TTPU

Connect

  • +998 71 2467082
  • uralbekbaev@gmail.com

Ural Bekbaev

NATURAL-MATHEMATICAL SCIENCE department​

Associate Professor Dr.

ACADEMIC DEGREE

PhD

Scopus Profile

view profile

Teaching Subjects

Mathematics

1984 yearPhD degree obtained
1979 yearM.S. with distinction diploma from the Moscow State University (Lomonosov).
1973 yearHigh school diploma from the Republican special physics and mathematics high school. Tashkent

2019 -             Associate Professor at the Department of Natural and Mathematical  

                      Sciences, TTPU, Tashkent Uzbekistan.

2012- 2019    Associate Professor at the Department of Science in Engineering, Faculty of 

                      Engineering, International Islamic University Malaysia.

 

2009-  2012   Associate Professor at the Mathematical and Natural Sciences    

                      Department, Turin Polytechnic University in Tashkent.

 

2007- 2009   Associate Professor at the Department of
                     Mathematical Modeling in Economics and Informatics,
                      Faculty of International Economic Relations,
                     University World Economy and Diplomacy.
                      Tashkent, Uzbekistan

 

2000- 2007   Associate Professor at the Mathematics Department,
                      Faculty of Sciences and Environmental Studies.
                      Universiti Putra Malaysia. Malaysia

1998-1999    Visiting Associate Professor at the Mathematics Department,
                       Faculty of Sciences and Environmental Studies.
                      Universiti Putra Malaysia. Malaysia.

1988-1997    Senior Researcher at the Institute of Mathematics of Academy of Science.

1987-1988    Associate Professor at the Mathematics Department,
                     Tashkent State University,
                     Tashkent, Uzbekistan.

1979-1987     Lecturer, Mathematics Department,
                      Tashkent State University,
                      Tashkent, Uzbekistan.

1976-1979    Student of Mechanics - Mathematics Department of
                     Moscow State University
                      Moscow, Russia.

1973-1976    Student of Mathematics Department of Tashkent State University
                     Tashkent, Uzbekistan.

Teaching Experience In Malaysia, 1998-2019 YEAR

  1. Taught: MTH3004/Finance Mathematics, MTH3100/Calculus, MTH3101/ Advance Calculus, MTH3202 /Modern Algebra to the 1-st and 2-nd year students (Universiti Putra Malaysia), Engineering Math 1 and 2(IIUM), Linear Algebra & Differential Equations (IIUM).
  2. Taught: Special courses on MTH4201/Abstract Algebra and MTH4005/Algebra to the students majoring in mathematics (Universiti Putra Malaysia)

My main research deals with differential algebra, invariant theory, differential invariant theory and nonlinear analysis (matrix representations, quadratic maps, their ergodicity and regularity properties).  Particularly I am interested in differential rational invariants of curves, paths, surfaces, linear differential equations relative to the transformation of variables and unknown functions and ergodicity, regularity problems of nonlinear maps as well .

