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# RESEARCH INSTITUTE OF MATHEMATICS AND MECHANICS

The Institute was established by the Academic Council of KazGU named after Al-Farabi Order № 167 of October 13, 1994, and in September 2002 by Resolution #984 of the Government of the Republic of Kazakhstan. It was reorganized into subsidiary State Enterprise with the right of economic management “Research Institute of Mathematics and Mechanics“ of Republican State Enterprise with the right of economic management “Kazakh National University named after Al-Farabi”.

Key research areas

MM Research Institute consists of 10 research laboratories, which correspond to the following activities:

- Algebra and logic;
- Differential equations and control theory;
- Computational Mathematics and mathematical modeling;
- Computational technologies and challenges in the oil and gas industry;
- Mechanics of liquid, gas, plasma, and energy;
- Laboratory of Space Technology;
- Intellectual informational system;
- Computer Science;
- Corporate systems and technologies;
- Student laboratory “Information technology and design”
- Laboratory study of the mechanics of materials and processes

### Brainpower

Currently, the Institute employs 87 full-time employees and a large number of part-time faculty numbers, students, doctoral students of the Faculty of Mathematics and Mechanics of Kazakh National University named after Al-Farabi and other universities of the country. The scientific potential is of more than 60 doctors and 100 candidates of science, 11 doctors PhD. There are about 180 doctoral students, graduate students and undergraduates of Kazakh National University named after Al-Farabi at the Institute, who recruited the knowledge and experience in scientific research work on partial payment base.

### Research work

The Institute carries out research work on more than 70 projects in fundamental and applied research in the fields of science, technology and education, including the works for international grants and commercial contracts with foreign and national companies of Kazakhstan. That includes R & D performed on 64 projects for the following grant funding priorities: “Energy “, ” Deep processing of raw materials and products “, “Information and communication technologies” and “The intellectual potential of the country”.

### International cooperation

MM Research Institute develops and supports information and advisory scientific relations and cooperation on international projects, agreements on the implementation of joint activities, it conducts the organization of international conferences and competitions with more than 40 foreign universities and research centers.

It curried out research work in the field of education on 2 grants of European Union: TEMPUS «Teaching Competency and Infrastructure for e-Learning and Retraining» (2010-2013), TEMPUS – ERAMIS «European-Russian-Central Asian Network of Master’s degrees” Informatics as Second Competence” (2010-2013).

The Institute is actively collaborating with Chinese company INSPUR on delivery to Kazakh National University named after Al-Farabi of new generation supercomputer high performance calculation. The Laboratory of Fluid Mechanics, Gas and Energy since 2010 works with Franco – Kazakh Scientific-Educational Center “Geo- Energy “, and together with the University of Tokyo, Nagoya and Aoyama (Japan) are working on the implementation of scientific and technical program “Student Nano satellite.”

It carries out on basic of joint research projects and exchanges with 20 overseas centers and organizations in the countries of the European Union, there are contracts and agreements with universities in Korea, Japan, China and India. Scientists of the Institute continue to develop cooperation in the form of scientific exchange, consultation, discussion of the results of research work with U.S. universities.

It supports long-term scientific relations with Russian universities and academic institutions: Moscow State University, Institute of Heat and Mass Transfer them named after Lykov of the Republic of Belarus, Novosibirsk State Research University, Institute of Computing Technology, Institute of Mathematics named after S.L. Sobolev, Institute of Hydrodynamics named after M.A. Lavrentyev of Siberian branch of RAS and others.

### Material and technical base

Material and technical base of the Institute includes HPC center equipped with multiprocessor clusters and URSA with capacity of 600 HEP and T-Cluster with Performance 3 TFL and certified laboratories: solid mechanics , theoretical and applied mechanics, hydraulics and filtration, mechanics of structural elements, robotics and manipulators , fluid mechanics , gas, plasma and geo energetics.

### Innovative activities

Own multiprocessor computer complex (URSA) with 600 HEP was installed and commissioned for the first time in Kazakhstan in BPH “Research Institute of Mathematics and Mechanics” named after al-Farabi in 2007 and T -Cluster of capacity of 3 TFL was installed in 2012. It is develop the platform for composite cloud computing for mobile devices with using intelligent agents.

