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 ...

We study the stability of an interconnected system of Euler−Bernoulli beam and heat equation with boundary coupling, where the boundary temperature of the heat equation is fed as the boundary moment of the Euler−Bernoulli beam and, in turn, the boundary angular velocity of the Euler−Bernoulli beam is fed into the boundary heat flux of the heat equation. We show that the spectrum of the closed-l...

In these lectures I shall present some of the ideas and methods used in the proof of the celebrated theorem stating that two Bernoulli schemes are isomorphic if and only if they have the same entropy. I shall concentrate, because of lack of time, on a well known partial result, Sinai's theorem, which states that two Bernoulli schemes are weakly isomorphic if and only if they have the same entro...

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves discontinuous, and even distributional, coefficients and right-hand side. The general problem is solved by application of functional analytic techniques to obt...

In this article we prove some relations between two-variable q-Bernoulli polynomials and two-variable q-Euler polynomials. By using the equality eq (z)Eq (−z) = 1, we give an identity for the two-variable qGenocchi polynomials. Also, we obtain an identity for the two-variable q-Bernoulli polynomials. Furthermore, we prove two theorems which are analogues of the q-extension Srivastava-Pinter add...

Free vibration analysis of higher-order shear deformation beam resting on one- and two-parameter elasticfoundation is studied using differential transform method (DTM) as a part of a calculation procedure. First,the governing differential equations of beam are derived in a general form considering the shear-freeboundary conditions (zero shear stress conditions at the top and bottom of a beam). ...

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...

An investigation of the beam-beam interaction as a function of transverse separation of colliding proton and antiproton bunches is presented. A mathematical model describing resonant excitation of separated beams is examined. Beam-beam experiments in the Fermilab collider measure beam-beam resonant excitation ~particle losses! at different transverse beam separations in the storage ring. The ex...

We present a construction of an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of T d (the ‘harmonic model’). A similar map is constructed for the dissipative abelian sandpile model and is used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model.

The car sequencing problem seeks a production sequence of different car models launched down a mixed-model assembly line. The models can be distinguished by selected options, e.g., sun roof yes/no. For every option, car sequencing applies a so-called sequencing rule to avoid that consecutive models requiring this option lead to a work overload of the respective assembly operators. The aim is to...