Direct Renormalizations of the One-Dimensional Torus

Renormalization formulas connecting the points of the orbits O ₀ ^± , i.e., the sequences generated by an irrational shift on the half-open interval [0, 1) or (0, 1], and the points of the orbits' derivatives d^mO ₀ ^± , i.e., the sequences obtained by restricting O ₀ ^± to half-open intervals of smaller length, are obtained. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 142–154.     

A study of structural, compositional and optical properties of spray-deposited non-stoichiometric (Zn,Fe)S thin films

Non-stoichiometric ternary chalcogenides (Zn,Fe)S were prepared in the film form by pyrolytic spray deposition technique, using air/nitrogen as the carrier gas. The precursor solution comprised of ZnCl₂, FeCl₂ and thiourea. The depositions were carried out under optimum conditions of experimental parameters viz. carrier gas (air/nitrogen) flow rate, concentration of precursor constituents, nozzle substrate distance and temperature of quartz substrate. The deposited thin films were later sintered in argon at 1073 K for 120 min.The structural, compositional and optical properties of the sintered thin films were studied. X-ray diffraction studies of the thin films indicated the presence of (Zn,Fe)S solid solution with prominent cubic sphalerite phase while surface morphology as determined by scanning electron microscopy (SEM) revealed a granular structure.The chemical composition of the resulting thin films as analyzed by energy dispersive X-ray analysis (EDAX) reflected the composition of the precursor solutions from which the depositions were carried out with Fe at% values ranging from 0.4 up to 33.SEM micrographs of thin films reveal that the grain sizes of the thin films prepared using air as carrier gas and N₂ as carrier gas are in the vicinity of 300 and 150 nm, respectively.The diffuse transmittance measurements for thin films, as a function of wavelength reveal the dependence of direct optical band gap on Fe content and type of phase.     

Study of thermal currents in powder β-spodumene ceramics doped with Cuo, FeO and TiO2

Ternary-phase ceramic system of Li₂O Al₂O₃ 4SiO₂ doped with CuO, FeO and TiO₂ has been prepared and subjected to dc electrical conductivity and thermally stimulated depolarization current (TSDC) measurements as a function of temperature (30-250 °C) and field strength. The electrical conductivity results are explained by assuming both ionic and electronic conduction mechanisms coexist with different contributions over the whole temperature range of experiments. TSDC spectra have been found to be characterized by a broad intense relaxation peak, which can be attributed to an ionic charge polarization. The broad relaxation transitions are apparently a result of the nonuniform nature of this process. Activation energies are calculated for both dc electrical conductivity and TSDC according to Arrhenius equation and initial rise method, respectively.     

Damped waves in a cylinder shadow

The sound field in the region of a deep shadow behind an impedance cylinder is analyzed for the case of plane wave diffraction by the cylinder surface. The main part of the field is represented by a cylindrical wave that has a complex index determined from the boundary conditions and decays with the angular coordinate. An expression for the amplitude of this wave is determined by extracting it from the total field formed in the shadow region. It is demonstrated that this wave approximates more closely the total field behind the cylinder, as compared to the least damped wave in the field representation obtained on the basis of the Watson transform. A way to improve the sound barriers is indicated.     

Noiselike magnetic resonance fine structure for ferromagnetic powders: Dipole-dipole interaction effects

A noiselike fine structure of ferromagnetic resonance spectra in magnetic powders was investigated after ultrasonic treatment. Magnetic interactions between particles are proved to have an influence upon the fine structure formation. After decreasing dipole-dipole magnetic interactions in dilute suspension a special order appears in fine-structure spectra, which is generally the same for different systems.     

Investigations of Solid State Dynamics at the NRSSR Beamline at PETRA II. An Overview

The present status of the new nuclear resonance beamline PETRA 1 at HASYLAB, DESY, Hamburg is described. Besides an overview of the experimental setup some examples of recent experiments are given. Those cover the main applications, i.e., inelastic scattering from iron alloys and quasielastic scattering from glass-forming liquids. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002