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

It is well known that on the one dimensional space, any bounded monotone increasing or monotone decreasing sequence converges to a unique limiting point. In order to generalize this result into the higher dimensional space, we should consider an appropriate order (or pre-order). A Majorization is a partial ordering on vectors which determines the d

In this paper, a design of a quad-wavelength fiber laser (QWFL) operating in two different regions namely the O-band covering from 1302 nm to1317.4 nm and C-band from 1530.5 nm to 1548.0 nm is presented. Two different ASE sources from semiconductor optical amplifiers (SOAs) are used, one at 1310 nm and the other at1550 nm. By using a 1×24 channels

In this paper, a simple design of linear cavity dualwavelength fiber laser (DWFL) is proposed. Operating in the Cband region stretching from 1538.3 nm to 1548.6 nm, an arrayed waveguide grating (AWG) is used to generate the dualwavelengths output together with a broadband fiber Bragg grating as a back reflector and an optical circulator with a 10%

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

This study aims at highlighting the experience of Islamic Banking Industry in Thailand in terms of the history, development, and its role in serving the community as well and the Muslim minority. The study also aims at identifying the Law of the Islamic Bank in Thailand, whether it is relevant to what is being applied in the reality. Finally, some

The discrete-time approach to real option valuation has typically been implemented in the finance literature using a binomial tree framework. Instead we develop a new model by randomizing the environment and call such model a random binomial tree. Whereas the usual model has only one environment (u, d) where the price of underlying asset can move b

Warning alerts are specially designed to protect user rights and safety to avoid serious damage caused by overlooking the essence of warning alerts. Today’s world of Information Communication Technology (ICT) needs improvement and to review the decisions of security experts in terms of improving warning designs and dialogues, and timely inform th

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.On classification of associative non-division genetic algebras Nasir Ganikhodjaev and Gavha

One of the simplest unsolved problems in the theory of nonlinear dynamical systems is to study asymptotic behaviors of quadratic stochastic operators (in short QSO) on the finite dimensional simplex. However, this problem is not fully finished even in 2D case. The reason is that, in such systems, we may observe some chaotic behaviors (more precisel