Research work is curried out with the aim to develop new information technologies for oil facilities of Kazakhstan in order to create an information system analysis on thermal effects on the near-well formation zone and the optimization of sucker rod of deep pumping equipment. Years of research have created the basis for the development of a unified information system analysis of operation of oil and gas fields (ISAR). High performance computing is using currently for modernization ISAR. Developed software packages have been tested and implemented in a number of companies in Kazakhstan, such as JSC “Mangistaumunaigas “, JSC “Turgai Petroleum”, PF “EMG “JSC ” KazMunaiGas”, etc.

Mechanics scientists of the Institute cooperate fruitfully with NAC “Kazatomprom”, they carry out scientific researching modeling work and study the extraction of minerals ISL method and mineral extraction from the productive solution on the sorption columns, and existing software products are planned to further implementation in industry.

The scientists of the laboratory “Intelligent Information Systems” together with specialists of “Institute of Transport and Communications” works on the program “Modeling urban traffic AutoSim”. Research is being conducted under the program of work on the development and improvement of environmental monitoring in cosmodrome “Baikonur” (expert system ECOS).

MM Research Institute is actively engaged in innovation and applied research work in the field of education. The Institute has a perpetual state license to engage in activities on publishing e-books issued by the MES and, along with well-known companies in Romania, Poland, Russia, “National Center of Information” as operator of the Ministry of Education and Science of Kazakhstan in the field of education information the Institute is member of the International Consortium for the development of digital educational resources (COR). Mission of the Consortium is to introduce into Kazakhstan education system the best international experience in e-learning and create of digital content.

MM Research Institute commissioned by MES has developed over 100 e-learning editions in Kazakh and Russian languages for secondary and higher education establishments in humanities, natural and technical sciences for education portal of the MES.

More than 20 (Committee on Intellectual Property Rights, Ministry of Justice) certificates of state registration of intellectual property were received. Electronic educational editions of the SRI MM were entered to the MES of RK Order “On Approval of the List of educational publishing, MES approved for use in educational institutions in the 2011 – 2012 academic year” of February 21, 2011, # 68

MM Research Institute provides substantial support to Students Business Incubator (SBI) of Mechanics and Mathematics Faculty of the KNU named after al -Farabi, thus encouraging young people to develop entrepreneurial skills.

## Contacts

**ADMINISTRATION**** **

Director

Doctor of Technical Sciences , Professor

**Kydyrbekuly Almatbek**** **

E-mail: **almatbek@list.ru**

Contact phone number .: +7 (727) 377- 35-76;

Scientific Secretary

**Aetova Baghdad**

E-mail: **aetovab@mail.ru**

Contact phone number .: +7 (727) 377- 32-23

Chief Accountant

**Tolegenova Kulzuyga**

E-mail: **tolegenova@bk.ru**

Contact phone number .: +7 (727) 377- 34-70

**MAP**

Address:

Research Institute of Mathematics and Mechanics

050040 , Almaty , Al-Farabi , 71 , the main academic building, 13

Tel. / Fax: +7 ( 727 ) 377-31-90

## Service

The purpose of the Research Institute of MM is the planning, organization, coordination and support of scientific research, design, development and implementation of research results and development activities in the respective branches of industry, aimed at the recovery and stabilization of the economy of the Republic of Kazakhstan.

To achieve this goal the MM Research Institute performs the following activities:

1) basic and applied research in the natural sciences and engineering;

2) the creation of new techniques, technologies and materials;

3) participation in the design and development of scientific and technical programs and projects, plans, research and development activities;

4) organization of scientific, technical and techno-economic examination conducted research at the Institute of MM, completed the identification of applied research for the further practical development of scientific products and software patent cleanliness of scientific research;

5) provision of measures to protect copyright, intellectual property scholars and the right to execute them. Al-Farabi on the scientific production;

6) provision of the means and methods of measurement, produced scientific and technical production and development of design documentation applicable State standards, technical conditions and other normative documents of the state system of certification, standardization and metrology;

7) information provision and maintenance of scientific research conducted at the Institute of MM.

## Laboratory of differential equations and control theory

Head of the Laboratory of differential equations and control theory

**Kanguzhin Baltabek**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements.** An efficient mathematical tool for the study of nonlocal boundary value problems internally, allows you to explore both common and multi-dimensional differential operators. The foundations of a new theory of spectral analysis of multidimensional non-local boundary value problems for partial differential equations.

