MAIN DATES OF THE LIFE AND ACTIVITIES OF MUKHTARBAI OTELBAEV,
ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES
OF THE REPUBLIC OF KAZAKHSTAN
Mukhtarbay Otelbaev was born on October 3, 1942 in the village Karakemer of the Kordai district of the Zhambyl region.
1951 — 1959 Studies at the secondary school in the village Karakonyz (now Masanchi) of the Kordai district of the Zhambyl region.
1959 — 1960 Studies at the agricultural high school in the town Tokmak (Kyrgystan).
1960 — 1962 Studies at the evening school of the village Karakonyz. Worked as a machine operator in the village Karakemer.
1962 Entered the mathematical faculty of the Kyrgys State University in Frunze (now Bishkek).
1962 — 1965 Service in the Soviet Army (Tadzhic SSR, Chkalovsk-1).
1965 — 1966 Teacher of mathematics at the Chapaev evening school in the village Karakemer of the Kordai district of the Zhambyl region.
1969 Graduated from the Faculty of mechanics and mathematics of the M.V. Lomonosov Moscow State University (MSU).
1972 Completed post-graduate studies at the Faculty of mechanics and mathematics of the MSU.
Defended the PhD thesis titled “About the spectrum of some differential operators”.
1973 — 1978 Research fellow of the Institute of mathematics and mechanics of Academy of Sciences of the Kazakh SSR.
1978 Defended the Doctor of Sciences thesis in physics and mathematics titled “Estimates of the spectrum of elliptic operators and related embedding theorems”.
1978 – 1979 Head of the Laboratory of approximate methods of analysis at the Institute of mathematics and mechanics of the Academy of Sciences of the Kazakh SSR.
1979 — 1983 Head of the Laboratory of applied methods of analysis at the Institute of mathematics and mechanics of the Academy of Sciences of the Kazakh SSR.
1983 Awarded the academic title of professor.
1983 — 1984 Head of the Department of applied analysis of the S.M. Kirov Kazakh State University . 1984 — 1986 Rector of the Zhambul pedagogical institute.
1985 — 1986 Deputy of the Zhambul City Council of People’s Deputies
1987 — 1989 Head of the Laboratory of mathematical analysis at the Institute of mathematics and mechanics of Academy of Sciences of the Kazakh SSR.
1989 Elected a corresponding member of the Academy of Sciences of the Kazakh SSR.
1989 — 1991 Head of the Department of applied mathematics at the Institute of mathematics and mechanics of the Central-Kazakhstan branch of the Academy of Sciences of the Kazakh SSR (Karaganda).
1991 — 1993 Director of the Institute of applied mathematics of the Academy of Sciences and the Ministry of Education of the Republic of Kazakhstan (Karaganda).
1993 — 1995 Head of the Department of aerodynamics of the National Aerospace Agency of the Council of Ministers of the Republic of Kazakhstan.
1995 — 1998 Head of the Department of applied analysis of the Abai Almaty State University.
1998 — 2000 Head of the Department of functional analysis and probability theory of the Al-Farabi Kazakh State University.
2000 — 2001 Head of the Scientific centre of research in mathematics and technology, professor of the Department of computer sciences of the L.N. Gumilyov Eurasian State University.
2001-2009 Professor of the Departments of applied and computational mathematics and of methods of mathematical modeling of the L.N. Gumilyov Eurasian State University.
Since 2001 Deputy Director of the Kazakhstan branch of the M.V. Lomonosov Moscow State University.
2004 Elected a real member of the Academy of Sciences of the Republic of Kaakhstan.
2004 Awarded the title of laureate of the Economic Cooperation Organization (headquarters in Tehran) in the category «Science and Technology».
2006, 2011 Holder of the state grant «The best university teacher».
2007 Awarded the State Prize of the Republic of Kazakhstan in the field of science and technology.
Since 2009 Professor of the Department of fundamental and applied mathematics of the L.N. Gumilyov Eurasian State University.
A short overview of scientific, pedagogical, and public work of Professor Mukhtarbay Otelbaev, academician of the National Academy of Sciences of the Republic of Kazakhstan
Mukhtarbay Otelbaev, professor of the Department of fundamental and applied mathematics of the L.N. Gumilyov Eurasian National University, deputy director of the Kazakhstan branch of the M.V. Lomonosov Moscow State University, doctor of physical-mathematical sciences, academician of the National Academy of Sciences of the Republic of Kazakhstan was born on October 3, 1942 in the village Karakemer of the Kordai district of the Zhambyl region. He started his labour life as a machine operator in his native village. After graduating from the evening school in 1962 in the village Karakonyz (now Masanchi), he entered the Kyrgyz State University in Frunze (now Bishkek). In 1962-1965 he served in the Soviet Army. Further he continued studies at the Faculty of mechanics and mathematics of the M.V. Lomonosov Moscow State University and graduated in 1969. In the same year he entered postgraduate studies at the same faculty under supervision of famous scientists, Professors B.M. Levitan and A.G. Kostyuchenko. In 1972 he defended the PhD thesis titled “About a spectrum of some differential operators”.
