МATHEMATICS Zimireva K.V. Linear representation of cactus groups ................................................................ 5 Ibragimov M.M., Arziev A.D. Properties of geometric Peirce decompositions of facially symmetric spaces ................................................................................................. 14 Korytov I.V. Representation of a linear functional in a Hilbert Sobolev space ....................................................................................................................... 28 MECHANICS Klyukin D.A., Sufiyanov V.G., Fyodorova E.A. Validation of a quasi-one-dimensional model of longitudinal and transverse vibrations of the barrel on firing ................................ 42 Kupriyanov V.V, Kistenyov Yu.V., Krivova N.A., Dunaevskiy G.E. Development of a mathematical criterion for determining the configuration of a bimodal spectroscopic device providing the most effective diagnosis of non-melanoma skin cancer based on the clinical parameters of samples ................................................................................... 53 Lepakova O.K., Shkoda O.A. Possibilities of using Ti–B–Fe system powders in producing hard alloys with improved mechanical properties ................................................................. 66 Moiseeva K.M., Mitrofanov A.A., Chura E.S. A study of the burning rate of an air suspension of the aluminum powder with allowance for radiant heat transfer ...................... 81 Pivkin P.M., Babaev A.S., Kozlov V.N., Semyonov A.R., Nazarenko E.S., Nadykto A.B. Methodology of the numerical modeling of cutting for calculating the contact stress distribution: a case study on steel milling ................................................. 92 Promakhov V.V., Matveev A.E., Schulz N.A., Bakhmat V.R., Turanov T.E. Mechanical properties of composite materials produced with the use of Al–TiB2 SHS powders by direct laser deposition .............................................................................. 108 Savel’kaev S.V. Dynamic analysis of a three-mass crank-slider mechanism based on its two-mass analog ........................................................................................................ 118 Svetashkov A.A., Pavlov M.S., Pustovykh O.S. Analytical correspondence principle for the elastic and viscoelastic problems ............................................................................. 131 Solomakha A.E., Shvab A.V. Simulation of aerodynamics of a swirling turbulent flow in the expanding channel of an air-centrifugal classifier ..................................................... 145