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pro vyhledávání: '"Saff, E. B."'
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We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on cardinality of codes
Externí odkaz:
http://arxiv.org/abs/1801.07334
We study minimum energy problems relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$, $\alpha\in(0,2]$, over signed Radon measures $\mu$ on $\mathbb R^n$, $n\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relat
Externí odkaz:
http://arxiv.org/abs/1711.05484
We study the constrained minimum energy problem with an external field relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$ for a generalized condenser $\mathbf A=(A_i)_{i\in I}$ in $\mathbb R^n$, $n\geqslant 3$, whose o
Externí odkaz:
http://arxiv.org/abs/1710.01950
We investigate separation properties of $N$-point configurations that minimize discrete Riesz $s$-energy on a compact set $A\subset \mathbb{R}^p$. When $A$ is a smooth $(p-1)$-dimensional manifold without boundary and $s\in [p-2, p-1)$, we prove that
Externí odkaz:
http://arxiv.org/abs/1707.03926
For "Riesz-like" kernels $K(x,y)=f(|x-y|)$ on $A\times A$, where $A$ is a compact $d$-regular set $A\subset \mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\mu=\int K(x,y)d\mu(x)$, where $\mu$ is a Borel measure supported on $A$. Sett
Externí odkaz:
http://arxiv.org/abs/1607.07283
There are many ways to generate a set of nodes on the sphere for use in a variety of problems in numerical analysis. We present a survey of quickly generated point sets on $\mathbb{S}^2$, examine their equidistribution properties, separation, coverin
Externí odkaz:
http://arxiv.org/abs/1607.04590
For $s\geqslant d$, we obtain the leading term as $N\to \infty$ of the maximal weighted $N$-point Riesz $s$-polarization (or Chebyshev constant) for a certain class of $d$-rectifiable compact subsets of $\mathbb{R}^p$. This class includes compact sub
Externí odkaz:
http://arxiv.org/abs/1606.04128
For a compact $ d $-dimensional rectifiable subset of $ \mathbb{R}^{p} $ we study asymptotic properties as $ N\to\infty $ of $N$-point configurations minimizing the energy arising from a Riesz $ s $-potential $ 1/r^s $ and an external field in the hy
Externí odkaz:
http://arxiv.org/abs/1605.03840