This study refers to EVOLUTE (a project of Information Society Technologies (IST)) that combines Session Initiation Protocol (SIP) with Mobile IP (MIP) to support macro-mobility management and provides seamless multimedia services for roaming users. Moreover, this study utilizes Multicast-based Mobility (M&M) to assist Cellular IP (CIP) in micro-mobility management. The aim of this work is to g...

Jørgensen’s inequality gives a necessary condition for a non-elementary two generator group of isometries of real hyperbolic 2-space to be discrete. We give analogues of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic n-space generated by two elements, one of which is loxodromic. Mathematics Subject Classifications (2000): 20H10, 22E40, 57S30.

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic n–orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a new subgroup separability result for general arithmetic lattices. Cusps of arithmetic orbifolds 1

Some complex quaternionic equations in the type AX - XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

The contribution of this work is to generalize the real and complex wavelet transforms and to derive for the first time a quaternionic wavelet pyramid for multi-resolution analysis using three phases. The paper can be very useful for researchers and practitioners interested in understanding and applications of the quaternion wavelet transform.

A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J,K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov and Chern-Levine-Niren...