We consider a first-passage percolation (FPP) model on a Delaunay triangulation D of the plane. In this model each edge e of D is independently equipped with a nonnegative random variable τe, with distribution function F, which is interpreted as the time it takes to traverse the edge. Vahidi-Asl and Wierman [9] have shown that, under a suitable moment condition on F, the minimum time taken to r...

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...

Let P be a Poisson process of intensity one in a square Sn of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that for c < ccrit, Gn,⌊c logn⌋ is disconnected with probability tending to 1 as n → ∞, and for c > ccrit, Gn,⌊c logn⌋ is connected with probab...

In this paper, linear stability analysis of non-prismatic beam resting on uniform Winkler-Pasternak elastic foundation is carried out based on Eringen's non-local elasticity theory. In the context of small displacement, the governing differential equation and the related boundary conditions are obtained via the energy principle. It is also assumed that the width of rectangle cross-section varie...

We propose a description of open string fields on a D25-brane in vacuum string field theory. We show that the tachyon mass is correctly reproduced from our proposal and further argue that the mass spectrum of all other open string states is correctly obtained as well. We identify the string coupling constant from the three-tachyon coupling and show that the tension of a D25-brane is correctly e...

A profound relationship between the ENU (Expansive Nondecelerative Universe) and dimensionless constants of the fundamental physical interactions is presented. The contribution corrects the Dirac presumption on a time decrease of the gravitational constant G and using simple relations it precises the values of the vector bosons x and y. There is no problem in defining dimensionless physical con...