Dimension and entropy of a non-ergodic Markovian process and its relation to Rademacher Riesz Products

Given a Markov chain (not necessarily stationary or homogeneous) with finite state space and an initial distribution, we can construct a measure on the unit interval [0, 1]. In this work we examine the equality (up to a constant) of the Hausdorff dimension of and of a suitably defined entropy for the Markovian process. The results are applied to the so-called Rademacher-Riesz Products.     

World-line techniques for resumming gluon radiative corrections at the cross-section level

We employ the Polyakov world-line path-integral version of QCD to identify and resum at leading perturbative order enhanced radiative gluon contributions to the Drell-Yan type ( pair annihilation) cross-sections. We emphasize that this is the first time that world-line techniques are applied to cross-section calculations. Received: 10 June 2002 / Published online: 31 October 2002 RID="a" ID="a" e-mail: akaranik@cc.uoa.gr RID="b" ID="b" e-mail: cktorid@cc.uoa.gr RID="c" ID="c" e-mail: stefanis@tp2.ruhr-uni-bochum.de     

On A Generalized Entropy’s Formula

An Eggleston- type formula is given, as the Hausdorff dimension of a set of positive Rademacher- Riesz product measure.     

Dynamic colloidal stabilization by nanoparticle halos

We explore the conditions under which colloids can be stabilized by the addition of smaller particles. The largest repulsive barriers between colloids occur when the added particles repel each other with soft interactions, leading to an accumulation near the colloid surfaces. At lower densities these layers of mobile particles (nanoparticle halos) result in stabilization, but when too many are added, the interactions become attractive again. We systematically study these effects--accumulation repulsion, reentrant attraction, and bridging--by accurate integral equation techniques.     

Truncation Error on Wavelet Sampling Expansions

We estimate the truncation error of sampling expansions on translationinvariant spaces, generated by integer translations of a single functionand on wavelet subspaces of L ₂(R). As a byproduct of themain result, we get the classical Jagerman's bound for Shannon's samplingexpansions. We also examine this error on certain wavelet sampling expansions.     

Gibbs Phenomenon in Wavelet Analysis

We prove Dirichlet-type pointwise convergence theorems for the wavelet transforms and series of discontinuous functions and we examine the Gibbs ripples close to the jump location. Examples are given of wavelets without ripples, and an example (the Mexican hat) shows that the Gibbs ripple in continuous wavelet analysis can be 3.54% instead of 8.9% of the Fourier case. For the discrete case we show that there exist two Meyer type wavelets the first one has maximum ripple 3.58% and the second 9.8%. Moreover we describe several examples and methods for estimating Gibbs ripples both in continuous and discrete cases. Finally we discuss how a wavelet transform generates a summability method for the Fourier case.     

Theoretical evidence for a tachyonic ghost-state contribution to the gluon propagator in high-energy,forward quark-quark “scattering”

Implications stemming from the inclusion of nonperturbative confining effects, as contained in the stochastic vacuum model of H. Dosch and Yu.A. Simonov, are considered in the context of a (hypothetical) quark-quark “scattering process” in the Regge kinematical region. In a computation wherein the nonperturbative input enters as a correction to established perturbative results, a careful treatment of infrared divergences is shown to imply the presence of an effective propagator associated with the existence of a linear term in the static potential. An equivalent statement is to say that the modified gluonic propagator receives a contribution from a tachyonic ghost state, an occurrence which is fully consistent with earlier suggestions made in the context of low-energy QCD phenomenology.