Mathematics |
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2003, The Second Special Issue
Y.S. Baburin
This paper continues [1]. Therefore the terminology is kept according to the previous discussion. Formulas and theorems numeration succeeds [1]. The structure of left singularisator Kl and right singularisator Kr for starting complete SI-operator K1 of type (1) is found in the simplest case, when the regular part of kernel k1(t, τ) has onesymbolic analytic continuations k+,1(z, τ) and k+,1(t,w) are holomorphic in the domain D+L.
L.M. Berkovich
The present paper is dedicated to a discovery in physics due to computing experiments and computer simulation and since then (substantially late) confirmed by full-scale experiments. Major role in this discovery has been played by the large group of the scientists from the Institute of Applied Mathematics of USSR Academy of Sciences (now the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences) and the Institute of Theoretical and Applied Mechanics of the Siberian branch of the USSR Academy of Sciences. This discovery originally related to processes of burning and explosion, namely the discovery of so-called T-stratum (temperature stratum), now is applied to nonlinear dynamics and synergetics. From a mathematical point of view this means unlimited solutions of the nonlinear equations of the parabolic type circumscribing the processes with a peaking in three various combustion regimes. The head of the group of scientists who realized and applied this discovery to various problems of natural science was Professor S.P. Kurdyumov (see the collection of papers "Modes with a peaking. Evolution of idea" published by Nauka Publisher in 1999).
Ch.A. Chikhanov
THE LANDEN TRANSFORMATION OF THE GENERALIZED ELLIPTIC JACOBI FUNCTIONS AND THE APPEL ROWS
In the paper a new class of elliptic functions, generalized the classical Jacobi elliptic functions, and the Landen transformation related to the Appel rows are studied.