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The Exponent of covergence and a theorem of astala

Indiana University Mathematics Journal, 2002
Summary: We provide bounds on the exponent of convergence of a planar discrete quasiconformal group in terms of the associated dilatation and (a) the Hausdorff dimension of its conical limit set, or (b) the exponent of convergence of an underlying Kleinian group.
Bonfert-Taylor, Petra, Taylor, Edward C.
openaire   +2 more sources

-convergence of power-law functionals with variable exponents

Nonlinear Analysis: Theory, Methods & Applications, 2010
The paper is focused on the \(\Gamma\)-convergence of integral functionals of the type \[ I_n(u)= \begin{cases} \int_\Omega \displaystyle \frac{1}{p_n(x)}|\lambda(x) \nabla u(x)|^{p_n(x)}dx &u \in W^{1,p_n(\cdot)}(\Omega)\\ \infty&\text{elsewhere in} \;\;L^1(\Omega) \end{cases} \] and \[ J_n(u)= \begin{cases} \inf\left\{ \mu >0 : \int_\Omega \left ...
Bocea, Marian, Mihăilescu, Mihai
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Irrationality exponent and convergence exponent in continued fraction expansions

Nonlinearity
Abstract Let x ∈ ( 0 , 1 ) be an irrational number with continued ...
Song, Kunkun   +2 more
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On the exponent of convergence of a packing of spheres

Mathematika, 1966
Suppose, in n-dimensional Euclidean space, a sequence of disjoint closed spheres is packed into the open unit n-cube In in such a way as to ensure that the residual set has zero volume. Then, of course, is convergent and it can be shown, for n = 2, that is divergent. Let the exponent of convergence of the packing be the supremum of those real numbers t
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Convergence Exponent of a Singular Series for a Multi–Dimensional Problem

Moscow University Mathematics Bulletin, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arkhipova, L. G., Chubarikov, V. N.
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A Convergence exponent for multidimensional continued-fraction algorithms

Journal of Statistical Physics, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convergence to a Gaussian limit as the normalization exponent tends to

Statistics & Probability Letters, 1991
Abstract Certain quadratic forms with long-range dependence, normalized by Nd with d > 1 2 , have a non-Gaussian limit, but under further normalization, as d → 1 2 , the limit becomes Gaussian.
Norma Terrin, Murad S. Taqqu
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Relation between fractal dimension and convergence exponents

Physics Letters A, 1984
Abstract The convergence exponents α and β introduced by Grassberger for the box-counting algorithm are discussed. We show that α (1 + β) is an estimate from above of the fractal dimension and we verify the relation in two cases.
R. Badii, A. Politi
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Convergent Series with Exponents: 10928

The American Mathematical Monthly, 2003
Christopher J. Hillar   +1 more
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The Exponent of Convergence of Poincaré Series

Proceedings of the London Mathematical Society, 1968
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