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
Shadimetov Kholmatvay Makhkambayevich
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Scopus.com
academic degree: DSc,
academic title: Professor,
position: Chief Researcher,
speciality: Computational mathematics
room number: 307,
phone: +998¬94 620 20 84,
email: kholmatshadimetov@mail.ru
The main scientific direction: The theory of optimal quadrature and cubature grid formulas, optimal interpolation formulas, and spline theory. Optimal differential methods for the approximate solution of differential equations. Problems of constructing discrete analogs of differential operators. Optimal methods for the approximate solution of integral equations


Hayotov Abdullo Rahmonovich
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Scopus.com
academic degree: DSc,
academic title: Professor,
position: Laboratory manager,
speciality: Computational mathematics
room number: 308,
phone: +998¬94 618 65 53,
email: hayotov@mail.ru
The main scientific direction: The theory of optimal quadrature and cubature grid formulas, optimal interpolation formulas, and spline theory. Optimal differential methods for the approximate solution of differential equations. Problems of constructing discrete analogs of differential operators. Optimal methods for the approximate solution of integral equations


Akhmedov Dilshod Mashrabovich
Google Scholar
Scopus.com
academic degree: PhD,
academic title: Senior Research Fellow,
position: Leading researcher,
speciality: Computational mathematics
room number: 307,
phone: +998¬90 317 73 80,
email: axmedovdilshod@mail.ru
The main scientific direction: The theory of grid optimal quadrature and cubature formulas. Optimal methods for approximate solution of integral equations


Boltayev Aziz Qo`ziyevich
Google Scholar
Scopus.com
academic degree: PhD,
academic title: Senior Research Fellow,
position: Senior researcher,
speciality: Computational mathematics
room number: 308,
phone: +998¬97 308 33 31,
email: aziz_boltayev@mail.ru
The main scientific direction: The theory of optimal quadrature and cubature grid formulas, optimal interpolation formulas, and spline theory. Problems of constructing discrete analogs of differential operators.


G`ulomov Otabek Xudoyberdiyevich
Scopus.com
academic degree: DSc,
academic title: Senior Research Fellow,
position: doctoral student,
speciality: Algebra and number theory
room number: 301,
phone: +998 97 317 06 50,
email: otabek10@mail.ru
The main scientific direction: The theory of grid optimal quadrature and cubature formulas. Quadratic forms in number theory.


Mirzakobilov Ravshan Norkozievich
Scopus.com
academic degree: ,
academic title: ,
position: base doctoral student,
speciality: Computational mathematics
room number: 301,
phone: +998 94 577 63 53,
email: ravshan.m.n@mail.ru
The main scientific direction: Optimal difference methods for approximate solution of differential equations.


Khayriyev Umedjon
Google Scholar
academic degree: ,
academic title: ,
position: base doctoral student,
speciality: Computational mathematics
room number: 301,
phone: +998 97 300 33 43,
email: khayrievu@gmail.com
The main scientific direction: The theory of grid optimal quadrature formulas. Optimal methods for approximate solution of integral equations.


Karimov Roziq
academic degree: ,
academic title: ,
position: Trainee researcher,
speciality: Computational mathematics
room number: 301,
phone: +998 93 654 02 58,
email: roziq.s.karimov@gmail.com
The main scientific direction: Optimal difference methods for approximate solution of differential equations.


Davronov Javlon
academic degree: ,
academic title: ,
position: Trainee researcher,
speciality: Computational mathematics
room number: 301,
phone: +998 94 5421313,
email: javlondavronov77@gmail.com
The main scientific direction: The theory of grid optimal quadrature formulas. Optimal methods for approximate solution of integral equations. Optimal difference methods for approximate solution of differential equations.


Seminars 
Seminar leader: A.R. Hayotov, Doctor of Physical and Mathematical Sciences, professor., laboratory manager, Seminar Secretary: A.K. Boltaev, senior researcher
The place of the seminar: Zoom online
The seminar is held every Thursday at 2 pm.
Seminar Leader: Kh.M. Shadimetov, Doctor of Physical and Mathematical Sciences, professor, chief researcher, Seminar secretary: D.M. Akhmedov, senior researcher.
The place of the seminar: Zoom online
The seminar is held every Wednesday at 9 am.

