Logarithmic Potentials with External Fields
This treatment of potential theory emphasizes the effects of an external field (or weight) on the minimum energy problem. Several important aspects of the external field problem (and its extension to…
Distributing many points on a sphere
- E. Saff, A. Kuijlaars
- Mathematics
- 1997
Constrained energy problems with applications to orthogonal polynomials of a discrete variable
- P. Dragnev, E. Saff
- Mathematics
- 1 December 1997
Given a positive measure Σ with gs > 1, we write Με ℳΣ if Μ is a probability measure and Σ—Μ is a positive measure. Under some general assumptions on the constraining measure Σ and a weight…
Asymptotics for minimal discrete energy on the sphere
- A. Kuijlaars, E. Saff
- Mathematics
- 1995
We investigate the energy of arrangements of N points on the surface of the unit sphere Sd in Rd+1 that interact through a power law potential V = 1/rs, where s > 0 and r is Euclidean distance. With…
QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- J. Brauchart, E. Saff, I. Sloan, R. Womersley
- MathematicsMathematics of Computation
- 16 August 2012
It is proved that point sets that maximize the sum of suitable powers of the Euclidean distance between pairs of points form a sequence of QMC designs for H^s(S^d) with $s\in(d/2, d/2+1)$.
On univalent functions convex in one direction
- A. Goodman, E. Saff
- Mathematics
- 1 February 1979
Let f(z) = z + "L2akzk be analytic and univalent in the unit disk E: \z\ < 1 and map the disk onto a domain which is convex in the direction of the imaginary axis. We show by example that for V2 -1 <…
Minimal Discrete Energy on the Sphere
- E. Rakhmanov, E. Saff, Y. M. Zhou
- Mathematics
- 1994
We investigate the energy of arrangements of N points on the surface of a sphere in R3, interacting through a power law potential V = rα, −2 < α < 2, where r is Euclidean distance. For α = 0, we take…
Discretizing Manifolds via Minimum Energy Points
1186 NOTICES OF THE AMS VOLUME 51, NUMBER 10 T here are a variety of needs for the discretization of a manifold—statistical sampling, quadrature rules, starting points for Newton’s method,…
Electrons on the Sphere
- E. Rakhmanov, E. Saff, Y. M. Zhou
- Physics
- 1 December 1995
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