Uychi, Uzbekistan
Uychi, Uzbekistan

Namangan State University is a fulcrum higher education institution among the three institutions, and it was established in 1942 as a pedagogical institute. It is located in Namangan province in eastern part of Uzbekistan. Today, 6306 undergraduate students and 153 graduate students are enrolled at the University. 36% of the University's 430 faculty members have PhD or other doctorate degrees. Namangan State University offers 26 bachelor's educational programs, 20 master's specialization programs, 13 programs for PhD, and 1 doctoral program. These programs are in languages, literature, social science, law, political science, history, philology, philosophy, pedagogy, education, early childhood education, sport, applied art, geography, economics, mathematics, physics, chemistry, and technical science. Wikipedia.


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Rozikov U.A.,Institute of Mathematics | Khakimov R.M.,Namangan State University
Theoretical and Mathematical Physics | Year: 2013

We study the Potts model on the Cayley tree. We demonstrate that for this model with a zero external field, periodic Gibbs measures on some invariant sets are translation invariant. Furthermore, we find the conditions under which the Potts model with a nonzero external field admits periodic Gibbs measures. © 2013 Pleiades Publishing, Ltd.


Kulske C.,Ruhr University Bochum | Rozikov U.A.,Institute of Mathematics | Khakimov R.M.,Namangan State University
Journal of Statistical Physics | Year: 2014

For the q-state Potts model on a Cayley tree of order k≥ 2 it is well-known that at sufficiently low temperatures there are at least q+1 translation-invariant Gibbs measures which are also tree-indexed Markov chains. Such measures are called translation-invariant splitting Gibbs measures (TISGMs). In this paper we find all TISGMs, and show in particular that at sufficiently low temperatures their number is 2q-1. We prove that there are [q/2] (where [a] is the integer part of a) critical temperatures at which the number of TISGMs changes and give the exact number of TISGMs for each intermediate temperature. For the binary tree we give explicit formulae for the critical temperatures and the possible TISGMs. While we show that these measures are never convex combinations of each other, the question which of these measures are extremals in the set of all Gibbs measures will be treated in future work. © 2014 Springer Science+Business Media New York.


Samatov B.T.,Namangan State University
Cybernetics and Systems Analysis | Year: 2013

The paper studies problems of group pursuit for differential games with integral constraints imposed on the controls of players such as the Pontryagin control example and a group pursuit with a simple motion for the case of l-catch. The problems are solved on the basis of Chikrii's method of resolving functions. A structure to construct the resolving function is proposed, which substantiates the parallel approach strategy, i.e., the Π-strategy for pursuers. New sufficient solvability conditions for problems of group pursuit are obtained. © 2013 Springer Science+Business Media New York.


Samatov B.T.,Namangan State University
Cybernetics and Systems Analysis | Year: 2013

The paper studies problems of group pursuit for linear differential games with integral constraints. The problems are analyzed on the basis of Chikrii's method of resolving functions. The proposed method substantiates the parallel approach strategy, i.e., the Π-strategy. The new sufficient solvability conditions are obtained for problems of group pursuit. As an example, two classes of problems are considered, namely, the Pontryagin control example and a group pursuit with a simple motion for the case of "l-catch." © 2013 Springer Science+Business Media New York.


Kodirkhonov M.R.,Namangan State University
Fibre Chemistry | Year: 2016

Chitin and chitosan with degree of deacetylation (DD) 57, 85, 89, and 90% were obtained as 250-μm microparticles. Their behavior with shear flow in aqueous and acidic solutions was studied. It was found that chitosan microparticles with various DD converted into gels as a result of swelling in water. Chitosan hydrogel particles with DD >85% were destroyed in shear flow without destroying the chains. The macromolecules were ordered in the direction of the flow. © 2016 Springer Science+Business Media New York


Samatov B.T.,Namangan State University
Automation and Remote Control | Year: 2013

We study the pursuit-evasion problem for a model game with simple motions when pursuer controls are subject to both integral and geometric constraints while evader controls are only subject to geometric ones. Depending on initial conditions of the players and parametric values participating in control constraints, we prove the theorem of alternative. To solve the pursuit problem, we propose a parallel pursuit strategy (Π-strategy) that ensures optimal convergence of the players and study its structure depending on the parameters. To solve the evasion problem, we find lower bounds on the convergence that also depend on given parameters. This work develops and extends the works of Isaacs, Petrosyan, Pshenichnyi and other researchers, including the author. © 2013 Pleiades Publishing, Ltd.


Khatamov N.M.,Namangan State University
Theoretical and Mathematical Physics | Year: 2014

We consider the Potts model with random competing interactions on a Cayley tree. We study the domain of ground states of this model. © 2014 Pleiades Publishing, Ltd.


Khakimov R.M.,Namangan State University
Theoretical and Mathematical Physics | Year: 2014

We study Potts and "solid-on-solid" models with q ≥ 2 states on the Cayley tree of order k ≥ 1. For any values of the parameter q in the Potts model and q ≤ 6 in the "solid-on-solid" model, we find sets containing all translation-invariant Gibbs measures. © 2014 Pleiades Publishing, Ltd.


Rozikov U.A.,National University of Uzbekistan | Khakimov R.M.,Namangan State University
Theoretical and Mathematical Physics | Year: 2012

We study the hard-core model on the Cayley tree. We show that this model admits only periodic Gibbs measures with the period two. We find sufficient conditions for all weakly periodic Gibbs measures to be translation invariant. © 2012 Pleiades Publishing, Ltd.


Rahmatullaev M.M.,Namangan State University
Applied Mathematics and Information Sciences | Year: 2010

Recently Rozikov studied an Ising model with competing interactions and spin values ±1, on a Cayley tree of order k ≥ 1 and described the ground states of the model. In this paper we describe some weak periodic ground states of the model. © 2010 Dixie W Publishing Corporation, U. S. A.

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