History of the laboratory
By the twentieth century, classical computation had
evolved into distribution theory. The main central objects of modern
mathematical analysis are integrals according to Lebesgue and derivatives
according to Sobolev.
The
Lebesgue and the Sobolevs went down in history with a whole and fresh look at
their products. It is known that mathematical talent is passed from teacher to
student. It is a chain, the loops of which are closely connected, and it
connects the schools of mathematics. This can be seen in the famous school of
Euler Sobolev.
Academician
N.N. Luzin says: “The older
the scientific school, the higher its value. In it, traditions, customs,
customs, methods of work, which have been selected and developed over the
centuries, reach even modern mathematicians.
It
is known that S.L. Sobolev
wrote his dissertation under the guidance of P.L.
Chebyshev's student N.M.
Gunther. S.L. Sobolev
considered V.A.Steklov's
student V.I.Smirnov
to be his mentor
In
1935, S.L. Sobolev
applied his methods of functional analysis to equations of mathematical physics
and developed a new theory, namely generalized functions, generalized
derivatives, and Sobolev spaces. Ten years after S.L.
Sobolev, the French mathematician Laurent Schwartz
introduced Fourier substitutions into distribution theory. S.L.
Sobolev began work on the nuclear project in 1942.
Here in Laboratory 2,
Academicians I.V. Kurchatov,
S.L. Sobolev, and
Corresponding Academy Members I.K. Kikoin
and Voznesensky enriched uranium235 and plutonium239 to create explosive weapons.
For this work, Sobolev was awarded the title of Hero of Socialist Labor in
1952. Sobolev's
main role in the development of the atomic bomb was to lead this huge
calculation. During this time, more than 200 only girls worked for him.
Professor
M.D. Ramazanov asked his
teacher S.L. Sobolev,
"Why you?" "There could have been others, but I did it very
well," he said. The nuclear project greatly enriched Sobolev's scientific
and personal potential. Therefore, until the end of his life, computational
mathematics occupied a high place in his scientific research.
From
1952 to 1960, S.L. Sobolev
headed the Department of Computational Mathematics at Moscow State University
which he organized. In Siberia, he headed the Institute of Mathematics. It was
during this time that he developed his theory of cubature formulas.
It
is well known that S.L Sobolev
made a worthy contribution to the development of functional analysis in
Uzbekistan.
U
1967 yilda O‘zR FA “Kibirnetika” instiutida “Integrallarni taqribiy hisoblash”
laboratoriyasiga asos solgan. Bu laboratoriyaning birinchi mudiri,
S.L.Sobolevning shogirdi, professor G‘.N.Salixov bo‘lgan. Ushbu laboratoriyani
19761995 yillarda dunyoga mashhur olim N.P.Romanovning shogirdi, professor
M.I.Isroilov boshqargan, hamda 19952019 yillarda S.L.Sobolevning shogirdi,
professor X.M.Shadimetov boshqargan. Bu laboratoriyani 2019 yildan shu kungacha
S.L.Sobolevning nevara shogirdi, professor A.R.Hayotov boshqarib kelmoqda.
S.L.Sobolev rahbarligida doktorlik dissertasiyalarini G‘.N.Salixov va
X.M.Shadimetovlar, nomzodlik dissertasiyalarini Z.J.Jamalov, T.X.Sharipov va
I.I.Jalolovlar himoya qilganlar.
In
1967 he founded the Laboratory of Approximate Integrals at the Institute of
Cybernetics of the Academy of Sciences of the Republic of Uzbekistan. The first
director of this laboratory was Professor G.N.
Salikhov, a student of S.L.
Sobolev. From 1976 to 1995, this laboratory was headed
by Professor M.I. Isroilov,
a student of the worldfamous scientist N.P
Romanov, and from 1995 to 2019, it was headed by
Professor Kh.M. Shadimetov,
a student of S.L. Sobolev.
The laboratory has been headed by Professor A.R.
Hayotov, a grandson student
of S.L. Sobolev,
since 2019. G.N. Salikhov
and Kh.M. Shadimetov
defended their doctoral dissertations under the supervision of S.L.
Sobolev, and Z.J. Jamalov,
T.Kh. Sharipov, and I.I.
Jalolov defended their dissertations.
In Uzbekistan, S.L.
Sobolev's students continue his scientific work with
dignity. They are doing research in the following areas.
The theory of optimal quadrature and cubature
formulas with grids.
Optimal interpolation formulas and splines theories.
 Optimal differential methods for approximate
solution of differential equations.
 Problems of construction of discrete analogs of
differential operators.
Optimal methods for approximate solution of integral
equations.
Research directions
The laboratory
currently conducts research in the following areas:
1. The
theory of grid optimal quadrature and cubature formulas.
In
this direction, the optimal quadratic and cubic formulas for the approximate
calculation of regular, singular, and Fourier integrals in Sobolev spaces were
constructed and their estimates were obtained. These results were obtained by
Kh.M.Shadimetov, A.R.Hayotov, F.A.Nuraliev, O.X.Gulomov, N.H.Mamatova,
I.O.Jalolov, D.M.Akhmedov, S.S.Azamov, N.D.Boltaev, A.K.Boltaev, S.Babaev,
B.N.Abdukayumov, X.Quldoshev, G.Akhmadaliev, I.I.Jalolov, B.Daliev, B.Bozarov,
R.Rasulov, U.Khayriev and J.Davronov.
2. Optimal
interpolation formulas and spline theories.
The
problems of construction of optimal interpolation formulas and splines in
different Gilbert spaces have been studied in the scientific researches of
Kh.M.Shadimetov, A.R.Hayotov, F.A.Nuraliev,
N.H.Mamatova, I.O.Jalolov, A.K.Boltaev, S.Babaev
and J.J.Eshniyozov
3. Optimal
difference methods for approximate solution of differential equations.
Kh.M.Shadimetov,
A.R.Hayotov, R.N.Mirzakabilov, R.Karimov, and
Sh.Esanov are conducting research on the construction
of optimal differential formulas for the approximate solution of differential
equations in certain spaces based on the methods of functional analysis.
4. Kh.M.Shadimetov,
A.R.Hayotov, F.A.Nuraliev, S.S.Azamov, A.K.Boltaev, X.M.Quldoshev,
I.I.Jalolov and Sh.Esanov
are engaged in the construction of discrete analogs of differential
operators.
Optimal
methods for approximate solution of integral equations. Kh.M. Shadimetov, A.R. Hayotov, D.M. Akhmedov, B. Daliev are conducting research in
this area
The main results
The quadrature and
interpolation formulas in different functional spaces were found to be the
extreme functions of the error functions and the corresponding error function
norms were calculated.
The problem of the existence and uniqueness of optimal
quadrature and interpolation formulas in differentiated functions in the
Hilbert spaces is solved, which proved that the
solution gives a minimum to the norms of the error functionals in the
corresponding spaces.
Discrete analogs of known differential
operators were constructed.
Optimal quadrature formulas with positive
coefficients were constructed in Sobolev space and the optimal error functional
norm was calculated.
Optimal quadrature formulas in the sense of
Sard were constructed that were exact for polynomials and exponential functions
not exceeding m2, and for polynomials and trigonometric functions not
exceeding m3.
Sobolev's grid optimal interpolation
formulas were constructed in the space of periodic functions with n variables.
In Sobolev space, optimal quadrature
formulas were constructed for the approximate calculation of Fourier
coefficients and singular integrals.
The problem of constructing optimal
EulerMaclaren type quadrature formulas was completely solved in Sobolev's
space, and the exact value of such quadrature formulas was found..
An optimal quadrature formula was developed
for the approximate calculation of Fourier integrals, which served as the basis
for the development of a new algorithm for image reconstruction in the field of
computed tomography.
Awards

