Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

Wojciech Szpankowskit Department of Computer Science Purdue University W. Lafayette, IN 47907 U.S.A. [email protected] In combinatorics and analysis of algorithms often a Poisson version of a problem (called further Poisson model or poissonization) is easier to solve than the original one, which we name here as the Bernoulli model. Poissonization is a technique that replaces the original input ...

We consider the discrete Hammersley-Aldous-Diaconis process (HAD) and the totally asymmetric simple exclusion process (TASEP) in Z. The basic coupling induces a multiclass process which is useful in discussing shock measures and other important properties of the processes. The invariant measures of the multiclass systems are the same for both processes, and can be constructed as the law of the ...

Abstract. The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iter...

Queueing network models have proven to be very useful in the analysis of communication systems. The departure process of a queue in a queueing network is of special interest because it is the arrival process to other queues in the network. For high speed networks, correlation and burstiness are very important factors for system performance and thus the smooth Bernoulli process is no longer a go...

The concepts of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the generalized Bernoulli numbers B n (a, b) are generalized to the one B n (x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B n , B n (x), B n (a, b), and B n (x; a, b, c) are established.

in this study, the bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. to this aim, the operational matrices of integration and the product for bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. some examples are presented to illustrate the efficien...