# Another Motivation for the Hyperbolic Plane Segments Moving on the Line

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Let 1 â†’ (K, K1) â†’ (G, NG(K1)) â†’ (Q,Q1) â†’ 1 be a short exact sequence of pairs of finitely generated groups with K1 a proper non-trivial subgroup of K and K strongly hyperbolic relative to K1. Assuming that, for all g Ïµ G, there exists kg Ïµ K such that gK1g-1 =...

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We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, $E\_q(A+B)\; =...$

- Disentangling q-Exponentials: A General Approach. Quesne, C. // International Journal of Theoretical Physics;Feb2004, Vol. 43 Issue 2, p545
We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, $E\_q(A+B)\; =...$

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We complete the determination of how far convex maps can deform discs in each of the three classical geometries. The euclidean case was settled by Nehari in 1976, and the spherical case by MejÃa and Pommerenke in 2000. We find the sharp bound on the Schwarzian derivative of a hyperbolically...

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We prove the existence of Alexandrov embedded closed magnetic geodesics on closed hyperbolic surfaces. Closed magnetic geodesics correspond to closed curves with prescribed geodesic curvature.