Related papers: The Sphere-Packing Problem
I comment on a recent preprint "A Proposal to Measure Photon-Photon Scattering" that appeared recently as arXiv:1106.0465v1 [hep-ph].
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
In this note we briefly survey and propose some open problems related to isoparametric theory.
We study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that no two centers…
Column chromatography is an important process in downstream biopharmaceutical manufacturing that enables high-selectivity separation of proteins through various modalities, such as affinity, ion exchange, hydrophobic interactions, or a…
Recent developments in cosmic strings are reviewed, with emphasis on unresolved problems.
In this brief write-up, I overview recent developments on the theoretical description of jet quenching.
We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the…
This is the eighth and final paper in a series giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is…
We present a short review of the existing evidence in favor of neutrino mass and neutrino oscillations which come from different kinds of experiments. We focus our attention in particular on solar neutrinos, presenting a global updated…
A new theory of edge waves over a slowly varying depth.
The current state of this problem has briefly been considered. The hypothesis on the formation of the ozone hole due to the action of some molecules emitted by the rockets has been suggested.
Some recent developments in the theory of quantum spin systems are reviewed.
Given a sphere of any radius $r$ in an $n$-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
We briefly review some of the recent developments in QCD spin physics.
Some observations on the Wu-Sprung potential.
Some problems of testology are discussed.