

The liquid–liquid extraction of copper(II) with Schiff bases in chloroform from sulfate media is studied for pH and concentration of the extractant. Stoichiometry coefficients of the extracted species are determined by the slope analysis method. With salicylideneaniline, the copper(II) is extracted as a mixed chelate complex, CuL₂HL. In the presence of substituent, the copper is extracted as simple chelates, CuL₂. The trends in the values of extraction constants were explained in terms of the nature of the substituents.     

Cyclopalladated ferrocenylimine as an efficient catalyst for the syntheses of diarylmethane derivatives

The cyclopalladated ferrocenylimine adducts Ia , Ib , Ic were evaluated in the Suzuki cross‐coupling reaction of benzyl halides with arylboronic acids. The tricyclohexylphosphine adduct Ia exhibited highly catalytic activity for the coupling of aryl and heteroaryl boronic acids containing various functional groups with benzylic bromides and chlorides (up to 99% yield), furnishing diarylmethane derivatives with low catalyst loading (1 mol%). It is worth noting that catalyst Ia can be reused eight times without losing its catalytic activity. Copyright © 2012 John Wiley & Sons, Ltd.     

Newton trajectories for the tilted Frenkel–Kontorova model

ABSTRACT

Newton trajectories are used for the Frenkel–Kontorova model of a finite chain with free-end boundary conditions. We optimise stationary structures, as well as barrier breakdown points for a critical tilting force were depinning of the chain happens. These special points can be obtained straight forwardly by the tool of Newton trajectories. We explain the theory and add examples for a finite-length chain of a fixed number of 2,?3,?4,?5 and 23 particles.     

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the $\delta \overrightarrow{k}$-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum $\overrightarrow{k}$ is independent of the Rashba coupling strength.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.