Optimal Antipodal Configuration of $2d$ Points on a Sphere in $\mathbb R^d$ for Covering
We show that among antipodal $2d$-point configurations on the sphere $S^{d-1}$ in $\mathbb R^d$, the set of vertices of a regular cross-polytope inscribed in $S^{d-1}$ uniquely solves the best-covering problem (this is new for $d\geq 5$) and the maximal polarization problem for potentials given by a...
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| creator | Borodachov, Sergiy |
| description | We show that among antipodal $2d$-point configurations on the sphere
$S^{d-1}$ in $\mathbb R^d$, the set of vertices of a regular cross-polytope
inscribed in $S^{d-1}$ uniquely solves the best-covering problem (this is new
for $d\geq 5$) and the maximal polarization problem for potentials given by a
function of the distance squared with a positive and convex second derivative
($d\geq 3$). |
| doi_str_mv | 10.48550/arxiv.2210.12472 |
| format | Article |
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$S^{d-1}$ in $\mathbb R^d$, the set of vertices of a regular cross-polytope
inscribed in $S^{d-1}$ uniquely solves the best-covering problem (this is new
for $d\geq 5$) and the maximal polarization problem for potentials given by a
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$S^{d-1}$ in $\mathbb R^d$, the set of vertices of a regular cross-polytope
inscribed in $S^{d-1}$ uniquely solves the best-covering problem (this is new
for $d\geq 5$) and the maximal polarization problem for potentials given by a
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$S^{d-1}$ in $\mathbb R^d$, the set of vertices of a regular cross-polytope
inscribed in $S^{d-1}$ uniquely solves the best-covering problem (this is new
for $d\geq 5$) and the maximal polarization problem for potentials given by a
function of the distance squared with a positive and convex second derivative
($d\geq 3$).</abstract><doi>10.48550/arxiv.2210.12472</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Optimization and Control Mathematics - Symplectic Geometry |
| title | Optimal Antipodal Configuration of $2d$ Points on a Sphere in $\mathbb R^d$ for Covering |
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