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 MATHEMATICS On the asymptotics of the number of summands in a multidimensional additive problem with prime numbersG. I. Arkhipov, V. N. Chubarikov 5 Nontrivial solutions of some classes of operator equationsS. A. Vavilov 7 Cyclic bilinear forms of enumerated graphsV. A. Gurvich 11 The inverse image of any nonextremal value of almost every continuous function has the cardinality of the continuumA. V. Kuz'minykh 14 Exponential stability with respect to some of the variablesA. A. Martynyuk 17 Monte Carlo methods for solving metaharmonic equations of the form $\Delta^{p+1}u+cu=(-1)^{p+1}g$G. A. Mikhailov 20 A method for the functionalization of the parameter in iterative procedures for investigating the Hopf bifurcation for equations with aftereffectM. G. Yumagulov 24 PHYSICS Description of the convective heat transfer in the vortex tubeA. A. Borisov, P. A. Kuibin, V. L. Okulov 28 The conjugation of harmonic effects in the simplest mechanical systems (the addition of D-SELF model)A. G. Ivanov-Rostovtsev, L. G. Kolotilo 32 Singlet states in Hubbard model with $U=\infty$E. V. Kuz'min 36 Does the anomalous heat production in $\mathrm{Pd}$–$\mathrm{D}(\mathrm{H})$ system need “cold fusion” hypothesis to understand it?A. G. Lipson, B. F. Lyakhov, B. V. Deryagin, D. M. Sakov 39 On the wave instability of periodic structure of vortices in the turbulence boundary layerM. G. Mayorov, S. A. Rybak 43 MECHANICS Determination of the elasticity tensor from the velocities of quasitransverse wavesL. V. Nikitin, O. V. Mikhailov 46 Equations of the steady motion of an aircraft under spin and spiral descentA. A. Shilov 49 GEOPHYSICS Ground-based radiation measurements of the stratospheric ozone in region $9{.}6$ mkmL. S. Ivlev, D. N. Shchepkin, V. V. Bertsev, Yu. V. Lebedeva 99 Synergetic approach to multidimensional matrixes inadvertent classificationE. Ya. Ostrovski 101