On the quantization of solid body rotation

A general method for solving the problem of quantization of a top is proposed that allows for finding the Hamiltonian eigenfunctions in the form of polynomials of various degree n in the Cartesian coordinates with the use of the Lamé functions. All three coordinates x, y, and z are equivalently involved in computations, as well as their relations with ellipsoidal coordinates, which makes the computations symmetric.     

On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

100-TW femtosecond laser based on parametric amplification

In experiments on the parametrical amplification of femtosecond pulses in wide-aperture DKDP crystals, a power of more than 100 TW has been reached, which is much higher than the record level achieved in such lasers. The energy efficiency obtained for the parametric amplifier is equal to 27%. The energy of a 72-fs pulse is equal to 10 J.     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Signal recording in acoustooptical imaging of scattering media

An expression for a signal at the ultrasonic frequency from a photodetector arising when diffraction waves at the cathode mix is obtained for the case when the optical and acoustic beams are space-limited and Bragg angles are small. The alternating current generated when the scattering medium is crossed by a focused 3-MHz ultrasonic beam and illuminated by a cw He-Ne laser is measured. Satisfactory agreement between experimental results and those calculated from the formulas obtained indicates that our model treating acoustooptical interaction in the medium in terms of Raman-Nath diffraction is valid. Conditions for measuring the alternating current (which is a parameter of acoustooptical imaging) that are optimal from the viewpoint of maximizing the signal and signal-to-noise ratio are predicted theoretically and corroborated experimentally.     

Creation of a donor-acceptor pair for studying intraprotein electron transfer with the participation of amino-acid derivatives of fullerene C60

Efficient quenching of eosin phosphorescence by amino-acid derivatives of fullerene (AADFs) such as C₆₀-alanine and C₆₀-glycine in aqueous solutions indicates the possibility of transferring electrons from eosin to fullerene upon collisions or in the exciplex state. To investigate electron transfer in the protein structure, we studied the process of incorporation of C₆₀-alanine and C₆₀-glycine into the heme pocket of myoglobin by controlling Förster quenching. The dissociation constant for the protein-AADF complex was estimated.     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

On the polarization interaction between two closely spaced conducting spheres in a uniform electrostatic field

An electrostatic interaction between two separate, grounded, uncharged, perfectly conducting spheres of different radii in a uniform electrostatic field is investigated. It is shown that at a small center-to-center distance of the spheres, the force of the polarization interaction between the spheres depends appreciably more weakly on that distance in comparison to the force of the electrostatic interaction of two elementary dipoles as it should be in view of the interaction between two like polarization charges.     

Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

Effect of the paste molding pressure on the mechanical strength of an iron oxide catalyst in the dehydrogenation of methylbutenes

The effect of the paste molding pressure on the physicomechanical and texture characteristics of catalysts was studied. An indirect criterion is suggested to evaluate the molding pressure in industrial extruders, whose optimal value ensures good physicomechanical properties of the catalysts and kinetic control over the catalyzed reaction. The results obtained were verified in paste molding on various industrial extruders, and this enabled the optimal choice of the molding equipment.