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
A. G. Bagdasaryan, A. Kalampakas, M. Kh. Saburov, “Dynamics of replicator equations on Wardrop optimal networks”, Russian Math. Surveys, 79:1 (2024), 176–178
2.
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
3.
M. Saburov, “Stable and historic behavior in replicator equations given by nonlinear mappings”, Russian Math. Surveys, 78:2 (2023), 387–389
4.
Math. Notes, 114:6 (2023), 1488–1493
5.
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
6.
Math. Notes, 112:2 (2022), 332–336
7.
Math. Notes, 106:1 (2019), 142–145
8.
M. Kh. Saburov, “Dichotomy of Iterated Means for Nonlinear Operators”, Funct. Anal. Appl., 52:1 (2018), 74–76
9.
Math. Notes, 103:2 (2018), 328–333
10.
M. Saburov, “A note on surjective polynomial operators”, Vladikavk. matem. zhurn., 19:4 (2017), 70–75
11.
M. Saburov, N. A. Yusof, “$\mathbf{p}-$majorizing quadratic stochastic operators”, Theory Stoch. Process., 22(38):1 (2017), 81–88
12.
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
13.
M. Kh. Saburov, “On the Surjectivity of Quadratic Stochastic Operators Acting on the Simplex”, Math. Notes, 99:4 (2016), 623–627
14.
M. Kh. Saburov, Mat. Zametki, 100:4 (2016) (to appear)
15.
Math. Notes, 97:5 (2015), 759–763
16.
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
17.
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
18.
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;
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