Let A be a matrix and λ0 be one of its eigenvalues having g elementary Jordan blocks in the Jordan canonical form of A. We show that for most matrices B satisfying rank (B) ≤ g, the Jordan blocks of A+B with eigenvalue λ0 are just the g− rank (B) smallest Jordan blocks of A with eigenvalue λ0. The set of matrices for which this behavior does not happen is explicitly characterized through a scal...

Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras an...

A purely geometric method for constructing reflections in Jordan curves on the Riemann sphere based on hyperbolic geodesics is introduced. It is then possible to investigate the relations between the geometry of a Jordan domain D and the properties of the reflection by studying properties of hyperbolic geodesics. This idea is used to characterize unbounded Jordan John domains in terms of reflec...

We study the elements in the structure group of an algebraic curvature tensor R by analyzing Jordan normal forms. Because every matrix has a unique Jordan normal form representation, up to a permutation of the Jordan Blocks, we are able to determine which matrices taking on a specific form will be in the structure group of some algebraic curvature tensor. A method for analyzing these forms is d...

This volume has emerged from a theme session with the same title as that of this introductory chapter, organized at the Towards a Science of Consciousness conference in Budapest, on July 23, 2007. Both the session and this volume have been motivated by the wish to redress the peculiarly low profile of informed discussions of the place of language within the modern field of consciousness studies...

Climate change and increased urban demand can significantly stress water supply systems, emphasizing the importance of reallocating reservoir storage for the designed uses. Most studies on climate change assessment have analyzed arid region reservoirs due to high interannual variability in streamflows. This study focuses on a within-year reservoir system, Lake Jordan in North Carolina, from a t...