On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

Proof of expansion of the reciprocal distance in spheroidal coordinates

A concise proof is given for the expansion of the reciprocal distance between two points in spheroidal harmonics. The proof is given for an oblate and a prolate spheroid.     

Optimization of Mass Transfer Processes in the Zone of the Air Electrode of a Fuel Cell with a Solid Polymer Electrolyte

A two-dimensional mathematical model for the transport of reactants in a fuel cell with a solid polymer electrolyte is developed. The model is used for analyzing spatial distributions of the concentration of reactants and current density over the cell. The effect of the catalytic-layer activity, reactant speed, bipolar-plate geometry, thickness and porosity of current collector and/or gas-diffusion sublayer, and the reaction mixture composition on the fuel cell efficiency is estimated theoretically and experimentally.     

Structural phase transformations and physical properties of intercalation compounds in the Cr0.5Ti(Se1−x Tex)2 system

The atomic structure and magnetic and electric properties of the Cr_0.5TiSe₂-Cr_0.5TiTe₂ system of intercalated phases were studied in detail by gradually replacing selenium by tellurium. It was revealed that this replacement changes the crystalline structure from monoclinic in the initial compounds to hexagonal in the compounds containing various types of chalcogen atoms; this is accompanied by disordering of chromium atoms in the van der Waals gaps. The electrical resistance and magnetic characteristics vary nonmonotonically on replacement of selenium by tellurium, which is associated with a change in the degree of atomic disordering during the transition from Cr_0.5TiSe₂ to Cr_0.5TiTe₂.     

Laser-induced breakdown threshold and fracture versus the nanostructure of two-phase glass

The radiation hardness and mechanical strength of single-and two-phase glasses are studied for the case when nanosecond laser pulses (λ= 1.06 μm, τ_0.5 ≈ 12.5 ns) are focused inside the material. Laser interferometry is applied to measure the displacement of the free surface, find optical breakage thresholds, and carry out the fractographic analysis of damaged regions. It is shown that breakdown channels and damage regions develop in a nonlinear manner according to optical breakdown mechanisms, changing each other with an increase in the laser energy. The strength of the two-phase glass is found to be more than four times that of the single-phase glass, although their elastic properties differ insignificantly. Such a considerable difference in the hardness of these materials with chemically similar constitutents is attributed to the presence of the double-lattice nanometer-scale structure of the two-phase glass.     

Modeling of the Kinetics of Intramolecular Processes and Transient Spectra with Allowance for Nonradiative Transitions

It has been shown that the kinetics of intramolecular processes and time-resolved spectra with allowance for the quantum beats of the resonant states of isomers or isolated subsystems of levels of one isomeric form can be described with the use of a molecular model interpreting the effect of beats as a nonradiative transition. We have obtained an expression for the nonradiative transition probability, which is directly proportional to the beat frequency and depends oscillatorily on time, thus modeling the effect of beats. The parameter of the molecular system model is the beat frequency directly related to the parameter characterizing the intramolecular interisomeric interactions (the corresponding nondiagonal element of the energy matrix) rather than the value of the nonradiative transition probability. The character of the change in the level populations and, accordingly, in the band intensities in the spectra in the proposed model is in good agreement with the experiment, including the fine structure of the time dependences — oscillations of the line intensities. In analyzing the temporal experiment with a high resolution, it is necessary to take into account the instrument function leading to quantitative and qualitative changes in the time dependences. The traditional model of nonradiative transitions with a constant probability value has a very limited range of applicability — very high beat frequencies compared to the probability of optical transitions.     

Exchange interactions of excitons localized at opposite interfaces in type-II GaAs/AlAs superlattices: Optically detected magnetic resonance and level anticrossing

Two types of excitons, localized at opposite interfaces and characterized by different magnitudes of the exchange interactions at the same radiation energies, are simultaneously in type-II GaAs/AlAs superlattices. It is shown that the additional long-wavelength luminescence line in superlattices grown with growth interruptions after the GaAs layers is due to the recombination of an exciton localized at an inverted interface in regions where the quantum-well width is increased by one monolayer. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 701–706 (25 November 1996)     

Activation of cells in a cavitation flow

A cavitation flow in an expanding nozzle is numerically simulated. The cavitation activation of cells is studied experimentally.     

Production of Ωscb baryons in photon-photon collisions

Methods for calculating the total and differential cross sections for the production of Ω_scb baryons in photon-photon collisions and the results of respective calculations are described.