Overview about the Department of Mathematics and Computer Science

Meeting Seminar of the Department of Mathematics and Informatics

A Brief History of the Department

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 work OMI DSC RAS carried out in the following three areas:

  • Approximation theory: functional classes and their approach, series and Fourier transform Radon transform and its treatment, 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: optimization of schedules, questions about 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.
Discussion of the work plans of the Department of Mathematics and Informatics

Discussion of the work plans of the Department of Mathematics and Informatics

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;
  • proved the fundamental theorem of G-convergence and homogenization of generalized Beltrami operators;
  • set simple criteria of geometrical character for k-fold completeness in the spaces of functions summable with square root functions of beam system of ordinary differential operators;
  • necessary and sufficient conditions for the solvability of the defragmentation task matrix retaining element sets in the lines;
  • derived formulas for the three-dimensional Radon transform;
  • we developed a method of auxiliary equations to study the stability of stochastic functional differential equations.

Presentation of a computer program

Presentation of a computer program

Scientific projects OMI

Scientists of the Department took active part in competitions of the Russian Foundation for Basic Research Projects (RFBR). In particular, the Russian Federal Property Fund OMI performed following projects:

  • Some questions in the theory of approximation of smooth and analytic functions by mixed poison in orthogonal polynomials (RFBR project 03-01-00611-a, 2003-2005, project leader Sharapudinov I.I.);
  • Orthogonal bases and some problems of approximation theory in Lebesgue and Sobolev spaces with variable exponent (RFBR project 07-01-00143-a, 2007-2009, project leader Sharapudinov I.I.);
  • The asymptotic properties of polynomials orthogonal on the unit circle nonuniform grids, and the number axis (RFBR 10-01-00191-a project, 2010-2012, project leader Sharapudinov I.I.);
  • The development of an integrated network of DSC RAS and database development research center studies using GIS (RFBR project 02-07-90478-in, 2002-2003, project leader Abdulaev SH.-S.O.);
  • Publication of the book "computer-aided design in microelectronics devices (CAD microelectronics)" (RFBR project 11-07-07010-d, 2011-2012., project manager Abdulaev SH.-S.O.).

The head of OMI, Prof. Professor Sharapudinov I.I.

The head of OMI, Prof. Professor Sharapudinov I.I.

In addition, OMI employees took part in the 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".

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.

Scientific and educational activities

OMI Most employees are teachers in higher education institutions of the Republic of Dagestan and as such engaged in intensive research in the field of teaching methodology relevant disciplines. They are prepared and published in this direction numerous scientific articles and tutorials for students.

Scientists OMI developed algorithms and software systems, which are now successfully used in the field of processing and analysis of time-series digital signals and images.

On a regular basis organized a scientific seminar in OMI made numerous presentations by representatives of the Institute of Geology, Geothermy, socio-economic development and IYALI.

Discussion of the problem: Ramazanov A.K. and Sharapudinov I.I.

Discussion of the problem: Ramazanov A.K. and Sharapudinov I.I.

In the laboratories of the Institute of Geology of the large quantity of numerical arrays resulting set of experiments to study these processes in the world. These data sets need to be careful and deep-cal mathematics and statistical analysis to identify the most susche-governmental factors that depend on those or other processes taking place in the earth and atmosphere. Now scientists OMI most actively involved in research directly related to these tasks. We (mathematics) is currently studying the relevant literature sources where such problems were investigated for other regions of the world. We are engaged in the search for the most appropriate mathematical models describing the relevant geological and atmospheric processes involved in computer modeling of these processes. The results of our research, performed in collaboration with scientists from the Institute of Geology, will soon be published. This work is not easy and requires us not only a huge routine work, but also a creative approach to solving these applications involving new co-temporal mathematical ideas developed by scientists OMI. In particular, these include methods for approximating discrete functions convent-rows in orthogonal systems, intensively studied in OMI's in recent years and the relevant software packages.

Together with the Institute of Social and Economic Research SMI is looking for mathematical models that adequately describe the processes in various sectors of economy of Dagestan, as well as models for predicting the ways of sustainable development of the economy of individual regions of Dagestan and the whole of Dagestan as a whole.

Speech doctor of - mathematical science Alishayev M.G.

Speech doctor of - mathematical science Alishayev M.G.

Scientists OMI DSC RAS ​​actively engaged in mathematical linguistics. Here, the greatest interest is in our creation of electronic dictionaries. On a weekly (on Thursdays) Research Seminar OMI DSC RAS ​​regularly discussed issues relating to the creation of electronic dictionaries Dagestan languages. We are deeply convinced impressive scientific results can be achieved in this way. The fact is that, to our knowledge, has not yet created any Russian-Dagestani electronic dictionary. We are not talking about English-Dagestani electronic dictionaries. In connection with this growing urgent need for close cooperation between the Institute of Language and Literature (IYALI) DSC RAS ​​and OMI DSC RAS. We need to create a joint research workshop where scientists and IYALI OMI will discuss modern methods of creating electronic dictionaries and their application to create a Russian-Dagestani and foreign-Dagestani electronic dictionaries. In addition, scientists and OMI IYALI could cooperate in a number of other areas related to the development of mathematical and computer models of the processes that are associated with the development of language, their syntax and semantics.

Scientists OMI DSC RAS ​​conduct intensive research in the field of signal processing. We have no doubt that we have developed in this field, new methods will find practical application in matters of weather forecasting, medical signal processing (ECG) data obtained in experimental studies of geologists, biologists, economists and others. In particular, we have developed new methods of identification of parameters of stationary economic systems based on the use of orthogonal polynomials on uniform grids. OMI Graduate students are currently involved in the development of software packages for numerical implementation of these methods in practice.

Young scientists SMI actively cooperate with the Regional Centre for Ethno-Political Studies DSC RAS - developing a program for statistical analysis of opinion polls. In the long term - development of specialized software package for designing arbitrary polls, their automated filling and complete statistical data.

Young scientists OMI at the international conference in Tseyskoe Gorge

Young scientists OMI at the international conference in Tseyskoe Gorge

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