24 citations · 79 across the 31 of their papers we have counts for
6 papers · 1 filter
Logarithmic Equilibrium on the Sphere in the Presence of Multiple Point Charges
A. R. Legg, P. D. Dragnev
With the sphere as a conductor holding a unit charge with logarithmic interactions, we consider the problem of determining the support of the eq…
Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
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 dis…
Log-optimal (d+2)-configurations in d-dimensions
Peter D. Dragnev, Oleg R. Musin
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attai…
Upper bounds for energies of spherical codes of given cardinality and separation
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
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 interpol…
Universal bounds for spherical codes: the Levenshtein framework lifted
Peter Boyvalenkov, Peter Dragnev, Douglas Hardin +2
Based on the Delsarte-Yudin linear programming approach, we extend Levenshtein's framework to obtain lower bounds for the minimum -energy of spherical codes of prescribed dimens…
On point-mass Riesz external fields on the real axis
David Benko, Peter Dragnev, Ramon Orive
The purpose of this work is twofold. First, we aim to extend for the results of one of the authors about equilibrium measures in the real axis in external fields created by…