A.M.Elizarov

Universitetskaya Str. 17, Kazan, 420008, Russia

e-mail: elizarov@ksu.ru

Chebotarev Institute for Mathematics and Mechanics (CIMM) of Kazan State University (KSU) is one of the oldest university research institutes in Russia where the author of these lines has come a way from a junior researcher to its director. First of all, let us briefly dwell on the "biography" of CIMM (more detailed information is published in [1,2]).

The need for the organization of CIMM in Kazan, a large center of science, emerged in 1928 when N.G.Chebotarev, a well-known professor of algebra, came to the city. By that time, young scholars, progeny of N.N.Parfentiev and D.N.Seiliger, noted Kazan professors, had conducted important research and founded new independent scientific trends in Mathematics and Mechanics. N.G.Chebotarev, who was elected a correspondent member of the Academy of Sciences of the USSR in 1929, stayed in Kazan where he was trying to attract to research more under-and post-graduate students. This required proper economic conditions and a research center. An idea of organizing CIMM in Kazan, where the group of creative and competent mathematicians and mechanical engineers had been formed, was generated and developed in discussions of N.G.Chebotarev with N.N.Parfentiev, P.A.Shirokov and N.G.Chatayev. The 2^nd All-Union Mathematical Congress that took place on June 24-30 in Leningrad and supported the initiative of Kazan scholars contributed a lot to the organization of the Institute. The Institute was opened on September 1, 1934. Already in 1933-1934 there were five research seminars and a big group of post-graduate students working in CIMM. Some of them later became prominent scholars.

Problems studied at the Institute referred to new modern areas of Mathematics and Mechanics:

Algebra - resolvent problems and continuous groups (N.G.Chebotarev, I.D.Ado); extendable polynomials (L.I.Gavrilov, I.N.Meiman); theory of Lie groups, Galois theory, algebra and tensor analysis (N.G.Chebotarev).

Analysis - orthogonal polynomials (B.M.Gagayev); critical points of differential equation systems (M.I.Almukhamedov); Chaplygin method applied to linear differential equations of n order (G.Kh.Maksudov); linear boundary-value problems for analytical functions (F.D.Gakhov); generalization of the law of large numbers (K.P.Persidskiy).

Geometry - linear helical functions, symmetrical spaces with undefined metric; tensor analysis (P.A.Shirokov); conjugation in null systems (V.A.Yablokov); Finsler spaces (B.L.Laptev).

Mechanics - stability of trajectory dynamics, Kronecker behavior and its application in dynamic stability (N.G.Chetayev); general problems of stability theory (K.P.Persidskiy, I.G.Malkin); some problems of vibration theory (N.N.Parfentiev).

When the WW2 broke out junior researchers of the Institute went to the battlefield but scientific life was going on. N.G.Chebotarev himself as well as other scholars evacuated to Kazan from different Moscow and Leningrad academic institutions were conducting research in near-practice areas. There were joint sessions of Kazan Physical and Mathematical Society together with Moscow Mathematical Society. N.G.Chebotarev managed to recommence the work of the Institute in 1944.

N.G.Chebotarev died on July 2, 1947 full of new plans, in the prime of his research and administrative activity. His death was a heavy loss for Kazan University. Acknowledging scientific achievements of Prof. Chebotarev the Institute was named after him while it became headed by Prof. V.V.Morozov.

The Institute had many scientific achievements during the post-war period but we cannot mention them all in this article. We will just give some names of those who were fruitfully working at CIMM. They are V.V.Morozov, F.D.Gakhov, A.P.Norden, S.N.Andrianov, M.T.Nuzhin, G.G.Tumashev, B.L.Laptev, A.Z.Petrov, P.I.Petrov, S.F.Saikin.

The life of the Institute later in the 20^th century may be divided into three parts: 1950s, the period of stability (1960-80s) and the years of reform changes. The boundaries between them are defined by the drastic changes in external environment for university scholars.

A noted mechanical engineer, Professor G.G.Tumashev, whose doctor thesis (1943) laid the foundation of the new scientific trend on inverse boundary-value problems (IBVP) at Kazan University becomes director of CIMM in 1954. This area has been one of the most fruitful at RIMM since that time. In the 1950s Prof. M.T.Nuzhin provided the general IBVP statement for analytical functions, IBVP classification and methods of solution, which were the basis of a new approach for projecting dam foundations.

CIMM had its second birth in the beginning of the 1960s when it was significantly enlarged. Mechanics was strengthened, mathematics was revived, new departments and laboratories were organized to develop new scientific trends. Prof. B.L.Laptev, a well-known geometrician and a scholar of authority was appointed to be director of the Institute in 1961. Under his leadership (1961-1980) CIMM obtains the recognition of one of the largest university research institutes in Russia. The main Institute's achievements of this period are the following.