Since 1973, M. Otelbaev was in Alma-Ata, worked as a junior researcher, a senior researcher, the head of a laboratory at the Institute of mathematics and mechanics of the Academy of Sciences of the Kazakh SSR. In 1978 he brilliantly defended the doctor thesis titled “Estimates of the spectrum of elliptic operators and related embedding theorems” at the Dissertation council number 1 of the Faculty of mechanics and mathematics of the M.V. Lomonosov Moscow State University headed by Professor A.N. Kolmogorov, a prominent mathematician, academician of the Academy of Sciences of the USSR. In 1989 M .Otelbaev was elected a corresponding member of the Academy of Sciences of the Kazakh SSR, M. Otelbaev is an expert in the field of functional analysis and its applications, the author of 3 monographs and over 210 scientific papers and inventions widely recognized both in Kazakhstan and abroad. More than 70 of his works were published in rating international scientific journals (with the impact-factor ISI or included in the SCOPUS database).
His main works are grouped around the following fields:
I. Spectral theory of differential operators.
M. Otelbaev developed new methods for studying the spectral properties of differential operators, which are the result of a consistent and skilled implementation of the general idea of the localization of the problems under consideration. In particular, he invented a construction of averaging coefficients well describing those features of their behaviour which influence the spectral properties of a differential operator. This construction known under the name made it possible to answer many of the hitherto open questions of the spectral theory of the Schrödinger operator and its generalizations.
The function and its different variants have a number of remarkable properties, which allowed to apply this function to a wide range of problems. Here we note some problems for the first time solved by M. Otelbaev by using the function on the basis of sophisticated analysis of the properties of differential operators.
1) A criterion for belonging of the resolvent of the Schrödinger type operator with a non-negative potential to the class was found (previously only a criterion for belonging to was known) and two-sided estimates for the eigenvalues of this operator were obtained with the minimal assumptions of the smoothness of the coefficients.
2) The general localization principle was proved for the problems of selfadjointness and of the maximal dissipativity (simultaneously with the American mathematician P. Chernov) which provided significant progress in this area.
3) Examples were given showing the classical Carleman-Titchmarsh formula for the distribution function of the eigenvalues of the Sturm-Liouville operator is not always correct even in the class of monotonic potentials and a new formula was found valid for all monotonic potentials .
4) The following result of M. Otelbaev is principally important: for there is no universal asymptotic formula.
5) From the time of Carleman, who found the asymptotics for and, by using it, the asymptotics of the eigenvalues themselves, all mathematicians started with finding the asymptotics for and as a result they could not get rid of the so-called Tauberian conditions. M. Otelbaev was the first who, when looking for the asymptotics of the eigenvalues, omitted the interim step of finding the asymptotics for , which allowed getting rid of all non-essential conditions for the problem including Tauberian conditions.
6) The two-sided asymptotics for for the Dirac operator was for the first time found when and are not equivalent.
The results of M. Otelbaev on the spectral theory were included as separate chapters in the monographs of B.M .Levitan and I.S. Sargsyan “ Sturm-Liouville and Dirac operators» (Moscow: Nauka, 1985), and of A.G. Kostyuchenko and I.S. Sargsyan «Distribution of eigenvalues» (Moscow: Nauka, 1979), which became classical
II. Embedding theory and approximation theory.
This field of mathematics has developed as a separate branch in the works of S.L.Sobolev in 1930. Beginning with the works of L.D.Kudryavtsev (around 1960) appears a new era of weighted function spaces used in the theory of differential operators with variable coefficients. M.Otelbaev began the researches in this field being a mature mathematician and managed to create a new method of enclosure theorem obtaining which is a local approach to another type of problems according to the form and to the essence. In the theory of weighted Sobolev spaces, most used weighted function spaced, M.Otelbaev obtained the following fundamental results.
1) A criterion for an embedding and for the compactness of an embedding.
2) Two-sided estimates for the norm of an embedding operator.
