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.

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

This paper features the proposed modeling and design of a Robust Decentralized Periodic Output Feedback (RDPOF) control technique for the active vibration control of smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the E...