Regional branch of V.I. Romanovsky Institute of Mathematics of Uzbekistan Academy of Sciences in Khorezm region was organized according to the paragraph 17 of the Decree of the President of
the Republic of Uzbekistan dated May 7, 2020 No DP-4708. In accordance with Annex 2 of this Decree, the department involves 10 research staff and the office of the department is located at the Urgench State
University. Currently, DSc. S.A.
Imamkulov is head of the department. In the department, Academician A. Sadullaev,
DSc. G. Urazboev, leading researcher
B.Babajanov, senior researchers Z.Ibragimov, U.Xoitmetov,
A.Atamuratov, B.Yusupov, A.Babadjanova and junior researcher Sh. Atanazarova also
conduct scientific activities.
The department is
currently conducting research in the following areas:
- Non-associative Lie
and Leibniz algebras and their local derivation;
- Analytical continuation of functions in
multidimensional complex space;
-
Complex potentials and its application;
-
Theory of analytical functions in parabolic polynomials;
- Direct and inverse
spectral problems for differential operators and their applications.
- Local and 2-local derivations
and automorphisms on Leibniz algebras;
- Investigation of functions with
one-dimensional holomorphic continuity in multidimensional complex space;
- Study of the class of α-separat-subharmonic functions;
- Approximation of analytical
functions to simple functions (polynomials) in parabolic polynomials.
- Determined metric charakteristics of
removable singularity sets of m-subharmonic and α-subharmonic functions.
-It is proved an analogue of
Osgood-Brown theorem for separately harmonic functions. It is proved several
theorems about properties of removable singular sets of separately harmonic
functions
It is proved real analytic version of Hartogs’s theorem about
analytic extension along fixed directions and real analytic version of
well-known Forellies theorem. Here although real analytic function admits real
analytic extension along each line, it doesn’t have to be real analytic on
domain that is formed by union of all such lines. But even so we can give total
description of structure of the set where function is not real analytic.
-Determined conditions of regular
parabolicity of complements of Weierstrass algebroidal sets in complex spaces.
Given description of polynomials on this type of manifolds.
--Integrated the Harry Dym equation
with an integral type source in the class of the decreasing functions;
- Integrated the periodic Harry Dym
equation with a source in the class of the periodic functions
- Integrated the semi-discrete
Sine-Gordon equation with a self-consistent source in the class of the
decreasing functions
- Integrated the Kortewege-de Vries
equation with a loaded source in the class of the decreasing functions
- Integrated the Kortewege-de Vries
equation with a loaded source in the class of the decreasing complex valued
functions