  1. Ahmed, H., Bekbaev, U. and Rakhimov, I., Subalgebras, idempotents, ideals and quasi-units of two-dimensional algebras, International Journal of Algebra and Computation 2 (2020), pp. 1—27, World Scientific Publishing Company, DOI: 10.1142/S0218196720500253
  2. Ahmed, H., Bekbaev, U. and Rakhimov, I., Classification of Two-Dimensional Jordan Algebras Over R,  Malaysian Journal of Mathematical Sciences 12(3): 287–303 (2018)
  3. U. Bekbaev, On classification and invariants of second order non-parabolic linear partial differential equations in two variables, AIP Conference Proceedings 1974, 020047 (2018); https://doi.org/10.1063/1.5041578
  4. H. Ahmed, U. Bekbaev, I.Rakhimov, The automorphism group and derivation algebras of two-dimensional algebras, 9 pages,  Journal of Generalized Lie Theory and Applications, 2018, 12-1, doi 10.4172/1736-4337.1000290.
  5. U. Bekbaev, M. A. M. Johari, 13 pages, Ergodicity of power series-maps on the simplexes of group algebras of finite groups, IOP Conf. Series: Journal of Physics: Conf. Series 949 (2017) 012023 doi:10.1088/1742-6596/949/1/012023.
  6. U. Bekbaev, 6 pages, A note on a separating system of rational invariants for finite dimensional generic algebras, IOP Conf. Series: Journal of Physics: Conf. Series 949 (2017) 012004 doi:10.1088/1742-6596/949/1/012004.
  7. U. Bekbaev, 39 pages, Complete classification of a class of $3$-dimensional algebras. arXiv 1710.10734(1)
  8. H. Ahmed, U. Bekbaev, I.Rakhimov, Classification of two-dimensional Jordan algebras, 9 pages, AIP Conference Proceedings, 1905, 030003, 2017, doi 10.1063/1.5012149.
  9. H. Ahmed, U. Bekbaev, I.Rakhimov, Complete classification of two-dimensional algebras, 12 pages, AIP Conference Proceedings, 1830, 070016, 2017, doi 10.1063/1.4980965. 
  10. Bekbaev U., On classification of $m$-dimensional algebras, 8 pages, IOP Conf. Series: Journal of Physics: Conf. Series 819 (2017) 012012 doi:10.1088/1742-6596/819/1/012012
  11. Bekbaev U., The Fundamental Basis Theorem of Geometry from an algebraic point of view, 10 pages, IOP Conf. Series: Journal of Physics: Conf. Series 819 (2017) 012013 doi:10.1088/1742-6596/819/1/012013
  12. Bekbaev U., On classification of finite dimensional algebras with respect to the orthogonal (unitary) changes of basis, 4 pages, AIP Proceedings of International Conference “Algebra, Analysis and Quantum Probability” 2015.
  13. Bekbaev U. , On matrix representation of nonlinear maps, International Journal of Engineering and Technology, 8 pages, 13(1) (2016), ISSN  2319-8613.
  14. Bekbaev Ural, On equivalence of parameterized surfaces with respect to linear change of parameters. Malaysian Journal of Mathematical Sciences. V,10(S), 2016, Part I,pp. 75--90.
  15. Bekbaev Ural, On Matrix Representation of Nonlinear Maps, FEIIC-International Conference on Engineering Education and Research, Madinah, Kingdom of Saudi Arabia,19-21 December 2015, ISNB 978-967-5995-11-8@2015 FEIIC, pp. 36-43. http://icee.saudieng.sa
  16. On differential rational invariants of patches with respect to motion groups Ural Bekbaev1  AIP Conf. Proc. 1660, 090048 (2015); http://dx.doi.org/10.1063/1.4926637 Conference date: 28–30 May 2014 ,Location: Penang, Malaysia
  17. Ural Dj. Bekbaev, Isamiddin S. Rakhimov, and Qabildjan K. Muminov, On differential rational invariants of classical motion groups.  J. Algebra Appl. 14, 1550023 (2015) [14 pages] DOI: 10.1142/S0219498815500231
  18. Bekbaev U., On relation between algebraic and ordinary differential algebraic invariants of motion groups. ISSN 1995-0802, Lobachevskii Journal of Mathematics, 2014, vol.35, No. 3, pp. 172-184.
  19. Bekbaev U., Rakhimov I.S.  On differential invariants of some classical groups.  A.Kilicman et al. International Conference on Mathematical Sciences and Statistics, 2013, pp.255-263.Springer Science+Business Media Singapore
  20. Bekbaev U. Dj., A radius of absolute convergence for multivariate power series.  International Journal of Pure and Applied Mathematics ,Volume 84 No. 5 2013, 463-476ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v84i5.2
  21. Bekbaev U. Dj.  An iteration problem. J. Phys.: Conf. Ser. 435 012007, 2013. (http://iopscience.iop.org/1742-6596/435/1/012007)
