One of the most attractive problems in 1740s was a motion of a rotating tube around a fixed point and that of a small body included in it. Representative mechanicians in those days, such as Daniel Bernoulli, Alexis-Claude Clairaut, Leonhard Euler and Jean le Rond d’Alembert, tried to solve this problem. This problem was later applied to astronomical mechanics. It was posed by Euler for Johann B...

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

the vibration of cable-stayed bridges subjected to the passage of high-speed trains is studied in this article. the moving train includes a number of wagons, each of which is modeled as a four-axle system possessing 48 degrees of freedom. the car model is nonlinear and three-dimensional and includes nonlinear springs and dampers of primary and secondary suspensions, dry friction between differe...

Six approaches to the theory of Bernoulli polynomials are known; these are associated with the names of J. Bernoulli [2], L. Euler [4], E. Lucas [8], P. E. Appell [1], A. Hürwitz [6] and D. H. Lehmer [7]. In this note we deal with a new determinantal definition for Bernoulli polynomials recently proposed by F. Costabile [3]; in particular, we emphasize some consequent procedures for automatic c...

The main purpose of this article is to derive several convolutions for generalized Bernoulli and Euler–Genocchi polynomials order (r,m), Bn(r,m)(x) An(r,m)(x), respectively. These have been introduced recently contain the Bernoulli, Euler Genocchi as special members. Some our results extend M. Merca others concerning numbers polynomials. Probabilistic interpretations presented are also given.