Coordination chemistry of tripyridinedimethane

The ligand tripyridinedimethane (tpdm), consisting of three pyridine residues linked at their ortho carbons by two CH(2) groups, is shown to be a sterically flexible ligand capable of binding in a meridional arrangement in trigonal bipyramidal (tpdm) Cu(II)Cl(2) but binding in a facial arrangement in tetrahedral (tpdm) Cu(I)Cl. Nucleophilic substitution of chloride by (t)BuO(-) and PhC[triple bond]C(-) is possible, and deprotonation of the acidic benzylic protons does not take place because the resulting carbanion cannot achieve coplanarity with the aryl rings. RhCl(3) forms, with tpdm in boiling methanol, a 1:1 kinetic mixture of fac- and mer-isomers RhCl(3)(tpdm). The former isomerizes slowly at RT (room temperature) in DMSO solution into the latter with Rh-N bond dissociation as the rate-determining step.     

Precipitation of inorganic salts inside hollow micrometer-sized polyelectrolyte shells

Hollow polymer shells formed by layer-by-layer adsorption of oppositely charged polyelectrolytes onto micrometer-sized colloidal particles with subsequent decomposition of the colloidal core were employed as a model system for the study of inorganic crystallization reactions in restricted volumes. The size-selective permeability of shells is used for spatially controlling the precipitation of inorganic salts CaCO3 and BaCO3 into the shell interior. Outside the shells the precipitation was suppressed by the polymers, which are unable to penetrate the shell wall. The precipitates were studied by scanning electron microscopy and atomic force microscopy. The fundamental and applied aspects of research on spatially confined synthesis of inorganic particles are under discussion.     

Theory of ferromagnetism in Ca(1-x)La(x)B(6)

Novel ferromagnetism in Ca(1-x)La(x)B(6) is studied in terms of the Ginzburg-Landau theory for excitonic-order parameters, taking into account symmetry of the wave functions. We found that the minima of the free energy break both inversion and time-reversal symmetries, while the product of these two remains preserved. This explains various novelties of the ferromagnetism and predicts a number of magnetic properties, including the magnetoelectric effect, which can be tested experimentally.     

Uniqueness of solutions of aH ∞ optimization problem and complex geometric convexity

We study uniqueness of an H^∞ optimization problem which is central to the worst case frequency domain system design. It was known that if the so-called sublevel sets are strictly convex inC ^N, then the uniqueness holds. On the other hand, there are examples of non-uniqueness if the sublevel sets are just strictly pseudoconvex. In this paper we prove that uniqueness holds for a type of convexity which is strictly in-between geometric and pseudoconvexity.     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

Maxwell equation for coupled spin-charge wave propagation

We show that the dissipationless spin current in the ground state of the Rashba model gives rise to a reactive coupling between the spin and charge propagation, which is formally identical to the coupling between the electric and the magnetic fields in the (2 + 1)-dimensional Maxwell equation. This analogy leads to a remarkable effect of fractionalization of spin packets (FSP) where a density packet can spontaneously split into two counterpropagation packets, each carrying the opposite spin. In a certain parameter regime, the coupled spin and charge wave propagates like a transverse "photon." We propose both optical and purely electronic experiments to detect the FSP effect.     

Spin wave mode excited by spin-polarized current in a magnetic nanocontact is a standing self-localized wave bullet

We demonstrate that the lowest threshold of spin-wave excitation in an in-plane magnetized magnetic nanocontact driven by spin-polarized current is achieved for a nonlinear self-localized spin-wave mode-standing spin-wave bullet--stabilized by current-induced nonlinear dissipation. This nonlinear mode has a nonpropagating evanescent character, is localized in the region comparable with the contact radius, and has a frequency that is lower than the frequency of the linear ferromagnetic resonance. The threshold current and generated frequency at the threshold theoretically calculated for this mode are in quantitative agreement with experiment.