Russian State Pedagogical University
Moyka, 48, 191186 Saint-Petersburg,
Russia
The scientific Conference "Problems of modern
mathematics" was organized by the mathematical department of Kazan State
Pedagogical University with a wide support of a scientific public of Kazan and
outstanding scientists from other cities of Russia. This circumstance has
predetermined a high scientific significance of the Conference on
representation of scientific schools and depth of considered results.
The Conference began with plenary
session and then there were four sections: "Differential equations"
(chairman – V.I.Zhegalov), "Mathematical modeling and programming"
(chairman – R.V.Shaimuratov), "Theory of functions and
approximations" (chairman – B.G.Gabdulkhaev) and "Modern geometry and
its applications" (chairman – Yu.I.Ignatjev).
During plenary reports the reviews
of the last achievements were given. The following branches of mathematics were
presented: inverse problems for systems of ordinary differential equations
(R.G.Mukharlyamov, Moscow), spectral problems for equations of mixed type
(K.B.Sabitov, Sterlitamak), universal description of symmetries of differential
equations on a basis of the theory of formal operators (V.F.Zaitsev,
Saint-Petersburg), the theory of singular elliptical equations (F.G.Mukhlisov,
Kazan), variational principles in underground hydrodynamics (R.V.Shaimuratov, Kazan).
The section "Differential
equations" was the most representative and so its evening session was
divided into two subsections (chairmen – K.B.Sabitov, F.G.Mukhlisov). Most of
the reports were devoted to traditional directions of Kazan mathematical school
and themes close to them. The different aspects of the theory of equations of
mixed type were represented in the reports of R.S.Khaipullin (Kazan),
K.B.Sabitov, A.N.Kuchkarova and S.L.Khasanova (Sterlitamak), equations with
degeneration were considered in the reports of A.A.Andreev, E.N.Ogorodnikov (Samara), S.M.Gafurova,
I.B.Garipov (Kazan). Precise solutions of partial differential equations
were considered in the reports of
V.I.Zhegalov, N.V.Barinova (Kazan), I.N.Saushkin (Samara). The last report was
devoted to hyperbolic differential-delay equation. The theory of ordinary
differential equations was represented by directions investigating methods of
search of precise solutions that are closely to a problem of a decomposition of
models. The development of the operational method was shown in the report of
Yu.V.Maly-shev (Kazan). Ideas of
factorization on the basis of group analysis were considered in the reports of
V.F.Zaitsev and L.V.Linchuk (Saint-Petersburg). Moreover in the last report the
theory of formal operators is extended to the class of functional differential
equations including practically important differential-delay equations. The
report of F.N.Garifyanov (Kazan) about analytical solutions of difference
equations is also adjacent to these themes.
Unfortunately the author of this
review could not be present on all session therefore his impression from other
performances is not complete and is subjective to a greater degree. The full
review of the Conference reports one can find in the Proceedings (see
"Proceedings of Mathematical center named after N.I.Lobachevsky",
volume 11). It is necessary to mark that in spite of fundamental mathematical
trend many reports announce results having the great importance for
applications. First of all it is possible to point out researches in gas and
hydrodynamics that are traditional for scientist of petroleum and gas producing
area like Tatarstan. These problems are considered in reports of M.M.Asatov,
I.N.Mubarkzyanov, N.M.Galiev, D.K.Galiullin, R.Z.Ilyasov, R.V.Shaimuratov,
O.A.Shirokova (Kazan). The second line of investigations relatives to
theoretical physics and covers some areas of cosmology, relativistic mechanics,
quantum theory of a field and relativistic magnetohydrodynamics of plasma
(reports of D.N.Gorohov, F.Sh.Zaripov, Yu.G.Ignatjev, A.I.Chepkunov,
E.G.Chepkunova, A.A.Popov, S.V.Sushkov (Kazan)). The reports of E.K.Lipachev,
N.A.Moskalev, I.N.Pleschinsky, E.D.Khusainova (Kazan) were devoted to problems
of diffraction. Finally we shall mark works developing some directions of
mechanics of a rigid body (reports of V.R.Kristalinsky (Smolensk),
R.M.Mulyukov, E.G.Saifullin, A.F.Galimyanov, N.Z.Yakushev (Kazan)).
In summary it needs to thank to
Organizing Committee of the Conference for warm reception and excellent
organization of the work. Note that in a period of 3 days it was led the
valuable scientific forum with the numerous informative reports and discussions
on a wide area of problems of modern mathematics and the interesting cultural
program. Especially it would be desirable to mark the concert organized by
amateurs, among which were participants of the Conference and students of Kazan State Pedagogical University.