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Title:Prescribing Dilatations in Space
Author(s):Sinthaveelert, Malinee
Doctoral Committee Chair(s):Miles, Joseph
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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.
Issue Date:2008
Description:134 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008.
Other Identifier(s):(MiAaPQ)AAI3314896
Date Available in IDEALS:2015-09-28
Date Deposited:2008

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