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We describe generalized translation-invariant -adic Gibbs measures for the Potts model on the Cayley tree of order three, confirming and extending the related results in the literature. We introduce a cube root function over the -adic field , which enables us to explicitly prescribe all roots of the cubic monomial equation over . [ABSTRACT FROM AUTHOR]

In this paper, we provide counterexamples to Ganikhodjaev's conjecture on mean ergodicity of quadratic stochastic operators acting on the finite dimensional simplex. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of periodic one-dimensional cellular automata of period-2 and study different properties of such kind of cellular automata. Moreover, we shall introduce an A- cellular automata which is not shift commuting of any power. We calculate entropy of some periodic cellular automata with period two and present simulation for some fractal type periodic cellular automata. [ABSTRACT FROM AUTHOR]

A vector majorization is a preorder of dispersion for vectors with the same length and same sum of components. The vector majorization can be viewed as a preorder of distance from a uniform vector. A preorder of distance from any fixed non-uniform vector of positive components, so-called r-majorization, is a generalization of usual vector majorization. In this paper, a new class of mappings so-called r-majorizing quadratic stochastic operators was introduced. The r-majorizing quadratic stochastic operator is a generalization of a quadratic doubly stochastic operator. Some relevant examples are provided. Moreover, the dynamics of some non-scrambling r-majorizing quadratic stochastic operators are studied. [ABSTRACT FROM AUTHOR]

Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p-adic number fields Qp, say p = 17, 41, ⋯. Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p-adic number fields Qp. In this paper, we provide solvability criteria for the bi-quadratic equation x4 + ax² = b over domains Z*p, Zp \ Z*p, Qp \ Zp, Qp, where p > 2. Moreover, we also provide the number of roots of the bi-quadratic equation over the mentioned domains. [ABSTRACT FROM AUTHOR]

We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models.