In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors Fi from finitely generated kE-modules of constant Jordan type to vector bundles over projective space Pr−1. The fibers of the functors Fi encode complete information about the Jordan type of the module. We prove that given any vector bundle F of rank s on Pr−1, there is a kE-module M...

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

Fung 11, Abu-Elmagd K, Todo S, Shapiro R, Tzakis A, Jordan M, Armitage J, Jain A, Martin M, Bronster 0, Stieber A, Kormos R, Selby R, Gordon R, Starzl TE. FK506 in clinical organ transplantation. John J. Fung, Kareem Abu-Elmagd, Saloro Todo, Ronald Shapiro, Andreas Tzakis, Mark Jordan, John Armitage, Ashok Jain, Maureen Martin, Oscar Bronster, Andrei Stieber, Robert Kormos, Robert Selby, Robert...

Let L be the generalized mixed product ideal induced by a monomial ideal I. In this paper we compute powers of the genearlized mixed product ideals and show that Lk  have a linear resolution if and only if Ik have a linear resolution for all k. We also introduce the generalized mixed polymatroidal ideals and prove that powers and monomial localizations of a generalized mixed polymatroidal ideal...

PURPOSE To evaluate clinical outcomes, quality-adjusted life years (QALY), cost effectiveness and cost utility associated with VNS therapy in children with refractory epilepsy in a developing country. METHODS Retrospective review of all children who underwent VNS implantation at King Abdullah University Hospital and Jordan University Hospital in Jordan. RESULTS Twenty eight patients (16 mal...