Detail publikačního výsledku

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

CHVALINA, J.; NOVÁK, M.; SMETANA, B.; STANĚK, D.

Original Title

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

English Title

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

Type

WoS Article

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.

English 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

Key words in English

hyperstructure theory; linear differential operators; ODE; automata theory

Authors

CHVALINA, J.; NOVÁK, M.; SMETANA, B.; STANĚK, D.

RIV year

2021

Released

05.02.2021

Publisher

MDPI

ISBN

2227-7390

Periodical

Mathematics

Volume

9

Number

4

State

Swiss Confederation

Pages from

1

Pages to

16

Pages count

16

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"
}

Documents

mathematics-09-00319