  22. Bekbaev U. Dj.,  A formula for higher order partial derivatives. International conference on Operator algebras and related topics”, Tashkent, National University of Uzbekistan, 12-14 Seprember, 2012
  23. Bekbaev U. Dj, An inversion formula for multivariate power series arXiv:1203.3834, math.AG, 4 pages.
  24. Bekbaev U. Dj, The Symmetric Product of Matrices. Proceedings. “  International Training and Seminars on Mathematics”(ITSM-2011) in connection with the joint mathematical meeting, 2011 between Samarkand  State University and Malaysian Mathematical Sciences Society. 3th-5th June, Samarkand State University ISBN 978-967-5878-48-0, Pp. 104-106.
  25. Bekbaev U. Dj., Matrix representation for multi-linear maps.  Proceedings of TTPU conference, held on 25-26.04.11. The  Second scientific-practical conference of TTPU  ”Today’s Research for Tomorrow’s Technology”, to appear.
  26. Bekbaev U.Dj., Rakhimov I.S. On isomorphisms and invariants of finite dimensional complex filiform Leibniz algebras. Communications in Algebra,  38(12), 2010, 4705 - 4738. DOI: 10.1080/00927870903527477
  27. Ural Bekbaev. Matrix Representations for Symmetric and Antisymmetric Multi-Linear Maps. arXiv:1010.2579, math.RA.
  28. Ural Bekbaev.   A radius of absolute convergence for power series in many variables.   arXiv:1001.0622 math. CV (math.AC).
  29. Ural Bekbaev. A matrix representation of composition of polynomial maps. arXiv:0901. 3179,  math.AC (math.DS).
  30. Bekbaev U.D., Rakhimov I.S. On classification of finite dimensional complex filiform Leibniz algebras(part I) Proceedings of  the third International Conference on Research and Education in Mathematics (ICREM3), 10-12 April 2007, Kuala Lumpur, pp138-150. ISBN 987-983-3455-88-1(v.I)
  31. Bekbaev U.D., Rakhimov I.S. On classification of finite dimensional complex filiform Leibniz algebras(Second class) Proceedings of  the third International Conference on Research and Education in Mathematics (ICREM3), 10-12 April 2007, Kuala Lumpur, pp151-163. ISBN 987-983-3455-88-1(v.I)
  32. Bekbaev U.D., Rakhimov I.S. On classification of finite dimensional complex filiform Leibniz algebras(Part 2) http://front.math.ucdavis.edu/, arXiv: math.RA/0704.3885, 12 pages.
  33. Bekbaev U.D., Rakhimov I.S. On classification of finite dimensional complex filiform Leibniz algebras(part I) http://front.math.ucdavis.edu/, arXiv: math.RA/0612805, 14 pages.
  34. Bekbaev U.D. with Mohamat Aidil M.J., On  Behavior  of  the  Coefficients of a Sequence of Nested Power Series. Konferensi Kebangsaan Pemodelan Matematik & Statistik Sempena 75 Tahun UPM,  Jabatan Matematik, UPM 5-6 September 2006 pp 265 - 268.
  35. Ural Bekbaev. A note on Quadratic Volterra Operators. Science Putra, v.14, N 2, July 2006, pp. 5-8.
  36. Ural Bekbaev. On the field of differential rational invariants of a subgroup of affine group (Ordinary differential case). http://front.math.ucdavis.edu/, arXiv:math.AG/0608479. 10 pages.
  37. Ural Bekbaev. On the field of differential rational invariants of a subgroup of affine group (Partial differential case). http://front.math.ucdavis.edu/, arXiv:math.AG/0609252, 12 pages.
  38. Mohamat Aidil, Ural Bekbaev. Ergodicity of power series-map on the simplex of group algebra of a finite group. http://front.math.ucdavis.edu/, arXiv:math.DS/0608207 , 12 pages
  39. Regularity and Ergodicity Properties of Polynomial Maps Induced by the Multiplication of Group Algebra of a Finite Group. Proceedings of 2nd International Conference on  Research and Education in Mathematics  (ICREM2) “  Enhancing Cooperation in the promotion of Research and Education in Mathematics, 25th-27th May 2005.pp.134-144.
  40. Regularity and Ergodicity Properties of Polynomial Maps Induced by the Multiplication of Group Algebra of a Finite Group( Non Zero Constant Case) Proceedings of 2nd International Conference on  Research and Education in Mathematics  (ICREM2) “  Enhancing Cooperation in the promotion of Research and Education in Mathematics, 25th-27th May 2005.pp.145-153.
  41. On differential rational invariants of finite subgroups of Affine group. Bulletin of Malaysian Mathematical Society, 2005, Volume 28, N1, pp. 55-60.
  42. An algebraic approach to invariants of surfaces.   Proceedings of IPTA Research & Development Exposition 2003. 9-12 October 2003. Putra World Trade Center, Kuala Lumpur. Vol. 5: Science and Engineering, ed. Y.A. Khalid  et al.,pp. 299-306.  University Putra Malaysia Press, Serdang, Selangor, Malaysia.
