We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

@ARTICLE{HeniklAT2012, author={J. Henikl and J. Schr\"ock and T. Meurer and A. Kugi}, title={{Infinit-dimensionaler Reglerentwurf f\"ur Euler-Bernoulli Balken mit Macro-Fibre Composite Aktoren}}, journal={at -Automatisierungstechnik}, year={2012}, volume={60}, number={1}, pages={10--19}, doi = {10.1524/auto.2012.0967}, url = {http://www.degruyter.com/view/j/auto.2012.60.issue-1/auto.2012.0967/a...

The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature meth...

the complete 3d nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. for describing the dynamics of the system, the newtonian derivation procedure is followed. the velocity field inside the pipe formulated using hydrostatic and bernoulli equations. the hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

Absorbing boundary conditions are generally associated to long-range memory behaviors. In the case of the Euler-Bernoulli beam, they are naturally based on Abel-Volterra operators of order 1/2. Diiusive real-izations of them are introduced and used for the construction of an original and eecient boundary dynamic feedback control.

We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.

We consider an optimal control problem with indeenite cost for an abstract model which covers in particular hyperbolic and hyperbolic-like systems in a general bounded domain. Necessary and suucient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory also extends a nite-dimensional...