Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Borodachov, S."'
We derive universal lower and upper bounds for max-min and min-max problems (also known as polarization) for the potential of spherical $(k,k)$-designs and provide certain examples, including unit-norm tight frames, that attain these bounds. The univ
Externí odkaz:
http://arxiv.org/abs/2411.00290
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
Autor:
Borodachov, S. V., Bosuwan, N.
We prove a conjecture of T. Erd\'{e}lyi and E.B. Saff, concerning the form of the dominant term (as $N\to \infty$) of the $N$-point Riesz $d$-polarization constant for an infinite compact subset $A$ of a $d$-dimensional $C^{1}$-manifold embedded in $
Externí odkaz:
http://arxiv.org/abs/1307.1160
Let $A$ be a compact $d$-rectifiable set embedded in Euclidean space $\RR^p$, $d\le p$. For a given continuous distribution $\sigma(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, our earlier results provided a method for generating $N$
Externí odkaz:
http://arxiv.org/abs/1305.6337
We consider finite systems of contractive homeomorphisms of a complete metric space, which are non-redundant on every level. In general this separation condition is weaker than the strong open set condition and is not equivalent to the weak separatio
Externí odkaz:
http://arxiv.org/abs/0911.2126
Publikováno v:
Transactions of the American Mathematical Society, 2018 Oct 01. 370(10), 6973-6993.
Externí odkaz:
https://www.jstor.org/stable/90024071
We investigate the asymptotic behavior, as $N$ grows, of the largest minimal pairwise distance of $N$ points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurat
Externí odkaz:
http://arxiv.org/abs/math-ph/0605021
Given a compact $d$-rectifiable set $A$ embedded in Euclidean space and a distribution $\rho(x)$ with respect to $d$-dimensional Hausdorff measure on $A$, we address the following question: how can one generate optimal configurations of $N$ points on
Externí odkaz:
http://arxiv.org/abs/math-ph/0602025
Akademický článek
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Publikováno v:
Transactions of the American Mathematical Society, 2008 Mar 01. 360(3), 1559-1580.
Externí odkaz:
http://dx.doi.org/10.1090/S0002-9947-07-04416-9