Nasir Ganikhodjaev
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Nasir Ganikhodjaev has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Hasan Akin
Harran University
3 shared publications - Uygun U. Jamilov
V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
3 shared publications - Selman Uğuz
Harran University
2 shared publications - Seyit Temir
Harran University
2 shared publications - Utkir Abdulloyevich Rozikov
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
2 shared publications - Chin Hee Pah
Department of Computational and Theoretical Sciences Faculty of Science IIUM Kuantan Malaysia
1 shared publication
Latest Publications
- 31 March 2017
- Published by The Korean Mathematical Society in Bulletin of the Korean Mathematical Society
- Vol. 54 (2) , 607-618
ON LEBESGUE NONLINEAR TRANSFORMATIONS
- 31 March 2017
- Published by The Korean Mathematical Society in Bulletin of the Korean Mathematical Society
- Vol. 54 (2) , 607-618
ON LEBESGUE NONLINEAR TRANSFORMATIONS
- Open Access
On the Lebesgue nonlinear transformations
In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0,1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators
Open AccessOn the Lebesgue nonlinear transformations
In this paper, we introduce a quadratic stochastic operators on the set of all probability measures of a measurable space. We study the dynamics of the Lebesgue quadratic stochastic operator on the set of all Lebesgue measures of the set [0,1]. Namely, we prove the regularity of the Lebesgue quadratic stochastic operators
- 20 June 2014
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 35 (5) , 1443-1473
Quadratic stochastic operators and zero-sum game dynamics
In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex $S^{4}$ and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-paper-scissors game if either the Volterra operator is a uniform operator or for a non-uniform Volterra operator $V$ there exists a subset $I\subset \{1,2,3,4,5\}$ with $|I|\leq 2$ such that $\sum _{i\in I}(V^{n}\mathbf{x})_{i}\rightarrow 0,$ and the restriction of $V$ on an invariant face ${\rm\Gamma}_{I}=\{\mathbf{x}\in S^{m-1}:x_{i}=0,i\in I\}$ is a uniform Volterra operator.- 20 June 2014
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 35 (5) , 1443-1473
Quadratic stochastic operators and zero-sum game dynamics
In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex $S^{4}$ and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-paper-scissors game if either the Volterra operator is a uniform operator or for a non-uniform Volterra operator $V$ there exists a subset $I\subset \{1,2,3,4,5\}$ with $|I|\leq 2$ such that $\sum _{i\in I}(V^{n}\mathbf{x})_{i}\rightarrow 0,$ and the restriction of $V$ on an invariant face ${\rm\Gamma}_{I}=\{\mathbf{x}\in S^{m-1}:x_{i}=0,i\in I\}$ is a uniform Volterra operator.- Open Access
Hamiltonian Cycle on the Set of Genotypes and Non-Ergodic Quadratic Stochastic Operators
On the set of genotypes $\Phi=\{1,...,m\}$ we introduce a binary relation generated by Volterra quadratic stochastic operator $V$ on $(m-1)$ dimensional simplex $S^{m-1}$ and prove that the operator $V$ be non-ergodic if either there exists a Hamiltonian cycle or one of the vertices $M_i=(\delta_{1i},\delta_{2i},...,\delta_{mi})$ of the simplex $S^{m-1}$ is a source and restriction of $V$ to the invariant face $F_i=\{x\in S^{m-1}: x_i=0\}$ is non-ergodic. In this paper we prove this result for $m=2,3,4.$Open AccessHamiltonian Cycle on the Set of Genotypes and Non-Ergodic Quadratic Stochastic Operators
On the set of genotypes $\Phi=\{1,...,m\}$ we introduce a binary relation generated by Volterra quadratic stochastic operator $V$ on $(m-1)$ dimensional simplex $S^{m-1}$ and prove that the operator $V$ be non-ergodic if either there exists a Hamiltonian cycle or one of the vertices $M_i=(\delta_{1i},\delta_{2i},...,\delta_{mi})$ of the simplex $S^{m-1}$ is a source and restriction of $V$ to the invariant face $F_i=\{x\in S^{m-1}: x_i=0\}$ is non-ergodic. In this paper we prove this result for $m=2,3,4.$ - Open Access
Contracting Quadratic Operators of Bisexual Population
In this paper we find a sufficient condition under which the operator of bisexual population is contraction and show that this condition is not necessary.
Open AccessContracting Quadratic Operators of Bisexual Population
In this paper we find a sufficient condition under which the operator of bisexual population is contraction and show that this condition is not necessary.
- 14 June 2011
- Published by Taylor & Francis in Phase Transitions
- Vol. 84 (11-12) , 1045-1063
Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions
One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.
- 14 June 2011
- Published by Taylor & Francis in Phase Transitions
- Vol. 84 (11-12) , 1045-1063
Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions
One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.
- 1 March 2011
- Published by IOP Publishing in Journal of Statistical Mechanics: Theory and Experiment
- Vol. 2011 (03) , P03025
On extreme Gibbs measures of the Vannimenus model
- 1 March 2011
- Published by IOP Publishing in Journal of Statistical Mechanics: Theory and Experiment
- Vol. 2011 (03) , P03025
On extreme Gibbs measures of the Vannimenus model
- 12 November 2009
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 137 (4) , 701-715
Modulated Phase of a Potts Model with Competing Binary Interactions on a Cayley Tree
- 12 November 2009
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 137 (4) , 701-715
Modulated Phase of a Potts Model with Competing Binary Interactions on a Cayley Tree
- 17 July 2009
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 13 (1) , 1-18
Griffith–Kelly–Sherman Correlation Inequalities for Generalized Potts Model
- 17 July 2009
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 13 (1) , 1-18
Griffith–Kelly–Sherman Correlation Inequalities for Generalized Potts Model
- 10 February 2009
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 12 (2) , 141-156
On Ising Model with Four Competing Interactions on Cayley Tree
- 10 February 2009
- Published by Springer Nature in Mathematical Physics, Analysis and Geometry
- Vol. 12 (2) , 141-156
On Ising Model with Four Competing Interactions on Cayley Tree