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 Title: Prescribing Dilatations in Space Author(s): Sinthaveelert, Malinee Doctoral Committee Chair(s): Miles, Joseph Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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 Type: Text Language: English Description: 134 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. URI: http://hdl.handle.net/2142/86903 Other Identifier(s): (MiAaPQ)AAI3314896 Date Available in IDEALS: 2015-09-28 Date Deposited: 2008
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