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Construction of an Infinite Cyclic Group Formed by Artificial Differential Neurons

Author

Listed:
  • Jan Chvalina

    (Department of Mathematics, Faculty of Electrical Engineeering and Comunication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic)

  • Bedřich Smetana

    (Department of Quantitative Methods, University of Defence, Kounicova 65, 662 10 Brno, Czech Republic)

  • Jana Vyroubalová

    (Department of Mathematics, Faculty of Electrical Engineeering and Comunication, Brno University of Technology, Technická 8, 616 00 Brno, Czech Republic)

Abstract

Infinite cyclic groups created by various objects belong to the class to the class basic algebraic structures. In this paper, we construct the infinite cyclic group of differential neurons which are modifications of artificial neurons in analogy to linear ordinary differential operators of the n -th order. We also describe some of their basic properties.

Suggested Citation

  • Jan Chvalina & Bedřich Smetana & Jana Vyroubalová, 2022. "Construction of an Infinite Cyclic Group Formed by Artificial Differential Neurons," Mathematics, MDPI, vol. 10(9), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1571-:d:809947
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    References listed on IDEAS

    as
    1. Jan Chvalina & Michal Novák & Bedřich Smetana & David Staněk, 2021. "Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
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    Cited by:

    1. Dario Fasino & Domenico Freni, 2023. "Preface to the Special Issue on “Hypergroup Theory and Algebrization of Incidence Structures”," Mathematics, MDPI, vol. 11(15), pages 1-3, August.

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