The boundary problem is considered for inhomogeneous increasing random walks on the square lattice Z2+ with weighted edges. Explicit solutions are given for some instances related to the classical and generalized number triangles.

We prove that if a countable discrete group Γ contains an infinite normal subgroup with the relative property (T) (e.g. Γ = SL(2,Z) ⋉Z, or Γ = H × H with H an infinite Kazhdan group and H arbitrary) and V is a closed subgroup of the group of unitaries of a finite von Neumann algebra (e.g. V countable discrete, or separable compact), then any V-valued measurable cocycle for a Bernoulli Γ-action ...

The physical nature of beamstrahlung during beam-beam interaction in linear colliders is reviewed. We first make the distinction between a dense beam and a dilute beam. We then review the characteristics of synchrotron radiation (SR) and bremsstrahlung, and argue that for a wide range of beam parameters beamstrahlung is SR in nature, even if the beam is dilute. Some issues concerning the specif...

Let Nn = {(Tnk,Xnk), k ≥ 1} be a Bernoulli p.p. on Z = (0,∞) × [0,∞). We discuss weak limit theorems for Nn as well as for the associated sum and extremal processes Sn(t) = { ∑ Xnk : Tnk ≤ t} and Yn(t) = {∨Xnk : Tnk ≤ t} on an open subset of Z.

In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved.  A Dirac-delta function is used to describe the position of the moving mass along the beam and its iner...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

In this paper, the capabilities of displacement curvature derived from static response data for finding the location and severity of damage in Euler-Bernoulli beams are assessed. Static response of a beam is obtained using the finite element modeling. In order to reduce the number of measured nodal displacements, the beam deflection is fitted through a polynomial function using a limited number...

Mechanical foundations and pavements design need a perfect prediction of the response of the material to reach a reliable and safe structure. This work deals with the thermoelastic response of microbeams rested on a two-parameter viscoelastic foundation due to a magnetic field in the context of the dual - phase lag thermoelasticity model. The solutions of the governing equations are attained us...