Ministry of Science and Education Republic of Azerbaijan

Institute of Mathematics and Mechanics

29/04/2020

**Misir
Mardanov** – Chief Director,

Corr.-member of
ANAS,

Former Minister of Education of Azerbaijan Republic,

Doctor of Physical and Mathematical
Sciences, Professor**Phone:** (994 12) 5393924**Email:** [email protected]

**Adalet Yavuz oglu Akhundov **– Deputy Director

Deputy
Director on science

Doctor of Sciences in Mathematics, Professor**Phone:** (994
12) 5397579**Email:** [email protected]

**Tamilla
Hasanova** – Scientific secretary

Ph.D. in Physical and Mathematical Sciences,
docent**Phone**: (994 12) 5399192**Email**: [email protected]

**Main area of activity of organization**

In the field of
mathematics: spectral analysis of operators and operator algebres; functional spaces and theory of functions;
problems of harmonic analysis; differential equations and problem of mathematical physics; history of
mathematical logic and mathematics.

**Main scientific achievements made over the last five years**:**Mathematical
analysis**.The boundedness theorems in the spaces of continuous and summable functions were proved for
potential type operators and singular integrals depending on the generalized shift generated by Bessel
differential operators and embedding theorems were established in Sobolev spaces and Sobolev weight spaces
generated by Bessel operator.

Necessary basicity condition of power system of the functions of the form in
the spaces was first found. Some analogy of the ” – Kadets” theorem in spaces at was found for perturbed
system of exponents. A problem on finding analogies of the ” – Kadets” theorem on the basicity of a system of
exponents for sines, cosines systems posed by Sedletskii in 1988 was completely solved. N.K.Bari’s classical
theorem on Riesz basicity of close systems in Hilbert spaces that is transferred to Banach case, is
revised.

In 1977 Yu. J. Kazmin pointed to impossibility of classical Stone- Weierstrass approximation
theorem to some systems, where linear shell is not algebra. Generalization of the mentioned theorem was found
for the complex case that is applied to Yu.J.Kazmin case.

Sufficient conditions and compactness and nucleus
property creation of weight composition operators, and also for weight composition type integral operators,
induced by holomorphic vector poles in uniform close subspaces of continuous functions on compacts are also
given.

**Differential equations**.The direct and inverse scattering
problems for a system of hyperbolic and ordinary differential equations were studied. A unique renewal of
coefficients with respect to scattering operator for the considered system was proved. In some cases the
scattering data were introduced.

A unique solvability of mixed problems and quality properties of their solutions in unbounded multivariate cylindric domains was researched for Sobolev type equations.

**Algebra**. The existence of invariant subspaces of semi – groups
and Lie algebra of quasinilpotent compact operators was proved. The joint spectral radius formulae were
obtained, new topological radicals were defined.

**Approximation theory**. A formula for calculation of the best
approximation was found and extremal function was constructed. The jump problem was solved in a class of
generalized analytic functions.

**Fluid and gas mechanics**. The possibility of estimation of
parameters of unbalanced structures arising at fluid displacement in porous medium by means of physical
parameters of such media is shown. The problem is theoretically solved on the basis of dependence of
resistance factor on the frequency of applied pressure.

The possibility of regulation of development of
unbalanced fractal structures by means of local pressure at the interface is proved, and oilgasfield
technological method was worked out for the realization of the obtained effect.

Stability and oscillations
analysis method of non-homogeneous elastico – plastic structural elements with regard for environment is
worked out.

**Mechanics of deformable solid**. Analytic solution of nonlinear
inverse boundary problem of axially symmetric large elastic deformations of circular orthographic membranes
accepting preassigned form of a segment of rotation of a body under the action of fluid and normal loading is
obtained.

The problem on eigen oscillation of a circular cylindric shell strengthened by a longitudinal
rigidity ribs situation at the same distance from one another and filled by linear elastic medium, is solved.
Under homogeneous boundary conditions on the ends the problem on stress -strain state of variable thickness
transversally isotropic plate restricted by two conic and two spherical surfaces at its axially symmetric
stretch – compression, is solved.

Equations of net motion in natural coordinates were derived.

Strong
break front at self – model motion was found.

The problem on unstationary waves propagation in right prism
was first considered and exact analytic solutions were found for concrete cases. Some facts discovered
previously only experimentally for example, fact on propagation of main energy along the axis with rod
velocity involving free lateral surfaces and etc. were affirmed theoretically.

Motion of circular inclusion
containing elastically fixed mass with acoustic and elastic medium was studied.

Velocity potential, forces
of medium reaction, elastic potentials and inclusions displacements were also determined.

Effective
mathematical theory of cracking of corroding materials under mechanical stress was worked out.

The theorems
admitting to represent the solutions of the problems of linear and a class of nonlinear elasticity theory by
the solutions of the corresponding problem of elasticity theory were proved.

Mathematical theory of
simulation of destruction of constructions made of visco – elasticoplastic material was suggested.