Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

In this paper, we study the module structure of homology Artin kernels, i.e., kernels non-resonant characters from right-angled groups onto integer numbers, being with respect to ring $\mathbb{K}[t^{\pm 1}]$, where $\mathbb{K}$ is a field characteristic zero. Papadima and Suciu determined some part by means flag complex graph group. work, provide more properties torsion module, e.g., dimension ...

Let K be a field of characteristic zero. For integers n,D≥1, let Jn(D) the degree n component free Jordan algebra J(D) over D generators. A conjecture for character (in particular dimension) GL(D)-module is proposed. sl2J(D) Tits-Allison-Gao construction J(D). Two natural conjectures homology Lie are stated, and each them implies previous conjecture. The cyclicity structures, namely that symmet...

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...