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 dc.contributor.author Grassmann, Eckhard eng dc.contributor.author Rokne, Jon eng dc.date.accessioned 2008-05-08T18:37:31Z dc.date.available 2008-05-08T18:37:31Z dc.date.issued 1977-09-01 eng dc.identifier.uri http://hdl.handle.net/1880/46394 dc.description.abstract Let \$S\$ be the usual class of univalent functions in {\${|z|~<~1}\$} normalized by \$f(z)~=~z~+\$ \$sum from i=2 to {inf}\$ \$a sub i z sup i\$ and \$V sub n\$ the coefficient region of \$S\$. It is well known that \$f\$ corresponds to a boundary point of \$V sub n\$ if and only if \$f\$ satisfies a quadratic equation of the form \$Q(w)dw sup 2~=~R(z)dz sup 2\$ called Schiffers equation that maps {\${|z|~<~1}\$} onto a slit domain. We treat the following problems numerically for \$V sub 4\$: 1. Given \$Q\$ find \$R\$ and \$f\$. 2. Find the function that maximizes \$Re~e sup i sup phi\$ \$a sub 4\$ with theconstraint that \$a sub 2\$ and \$a sub 3\$ are some given complex numbers in \$V sub 3\$. In this case Schiffers equation is a sufficient condition for \$f\$ to be extremal. The critical trajectories of \$Q(w)dw sup 2\$ and \$R(z)dz sup 2\$ are in each case displayed graphically for some particular examples. eng dc.language.iso Eng eng dc.subject Computer Science eng dc.title CALCULATION OF EXTREMUM PROBLEMS FOR UNIVALENT FUNCTIONS eng dc.type unknown dc.publisher.corporate University of Calgary eng dc.publisher.faculty Science eng dc.description.notes We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.ca eng dc.identifier.department 1977-20-9 eng dc.date.computerscience 1999-05-27 eng dc.identifier.doi http://dx.doi.org/10.11575/PRISM/30971 thesis.degree.discipline Computer Science eng
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