Seyit Temir

On infinite dimensional quadratic Volterra operators

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators for which their trajectories do not converge. Finally, we define a compatible sequence of finite dimensional Volterra operators and prove that any power of this sequence converges in weak topology.

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.

On extreme Gibbs measures of the Vannimenus model

One of the main problems of statistical physics is that of describing 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 paper is to investigate extreme Gibbs measures of the Vannimenus model.

Convergence theorems by a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in Banach spaces

In this paper, we study a new iteration process for a finite family of nonself asymptotically nonexpansive mappings with errors in Banach spaces. We prove some weak and strong convergence theorems for this new iteration process. The results of this paper improve and extend the corresponding results of Chidume et al. (2003) [10], Osilike and Aniagbosor (2000) [3], Schu (1991) [4], Takahashi and Kim (1998) [9], Tian et al. (2007) [18], Wang (2006) [11], Yang (2007) [17] and others.

On phase transitions of the Potts model with three competing interactions on Cayley tree

In the present paper we study a phase transition problem for the Potts model with three competing interactions, the nearest neighbors, the second neighbors and triples of neighbors and non-zero external field on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing by limiting Gibbs measures to the problem of solving a system of nonlinear functional equations. We extend the results obtained by Ganikhodjaev and Rozikov [Math. Phys. Anal. Geom., 2009, 12, No. 2, 141‐156] on phase transition for the Ising model to the Potts model setting.

A note on dominant contractions of Jordan algebras

In the paper we consider two positive contractions

Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order

T,S:L^{1}(A,\tau)\longrightarrow L^{1}(A,\tau)

Periodic extreme Gibbs measures with memory length 2 of Vannimenus model

such that

Strange Attractors in the Vannimenus Model on an Arbitrary Order Cayley Tree

T\leq S

Modulated Phase of an Ising System with Competing Interactions on a Cayley Tree of Arbitrary Order

, here