Generalizing a result of Furstenberg, we show that for every infinite discrete group $G$, the Bernoulli flow $2^G$ is disjoint from minimal $G$-flow. From this, deduce algebra generated by functions $\mathfrak{A}(G)$ proper subalgebra $\ell^\infty(G)$ and enveloping semigroup universal $M(G)$ quotient $\beta G$. When $G$ countable, also prove any metrizable, $G$-flow, there exists free, it exis...

In particular, the values at x = 0 are called Bernoulli numbers of order k, that is, Bn (0) = Bn k) (see [1, 2, 4, 5, 9, 10, 14]). When k = 1, the polynomials or numbers are called ordinary. The polynomials Bn (x) and numbers Bn were first defined and studied by Norlund [9]. Also Carlitz [2] and others investigated their properties. Recently they have been studied by Adelberg [1], Howard [5], a...

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

This paper analyses a discrete-time (s, S) queueing inventory model with service time and back-order in inventory. The arrival of customers is assumed to be the Bernoulli process. Service follows geometric distribution. As soon as level reaches pre-assigned due demands, an order for replenishment placed. Replenishment also When reduces zero or non-replenishment items, maximum k are allowed syst...

Previous work showed that every pair of nontrivial Bernoulli shifts over a fixed free group are orbit equivalent. In this paper, we prove that if G 1 , G 2 are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over G 1 is stably orbit equivalent to every nontrivial Bernoulli shift over G 2. This answers a question of S. Popa.

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.

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.