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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
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.
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
Faculty Research and Creative Activity
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.
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
Faculty Research and Creative Activity
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.
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
Faculty Research and Creative Activity
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 …