A mobile systems interface protocol

Recent progresses in the software development world has assisted a change in hardware from heavy mainframes and desktop machines to unimaginable small devices leading to the prophetic "third computing paradigm", Ubiquitous Computing. Still, this novel unnoticeable devices lack in various capabilities, like computing power, storage capacity and human interface. Connectivity associated to this devices is also considered an handicap which comes generally associated expensive and limited protocols like GSM and UMTS. Considering this scenario as background, this paper presents a minimal communication protocol introducing better interfaces for limited devices. Special attention has been paid to the limitations of connectivity, storage capacity and scalability of the developed software applications. Illustrating this new protocol, a case-study is presented addressing car sensors communicating with a central

On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.