Mukhamedov, Farrukh Maksutovich

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Total publications: 28
Scientific articles: 27
Presentations: 1

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Mukhamedov, Farrukh Maksutovich

Doctor of physico-mathematical sciences (2005)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 2.01.1975
Phone: +60179426800
E-mail: , , ,
Keywords: dynamical systems, trajectory theory of dinamical systems, nonlinear operators and processes, random walks in random environment, $p$-adic analysis, the Gibbs measures, lattice models of statistical mechanics, ergodic averages, von Neumann algebras, quantum lattice models, operator theory, quantun chaos.
UDC: 517.98, 517.987, 517.998, 517.958, 519.217, 519.248, 530.1, 519.21, 531.19
MSC: 28d05, 28d15, 22d20, 22d25, 46l35, 60g99, 60b15, 82b20, 92b05, 97b10, 37a45, 47a35, 47a99


Investigation of phase transition for lattice models and description of types of the corresponding von Neumann algebras constructed by GNS-repesentation of Gibbs measures of some lattice models.
Investigations of Gibbs measures of certain lattice models over the $p$-adic number field.
Investigations of attractors and Siegel disc of certain $p$-adic dynamical systems.
Investigations of ergodic properties of quantum quadratic stochastic processes on von Neumann algebras.
Investigations of ergodic theorems for $C^*$-dynamical systems and noncommutative ergodic theory.
Study of quantum Markov chains.


Tashkent State University 1991–1996 Student.
Institute of Mathematics Academy Sciences of Uzbekistan, 1996–1998 Graduate Student.
Institute of Mathematics Academy Sciences of Uzbekistan, 1998–1999 Junior Scientific Fellow.
National University of Uzbekistan, 1999–2002 post doctora.
National University of Uzbekistan, 2003–2004 Associate Professor.
National University of Uzbekistan, 2004–2005 Senior Scientific Fellow.
Universidade de Aveiro, Portugal, 2005–2007 PosDoc.
International Islamic University Malaysia, 2007 up to now.

Main publications:
  1. Accardi L., Fidaleo F., Mukhamedov, F., “Markov states and chains on the CAR algebra.”, Infinite Dimensional Analysism, Quantum Probab. Related Topics, 10:2 (2007), 165-183
  2. Khrennikov A.Yu., Mukhamedov F.M., Mendes J.F.F., “On $p$-adic Gibbs measures of countable state Potts model on the Cayley tree,”, Nonlinearity, 20 (2007), 2923-2937
  3. Mukhamedov, F. Akin H., Temir S., “On infinite dimensional quadratic Volterra operators,”, Jour. Math. Anal. Appl., 310 (2005), 533-556
  4. Fidaleo, F., Mukhamedov, F., “Strict weak mixing of some $C^*$–dynamical systems based on free shifts,”, Jour. Math. Anal. Appl., 336 (2007), 18-187
List of publications on Google Scholar
List of publications on ZentralBlatt
Full list of publications: Download file (136 kB)

