We investigate, by “ à la Marcinkiewicz” techniques applied to the (asymptotic) density function, how dense systems of equal spheres of Rn, n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the systems of balls in the sense of Marcinkie...

Modeling the event horizon of a black hole by a fuzzy sphere leads us to modify some suggestions in the literature concerning black hole mass spectra. We derive a formula for the mass spectrum of quantum black holes in terms of four integers which define the area, angular momentum, electric and magnetic charge of the black hole. Although the event horizon becomes a commutative sphere in the cla...

Abstract We analyze the stress-energy tensor, and the resulting energy conditions, for a scalar field with general curvature coupling, outside a perfectly reflecting sphere with Dirichlet boundary conditions. For conformal coupling we find that the null energy condition is always obeyed, and therefore the averaged null energy condition (ANEC) is also obeyed. Since the ANEC is independent of cur...

In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how toconfigure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjecturedthat the sum of distances is maximal if 5 points form a bipyramid configuration in which case two pointsare positioned at two poles of the sphere and the other three are position...

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that cu...

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands,...

Explicitly or implicitly, feminist or not, much of the literature employing a political economy perspective has assumed the existence of two largely separate spheres: a public sphere located in the formal economy and dominated by men, and a private sphere confined to the household and managed by women. For non-feminist theorists, this assumption is evident in the focus on the formal economy to ...

It is one of the most important facts in 4–dimensional topology that there are 4–manifolds in which not every spherical homology class of degree 2 can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case, many of the obstructions to constructing such a sphere vanish if one modifies the ambient 4–manifold by adding products of 2–spheres...

This paper presents a global diffeomorphism from a suitably defined “visible set” of rigid body configurations — a subset of SE(3) — to an imagespace. The mapping between the visible set and the image-space is given by the projection of a set of features of a specially designed visual target. The target is a sphere marked with a feature point and a vector tangent to the sphere at the feature po...

We investigate, by “ à la Marcinkiewicz” techniques applied to the (asymptotic) density function, how dense systems of equal spheres of Rn, n ≥ 1, can be partitioned at infinity in order to allow the computation of their density as a true limit and not a limsup. The density of a packing of equal balls is the norm 1 of the characteristic function of the systems of balls in the sense of Marcinkie...