Institute of Mathematics and Mechanics of ANAS

1959 - The Institute of Mathematics and Mechanics was established on the basis of the department of the Physics and Mathematics Institute of the Academy of Sciences of the Azerbaijan SSR (Decision of the Council of Ministers of the Azerbaijan SSR No. 319 dated April 27, 1959, protocol No. 11 of the meeting of the Presidium of the Academy of Sciences of the Azerbaijan SSR May 6, 1959).

1959 - The Institute has 5 departments with specialization: functional analysis, theory of functions, differential and integral equations, mathematical analysis, department of plasticity theory and a computer center. Such important scientists as M.V. Keldysh, M. A. Lavrentyev, N. I. Muskhelishvili , I. G. Petrovsky, S. L. Sobolev, S. N. Bernshtein and A.I. Maltsev.

The purpose of creating the institute was the development of mechanical and mathematical sciences in the country. The main base of the institute was formed in 1945, that is, when the Academy of Sciences of Azerbaijan was established, the mathematics sector at the Institute of Physics and Mathematics. Many employees of Azerbaijan State University and the Azerbaijan Pedagogical Institute were listed as part-time workers and conducted scientific work in traditional areas at the Institute of Physics and Mathematics.

In 1950-1957, the outstanding mathematician Z. I. Khalilov led the Institute of Physics and Mathematics. He also headed the Institute of Mathematics and Mechanics, created in 1959, and Ph.D. became deputy director. Sciences G. N. Agaev, Scientific Secretary - Yu. I. Domshlak.

When the institute was created, the following departments and laboratories were formed in its structure: the department of functional analysis (ruk. Academician Z. I. Khalilov), the department of function theory (ruk. Academician I.I. Ibragimov), the department of differential equations (ruk. G. N. Agaev), Department of Integral Equations (Sh.I. Vekilov, Ph.D.), Department of Approximate Analysis (A.S. Jafarov, Head of the Department of Ph.D. ), Department of Theory of Elasticity (Head of the Department of Physics and Mathematics, Yu. A. Amenzadeh ), Laboratory of Dynamic Strength (Head of the Department of Physics and Mathematics of the Sciences K. A. Kerimov) and Computer Center (Manual for .ph. AUC SA Alaskarov). Thus, when creating the Institute of Mathematics and Mechanics, there were only 3 doctors of physical and mathematical sciences in its staff and the main goal of the institute's activity was also to prepare scientific personnel in the field of mathematics and mechanics.

In 1960, the computer center separated from the institute and became an independent institute of the Academy of Sciences, after some time the Institute of Cybernetics of the Academy of Sciences was created on the basis of this center.

Z. I. Khalilov was the founder of the Azerbaijani school of functional analysis and had outstanding achievements in the further development of this field of science. After graduating from the Azerbaijan State Pedagogical Institute, he worked as an assistant professor at the Tbilisi Institute of Railway Engineers , since 1937 he studied at graduate school with academician N.I. Muskhelishvili, in 1940, after defending his dissertation, he returned to Baku, becoming an assistant professor at Azerbaijan State University . In 1942 he worked in the physics sector of the Azerbaijan branch of the USSR Academy of Sciences as the only mathematician. In 1945, the Physics and Mathematics Institute was created on the basis of this sector. In 1946, Zahid Muallim defended his doctoral dissertation and became the first Azerbaijani to become a doctor of sciences in this field. Zahid Muallim was the only Soviet scientist who felt the importance of functional analysis, functional methods in the theory of differential and integral equations. The book he wrote, "Principles of Functional Analysis," was the first book in the USSR devoted to functional analysis. He was also the first USSR scientist to study the spectrum of non-self-adjoint operators in the Banach space. In 1955, Zahid Muallim was elected an academician, in 1957–1959 he was vice-president of the Academy, 1959–1962 - academician-secretary of the FMTS, 1962–1967 - president of the Academy, 1967–1974 - director of the Institute of Mathematics.

