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Miles, Joseph Sinthaveelert, Malinee 2015-09-28T15:20:06Z 2015-09-28T15:20:06Z 10000-01-01 2008 2008 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. http://hdl.handle.net/2142/86903 (MiAaPQ)AAI3314896 eng Mathematics Prescribing Dilatations in Space text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.