Prescribing Dilatations in Space

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Sinthaveelert, Malinee

Contributors dc:contributor

• Miles, Joseph

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3314896

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86903