It is shown that for each convex body A/R n there exists a naturally defined family G A /C(S n&1 ) such that for every g # G A , and every convex function f : R Γ R the mapping y [ S n&1 f ( g(x)&( y, x)) d\_(x) has a minimizer which belongs to A. As an application, approximation of convex bodies by
Powers of Chords for Convex Sets
β Scribed by Dr. sc. K. Voss
- Publisher
- John Wiley and Sons
- Year
- 1982
- Tongue
- English
- Weight
- 154 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We study the problem of optimal recovery in the case of a nonsymmetric convex class of functions. We compare adaptive and nonadaptive methods and prove a bound on how much better adaptive methods can be. We use new inequalities between Gelfand widths and Bernstein widths and new relations between th
## Abstract We consider continuous monotone linear functionals on a locally convex ordered topological vector space that are sandwiched between a given \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(\mathbb R\cup \lbrace +\infty \rbrace )$\end{document}βvalued subline
We show that in any family \(F\) of \(n \geqslant 5\) convex sets in the plane with pairwise disjoint relative interiors, there are two sets \(A\) and \(B\) such that every line that separates them, separates either \(A\) or \(B\) from at least \((n+28) / 30\) sets in \(F\).
This work is devoted to the investigation of the basic relationship between the geometric shape of a convex set and measure theoretic properties of the associated curvature and surface area measures. We study geometric consequences of and conditions for absolute continuity of curvature and surface a
A subset R of the integers modulo n is defined to be a root set if it is the set of roots of some polynomial. Using the Chinese Remainder Theorem, the question of finding and counting root sets mod n is reduced to finding root sets modulo a prime power. In this paper, we provide a recursive construc