The theory of probabilistic automations was formulated and synthesis methods of probabilistic processors for personal computers were developed at the Department of Cybernetics. Professors R.G.Bukharayev, V.M.Zakharov as well as their followers and progeny were contributing the most to these finds. The work of the Department had enjoyed a wide recognition already by the end of the 1960s. The First All-Union Symposium on Probabilistic Automations took place in Kazan in 1969.

The activity of the Department of Probability Theory and Mathematical Statistics was oriented at the study of probability structures connected with other areas of mathematics. Experts of the Department undertook the following work:

· Developed a topological method of probability investigation

· Developed a new concept in stochastic analysis based on the use of Sobolev type spaces

· Substantiated a new approach to the problem of guarantee statistical conclusion

· Constructed and investigated new effective statistical criteria.

The achieved results served as the foundation for the organization of the field of "Probability Structures and their Application" at Kazan University. The All-Union School for Noncommutative Probability Theory organized by RIMM in 1971 has significantly stimulated the development of this area. Research schools of professors A.N.Sherstnev, I.N.Volodin and D.Kh.Mushtari were contributing to these results.

The Department and Laboratory of Subsurface Hydromechanics developed singular calculation methods of pressure fields and oil saturation in heterogeneous strata; contributed a lot to the theory of nonlinear filtration of abnormally viscous oils; developed mathematical foundations of relaxation filtration theory; proposed and substantiated a new approach towards the study of filtration consolidation problems. Several models for the investigation of filtration problems were constructed and a method of the increase of recoverable oil was proposed based on the results of tests. These results were generated by the following professors: G.G.Tumashev, V.Ya.Bulygin, S.F.Saikin, Yu.M.Molokovich, A.V.Kosterin, E.V.Skvortsov, A.N.Chekalin.

The Department of Hydromechanics mainly deals with fluid flows theory with free boundaries (fair speed hydrodynamics). Professors A.V.Kuznetsov, A.G.Terentiev, O.M.Kisilev, L.M.Kotlyar, D.V.Maklakov were the core of the Department who developed solution and calculation methods of nonlinear problems of continuous and cavitation profile streamline near the free surface. They also developed methods of vacillating profile with stream separation and that of cascade as well as problems of electrochemical metal sizing. The generated results were widely recognized and published in specialized reviews, textbooks and treatises on stream and cavitation theory.

The Department of Boundary Problems and Laboratory of Analog Simulation have contributed a lot to the projecting theory of hydrodynamical objects with set characteristics. Professors M.T.Nuzhin, N.B.Ilyinskiy, Ye.G.Sheshukov, N.D.Yakimov, F.G.Avkhadiev, A.M.Yelizarov, A.V.Potashev, S.R.Nasiriv and their followers have developed methods of the construction of underground dam outline, solved several new problems of excavating explosions in impulsive-hydrodynamical setting, created new methods of high-performance wing profile construction as the quasisolution of IBVP and investigated the issues of solution univalence of these problems. Several treatises have been written. The school of inverse boundary-value problems at Kazan University have been recognized in this country and enjoys authority with many experts.

The Department of Gas Dynamics was organized on the basis of Hydromechanics Department at CIMM in 1974. The main areas of its research are the investigation of glow discharge in gas longitudinal flow and its applications, modeling of gas lasers optical resonators, mathematical modeling of the dissemination of point source emission in atmosphere, mathematical modeling of aerosol flows and three-dimensional gas flows in the areas of complex geometry. The new field of physical gas dynamics was organized at KSU in a short space of time thanks to the efforts of the Department.

The Laboratory of Shell Mechanics was organized in 1960 for the investigation of the mechanical behavior of thin-slab structures. It continued to develop methods of defining stress and strain state of plates and shells under local loads as well as calculation methods of free oscillations and shell stability. It developed a theoretical and experimental approach of high-performance that enables to successfully solve the whole variety of problems. These methods were applied for the manufacture of aircraft, trunk pipelines, large-sized capacities, optical and mechanical constructions and other structures. These results were generated by professors A.V.Sachenkov, Yu.G.Konoplev, Yu.P.Artyukhin, Yu.P.Zhigalko, A.K.Shalabanov, A.I.Golovanov as well as be their progeny and followers.

B.L.Laptev leaves the position (retires) of director of CIMM in 1980. Prof. N.B.Ilyinskiy becomes his successor. The new leadership was trying very hard to strengthen the prestige of CIMM. CIMM's 50^th anniversary was celebrated in 1984 and together with it "Current Issues of Mathematics and Mechanics", a big research conference, was organized.

Some drastic changes have taken place in CIMM's organization during the last decade. Thus, new mathematical departments were organized, some units were reorganized and some cancelled, departments were united into four larger units - Sections (of Mathematics, Mechanics, Mathematical Modeling and Information Science). Below are some results that have been generated during these last years.

