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

Vitreolenticular interface

Interest in the study of vitreolenticular interface (VLI) increases due to the expansion of indications for manipulations in this area of the eyeball. Active studies of the last decades dictate the need to modify and detail our concepts about the structure and functional significance of VLI as well as to introduce this knowledge into the surgical practice. The article presents a historical background on the study of VLI structures, as well as an analysis of research in this area conducted in recent decades. It highlights issues related to the support and barrier functions of the VLI, as well as participation in the processes of accommodation and hydrodynamics of the eye. Modern generalized data on anatomical-topographical and functional features of vitreolenticular interface give us an integrity understanding of the interaction of various eye structures and a possibility to optimize surgical approaches to minimize complications and to improve anatomical and functional results

Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function

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

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

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

Synthesis, Structure and Conductivity of Solid Solutions Based on La2ZnAlO5.5 Doped with CaO

This paper devoted to the synthesis and investigation of physico-chemical properties of solid solutions based on new perovskite La2ZnAlO5.5. The solid state synthesis of calcium-doped samples were realized. Structure, phase composition and conductivity of samples were investigated.This work was supported by the State Assignment no. АААА-А20-120061990010-7

ULTRAFINE MODIFYING ZEOLITE ADDITIVE FOR GYPSUM CONCRETE

Ultrafine modifying additive obtained mechano-chemical activation of natural zeolite rocks and plasticizer dibutylphthalate. Shows the effect of additives on the properties and microstructure of gypsum concrete

Studying the effect of the OsGATA rice transcription factor on salt stress tolerance in wheat

This study shows the possibility of using the OsGATA rice transcription factor in transgenic lines of high-yielding wheat cultivars to increase their tolerance to salinity, which was confirmed using physiological and biochemical methods according to standard protocols. Wheat plants were grown in an artificial climate under optimal growing conditions. Genetic transformation methods were used to introduce the GATA gene into the genome of the used wheat genotypes. Transgenic lines were selected on selective media under in vitro conditions.The results of the experimental work showed that the expression of the GATA gene under salt stress may be responsible for the increased compartmentalization of Na+ in the vacuole, which provides improved salt tolerance. As a result of the experiment, collections of T1 transgenic wheat lines from cvs. ‘Zlata’, ‘Emir’ and ‘Agata’ expressing the GATA gene were obtained and studied for salt tolerance. Lines Zl.01, Zl.02, Zl.03 and Ag.02 were selected with PCR. Under NaCl salinity conditions, some of the transgenic lines showed a statistically significant increase in salinity resistance. The results of the study laid the foundation for studying GATA genes in wheat and for producing salinity-tolerant lines without growth defects or reduced productivity