For a pair potential Φ in Euclidean space ℝ^d satisfying some natural and sufficiently general conditions in the sense of Penrose [1] and Poghosyan and Ueltschi [2] we define by means of the so-called Ursell kernel a function r which is shown to be the correlation function of a unique process G, the limiting Gibbs process for (Φ, ρ) with empty boundary conditions. This process is exhibited as a Gibbs process in the sense of Dobrushin, Lanford and Ruelle for a class of pair potentials, which contains classical stable and hard-core potentials that are called Penrose potentials here. Particularly, a class of positive potentials is included. Finally, for some class of Penrose potentials we show that G is the unique Gibbs process for Φ. We use the classical method of Kirkwood-Salsburg equations. A decisive role is played by a generalization of Ruelle’s estimate for correlation functions.
We study the distributions of the overlap number and the overlapping time that a tagged customer experiences in a network of two infinite server queues in series. While allowing general service time distributions in both queues, we specify the results in some detail for the cases of exponential and deterministic service time distributions. We furthermore outline how one can obtain joint overlap number distributions in more general feedforward networks of infinite server queues.
We present a review of some published results concerning evolution of the notion of (conventional) Bose-Einstein condensation (BEG) predicted in Ideal Bose-Gas (IBG) in 1925. The first step forward was the notion of the conventional generalised BEG a` la van den Berg-Lewis-Pule discovered in the IBG and later in certain models with interactions in 1980s. The next development was a discovery of non-conventional condensation of bosons that occurs only due to interaction. Finally we discuss an example of (non-ideal) the Weakly Imperfect Bose-Gas (WIBG), where the conventional and non-conventional condensates may coexist due to interaction.
In this paper we review the contribution of Evgueny (Euge`ne for the French community) Pechersky to image processing. Euge`ne discovered image processing as he was visiting Telecom Paris in 1994. During his stay at Telecom Paris and later on, during some visits and collaboration at INRIA Sophia Antipolis, his work was focused on designing multi-body interaction models to overcome the limits of the well known Ising and Potts model for image processing applications. Notably, the derived models were applied to different applications both in remote sensing and biomedical images. In this paper we summarize Euge`ne's contribution to the so-called Bayesian approach in image processing.
We prove a dispersive decay in weighted norms for solutions to 1D Schrödinger and Klein-Gordon equations with a δ-function potential.