The Department of Mathematical Logic was founded in 1993 on the basis of the Department of Cybernetics. Working there Prof. M.M.Arslanov and his followers obtained some basic results on the elucidation of the algebraic nature of semilattices of degrees unsolvability, investigated the algebraic structure of semilattices defined by enumeration reducibility. Some results received by the team of the Department solve problems that had stayed unsolved for long time. In particular, M.M.Arslanov together with S.Lempp and R.Shore, American mathematicians, generated a negative solution of a well-known problem referring to recursion theory. Professor V.D.Soloviev investigated pre-complete classes of the functional system of one-place functions and predicates with program closing provisions, solved Ershov-Liapunov problem on completeness and thoroughly studied closed class system of recursive functions. S.M.Skriabin, Doctor of Physical and Mathematical Sciences, studied Cartan algebra representations. One of his major results is isomorphism general theorem and, as the result of it, the standard form definition of Cartan algebra.

The Department of Mathematical Analysis was founded in 1994 on the basis of the Department of Boundary Problems. The main areas and subjects studied at the Department are

· Various nonlinear problems of function theory observed in boundary problems with free boundaries;

· Embedding evaluations of norms of operators in Sobolev spaces in n-dimensional region through geometric parameters;

· Hydroprofile construction using cavitation diagram;

· Extremal problems for analytical functions from Bloch space;

· Solution of problems connected with the construction and evaluation of the number solutions of boundary problems with free boundaries;

· Conformal maps and Riemannian surfaces study;

· Construction and study of iterative solution methods of net approximations of elliptic variational inequalities;

· Mathematical model construction and numerical solution of problems on solution filtration in frozen ground.

The development of these themes was promoted by problem research seminars that were organized before by professors F.G.Avkhadiev and A.V.Lapin while they were helped a lot at this by professors A.M.Elizarov, D.V.Maklakov, S.R.Nasirov, O.M.Kiselev and others.

The Department of Information Science was organized under the direction of Prof. F.M.Ablayev in 1995. The major themes of the Department are the study of information and complex calculation properties, investigation of applications of information and complex approaches in problems of information science, discrete and continuous mathematics and practical issues of introducing new technologies. The main research areas are the study of communication and information aspects of deterministic and probabilistic calculations; complexity relations of probabilistic, deterministic and nondeterministic scheme models, in particular, binary programs with various limitations; issues of computational model diagnosis; the study of various models of parallel algorithms. Moreover, several all-University and regional telecommunication projects have been implemented on the basis of the Department of Information Science. Their objective is to develop, use and disseminate up-to-date telecommunication, information and publishing technologies at Kazan State University, provide an access to international on-line data bases, teach university students and staff members how to use these technologies and provide them with the access to these technologies.

The Department of Geometry at CIMM has a long history. It was organized right after the Institute was founded. For long time it was headed by Prof. P.A.Shirokov, a well-known Russian geometrician, and then by Prof. B.L.Laptev, Director of the Institute. But the Department was closed in the end of the 1970s due to the reorientation of the Institute at applied research. The Department of Geometry was restored in 1996 under the direction of Prof. A.P.Shirokov. At present research is conducted in the following areas: bundle space and foliation theory, spaces over algebra, tangent bundles and their application to non-Euclidean space. Mainly, the research is concentrated on the study of algebraic structures on varieties which is traditional for the Kazan school of geometry that originates from N.I.Lobachevskiy. The following professors have significantly contributed to research finds: B.N.Shapukov, V.V.Shurigin, B.P.Komrakov and associate professors: M.A.Malakhaltsev and B.M.Dubrov.

119 research fellows work today at CIMM, of them 23 are doctors and 65 candidates of science. 30 candidate and 15 doctor theses were defended from 1993 to 1999. Scientific conferences of the highest level are constantly conducted.

And some more key details before I close. First, thanks to the creation of the Institute at KSU classical fields of mathematical research were organized and developed in a short period of time and mathematical departments of a very high level were started. This high level has been supported until now, to the large extent, because these departments have been hiring alumni of CIMM as their new employees. Furthermore, the Institute still maintains the high level of departmental mathematical science at different universities and colleges in Kazan inviting for research and grant implementation faculty members from these departments while many of them are alumni of CIMM.

Second, CIMM plays an extremely important role in training highly-qualified researchers. N.G.Chebotarev himself was promoting doctoral training which could not be as developed as it is if CIMM had not played its role in this process.

And last but not least, such university research institutes and research institutes of mechanics and mathematics do not wholly depend on higher authorities from the Ministry but their work mainly, if not completely, is determined by the policy of the university itself. Having become culture preserves and having gathered spiritual university elite, these research institutes do not demand much for their maintenance and that is why if one wants them to disappear it would suffice just to cease to support them.

References

1. The Essay on History of Chebotarev Institute for Mathematics and Mechanics - Kazan: Publishing House of Kazan University, 1989, - pp.175.

2. Chebotarev Institute for Mathematics and Mechanics. 1993-1997/Edited by A.M.Elizarov and S.A.Kuznetsov - Kazan: Publishing House of Kazan Mathematical Society. DAS Publishing House, 1998.- pp. 235.