On some methods of descent over groups of variables

Translated fromIssledovaniya po Prikladnoi Matematike, No. 19, 1992, pp. 24–33.     

Micron-image transfer system with brightness amplifier in gold-vapor laser

A gas-discharge gold-vapor laser on self-terminating transitions with operating wavelength λ=312.2 nm has been used to develop a highly efficient system for image transfer. An optical scheme and all its parameters have been chosen optimal for image quality. It has been found both theoretically and experimentally that the best results on micron-structure image transfer are obtained with 2–5-times image reduction. Various types of masks have been used. A 1-µm structure has been resolved due to the choice of optimal exposure time of 10 ms under a period of pulse repetition (0.6 – 0.8) ms; in this case, the minimal fringe dimension was ≈2 µm with an image dimension of 2 mm for a laser tube 1.8 cm in diameter.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.     

Spectral expansions of some representations of Lie groups

We investigate representations of classical noncompact Lie groups induced by representations of the maximal parabolic subgroup. Formulas are obtained for 5O₀(2p, 2q)/U(p, q) and U(2p, 2q) Sp(p, q).Translated from Ukrainskii Mathematicheskii Zhurnal, Vol. 42, No. 1, pp. 128–131, January, 1990.     

Bahadur effectiveness of Watson-Darling goodness-of-fit tests

The rough asymptotic behavior of the probability of large deviations is found for Watson-Darling goodness-of-fit tests, which are centered versions of Kolomogorov-Smirnov statistics. Their Bahadur effectiveness is calculated and conditions for local asymptotic optimality for the alternative of translation are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 138–145, 1987.     

2-Amino-4,4-disubstituted-5-carboxymethyl-Δ2-1,3,4-oxadiazolin-4-ium chlorides and their recyclization in acetic anhydride

2-Methylamino-4,4-disubstituted-5-carboethoxymethyl-²-1,3,4-oxadiazolin -4-ium chlorides were obtained from the reaction of 1,1-disubstituted-4-methylsemicarbazides with ethyl propiolate in the presence of hydrochloric acid. After hydrolysis of the ester these chlorides recyclize in acetic anhydride to 1-substituted-3-acetoxy-1H-pyrazoles. The difference in the direction of ring opening with acetic anhydride in the betaines of 1,3,4-oxadiazolin-5-acetic acids and their thia-analogs has been demonstrated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1685–1688, 1992.     

Effect of hydrothermal treatment on catalytic properties of superhigh-silica zeolites

The effect of hydrothermal treatment of decationized superhigh-silica zeolite on the mechanism of n-hexane conversion has been studied. It has been established that thermosteam modification sharply decreases the cracking activity and increases the selectivity to aromatization reactions. Zeolite acidity markedly decreases, but its crystal structure does not become amorphous.

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