3) Two-sided estimates for Kolmogorov’s width of an embedding enclosure and for the approximation numbers of an embedding operator and a criterion for belonging of an embedding operator to the classes . It turned out that one of the variants of the function is an adequate tool for description of the exact conditions ensuring an embedding. For applications it is particularly important that all the estimates are given in terms of weight functions and allow taking into account the characteristics of their local behavior
III. Divisibility and coercive estimates for differential operators.
The term “divisibility” was suggested by famous English mathematicians Everitt and Geertz around 1970s, who investigated the smoothness of solutions to the Sturm-Liouville equation. Soon after that, M. Otelbaev was involved in research on this topic. He developed a method for studying the divisibility of more general, multi-dimensional operators and variable type operators, as well for the smoothness of solutions to nonlinear equations. In particular, by using this method one can study the divisibility of general differential operators in weighted, not necessarily Hilbert spaces. With his interest in solving problems in the most general setting, M. Otelbaev obtained 1) weighted estimates not only the derivatives of solutions of the higher order, but also of intermediate derivative for a wide class of linear and nonlinear equations, 2) estimates of the approximation numbers of divisible operators exact in a certain class of coefficients.
IV. General theory of boundary problems.
The classical formulation of the boundary value problem is as follows: given an equation and boundary conditions, to investigate solvability of this problem and the properties of the solution, if it exists (in the sense of belonging to a certain space).
Beginning with M.I. Vishik (1951), there is another, more general approach: there is given an equation and a space to which the right-hand side and the solution should belong, describe all the boundary conditions for which the problem is correctly solvable in this space. Also in this problem, despite the numerous previuos studies, M. Otelbaev has obtained new results remarkable in depth and transparency. The rich mathematical intuition, the depth of thinking and extensive knowledge, coupled with rejection of traditional constraints on the considered operators and spaces, allowed him to develop an abstract theory of extension and restriction of not necessarily linear operators in linear topological spaces. Using this theory, M. Otelbaev and his students were the first to describe all correct boundary value problems for such «pathological» operators as the Bitsadze-Samarskyiy operator, an ultrahyperbolic operator, a pseudoparabolic operator, the Cauchy-Riemann operator and others. (For some of them previously no correct boundary value problems were known !) Moreover, considerations were carried out in non-Hilbert spaces of and . This theory also allowed describing the structural properties of the spectrums of correct restrictions of a given differential operator.
V. Theory of generalized analytic functions.
In the theory of generalized analytic functions, built by the well-known scientist I.N. Vekua, a real member of the Academy of Sciences of the USSR, the main facts are: a) a theorem on the representation of a solution, b) a theorem on the continuity of a solution, c) a theorem on the Fredholm property. All other facts of the theory are deduced from a), b), and c). Various authors have gradually widened the class of spaces in which the Vekua theory was valid. M. Otelbaev found the widest space among the spaces close to the so-called ideal spaces, to which the coefficients and the right-hand side should belong, so that the facts a), b) and c) remain valid.
VI. Computational mathematics.
M. Otelbaev proposed a new numerical method for solving boundary value problems (as well as general operator equations). By using the embedding and extension theorems, he reduced the considered boundary value problem to minimizing a functional. The boundary conditions and also nonlinearities are «hidden» in the integral expressions. Moreover, by this method the problem of «the choice of a basis» was solved, in which many prominent mathematicians have been interested for a long time. Method of M. Otelbaev can be easily algorithmized and allows finding the solution with the required accuracy. Moreover, the procedure of finding a numerical solution is stable. Computer calculations conducted by his students and students of Professor Sh. Smagulov showed the effectiveness of the method.
M. Otelbaev developed a method of approximate calculation of eigenvalues and eigenvectors of the non-selfadjoint matrices, based on a variational principle. The method reduces the problem to the analogous problem for self-adjoint matrices, for which there is a well-developed theory. Unlike other methods, for example, the maximum gradient method, this method 1) provides global convergence, 2) is convenient for calculating the initial approximation, 3) allows calculating the eigenvalues with the smallest real part, 4) can be used in the general case of a compact non-selfadjoint operator.
M. Otelbaev obtained a two-sided estimate for the smallest eigenvalue of a difference operator which is important for computational mathematics. Due to the need for cumbersome calculations methods for parallelization are actively developed in the world. M. Otelbaev offered an effective algorithm of parallelization for approximate solutions of boundary value problems and Cauchy problem for various classes of differential equations.
VII. Nonlinear evolutional equations.
In hydrodynamics for describing a laminar flow of an incompressible fluid, as well as a turbulent flow the system of the Navier — Stokes equations is used. However, mathematically, it is not well justified, since the existence of a global solution has not yet been proved. Therefore, there are some doubts about the rightness of using this system as a mathematical model. М. Otelbaev managed to reduce the existence problem of a global solution to the Navier — Stokes equation to other equivalent problems, in particular, to the problem of the existence of the so-called «dividing function». He obtained a criterion for strong solvability of nonlinear evolution equations, similar to the Navier — Stokes equation, and also built the examples of equations not globally strongly solvable to which the system of Navier-Stokes equations reduces.