Publications in Math-Net.Ru
1. F. M. Mukhamedov, O. N. Khakimov, “$p$-adic monomial equations and their perturbations”, Izv. RAN. Ser. Mat., 84:2 (2020),  152–165  mathnet  elib; Izv. Math., 84:2 (2020), 348–360  isi  scopus
2. A. Dhahri, F. Mukhamedov, “Open Quantum Random Walks and Quantum Markov Chains”, Funktsional. Anal. i Prilozhen., 53:2 (2019),  72–78  mathnet  elib
3. F. M. Mukhamedov, U. U. Jamilov, A. T. Pirnapasov, “On Nonergodic Uniform Lotka–Volterra Operators”, Math. Notes, 105:2 (2019), 258–264  mathnet  isi  elib  scopus
4. F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the $\lambda$ model on the Cayley tree”, TMF, 194:2 (2018),  304–319  mathnet  elib; Theoret. and Math. Phys., 194:2 (2018), 260–273  isi  scopus
5. F. Mukhamedov, “On the uniform zero-two law for positive contractions of Jordan algebras”, Eurasian Math. J., 8:4 (2017),  55–62  mathnet  isi
6. F. M. Mukhamedov, M. A. Mukhamedov, “Ergodicity Coefficient and Ergodic Properties of Inhomogeneous Markov Chains in Ordered Normed Spaces with a Base”, Mat. Zametki, 99:3 (2016),  477–480  mathnet  mathscinet  elib; Math. Notes, 99:3 (2016), 480–483  isi  scopus
7. F. M. Mukhamedov, M. Kh. Saburov, O. N. Khakimov, “Translation-invariant $p$-adic quasi-Gibbs measures for the Ising–Vannimenus model on a Cayley tree”, TMF, 187:1 (2016),  155–176  mathnet  mathscinet  elib; Theoret. and Math. Phys., 187:1 (2016), 583–602  isi  scopus
8. F. M. Mukhamedov, “On the Existence of Phase Transition for the 1D $p$-Adic Countable State Potts Model”, Math. Notes, 98:2 (2015), 283–288  mathnet  mathscinet  isi  elib  scopus
9. F. M. Mukhamedov, B. A. Omirov, M. Kh. Saburov, K. K. Masutova, “Solvability of cubic equations in $p$-adic integers ($p>3$)”, Sibirsk. Mat. Zh., 54:3 (2013),  637–654  mathnet  mathscinet; Siberian Math. J., 54:3 (2013), 501–516  isi  scopus
10. F. M. Mukhamedov, H. Akin, “The $p$-adic Potts model on the Cayley tree of order three”, TMF, 176:3 (2013),  513–528  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 176:3 (2013), 1267–1279  isi  elib  scopus
11. F. M. Mukhamedov, U. A. Rozikov, “A polynomial $p$-adic dynamical system”, TMF, 170:3 (2012),  448–456  mathnet  mathscinet  elib; Theoret. and Math. Phys., 170:3 (2012), 376–383  isi  elib  scopus
12. L. Accardi, F. M. Mukhamedov, M. Kh. Saburov, “Uniqueness of Quantum Markov Chains Associated with an $XY$-Model on a Cayley Tree of Order $2$”, Mat. Zametki, 90:2 (2011),  168–182  mathnet  mathscinet; Math. Notes, 90:2 (2011), 162–174  isi  scopus
13. F. Mukhamedov, “On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model”, Tr. Mat. Inst. Steklova, 265 (2009),  177–188  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 265 (2009), 165–176  isi  scopus
14. F. M. Mukhamedov, “On the Chaotic Behavior of Cubic $p$-Adic Dynamical Systems”, Mat. Zametki, 83:3 (2008),  468–471  mathnet  mathscinet  zmath; Math. Notes, 83:3 (2008), 428–431  isi  scopus
15. F. M. Mukhamedov, “On Strictly Weakly Mixing $C^*$-Dynamical Systems”, Funktsional. Anal. i Prilozhen., 41:4 (2007),  79–82  mathnet  mathscinet  zmath; Funct. Anal. Appl., 41:4 (2007), 311–313  isi  scopus
16. F. M. Mukhamedov, “On expansion of quantum quadratic stochastic processes into fibrewise Markov processes defined on von Neumann algebras”, Izv. RAN. Ser. Mat., 68:5 (2004),  171–188  mathnet  mathscinet  zmath  elib; Izv. Math., 68:5 (2004), 1009–1024  isi  scopus
17. N. N. Ganikhodzhaev, F. M. Mukhamedov, “Some Properties of a Class of Diagonalizable States of von Neumann Algebras”, Mat. Zametki, 76:3 (2004),  350–361  mathnet  mathscinet  zmath; Math. Notes, 76:3 (2004), 329–338  isi  scopus
18. A. K. Karimov, F. M. Mukhamedov, “An individual ergodic theorem with respect to a uniform sequence and the Banach principle in Jordan algebras”, Mat. Sb., 194:2 (2003),  73–86  mathnet  mathscinet  zmath; Sb. Math., 194:2 (2003), 237–250  isi  scopus
19. F. M. Mukhamedov, “On the ergodic principle for Markov processes associated with quantum quadratic stochastic processes”, Uspekhi Mat. Nauk, 57:6(348) (2002),  193–194  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:6 (2002), 1236–1237  isi  scopus
20. N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, TMF, 130:3 (2002),  500–507  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 130:3 (2002), 425–431  isi
21. F. M. Mukhamedov, U. A. Rozikov, “Von Neumann algebra corresponding to one phase of the inhomogeneous Potts model on a Cayley tree”, TMF, 126:2 (2001),  206–213  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 126:2 (2001), 169–174  isi
22. N. N. Ganikhodzhaev, F. M. Mukhamedov, “Ergodic properties of discrete quadratic stochastic processes defined on von Neumann algebras”, Izv. RAN. Ser. Mat., 64:5 (2000),  3–20  mathnet  mathscinet  zmath; Izv. Math., 64:5 (2000), 873–890  isi  scopus
23. F. M. Mukhamedov, “On the Blum–Hanson theorem for quantum quadratic processes”, Mat. Zametki, 67:1 (2000),  102–109  mathnet  mathscinet  zmath; Math. Notes, 67:1 (2000), 81–86  isi
24. F. M. Mukhamedov, “Infinite-dimensional quadratic Volterra operators”, Uspekhi Mat. Nauk, 55:6(336) (2000),  149–150  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:6 (2000), 1161–1162  isi  scopus
25. F. M. Mukhamedov, “On uniform ergodic theorems for quadratic processes on $C^*$-algebras”, Mat. Sb., 191:12 (2000),  141–152  mathnet  mathscinet  zmath; Sb. Math., 191:12 (2000), 1891–1903  isi  scopus
26. F. M. Mukhamedov, U. A. Rozikov, “The disordered phase of the inhomogeneous Potts model is extremal on the Cayley tree”, TMF, 124:3 (2000),  410–418  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 124:3 (2000), 1202–1210  isi
27. F. M. Mukhamedov, “Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice”, TMF, 123:1 (2000),  88–93  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 123:1 (2000), 489–493  isi
28. N. N. Ganikhodzhaev, F. M. Mukhamedov, “Ergodic properties of quantum quadratic stochastic processes defined on von Neumann algebras”, Uspekhi Mat. Nauk, 53:6(324) (1998),  243–244  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:6 (1998), 1350–1351  isi  scopus

29. Sh. A. Ayupov, V. I. Chilin, R. N. Ganikhodzhaev, K. K. Muminov, A. Artikbaev, B. S. Zakirov, A. Alimov, K. K. Kudaybergenov, F. Mukhamedov, U. Bekboev, I. Rakhimov, “To the memory of Inomjon Gulomjonovich Ganiev”, Vladikavkaz. Mat. Zh., 20:1 (2018),  98–102  mathnet

Presentations in Math-Net.Ru
1. One pure quasi quantum quadratic operators
F. M. Mukhamedov
International conference "QP 34 – Quantum Probability and Related Topics"
September 17, 2013 14:30   

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