Asymptotic methods in the theory of nonlinear stochastic oscillations

We study applications of asymptotic methods of nonlinear mechanics and the method of Fokker-Planck-Kolmogorov equations to stochastic oscillations in quasilinear oscillating systems with random perturbations. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 510–518, October–December, 2007.     

Neocompact Sets and the Fixed Point Property

We use a newly introduced concept of neocompactness to study problems from metric fixed point theory. In particular, we give a sufficient condition for a superreflexive Banach space X to have the fixed point property and obtain shorter proofs of some well-known results in that theory.     

Characterization of high-order harmonic radiation on femtosecond and attosecond time scales

We characterize the temporal structure of high-order harmonic radiation on both the femtosecond and attosecond time scales. The harmonic emission is characterized by mixed-color two-photon ionization with an infrared femtosecond laser using a Mach–Zehnder interferometer where both pump and probe arms travel completely separate paths. In a first experiment, we measure the duration and chirp of individual harmonics. In a second experiment, we resolve, for the first time with this type of setup, the attosecond beating of several harmonics generated under conditions similar to the first experiment. We suggest that the results of both measurements can be combined to determine the full attosecond time structure of the harmonic emission. PACS 32.80.Rm; 42.65.Ky     

Mineral and chemical compositions and structure-sorption properties of bottom sediments as the basic components of enterosorbents and application materials

The mineral and chemical compositions, as well as some structure-sorption characteristics were determined for clay minerals selected for examination. The integrated coefficients of contamination of bottom sediments with each of the toxicant metals (Fe, Ni, Co, Cu, Zn, Pb, Mn) were calculated. The minerals examined presumably can be used in medicine as efficient application materials, cosmetic agents, and sorbents (enterosorbents).     

123 Phases in CeLa2Cu2MgO8 samples

A tetragonal 123 phase with the composition close to CeLa₂ { Cu ₂ ²⁺ } [Mg²⁺]O₈ (the braces indicate the Cu(2) positions; the brackets indicate the Cu(1) positions) with the parameters a = b = 0.3909(3) nm, c = 1.6591(8) nm was prepared at 860°C under an oxygen atmosphere with an elevated oxygen pressure. When the lanthanum-for-barium substitution was incomplete, the resulting 123 phase had the composition close to CeLa_1.7Ba_0.3{ Cu _1.7 ²⁺ } [Mg]O₈ with the unit cell parameters a = b = 0.3868(3) nm, c = 1.6578(8) nm that contains Cu³⁺ in the Cu(2) positions. The partial substitution of barium for lanthanum (the melting point of barium oxide is almost 500°C lower that of the lanthanum oxide) appreciably facilitated the synthesis: the 123 phase in this sample was more than 90%. The existence of Cu³⁺ in the Cu(2) positions enhanced the electrical conductivity of the sample.     

Instability of Fabry-Perot interferometer with a multilayered paramagnetic filling

The results of the analysis of the stability of stationary solutions of wave equations discribing a behavior of the nonlinear Fabry-Perot interferometer with a saturated paramagnetic filling are presented in this paper. The cases when paramagnetic medium is characterized by a homogeneously and nonhomogeneously broadened line of the magnetic resonance have been considered. Areas of unstable behavior of these characteristics of the resonance structure have been found.     

The mechanism of selective NOx reduction by hydrocarbons in excess oxygen on oxide catalysts: V. Adsorption properties of a commercial Ni-Cr oxide catalyst

According to X-ray diffraction analysis data, the test catalyst was a Ni-Cr spinel with an impurity of NiO. With the use of in situ IR spectroscopy, it was found that nitrite, nitrate, and acetate surface complexes occurred under the reaction conditions of the selective catalytic reduction of nitrogen oxides by propane in the presence of oxygen on the nickel-chromium catalyst. As the temperature was increased, the nitrite complexes were converted into nitrate species. The molar absorption coefficient of surface nitrate complexes was determined. According to IR-spectroscopic and TPD data, the nitrate complexes were bound relatively weakly to the surface. The temperature region of their existence was 50–200°C. The temperature region of existence of the surface acetate complexes was 200–400°C. The individual adsorption of oxygen was not observed; however, oxygen-containing surface sites (Cr⁵⁺=O) participated in the formation of the surface complexes of reactants.     

Anomalous behavior of conductivity of the confined Q1D electron system over liquid helium

Conductivity of electrons in a quasi-one-dimensional (Q1D) system over liquid helium in narrow channels with the parabolic profile of the potential well has been investigated at temperature T, from 0.4 to 1.8 K, for different driving electric fields and radius of channel curvature. The interval of linear electron densities varied from 2.18×10³ up to 1.7×10⁶ cm⁻¹.

The inverse mobility (1/μ_eff) in the electron-ripplon scattering region at the high linear densities of charges in the channel increases with temperature decreasing. This anomalous behavior of the electron transport in the low-temperature region has been explained by either the electron ordering or the polaronic effects in confined conducting channels. The nonlinear behavior of the electron velocity as a function of a driving electric field is supposed to be due to Breg–Cherenkov radiation of the ripplons. The radiation occurred if the velocity of electrons in the channel approaches to the critical value.     

Copper-D-penicillamine complex as potential contrast agent for MRI.

In vitro and in vivo proton T1 data are reported that demonstrate that the paramagnetic copper-D-penicillamine complex can be applied as a potential contrast agent to magnetic resonance imaging.     

Specific carbon-13 labelling of leucine residues in human growth hormone.

Biosynthetic human growth hormone specifically 13C-labelled in the carbonyl positions of all 26 leucine residues has been obtained by recombinant DNA techniques using 13C-labelled leucine and an E. coli strain that requires leucine. It is shown that, on the whole, the labelling is specific with no significant mislabelling as would have been the case had the 13C-labelled leucine been metabolized.