On the coset category of a skew lattice

Skew lattices are non-commutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute $\wedge$-distributive skew lattices.Comment: 17 pages, submitted to Demonstratio Mathematica. arXiv admin note: text overlap with arXiv:1212.649

On ideals of a skew lattice

Ideals are one of the main topics of interest to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be derived, respectively, from the two concepts of order that arise in the context of skew lattices. The correspondence between the ideals of a skew lattice, derived from the preorder, and the ideals of its respective lattice image is clear. Though, skew ideals, derived from the partial order, seem to be closer to the specific nature of skew lattices. In this paper we review ideals in skew lattices and discuss the intersection of this with the study of the coset structure of a skew lattice.Comment: 16 page

Hot Topics in BaBar

We present recent results concerning the searches for light Higgs-like particles in the decay $\Upsilon (3S) \to \gamma A^{0}, A^{0}\to \mu^{+}\mu^{-}$ as well as for the lepton flavour violation in the decays $\Upsilon (3S) \to e^{\pm}\tau^{\mp},\mu^{\pm}\tau^{\mp}$ and $\tau \to 3l (l=e,\mu)$ with the BaBar experiment.Comment: 5 pages, 3 figures, proceeding for Rencontres de Moriond EW 200

Network Information Flow in Small World Networks

Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class of networks are said to have a small-world topology. In the context of communication networks, navigable small-world topologies, i.e. those which admit efficient distributed routing algorithms, are deemed particularly effective, for example in resource discovery tasks and peer-to-peer applications. Breaking with the traditional approach to small-world topologies that privileges graph parameters pertaining to connectivity, and intrigued by the fundamental limits of communication in networks that exploit this type of topology, we investigate the capacity of these networks from the perspective of network information flow. Our contribution includes upper and lower bounds for the capacity of standard and navigable small-world models, and the somewhat surprising result that, with high probability, random rewiring does not alter the capacity of a small-world network.Comment: 23 pages, 8 fitures, submitted to the IEEE Transactions on Information Theory, November 200

A multiplicative product of distributions and a class of ordinary differential equations with distributional coefficients

We construct a generalization of the multiplicative product of distributions presented by L. H\"ormander in [L. H\"ormander, {\it The analysis of linear partial differential operators I} (Springer-Verlag, 1983)]. The new product is defined in the vector space {\mathcal A}(\bkR) of piecewise smooth functions f: \bkR \to \bkC and all their (distributional) derivatives. It is associative, satisfies the Leibniz rule and reproduces the usual pointwise product of functions for regular distributions in {\mathcal A}(\bkR). Endowed with this product, the space {\mathcal A}(\bkR) becomes a differential associative algebra of generalized functions. By working in the new {\mathcal A}(\bkR)-setting we determine a method for transforming an ordinary linear differential equation with general solution $\psi$ into another, ordinary linear differential equation, with general solution $\chi_{\Omega} \psi$, where $\chi_{\Omega}$ is the characteristic function of some prescribed interval \Omega \subset \bkR.Comment: 23 pages, Latex fil

A SCADA System for Energy Management in Intelligent Buildings

This paper develops an energy management platform for intelligent buildings using a SCADA system (Supervisory Control And Data Acquisition). This SCADA system integrates different types of information coming from the several technologies present in modern buildings (control of ventilation, temperature, illumination, etc.). The developed control strategy implements an hierarchical cascade controller where inner loops are performed by local PLCs (Programmable Logic Controller), and the outer loop is managed by a centralized SCADA system, which interacts with the entire local PLC network. In this paper a Predictive Controller is implemented above the centralized SCADA platform. Tests applied to the control of temperature and luminosity in huge-area rooms are presented. The developed Predictive Controller optimizes the satisfaction of user explicit preferences coming from several distributed user-interfaces, subjected to the overall constraints of energy waste minimization. In order to run the Predictive Controller with the SCADA platform a communication channel was developed to allow communication between the SCADA system and the MATLAB application where the Predictive Controller runs