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CHVALINA, J. NOVÁK, M. SMETANA, B. STANĚK, D.
Original Title
Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators
Type
journal article in Web of Science
Language
English
Original 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
Authors
CHVALINA, J.; NOVÁK, M.; SMETANA, B.; STANĚK, D.
Released
5. 2. 2021
Publisher
MDPI
ISBN
2227-7390
Periodical
Mathematics
Year of study
9
Number
4
State
Swiss Confederation
Pages from
1
Pages to
16
Pages count
URL
https://www.mdpi.com/2227-7390/9/4/319/htm
Full text in the Digital Library
http://hdl.handle.net/11012/196740
BibTex
@article{BUT169178, author="Jan {Chvalina} and Michal {Novák} and Bedřich {Smetana} and David {Staněk}", title="Sequences of Groups, Hypergroups and Automata of Linear Ordinary Differential Operators", journal="Mathematics", year="2021", volume="9", number="4", pages="1--16", doi="10.3390/math9040319", issn="2227-7390", url="https://www.mdpi.com/2227-7390/9/4/319/htm" }