Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.Comment: 23 page

Improving the efficiency of university management : teacher’s performance monitoring as a tool to promote the quality of education

This study aims to examine the essence of education monitoring, its place in the higher education management system and the practical implementation of teacher’s performance monitoring as a tool to promote the quality of education. The article considers theoretical aspects of monitoring as a tool to promote the quality of education, assesses the performance of the university departments, research and teaching staff and discusses the results and suggestions on how to improve monitoring activities in higher education. Based on their research and findings, the authors claimed that the monitoring of the performance of the university research and teaching staff on the base of an indicator system in terms of education, methodology, research, organization and counselling services would lead to valid conclusions as to the effective performance of both individual researchers and teachers and university departments, in general.peer-reviewe

Spectrum of cosmic rays, produced in supernova remnants

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants is employed to calculate CR spectra. The magnetic field in SNRs is assumed to be significantly amplified by the efficiently accelerating nuclear CR component. It is shown that the calculated CR spectra agree in a satisfactory way with the existing measurements up to the energy $10^{17}$ eV. The power law spectrum of protons extends up to the energy $3\times 10^{15}$ eV with a subsequent exponential cutoff. It gives a natural explanation for the observed knee in the Galactic CR spectrum. The maximum energy of the accelerated nuclei is proportional to their charge number $Z$. Therefore the break in the Galactic CR spectrum is the result of the contribution of progressively heavier species in the overall CR spectrum so that at $10^{17}$ eV the CR spectrum is dominated by iron group nuclei. It is shown that this component plus a suitably chosen extragalactic CR component can give a consistent description for the entire Galactic CR spectrum.Comment: 4 pages with emulateapj, 3 figures, accepted for publication in the Astrophysical Journal Letter

Effect of the nature of silicon oxide structures on the activity of an alumina-chromium catalyst in the reaction of iso-butane dehydrogenation

The formation of silicon oxide structures in the composition of an alumina-chromium catalyst for the dehydrogenation of iso-butane is studied by means of nitrogen adsorption, XRD analysis, solid-state 29Si NMR spectroscopy, temperature-programmed desorption of ammonia, and UV-Vis and Raman spectroscopy. It is established that 0.5-1.2 wt % silicon was distributed on the catalyst surface in the form of Si(OSi)4 structures. As the silicon content was increased to 2.2-3.6 wt %, Si(OSi)3(O-) structural elements were present on the surface in addition to Si(OSi)4. The formation of silicon oxide structures on the catalyst surface was responsible for an increase in the concentration of Cr(III) ions and a decrease in the surface acidity; the activity and selectivity of the catalysts in the reaction of iso-butane dehydrogenation increased. © Pleiades Publishing, Ltd., 2014

Effect of high-temperature treatment on the properties of an alumina-chromium catalyst for the dehydrogenation of lower paraffins

The crystal and pore structures of a microspherical alumina-chromium catalyst calcined at 800-1100 C were studied using a set of currently available physicochemical techniques (X-ray diffraction, lowtemperature nitrogen adsorption, diffuse reflectance UV-vis spectroscopy, Raman spectroscopy, and EPR spectroscopy); the state of its active component and the catalytic properties in isobutane dehydrogenation were examined. As the calcination temperature was increased from 800 to 900-1000 C, the properties of the catalyst were improved as a result of the formation of Cr2O3 clusters in an optimum amount and a decrease in the surface acidity of the catalyst due to the dehydroxylation and phase transformations of the aluminum oxide support. Calcination at 1100 C was accompanied by a decrease in the yield of isobutylene as a result of the formation of inactive macrocrystalline chromium (III) oxide and a chromium species inaccessible to reacting molecules; this chromium species was encapsulated in closed pores as the constituent of a solid solution of α-Al2O3-Cr2O3. © 2013 Pleiades Publishing, Ltd

Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of solutions of the Korteweg--de Vries equation which are decaying perturbations of a quasi-periodic finite-gap background solution. We compute a nonlinear dispersion relation and show that the $x/t$ plane splits into $g+1$ soliton regions which are interlaced by $g+1$ oscillatory regions, where $g+1$ is the number of spectral gaps. In the soliton regions the solution is asymptotically given by a number of solitons travelling on top of finite-gap solutions which are in the same isospectral class as the background solution. In the oscillatory region the solution can be described by a modulated finite-gap solution plus a decaying dispersive tail. The modulation is given by phase transition on the isospectral torus and is, together with the dispersive tail, explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve.Comment: 45 pages. arXiv admin note: substantial text overlap with arXiv:0705.034

Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape

We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length

Effect of Fe content on atomic and electronic structure of complex oxides Sr Ti,Fe O3 delta

Two series of SrTi1 xFexO3 amp; 948; STFO powders with different Fe content produced by two different methods, solid state reaction or modified Pechini synthesis, have been investigated by soft X ray absorption spectroscopy. The O1s K , Fe2p L2,3 and Ti2p L2,3 absorption spectra of STFO powders were analyzed. Partial substitution of Ti by Fe atoms in SrTiO3 were found to cause asymmetric distortion of TiO6 octahedrons which may violate the cubic symmetry of STFO. It was established that the distortion of TiO6 octahedrons increases with increasing Fe content. The joint analysis of the STFO spectra along with the reference compounds points to the presence mainly of Fe3 states in octahedral environment at small concentration of Fe atoms along with essentially smaller content of Fe4 states in octahedral environment where the latter contribution increases with increasing Fe content. Also a presence of Fe3 states in tetrahedral environment with Fe content higher than 50 is traced. A certain amount of Fe2 ions in an octahedral environment was also found in the STFO compound prepared by spray pyrolysis with Fe content higher than 75 . The O1s K absorption spectra point to increase in oxygen vacancy concentration with increasing Fe content. The lowest degree of structure distortions was traced in STFO35. Hence, the STFO35 compound seems to be mostly appropriate for technical application