International relations
Researchers
of the Laboratory of Computational Mathematics of the V.I. Romanovsky Institute
of Mathematics of the Academy of Sciences of Uzbekistan and professors of the
Department of Informatics and Computer Graphics of Tashkent State Transport
University together with scientists from leading scientific centers and
universities of the world study current problems of modern computational
mathematics are conducting scientific collaborations on solutions. In
particular, scientific cooperation with the following scientists and their
scientific schools is very well established.
1)
Professor V.L.Vaskevich,
S.L.Sobolev Institute of
Mathematics, Siberian Branch of the Russian Academy of Sciences, Russia.
2)
Professor M.D.Ramazanov, Ufa
Institute of Mathematics, Russia.
3)
Professor M.V.Noskov, Siberian Federal University, Krasnoyarsk, Russia.
4)
Academic G.V.Milovanovich, Institute of Mathematics, Serbian Academy of
Sciences and Culture, Serbia.
5)
Professor E.Novak, FriedrichSchiller University of Jena, Germany.
6)
Professor A.Kabada, Santiyago de Kompostela
universiteti, Ispaniya.
7)
Professor Ch.O. Li, KAIST, South
Korea.
8)
Professor S.S.Sherbakov, Belarus State University, Republic of Belarus.
9)
Professor Parovik R.I., V. Bering Kamchatka State University, Russia.


