Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights

We present two approaches to the spectral studies for infinite Jacobi matrices with monotonic or near-to-monotonic weights. The first one is based on the subordination theory due to Khan and Pearson [17] combined with the detailed analysis of the transfer matrices for the solutions of the formal eigenequation. The second one uses an extension of the commutator approach developed by Putnam in [19]. Applying these methods we prove the absolute continuity for several classes of weights and diagonals. For some other cases we prove the emptiness of the point spectrum. The results are illustrated with examples and compared with the results of Dombrowski [7]-[13], Clark [2] and of Máté and Nevai [18]. We show that some of our results are stronger.The research of the first author has been supported by the KBN grant PB 2 P03A 002 13.     

A theoretical study on the formation of EX4+ and E2X5+(E = P, As; X = Br, I) from Ag+ and EX3/X2

The mechanism and the thermodynamics of the formation of EX2+, EX4+ and E2X5+ (E = As, P; X = Br, I) was carefully analyzed with MP2/TZVPP calculations and inclusion of entropy and solvation effects (COSMO model approximating CH2Cl2). Thus, as likely intermediates the complexes of Ag+ and one or two EX3 as well as EX3/X2 were optimized. The global minimum isomers of the Ag(EX3)2+ intermediates were found to be P-coordinated Ag(PI3)2+ and (BrPBr2)Ag(PBr3)+ but exclusively halogen coordinated Ag(X2AsX)2+ complexes. Similarly complicated is the situation for the Ag(EX3)(X2)+ intermediates: (I3E)Ag(I2)+, (BrAsBr2)Ag(Br2)+ and (Br3P)(Br-Br)Ag+ complexes were found to be the global minima. Based on all available results likely mechanisms for the formation of the known PX4+, AsBr4+, P2X5+ salts (X = Br, I) from these intermediates were proposed. An explanation for the failure to prepare an AsI4+ salt is also given.     

Kinetics of contact electrification between metals and polymers

Kinetics of charge transfer between metals and polymers was studied using an analytical rolling-sphere tool. The rates of charge transfer were related to the area of contact between contacting surfaces and the tunneling current between them. The derived rate equations accounted for the experimentally observed sigmoidal charging curves. Furthermore, for a model system of steel spheres rolling on modified polystyrene supports, it was shown that the magnitudes of separated charges can be varied by adjusting the polymer's surface properties and/or ambient conditions.     

TiO2 phytate films as hosts and conduits for cytochrome c electrochemistry

Cytochrome c is accumulated into a film of TiO(2) nanoparticles and phytate by adsorption from an aqueous solution into the mesoporous structure. Stable voltammetric responses and high concentrations of redox protein within the TiO(2) phytate layer can be achieved. Two types of electrode systems are reported with (i) the modified TiO(2) phytate film between electrode and aqueous solution phase and (ii) the modified TiO(2) phytate film buried under a porous gold electrode ('porotrode'). The electrical conductivity of TiO(2) phytate films is measured and compared in the dry and in the wet state. Although in the dry state essentially insulating, the TiO(2) phytate film turns into an electrical conductor (with approximately 4 Omega cm specific resistivity assuming ohmic behaviour) when immersed in aqueous 0.1 M phosphate buffer solution at pH 7. The redox protein cytochrome c is therefore directly connected to the electrode via diffusion and migration of electrons in the three dimensional mesoporous TiO(2) phytate host structure. Electron transfer from cytochrome c to TiO(2) is proposed to be the rate-determining step for this conduction mechanism.     

Wave optics of Liesegang rings

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.