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.

corrective feedback (cf) and its different types have long absorbed many scholars and practitioners. as ellis (2009) mentioned some experimental studies need to be carefully designed to discover the relative effectiveness of each of these cf techniques. the goal of this qualitative study was to discover whether the employment of different cf strategies could bring about an attitudinal shift. to...

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.

In this work we provide a new short proof of Carlitz’s identity for the Bernoulli numbers. Our approach is based on the ordinary generating function for the Bernoulli numbers and a Grassmann-Berezin integral representation of the Bernoulli numbers in the context of the Zeon algebra, which comprises an associative and commutative algebra with nilpotent generators.