The Szegö function on a non-rectifiable arc

Let Γ be a simple Jordan arc in the complex plane. The Szegö function, by definition, is a holomorphic in ? \ Γ function with a prescribed product of its boundary values on Γ. The problem of finding the Segö function in the case of piecewise smooth Γ was solved earlier. In this paper we study this problem for non-rectifiable arcs. The solution relies on properties of the Cauchy transform of certain distributions with the support on Γ.     

On the reactions of methyl radicals with nitrilotris(methylenephosphonic-acid) complexes in aqueous solutions

Abstract

The reactions of methyl radicals with M^II-(ntp)(H₂O)₂ complexes were studied. The formation of an unstable intermediate (ntp)(H₂O)M^III-CH₃ is observed. This reaction is an equilibrium process, i.e. the M^III-C bond decomposes via homolysis. The (ntp)(H₂O)M^III-CH₃ complexes isomerize to a more stable form. The results compared to those obtained in analogous reactions of the M^II-(nta)(H₂O)₂ complexes were shown to be similar with one exception – for the nta complexes no isomerization process is observed.     

Ultrasonic crystallizer of CuSO4 solution: Engineering simulation

Ultrasound crystallizer of copper sulfate solution based on creating the solidification front with the aid of a gradient of temperature, which was exposed to ultrasonic waves with use of a magnetostrictive transducer, was proposed. The algorithm for the calculation of critical process parameters of the crystallization was developed jointly using the differential transport equations of momentum, mass, energy, sound waves, and a method of similarity and dimensional analysis.     

Nonchiral ferroelectric smectic-C films

Free-standing films of nonchiral liquid crystal compound are studied by optical reflectivity measurements. The existence of macroscopic ferroelectric properties and orientation of the tilt plane parallel to an electric field in the temperature range above the smectic-C-smectic-A bulk transition is demonstrated. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 808–813 (25 May 1998)     

Growth of commensurate and incommensurate smectics on crystal substrates

The nematic-smectic transition near a crystal substrate with a periodic potential relief is investigated. It is shown that structures which are commensurate or incommensurate with the substrate potential can form, depending on the values of the physical parameters of the system and the temperature. The possibility of realizing and observing such structures is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 708–712 (10 May 1996)