Mathematics |
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2002, No. 2
L.M. Berkovich, O.L. Starinova
THE PROBLEM OF GYLDEN-MESHCHERSKII: TRAJECTORIES OF MOVEMENT
The Gylden-Meshcherskii problem is used for a description of double stars evolution for want of to secular loss of mass at the expense of photon and corpuscular activity. It is also mathematical model for various cases of dynamics of two skew fields of variable mass.
In the present work the laws of mass variation supposing reduction are considered the equations of movement to a stationary form. The trajectories relative are constructed movements as for want of before known the laws of Eddington-Jeans, and for want of other laws of mass variation.
N.A. Zaychikova
THE EXACT UPPER DIFFERENTIAL INCLUSION CONSTRUCTION FOR THE PROBLEMS WITH CONTINUOUS RIGHT-HAND SIDE
In this paper the exact upper differential inclusion construction problem for a slow variables case is considered, when the right-hand side is continuous on a phase variable uniformly with respect to time. The proof of the theorem about exact upper differential inclusion is based on the upper approximation theorem. For an approximating differential inclusion right-hand side construction is used the averaged supporting function definition through uniform on the initial conditions upper limit.
The exact upper differential inclusion construction example for the problem with a continuous right-hand side is given. One more example given shows that the upper limit uniformity condition from the averaged supporting function definition is essential.
A.N. Panov
We present classification of Manin pairs for semisimple real and complex Lie algebras. We prove the decomposition statement for reductive Lie algebras and study a decomposition of Manin pairs in general setting.
E.V. Sokolovskaya
ON AN UPPER APPROXIMATION OF THE DIFFERENTIAL INCLUSIONS WITH NON-LIPSCHITZ RIGHT-HAND SIDE
A theorem about upper approximation of differential inclusions with non-Lipschitz right-hand side and slow variables is proved. The inclusions with one-sided Lipschitz right-hand are used for the approximation.
O.P. Filatov
THE NECESSARY AND SUFFICIENT CONDITIONS IN THE AVERAGING THEOREMS OF DIFFERENTIAL INCLUSIONS
It is proved that the principal conditions of the averaging theorem of control differential inclusions with slow variables are the necessary conditions.
E.V. Filimonova
AN ANALOG OF BITSADZE--SAMARSKI PROBLEM FOR GELLERSTEDT EQUATION IN UNBOUNDED RANGE
An analog of Bitsadze-Samarski problem had been investigated for Gellerstedt equation in unbounded range, when boundary condition contains linear combination of generalized fractional integro-differential operators with the Gauss hypergeometric function F(a,b;c;x) in the kernel.
S.Y. Shatskih
The paper is devoted to the study of properties of transformation of independence of random vectors which possess the reproducibility property of conditional quantiles under restriction on conditional quantiles of smaller dimension. It is determined that for such random vectors triangular transformation of independence can be presented by using superposition of two-dimensional conditional distribution functions only. Inversions of such transformations are used for construction of sequence of random variables wich possess the reproducibility of conditional quantiles.