## Laboratory of algebra and logic

Head of the Laboratory of Algebra and logic

Badaev Serikzhan

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements:**

Proved (together with Steffen Lempp, USA) existence of a family of dce sets, Rogers semilattice which can be partitioned into a principal ideal and the principal filter generated Fridberg numbering. In particular, such a family has exactly two minimum numbering are Fridberg. It is proved (with S.S.Goncharov, Russia) that any computable family of infinite sets in the arithmetical hierarchy has infinitely many minimal computable numberings. (Note that any finite family has the lowest numbering). In the Ershov hierarchy found a family consisting of a pair of nested sets and having a singleton Rogers semilattice.

## Name of the laboratory

**Information about the research laboratories MM Research Institute of Kazakh National University. al Farabi**

**List of laboratories**

1. Laboratory of algebra and logic

Head of Laboratory: Badaev S.

2. Laboratory of computer science

Head of Laboratory: Ahmed-Zaki D.

3.Student Laboratory of information technologies and design

Head of Laboratory: Bektemesov A.

4. Laboratory of differential equations and control theory

Head of Laboratory: Kanguzhin B.

5. Laboratory of fluid mechanics, gas, plasma and energy

Head of Laboratory: Kaltayev A.

6. Laboratory of intelligent information systems

Head of Laboratory: Tukeyev W.

7. Laboratory of space technology

Head of Laboratory: Rakisheva Z.

8. Laboratory of computational technologies and challenges in the oil and gas industry

Head of Laboratory: Issakhov A.

9. Laboratory of computational mathematics and mathematical modeling

Head of Laboratory: Urmashev B.

10. Laboratory study of mechanics of materials and processes

Head of Laboratory: Seidakhmet A.

## Scientists of the institute

**Ershin Shahbaz**

Doctor of Physical and Mathematical Sciences, professor, academician of NAS RK

**Main scientific achievements:**

Ershin Sh It is one of the founders of the theory of aerodynamic gas torch. His project is the restoration of the Aral Sea in 1993 was awarded the Ministry of Ecology and Bioresources of Kazakhstan Prize. Ershin Sh. and his students for the first time the existence of free Taylor vortices – Gertler. Studied the wear problem of intra-field pipelines, reveal the mechanism of pipeline erosion, known as “crevice effect”. He proposed a thermomechanical process for recovering oil and cleaning the barn area of these deposits by oil pollution. He proposed a new version of the rotary wind turbine and Bidart Bidart – 2. He has published over 140 scientific papers. Under his supervision 29 candidate and 6 doctoral theses.

**Aisagaliev Serikbai**

Doctor of Technical Sciences, Professor

**Main scientific achievements:**

Developed new criteria for absolute stability of dynamical systems based on the evaluation of improper integrals along the solutions of the system. Developed new criteria for the global asymptotic stability of dynamical systems with cylindrical phase space. The theory of control of dynamic systems described by ordinary differential equations and the equations of parabolic type. Created constructive method for solving boundary value problems of optimal control of dynamic sistemami.Razrabotana nonlinear mathematical model of the educational planning process. According to the results of research released monograph “The quantitative analysis of the educational process”.

**Abdibekov Ualikhan**

Doctor of Physical and Mathematical Sciences, professor,

academician of the National Academy of Engineering Republic of Kazakhstan

**Main scientific achievements:**

We studied the problem of turbulence in the presence of external forces. Developed semi-empirical turbulence models for stratified environment, as well as MHD conducting medium built turbulence models that take into account the effect of centrifugal forces. The effective numerical methods for solving the equations of mathematical physics, which are used to study a wide range of practical problems. Proposed different models and methods of hydrodynamic processes, as well as turbulence transporting of admixture in a stratified medium, widely used in the environmental objectives. It implemented a theoretical justification for the proposed approaches and methods developed numerical algorithms and their implementation.

**Tukeyev Ualsher**

Doctor of Technical Sciences, Professor

**Main scientific achievements:**

The scientific and technological bases of the automated database design and program complex real-time systems. The scientific and methodological foundations of integration into the world educational space of the educational process of higher and postgraduate education, including the model of the European educational space, the model setting the major components of the educational process, the methodology of setting the quality of the educational process of the European educational space, complemented by the inclusion of quality management model at the level of teacher-student professional standards of specialties and a national qualification framework. Intensive research is underway to develop the scientific and technological bases of machine translation of the Kazakh language.

**Mutanov Galimkair**

doctor of technical sciences, professor, academician of NAS RK,

member of the World Academy of Arts and Sciences (The World Academy of Art and Science)

**Main scientific achievements:**

G. Mutanov is an academician of over ten international academies, the author of over 400 scientific publications, including more than 20 monographs, textbooks, teaching aids in the management of socio-economic, technical processes and systems, teaching materials published in the United States, the Czech Republic, Sweden, Germany, Switzerland; author of more than 40 patents and inventions. In 2014, the world-renowned publishing house “Springer” recognizing the merits of the author, published his book «Mathematical Methods and Models in Economic planning, Managemen.

