28 citations · 134 across the 17 of their papers we have counts for
19 papers
Branching Gaps, Coexistence, and Boundary Influence for the Ising Model on Spherically Symmetric Trees
Farrukh Mukhamedov, Otabek Khakimov
In this paper, we study the ferromagnetic nearest-neighbor Ising model on rooted spherically symmetric trees with one or \(q\) children per vertex, according to a prescribed sequen…
Local Rota--Baxter operators of weight zero on nilpotent evolution algebras with maximal nilindex
Izzat Qaralleh, Farrukh Mukhamedov, Otabek Khakimov
Let be an -dimensional nilpotent evolution algebra of maximal nilindex over a field of characteristic zero. The Rota--Baxter operators of weights zero and one on such algebr…
Rota-Baxter operators of nilpotent evolution algebras with maximal nilindex
Izzat Qaralleh, Farrukh Mukhamedov, Otabek Khakimov
Nilpotent evolution algebras of maximal nilindex admit a natural basis in which the structure matrix is strictly upper triangular. In this paper we classify Rota{Baxter operators o…
p-adic dynamical systems for -adic -models on the Cayley trees
Farrukh Mukhamedov, Otabek Khakimov
We review and propose to use of associated dynamical system to explore the phase transition phenomena in -adic statistical mechanics setting, by means of the renormalization tec…
On of nilpotent evolution algebras
Farrukh Mukhamedov, Otabek Khakimov, Izzat Qaralleh
In the present paper, every evolution algebra is endowed with Banach algebra norm. This together with the description of derivations and automorphisms of nilpotent evolution algebr…
Projective surjectivity of quadratic stochastic operators and its application
Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong
A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov…
-adic monomial equations and their perturbation
Farrukh Mukhamedov, Otabek Khakimov
In this paper, we describe the set of all solutions of monomial equation over . Moreover, as an application of the result, we study several perturbations of th…
On omega limiting sets of infinite dimensional Volterra operators
Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong
In the present paper, we are aiming to study limiting behavior of infinite dimensional Volterra operators. We introduce two classes and $\tilde{\mathcal{V}…
Chaotic behavior of the -adic Potts-Bethe mapping II
Farrukh Mukhamedov, Otabek Khakimov
In our previous investigations, we have developed the renormalization group method to -adic -state Potts model on the Cayley tree of order . This method is closely related…
On a -Adic Generalized Gibbs Measure for Ising Model on a Cayley Tree
Muzaffar Rahmatullaev, Otabek Khakimov, Akbarxoja Tukhtaboev
In this paper we consider a -adic Ising model on the Cayley tree of order . We give full description of all -adic translation-invariant generalized Gibbs measures fo…
Positive solutions of nonlinear integral equations and surjectivity of Non-Linear Markov Operators On Infinite Dimensional Simplex
Farrukh Mukhamedov, Otabek Khakimov, Ahmad Fadillah Embong
In the present paper, we consider the solvability of positive solutions of nonlinear integral equations by means of investigating non-linear Markov operators. To solve the problem…
Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex
Farrukh Mukhamedov, Otabek Khakimov, Bakhrom Omirov +1
In this paper is devoted to nilpotent finite-dimensional evolution algebras E with . We described Lie algebras associated with evolution algebras whose nilindex is…
Gibbs measures and free energies of Ising-Vannimenus Model on the Cayley tree
Farrukh Mukhamedov, Hasan Akin, Otabek Khakimov
In this paper, we consider the Ising-Vannimenus model on a Cayley tree for order two with competing nearest-neighbor and prolonged next-nearest neighbor interactions. We stress tha…
Hypercyclic and supercyclic linear operators on non-Archimedean vector spaces
Farrukh Mukhamedov, Otabek Khakimov
A main objective of the present paper is to develop the theory of hypercyclicity and supercyclicity of linear operators on topological vector space over non-Archimedean valued fiel…
Chaotic behavior of the -adic Potts-Bethe mapping
Farrukh Mukhamedov, Otabek Khakimov
In our previous investigations, we have developed the renormalization group method to -adic models on Cayley trees, this method is closely related to the investigation of -ad…
On unconventional limit sets of contractive functions on
Farrukh Mukhamedov, Otabek Khakimov
In the present paper, we are going to study metric properties of unconventional limit set of a semigroup generated by contractive functions on the unit ball…
On -adic Ising-Vannimenus model on an arbitrary order Cayley tree
Farrukh Mukhamedov, Mansoor Saburov, Otabek Khakimov
In this paper, we continue an investigation of the -adic Ising-Vannimenus model on the Cayley tree of an arbitrary order ). We prove the existence of -adic quas…
Gibbs measures and free energies of the Ising-Vannimenus Model on the Cayley tree
Farrukh Mukhamedov, Hasan Akin
In this paper, we consider Ising-Vannimenus model on a Cayley tree for order two with competing nearest-neighbor, prolonged next-nearest neighbor interactions. We stress that the m…
Description of all translation-invariant -adic Gibbs measures for the Potts model on a Cayley tree
U. A. Rozikov, O. N. Khakimov
Recently it was proved that usual (real) Potts model on a Cayley tree has up to translation-invariant Gibbs measures. This paper is devoted to description of translation- i…