Supplement to the work “diffraction losses of a confocal resonator with mirrors of arbitrary shape”

Two-sided estimates are obtained for the diffraction losses of all proper oscillations of a symmetric confocal resonator and also of a confocal resonator with mirrors of different sizes.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 51, pp. 170–171, 1975.     

Shape of the amplification line corresponding to an adjacent transition in a strong field

An analysis is made of the effect of a strong field on the shape of the amplification line for monoenergetic atoms. There are three strong-field contributions, differing in their dependence on the set of relaxation parameters of the medium and on the differences among the populations corresponding to the Raman transitions. An analysis is made of the conditions under which each of the contributions is predominant. The change in the line shape by an intensified external field is found for each case. Neon atoms are discussed as an example. The results are compared with those corresponding to a Maxwellian velocity distribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 38–44, November, 1970.The authors thank S. G. Rautian for useful discussions and S. I. Mortsev for assistance in the numerical calculations.     

Laws governing the development of structure in the films formed by the vacuum evaporation of certain pure metals and fractionating copper alloys

The phase composition of the films produced by the vacuum evaporation of several pure metals and fractionating copper-base alloys, with deposition on a sodium chloride (100) cleavage, is studied by transmission electron microscopy and electron diffraction. The phase compositions of films deposited at different stages in the evaporation of alloys containing elements with severely differing vapor tensions differ considerably. Certain conclusions are drawn regarding the distribution of the alloying elements over the thickness of the films so formed during the complete evaporation of the alloy samples.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–31, October, 1973.In conclusion, the authors wish to thank Doctor of Technical Sciences Professor A. M. Korol'kov and Junior Scientific Assistant E. V. Lysova for preparing the required alloys.     

Effect of the solvent on selective hydrogenation of 6, 10-dimethylundeca-3,5,9-trien-2-one

Reaction mechanism for selective hydrogenation of pseudo-ionon on Raney-Ni in the presence of n- and iso-alcohols has been studied. From the analysis of ESR spectra, the dependence of selectivity on the solvent is concluded.

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- Ni- . .

     

Best mean-square approximation of functions of m variables

Let be the best mean-square approximation of a functionf(x) L₂(R_m) (m=1, 2, ...) by integral functions of the exponential spherical type (in the sense of thel _q metric, 0>0, where(f,/; l _p)L₂(R_m) is the spherical (in the sense of the metricl _p, 0f(x) L₂(R_m). For the quantity two-sided estimates are obtained which are uniform in the parameters m, q, and p. Similar results are also obtained in the case of q=p=2 for classes of functions W _f2 (R_m) (=1,2,...).Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 913–924, December, 1973.The author would like to express his deep gratitude to N. I. Chernykh under whose guidance this work has been carried out.