This HTML5 document contains 48 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n11https://global.dbpedia.org/id/
dbpedia-ruhttp://ru.dbpedia.org/resource/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
dbchttp://dbpedia.org/resource/Category:
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Rolf_Schneider
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:Projection_body
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:Geoffrey_Colin_Shephard
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:List_of_convexity_topics
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:Shephard's_problem
rdfs:label
Shephard's problem Задача Шепарда
rdfs:comment
Задача Шепарда — вопрос выпуклой геометрии о сравнении объёмов двух симметричных выпуклых тел при условии, что в любом направлении площадь проекции первого не превосходит площади проекции второго. Вопрос был сформулирован в 1964 году. Ответ на этот вопрос — «да» в размерности 2 и «нет» в размерности 3 и выше.Последнее было доказано независимо и Шнайдером в 1967 году. In mathematics, Shephard's problem, is the following geometrical question asked by Geoffrey Colin Shephard in 1964: if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the projection of L, then does it follow that the volume of K is smaller than that of L? Vk(πk(K)) is sometimes known as the brightness of K and the function Vk o πk as a (k-dimensional) brightness function.
dcterms:subject
dbc:Convex_analysis dbc:Convex_geometry
dbo:wikiPageID
10614436
dbo:wikiPageRevisionID
1105059359
dbo:wikiPageWikiLink
dbr:Dimension dbr:Volume dbr:Hyperplane dbr:Mathematics dbr:Projection_(mathematics) dbr:Convex_body dbr:Minkowski's_first_inequality_for_convex_bodies dbr:Israel_Journal_of_Mathematics dbc:Convex_analysis dbr:Geoffrey_Colin_Shephard dbc:Convex_geometry dbr:Euclidean_space dbr:Projection_body dbr:Busemann–Petty_problem dbr:Reflection_symmetry
owl:sameAs
freebase:m.02qk7sg n11:4uVG6 dbpedia-ru:Задача_Шепарда wikidata:Q7494442
dbp:wikiPageUsesTemplate
dbt:Cite_journal dbt:Reflist dbt:No_footnotes dbt:Pi dbt:Sfn dbt:Citation dbt:Cite_book
dbo:abstract
In mathematics, Shephard's problem, is the following geometrical question asked by Geoffrey Colin Shephard in 1964: if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the projection of L, then does it follow that the volume of K is smaller than that of L? In this case, "centrally symmetric" means that the reflection of K in the origin, −K, is a translate of K, and similarly for L. If πk : Rn → Πk is a projection of Rn onto some k-dimensional hyperplane Πk (not necessarily a coordinate hyperplane) and Vk denotes k-dimensional volume, Shephard's problem is to determine the truth or falsity of the implication Vk(πk(K)) is sometimes known as the brightness of K and the function Vk o πk as a (k-dimensional) brightness function. In dimensions n = 1 and 2, the answer to Shephard's problem is "yes". In 1967, however, Petty and Schneider showed that the answer is "no" for every n ≥ 3. The solution of Shephard's problem requires Minkowski's first inequality for convex bodies and the notion of projection bodies of convex bodies. Задача Шепарда — вопрос выпуклой геометрии о сравнении объёмов двух симметричных выпуклых тел при условии, что в любом направлении площадь проекции первого не превосходит площади проекции второго. Вопрос был сформулирован в 1964 году. Ответ на этот вопрос — «да» в размерности 2 и «нет» в размерности 3 и выше.Последнее было доказано независимо и Шнайдером в 1967 году.
prov:wasDerivedFrom
wikipedia-en:Shephard's_problem?oldid=1105059359&ns=0
dbo:wikiPageLength
3193
foaf:isPrimaryTopicOf
wikipedia-en:Shephard's_problem
Subject Item
dbr:Busemann–Petty_problem
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:Shepherd_(name)
dbo:wikiPageWikiLink
dbr:Shephard's_problem
Subject Item
dbr:Shephard_problem
dbo:wikiPageWikiLink
dbr:Shephard's_problem
dbo:wikiPageRedirects
dbr:Shephard's_problem
Subject Item
wikipedia-en:Shephard's_problem
foaf:primaryTopic
dbr:Shephard's_problem