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A Gentle Introduction To Pythontex, Andrew Mertz, William A. Slough
A Gentle Introduction To Pythontex, Andrew Mertz, William A. Slough
William A. Slough
No abstract provided.
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Kamlesh Parwani
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the …
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani
Kamlesh Parwani
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.
A Tikz Tutorial: Generating Graphics In The Spirit Of Tex, Andrew Mertz, William Slough
A Tikz Tutorial: Generating Graphics In The Spirit Of Tex, Andrew Mertz, William Slough
Andrew Mertz
TikZ is a system which can be used to specify graphics of very high quality. For example, accurate place- ment of picture elements, use of TEX fonts, ability to incorporate mathematical typesetting, and the possi- bility of introducing macros can be viewed as positive factors of this system. The syntax uses an amal- gamation of ideas from METAFONT, METAPOST, PSTricks, and SVG, allowing its users to \program" their desired graphics. The latest revision to TikZ introduces many new features to an already feature- packed system, as evidenced by its 560-page user manual. Here, we present a tutorial overview of this …
The Two Covering Radius Of The Two Error Correcting Bch Code, Andrew Klapper, Andrew Mertz
The Two Covering Radius Of The Two Error Correcting Bch Code, Andrew Klapper, Andrew Mertz
Andrew Mertz
The m-covering radii of codes are natural generalizations of the covering radii of codes. In this paper we analyze the 2-covering radii of double error correcting BCH code.
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
C^1 Actions Of The Mapping Class Group On The Circle, Kamlesh Parwani
Kamlesh Parwani
Let S be a connected orientable surface with finitely many punctures, finitely many boundary components, and genus at least 6. Then any C^1 action of the mapping class group of S on the circle is trivial. The techniques used in the proof of this result permit us to show that products of Kazhdan groups and certain lattices cannot have C^1 faithful actions on the circle. We also prove that for n > 5, any C^1 action of Aut(F_n) or Out(F_n) on the circle factors through an action of Z/2Z.
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
The Two Variable Substitution Problem For Free Products Of Groups, Leo P. Comerford, Charles C. Edmunds
Leo Comerford
We consider equations of the form W(x,y) = U with U an element of a free product G of groups. We show that with suitable algorithmic conditions on the free factors of G, one can effectively determine whether or not the equations have solutions in G. We also show that under certain hypotheses on the free factors of G and the equation itself, the equation W(x,y) = U has only finitely many solutions, up to the action of the stabilizer of W(x,y) in Aut().
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
Kamlesh Parwani
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
Kamlesh Parwani
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
Andrew Mertz
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
Andrew Mertz
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
Andrew Mertz
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.
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Simple Braids For Surface Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let S be a compact, oriented surface with negative Euler characteristic and f:S→S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (p→,q), then there exists a simple braid with the same rotation vector.
Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani
Actions Of Sl(N,Z) On Homology Spheres, Kamlesh Parwani
Kamlesh Parwani
Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a finite group action.
Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani
Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani
Kamlesh Parwani
Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.
Beamer By Example, Andrew Mertz, William Slough
Beamer By Example, Andrew Mertz, William Slough
Andrew Mertz
There are a variety of LaTeX classes which can be used to produce "overhead slides" for presentations. One of these, beamer, provides flexible and powerful environments which can be used to create slides and PDF-based documents suitable for presentations. Although the class is extensively documented, first-time users may prefer learning about this class using a collection of graduated examples. The examples presented here cover a wide spectrum of use, from the simplest static slides to those with dynamic effects.
Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles C. Edmunds, Gerhard Rosenberger
Commutators As Powers In Free Products Of Groups, Leo Comerford, Charles C. Edmunds, Gerhard Rosenberger
Leo Comerford
The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified