Results 101 to 110 of about 1,596 (215)
The dynamics of Super-Apollonian continued fractions
Transactions of the American Mathematical Society, 2019 We examine a pair of dynamical systems on the plane induced by a pair of spanning trees in the Cayley graph of the Super-Apollonian group of Graham, Lagarias, Mallows, Wilks, and Yan. The dynamical systems compute Gaussian rational approximations to complex numbers and are “reflective” versions of the complex continued fractions of A. L. Schmidt.
Chaubey, Sneha +3 more
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Ising models on the regularized Apollonian network.
, 2013 We investigate the critical properties of Ising models on a regularized Apollonian network (RAN), here defined as a kind of Apollonian network in which the connectivity asymmetry associated with its corners is removed.
SERVA, Maurizio +2 more
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Apollonian Packings And Kac-Moody Root Systems
We study Apollonian circle packings using the properties of a certain rank 4 indefinite Kac-Moody root system ϕ. We introduce the generating function Z(s) of a packing, an exponential series in four variables with an Apollonian symmetry group, which is a
Whitehead, Ian
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Vertex labeling and routing in expanded Apollonian networks [PDF]
, 2007 We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered.
Zhang, Zhongzhi +5 more
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De la sensation de l’odeur à la sensation du goût
Cahiers Balkaniques, 2017 This paper focuses on two Mediterranean poets of different backgrounds, namely the Greek poet Odysseas Elytis and the Turkish poet Nazim Hikmet, aims at comparing their divergent worldviews.
Nadia Stylianou
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Images of Time and Timelessness: A Musical Reading of Death in Venice
Current Musicology, 2014 This essay is based on an old, well–known question in aesthetics: how to represent time in its fleetingness without halting, appropriating, objectifying, or transcending it?
Marlies De Munck
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Regular polytopes, sphere packings and Apollonian sections
In this paper, we explore the geometry and the arithmetic of a family of polytopal sphere packings induced by regular polytopes in any dimension. We prove that every integral polytope is crystallographic, and we show that there are 11 crystallographic ...
Rasskin, Iván
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A New Look at Apollonian Circle Packings
, 2017 We define an abstract Apollonian supergasket using the solution set of a certain Diophantine equation, showing that the solutions are in bijective correspondence with the circles of any concrete supergasket.
O\u27Connell, Dylan +3 more
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On certain properties of random apollonian networks [PDF]
, 2012 . In this work we analyze fundamental properties of Random Apollonian Networks [34,35], a popular random graph model which generates planar graphs with power law properties. Specifically, we analyze (a) the degree distribution, (b) the k largest degrees,
Charalampos E. Tsourakakis, Alan Frieze
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Classica, Revista Brasileira de Estudos Clássicos, 1989 Both Philosophy and Tragedy are derived from ancient Greek religion. The former appeared when myths ceased to satisfy the curiosity and the desire of those thinkers who searched for a rational explanation of the origin of the universe; the latter, at the
João Pedro Mendes
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