We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equat...

The theory of complex hyperbolic discrete groups is still in its childhood but promises to grow into a rich subfield of geometry. In this paper I will discuss some recent progress that has been made on complex hyperbolic deformations of the modular group and, more generally, triangle groups. These are some of the simplest nontrivial complex hyperbolic discrete groups. In particular, I will talk...

In this paper we study the chaotic bands of any Mandelbrot set hyperbolic component. We use external arguments in order to identify the hyperbolic components. If we use harmonics as a tool, we can calculate the chaotic bands. Indeed, as we clearly show here, the harmonics of the external arguments of a given hyperbolic component (gene) are the external arguments of the last appearance hyperboli...

This paper describes a general algorithm for finding the commensurator of a non-arithmetic hyperbolic manifold with cusps, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding horosphere packings and canonical cell decompositions. For example, we use this to find the commensurators of all non-arithmetic hyperbolic once-punctur...

We study the geometry of non-relatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with non-relatively hyperbolic peripheral subgroups is a quasi-isometry invariant...

In this paper, a numerical study is conducted in order to compare hyperbolic range of equations of isotherm two-fluid model governing on two-phase flow inside of pipe using conservative Shock capturing method. Differential equations of the two-fluid model are presented in two forms (i.e. form I and form II). In forms I and II, pressure correction terms are hydrodynamic and hydrostatic, respecti...

Manami Hara, Restituto F. Dizon, Benjamin S. Glick, Catherine S. Lee, Klaus H. Kaestner, David W. Piston, and Vytautas P. Bindokas Departments of Medicine, Molecular Genetics and Cell Biology, and Neurobiology, Pharmacology and Physiology, University of Chicago, Chicago, Illinois; Department of Genetics, University of Pennsylvania, Philadelphia, Pennsylvania; and Department of Molecular Physiol...

B category, and a bubble attached to a node represents a set of archaeological records. The size of a bubble attached to a node reflects the number of records belonging to that category. The hyperbolic tree supports ‘‘focus + context’’ navigation; it also provides an overview of records organized in the archaeological digital library. It shows that the records are from seven archaeological site...

Abstra t|Speedup is one of the main performan e hara teristi s of distributed appli ations. It is de ned as the ratio of appli ation's exe ution time on a single pro essor to the exe ution time, of the same workload, on a system omposed on N pro essors. This paper analyzes, in very general terms, the speedup that an be a hieved in distributed environments and shows why some appli ations s ale v...

Manami Hara, Restituto F. Dizon, Benjamin S. Glick, Catherine S. Lee, Klaus H. Kaestner, David W. Piston, and Vytautas P. Bindokas Departments of Medicine, Molecular Genetics and Cell Biology, and Neurobiology, Pharmacology and Physiology, University of Chicago, Chicago, Illinois; Department of Genetics, University of Pennsylvania, Philadelphia, Pennsylvania; and Department of Molecular Physiol...