†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 NLC linac train-by-train feedback system is designed to stabilize the beam trajectory, but is also a valuable element in the strategy for emittance preservation. New simulations employ improved strategies [1], allowing beam steering to be performed significantly less often than without the feedback system. Additional simulations indicate that the linac feedback can contribute towards succes...

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...