One-sided Diophantine approximations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA2001XOZ" target="_blank" >RIV/61988987:17310/19:A2001XOZ - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/19:00501142
Result on the web
<a href="https://iopscience.iop.org/article/10.1088/1751-8121/aaf5d3" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/aaf5d3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/aaf5d3" target="_blank" >10.1088/1751-8121/aaf5d3</a>
Alternative languages
Result language
angličtina
Original language name
One-sided Diophantine approximations
Original language description
The paper deals with best one--sided (lower or upper) Diophantine approximations of the $ell$-th kind ($ellinmathbb{N}$). We use the ordinary continued fraction expansions to formulate explicit criteria for a fraction $frac{p}{q}inmathbb{Q}$ to be a best lower or upper Diophantine approximation of the $ell$-th kind to a given $alphainmathbb{R}$. The sets of best lower and upper approximations are examined in terms of their cardinalities and metric properties. Applying our results in spectral analysis, we obtain an explanation for the rarity of so-called Bethe--Sommerfeld quantum graphs.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
J PHYS A-MATH THEOR
ISSN
1751-8113
e-ISSN
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Volume of the periodical
52
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
24
Pages from-to
045205
UT code for WoS article
000455380000004
EID of the result in the Scopus database
2-s2.0-85061427032