The Radon-Nikodym theorem for random measures

Translated from Ukrainskii Materaaticheskii Zhurnal, Vol. 41, No. 1, pp. 63–67, January, 1989.     

Contravariant densities, complete distancesand relative fidelities for quantum channels

Introducing contravariant trace densities for quantum states, we restore one-to-one correspondencebetween quantum operations described by normal CP maps and their trace densities as Hermitian-positive operator-valued contravariant kernels. The CB-norm distance between two quantum operations is explicitly expressed in terms of these densities as the supremum over the input states. A larger C-distance is given as the natural norm distance for the channel densities, and another, Helinger type complete distance (CH distance), related to the minimax mean square fidelity optimization problem by purification of quantum channels, is also introduced and evaluated in terms of their contravariant trace densities. It is proved that the CH distance between two channels is equivalent to the CB distance. An operational meaning for these distances and relative complete fidelity for quantum channels is given in terms of quantum encodings producing optimal entanglements of quantum states for an opposite and output systems.     

Capacitive Impedance for Following In-Situ Grafting Kinetics of Diazonium Salts

A new method to follow in-situ grafting kinetics of diazonium compounds based on imposing small amplitude high frequency AC oscillations at grafting potential, is outlined. This enables the time-resolved measurements of capacitive impedance concomitantly with the growth of the organic layer at the working electrode. The impedance values were quantitatively correlated with the ex-situ (from voltammograms) and in-situ (from quartz crystal microbalance) measured surface coverages, providing a validation of the new methodology. The versatility of the developed approach was demonstrated on the grafting via reduction of 4-nitrobenzenediazonium on Au and glassy carbon (GC) substrates and via deposition of in-situ generated diazonium salts from 1-aminoanthraquinone and 4-ferrocenylaniline on GC. The capacitive impedance measurements are simple, fast, and non-destructive, making it an appealing methodology for an exploration of grafting kinetics of a wide range of diazonium salts.     

Transport phenomena in metal nanocomposites

Ferromagnetic nanocomposites are the special case of metal composites; they are of practical interest for spintronics. Temperature dependences of resistivity ρ(T) and thermoelectric power α(T) of ferromagnetic nanocomposites with the composition Co _x (Al₂O₃)_{100 ? x} (36.6 ≤ x ≤ 52.5 at %) are investigated near the percolation threshold (x _p ≈ 43.3 at %) in a temperature range of 77–300 K. Sizes of Co nanoparticles are no larger than 25 nm. Specific features are observed in the dependences α(T) in the form of a kink at T _b ≈ 170 K. The analysis of the structural and electrical schematics as well as energy diagrams of percolation channels of electrons shows that only the diffusion thermoelectric power appears in Co nanoparticles, at which α(T) is the linear function. No mechanisms of the thermoelectric power caused by nanosizes of Co particles or by electron tunneling between them are found. The kink of the α(T) linear dependence is explained by the existence of the oxide shell of Co nanoparticles. It is assumed that the temperature dependences of energy barriers of oxide shells of metal nanoparticles (including ferromagnetic ones) in oxygen-containing dielectric matrices determine the features of α(T) and ρ(T) dependences of such nanocomposites.     

Dual reactivity of N-heterocyclic carbenes towards copper(II) salts

Complexes of N-heterocyclic carbenes (NHCs) with copper(II) halogenides are unstable. Upon formation, these complexes decompose to give haloamidinium salts. Contrastingly, O-substituted copper(II) NHC complexes are fairly stable. A series of new five-, six- and seven-membered ring NHC complexes of Cu(OAc)(2) have been synthesised and characterised in the solid state.     

Method of calculating the fields of residual stresses and plastic strains in cylindrical specimens with allowance for surface hardening anisotropy

A mathematical model is proposed for calculating the stress-strain state of a cylindrical specimen, which arises as a result of plastic surface hardening leading to material deformation anisotropy. The model adequacy is verified through comparisons with experimental data for cylindrical specimens made of 30KhGSA and St. 45 steels. A method of identifying model parameters on the basis of results of a fundamental experiment is developed. Good agreement of the calculated and experimental data is demonstrated.     

Formation of polymer–colloid complexes of aluminoxane particles with poly(acrylic acid) and its copolymers with acrylamide

Formation of polymer–colloid complexes formed by positively charged aluminoxane particles with a size of ~4.6 nm, which constitute the main part of the dispersed phase in aluminum polyhydroxychloride sols with poly(acrylic acid) and acrylic acid copolymers with acrylamide, is studied. Conditions of preparing water-soluble polymer–colloid complexes are determined. It is shown that water-soluble polycomplexes are obtained through the interaction of aluminoxane particles with acrylic acid–acrylamide copolymers containing no more than 0.8 mol% acrylic acid units. In the polymer–colloid complex, aluminoxane particles are uniformly distributed over polyelectrolyte macromolecules and the optimum composition is attained at the molar ratio of components Z equal to 1:1. In semidilute solutions, the addition of aluminoxane particles to the copolymer brings about formation of the gel featuring viscoelastic properties. For all copolymers, the maximally elastic properties of the gels are attained at Z ≈ 1.     

Simulation of disk extruder operation

Mathematical simulation of thermoplastic polymer processing by a disk extruder was considered. The results were compared with experimental data obtained in an extruder of a 200 mm diameter. The developed technique of calculation allows selection of design parameters of operational parts and disk speed for preset output of the disk extruder as well as energy-power parameters of extrusion.