Related papers: The $\eps-\eps^\beta$ property for clusters with d…
We prove the validity of the $\varepsilon-\varepsilon^\beta$ property in the isoperimetric problem with double density, generalising the known properties for the case of single density. As a consequence, we derive regularity for…
In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of $\mathbb{R}^n$ with fixed volume, where volume and perimeter are relative to…
We present an extensive study of the double beta model for the X-ray surface brightness profiles of clusters, and derive analytically the gas density and total masses of clusters under the hydrostatic equilibrium hypothesis. It is shown…
In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-Lempert result and to establish (almost free of charge) the algebraic density property for all…
This addendum adds some comments to a published paper (B. Schroer, Class. Quantum Grav. 23, (2006) 5227) on area density of localization-entropy. The setting of holography and localization-entropy is generalized to double cones and black…
Two-dimensional high-resolution density field of galaxies of the Early Data Release of the Sloan Digital Sky Survey with a smoothing lengths 0.8 h^{-1} Mpc is applied to extract clusters of galaxies, and a low-resolution field with…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…
Fluids made of two-dimensional hard particles with polygonal shapes may stabilize symmetries which do not result directly from the particle shape. This is due to the formation of clusters in the fluid. Entropy alone can drive these effects,…
Cluster structures of excited $^{10}$Be states are investigated with a hybrid model of dineutron condensate wave functions and $^6$He+$\alpha$ cluster wave functions. Two kinds of cluster states are theoretically suggested a few MeV above…
A new $\alpha$-cluster wave function is proposed which is of the $\alpha$-particle condensate type. Applications to $^{12}$C and $^{16}$O show that states of low density close to the 3 resp. 4 $\alpha$-particle threshold in both nuclei are…
In this paper, assuming the validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$, where $D_A(z)$ and $D_L(z)$ are the angular and the luminosity distance respectively, we explore two kinds of gas mass density profiles of…
The formation of alpha-clusters in nuclei close to the decay thresholds is discussed. These states can be considered to be boson-condensates, which are formed in a second order phase transition in a mixture of nucleons and alpha-particles.…
We study in detail the properties of clusters of ultra high energy cosmic ray events, looking in particular to their angular correlation function, to the relative frequency of clusters with different multiplicities (e.g. doublets vs.…
Lens models appropriate for representing cusped galaxies and clusters are developed. The analogue of the odd number theorem for cusped density distributions is given. Density cusps are classified into strong, isothermal or weak, according…
We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also…
In this paper we are concerned with the recent summability notion of I-statistically pre-Cauchy real double sequences in line of Das et. al. [6] as a generalization of I-statistical convergence. Here we introduce the notion of double…
In this paper, we study geometric properties of $\ell^{p}$-spaces associated with the unitary dual of a compact group. More precisely, we prove uniform smoothness, uniform convexity, Clarkson type inequalities, Kadec-Klee property, as well…
Based on the competition between members of a hierarchy of length scales in complex multi-scale systems, it is shown how clustering of active quantities into concentrated sets, like bubbles in a Swiss cheese, is a generic property that…
In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the…
We study the sensitivity to doubly charged Higgs bosons, $\Delta^{--}$, in the process $e^-\gamma\to e^+ \mu^-\mu^-$ for centre of mass energies appropriate to future high energy $e^+e^-$ collider proposals. For $M_\Delta <…