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 MATHEMATICS Stability by means of a linear approximation of periodic solutions of a system of differential equations with discontinuous right-hand sidesM. A. Aizerman, F. R. Gantmakher 527 On imbedding theoremsYa. S. Bugrov 531 The reducibility of a certain class of simultaneous differential equations containing quasiperiodic coefficientsA. E. Gel'man 535 The representations of the group of rotations of an $n$-dimensional Euclidean space by spherical vector fieldsA. A. Kirillov 538 On the boundedness in $L_p$ of derived solutions of elliptical equations and elliptical systemsA. I. Koshelev 542 A representation of solutions of Euler–Poisson–Darboux's equation with analytical functionsYu. P. Krivenkov 545 Some theorems on the resolution of infinitely divisible laws into componentsYu. V. Linnik 549 On the existence and uniqueness of a solution to the general type of equation in connection with reversibility in semigroups of transformationsE. S. Lyapin 552 On completely continuous vector fields in Banach spaceA. M. Rodnyanskii 556 Cauchy problem for a system of linear partial differential equations with a weight exceeding unityYu. V. Sidorov 560 New sufficient conditions for stability, semistability and instability of the limit cycle of the $\frac{dy}{dx}=\frac{P(x,y)}{Q(x,y)}$ equationV. F. Tkachev 564 Permutations within a trigonometric systemP. L. Ul'yanov 568 FLUID MECHANICS An asymptotic solution of equations for one-dimensional unsteady motion of ideal gas with cylindrical symmetryG. M. Shefter 572 MATHEMATICAL PHYSICS A solution of Stephan's problem by reduction to a system of ordinary differential equationsV. G. Melamed 577 PHYSICS A study of the $\beta^+$ decay in $\mathrm{Ho}^{160}$B. S. Dzhelepov, O. E. Kraft, B. K. Preobrazhenskii 581 Deviations from Boltzman's distribution in the breakdown of diatomic moleculesE. E. Nikitin 584 Absorption spectra with cold light sourcesB. I. Stepanov, Ya. S. Khvashchevskaya 588 GEOPHYSICS Turbulent viscosity in a shallow sea, due to wavesO. D. Shebalin 591 ENERGETICS On the insertion of bonds against the disturbing action in automatic control systemsO. P. Demchenko 601 CRYSTALLOGRAPHY The mechanism of the formation of kink bandsE. V. Kolontsova, I. V. Telegina 605 CHEMISTRY The effect of perchlorates on styrene polymerizationB. I. Losev, Yu. I. Zakharova 609 Investigation of systems of $n$-paraffins $\mathrm C_{20}$– $\mathrm C_{30}$ and $\mathrm C_{30}$– $\mathrm C_{32}$N. A. Nechitailo, L. M. Rozenberg, E. M. Terent'eva, A. V. Topchiev 613 The kinetics of the electrophile substitution at a saturated carbon atomO. A. Reutov, I. P. Beletskaya, R. E. Mardaleishvili 617 The hydrogenolysis of furane homologues on a platinum catalystN. I. Shuykin, I. F. Bel'skii 621 PHYSICAL CHEMISTRY The influence of gases on the flotability of certain non-sulphide minerals, as related to their crystalline structureV. V. Bakakin, I. N. Plaksin, E. M. Chaplygina 625 The mechanism of organic glass fusionN. A. Grishin, S. S. Voyutskii, M. M. Gudimov 629 The role of hydrogen atoms in the catalytic oxidation of hydrogen on palladiumV. B. Kazanskii, V. V. Voevodskii 633 The rheological properties of surface layers at the oil – water interface and their role in the stability of oil emulsionsM. M. Kusakov, A. A. Petrov 637 On intermediate products in redox photoreactions of xanthene dyesV. F. Tsepalov, I. Ya. Shlyapintokh 641