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...

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...

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...

The holonomy-flux *-algebra was recently proposed as an algebra of basic kinematical observables for loop quantum gravity. We show the conventional GNS construction breaks down when the the holonomyflux *-algebra is allowed to be a Jordan algebra of observables. To remedy this, we give a Jordan GNS construction for the holonomy-flux *-algebra that is based on trace. This is accomplished by assu...

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...

We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having the exceptional Jordan algebra as a direct summand. We then construct several dagger compact categories of such Jordan-algebraic models. One of these neatly unifies real, complex and quaternionic mixed-stat...

The Jordan center of a graph is defined as a vertex whose maximum distance to other nodes in the graph is minimal, and it finds applications in facility location and source detection problems. We study properties of the Jordan center in the case of random growing trees. In particular, we consider a regular tree graph on which an infection starts from a root node and then spreads along the edges...

The aim of the famous Born and Jordan 1925 paper was to put Heisenberg's matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg's theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger's wave mechanics cannot...

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...

* 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...