We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the Minkowskian spacetimes by an extra “dilatonic” coordinate, whose rotation, Lorentz and conformal groups are SO(d−1), SO(d−1, 1)×SO(1, 1) and SO(d, 2)×SO(2, 1), respective...

The structure of the set of compact constant mean curvature surfaces whose boundary is a given Jordan curve in R seems far from being understood. We shall consider a simple, but interesting, situation concerning this problem: Assume that M be an embedded compact H-surface in R+ = {x3 ≥ 0} with ∂M = Γ ⊂ P = {x3 = 0}. Then, there is little known about the geometry and topology of M in terms of Γ....

Physically meaningful regions can be modeled by regular open semianalytic sets with bounded boundaries. These sets are named as Yin sets and they form a topological space called the Yin space. Due to the regularity, the Yin sets can be represented by a collection of particular sets of oriented Jordan curves; this collection is referred to as the Jordan space. After defining a meet operation, a ...

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...

Based on recent developments and the predicted future advancement of lighting technologies, researchers are now questioning extent to which daylight is effective in lowering overall energy consumption buildings. As light-emitting diode (LED) luminaires highly efficient, amount power consumed for purposes can be reduced, even situations where system at its full power. It has already been demonst...

Bounded symmetric domains (Cartan domains and exceptional domains) are higher-dimensional generalizations of the open unit disc. In this note we give a structure theory for the C*-algebra T generated by all Toeplitz operators Tf(h) := P{fh) with continuous symbol function ƒ G C(S) on the Shilov boundary 5 of a bounded symmetric domain D of arbitrary rank r. Here h belongs to the Hardy space H(S...

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...