Address
100174, Tashkent city,
Olmazor district, University
street, house 9
Tel.: +998712079140
Fax: +998712625236
Web site: www.mathinst.uz
Email: uzbmath@umail.uz
Exat: math@exat.uz

Staff
Ikromov Isroil Akramovich
Google Scholar
Scopus.com
academic degree: DSc,
academic title: Professor,
position: Leading researcher,
speciality: Mathematical Analysis  01.01.01.
room number: 903,
phone: +99891 5270716,
email: ikromov1@rambler.ru
The main scientific direction: Oscillation integrals and their applications, Coordinated smooth measurement values of Fourier transforms in hyper plains.


Boltaev Asomiddin Tulkinovich
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Scopus.com
academic degree: PhD,
academic title: ,
position: Senior researcher,
speciality: Mathematical Analysis  01.01.01.
room number: 905,
phone: +99890 1928323, +998994257788,
email: atboltaev@mail.ru
The main scientific direction: Spectral analysis of generalized Friedrichs model corresponding to some system with a nonconserved number particles


Safarov Akbar Rakhmanovich
Google Scholar
academic degree: PhD,
academic title: ,
position: Junior researcher,
speciality: Mathematical Analysis  01.01.01.
room number: 903,
phone: +99891 5306096,
email: safarovakbar@mail.ru
The main scientific direction: Oscillation integrals and their applications, Coordinated smooth measurement values of Fourier transforms in hyper plains.


Khamidov Shakhobiddin Ilkhom ugli
academic degree: ,
academic title: ,
position: Junior researcher,
speciality: Mathematical Analysis  01.01.01.
room number: 905,
phone: +99897 3946419,
email: shoh.hamidov1990@mail.ru
The main scientific direction: Spectral theory of Schrödinger operators on a lattice.


Khalkhuzhaev Ahmad Miyassarovich
Google Scholar
Scopus.com
academic degree: DSc,
academic title: ,
position: Head of Samarkand Branch of the Institute of Mathematics named after V.I. Romano,
speciality: Mathematical Analysis  01.01.01.
room number: 902,
phone: +998915477918,
email: ahmad_x@mail.ru
The main scientific direction: The spectral theory of Schrödinger operators in the lattice, the study of essential and discrete spectrum of bilaplasian with compact motion.


History of the laboratory
The Samarkand branch was established in accordance
with the Decision of the President of the Republic of Uzbekistan dated May 7,
2020 No PP4708 "On measures to improve the quality of education and
development of research in the field of mathematics."
The Samarkand branch of the Institute conducts
research in the following areas:
 Friedrichs models and spectral theory of
Schrödinger operators on a lattice.
 Oscillation integrals and their applications.
 Inverse problems of spectral analysis and
application of the document to nonlinear evaluation equations.
 Mathematical modeling of leakage of heterogeneous
formations in porous media.
 Hardytype inequalities and their applications.
Research directions
At present, the
Samarkand branch of the Institute conducts research in the following areas:
1.
Friedrichs models and spectral theory of Schrödinger
operators on a lattice
The results in this direction were obtained by academicians S.N. Lakaev, J. Abdullaev, A.M. Khalkhozhaev, M. Muminov, Z. Muminov, Sh. Alladustov, A. Boltaev, Sh. Khamidov.
2.
Oscillation integrals and
their applications.
The results in this
direction were obtained by I.A. Ikromov, A. Safarov.
3.
The inverse problems of
spectral analysis and their application to nonlinear evolutionary equations.
The results in this direction were obtained by A.Hasanov.
4.
Problems of mathematical modeling of heterogeneous fluid
filtration in porous media are being
studied by B.Khuzhayorov and his students.
5.
Hardytype inequalities and their applications.
The results
in this direction were obtained by K.Kuliev.
The main results
1.
Friedrichs models and spectral
theory of Schrödinger operators on a lattice
·
For the Schrödinger
operator corresponding to a system of three arbitrary particles (two bosons and
another particle, respectively) that interact with a pair of one and
twodimensional laticces using contact potentials, it is proved that there is a
threeparticle bound state at certain values of the impact constant. In
particular, it has been shown that at some values of the interaction energy,
there are cases where the important spectrum is connected below the lower
threshold or above the upper threshold.
·
A generalized Friedrichs model
with the same color of motion was studied. Its important spectrum has been
described. Conditions for the existence of a eigenvalue outside the essential
spectrum were found. The number and location of eigenvalues were determined, and
approximations were found for eigenvalues.
·
The family of discrete
Schrödinger operators, whose potential depends on two parameters
consisting of a delta function and a perturbation operator, is considered in a ddimensional
lattice. The existence of eigenvalues was proved, and the existence of boundary
eigenvalues and resonances, as well as their dependence on the given parameters
and the size of the lattice, were clearly shown.
2.
Oscillation integrals and
their applications.
·
Estimates
of the Fourier transform of charges (measures) concentrated on smooth
hypersurfaces are considered. Following M. Sugumoto, three classes of smooth
hypersurfaces are defined. Depending on the class, estimates of the Fourier
transform of charges are obtained in terms of Randol maximal functions. The
obtained estimates are applied to the solution of the integrability problem for
the Fourier transform of measures concentrated on some nonconvex hypersurfaces.
The sharpness of the obtained estimates is shown. Moreover, The problem posed
by KevrikidisStefanov on the discrete KleinGordon was solved.
3.
The inverse problems of
spectral analysis and their application to nonlinear evolutionary equations.
·
The nonoscillation conditions
of the SturmLiouville problem were created using Hardy's inequalities. Using the Carleman
function, the harmonic function and its derivatives were reconstructed to a
given value at a part of the boundary of the field. For elliptic
equations, the solution of the Cauchy problem and the regulation of the product
of the solution were constructed, and the stability value was obtained in the
classical sense. It has been shown that the efficient construction of the
Carleman function is equivalent to the construction of a regulated solution of
the Cauchy problem.
4.
Hardytype
inequalities and their applications.
·
There are obtained conditions for boundedness of HardyVolterra type operators acting in weighted Lebeg spaces.
Awards

