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 A realization of Cartan extensionsYu. B. Ermolaev 3 Construction of noniterated Boolean functions in the basis $\{&,\vee,-\}$ and estimation of their numberO. V. Zubkov 17 Hypercomplex numbers in the theory of physical structuresG. G. Mikhailichenko, R. M. Muradov 25 Approximation of Dual Spaces and Dual OperatorsN. B. Pleschinskii, Ê. Sh. Muëhutdinov 31 Convergence in the integral metrics of the general projective solution method for singular integral equations of the first kind with the Cauchy kernelA. V. Ozhegova 39 The Hicks property for a variational problem on a graphYu. V. Pokornyi, E. V. Gulynina, T. V. Perlovskaya 48 Quasistrategies in an abstract guidance control problemA. G. Chentsov 55 Brief communications A nonlinear boundary eigenvalues problem for TM-polarized electromagnetic waves in a nonlinear layerD. V. Valovik, Yu. G. Smirnov 70 Characterization of the analytic weighted Besov space in terms of the radial differentiation operatorsF. D. Kodzoeva 75 Projection solution methods for one nonlinear singular integral equationL. E. Shuvalova 79 Abstracts of papers deposited at VINITI 84 News of mathematical life in Russia and the CIS 85