We analyze the asymptotic behavior of the degree sequence of Random Apollonian Networks [11]. For previous weaker results see [10, 11].

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...

Abstract We call a packing of hyperspheres in n dimensions an Apollonian sphere if the spheres intersect tangentially or not at all; they fill -dimensional Euclidean space; and every is member cluster $n+2$ mutually tangent (and few more properties described herein). In this paper, we describe eight that naturally arises from study generic nodal Enriques surfaces. The $E_7$ , $E_8$ Reye lattice...

Abstract This article provides a comparative study of the underlying cognitive structures laid out in Arthur Machen’s decadent novella The Great God Pan (1894) and Friedrich Nietzsche’s “On Truth Lying Non-Moral Sense” (1873). It scrutinizes images “chamber consciousness” “the house life”, deployed by German philosopher Welsh author respectively, explores how use stylistic qualities both affect...