The problem of computing the exact value of ∑ 1/n is so classical (dating back to 1644) that it even has a name of its own: the Basel problem. The city of Basel was the hometown both of the famous brothers Jakob and Johann Bernoulli, who made serious but unsuccessful attempts to solve the problem, and to the prodigious mathematician Leonhard Euler, who found the first solution in 1735, see [3]....

the accuracy and efficiency of the elements proposed by finite element method (fem) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. in the present study, novel functions, namely basic displacements functions (bdfs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava–Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

The Bernoulli polynomials have important applications in number theory and classical analysis. They appear in the integral representation of differentiable periodic functions since they are employed for approximating such functions in terms of polynomials. They are also used for representing the remainder term of the composite Euler-MacLaurin quadrature rule (see [15]). The Bernoulli numbers [3...

We consider the Cauchy problem for the Euler-Bernoulli equation of the vibrating beam and solve it in Gevrey classes under appropriate Levi conditions on the lower order terms.

Articles you may be interested in Direct measurement of shear properties of microfibers Rev. Noncontact quantitative spatial mapping of stress and flexural rigidity in thin membranes using a picosecond transient grating photoacoustic technique Displacement of droplets and deformation of thin liquid layers using flexural vibrations of structures. Influence of acoustic radiation pressure Flexural...

The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using Euler─Bernoulli model. study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clamped-simply supported nanotube. Using Bubnov─Galerkin Petrov─Galerkin methods, continuum model estimates load. main advantage these two approximate methods is to obtain ...

This paper is aimed at sharpen a weak invariance principle for stationary sequences in Doukhan & Louhichi (1999). Our assumption is both beyond mixing and the causal θ-weak dependence in Dedecker and Doukhan (2003); those authors obtained a sharp result which improves on an optimal one in Doukhan et alii (1995) under strong mixing. We prove this result and we also precise convergence rates unde...