In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion form...

Christopher Martin Leslie Ball Jacqueline Archibald Lloyd Carson School of Computing & Engineering Systems School of Computing & Engineering Systems School of Computing & Engineering Systems School of Social & Health Sciences University of Abertay, Bell Street, Dundee University of Abertay, Bell Street, Dundee University of Abertay, Bell Street, Dundee University of Abertay, Bell Street, Dundee...

We establish an extension of Spivey’s Bell number formula and its associated Bell polynomial extension by using Hsu-Shiue’s generalized Stirling numbers. By means of the extension of Spivey’s Bell number formula we also extend Gould-Quaintance’s new Bell number formulas.

The paper presents an algorithm for automatic transcription of recordings of bell-playing clocks. Bell-playing clocks are clocks containing a hidden bell-playing mechanism that is periodically activated to play a melody. Clocks from the eighteenth century give us unique insight into the musical taste of their owners, so we are interested in studying their repertoire and performances thus the ne...

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

Abstract This study investigates bell-bearing structures and their historical context in Cyprus. The aim is to shed light on when which ways bells were introduced into Greek religious practice the island, taking account that they are often a sign of cultural exchange between Latins Greeks other areas Mediterranean. shall be achieved through focus material evidence preserved from mainly building...

We provide an analytical expression for optimal Lewenstein-Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the KarushKuhn-Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of sep...