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 MATHEMATICS Fully idempotent rings and the generalized nil-radicalV. A. Andrunakievich, Yu. M. Ryabukhin 1015 On the rate of convergence of the distribution of the maximum deviation of an estimate of the spectrum of a Gaussian randon sequenceT. Arak 1019 On the Cauchy problem in a class of generalized functionsSh. A. Akhmedov 1022 On some analytic properties of the resolvent kernel of an ordinary differential operator of even order on a Riemann surfaceM. M. Gekhtman 1025 Selfadjoint boundary value problems for certain classes of differential- operator equations of higher orderM. L. Gorbachuk, A. N. Kochubei 1029 On some differential-operator equations of a general kindYu. A. Dubinskii 1033 On estimates of best approximations of a function of several variables by sums of two functions of a smaller number of variablesI. I. Ibragimov, M.-B. A. Babayev 1037 On radial connections of equations of Bessel classM. B. Kapilevich 1041 On the discreteness of the spectrum of a nonlinear Sturm–Liouville equationJindrich Nečas 1045 On the dimension of normal spacesB. A. Pasynkov 1049 An example of an $ACTL^p$ homeomorphism not absolutely continuous in the sense of BanachS. P. Ponomarev 1053 Quasi-elliptic pseudodifferential operators and the Cauchy problem for parabolic equationsV. S. Rabinovich 1055 Green’s formula and homeomorphism theorems for nonlocal elliptic boundary value problemsYa. A. Roitberg, Z. G. Sheftel 1059 On coercive solvability of difference equationsP. E. Sobolevskii 1063 Homotopic classification of Hilbert boundary value problems for a holomorphic vectorV. I. Shevchenko 1067 FLUID MECHANICS Waves at the surface of a flow of finite depth excited by a underwater sourceA. A. Zaitsev 1070 PHYSICS On the theory of stochastic acceleration of particlesA. I. Akhiezer, A. S. Bakay 1074 On the energy – impulse determination in the general relativity theoryV. A. Zhelnorovich 1078 GEOPHYSICS Horizontal stresses in the isostatically balanced lithosphereE. V. Artyushkov 1084 Thermobaric waves in a rotating basin with waterF. A. Isaev 1088 CRYSTALLOGRAPHY Deciphering of vector system by the parallel vector method using peaks of arbitrary multiplicity ($\ge3$). Fedorov's group $P1$È. A. Kuz'min, V. V. Ilyukhin, N. V. Belov 1092 Crytalline structure of $\mathrm{LaTaO}_4$T. A. Kurova, V. B. Aleksandrov 1095