We study a noncommutative generalization of Jordan algebras called Leibniz— Jordan algebras. These algebras satisfy the identities [x1x2]x3 = 0, (x 2 1 , x2, x3) = 2(x1, x2, x1x3), x1(x 2 1 x2) = x 2 1 (x1x2); they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits— Kantor—Koecher construction for Leibniz—Jordan a...

introduction: to report the experience of the jordan university hospital with respect to the surgical treatment of otosclerosis and to compare results and complications with published studies.   materials and methods: the medical records of all patients who underwent stapes surgery for otosclerosis at the jordan university hospital during the period january 2003 to december 2010 were reviewed. ...

OBJECTIVE Non-Hodgkin lymphoma (NHL) is one of the most frequent malignancies in Jordan. The aims of this study are: 1. To classify NHL cases in Jordan, using the new World Health Organization (WHO) classification system, 2. To identify the most common types of NHL in Jordan, and 3. To compare lymphoma types and patterns in Jordan with those in surrounding countries and the West. METHODS We s...

background : the incidence of thyroid cancer has varied from 2 per 100,000 in europe to 21 per 100,000 in the hawaiian chinese population and is 2-3 fold more common in females. middle east cancer consortium figures from 1996-2001 have recorded different age standardized incidence rates that ranged from 2 per 100,000 in egypt to 7.5 per 100,000 among israeli jews. in jordan the age standardized...

Any linear transformation can be represented by its matrix representation. In an ideal situation, all linear operators can be represented by a diagonal matrix. However, in the real world, there exist many linear operators that are not diagonalizable. This gives rise to the need for developing a system to provide a beautiful matrix representation for a linear operator that is not diagonalizable....

We have recently proposed a pre-quantum, pre-spacetime theory as matrix-valued Lagrangian dynamics on an octonionic spacetime. This offers the prospect of unifying internal symmetries standard model with pre-gravitation. explain why such quantum gravitational is in principle essential even at energies much smaller than Planck scale. The can also predict values free parameters low-energy model: ...

This theory provides a compact formulation of Gauss-Jordan elimination for matrices represented as functions. Its distinctive feature is succinctness. It is not meant for large computations. 1 Gauss-Jordan elimination algorithm theory Gauss-Jordan-Elim-Fun imports Main begin Matrices are functions: type-synonym ′a matrix = nat ⇒ nat ⇒ ′a In order to restrict to finite matrices, a matrix is usua...

This paper outlines a proof of the Jordan Normal Form Theorem. First we show that a complex, finite dimensional vector space can be decomposed into a direct sum of invariant subspaces. Then, using induction, we show the Jordan Normal Form is represented by several cyclic, nilpotent matrices each plus an eigenvalue times the identity matrix – these are the Jordan