Integral representation of a class of univalent functions

We refine and generalize a result of V. A. Zmorovich on the integral representation of a class of univalent functions which are convex in some direction. We prove that all function of the class being considered can be approximated by a Schwarz-Christoffel integral of a special form belonging to the same class.Translated from Matematicheskii Zametki, Vol. 19, No. 1, pp. 41–48, January, 1976.     

Quantum terahertz electrodynamics and macroscopic quantum tunneling in layered superconductors

We derive a quantum field theory of Josephson plasma waves (JPWs) in layered superconductors, which describes two types of interacting JPW bosonic quanta (one heavy and one lighter). We propose a mechanism of enhancement of macroscopic quantum tunneling (MQT) in stacks of intrinsic Josephson junctions. Because of the long-range interaction between junctions in layered superconductors, the calculated MQT escape rate Gamma has a nonlinear dependence on the number of junctions in the stack. We show that the crossover temperature between quantum and thermal escape increases when increasing the number of junctions. This allows us to quantitatively describe striking recent experiments in Bi2Sr2CaCu2O8+delta stacks.     

Complex formation of crown ethers with α-amino acids: Estimation by NMR spectroscopy

Complex formation of 18-crown-6 and dibenzo crowns with glycine, leucine, and norleucine was studied by NMR spectroscopy. The efficiency of non-valence interactions with participation of different active centers of the host and guest molecules is determined by solvation effects, mutual arrangement of benzene rings in dibenzo crowns, and the presence of bulky aliphatic substituents in the α-amino acid. The complexation of dibenzo crowns with α-amino acids in acid medium involves a system of different non-valence interactions, the most efficient of which are NH ₃ ⁺ ... O hydrogen bond between the ammonium group in the guest molecule and ether oxygen atoms in the host molecule and dipole-dipole interaction between the guest ammonium group and host benzene ring (NH ₃ ⁺ ... Ar). The efficiency of NH ₃ ⁺ ... O hydrogen bonding decreases in going from 18-crown-6 to dibenzo crowns due to distortion of symmetry of the macroring cavity and violation of geometric complementarity of some ether oxygen atoms. The integral efficiency of non-valence interactions in the system dibenzo crown-α-amino acid was estimated on a quantitative level by ¹H NMR relaxation technique.     

On the nature of the processes occurring in silver doped SiO<Subscript>2</Subscript> films under heat treatment

The processes taking place on air-heating of SiO₂−Ag⁺ films and xerogels produced from the SiO₂ sols of different pH (3.7 or 9.5) were investigated. Silver nanoparticles 10–40 nm in size tolerant to oxidation at temperatures above 600 °C were found to be formed in the systems whatever the pH value of the starting sol. SiO₂ crystallization giving the cristobalite phase in the temperature range from 500 to 800 °C was shown to proceed only in the films produced from the acidic sol, while in those formed from the alkali one SiO₂ remained amorphous. A mechanism by which the formation of Ag nanoparticles and the cristobalite phase occurs in the films at the oxidative conditions is suggested.