Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000475668> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W2000475668 endingPage "638" @default.
- W2000475668 startingPage "625" @default.
- W2000475668 abstract "For a real set A consider the semigroup S(A), additively generated by A; that is, the set of all real numbers representable as a (finite) sum of elements of A. If A ⊆ (0, 1) is open and non-empty, then S(A) is easily seen to contain all sufficiently large real numbers, and we let G(A): = sup{u ∈ R: u ∉ S(A)}. Thus G(A) is the smallest number with the property that any u > G(A) is representable as indicated above. We show that if the measure of A is large, then G(A) is small; more precisely, writing for brevity α: = mes A, we have G ( A ) ⩽ { ( 1 − α ) ⌊ 1 / α ⌋ if 0 < α ⩽ 0.1 , ( 1 − α + α { 1 / α } ) ⌊ 1 / α ⌋ if 0.1 ⩽ α ⩽ 0.5 , 2 ( 1 − α ) if 0.5 ⩽ α ⩽ 1 . Indeed, the first and the last of these three estimates are the best possible, attained for A = (1−α, 1) and A = (1−α, 1){2(1−α)}, respectively; the second is close to the best possible and can be improved by α{1/α}⌊1/α⌋ ⩽ {1/α} at most. The problem studied is a continuous analogue of the linear Diophantine problem of Frobenius (in its extremal settings due to Erdös and Graham), also known as the ‘postage stamp problem’ or the ‘coin exchange problem’." @default.
- W2000475668 created "2016-06-24" @default.
- W2000475668 creator A5009343444 @default.
- W2000475668 date "2006-06-01" @default.
- W2000475668 modified "2023-10-16" @default.
- W2000475668 title "THE CONTINUOUS POSTAGE STAMP PROBLEM" @default.
- W2000475668 cites W1970410060 @default.
- W2000475668 cites W1980163873 @default.
- W2000475668 cites W2000475668 @default.
- W2000475668 cites W2051793589 @default.
- W2000475668 cites W2129280633 @default.
- W2000475668 cites W229079384 @default.
- W2000475668 cites W2495618919 @default.
- W2000475668 doi "https://doi.org/10.1112/s0024610706022939" @default.
- W2000475668 hasPublicationYear "2006" @default.
- W2000475668 type Work @default.
- W2000475668 sameAs 2000475668 @default.
- W2000475668 citedByCount "3" @default.
- W2000475668 countsByYear W20004756682015 @default.
- W2000475668 crossrefType "journal-article" @default.
- W2000475668 hasAuthorship W2000475668A5009343444 @default.
- W2000475668 hasBestOaLocation W20004756682 @default.
- W2000475668 hasConcept C114614502 @default.
- W2000475668 hasConcept C118615104 @default.
- W2000475668 hasConcept C134306372 @default.
- W2000475668 hasConcept C162392398 @default.
- W2000475668 hasConcept C177264268 @default.
- W2000475668 hasConcept C199360897 @default.
- W2000475668 hasConcept C206530611 @default.
- W2000475668 hasConcept C207405024 @default.
- W2000475668 hasConcept C2777735758 @default.
- W2000475668 hasConcept C2780009758 @default.
- W2000475668 hasConcept C33923547 @default.
- W2000475668 hasConcept C41008148 @default.
- W2000475668 hasConcept C77088390 @default.
- W2000475668 hasConcept C94020503 @default.
- W2000475668 hasConceptScore W2000475668C114614502 @default.
- W2000475668 hasConceptScore W2000475668C118615104 @default.
- W2000475668 hasConceptScore W2000475668C134306372 @default.
- W2000475668 hasConceptScore W2000475668C162392398 @default.
- W2000475668 hasConceptScore W2000475668C177264268 @default.
- W2000475668 hasConceptScore W2000475668C199360897 @default.
- W2000475668 hasConceptScore W2000475668C206530611 @default.
- W2000475668 hasConceptScore W2000475668C207405024 @default.
- W2000475668 hasConceptScore W2000475668C2777735758 @default.
- W2000475668 hasConceptScore W2000475668C2780009758 @default.
- W2000475668 hasConceptScore W2000475668C33923547 @default.
- W2000475668 hasConceptScore W2000475668C41008148 @default.
- W2000475668 hasConceptScore W2000475668C77088390 @default.
- W2000475668 hasConceptScore W2000475668C94020503 @default.
- W2000475668 hasIssue "03" @default.
- W2000475668 hasLocation W20004756681 @default.
- W2000475668 hasLocation W20004756682 @default.
- W2000475668 hasOpenAccess W2000475668 @default.
- W2000475668 hasPrimaryLocation W20004756681 @default.
- W2000475668 hasRelatedWork W1979733105 @default.
- W2000475668 hasRelatedWork W2023434610 @default.
- W2000475668 hasRelatedWork W2040467663 @default.
- W2000475668 hasRelatedWork W2130835224 @default.
- W2000475668 hasRelatedWork W2164029925 @default.
- W2000475668 hasRelatedWork W2996654955 @default.
- W2000475668 hasRelatedWork W3021816235 @default.
- W2000475668 hasRelatedWork W3032844323 @default.
- W2000475668 hasRelatedWork W3200022417 @default.
- W2000475668 hasRelatedWork W4308322930 @default.
- W2000475668 hasVolume "73" @default.
- W2000475668 isParatext "false" @default.
- W2000475668 isRetracted "false" @default.
- W2000475668 magId "2000475668" @default.
- W2000475668 workType "article" @default.