In 1959-1963, the director of the Institute of Mathematics was the founder of the school of the theory of functions in Azerbaijan, Ibrahim Ibish oglu Ibragimov. After graduating from AGPI, Ibrahim muallim begins working both at his institute and at ASU. He is sent to graduate school in Moscow, where he, under the guidance of an outstanding scientist A.O. Gelfond, studies at graduate school. In 1939, I. Ibragimov became the first Azerbaijani to receive a Ph.D. in mathematics. In 1947 he defended his doctoral dissertation in Moscow. Ibrahim Muallim was a well-known scientist in the USSR and in the world, the main research of I. Ibragimov relates to the theory of analytical functions, approximation theory, theory of functions of a real and complex variable. Joint work with M.V. Keldysh and A.O. Gelfond made a significant contribution to the theory of functions. He also worked closely with S. N. Bernshtein in the field of the constructive theory of functions of a complex and real variable.

In 1959, Ibrahim Muallim was elected a member. correspondent Academy, in 1968 he was elected an academician.

In the field of mathematics

• Harmonic and non-harmonic analysis.

• Spectral and qualitative theory of differential equations.

• Optimal control, Algebra and mathematical logic.

• Disciplinary calculation of information technology.

• History of science and technology.

In the field of mechanics

• Theoretical and applied problems of the mechanics of a deformable solid, fluid and gas mechanics.

• In the field of harmonic and non-harmonic analysis: the Kostyuchenko problem, known in the theory of spectral operators, is completely solved, methods for forming frames and new bases in approximation theory are developed, abstract analogues of sines, cosines of the well-known Cadets theorem are obtained, a new concept of µ-statistical convergence is introduced. We prove the boundedness of linear and nonlinear operators important in harmonic analysis in Lebesgue spaces with varying degrees, local Mori-type spaces, and Banach function spaces.

• In the field of optimal control: In order to study a wide class of extremal problems of practical importance, new concepts were given and with their help stronger stronger necessary conditions for optimality were obtained. The optimal control problem with delay in the control function was considered, and for the first time for the optimality of private control a sequence of new necessary high-level conditions was proved, such as equality and matrix momentum, Kopo-Moer, Kelly's recurrent form.

• In the field of fluid and gas mechanics: correction methods have been developed and non-stationary cases of fluid trapping and filtration in an inhomogeneous porous medium have been investigated.

• Studying the mathematical and logical works of the Azerbaijani scientist Nasireddin Tusi.

Currently, the Institute of Mathematics and Mechanics employs 222 people. Of these, doctors of sciences in mathematics - 39, doctors of philosophy in mathematics −68, employees without a scientific degree - 21, the total number of researchers is 128 people. Departments involved in scientific activities - 14, technical departments - 1, other departments - 7.

For 50 years, scientists of the Institute have published over 8700 articles, 77 monographs, and dozens of popular science articles.

The Institute prepared 67 Doctors of Sciences, 215 Candidates of Sciences, who work both at universities in our country and abroad. Since 2001, scientists from the institute have taken part in many international grants, including grants from the NATO Science Committee, grants from the US National Research and Development Fund, the US-Russia-Azerbaijan Joint Grant, INTAS grants, grants from the Presidential Science Development Fund of the Republic of Azerbaijan, TUBITAK grants, SOCAR grants, as well as a number of other grants.

• In 1959-1963, the director of the Institute of Mathematics was the founder of the school of the theory of functions in Azerbaijan, Ibrahim Ibish oglu Ibragimov.
• 1963-1967 student Zahid muallima G. Agaev replaced the director of the Institute of Mathematics, in those years F. G. Maksudov was appointed deputy director for scientific work.

• From 1967-1974, Z. I. Khalilov again became the director of the institute.

• From 1974-2000, the director of the institute was F. G. Maksudov.

• After the death of Maksudov in 2004, the director of the institute was Doctor of Sciences I. Mamedov.

• From April 2004 to May 2013, the Director of the Institute was the Honored Worker of Sciences, Academician Akif Hajiyev.

• Since May 2013, IMM has been led by ANAS Corresponding Member, Professor Misir Mardanov.

