In this paper, we prove that a self-avoiding walk of infinite length provides a structure that would resolve Olbers’ paradox. That is, if the stars of a universe were distributed like the vertices of an infinite random walk with each segment length of about a parsec, then the night sky could be as dark as actually observed on the Earth. Self-avoiding random walk structure can therefore resolve ...

ππ scattering length in the I = 2 channel is calculated within quenched approximation using improved gauge and improved Wilson fermion actions on anisotropic lattices. The results are extrapolated towards the chiral, infinite volume and continuum limit. This result improves our previous result on the scattering length. In the chiral, infinite volume and continuum limit, we obtain a (2) 0 mπ = −...

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that off-periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a finite...

In this paper, an ideal cylindrical metamaterial invisibility cloak with infinite-length which its electric permittivity and magnetic permeability mapped to the Drude dispersion model is simulated. The sinusoidal plane waves with microwave frequencies used as sources. To this end, the dispersive finite-difference time-domain method (FDTD) used with Convolutional Perfectly Matched Layered (CPML)...

In this paper, we explore the dynamic properties of an endogenous growth model with finite patent length. We show that there exists a unique equilibrium growth path and that this path exhibits damped oscillations in contrast to the equilibrium path of an endogenous growth model with infinite patent length.We also examine the effects of patent policy on social welfare and show that infinite pate...

In this paper we explore a new hierarchy of classes of languages and infinite words and its connection with complexity classes. Namely, we say that a language belongs to the class Lk if it is a subset of the catenation of k languages S1 · · ·Sk, where the number of words of length n in each of Si is bounded by a constant. The class of infinite words whose set of factors is in Lk is denoted by W...

We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shorteningstraightening flow. In this paper, first we prove a long time existence result for the shortening-straightening flow for non-closed plan...

We study the notion of quasiperiodicity, in the sense of “coverability”, for biinfinite words. All previous work about quasiperiodicity focused on right infinite words, but the passage to the biinfinite case could help to prove stronger results about quasiperiods of Sturmian words. We demonstrate this by showing that all biinfinite Sturmian words have infinitely many quasiperiods, which is not ...

A model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation,...