* Correspondence: [email protected] Department of Mathematics, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, South Korea Full list of author information is available at the end of the article Abstract The q-analogues of many well known formulas are derived by using several results of q-Bernoulli, q-Euler numbers and polynomials. The q-analogues of ζ-type functions are given by usi...

By the past two decades IPMCs have been intensively studied because of their special capabilities for actuation and sensing.This paper presents a theoretical physics based model for analyzing the behavior of IPMC sensors in fluid environments. The mechanical vibration of the IPMC strip is described by the classical Euler–Bernoulli beam theory. The model also takes in to account the physical pro...

The dynamic response of the railway under accelerated moving load using Dynamic Green Function is presented in this paper. For this purpose, an exact and direct modeling technique is introduced for the railway modeling as the damped Euler-Bernoulli beam on the partial Winkler foundation with arbitrary boundary conditions subjected to the moving load. The effects of the elastic coefficient of Wi...

in this paper, surface and piezoelectric effects on the vibration behavior of nanowires (nws) are investigated by using a timoshenko beam model. the electric field equations and the governing equations of motion for the piezoelectric nws are derived with the consideration of surface effects. by the exact solution of the governing equations, an expression for the natural frequencies of nws with ...

We connect and generalize Matiyasevich’s identity #0102 with Bernoulli numbers and an identity of Candelpergher, Coppo and Delabaere on Ramanujan summation of the divergent series of the infinite sum of the harmonic numbers. The formulae are analytic continuation of Euler sums and lead to new recursion relations for derivatives of Bernoulli numbers. The techniques used are contour integration, ...

We use contour integrals and the Cauchy residue theorem in order to derive several summation formulas, in terms of the higher-order Bernoulli polynomials and the ordinary Bernoulli and Euler polynomials, for a remarkably general family of secant sums. Numerous (known or new) special cases are shown to follow readily from the summation formulas presented in this paper. 2007 Elsevier Inc. All rig...

The earliest example of bifurcation is the buckling of of an elastic beam. In engineering, buckling is a failure mode characterized by a sudden failure of a structure subjected to high compressive stresses, where the actual compressive stresses at failure are greater than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as fa...

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.