On the Connecting Thickness of Arithmetical Discrete Planes
Identifieur interne : 003999 ( Main/Merge ); précédent : 003998; suivant : 003A00On the Connecting Thickness of Arithmetical Discrete Planes
Auteurs : Eric Domenjoud [France] ; Damien Jamet [France] ; Jean-Luc Toutant [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
English descriptors
- mix :
Abstract
Abstract: While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal vector of which the coordinates are not ℚ-linear dependent. Given v ∈ ℝ3, we compute the lower bound of the thicknesses 2-connecting the arithmetical discrete planes with normal vector v. In particular, we show how the translation parameter operates in the connectedness of the arithmetical discrete planes.
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- https://api.istex.fr/ark:/67375/HCB-MPNH552S-9/fulltext.pdf
- https://hal.archives-ouvertes.fr/hal-00438106
DOI: 10.1007/978-3-642-04397-0_31
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34090 Montpellier</addrLine><country key="FR"></country></address><ref type="url">http://www.umontpellier.fr/</ref></desc></org></tutelle><tutelle name="UMR5506" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>France</country></affiliation></author></analytic><idno type="DOI">10.1007/978-3-642-04397-0_31</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Connectedness</term><term>Discrete Geometry</term><term>Hyperplane</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal vector of which the coordinates are not Q-linear dependent. Given v in R^3, we compute the lower bound of the thicknesses 2-connecting the arithmetical discrete planes with normal vector v. In particular, we show how the translation parameter operates in the connectedness of the arithmetical discrete planes.</div></front></TEI></HAL><ISTEX><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On the Connecting Thickness of Arithmetical Discrete Planes</title><author><name sortKey="Domenjoud, Eric" sort="Domenjoud, Eric" uniqKey="Domenjoud E" first="Eric" last="Domenjoud">Eric Domenjoud</name></author><author><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name></author><author><name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:12D69851128E417EF1BC08B7D3E944A7A0036436</idno><date when="2009" year="2009">2009</date><idno type="doi">10.1007/978-3-642-04397-0_31</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-MPNH552S-9/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">000416</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000416</idno><idno type="wicri:Area/Istex/Curation">000414</idno><idno type="wicri:Area/Istex/Checkpoint">000A28</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000A28</idno><idno type="wicri:doubleKey">0302-9743:2009:Domenjoud E:on:the:connecting</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On the Connecting Thickness of Arithmetical Discrete Planes</title><author><name sortKey="Domenjoud, Eric" sort="Domenjoud, Eric" uniqKey="Domenjoud E" first="Eric" last="Domenjoud">Eric Domenjoud</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Loria, Université Nancy 1 - CNRS, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>Loria, Université Nancy 1 - CNRS, Campus Scientifique, BP 239, 54506, Vandœuvre-lès-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author><author><name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name><affiliation></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal vector of which the coordinates are not ℚ-linear dependent. Given v ∈ ℝ3, we compute the lower bound of the thicknesses 2-connecting the arithmetical discrete planes with normal vector v. In particular, we show how the translation parameter operates in the connectedness of the arithmetical discrete planes.</div></front></TEI></ISTEX></double></record>Pour manipuler ce document sous Unix (Dilib)
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