Mark Grigor'evich Krein

Obituary

Mark Grigor'evich Krein     

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.     

Investigation of preheating of laser thermonuclear targets

The preheating level of the thermonuclear fuel and of the gas-compressing shell is the main criterion of the target-compression efficiency in experiments on laserdriven thermonuclear fusion. This paper contains the result of investigations of electronic, radiative, and impact preheating in experiments on compression and heating of hlgh-aspect shell targets in the Del'fin-l laser-derived thermonuclear facility. A procedure, based on analysis of the epithermal emission of the plasma, is considered for measuring the target preheating by fast electrons. The radiative and impact preheating of compressing shells in DD gas are estimated. The results of the investigation demonstrate the high degree of adiabaticity of the compression of the thermonuclear fuel in experiments with the Del'fin-l facility.Nuclear Plasma Laboratory of the Lebedev Physics Institute. Translated from Preprint No. 3, Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1990.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Peak sets for analytic Hölder classes

A closed subset E of the unit circumference T is said to be a peak set for the analytic Hölder class A, 0 < < 1 there exists a functionf,fA such that f¦_E1 and ¦f(z)¦<1 for. It is shown that the set E is a peak set of the algebra A if and only if there exists a nonnegative Borel measure on T such that the function coincides almost everywhere with a function of the Hölder class , equal to zero on E. A sufficient condition in order that a closed set E should belong to the family of peak sets is obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 129–136, 1987.     

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.     

Mechanism of breakdown development in a gas in a subthreshold HF field

The development of a breakdown wave in subthreshold HF fields is considered for the condition that the field energy density exceed the plasma energy density E²/4 > nT. It is shown that the breakdown wave propagation mechanism is controlled by HF diffusion with a coefficient _iE²/4en. A model of breakdown development along the direction of the linear field polarization is constructed on the basis of this mechanism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 55–60, August, 1989.