One cannot fail to appreciate the enormous contribution of Russian-Soviet scientists to the creation of a scientific school in Azerbaijan in mechanics and mathematics, as well as in the development of the Institute of Mathematics and Mechanics, and the training of highly qualified scientists. Among them were such scientists as: M.V. Keldysh, A.N. Tikhonov, S.N. Bernshtein, N.I. Muskhelishvili, A.O. Gelfond, etc. Thanks to the efforts of these scientists, many graduate students were trained and Doctors of science. Since the mid-1970s, the Institute of Mathematics and Mechanics has become one of the leading scientific centers in the USSR. The scientific activity of IMM, every year gaining power, was closely related to the development of new areas of mechanical and mathematical science in our country. At the time of the creation of the institute, new scientific departments were added to 8 departments and laboratories. Among them are algebra and mathematical logic, equations of mathematical physics, mathematical analysis, inharmonic analysis, creep theory, computational mathematics and computer science, fluid and gas mechanics, and the department of applied mathematics. In 1978, a special design bureau was created at the Institute of Mathematics and Mechanics to implement implementations in the national economy. This bureau worked until 2001, more than 60 works were introduced into the national economy.

Thanks to the scientific activities of the Institute's employees in the main scientific areas, important results were obtained. The results are obtained on the following issues.

General tips for solving various functional analysis equations; stability solutions to operator equations; spectral analysis of the Sturm-Liouville operator and the solution of the inverse problem of two spectra, the solution of the inverse problem for a Dirac-type system, direct and inverse problems of scattering theory and spectral analysis for a number of equations of mathematical physics; completeness, basicity, questions of minimality; extended theorems for special and related functions.

Interpolation of functions in function theory, the completeness of a system of analytic functions, the consistent convergence of linearly positive operators, rational functions, functions with polynomials; extremal properties of entire functions; Bernstein-Nikolsky type equations in the class of a set of complete functions; convergence of combinations of small variable functions.

The existence of solutions to mixed problems and Cauchy problems for differential equations and for the set of equations of mathematical physics; uniqueness and asymptotic behavior of solutions; global and local solution of the Cauchy problem for hyperbolic and parabolic equations; the completeness of half of the special and adjoint functions of some simple derivatives of operators; the regularity of the solution of a wide class of elliptic and parabolic equations, the quality of the theory of differential equations.

Differential properties of the multidimensional integral singular symbol of Calderon-Sigmund in mathematical analysis; multipliers of Fourier series in spherical harmonics; embedding theorems; multidimensional Euclidean spaces, as well as theorems on the restriction of integral operators in certain intergroups.

Solution of the T. Evans problem of semigroup manifolds indecomposable in intersection; solution of the coherent MacLane problem in category theory. The solution of the Kostyuchenko problem known in the theory of spectral operators for inharmonic analysis; analogues of the well-known theorem "1/4 - Cadets"; Hausdorff-Young and Pele type inequalities for binary systems of exponentials with complex coefficients; Banach analogues of the classical Lax-Milgram theorem.

A theory of the stability of elastoplastic structural elements with initial stresses is developed. A method for calculating the stability and vibration of orthotropically inhomogeneous plates and shells is built taking into account the influence of various types of base. The optimization problems for circular and ring plates are investigated in detail.

Original and effective methods for determining the dynamic properties of elastoplastic materials impacted in wave dynamics, a dynamic theory of threads, membranes and networks has been developed.

Deformation and destruction of structures made of elastic-plastic, visco-elastic plastic materials; method for determining the time and place of corrosion failure.

Theory of stability of constructions of elasto-plastic elements in a fluid, gas mechanics, and plasticity theory.

Currently, the Institute of Mathematics and Mechanics employs 222 people. Of these, doctors of sciences in mathematics - 39, doctors of philosophy in mathematics −68, employees without a scientific degree - 21, the total number of researchers is 128 people. Departments involved in scientific activities - 14, technical departments - 1, other departments - 7.

• Institute of Mathematics and Mechanics
• Institute of Mathematics and Mechanics