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.
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