**Badaev Serikzhan**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements:**

Proved (together with Steffen Lempp, USA) existence of a family of dce sets, Rogers semilattice which can be partitioned into a principal ideal and the principal filter generated Fridbergov numbering. In particular, such a family has exactly two minimum numbering are Fridbergov. It is proved (with S.S.Goncharov, Russia) that any computable family of infinite sets in the arithmetical hierarchy has infinitely many minimal computable numberings. (Note that any finite family has the lowest numbering). In the Ershov hierarchy found a family consisting of a pair of nested sets and having a singleton Rogers semilattice.

**Kaltayev Aidarkhan**

Doctor of Physical and Mathematical Sciences, professor,

Academician of the National Academy of Engineering

**Main scientific achievements:**

The models and numerical methods developed for different modes of oxidation of hydrocarbons in a cold flame combustion of the combustible mixture in the combustion chamber at low Mach numbers, the transition combustion gas mixture in a detonation, minerals extraction by underground leaching. The regularities of the transition combustion gas mixture in a detonation, gas dynamics and turbulent to laminar and supersonic flows of the reacting mixture in the combustion chambers; ways to improve the efficiency of oil and gas and mineral extraction by underground leaching.

**Kanguzhin Baltabek**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements:**

An efficient mathematical tool for the study of nonlocal boundary value problems internally, allows you to explore both common and multi-dimensional differential operators. The foundations of a new theory of spectral analysis of multidimensional non-local boundary value problems for partial differential equations.

**Drakunov Yuri**

Doctor of Technical Sciences, Professor

**Main scientific achievements:**

The problems of kinematic and dynamic synthesis of planar and spatial mechanisms, machines, robotics and mechanical systems. New methods of solving the problems of dynamic analysis and synthesis of mechanical systems. An automatic system for the withdrawal and the solution of differential equations of continuum mechanics. Under his leadership and with his direct participation created and implemented in the production of mechatronic systems of modern logging unit, fluoroscopic systems laboratory and field device, at the stage of completion of the drilling robot ВЕЕР-1М.

**Dauylbaev Muratkhan**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements:**

A method of qualitative research singularly perturbed linear integrodifferential equations with initial conditions on the right or at an interior point of the segment under consideration. The features of the qualitative effect of the integral members on the asymptotic behavior of solutions to singularly perturbed integro-differential equations. Revealed the phenomenon of initial jumps of arbitrary order. New classes of nonlinear singularly perturbed integro-differential equations, which have initial jumps of arbitrary order phenomena. A method of constructing asymptotic expansions of solutions of singularly perturbed integro-differential equations with initial jumps of arbitrary order.

**Kydyrbekuly Almatbek**

Doctor of Technical Sciences, Professor

**Main scientific achievements:**

Is engaged in the development and analysis of the generalized models of dynamic systems with cavities partially filled with fluid, and elastic systems with nonlinear complicating factors (nonlinear elastic characteristics of the geometric and physical nature of nonlinear-viscous resistance, non-linear inertial the link between their face and the elastic movement) in relation to the tasks machine dynamics. Theoretical modeling of oscillatory processes in rotary systems with cavities partially filled with liquid and physically nonlinear elastic coupled systems with finite deformations, predicting their stability, the totality of which is a major achievement in the development of machine dynamics.

**Bektemesov Maktagali**

Doctor of Physical and Mathematical Sciences, professor,

corresponding member of National Engineering Academy of Kazakhstan

**Main scientific achievements:**

Built gradient methods for solving ill-posed problems for elliptic, parabolic and hyperbolic equations. The estimates of the strong convergence of the steepest descent method for the rate of incorrect initial value problems. Constructed Carleman estimates for ill-posed Cauchy problems. The estimates of conditional stability of the solution of inverse problem of boundary conditions of ill-posed Cauchy problems. For the first time in a complex fractal image obtained plane area stability of the solution of the Cauchy problem for the equations of the first and second order.

**Serovaiskii Semen**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements:**

The concept of extended derivative operator and is designed corresponding to its calculus, used to deal with new nonlinear infinite-dimensional problems of optimal control. We investigated optimization problems using a new concept of a weakened approximate solution in the absence of more severe forms of the approximate solution. For solving mathematical physics problems on the basis of a new concept of sequential decision given the constructive definition of a generalized and classical solutions of these problems.

