A characterization is obtained for the matrices A with the property that every (some) Jordan basis of every A-invariant subspace can be extended to a Jordan basis of A. These results are based on a criterion for a Jordan basis of an invariant subspace to be extendable to a Jordan basis of the whole space. The criterion involves two concepts: the constancy property and the depth property. "'Supp...

In a recent article [8], Gowda and Sznajder studied the concept of Schur complement in Euclidean Jordan algebras and described Schur determinantal and Haynsworth inertia formulas. In this article, we establish some more results on the Schur complement. Specifically, we prove, in the setting of Euclidean Jordan algebras, an analogue of the Crabtree-Haynsworth quotient formula and show that any S...

The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we continue a discussion of others [1, 2, 9, 11] that a Jordan curve can be quite fantastical both in some bizarre properties such a curve might ha...

for Proteins Based on PEG-8 Caprylic/Capric Glycerides and Polyglyceryl-6 Dioleate in a Mixture of Oleic Acid with Chitosan Shereen M. Assaf, Nawzat D. Al-Jbour, Ala’a F. Eftaiha, Amani M. Elsayed, Mayyas M. Al-Remawi, Nidal A. Qinna, Babur Chowdhry, Stephen Leharne, and Adnan A. Badwan Department of Pharmaceutical Technology, Faculty of Pharmacy, Jordan University of Science and Technology, Ir...

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...

* MIS Researcher, Department of Management Information Systems, Yarmouk University, Irbid, Jordan. E-mail: [email protected] ** MIS Researcher, Department of Management Information Systems, Yarmouk University, Irbid, Jordan. E-mail: [email protected] *** Lecturer, Department of Computer Information System, Computer Science and Information Technology College, Jordan University of Scienc...