We consider an Ising model on a Cayley tree with competing interactions of the next-nearest-neighbours of two types: prolonged and one-level interactions only. More recently, Ganikhodjaev and Zakaria investigated the same model and proved that its phase diagram contain only four phases, namely, ferromagnetic, paramagnetic, antiferromagnetic and ant

In this paper, we consider an Ising model with three competing interactions (nearest neighbor, next-nearest neighbor, and ternary prolonged neighbor) on the Cayley tree of order two, investigated by Ganikhodjaev et al. We study translation-invariant Gibbs measures of the Ising model with these competing interactions. Also, we investigate the set of

We study the phase diagram of the Blume-Emery-Griffiths-Vannimenus model on a Cayley tree with competing nearest-neighbour couplings and next-nearest-neighbour couplings and show that a detailed study of its properties can be carried out with essentially exact results, using rather simple numerical methods. In addition to the expected paramagnetic

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, (1 ).nnXX−World Applied Sciences Journal 21 (Mathematical Applications in Engineering): 84-87, 2013 ISSN 1818-4952 © IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.21.mae.99927 Corresponding Author: K. Bayram, Department of Computational and Theoretical Sciences, International Islamic University Malaysia, Jalan Istana, Bandar Indera Mah

A blood group provides an ideal opportunity for the study of human variation without cultural prejudice. It can be easily classified for many different genetically inherited blood typing systems. Also significant is the fact that we rarely take blood types into consideration in selecting mates. A few people know their own type today and no one did

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral

We consider simple version of the Blume-Emery-Griffiths model on the Cayley tree and investigate the problem of phase transition using the exact recursion equations for the Cayley tree of second order, so that every spin has three nearest neighbours. These equations are studied analytical-ly for D>0 and J>0. It is proved that one can reach

In general, the algebras which arise in genetics are non-division algebra. In this paper we describe genetic significance of non-invertible elements, present a construction of non-division genetic algebras, and investigate the problem of their classification.

We study the phase diagrams for the Potts model with restricted competing nearest-neighbor interactions J1 and ternary interactions Jpt on a Cayley tree of arbitrary order k. At vanishing temperature, the phase diagram is fully determined for all values and signs of Jpt/J1 and T/J1. The phase diagrams are obtained from stability conditions, and cha