{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86903"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86903","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Prescribing Dilatations in Space","abstract":"On this domain, we define the dilatation from the transformation matrix A = UDVT of an affine mapping in R3 . Let B = ATA = VD2VT = [ bij]. Define the dilatation m&ar; as m&ar;=1M b11b22-b2 12 b11b33-b2 13 b22b33-b2 23 , where M2 = b 11b22 -- b212 + b11b33 -- b213 + b22b33 -- b223 + lambda (det B)⅔ and lambda is a fixed positive constant. This dilatation involves only the entries of the matrices D and V. Thus we are able to follow f by another orthogonal transformation or conformal mapping without changing the modulus of the dilatation. Then we show that we can prescribe this dilatation for an affine mapping on a simplex in R3 . Furthermore, we show that we can prescribe dilatations for a continuous piecewise affine mapping on the domain that is a union of two simplices sharing a common face.","abstract_html":"On this domain, we define the dilatation from the transformation matrix A = UDVT of an affine mapping in R3 . Let B = ATA = VD2VT = [ bij]. Define the dilatation m&ar; as m&ar;=1M b11b22-b2 12 b11b33-b2 13 b22b33-b2 23 , where M2 = b 11b22 -- b212 + b11b33 -- b213 + b22b33 -- b223 + lambda (det B)⅔ and lambda is a fixed positive constant. This dilatation involves only the entries of the matrices D and V. Thus we are able to follow f by another orthogonal transformation or conformal mapping without changing the modulus of the dilatation. Then we show that we can prescribe this dilatation for an affine mapping on a simplex in R3 . Furthermore, we show that we can prescribe dilatations for a continuous piecewise affine mapping on the domain that is a union of two simplices sharing a common face.","abstract_has_math":false,"creators":["Sinthaveelert, Malinee"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Miles, Joseph"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:06Z","date_published":"2015-09-28T15:20:06Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3314896"],"render_values":[{"text":"(MiAaPQ)AAI3314896","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86903","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Miles, Joseph"]},{"key":"dc:creator","label":"Author","values":["Sinthaveelert, Malinee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:06Z","10000-01-01","2008"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86903","(MiAaPQ)AAI3314896"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["On this domain, we define the dilatation from the transformation matrix A = UDVT of an affine mapping in R3 . Let B = ATA = VD2VT = [ bij]. Define the dilatation m&ar; as m&ar;=1M b11b22-b2 12 b11b33-b2 13 b22b33-b2 23 , where M2 = b 11b22 -- b212 + b11b33 -- b213 + b22b33 -- b223 + lambda (det B)⅔ and lambda is a fixed positive constant. This dilatation involves only the entries of the matrices D and V. Thus we are able to follow f by another orthogonal transformation or conformal mapping without changing the modulus of the dilatation. Then we show that we can prescribe this dilatation for an affine mapping on a simplex in R3 . Furthermore, we show that we can prescribe dilatations for a continuous piecewise affine mapping on the domain that is a union of two simplices sharing a common face.","Made available in DSpace on 2015-09-28T15:20:06Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3314896.pdf: 1606621 bytes, checksum: 1ccd6661b15257b8094b09648643538f (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 88184 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","134 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."]},{"key":"dc:title","label":"Title","values":["Prescribing Dilatations in Space"]}]}],"canonical_facts":{"dc:contributor":["Miles, Joseph"],"dc:creator":["Sinthaveelert, Malinee"],"dc:date":["2015-09-28T15:20:06Z","10000-01-01","2008"],"dc:description":["On this domain, we define the dilatation from the transformation matrix A = UDVT of an affine mapping in R3 . Let B = ATA = VD2VT = [ bij]. Define the dilatation m&ar; as m&ar;=1M b11b22-b2 12 b11b33-b2 13 b22b33-b2 23 , where M2 = b 11b22 -- b212 + b11b33 -- b213 + b22b33 -- b223 + lambda (det B)⅔ and lambda is a fixed positive constant. This dilatation involves only the entries of the matrices D and V. Thus we are able to follow f by another orthogonal transformation or conformal mapping without changing the modulus of the dilatation. Then we show that we can prescribe this dilatation for an affine mapping on a simplex in R3 . Furthermore, we show that we can prescribe dilatations for a continuous piecewise affine mapping on the domain that is a union of two simplices sharing a common face.","Made available in DSpace on 2015-09-28T15:20:06Z (GMT). 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