Kalikow (1982) proved that the [T, T−1] transformation is not isomorphic to a Bernoulli shift. We show that the scenery factor of the [T,T−1] transformation is not isomorphic to a Bernoulli shift. Moreover, we show that it is not Kakutani equivalent to a Bernoulli shift.

A special attention is paid to the motion of flexible links in a robotic configuration. The elastic deformation is a dynamic value which depends on the total dynamics of the robot system movements. The Euler-Bernoulli equation should be expanded according to the requirements of the motion complexity of elastic robotic systems. The EulerBernoulli equation (based on the existing laws of dynamics)...

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz’s type qBernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz’s type q-zeta functions which interpolate multiple twisted Carlitz’s type q-Euler (Bernoulli) polynomials?” The aim of this paper is to give a part...

We prove that if G is a countable, discrete group having infinite, normal subgroups with the relative property (T), then the Bernoulli shift action ofG on Π g∈G (X0, μ0)g for (X0, μ0) an arbitrary probability space, has first cohomology group isomorphic to the character group of G.

x∈Λ px where px are prescribed and uniformly bounded above and below away from 0 and 1. Poincare inequalities are proved for the Glauber and Kawasaki dynamics, with constants of the same order as in the homogeneous case. 1. Inhomogeneous Bernoulli measures. Let hx ∈ [−K,K], x ∈ ZZ d be given and let px = ex 1 + ehx , x ∈ ZZ . For any Λ ⊂ ZZ d the inhomogeneous Bernoulli measure μΛ(η) on {0, 1} ...

and Applied Analysis 3 see 3, 4, 15, 16 . By 1.5 and 1.7 , the Witt’s formula for the q-Bernoulli numbers with weight α is given by ∫ Zp x qαdμq x β̃ α n,q , where n ∈ Z . 1.8 The q-Bernoulli polynomials with weight α are also defined by

In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on MX , where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ ↪→MX has almost invariant sets.

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

We consider initial and boundary value problems modelling the vibrations of a plate with piezoelectric actuator. The simplest model leads to the Bernoulli-Euler plate equation with right hand side given by a distribution concentrated in an interior curve multiplied by a real valued time function representing the voltage applied to the actuator. We prove that, generically with respect to the cur...