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  • 1.
    Bäck, Per
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Notes on formal deformations of quantum planes and universal enveloping algebras2019In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1194, no 1, article id 012011Article in journal (Refereed)
    Abstract [en]

    In these notes, we introduce formal hom-associative deformations of the quantumplanes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras.We then show that these deformations induce formal hom-Lie deformations of the correspondingLie algebras constructed by using the commutator as bracket.

  • 2.
    Bäck, Per
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-associative Ore extensions2018In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, no 1, article id 012006Article in journal (Refereed)
    Abstract [en]

    We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

  • 3.
    Mitrovic, Melanija
    et al.
    Faculty of Mechanical Engineering, University of Nis, Serbia.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Crvenkovic, S
    Department of Mathematics and Informatics, University of Novi Sad, Serbia.
    Romano, D. A.
    International Mathematical Virtual Institute, Banja Luka, Republic of Srpska, Bosnia and Herzegovina.
    Constructive Semigroups with Apartness: Towards a New Algebraic Theory2019In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1194, no 1, p. 1-8, article id 012076Article in journal (Refereed)
    Abstract [en]

    The theory of constructive semigroups with apartness is a new approach tosemigroup theory, and not a new class of semigroups. Of course, our work is partly inspired byclassical semigroup theory, but, on the other hand, it is distinguished from it by two signicantaspects: rst, we use intuitionistic logic rather than classical, secondly, our work is based onthe notion of apartness (between elements, elements and sets). Here, the focus is on E. Bishop'sapproach to constructive mathematics (BISH)

  • 4.
    Olsson, Tomas
    et al.
    Mälardalen University, School of Innovation, Design and Engineering.
    Funk, Peter
    Mälardalen University, School of Innovation, Design and Engineering.
    Case-based reasoning combined with statistics for diagnostics and prognosis2012In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 364, no 1, p. Article number: 012061-Article in journal (Refereed)
    Abstract [en]

    Many approaches used for diagnostics today are based on a precise model. This excludes diagnostics of many complex types of machinery that cannot be modelled and simulated easily or without great effort. Our aim is to show that by including human experience it is possible to diagnose complex machinery when there is no or limited models or simulations available. This also enables diagnostics in a dynamic application where conditions change and new cases are often added. In fact every new solved case increases the diagnostic power of the system. We present a number of successful projects where we have used feature extraction together with case-based reasoning to diagnose faults in industrial robots, welding, cutting machinery and we also present our latest project for diagnosing transmissions by combining Case-Based Reasoning (CBR) with statistics. We view the fault diagnosis process as three consecutive steps. In the first step, sensor fault signals from machines and/or input from human operators are collected. Then, the second step consists of extracting relevant fault features. In the final diagnosis/prognosis step, status and faults are identified and classified. We view prognosis as a special case of diagnosis where the prognosis module predicts a stream of future features.

  • 5.
    Ongong'a, Elvice
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Nairobi, Nairobi, Kenya .
    Richter, Johan
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Hom-Lie structures on 3-dimensional skew symmetric algebras2019In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1416, no 1, p. 1-8, article id 012025Article in journal (Refereed)
    Abstract [en]

    We describe the dimension of the space of possible linear endomorphisms that turn skew-symmetric three-dimensional algebras into Hom-Lie algebras. We find a correspondence between the rank of a matrix containing the structure constants of the bilinear product and the dimension of the space of Hom-Lie structures. Examples from classical complex Lie algebras are given to demonstrate this correspondence.

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