The Markov-Bernoulli geometric distribution is obtained when a generalization, as a Markov process, of the independent Bernoulli sequence of random variables is introduced by considering the success probability changes with respect to the Markov chain. The resulting model is called the MarkovBernoulli model and it has a wide variety of application fields. In this study, some characterizations a...

Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA...

As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two applications are provided here: i. an anti-concentration bound for a class of functions of independent random variables, where probabilistic bounds are extracted from ...

A measure-preserving endomorphism is one-sided Bernoulli if it is isomorphic to a noninvertible Bernoulli shift. We show that in piecewise smooth settings this property is very strong and far more subtle than the weak Bernoulli property, by extending of results of W. Parry and P. Walters and proving new results based on continuity of the Radon-Nikodym derivative. In particular, we provide tests...

We show that, for countable sofic groups, a Bernoulli action with infinite entropy base has infinite entropy with respect to every sofic approximation sequence. This builds on the work of Lewis Bowen in the case of finite entropy base and completes the computation of measure entropy for Bernoulli actions over countable sofic groups. One consequence is that such a Bernoulli action fails to have ...

Let (f, T n, μ) be a linear hyperbolic automorphism of the n-torus. We show that if A ⊂ T n has a boundary which is a finite union of C1 submanifolds which have no tangents in the stable (Es) or unstable (Eu) direction then the induced map on A, (fA, A, μA) is also Bernoulli. We show that Poincáre maps for uniformly transverse C1 Poincáre sections in smooth Bernoulli Anosov flows preserving a v...

A uniformly p to one endomorphism is a measure preserving map with entropy log p which is a.e. p to 1 and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is one sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite to one endomorphisms conjugate to this standard example by a condition on th...

This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering material Poisson’s ratio and flexoelectricity effects. The composite beam is composed of a regularly squared cut-out core with two piezoelectric face sheet layers. An analytical geometrical model adopted to obtain equivalent variables core. To capture effe...