A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented. © 2007 Elsevier Inc. All rights reserved.

We will give general sufficient conditions under which a controller achieves robust regulation for a boundary control and observation system. Utilizing these conditions we construct a minimal order robust controller for an arbitrary order impedance passive linear port-Hamiltonian system. The theoretical results are illustrated with a numerical example where we implement a controller for a one-d...

We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known ...

In order to extend the rail life and improve the firing accuracy, the electromagnetic launcher’s rail can be modeled as a beam on elastic foundation with simply supported beam by moving load. Euler beam theory is applied to build the Mechanical model and the analytical solution of the equation subjected to cosine magnetic pressure is derived in detail, which has successfully avoided the errors ...

The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol-Bernoulli...

The purpose of this paper is control of simply supported flexible core sandwich beam's linear vibration equipped with piezoelectric patches under different loads. The effects of external forces imposed on sandwich beam can be reached to a minimum value by designing an appropriate controller and control the beam's vibration. Three-layer sandwich beam theory is used for analytical modeling of san...

It is proposed to identify the behavior of steel beams prior to and after the inception of local buckling by using Digital Image Correlation. Full field measurements are used to evaluate kinematic and static fields for determining constitutive laws. It enables for the detection of local buckling inception and the evaluation of the postbuckled behavior. Constitutive models are tuned by using mea...

This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli’s functions and Bernoulli’s numbers, Euler...

Using a direct variational approach, we consider the existence of solutions and their dependence on a functional parameter for the elastic beam equation by means of investigating the critical points to the relevant Euler action functional.

In this thesis we consider sequences of non-negative integers which arise from counting the periodic points of a map T : X → X, where X is a non-empty set. Some of the main results obtained are concerned with the counting of the periodic points of an endomorphism of a group, in particular when the group is locally nilpotent, for which class of groups a local-global property is established. The ...