Matches in SemOpenAlex for { <https://semopenalex.org/work/W2040403401> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W2040403401 endingPage "209" @default.
- W2040403401 startingPage "187" @default.
- W2040403401 abstract "Given an integer $Nge 2$ and a real number ${beta}>1$, let $Gamma_{{beta},N}$ be the set of all $x=sum_{i=1}^infty {d_i}/{{beta}^i}$ with $d_iin{0,1,cdots,N-1}$ for all $ige 1$. The infinite sequence $(d_i)$ is called a ${beta}$-expansion of $x$. Let $mathbf{U}_{{beta},N}$ be the set of all $x$'s in $Gamma_{{beta},N}$ which have unique ${beta}$-expansions. We give explicit formula of the Hausdorff dimension of $mathbf{U}_{{beta},N}$ for ${beta}$ in any admissible interval $[{{beta}}_L,{{beta}}_U]$, where ${{beta}_L}$ is a purely Parry number while ${{beta}_U}$ is a transcendental number whose quasi-greedy expansion of $1$ is related to the classical Thue-Morse sequence. This allows us to calculate the Hausdorff dimension of $U{N}$ for almost every $beta>1$. In particular, this improves the main results of G{'a}bor Kall{'o}s (1999, 2001). Moreover, we find that the dimension function $f({beta})=dim_Hmathbf{U}_{{beta},N}$ fluctuates frequently for ${beta}in(1,N)$." @default.
- W2040403401 created "2016-06-24" @default.
- W2040403401 creator A5021248802 @default.
- W2040403401 creator A5056602178 @default.
- W2040403401 date "2014-12-11" @default.
- W2040403401 modified "2023-10-12" @default.
- W2040403401 title "Hausdorff dimension of unique beta expansions" @default.
- W2040403401 cites W1483208600 @default.
- W2040403401 cites W1662522380 @default.
- W2040403401 cites W1964378097 @default.
- W2040403401 cites W1967860487 @default.
- W2040403401 cites W1972868132 @default.
- W2040403401 cites W1974819605 @default.
- W2040403401 cites W1976097360 @default.
- W2040403401 cites W1995483531 @default.
- W2040403401 cites W1996332501 @default.
- W2040403401 cites W2000235240 @default.
- W2040403401 cites W2016876568 @default.
- W2040403401 cites W2075595154 @default.
- W2040403401 cites W2076789781 @default.
- W2040403401 cites W2078945039 @default.
- W2040403401 cites W2080003810 @default.
- W2040403401 cites W2089164015 @default.
- W2040403401 cites W2095035126 @default.
- W2040403401 cites W2160949125 @default.
- W2040403401 cites W2477604657 @default.
- W2040403401 cites W2962765323 @default.
- W2040403401 cites W2963549434 @default.
- W2040403401 cites W3102243653 @default.
- W2040403401 cites W3103310866 @default.
- W2040403401 cites W4206252072 @default.
- W2040403401 cites W4248374798 @default.
- W2040403401 cites W4249775755 @default.
- W2040403401 cites W4312344700 @default.
- W2040403401 cites W4312611793 @default.
- W2040403401 cites W4312884349 @default.
- W2040403401 cites W4312961545 @default.
- W2040403401 doi "https://doi.org/10.1088/0951-7715/28/1/187" @default.
- W2040403401 hasPublicationYear "2014" @default.
- W2040403401 type Work @default.
- W2040403401 sameAs 2040403401 @default.
- W2040403401 citedByCount "39" @default.
- W2040403401 countsByYear W20404034012016 @default.
- W2040403401 countsByYear W20404034012017 @default.
- W2040403401 countsByYear W20404034012018 @default.
- W2040403401 countsByYear W20404034012019 @default.
- W2040403401 countsByYear W20404034012020 @default.
- W2040403401 countsByYear W20404034012021 @default.
- W2040403401 countsByYear W20404034012022 @default.
- W2040403401 countsByYear W20404034012023 @default.
- W2040403401 crossrefType "journal-article" @default.
- W2040403401 hasAuthorship W2040403401A5021248802 @default.
- W2040403401 hasAuthorship W2040403401A5056602178 @default.
- W2040403401 hasBestOaLocation W20404034012 @default.
- W2040403401 hasConcept C114614502 @default.
- W2040403401 hasConcept C191399826 @default.
- W2040403401 hasConcept C194198291 @default.
- W2040403401 hasConcept C199360897 @default.
- W2040403401 hasConcept C2776174256 @default.
- W2040403401 hasConcept C2778112365 @default.
- W2040403401 hasConcept C33676613 @default.
- W2040403401 hasConcept C33923547 @default.
- W2040403401 hasConcept C41008148 @default.
- W2040403401 hasConcept C54355233 @default.
- W2040403401 hasConcept C86803240 @default.
- W2040403401 hasConceptScore W2040403401C114614502 @default.
- W2040403401 hasConceptScore W2040403401C191399826 @default.
- W2040403401 hasConceptScore W2040403401C194198291 @default.
- W2040403401 hasConceptScore W2040403401C199360897 @default.
- W2040403401 hasConceptScore W2040403401C2776174256 @default.
- W2040403401 hasConceptScore W2040403401C2778112365 @default.
- W2040403401 hasConceptScore W2040403401C33676613 @default.
- W2040403401 hasConceptScore W2040403401C33923547 @default.
- W2040403401 hasConceptScore W2040403401C41008148 @default.
- W2040403401 hasConceptScore W2040403401C54355233 @default.
- W2040403401 hasConceptScore W2040403401C86803240 @default.
- W2040403401 hasIssue "1" @default.
- W2040403401 hasLocation W20404034011 @default.
- W2040403401 hasLocation W20404034012 @default.
- W2040403401 hasLocation W20404034013 @default.
- W2040403401 hasOpenAccess W2040403401 @default.
- W2040403401 hasPrimaryLocation W20404034011 @default.
- W2040403401 hasRelatedWork W1965885664 @default.
- W2040403401 hasRelatedWork W2016287320 @default.
- W2040403401 hasRelatedWork W2071224126 @default.
- W2040403401 hasRelatedWork W2111715420 @default.
- W2040403401 hasRelatedWork W2354545140 @default.
- W2040403401 hasRelatedWork W2354845264 @default.
- W2040403401 hasRelatedWork W2953323654 @default.
- W2040403401 hasRelatedWork W4287824069 @default.
- W2040403401 hasRelatedWork W4288096853 @default.
- W2040403401 hasRelatedWork W4294437888 @default.
- W2040403401 hasVolume "28" @default.
- W2040403401 isParatext "false" @default.
- W2040403401 isRetracted "false" @default.
- W2040403401 magId "2040403401" @default.
- W2040403401 workType "article" @default.