An explicit global and unique isometric embedding into hyperbolic 3-space, H, of an axisymmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event hor...

We study a new discrete-time dynamical system on circle patterns with the combinatorics of the square grid. This dynamics, called Miquel dynamics, relies on Miquel’s six circles theorem. We provide a coordinatization of the appropriate space of circle patterns on which the dynamics acts and use it to derive local recurrence formulas. Isoradial circle patterns arise as periodic points of Miquel ...

We construct a holographic map from the loop equation of large-N QCD in d = 2 and d = 4, for planar self-avoiding loops, to the critical equation of an equivalent effective action. The holographic map is based on two ingredients: an already proposed holographic form of the loop equation, such that the quantum contribution is reduced to the evaluation of a regularized residue; a new conformal ma...

Various methods to create intricate tilings of 3D space are presented. They include modulated extrusions of 2D Escher tilings, free-form deformations of the fundamental domain of various 3D symmetry groups, highly symmetrical polyhedral toroids of genus 1, higher-genus cage structures derived from the cubic lattice as well as from the diamond and triamond lattices, and finally interlinked tiles...

The fluctuations of the cosmic microwave background (CMB) are investigated for a hyperbolic universe with finite volume. Four-component models with radiation, matter, vacuum energy, and an extra dark energy component, which is a particular version of quintessence, are considered. The general solution of the Friedmann equation for the cosmic scale factor a(η) is given for the four-component mode...

Let Γ ≤ SL2(R) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let E 2k be the holomorphic Eisenstein series of weight 2k on Γ that is nonvanishing at ∞ and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on Γ, and on a choice of a fundamental domain F , we prove that all but possibly c(Γ,F) of the non-trivial ze...

In this paper we address language engineering issues surrounding domain-specific modeling languages (DSMLs). By definition, such languages track the domain, meaning that changes to the domain require changes to the DSML in order to provide an intuitive specification of domain-specific models. For this work, our primary focus is on fundamental limitations that affect the preservation of semantic...

financial fines are regarded as a powerful implement in the hand of competition authorities which apply in the way of ceasing anticompetitive practices and hindering undertakings from entering into monopolization activities.  having regarded the nature and main function of this sanction, this paper in comparative study is going to clarify executive domain and primary stages of fine determining ...

In the past, it was a great triumph of Dirac’s theory to predict the fine structure in the energy levels of the simplest atom. Nevertheless, even the relativistic Dirac theory did not completely describe the spectrum of the electron in an H-atom. However, at that time, attempts to obtain accurate information through a study of the Balmer lines have been frustrated by the large Doppler width in ...

Abstract. In this paper we show that if G is a group acting on a tree X with inversions and if (T Y ) is a fundamental domain for the action of G on X, then there exist a group &tildeG and a tree &tildeX induced by (T Y ) such that &tildeG acts on &tildeX with inversions, G is isomorphic to &tilde G, and X is isomorphic to &tildeX. The pair (&tilde G &tildeX) is called the quasi universal cover...