21 research outputs found

    On the coset category of a skew lattice

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    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

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    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

    SMALL AND MEDIUM PORTS' ACTIVITIES MODELLING: INTRODUCTION TO THE PIXEL APPROACH

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    [EN] Port activities undeniably have an impact on their environment, the city and citizens living nearby. To have a better understanding of these impacts, the ports of the future will require tools allowing suitable modelling, simulation and data analysis. This challenge is also tied to another current reality: the heterogeneous data coming from different stakeholders converging into ports are not optimally exploited due to lack of interoperability. Thus, the forthcoming research and development initiatives must address these demands from a holistic point of view. PIXEL (H2020-funded project) aims at creating the first smart, flexible and scalable solution reducing the environmental impact while enabling optimization of operations in port ecosystems. PIXEL brings the most innovative IoT and ICT technology to ports and demonstrate their capacity to take advantage of modern approaches. Using an interoperable open IoT platform, data is acquired and integrated into an information hub comprised of small, low-level sensors up to virtual sensors able to extract relevant data from high level services. Finally, this hub integrates smart models to analyse port processes for prediction and optimization purposes: (i) a model of consumption and energy production of the port with the aim of moving towards green energy production; (ii) a model of congestion of multi-modal transport networks to reduce the impact of port traffic on the network; and (iii) models of environmental pollution of the port to reduce the environmental impacts of the port on the city and its citizens. The main issue tackled by PIXEL is to provide interoperability between these models and allow real integration and communication in the context of an environmental management model. Besides that, PIXEL devotes to decouple port¿s size and its ability to deploy environmental impact mitigation specifying an innovative methodology and an integrated metric for the assessment of the overall environmental impact of ports.The PIXEL project, the results of which are presented in this paper, is being funded from the European Union s Horizon 2020 research and innovation programme under grant agreement no. 769355 Port IoT for Environmental Leverage (PIXEL)Simon, E.; Garnier, C.; Lacalle, I.; Costa, JP.; Palau Salvador, CE. (2019). SMALL AND MEDIUM PORTS' ACTIVITIES MODELLING: INTRODUCTION TO THE PIXEL APPROACH. WIT Transactions on the Built Environment (Online). 187:149-163. https://doi.org/10.2495/MT190141S14916318
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