  43. On invariants of curves.       Proceedings of International Conference on  Research and Education in Mathematics       “ Towards enhancing Cooperation in the promotion of Research and Education in Mathematics, 2-4 April 2003. At: Hotel Equatorial, Kuala Lumpur, Malaysia. pp. 82-95. University Putra Malaysia Press.
  44. On solutions of some polynomial-functional equations. Pertanika Journal of Science and Technology, volume 10, N1, January 2002, pp. 111-119.
  45. A note on fixed fields of finite group automorphisms of differential fields. Proceedings of International Conference on  mathematics and its applications in the new millennium, 18-19 July 2000, pp. 389-392. University Putra Malaysia Press.
  46. On the Jacobian Conjecture. Proceedings of International Conference on mathematics and its applications in the new millennium, 18-19 July 2000. pp. 115-119. University Putra Malaysia Press.
  47. On  equivalence and  differential rational  invariants of second order  linear partial differential equations in two variables relative to transformations of variables. Izvestiya Visshix Uchebhix Zavedeniy. Matematika, 1999, N11(450),pp.3-10.
  48. Differential rational invariants of Hypersurfaces relative to Affine Group. In  Prociding Pengintegrasion Teknologi dalam Sains Matematik, ed. How Guang Aun, Leong Fook, Ong Boon Hua, Quah Soon Hoe, Safian Uda, Zarita Zainiddin, p. 58-64,  Pusat  Pengajian Sains Matemarik, USM, 1999.
  49. On invariants of second order linear partial differential equations in two variables.  Algebra and Operators Theory. Proceedings of the colloquium in Tashkent, The Netherlands, Kluwer Academic Publishers. 1998 pp.145-157. ISBN 0-7923-5094-4
  50. On  equivalence and  differential rational  invariants of second order  linear partial differential equations in two variables relative to  transformations of variables. Differential equations. V.34, N6, 1998. pp.1-3.
  51. (with Muminov K.K.) On differential rational invariants of classical motion groups of vector spaces. DAN RUz. N6, 1998, pp.6-9.
  52. (with Rakhimov I.S.) On equivalence of ordinary linear differential equations over associative rings. UMJ, 1997, N 1, pp.11-17.
  53. Preprint. On invariants of second order  linear partial differential equations in two variables (relative to transformations of variables).  June,1997.  School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, UK.
  54. (with Muminov K.K.) On equivalence and invariants of elementary surfaces relative to symplectic group. UMJ.  N4. 1997. pp. 26-30.
  55. (with Khakimjanova  K.) On Krull dimension of differential vector spaces. DAN RUz,   N11. 1997. pp.  3-7.
  56. (with Ibragimov F.) On commutative Artinian rings.  Uzbek Mathematical Journal, 1996, N 4, pp.17-22.
  57. Once again on equivalence and invariants of differential  equations y(n)+ a n-1 y (n-1)+ . . . + a 0 y=0. Uzbek  Mathematical Journal (UMJ), N3, 1995, pp.19-31.
  58. (with Rakhimov I. S.) Invariants and orbits of linear partial differential equations  relative to linear transformations of unknown functions. UMJ,  N3, 1994, pp.54-59
  59. On equivalence and invariants of ordinary linear differential equations. Differential Equations. 1994. v.30, N5.pp.911-912.
  60. On equivalence and Invariants of second order linear partial differential equations in two variables. International Congress of Mathematicians. Zurich (Switzerland).August. 1994. Abstracts of Short Communications. p.163
  61. Halphan's problem on equivalence of linear differential equations over differential ring. DAN UzSSR. N1, 1990, pp.3-5 (Russian).
  62. Higher order invariant differentials of functions in local coordinates. Dep.v VINITI, 25.07.90, n4225-B90.
  63. Some results connected with differential vector spaces.  DAN UzSSR, N9, 1989
  64. One representation of general linear group on the space of homogenous linear differential equations. Dep.v VINITI, 12.04.89, N 2421-B89.
  65. (with Rakhimov I.S. and Myminov K.A.) Differential rational invariants of finite system of points of finite dimensional vector space over ordinary differential field. Dep. v VINITI,18.10.89, N 6343-B89.