Using a differential geometric treatment, we analytically derived the expression for De Sitter geodesic precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild’s metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O’Connell 1970, 1975 in a different sett...

@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...

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...

This paper features the modeling and design of a Robust Decentralized Fast Output Sampling (RDFOS) Feedback control technique for the active vibration control of a smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Eul...

We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a 1751-paper and 1734-letter to Daniel Bernoulli. The corresponding q-analogue of the dilogarithm is introduced. The relation to the values at 1 and 2 of a q-analogue o...

The main purpose of this paper is to derive various Matiyasevich-Miki-Gessel type convolution identities for Bernoulli and Genocchi polynomials and numbers by applying some Euler type identities with two parameters.

This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal elasticity theory. The nano-beam is sandwiched with two piezoelectric layers through it’s upper and lower sides. The electromechanical coupled equations governing the problem are derived based nonlocal theory considering to Euler-Bernoulli beam assumptions and based on the nonlocal piezoelectricity acco...

A triangular model base on an investigation which has done by Sinha et al. has been developed for evaluating embedded crack localization in beam-column structures. In the assessment of this member’s behavior, the effects of displacement slope are necessary. In order to propose a crack localization method for embedded crack, an efficient static data based indicator is proposed for this crack in ...