**Shakenov Kanat**

Doctor of Physical and Mathematical Sciences, Professor

**Main scientific achievements: **

First solved by Monte Carlo full Navier-Stokes equation, the linearized Navier-Stokes equations perturbed Navier-Stokes equations, stationary Navier-Stokes equations. Solved filtration and relaxation filtration problem Monte Carlo methods. Solved by Monte Carlo parametric inverse problem of atmospheric optics.Resolved multidimensional parametric inverse problem of stochastic optimal control. Fixed some financial risk modeling tasks.

**Sikhov Mirbulat Bahytzhanovich**

Doctor of Physical and Mathematical Sciences, Associate Professor

**Main scientific achievements:**

Get reverse approximation theorem in the case of different metrics. The concept of “predpoperechnik Kolmogorov” and obtain estimates for Kolmogorov predpoperechnikov Nikolsky and Besov S-classes in the multidimensional case with approximations by trigonometric polynomials, when the spectrum approximating polynomials is determined by a majorant function. Established inequality of Bernstein and Jackson-Nikol’skii for trigonometric polynomials with the spectrum of an arbitrary finite set, will receive a final assessment of the Norms of Derivatives of Dirichlet kernels with the spectrum of an arbitrary finite set.

**Mukhambetzhanov Saltanbek**

Doctor of Physical and Mathematical Sciences, Professor,

corresponding member of National Engineering Academy of Kazakhstan

**Main scientific achievements:**

The correctness of mathematical models of phase transitions with relaxation. The methods for solving direct and inverse problems of the filtration theory. The mathematical modeling of liquid filtration processes in the porous medium, taking into account mass transfer processes, as well as computer simulations of liquid filtration processes in the near-well zone of the formation and change of technological parameters of the real fields with specific data.

**Ahmed Zaki Darkhan**

Doctor of Technical Sciences

** Main scientific achievements:**

A computational algorithm for solving 2D and 3D mathematical model of heat and mass transfer in porous media in the injection of heat-carriers and surfactants. The information system of distributed and parallel computing problems of filtration through a Web portal. Development in organizing a formal cloud computing model for the formation of multi-user systems “micro-cloud” of mobile devices.

## Strategic development plan

**Mission**

The mission of the Institute is to create conditions for a team of scientists to be an integration center for scientific research in the fields of mathematics, mechanics and information technology are at the forefront of world science and technology, is the largest source of new ideas and new innovative technologies in the world are of great practical importance, and an employee basis for the development of new high-performance industrial facilities, is a magnet for young creative people to become great scientists in their respective fields of scientific activity.

**Image**

Institute’s image – a highly intelligent scientific institution worldwide scientific community conducting research in the field of mathematics, mechanics and computer science at a high scientific level that deserves global recognition for its innovative approach to solving recognized the urgent tasks that lead to the creation of new high-performance industrial production, providing its employees a celebration individual liberty and the comfortable existence of his family and the people around him.

**Goals and objectives**

The strategic goal is to create efficient highly profitable research institution with the full financial and economic autonomy, capable of generating scientific highly intelligent products having a high commercial interest.

The strategic objectives are

- Creation and development of high rating of the scientific journal on various branches of mathematics, mechanics and information technology, which enjoys a high reputation in the scientific world;
- Creation and development of high rating of the scientific journal on various branches of mathematics, mechanics and information technology, which enjoys a high reputation in the scientific world;
- Formation of scientific schools in various branches of mathematics, mechanics and information technology, internationally recognized and high reputation in the scientific world;
- Formation of the authority of the Institute as a center of training at a high international level of scientific experts the highest category of the various branches of mathematics, mechanics and information technology;
- Development and implementation of technology research projects into production, bringing high economic impact, contributing to innovation and the industrial development of the country; a high reputation in the scientific world;
- Development of the technology decision-making in the formation of a list of research topics of high scientific and commercial importance;
- Develop an action plan to attract young professionals to the solution of scientific problems of perspective, with long-term nature.

**Institute**** of development**** strategy**

Creating recognized in the scientific community of scientists able to solve major economic problems that contribute to the output of the country in a number of developed countries of the world through the development and formation of the scientific basis of training young professionals due to their involvement in research projects that are of great practical importance and represents the output of industrial technology to create highly profitable production and standing at the forefront of global scientific research activities.