We consider a Potts model on a Bethe lattice with competing nearest-neighbour J and next-nearest-neighbour interactions Jp. The phase diagram of this model was studied by Ganikhodjaev et al. In this paper we investigate the problem of phase transition for the considered model and show that for some parameter values of the model there is phase trans

In this paper we consider a set of all extremal Volterra quadratic stochastic operators on three dimensional simplex S3, show that this set is parted into four equivalence classes with respect to group of transformations generated by permutations and describe the behaviour of trajectories extremal Volterra quadratic stochastic operators for each cl

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

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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

3,5,4′-Trihydroxy-6,7-dimethoxy-flavone (Eupalitin) has been isolated from the leaves of Asparagus falcatus (Linn.). Anti-proliferation and apoptosis studies were conducted on eupalitin. Results showed that eupalitin exhibited significant cytotoxicity against human colorectal tumor cells. It is found that eupalitin induces the activation of caspa

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, we attempt to provide mathematical models of Mendelian and Non-Mendelian inheritances of the bisexual population system having Fisher’s 1:1 principle. In our model, we always assume that distributions of the same phenotype of female and male populations are equal. We study the evolution of a Mendelian trait. As an application of a

Islamic science has a glorious past and it successfully contributes to the development of modern science. The emergence, developments and accomplishments of Islamic scientific trend are traced back to the advent of Islamic era when human mind had been radically reformed, and transformed from its irrational and superstitious tendency into a scientif

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