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Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators

Author

Listed:
  • Jan Chvalina

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

  • Michal Novák

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

  • Bedřich Smetana

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

  • David Staněk

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

Abstract

The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of groups linear differential operators we construct hypercompositional structures of linear differential operators. Moreover, we construct actions of groups of differential operators on rings of polynomials of one real variable including diagrams of actions–considered as special automata. Finally, we obtain sequences of hypergroups and automata. The examples, we choose to explain our theoretical results with, fall within the theory of artificial neurons and infinite cyclic groups.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:319-:d:494202
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    Citations

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    Cited by:

    1. 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.
    2. Gerasimos G. Massouros & Christos G. Massouros, 2022. "State Machines and Hypergroups," Mathematics, MDPI, vol. 10(14), pages 1-25, July.

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