Mansoor Saburov

ON DYNAMICS OF ξS QUADRATIC STOCHASTIC OPERATORS

In this research we introduce a new class of quadratic stochastic operators called xs-QSO which nare defined through coefficient of the operator from measure-theoretic (namely we are looking the ncoefficient as the measures which are absolute continuous or singular) point of view. We also nstudy the limiting behaviour of xs -QSO defined on 2D-simplex. We first describe xi-s -QSO on 2Dsimplex nand classify them with respect to the conjugacy and renumeration of the coordinates. We nfind six non-isomorphic classes of such operators. Moreover, we investigate the behaviour of each noperator from three classes and prove convergence of trajectories of these classes and study their ncertain properties. We showed trajectories of two classes converge to the equilibrium. For the third nclass, it is established only the negative trajectories converge to the equilibrium.

Solvability criteria for cubic equations over Z2

Solvability criteria for cubic equations over the p -adic field, where > 3, were studied in previous works. For small primes p = 2,3, this problem was open. In this paper, we study this problem in the case p = 2. The case p = 3 would be studied elsewhere in the future.

The dynamics of the Potts-Bethe mapping over ℚ_p: the case p ≡ 2 (mod 3)

In this paper, we study the dynamics of the Potts-Bethe mapping associated with the p-adic q-state Potts model over the Cayley tree of order three. Namely, we establish the nregularity of the Potts-Bethe mapping for the case p = 2 (mod 3) with p > 5.

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

In this paper we introduce a new class of quadratic stochastic operators called sξ-QSO. We classify such operators on 2D-simplex, into six non-isomorphic classes, with respect to their conjugacy and renumeration of the coordinates.