Laboratory Staff

Abdullayev Janikul Ibragimovich

Yetakchi ilmiy xodim More details →

Abduxakimov Saidakbar Xazratkul o‘g‘li

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Axmadova Muhayyo Olimjon qizi

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Barakayev Azamat Mansurovich

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Boltayev Asomiddin Tulkinovich

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Bozorov Islom Namozovich

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Hasanov Aknazar Bekturdiyevich

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Ikromov Isroil Akramovich

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Laqayev Saidaxmat Norjigitovich

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Mo‘minov Muxiddin Eshqobilovich

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Muminov Zaxriddin Eshkobilovich

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Xalxoʻjayev Axmad Miyassarovich

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Xamidov Shaxobiddin Ilxom o’g’li

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Xo‘jayorov Baxtiyor

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Scientific Activity

Currently, the Samarkand branch of the V.I. Romanovskiy Institute of Mathematics conducts scientific research in the following areas:

Friedrichs models and spectral theory of Schrödinger operators on lattices. The spectral properties of Schrödinger operators corresponding to two-particle systems on a lattice and Friedrichs models are investigated depending on the values of interaction energies at neighboring lattice sites, the total quasi-momentum of the two-particle system, and the lattice dimension. The spectral properties of Schrödinger operators corresponding to three-particle systems on a lattice and model operators corresponding to systems of a finite number of non-conserved particles are studied through the spectral properties of pairwise interacting two-particle subsystems.

Oscillatory integrals and their applications. Uniform estimates with respect to frequency direction are obtained for the Fourier transform of measures concentrated on a given level hypersurface. Upper bounds are obtained for solutions of the Cauchy problem for the Schrödinger equation in terms of initial conditions, and the sharpness of solution estimates in the class of smooth functions is demonstrated. Problems of finding sufficient conditions for the global existence of solutions to the Cauchy problem for nonlinear fractional-order discrete Schrödinger equations are solved.

Inverse problems in spectral analysis and their applications to nonlinear evolution equations. The nonlinear Hirota equation with an additional term is integrated in the class of periodic infinite-zone functions using the inverse spectral problem method for the Dirac operator. The existence and uniqueness of the solution to the Cauchy problem for the AB system is proved using the inverse scattering problem method. Conditions for non-oscillation of solutions to the Sturm-Liouville problem are derived using Hardy inequalities. The defocusing complex modified Korteweg-de Vries equation with an adapted source and non-zero boundary conditions at infinity is integrated using the inverse scattering transform.

Mathematical modeling of inhomogeneous fluid filtration in porous media. Filtration of inhomogeneous fluids in porous and fractured-porous media, mass transfer in porous and fractured-porous media, anomalous filtration and mass transfer, elastic-plastic filtration, relaxation filtration, and inverse problems of filtration and mass transfer are investigated, enabling the solution of problems in the analysis and design of oil and gas field operations.

International Cooperation

Members of the division have established cooperation with scientists from Great Britain, Italy, France, Germany, USA, Russia, Belgium, England, Turkey, Brazil, Armenia, China, Austria, Czech Republic, Australia, Malaysia, and Japan. The following activities have been implemented:

1. Scientific cooperation has been established with Ruhr, Bonn, Mainz, and Braunschweig Universities in Germany; Sussex University in England; SISSA and ICTP scientific centers and the University of Rome in Italy; Columbia University (Missouri) and UC Davis (California) in the USA; Moscow State University; the Institute for Information Transmission Problems in Russia and the Joint Institute for Nuclear Research in Dubna; the University of Malaysia and Universiti Teknologi MARA, as well as Universiti Putra Malaysia and Universiti Kebangsaan Malaysia in Malaysia; Charles University in Czechoslovakia; and several other major research centers.

2. S.N. Lakaev and his students conducted research for a total of 60 months during 2001-2011 in collaboration with Professor S. Albeverio from the University of Bonn (Germany), based on projects DFG 436 UZB 113/3, DFG 436 UZB 113/4, DFG 436 UZB 113/6, and DFG 436 UZB 113/7 funded by Germany's DFG Scientific Foundation.

3. S.N. Lakaev, as a Fulbright Grant recipient in 2013-2014, conducted research for 10 months at UC Davis (California) and the University of Missouri-Columbia in the USA, and delivered scientific lectures for students and scientists at scientific seminars at the University of Missouri-Columbia, Princeton University (New Jersey), California State University Fullerton, UC Irvine, UC Davis (California), and Ana G. Méndez University (Puerto Rico), and discussed scientific results.

4. Prof. I. Ikromov is conducting collaborative research based on the DFG-Grant MU 761/11-1 project "Fragen der Harmonischen Analysis im Zusammenhang mit Hyperflächen" (Questions of Harmonic Analysis Related to Hypersurfaces) funded by Germany's DFG Scientific Foundation, at the invitation of Professor D. Müller from Kiel University (Germany).

5. Prof. I. Ikromov has established cooperation with J.-C. Cuenin from Loughborough University in Great Britain and is currently publishing scientific articles in co-authorship with this scientist.

6. A. Safarov is scheduled to undertake a 2-month internship (01.10.2021-30.11.2021) at Ghent University in Belgium through the "El Yurt Umidi" foundation. Scientific cooperation with Professor M. Ruzhansky is planned there.

7. Regular contacts have been established with compatriots abroad; in particular, A. Khalkhojaev and M. Pardaboev have submitted 2 articles to foreign journals in collaboration with Professor Sh. Kholmatov from the University of Vienna, Austria.

8. K. Kuliyev has established scientific cooperation with Czech Republic scientists P. Drábek and A. Kufner.

9. Scientific collaborations have been established between Sh. Alladostov and Professors A. Kadirov and I. Bray from Curtin University in Australia.

10. Z. Muminov has established scientific cooperation with Professors A. Narzullaev, Z. Eshkuvatov, and F. Hiroshima from UCIM in Malaysia and Kyushu University in Japan.

Seminars