Related papers: The $\eps-\eps^\beta$ property for clusters with d…
Two-dimensional classical cluster of particles interacting through a screened Coulomb potential is studied. This system can be used as a model for "dusty particles" in high-frequency discharge plasma. For systems consisting of N = 2 - 40…
We continue the research of an extension $\widetilde{\mid}$ of the divisibility relation to the Stone-\v Cech compactification $\beta N$. First we prove that ultrafilters we call prime actually possess the algebraic property of primality.…
The observed clustering of Lyman-$\alpha$ lines is reviewed and compared with the clustering of CIV systems. We argue that a continuity of properties exists between Lyman-$\alpha$ and metal systems and show that the small-scale clustering…
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean space with two sizes of spheres are exactly those obtained by…
The existence of shell structure and the accompanying high degeneracy of electronic levels leads to the possibility of strong superconducting pairing in metallic nanoclusters with N~100-1000 delocalized electrons. The most favorable cases…
The distinguishable cluster approximation applied to coupled cluster doubles equations greatly improves absolute and relative energies. We apply the same approximation to the triples equations and demonstrate that it can also improve…
We present two different projects. The first one is related to the development of a semi-analytic model to follow the formation, the evolution and chemical enrichment of cluster galaxies in a hierarchical dark matter model. The second…
We generate the 2-dimensional high-resolution density field of galaxies of the Early Data Release of the Sloan Digital Sky Survey and the Las Campanas Redshift Survey with a smoothing length 0.8 Mpc/h to extract clusters and groups of…
We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $\beta$. A form for the helicity density is introduced, valid to first order in $\beta$,…
Working in doubling metric spaces, we examine the connections between different dimensions, Whitney covers, and geometrical properties of tubular neighborhoods. In the Euclidean space, we relate these concepts to the behavior of the surface…
Ultra compact stellar models with a two-zone uniform density equation of state are considered. They are shown to provide neat examples of optical geometries exhibiting double necks, implying that the gravitational wave potential has a…
We discuss a role of the double helicity-flip amplitudes and derive new unitary bounds for these amplitudes in elastic $pp$-scattering at small values of $t$. We show that the usual assumption on the smallness of such amplidudes can be…
We use both the conventional and more recently developed methods of cluster analysis to study the data of extra-solar planets. Using the data set with planetary mass M, orbital period P, and orbital eccentricity e, we investigate the…
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric…
We investigate the structure of 13-particle clusters in binary alloys for various size ratios and different concentrations via MD simulation. Our goal is to predict which systems are likely to form local icosahedral structures when rapidly…
We present a relation between sparsity and non-Euclidean isomorphic embeddings. We introduce a general restricted isomorphism property and show how it enables to construct embeddings of $\ell_p^n$, $p > 0$, into various type of Banach or…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
Correlations in interacting many-particle systems can lead to the formation of clusters, in particular bound states and resonances. Systematic quantum statistical approaches allow to combine the nuclear statistical equilibrium description…
We show that every isoperimetric set in R^N with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the…