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2003, Special Issue |
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L.M. Berkovich In the paper the methods of the factorization, autonomization and exact linearization developed by the author in a number of previous discussions are represented. They together with the methods of the group analysis and differential algebra permit to create a complete picture for study and integration of ordinary differential equations. It enables us to investigate constructively nonlinear and nonstationary problems known from a wide range of natural sciences and, first of all, problems of mechanics and physics. The paper is broken on two parts. The first part is devoted to the linear equations. The second part is devoted to the nonlinear equations. The paper in part is based on recently published monograph by the author. (Berkovich L.M. Factorization and transformations of differential equations: methods and applications. M.: R&C Dynamics, 2002. I.S. Logunov INVARIANT TENSORS OF ONE REPRESENTATION OF LIE ALGEBRA sl(3,C) Projective invariants of flat curves of the third order are calculated by means of the theory of representations of the semisimple Lie groups and Lie algebras by the aid of inclusion principle. Å.V. Sokolovskaya A theorem about upper approximation at slow variables of the systems of differential inclusions with non-Lipschitz right-hand side and slow and rapid variables is proved. The inclusions with one-sided Lipschitz right-hand side are used for the approximation. Y.V. Solodiannikov, D.P. Kojan CALCULATION OF DISTRIBUTION FUNCTIONS OF SOME FUNCTIONALS OF WIENER PROCESSES Convolutions of standard Wiener processes are considered. The analytical expressions of characteristic functions and probability densities for studied stochastic functionals of standard Wiener processes and Brownian bridges are received. The results are given contain numerical account of distribution functions and moments of convolution funcionals. O.P. Filatov THE STABILITY OF PROBLEMS OF CALCULATING LIMITES OF MAXIMUM MEANS The conditions of approximately calculating limits of maximum means by the aid of maximum means on segment for differential inclusions with the perturbed right-hand side are obtained. |
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