相关论文: Optimal Finite Homogeneous sphere approximation
Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function…
It is natural to expect the following loosely stated approximation principle to hold: a numerical approximation solution should be in some sense as smooth as its target exact solution in order to have optimal convergence. For piecewise…
We study uniqueness of best approximation in Orlicz spaces L$\Phi$, for different types of convex functions $\Phi$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation…
Consider a set P of N random points on the unit sphere of dimension $d-1$, and the symmetrized set S = P union (-P). The halving polyhedron of S is defined as the convex hull of the set of centroids of N distinct points in S. We prove that…
A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distance to exactly four spheres. This papers describes all the…
A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances…
In this paper, for a family of second-order parabolic equation with rapidly oscillating and time-dependent periodic coefficients, we are interested in an approximate two-sphere one-cylinder inequality for these solutions in parabolic…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
The Universe is inhomogeneous, and yet it seems to be incredibly well-characterised by a homogeneous relativistic model. One of the current challenges is to accurately characterise the properties of such a model. In this paper we explore…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
In this article, as a first contribution, we provide alternative proofs of recent results by Harrison and Jeffs which determine the precise value of the Gromov-Hausdorff (GH) distance between the circle $\mathbb{S}^1$ and the…
Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper…
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting,…
A reductive homogeneous space $G/H$ is always diffeomorphic to the normal bundle of an orbit of a maximal compact subgroup of $G$. We prove that if $G/H$ admits compact quotients, then the sphere bundle associated to this normal bundle is…
All spaces are assumed to be separable and metrizable. Building on work of van Engelen, Harrington, Michalewski and Ostrovsky, we obtain the following results: (1) Every finite-dimensional analytic space is $\sigma$-homogeneous with…
The complement of the codimension 2 complex coordinate subspace arrangement is shown to be homotopy equivalent to a wedge of spheres.
How should we place $n$ great circles on a sphere to minimize the furthest distance between a point on the sphere and its nearest great circle? Fejes T\'oth conjectured that the optimum is attained by placing $n$ circles evenly spaced all…
The Cohn-Elkies linear program for sphere packing, which was used to solve the 8 and 24 dimensional cases, is conjectured to not be sharp in any other dimension $d>2$. By mapping feasible points of this infinite-dimensional linear program…
We give an optimal bound for the remainder when counting the number of rational points on the $n$-dimensional sphere with bounded denominator for any $n\geq 2$.
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…