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

Jan Chvalina, Michal Novák, Bedřich Smetana and David Staněk
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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

Mathematics, 2021, vol. 9, issue 4, 1-16

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.

Keywords: hyperstructure theory; linear differential operators; ODE; automata theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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