Geometric regularity of direct-sum decompositions in some classes of modules

In this paper, we show that modules with semilocal endomorphism rings appear in abundance in applications, that their direct-sum decompositions are described by the so-called Krull monoids, and that this implies a geometric regularity of the direct-sum decompositions of these modules. Their direct-sum decompositions into indecomposables are not necessarily unique in the sense of the Krull-Schmidt theorem. The application of the theory of Krull monoids to the study of direct-sum decompositions of modules has been developed during the last five years. After a quick survey of the results obtained in this direction, we concentrate in particular on the abundance of examples. At present, these examples are scattered in the literature, and we try to collect them in a systematic way. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 231–244, 2004.     

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.     

The study and applications of photochemical-dynamical gravity wave model I

A two-dimensional, nonlinear, compressible, diabatic, nonhydrostatic photochemical-dynamical gravity wave model has been advanced. The model includes diabetic process produced by photochemistry and the effect of gravity wave on atmospheric chemical species. In the horizontal direction, the pseudospectral method is used. The finite difference approximations are used in vertical direction z and time t. The FICE method is used to solve the model. The model results on small amplitude fluctuation are very close to those of linear theory, which demonstrates the correctness of the model.

     

A study of formation of solid ionic conductors in the mixed system (CdI2)b[(Ag2O)·(CrO3)]100-b (20≤b≤80)

Using Wagner's polarization technique and EMF method the joinic and silver ionic transport number measurements of various compositions of the mixed system CdI₂-Ag₂O-CrO₃ have been made. The presence of AgI in these materials has been inferred from the typical β → α phase transition of AgI, which is characterized by an endothermic peak at around 420 K in the DSC traces of these specimens. While the structural analysis performed by means of powder X-ray diffraction has revealed the formation of ionic phases involving polycrystalline compounds, the Fourier transform infrared (FTIR) spectroscopic results have indicated the presence of ionic species thus confirming the ionic nature of the products. The complex impedance studies carried out in the frequency range 20 Hz - 1 MHz and over the temperature range 294 – 442 K have revealed that the best conducting composition, namely 55%(CdI₂) – 45%(Ag₂O·CrO₃), would exhibit a silver ionic conductivity of 1.3×10⁻⁵Scm⁻¹ at 294 K.     

Portable and Automatic Mössbauer Analysis

A portable Mössbauer spectrometer, developed for extraterrestrial applications, opens up new industrial applications of MBS. But for industrial applications, an available tool for fast data analysis is also required, and it should be easy to handle. The analysis of Mössbauer spectra and their parameters is a barrier for the popularity of this wide-applicable spectroscopic technique in industry. Based on experience, the analysis of a Mössbauer spectrum is time-consuming and requires the dedication of a specialist. However, the analysis of Mössbauer spectra, from the fitting to the identification of the sample phases, can be faster using by genetic algorithms, fuzzy logic and artificial neural networks. Industrial applications are very specific ones and the data analysis can be performed using these algorithms. In combination with an automatic analysis, the Mössbauer spectrometer can be used as a probe instrument which covers the main industrial needs for an on-line monitoring of its products, processes and case studies. Some of these real industrial applications will be discussed.     

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.     

Observation of dielectronic satellites in the K-spectrum of argon ions in plasma produced by femtosecond laser pulses

The satellite structure of 1s2p ^1,3 P ₁-1s ²¹ S ₀ lines of the He-like argon ion in plasma produced by a 45-fs laser pulse in a gas-jet cluster target is measured with a high spectral resolution. Radiation transitions 2p → 1s from autoionizing states (AISs) are detected for ions ranging from Li-like to F-like. The spectrum observed is theoretically simulated with the use of the spectroscopic data for the AISs of multicharged ions obtained within the multiconfiguration relativistic Hartree-Fock method. Good agreement with experimental data is obtained when the main population channels of these states are taken into account for typical values of cluster-target plasma parameters.