Normalization and averaging on compact lie groups in nonlinear mechanics

We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic properties of a system of zero approximation, the results obtained by the method of asymptotic decomposition coincide with the results obtained by the method of normal forms or the Bogolyubov averaging method. We develop a new algorithm of asymptotic decomposition by a part of the variables and its partial case — the algorithm of averaging on a compact Lie group. For the first time, it became possible to consider asymptotic expansions of solutions of differential equations on noncommutative compact groups.     

On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Temperature and field dependences of photo-induced changes in the magnetization in yttrium iron garnet

The changes in the magnetization of yttrium iron garnet (YIG) when irradiated by a pulsed neodymium laser beam with wavelength λ=1.06 μm are investigated. Measurements are performed in the temperature range from 100 K to 600 K in various external magnetic fields. YIG single crystals grown along the crystallographic (100), (110), and (111) directions are chosen so that the external anisotropy of the indicated processes can be determined. Characteristic temperature intervals dominated by different mechanisms of variation of the magnetization under the influence of a laser pulse are discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1263–1266 (July 1997)     

Temperature and frequency dependence of the spin-lattice relaxation times of E′1 centers in neutron-irradiated quartz glass

Results are reported for measurements of the spin-lattice relaxation times of E′₁ centers in quartz glass, produced by neutron irradiation, with the measurements made at two frequencies 9.25 and 24.0 GHz over a wide temperature interval 1.5–300 K. The experimental data are interpreted on the basis of interaction mechanisms of the spins with two-level systems with excitation energies ∼6, ∼26, and ∼420 cm⁻¹. A small modification of the existing theory allows us to explain a number of features of the observed temperature and frequency dependence of the relaxation rate. The results are compared with the data available in the literature on spin-lattice relaxation of irradiation centers in crystalline quartz and quartz glass. Fiz. Tverd. Tela (St. Petersburg) 39, 1335–1337 (August 1997)     

Experimental studies of microwave amplification in the ion-focusedregime

Studies of microwave amplification with an in-focused electron beam drawn from an induction injector are reported. A free-electron laser (FEL) operating at 9.4 GHz and employing ion-focusing within the interaction region has achieved power in excess of 30 MW at 9.4 GHz, with a beam energy of 0.8 MeV and current of 0.7 kA. Peak gain is 20 dB/m, with no saturation after 15 wiggler periods. Also reported are the first evolution and detuning data for an ion-channel laser/maser (ICL). Two shortcomings of the prematurely halted ICL studies are poor frequency discrimination and a large axial plasma gradient. Prospects for operation with an upgraded 1.6 MeV accelerator are discussed     

Pseudo-epitaxial C60 films prepared by a hot-wall method

We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C₆₀ evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C₆₀ planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C₆₀ is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy.     

Donor-acceptor complexes of quinoline N-oxides with boron trifluoride

Molecular n-v complexes of quinoline N-oxides with BF₃ have been studied by electronic and IR spectroscopy. In most case the donor centre is the oxygen atom of the N-oxide group.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1087–1092, August, 1994.     

Influence of the chemical composition of plant oils on cytochrome P-450

The influence of sunflowerseed and cottonseed oils and also of fractions of normal and oxidized triacylglycerols isolated from them on cytochrome P-450 from rat liver microsomes has been investigated.