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Physical Sciences and Mathematics Commons™
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Faculty Research and Creative Activity
We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions On S2, John Franks, Michael Handel, Kamlesh Parwani
Faculty Research and Creative Activity
We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Fixed Points Of Abelian Actions, John Franks, Michael Handel, Kamlesh Parwani
Faculty Research and Creative Activity
We prove that if $\F$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two then there is a common fixed point for all elements of $\F.$
Graphics With Pgf And Tikz, Andrew Mertz, William Slough
Graphics With Pgf And Tikz, Andrew Mertz, William Slough
Faculty Research and Creative Activity
Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a fine line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.
Graphics With Tikz, Andrew Mertz, William Slough
Graphics With Tikz, Andrew Mertz, William Slough
Faculty Research and Creative Activity
Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a thin line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.
Programming With Perltex, Andrew Mertz, William Slough
Programming With Perltex, Andrew Mertz, William Slough
Faculty Research and Creative Activity
PerlTEX couples two well-known worlds—the Perl programming language and the LATEX typesetting system. The resulting system provides users with a way to augment LATEX macros with Perl code, thereby adding programming capabilities to LATEX that would otherwise be difficult to express. In this paper, we illus- trate the use of PerlTEX with a variety of examples and explain the associated Perl code. Although Perl may perhaps be best known for its string manipula- tion capabilities, we demonstrate how PerlTEX indirectly provides support for “programming” graphics through the use of additional packages such as TikZ.