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 Some types of calculation connected with averaging in the theory of non-linear vibrationsV. M. Volosov 3 On a modificaition of N. I. Lobachevskii's method for calculating the moduli of the roots of an algebraic equationN. P. Salikhov 54 On certain applications of the operational calculus to problems of analysisN. A. Meller 71 The construction of discontinuous solutions of systems of quasi-linear equations. IIB. L. Rozhdestvenskii 79 On homogeneous difference schemes of high order of accuracy on non-uniform netsA. N. Tikhonov, A. A. Samarskii 99 The removal of singularities in the solution of boundary problems for the Laplace equation in a region with a smooth boundaryE. A. Volkov 109 Approximate methods of solving ill-posed problemsS. G. Krein, O. I. Prozorovskaya 120 On resonance in an essentially non-linear systemF. L. Chernous'ko 131 The asymptotic behavior of rapid rotationsN. N. Moiseev 145 The solution of the homogeneous plane problem of the motion of a piston in an ideal heat-conducting gasP. P. Volosevich, S. P. Kurdyumov, L. N. Busurina, V. P. Krus 159 On the proof of a method of calculation for irregular waveguidesA. G. Sveshnikov 170 Scientific communications Notes on a work of Greenstadt and of LotkinA. A. Abramov 180 Tables for the computation of multiple integrals using the method of optimal coefficientsA. I. Saltykov 181 Interpolation with respect to random pointsS. M. Ermakov 186 On the expansion of a polynomial of the operator $B_\alpha$S. I. Osipov 191 On asymptotic estimates of the error in the Runge-Kutta type methodA. N. Tikhonov, A. D. Gorbunov 195 On multi-parametric families of net equations for the numerical integration of non-stationary diffusion equationsV. K. Saul'ev 198 On a difference method for the calculation of shock wavesV. F. Kuropatenko 201 Scientific information Å. Durand. Solutions numeriques des equations algebriques. Book ReviewD. K. Faddeev 205 N. I. Muskhelishvili. Singular integral equations. boundary problems in the theory of functions and their applications to mathematical physics. Fizmatgiz. Book ReviewF. D. Gakhov 206 N. Ñuãlå. The laminar boundary layer equations (OxfordMathematical Monographs). Oxford, Clarendon Press. Book ReviewYu. N. Pavlovsky 207 ErrataO. M. Belotserkovskii 208