Publication detail

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

journal article in Web of Science

Language

en

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

Released

05.02.2021

ISBN

2227-7390

Periodical

Mathematics

Year of study

9

Number

4

State

CH

Pages from

1

Pages to

16

Pages count

16

URL

Documents

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",
  annote="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.",
  chapter="169178",
  doi="10.3390/math9040319",
  howpublished="online",
  number="4",
  volume="9",
  year="2021",
  month="february",
  pages="1--16",
  type="journal article in Web of Science"
}