On the Connecting Thickness of Arithmetical Discrete Planes
Identifieur interne : 000A28 ( Istex/Checkpoint ); précédent : 000A27; suivant : 000A29On 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 ]
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.
Url:
DOI: 10.1007/978-3-642-04397-0_31
Affiliations:
Links toward previous steps (curation, corpus...)
Links to Exploration step
ISTEX:12D69851128E417EF1BC08B7D3E944A7A0036436Le document en format XML
<record><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></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><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Domenjoud, Eric" sort="Domenjoud, Eric" uniqKey="Domenjoud E" first="Eric" last="Domenjoud">Eric Domenjoud</name></region><name sortKey="Domenjoud, Eric" sort="Domenjoud, Eric" uniqKey="Domenjoud E" first="Eric" last="Domenjoud">Eric Domenjoud</name><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name><name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Istex/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000A28 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Checkpoint/biblio.hfd -nk 000A28 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Istex
|étape= Checkpoint
|type= RBID
|clé= ISTEX:12D69851128E417EF1BC08B7D3E944A7A0036436
|texte= On the Connecting Thickness of Arithmetical Discrete Planes
}}
| This area was generated with Dilib version V0.6.33. |  |