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 Integrable cases of the dynamics of a rigid body, and integrable systems on the spheres $S^n$O. I. Bogoyavlenskii 899 Kolmogorov widths in the space $\widetilde L_q$ of the classes $\widetilde W_p^{\overline\alpha}$ and $\widetilde H_p^{\overline\alpha}$ of periodic functions of several variablesÈ. M. Galeev 916 On the function $G(n)$ in Waring's problemA. A. Karatsuba 935 Families of algebraic varieties and invariant cyclesG. A. Mustafin 948 Regular elements in spaces of linear representations. IID. I. Panyushev 979 Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functionsV. N. Temlyakov 986 Estimates of multiple trigonometric sums with prime numbersV. N. Chubarikov 1031 Reduction to general position of a mapping of a one-dimensional polyhedron, depending continuously on a parameterS. I. Yablokova 1068 Generalized Casimir elementsA. S. Dzhumadil'daev 1107