International relations
The
members of the department cooperate with scientists from Great Britain, Italy,
France, Germany, USA, Russia, Belgium, England, Turkey, Brazil, Armenia, China,
Austria, Czech Republic, Australia, Malaysia, Japan, including:
1. Ruhr, Bonn, Mainz,
Braunschweig of Germany,
Zussex University of England,
SISSA, ICTP Research Centers in Italy and the University of Rome, Columbia
(Missouri) and Davis (California) Universities in the USA, MSU, Russian
Information Problems Research Institute and Nuclear Research Institute in
Dubna, Scientific cooperation has been established between Malaysia and Mara
Technology, the group, Putra and Kebangsaan, Karlovy Vary University in
Czechoslovakia and a number of other research centers.
2. S.N. Lakaev and his
students in collaboration with Professor S. Albeverio of the University of Bonn
(Germany) on the basis of projects DFG 436 UZB 113/3, DFG 436 UZB 113/4, DFG
436 UZB 113/6, DFG 436 UZB 113/7 from 2001 to 2011, a total of 60 months of
research was conducted.
3. From 2013 to 2014, S.N.
Lakaev spent 10 months at Fulbright Grant Universities in Davis, California and
Columbia, Missouri. J. Mendez (Puerto Rico) gave scientific lectures and
discussed research for students and scholars at university seminars.
4. Prof. I. Ikromov at
the suggestion of Professor D. Muller, University of Kiel (Germany) German DFG
Scientific Foundation DFGGrant MU 761 / 111 (Fragen der Harmonischen Analysis
im Zusammenhang mit Hyperflachen) is conducting research jointly on the basis
of the project.
5. Prof. I.
Ikromov
has collaborated with J.C. Cuenin,
a scientist at Loughborough University in the United Kingdom is currently
coauthoring scientific papers with the scientist.
6. A.
Safarov is scheduled to go to the University of Ghent, Belgium for a two
month internship (01.10.2021 30.11.2021) through the
"El Yurt Umidi" Foundation. It
is planned to establish scientific cooperation with Professor M. Ruzhansky.
7. Regular
contacts have been established with compatriots abroad, including A. Khalkhozhaev,
M. Pardaboev, in collaboration with Professor of the University of Vienna,
Austria Sh. Kholmatov, 2 articles have been sent to foreign journals.
8. K.
Kuliev has established scientific cooperation with
scientists of the Czech Republic P.Drabek and A. Kufner.
9. Scientific
cooperation has been established with Sh. Alladustov
and professors of Curtin University of Australia A. Kadirov
and I. Bray.
10. Scientific
cooperation has been established with Z. Muminov
and UCIM of Malaysia, professors of Kyushe University of Japan A.
Narzullaev, Z. Eshquvvatov,
F. Hiroshima.


