In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

We give an asymptotic expansion for the Taylor coefficients of L(P (z)) where L(z) is analytic in the open unit disc whose Taylor coefficients vary ‘smoothly’ and P (z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.

We consider the Bernoulli first-passage percolation on Z (d ≥ 2). That is, the edge passage time is taken independently to be 1 with probability 1− p and 0 otherwise. Let μ(p) be the time constant. We prove in this paper that μ(p1)− μ(p2) ≥ μ(p2) 1− p2 (p2 − p1) for all 0 ≤ p1 < p2 < 1 by using Russo’s formula. AMS classification: 60K 35. 82B 43.

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 we study systems in which the system operator, A, has a Riesz basis of (generalized) eigenvectors. We show that this class is subset of the class of spectral operators as studied by Dunford and Schwartz. For these systems we investigate several system theoretic properties, like stability and controllability. We apply our theory to Euler-Bernoulli beam with structural damping.

We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and provide partial results in ot...

We investigate various properties of p-adic differential equations which have as a solution an analytic function of the form Fk(x) = ∑ n≥0 n!Pk(n)x , where Pk(n) = n +Ck−1n k−1+· · ·+C0 is a polynomial in n with Ci ∈ Z (in a more general case Ci ∈ Q or Ci ∈ Cp) , and the region of convergence is | x |p< p 1 p−1 . For some special classes of Pk(n), as well as for the general case, the existence ...