منابع مشابه
Carathéodory-type Theorems à la Bárány
We generalise the famous Helly-Lovász theorem leading to a generalisation of the BárányCarathéodory theorem for oriented matroids in dimension ≤ 3. We also provide a non-metric proof of the later colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.
متن کاملCarathéodory-Fejér type extremal problems on locally compact Abelian groups
We consider the extremal problem of maximizing a point value | f (z) | at a given point z ∈ G by some positive definite and continuous function f on a locally compact Abelian group (LCA group) G, where for a given symmetric open set Ω ∋ z, f vanishes outside Ω and is normalized by f (0) = 1. This extremal problem was investigated in R and Rd and for Ω a 0-symmetric convex body in a paper of Boa...
متن کاملOn the Integral Carathéodory Property
In this note we document the existence of a finitely generated rational cone that is not covered by its unimodular Hilbert subcones, but satisfies the integral Carathéodory property. We explain the algorithms that decide these properties and describe our experimental approach that led to the discovery of the examples.
متن کاملOn Liapunov-Krasovskii functionals under Carathéodory conditions
In this paper, a basic property that a Liapunov-Krasovskii functional must have when used for studying the stability of time delay systems under Carath¶eodory conditions is studied. This property concerns the equality, almost everywhere, of the upper right-hand Dini derivative of the Liapunov-Krasovskii functional evaluated at the solution, and of the Liapunov-Krasovskii derivative (computed by...
متن کاملAbout the Carathéodory Number
In this paper we give sufficient conditions for a compactum in R to have Carathéodory number less than n+ 1, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem and give a Tverberg-type theorem for families of convex compacta.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1985
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-125-3-187-193