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

Dehydration of methyl phenyl carbinol catalyzed by modified active aluminum oxide

The effect of modification with metal salts and acids on the acid-base characteristics and the catalytic properties of active aluminum oxide in the reaction of methyl phenyl carbinol dehydration to styrene was studied using the IR spectroscopy of adsorbed base molecules. The surface treatment of γ-Al2O3 with chromium and nickel cations decreased the catalyst activity because of the occurrence of hydrogenation side reactions. The appearance of strong Bronsted and Lewis acid sites as a result of modification with sulfate, nitrate, and fluoride anions accelerated the deactivation of the catalyst. Upon modification with acetic acid solutions, additional Lewis acid sites with Q CO = 33.5-34 kJ/mol were formed on the surface of aluminum oxide, and the concentration of strong basic sites with PA = 900 kJ/mol decreased; this facilitated an increase in the catalyst activity and a decrease in the rate of catalyst deactivation. © 2007 Pleiades Publishing, Ltd

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

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

Crystal Structure, Electrical Conductivity and Hydration of the Novel Oxygen-Deficient Perovskite La2 ScZnO5.5, Doped with MgO and CaO

This paper demonstrates the possibility of creating oxygen deficiency in perovskites A+3 B+3 O3 by introducing two types of cations with different charges into the B-sublattice. For this, it is proposed to introduce a two-charged cation, for example, Zn2+, as an alternative to alkaline earth metals. Previ-ously, this possibility was demonstrated for aluminate LaAlO3 and indate LaInO3 . In this article, we have focused on the modification of the scandium-containing perovskite LaScO3 . The novel oxygen-deficient perovskite La2 ScZnO5.5 and doped phases La1.9 Ca0.1 ScZnO5.45, La2 Sc0.9 Ca0.1 ZnO5.45, and La2 Sc0.9 Mg0.1 ZnO5.45 were obtained via a solid-state reaction process. Their phase composition and hydration were investigated by XRD and TGA + MS techniques. The conductivities of these materials were measured by the electrochemical impedance technique under atmospheres of various water vapor partial pressures. All phases crystallized in orthorhombic symmetry with the Pnma space group. The phases were capable of reversible water uptake; the proton concentration increased in the order of La2 ScZnO5.5 < La2 Sc0.9 Mg0.1 ZnO5.45 < La2 Sc0.9 Ca0.1 ZnO5.45 ≈ La1.9 Ca0.1 ScZnO5.45 and reached ~90% hydration limit for Ca2+-doped phases. The total conductivities increased withthe increase inthe free lattice volume inthe sequence of σLa2 ScZnO5.5 < σLa2 Sc0.9 Mg0.1 ZnO5.45 < σLa1.9 Ca0.1 ScZnO5.45 < σLa2 Sc0.9 Ca0.1 ZnO5.45, the activation energy decreased in the same sequence. The sample La2 Sc0.9 Ca0.1 ZnO5.45 showed the highest conductivity of about 10−3 S·cm−1 at 650◦ C (dry air pH2 O = 3.5·10−5 atm). Water incorporation was accompanied by an increase in conductivity in wet air (pH2 O = 2·10−2 atm) due to the appearance of proton conductivity. The sample La2 Sc0.9 Ca0.1 ZnO5.45 showed a conductivity of about 10−5 S·cm−1 at 350◦ C (pH2 O = 2·10−2 atm). A comparison of conductivities of obtained phase La2 ScZnO5.5 with the conductivities of La2 AlZnO5.5 and La2 InZnO5.5 was made; the nature of the B-cation did not significantly affect the total conductivity. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.Acknowledgments: The study was financially supported by the Ministry of Education and Science of the Russian Federation (state assignment no. AAAA-A20-120061990010-7)

Study of factors affecting the erosive wear of equipment for dehydrogenation units in fluidized beds of microspherical chromia-alumina catalysts under industrial operating conditions

© Pleiades Publishing, Ltd., 2014. © A.N. Kataev, A.A. Lamberov, S.R. Egorova, Kh.Kh. Gilmanov, 2014. The main problems associated with the operation of microspherical treating-type chromia-alumina catalysts with increased strength during isoparaffin dehydrogenation are discussed. The erosive wear of the walls of overflow pipelines when using a mixture of treating-type KDI and conventional IM-2201S catalysts and ways of solving the problem are emphasized. It is found that the main reason for an increase in erosive wear is the greater momentum of catalyst particles due to a higher mean particle size and gas transport rate; upon transitioning from IM-2201S to a mixture of IM-2201S and KDM (70 : 30), the mean particle size of the equilibrium catalyst grows from 68 to 74 μm. The optimum size range of a high-strength catalytic system in which the activity does not increase over time is calculated with a lower rate of transport gas injection while keeping the number of particles 20-40 μm in size at 20-30 wt %. Pilot batch production of high-strength catalyst in the optimum size range is recommended in order to shift units for the industrial dehydrogenation of isobutane to the use of treating-type KDI catalyst without the addition of IM-2201S

Protozoan and metazoan communities treating a simulated petrochemical industry wastewater in a rotating disc biological reactor

The microfauna of adhered biofilms treating a simulated petrochemical plant wastewater was investigated in relation to the organic loading and the toxicity. Experiments in a six-compartment laboratory rotating biological reactor were performed at organic loadings of 0.99,1.38 and 1.97 g/l.day. The concentration of organic compounds in the artificial wastewater (phenol, acetophenone and styrene), toxicity of the wastewater, number of representative types of microfauna, their biomass and species diversity were monitored along the reactor. During this study 25 species were identified and attributed to seven classes of the three types Sarcomastigophora, Ciliophora and Nemathelminthes. Eight species from 18 ciliates have been reported in the literature as being commonly found inhabitants of aerobic wastewater treatment plants. An inverse relationship between the number of microfauna representatives and the organic loading was found. The presence of the most common species was related to the reactor operating conditions. A correlation between the toxicity of the wastewater measured by the Paramecium express-test and the distribution and abundance of microfauna was established. This express-test made it possible to predict the biological quality of the biofilm of activated sludge. Therefore, it is recommended as one of the control parameters to monitor systems of biological wastewater treatment