Department of Mathematics and Computer Science DSC RAS

In March 2013 marked 12 years since the establishment of DSC RAS ​​Division of Mathematics and Informatics (OMI). The story begins with the adoption of OMI Bureau of the Department of Mathematics of the Russian Academy of Sciences, the decision of 25 April 2000 "On creation of the Department of Mathematics at the Presidium of the Dagestan Scientific Center RAS." In pursuance of this decision in the DSC RAS ​​went Order (№4, from 13.03.2001, the) for the establishment of the Presidium of DSC RAS ​​Division of Mathematics and Informatics (OMI). In it, in particular, the written approval of personnel of the SMI in the amount of 4 units. It should be noted the crucial role played in creating OMI support the Chairman of the Presidium of DSC RAS ​​Corresponding Member. RAS MK Kamilov and Chief Scientific Secretary of DSC RAS ​​Abdulaeva SH.-S.O. Currently, the staff of the Division schedule has 9 units. Scientific and research activities carried out 8 doctors of sciences, 3 candidates of sciences, and 6 young researchers
his scientific activity OMI DSC RAS ​​carries out the following three areas:.

  Approximation theory

Functional classes and their approach, and the ranks of the Radon transform and Fourier transform their appeal, the theory and applications of orthogonal polynomials of one and several variables, extreme properties of polynomials.

  Differential equations and modeling techniques

Spectral theory of linear differential operators beams, boundary value problems for equations of mathematical physics, optimization methods for solving the transport equations, statistical modeling in physics of fractals, modeling of the erosion of the Caspian Sea.

  Modern Problems of computer science and discrete mathematics

Optimize schedules, questions the complexity of algorithms, optimization program based on the Component Object technology, the creation of a package of handling and compression of digital information programs.

In each of these fundamental areas of OMI staff conducted intensive studies. Main Their results are published in the national press, as well as in leading international journals, and received wide international acclaim.      In particular, scientists OMI:

  • developed a theory of mixed series of orthogonal polynomials of a discrete variable and continuous;
  • created asymptotic theory of polynomials orthogonal on non-uniform grids;
  • developed the theory of approximations in spaces of integrable functions with a variable index. The necessary and sufficient conditions on a variable rate, which provides limited in spaces with variable Hilbert different types of transformations, the adjoint operator functions. On the basis of these results, it is proved that the trigonometric system and the system of Legendre polynomials under certain conditions, to a variable rate form bases in Lebesgue spaces with variable exponent.
  • studied boundary value problems of elliptic systems, Stokes systems and the theory of elasticity. The scientists of the Department obtained fundamental results on Noetherian criterion and an index formula for general elliptic operators;

Meeting of the scientific-practical seminar OMI

In addition, OMI employees take an active part in competitions of the Russian Foundation for Basic Research Projects (RFBR) and the Russian Science Foundation, as well as in the implementation of projects of the program of the Presidium of Russian Academy of Sciences. Presiding over these projects Abdulaev SH.-S.O., Nazaraliev Sh, Sharapudinov II Currently, SMI carried out fundamental research program of the project Presidium of the Russian Academy of Sciences on the theme "Approximation of functions in the Lebesgue and Sobolev spaces with variable exponent and quadrature formulas".
The OMI from the very beginning of its establishment carries out its research activities Scientific School "Approximation theory in function spaces and orthogonal systems". Head of School Prof. Sharapudinov II Scientists
OMI maintain close scientific relations with scientists from various countries. In particular, the scientific school headed by Prof. Sharapudinovym II, maintains close cooperation with scientists from the US (Columbia, SC), Portugal, Finland, China and Germany.



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