Contact points and fractional singularities for semigroups of holomorphic self-maps of the unit disc

We study boundary singularities which can appear for infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit disc. We introduce “regular” fractional singularities and characterize them in terms of the behavior of the associated semigroups and K?nigs functions. We also provide necessary and sufficient geometric criteria on the shape of the image of the K?nigs function for having such singularities. In order to do this, we study contact points of semigroups and prove that any contact (not fixed) point of a one-parameter semigroup corresponds to a maximal arc on the boundary to which the associated infinitesimal generator extends holomorphically as a vector field tangent to this arc.     

Dissipative heating of a viscoelastic piezoceramic ball with temperature-dependent properties under harmonic excitation

International Applied Mechanics -     

Separation of Ionic Rhodium and Iridium Species by Electrophoresis on Reversed-Phase Thin-Layer Chromatography Plates

Reversed-phase thin-layer chromatography plates can be effectively used for the separation of metal ions in low concentrations by classical low-voltage electrophoresis. Electropherograms of the ionic composition of hydrochloric and perchloric acid solutions of rhodium(III) and iridium(IV) were obtained. These electropherograms are comparable with the results of capillary electrophoresis. Special features of electrophoresis on reversed-phase plates were noted.     

Speciation studies by capillary electrophoresis – distribution of rhodium(III) complexed forms in acidic media

The feasibility of capillary electrophoresis for distinguishing between the rhodium(III) species occurring in different acidic environments has been demonstrated. The separation was optimum under acidic electrolyte conditions in which the complexed Rh species were at their most stable and the electroosmotic flow approached zero, thereby aiding resolution. Identification of the forms of Rh and estimation of their relative equilibrium content were accomplished by use of a diode-array detector. The distribution of the metal complexes was highly dependent on the nature and concentration of the acid and the age of the rhodium stock solutions. On dilution Rh(III) tends to be readily hydrolyzed, giving rise to a wider variety (and a varied distribution) of complexed forms. In 0.1 mol L^–1 HCl, four differently charged chloro complexes – RhCl₄(H₂O)₂ ^–, RhCl₃(OH)(H₂O)₂ ^–, RhCl₃(H₂O)₃, and RhCl₂(H₂O)₄ ⁺?–? were separated and identified. When a stock solution in 11 mol L^–1 HCl was run, Rh produced a major peak ascribed to RhCl₆ ^3–and two slowly migrating peaks from ions in which one or two of the chloride ligands were probably replaced by water and hydroxyl ion, as a result of hydrolysis. The aquatic cationic species were found to be predominant in HClO₄ and HNO₃ solutions, whereas only negatively charged forms of Rh(III) occurred in sulfuric acid. This speciation information opens also new possibilities of assessing the catalytic activity of Rh in kinetic reactions.     

Wear resistance of filled epoxypolyamide composites in aggressive media

The authors investigate the influence of certain aggressive media (toxic chemicals) on the wear resistance of filled epoxypolyamide composites. The presence of toxic chemicals in the zone of friction causes a sharp fall in the wear of the polymers. The maximum wear resistance is displayed by epoxypolyamide composites filled with iron powder, cement, or graphite.