VIII. Theoretical physics.
M. Otelbaev obtained a number of interesting mathematical results in this area. He
a) found explicit formulas for n-particle motion in the space (in the framework of Einstein’s relativity theory);
b) derived an integral formula of the matter motion;
c) proposed a new transformation of the type of the well-known Lorentz transformation works both for and for . If the Otelbaev transformation of coincides with the Lorentz transformation;
d) proved mathematically that the results of physics arising from the special Einstein’s relativity theory one can obtain while staying within the classical wave theory.
IX. Other fields.
The research interests of M. Otelbaev are extremely versatile. The following topics complete their partial characterization.
1) M. Otelbaev chose a certain nonlinear integral operator, for which he proved a criterion of continuity. This operator appeared to be an important model in the theory of nonlinear integral operators, based on which one can develop and test new methods. Due to this, M. Otelbaev together with Professor R. Oinarov obtained a necessary and sufficient condition ensuring the Lipschitz property (contractibility) of the Uryson operator in the spaces of summable and continuous functions.
2) He investigated spectral characteristics and smoothness of solutions of equations of mixed type. A criterion of coinciding of the generalized Neumann and Dirichlet problems for degenerate elliptic equations was found.
3) In recent years, the problem of oscillatory and non-oscillatory solutions of differential equations has become a fashionable topic in mathematics. Already in the late 80s M. Otelbaev obtained a sufficient condition ensuring the non-oscillation property of solutions to the Sturm-Liouville problem, close to a necessary one.
4) М. Otelbaev studied the problem of controlling a laser heat source, showed that under the usual formulation, it does not even have a generalized solution and proposed a new formulation of the problem in terms of «order» and «admittance precision » for surface treatment. He proved the solvability of this problem in such a formulation, and solved some optimization problems without using the well-known methods of optimal control. In addition, jointly with Prof. A. Hasanoglu he solved an inverse identification problem of an unknown time source, on the bases of the measured output data, when the boundary conditions are given in the form of Dirichlet, Neumann, as well as the final redetermination.
Summing up the review of scientific creativity of M. Otelbaev as the characteristics of his work can be marked out the versatility of his scientific interests, research fundamentality, the desire to solve problems in the most general formulation and to bring a solution to the level of the criterion. A large number of publications of M. Otelbaev characterizes his high efficiency, diligence and research productivity.
He was a member of several international scientific meetings, which took place in Russia, Ukraine, Poland, Czechoslovakia, Germany, Morocco, Turkey, Greece and Japan.
М.Otelbaev greatly works for preparing highly qualified science teachers. Over 35 years he held lectures for students of various universities of the republic, he organized a series of seminars and study groups for graduate students, interns, PhD , masters and students. The courses «Expansion and contraction of differential operators», «The theory of decoupling,» «Embedding theorems,» «Modern Numerical Methods,» and many others developed by M.Otelbaev are well known . He has created a large scientific school of mathematics in Kazakhstan. Under his leadership, defended their Ph.D. theses 70 people, 9 of which are doctorates.
М.Otelbaev made a significant contribution to the organization and development of science and education in Kazakhstan, in 1985-1986 worked as the rector of Dzhambul pedogogical Institute, from 1991 to 1993 organized and worked as director of the anew opened Institute of Applied Mathematics of Academy of Sciences and Ministry of Education of the Republic of Kazakhstan, Karaganda, in 1994-1995 he was the head of the Department of Aerospace Agency of the Republic, and since 2001 he is the deputy director of the Kazakh branch of Moscow State University by M.V.Lomonosov.
For a number of years М.Otelbaev worked as a member of the editorial board of the journal «Proceedings of the Academy of Sciences of RK. A physical-mathematical series, «and the international scientific journal» Applied and Computational Mathematics » of National Academy of Sciences of Azerbaijan. He was one of the participants, and worked as an editor of «Eurasian Mathematical Journal», published by ENU after L.N. Gumilev together with Moscow State University after M.V. Lomonosov in 2003-2009 . In 2010 he was the editor of «Eurasian mathematical journal», which is published in English. He was chairman of the international scientific conference «Modern Problems of Mathematics», held on the basis of ENU after L.N. Gumilev in 2002, was a member of program committees of 10 international scientific conferences devoted to problems of Mathematics and Computer Science held at the bases of the KazNU, Karaganda State University, Institute of Mathematics of MES of RK, PSU and the University «Semeyi.» In 2007 he was elected the Vice-President of Mathematical Society of Turkic-speaking countries.
In 2007, M. Otelbaev was awarded the State Prize of RK in the field of science and technology. In 2004 he was awarded the title of laureate of the Economic Cooperation Organization in the category «Science and Technology». In 2006 and in 2011 M. Otelbaev was awarded the state grant «The best teacher of high school.» In 1985 — 1986 years he was elected to the City Council Dzhambul People’s Deputies.