Constructions of forward and backward quantum Markov chains over the Cayley tree of any order; Investigations of existences of forward and backward quantum Markov chains associated with quantum models; Detections of the uniqueness of the quantum Markov chains and an existence of quantum phase transitions; Observations of quantum phase transitions which is not exhibiting at zero temperature; Studying fixed point theorems for different types of iterative schemes on Banach space; Investigation of the stability of nonlinear stochastic operators acting on the finite dimensional simplex; Descriptions of all extreme points of the set of quadratic doubly stochastic operators (Birkhoff's problem); Providing criteria for the solvability of polynomial equations over p-adic field.
Biography
B. Sc. — Faculty of Mathematics, National University of Uzbekistan (2001/2005);
M. Sc. — Faculty of Mathematics, National University of Uzbekistan (2005/2007);
R. A. — Faculty of Mathematics, National University of Uzbekistan (2007/2009);
Ph. D. — Faculty of Science, International Islamic University Malaysia (2009/2011).
Main publications:
Ganikhodzhaev R.N., Saburov M., “A Generalized Model of Nonlinear Operators of Volterra Type and Lyapunov Functions”, J. Sib. Fed. Univ. Math. Phys., 1:2 (2008), 188–196
Mukhamedov F., Saburov M., “Strong Convergence of an Explicit Iteration Process for a Totally Asymptotically I-Non-expansive mapping in Banach Space”, Appl. Math. Lett., 23 (2010), 143–147
Mukhamedov F., Saburov M., “On Homotopy of Volterrian quadratic stochastic operators”, Appl. Math. Inf. Sci., 4:1 (2010), 47–62
Accardi L., Mukhamedov F., Saburov M., “Uniqueness of quantum Markov chains on the Cayley tree of order two associated with XY–model”, Mathematical Notice, 90:2 (2011), 168–182
Accardi L., Mukhamedov F., Saburov M., “On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three”, Annales Henri Poincaré, 12:6 (2011), 1109–1144
M. Kh. Saburov, Kh. Kh. Saburov, “Krause Mean Processes Generated by Cubic Stochastic Matrices II: Off-Diagonally Positive Cubic Stochastic Matrices”, Mat. Sb. (to appear)
2024
2.
A. G. Bagdasaryan, A. Kalampakas, M. Kh. Saburov, “Dynamics of replicator equations on Wardrop optimal networks”, Russian Math. Surveys, 79:1 (2024), 176–178
2023
3.
M. Alp, Ch. X. Pakh, M. Kh. Saburov, “Opisanie obobschennykh translyatsionno-invariantnykh $p$-adicheskikh mer Gibbsa dlya modeli Pottsa na dereve Keli poryadka tri”, TMF, 214:3 (2023), 469–485;
4.
M. Saburov, “Stable and historic behavior in replicator equations given by nonlinear mappings”, Russian Math. Surveys, 78:2 (2023), 387–389
5.
Math. Notes, 114:6 (2023), 1488–1493
2022
6.
M. Saburov, Kh. Saburov, “Applications of quadratic stochastic operators to nonlinear consensus problems”, Science — Technology — Education — Mathematics — Medicine, CMFD, 68, no. 1, PFUR, M., 2022, 110–126
7.
Math. Notes, 112:2 (2022), 332–336
2019
8.
Math. Notes, 106:1 (2019), 142–145
2018
9.
M. Kh. Saburov, “Dichotomy of Iterated Means for Nonlinear Operators”, Funct. Anal. Appl., 52:1 (2018), 74–76
10.
Math. Notes, 103:2 (2018), 328–333
2017
11.
M. Saburov, “A note on surjective polynomial operators”, Vladikavk. matem. zhurn., 19:4 (2017), 70–75
12.
M. Saburov, N. A. Yusof, “$\mathbf{p}-$majorizing quadratic stochastic operators”, Theory Stoch. Process., 22(38):1 (2017), 81–88
2016
13.
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”, Theoret. and Math. Phys., 187:1 (2016), 583–602
14.
M. Kh. Saburov, “On the Surjectivity of Quadratic Stochastic Operators Acting on the Simplex”, Math. Notes, 99:4 (2016), 623–627
15.
M. Kh. Saburov, Mat. Zametki, 100:4 (2016) (to appear)
2015
16.
Math. Notes, 97:5 (2015), 759–763
2013
17.
F. M. Mukhamedov, B. A. Omirov, M. Kh. Saburov, K. K. Masutova, “Solvability of cubic equations in $p$-adic integers ($p>3$)”, Siberian Math. J., 54:3 (2013), 501–516
2011
18.
L. Accardi, F. M. Mukhamedov, M. Kh. Saburov, “Uniqueness of Quantum Markov Chains Associated with an $XY$-Model on a Cayley Tree of Order $2$”, Math. Notes, 90:2 (2011), 162–174
2008
19.
Rasul N. Ganikhodzhaev, Mansur Kh. Saburov, “Obobschennaya model nelineinykh operatorov volterrovskogo tipa i funktsii Lyapunova”, Zhurn. SFU. Ser. Matem. i fiz., 1:2 (2008), 188–196
2024
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