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Topic: Fuchsian model

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Fuchsian group

Kleinian model

Hyperbolic geometry

Fundamental group

Riemannian geometry

Spherical geometry

Riemannian manifold

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	Hyperbolic geometry (Site not responding. Last check: 2007-11-05)
		The Klein model, also known as the projective disc model and Beltrami-Klein model, uses the interior of a circle for the hyperbolic plane, and chords of the circle as lines.
		The Poincaré disc model, also known as the conformal disc model, also employs the interior of a circle, but lines are represented by arcs of circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.
		The quotient space H/Γ of the upper half-plane modulo the fundamental group is known as the Fuchsian model of the hyperbolic surface.
	hyperbolic-geometry.mindbit.com (711 words)

	[ info-about.be \| Hyperbolic geometry Resources ] (Site not responding. Last check: 2007-11-05)
		PoincarÃ© disc imitation of towering rhombitruncated {3,7} tiling The Klein model, as robust accepted as the projective disc imitation 'n Beltrami-Klein model, uses the domestic of a circle for the hyperbolic plane, 'n chords of the circle as lines.
		The PoincarÃ© disc model, as robust accepted as the conformal disc model, as robust employs the domestic of a circle, but scratchs are represented by arcs of circles that are orthogonal to the boundary circle, secondly diameters of the boundary circle.
		The quotient space H/Î“ of the upper half-plane modulo the grass roots machine is accepted as the Fuchsian model of the hyperbolic surface.
	www.info-about.be /Hyperbolic_geometry (1428 words)

	Fuchsian model - Wikipedia, the free encyclopedia
		In mathematics, a Fuchsian model is a representation of a hyperbolic Riemann surface R.
		The Fuchsian model of R is the quotient space
		An analogous construction for 3D manifolds is the Kleinian model.
	en.wikipedia.org /wiki/Fuchsian_model (245 words)

	Fuchsian group - Wikipedia, the free encyclopedia
		In mathematics, a Fuchsian group is a particular type of group of isometries of the hyperbolic plane.
		A Fuchsian group is always a discrete group, and thus is a lattice in one of the two semisimple Lie groups PSL(2,R) or PSL(2,C).
		All hyperbolic and parabolic cyclic subgroups of PSL(2,R) are Fuchsian.
	en.wikipedia.org /wiki/Fuchsian_group (1006 words)

	Hyperbolic_geometry info here at en.articles-on-stress-of.info (Site not responding. Last check: 2007-11-05)
		There are four models ordinarily used for hyperbolic geometry: the Klein model, the PoincarÃ© disc model, the PoincarÃ© half-plane model, and the Lorentz model, or hyperboloid model.
		The PoincarÃ© disc model, in addition notable as the conformal disc model, in addition employs the home of a circle, but rules are represented by arcs of circles that are orthogonal to the boundary circle, and diameters of the boundary circle.
		The quotient space H/Î“ of the upper half-plane modulo the axiological drove is notable as the Fuchsian model of the hyperbolic surface.
	en.articles-on-stress-of.info /Hyperbolic_geometry (1480 words)

	Hyperbolic_geometry info here at en.10-parenting-tips.info (Site not responding. Last check: 2007-11-05)
		There are four models regularly used for hyperbolic geometry: the Klein model, the PoincarÃ© disc model, the PoincarÃ© half-plane model, 'n the Lorentz model, or hyperboloid model.
		The PoincarÃ© disc model, counting accepted as the conformal disc model, counting employs the domestic of a circle, but configurations are represented by arcs of circles that are orthogonal to the boundary circle, also diameters of the boundary circle.
		The quotient space H/Î“ of the upper half-plane modulo the foundational clump is accepted as the Fuchsian model of the hyperbolic surface.
	en.10-parenting-tips.info /Hyperbolic_geometry (1491 words)

	Angela Vierling-Claassen: Models of Mathematical Surfaces
		Has a pretty extensive collection of models in the Division of Information Technology and Society, but only a couple were on display the last that I was there.
		Thanks to Yoshiaki ARAKI (who is involved in modeling of 3D quasi-fuchsian fractals) for the tip.
		They had a couple of plastic models showing intersections of surfaces that had stickers saying "Unterrights Modelle" and that they were made in Germany.
	www.math.harvard.edu /~angelavc/models/locations.html (766 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		A fairly wide class of discrete groups of transformations, which includes Fuchsian and crystallographic groups, is constituted by discrete subgroups (cf.
		The following description of freely-acting Fuchsian groups with a compact quotient space, which is due to Poincaré, may serve as an example of the above-said.
		is taken to be the standard model of the Lobachevskii geometry (Poincaré's model of the Lobachevskii plane).
	eom.springer.de /d/d033080.htm (1063 words)

	Explicit Isoperimetric Constants and Phase Transitions in the Random-Cluster Model, Olle Häggström, Johan ...
		The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models.
		In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster parameter $q \geq 1$.
		Such considerations are also used to prove nonrobust phase transition for the Potts model on nonamenable regular graphs.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aop/1020107775 (831 words)

