About: On the directions of segments and r-dimensional balls on a convex surface

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Dokazuje se, že množina směrů (n - 2)-dimenzionálních koulí na hranici konvexního tělesa K..R-, které nejsou obsaženy v žádné (n - 1)-dimenzionální podmnožině této hranice, je .delta.-1-rektifikovatelná. Je dokázána úzká souvislost mezi malostí množiny směrů úseček na té hranici a malostí množiny tečných nadrovin ke grafu d.c. funkce na Rn-2 . Pomocí této souvislosti je zkonstruováno K..R3, že množina směrů úseček na jeho hranici nelze pokrýt spočetně mnoha Jordanovými oblouky majícími všude polotečny. Také se dokazují nové výsledky o směrech r-dimenzionálních koulí rovnoběžných s pevným lineárním podprostorem. (cs) We prove that the set of directions of (n - 2)-dimensional balls which are contained in the boundary of a convex body K..Rn but in no(n -1)-dimensional convex subset of the boundary is .delta.-1-rectifiable. We also show that there exists a close connection between smallness of the set of directions of line segments on the boundary and smallness of set of tangent hyperplanes to the graph of a d.c. (delta-convex) function on Rn-2 . Using this connection, we construct K..R3 such that the set of directions of segments on the boundary cannot be covered by countably many simple Jordan arcs having half-tangents at all points. Also new results on directions of r-dimensional balls in the boundary parallel to a fixed linear subspace are proved. We prove that the set of directions of (n - 2)-dimensional balls which are contained in the boundary of a convex body K..Rn but in no(n -1)-dimensional convex subset of the boundary is .delta.-1-rectifiable. We also show that there exists a close connection between smallness of the set of directions of line segments on the boundary and smallness of set of tangent hyperplanes to the graph of a d.c. (delta-convex) function on Rn-2 . Using this connection, we construct K..R3 such that the set of directions of segments on the boundary cannot be covered by countably many simple Jordan arcs having half-tangents at all points. Also new results on directions of r-dimensional balls in the boundary parallel to a fixed linear subspace are proved. (en)
Title	On the directions of segments and r-dimensional balls on a convex surface On the directions of segments and r-dimensional balls on a convex surface (en) Směry úseček a r-dimensionálních koulí na konvexních plochách (cs)
skos:prefLabel	On the directions of segments and r-dimensional balls on a convex surface On the directions of segments and r-dimensional balls on a convex surface (en) Směry úseček a r-dimensionálních koulí na konvexních plochách (cs)
skos:notation	RIV/67985840:_____/07:00095133!RIV08-AV0-67985840
http://linked.open.../vavai/riv/strany	149;167
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/03/0931), Z(AV0Z10190503), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Pavlica, David
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	439349
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/07:00095133
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	segments and balls on the boundary of a convex body; Hausdorff measure; tangent hyperplane (en)
http://linked.open.../riv/klicoveSlovo	Hausdorff measure segments and balls on the boundary of a convex body tangent hyperplane
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[27B48927D07F]
http://linked.open...i/riv/nazevZdroje	Journal of Convex Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Theory of Real Functions and Distributions II.
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	14
http://linked.open...iv/tvurceVysledku	Pavlica, David Zajíček, L.
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi Metody moderní matematiky a jejich aplikace
issn	0944-6532
number of pages	19 (xsd:int)
is http://linked.open...avai/riv/vysledek of	On the directions of segments and r-dimensional balls on a convex surface On the directions of segments and r-dimensional balls on a convex surface On the directions of segments and r-dimensional balls on a convex surface

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