01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
2.01.1975
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.
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.
Biography
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:
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
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
Mukhamedov, F. Akin H., Temir S., “On infinite dimensional
quadratic Volterra operators,”, Jour. Math. Anal. Appl., 310 (2005), 533-556
Fidaleo, F., Mukhamedov, F., “Strict weak mixing of some
$C^*$–dynamical systems based on free shifts,”, Jour. Math. Anal. Appl., 336 (2007), 18-187
F. M. Mukhamedov, M. M. Rahmatullaev, A. M. Tukhtabaev, R. Mamadjonov, “The $p$-adic Ising model in an external field on a Cayley tree: periodic Gibbs measures”, TMF, 216:2 (2023), 383–400; Theoret. and Math. Phys., 216:2 (2023), 1238–1253
F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the $\lambda$-model on the binary Cayley tree”, TMF, 210:3 (2022), 470–484; Theoret. and Math. Phys., 210:3 (2022), 411–424
Farrukh Mukhamedov, Hasan Akın, “Characterization of Bistochastic Kadison–Schwarz Operators on $M_2(\mathbb C)$”, Trudy Mat. Inst. Steklova, 313 (2021), 178–191; Proc. Steklov Inst. Math., 313 (2021), 165–177
2020
5.
F. M. Mukhamedov, O. N. Khakimov, “$p$-adic monomial equations and their perturbations”, Izv. RAN. Ser. Mat., 84:2 (2020), 152–165; Izv. Math., 84:2 (2020), 348–360
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; Theoret. and Math. Phys., 194:2 (2018), 260–273
F. Mukhamedov, “On the uniform zero-two law for positive contractions of Jordan algebras”, Eurasian Math. J., 8:4 (2017), 55–62
2016
10.
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; Math. Notes, 99:3 (2016), 480–483
11.
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; Theoret. and Math. Phys., 187:1 (2016), 583–602
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
2013
13.
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; Siberian Math. J., 54:3 (2013), 501–516
F. M. Mukhamedov, H. Akin, “The $p$-adic Potts model on the Cayley tree of order three”, TMF, 176:3 (2013), 513–528; Theoret. and Math. Phys., 176:3 (2013), 1267–1279
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; Math. Notes, 90:2 (2011), 162–174
F. Mukhamedov, “On the Existence of Generalized Gibbs Measures for the One-Dimensional $p$-adic Countable State Potts Model”, Trudy Mat. Inst. Steklova, 265 (2009), 177–188; Proc. Steklov Inst. Math., 265 (2009), 165–176
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; Izv. Math., 68:5 (2004), 1009–1024
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; Math. Notes, 76:3 (2004), 329–338
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; Sb. Math., 194:2 (2003), 237–250
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; Theoret. and Math. Phys., 130:3 (2002), 425–431
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; Theoret. and Math. Phys., 126:2 (2001), 169–174
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; Izv. Math., 64:5 (2000), 873–890
F. M. Mukhamedov, “On uniform ergodic theorems for quadratic processes on $C^*$-algebras”, Mat. Sb., 191:12 (2000), 141–152; Sb. Math., 191:12 (2000), 1891–1903
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; Theoret. and Math. Phys., 124:3 (2000), 1202–1210
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; Theoret. and Math. Phys., 123:1 (2000), 489–493
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; Russian Math. Surveys, 53:6 (1998), 1350–1351
U. Goginava, F. M. Mukhamedov, “From differential equations to difference equations”, Math. Ed., 2023, no. 3(107), 38–47
2018
34.
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
Full list of publications
