a single server queue with bernoulli vacation has been considered. in addition the admission to queue is based on a bernoulli process and the server gives two type of services. for this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. some performance measures are calculated. ...

†Bernoulli News is the of󰅳icial newsletter of the Bernoulli Society, publishing news, calendars of events, and opinion pieces of interest to Bernoulli Societymembers, aswell as to theMathematical Statistics andProbability community at large. The views and opinions expressed in editorials and opinion pieces do not necessarily re󰅳lect the of󰅳icial views of the Bernoulli Society, unless explicitly...

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Ber...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in 2005 , 2001 , respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the cl...

The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of 21 the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials 22 admit extensions to this new family. A specific expression involving the Bernoulli–Barnes 23 polynomials has recently appeared in the context of self-dual sequences. The work pre24 sented here provides a proof of t...

In this paper we discuss loosely Bernoulli for Zd actions. In particular, we prove that extensions of zero entropy, ergodic, loosely Bernoulli Zd actions are also loosely Bernoulli.

The mixture of Bernoulli distributions [6] is a technique that is frequently used for the modeling of binary random vectors. They differ from (restricted) Boltzmann Machines in that they do not model the marginal distribution over the binary data space X as a product of (conditional) Bernoulli distributions, but as a weighted sum of Bernoulli distributions. Despite the non-identifiability of th...