	News \| Gainesville.com \| The Gainesville Sun \| Gainesville, Fla. (Site not responding. Last check: 2007-11-05)
		Eugenio Beltrami then provided models of it, and used this to prove that hyperbolic geometry was consistent if Euclidean geometry was.
		There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disc model, the Poincaré half-plane model, and the Lorentz model, or hyperboloid model.
		A particularly well-known paper model based on the pseudosphere is due to William Thurston.
	www.gainesville.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=hyperbolic_geometry (1323 words)

	JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
		The paper is devoted to the study of the basic ergodic properties (ergodicity and conservativity) of the horocycle flow on surfaces of constant negative curvature with respect to the Liouville invariant measure.
		In particular, we show that normal subgroups of divergent-type Fuchsian groups provide natural examples for the strictness of a number of inclusions in the classification of Fuchsian groups.
		A random perturbation of a dynamical system serving as a model for the drilling process is studied.
	www.wisdom.weizmann.ac.il /~yakov/JDCS/ABSTRACTS/2000-1.html (610 words)

	The Modular Group and Fractals
		Lattice models and fractal measures (33 pages) points out that the prototypical "multifractal measure", namely, the derivative of the Minkowski Question Mark function.
		Some crude attempts are made to explore alternative topologies, including topologies associated with one-dimensional lattice models, such as the Ising model or the Potts model.
		It is conjectured that the mutli-fractal measures correspond to smooth, differentiable Hamlitonians on one-dimensional lattice models.
	www.linas.org /math/sl2z.html (1772 words)

	Fuchsian Model of a Riemann Surface - Maple Application Center - Maplesoft
		This worksheet computes the fundamental region and tiling of a Fuchsian group with signature (g, [m[1],..m[r]], s, t), corresponding to a compact Riemann surface of genus g, with r branch points, from which s points and t closed disks have been deleted.
		To run the program, select the group signature, entered as Maple sequence model at the beginning of the next section, and execute the worksheet.
		The number of displayed images of the fundamental region is controlled by the variable levmax at the end of the worksheet.
	www.maplesoft.com /applications/app_center_view.aspx?AID=1291&CID=1&SCID=5 (118 words)

	Classical Hall Effect
		In the paper [MM] below, we propose a noncommutative geometry model on the hyperbolic plane for the fractional quantum Hall effect, extending earlier work done in [CHMM] and also building on fundamental work mainly by Bellissard and collaborators, who established a noncommutative geometry model on the Euclidean plane for the integer quantum Hall effect.
		The Hall conductance is derived to be a cyclic 2-cocycle on the algebra of observables and its expression resembles a generalized Kubo formula.
		Under the assumption that the Fermi level is in a spectral gap of the Hamiltonian, we establish that the Hall conductance is an integer mutiple of orbifold Euler characteristics of cocompact Fuchsian groups, and is therefore topological in character as well as fractional valued.
	www-math.mit.edu /~vmathai/qheweb.html (321 words)

	planet wragg (Site not responding. Last check: 2007-11-05)
		X1 For fifteen days I struggled to prove that no functions analogous to those I have since called Fuchsian functions could exist; I was then very ignorant.
		One evening, contrary to my custom, I took fl coffee; I could not go to sleep; ideas swarmed up in clouds; I sensed them clashing until, to put it so, a pair would hook together to form a stable combination.
		By morning I had established the existence of a class of Fuchsian functions, those derived from the hypergeometric series.
	www.switcht.com /raggy/coffee.htm (128 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		and the Beltrami-Klein models in the unit disc, the upper-half plane model.
		Fuchsian groups: the group PSL(2,R); discrete and properly
		Anosov closing lemma and Livshitz theorem for the geodesic flow.
	www.math.psu.edu /katok_s/597C-F99/597C-desc.html (163 words)

	riemann_surface (Site not responding. Last check: 2007-11-05)
		The Riemann surfaces with curvature -1are called hyperbolic; the open disk with the PoincarÃ©-metric of constant curvature -1 is the canonical local model.
		The set of representatives of the cosets are called fundamental domains.
		Similarly, for every hyperbolic Riemann surface, the fundamental group is isomorphic to a Fuchsian group, and thus the surface can be modelled by a Fuchsian model H/Γ where H is the upper half-plane and Γ is the Fuchsian group.
	www.holdemseriespoker.com /wiki/?title=Riemann_surface (1255 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-11-05)
		math-ph/0609074 Holonomy of the Ising model form factors.
		math-ph/0506065 Square lattice Ising model susceptibility: connection matrices and singular behavior of $\chi^{(3)}$ and $\chi^{(4)}$.
		math-ph/0407060 The Fuchsian differential equation of the square lattice Ising model $\chi(3)$ susceptibility.
	front.math.ucdavis.edu /author/Zenine-N* (145 words)

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