Zobrazeno 1 - 10
of 131
pro vyhledávání: '"Hardin, Douglas"'
Autor:
Borodachov, Sergiy, Boyvalenkov, Peter, Dragnev, Peter, Hardin, Douglas, Saff, Edward, Stoyanova, Maya
Universal bounds for the potential energy of weighted spherical codes are obtained by linear programming. The universality is in the sense of Cohn-Kumar -- every attaining code is optimal with respect to a large class of potential functions (absolute
Externí odkaz:
http://arxiv.org/abs/2403.07457
This article is devoted to the study of discrete potentials on the sphere in $\mathbb{R}^n$ for sharp codes. We show that the potentials of most of the known sharp codes attain the universal lower bounds for polarization for spherical $\tau$-designs
Externí odkaz:
http://arxiv.org/abs/2211.00092
In this article we investigate the $N$-point min-max and the max-min polarization problems on the sphere for a large class of potentials in $\mathbb{R}^n$. We derive universal lower and upper bounds on the polarization of spherical designs of fixed d
Externí odkaz:
http://arxiv.org/abs/2207.08807
We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with external fie
Externí odkaz:
http://arxiv.org/abs/2201.00474
Autor:
Hardin, Douglas P.1 (AUTHOR), Saff, Edward B.1 (AUTHOR), Vlasiuk, Oleksandr1,2 (AUTHOR) oleksandr.vlasiuk@vanderbilt.edu
Publikováno v:
Constructive Approximation. Apr2024, Vol. 59 Issue 2, p333-383. 51p.
We describe a framework for extending the asymptotic behavior of a short-range interaction from the unit cube to general compact subsets of $ \mathbb R^d $. This framework allows us to give a unified treatment of asymptotics of hypersingular Riesz en
Externí odkaz:
http://arxiv.org/abs/2010.11937
We investigate the large time behavior of $N$ particles restricted to a smooth closed curve in $\mathbb{R}^d$ and subject to a gradient flow with respect to Euclidean hyper-singular repulsive Riesz $s$-energy with $s>1.$ We show that regardless of th
Externí odkaz:
http://arxiv.org/abs/2010.05431
We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently large, form
Externí odkaz:
http://arxiv.org/abs/2002.06452
We employ signed measures that are positive definite up to certain degrees to establish Levenshtein-type upper bounds on the cardinality of codes with given minimum and maximum distances, and universal lower bounds on the potential energy (for absolu
Externí odkaz:
http://arxiv.org/abs/1910.07274
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpolation we construct polynomials to derive corresponding bounds. These b
Externí odkaz:
http://arxiv.org/abs/1909.00981